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Molecular Mobility Measurement of Hydrocarbons in Zeolites by NMR Techniques
ADVANCES IN CATALYSIS. VOLUME 39
Molecular Mobility Measurement of Hydrocarbons in Zeolites by NMR Techniques J. CAR0
H . JOBIC
Zentrum f u r Heterogene Katalyse D-I199 Berlin-Adlershof, Germany
Institut de Recherches sur la Catalyse 69626 Villeurbanne, France
M. BULOW
J. KARGER
The BOC Group Murray Hill, New Jersey 07974, U . S . A .
Fachbereich Physik der Universitat Leipzig 0-7010 Leipzig, Germany AND
B. ZIBROWIUS Department of Chemistry University of Manchester Institute of Science and Technology Manchester M601QD, England
1.
introduction
This article provides a review of the most relevant experimental methods to follow molecular translations and/or reorientations of guest molecules in zeolite pores. The benefit of combining these techniques is illustrated by a
35 1 Copyright 0 1993 by Academic Press, Inc. All rights of reproduction in any form reserved.
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series of diffusion studies of hydrocarbons adsorbed in zeolite catalysts. Because of the key role of structure-related diffusion processes in shapeselective catalysis and the unique possibilities of the NMR self-diffusion techniques to investigate such processes, the fundamentals of the NMR selfdiffusion techniques are presented in more detail and examples are given of their application to characterize zeolite catalysts. Zeolitic molecular sieves ex hibit remarkable properties that have made them an interesting topic of both fundamental research and industrial application. In shape-selective catalysis, the correspondence between the diameters of typical reactantlproduct molecules and those of the zeolite channels leads to an intense interplay between the host framework and the guest molecule. Therefore, Weisz introduced the term “configurational diffusion” to describe this special kind of molecular mass transport in zeolites ( I ) . Consequently, slight differences in the structure of the guest molecules can lead to a strong variation in their diffusivities. And vice versa, small changes in the zeolite pore structure (e.g., lattice imperfections such as structural defects, stacking faults, and intergrowths of different zeolite types) can significantly modify the diffusion and adsorption patterns. Recent reviews on mass transport in zeolites are given in Refs. 2 and .?. To understand the principles of shape-selective adsorption and catalysis, a detailed knowledge of the microdynamics of the molecules inside the zeolitic pore system is required. Garcia and Weisz ( 4 ) pointed out the relevance of NMR methods to yield a unifying picture for the phenomena, mechanisms, and magnitudes of “diffusivities.” In the past few years, a deeper insight into molecular motions in zeolites has been achieved, especially by combining investigations of molecular translation with studies of reorientation processes on different time scales (5-14). First we will review the relevant NMR techniques and their most recent developments: (1) pulsed-field gradient (PFG) NMR (315-18) for the measurement of translational molecular self-diffusion and (2) ’H (6,7,lO,19,20) and I3C (9,21,22)NMR lineshape analysis as well as ‘ H NMR relaxation analysis (5,23,24)for the study of molecular reorientation. For selected adsorbateladsorbent systems, we demonstrate the benefit of combining these experimental methods to reveal complex molecular transport phenomena. The results of these NMR methods will be compared with those of other experimental techniques, such as quasi-elastic neutron scattering (QENS) (12,13,25-27), the frequency-response technique (28,29) in its singlestep mode (14.30,31), and sophisticated sorption uptake experiments (39,32,33,113) as well as recent molecular dynamics (MD) calculations (34-41).
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HYDROCARBON MEASUREMENT IN ZEOLITES
II. Basic Principles of NMR Self-Diffusion Studies A. SELF-DIFFUSION MEASUREMENT BY PULSED-FIELD GRADIENT NMR In a magnetic field of strength B, the resonating nuclear spins precess with the Larmor frequency W = -yB (1) about the direction of the magnetic field, where y denotes the gyromagnetic ratio of the resonating nuclei. In NMR diffusion measurements (15-18,23, 24,42,43), this magnetic field consists of a strong time- and spaceindependent component (Bo)and a superimposed field (ABo)that is assumed to increase linearly in the z direction (i.e., ABo = gz). Consequently, the Larmor frequency becomes a function of the space coordinate ( z ) determined by the direction of the field gradient ( g ) . In PFG NMR, the magnetic field gradient is only applied during two short time intervals of identical duration (6) (“field gradient pulses”) and separation ( t ) . By applying an appropriate radio-frequency pulse sequence (a r / 2 - r sequence for generating the “primary” spin echo or a 7r/2-7r/2-7~/2 sequence for generating the “stimulated’ echo), one can observe the transverse nuclear magnetization, i.e., the component of the total magnetization perpendicular to the constant magnetic field, developing under the influence of these two gradient pulses. In order to calculate the vector sum of the total magnetization, one has to determine the difference A$(i) between the average phase and the actual phase for each of the spins after the second gradient pulse. Denoting the z coordinates for the ith spin during the first and second gradient pulses by zI“ and z!’, one obtains from Eq. (1) in the generally considered limiting case of sufficiently short field gradient pulses
A+(d =
I
I
~ d t -
2nd gradient pulse
o dt =
1st gradient
y6g(Zy’ -
zY)
(2)
pulse
Because each spin contributes to the total transverse magnetization via the cosine of the phase difference A+(’),the quantity observed in PFG NMR is given by the relation *(6g, t ) = M J M , ,
=
CoS”)‘@(Zi
-
ZZ)]P(ZI) P(Z2, Z I , t ) dZi dZ2(3)
where M, and M , denote the magnitudes of the total transverse magnetizations with and without field gradients, respectively, p ( z J dzl is the prob-
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ability of finding a molecule in a position with a z coordinate between z I and z1 + dz, and P (z2, z l , t ) dz2 denotes the conditional probability that a molecule that starts at the time of the first gradient pulse from position z I has reached a position between z2 and z2 + dz2 after the time t. For molecular self-diffusion in a homogeneous medium, one has P ( Z , zl, t) = ( 4 n ~ t ) - I ’exp[-(z ~ - zJ2/4 Dt)
(4)
Equation (4)corresponds to the solution of Fick’s second law in an infinite space for the initial condition c*(z, 0) = S(z - z1). With Eq. (4), Eq. (3) simplifies to *(Sg, t ) = exp{-y262g2Dt}
(5)
or, using the Einstein relation D = (r2(t))/6t, we can write *(Sg, t ) = e ~ p { - y ~ 6 ~ g ~ ( r ~ ( t ) ) / 6 }
(4)
with ( r 2 ( t ) )denoting the mean square displacement during the time interval t . According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal T versus (Sg)*. The “observation” time of self-diffusion is the separation between the two field gradient pulses, t . Owing to their relatively large gyromagnetic ratio and to their natural abundance of = 1, protons provide very suitable conditions for N M R self-diffusion studies, but I3C (44), 19F ( 4 3 , and 129Xe(46-48) resonances have also been used successfully in recent PFG N M R studies of zeolites. For diffusion in anisotropic systems such as the MFI structure (ZSM-5/ silicalite-I), Eq. ( 5 ) has to be replaced (3,17,42,49)by *(gJ,A) +
= exp[-y2S2
-
ZEZt]
(7)
with 5 and 2 denoting the diffusion tensor and the field gradient vector, respectively, instead of the scalar quantities D and g. Thus, in macroscopically oriented systems the principal elements of the diffusion tensor may be determined by varying the direction of the field gradient. In powder systems such as beds of zeolite crystallites, one has to integrate over all possible directions and, strictly speaking, the spin-echo attenuation is no longer exponential. For a diffusion tensor of axial symmetry with Dli > D,,Fig. 1 shows the influence of a diffusion anisotropy on the PFG N M R spin-echo attenuation as simulated in numerical calculations (49). The quantitative analysis shows, however, that for principal tensor elements not too different from each other (i.e., for tensor elements within one order of magnitude), the ini-
355
HYDROCARBON MEASUREMENT IN ZEOLITES
C
-
Dn,703
9
3-
10
5 1
10-
I
,
1
2
, 3
-
,
,
,
,
,
,
,
4
5
6
7
8
9
10
Y*g26*
(!I/
re( units
FIG. 1. Parameter calculations for the PFG NMR spin-echo attenuation due to anisotropic self-diffusion in a diffusion system of axial symmetry with Dll > D I (49).
tial part of the spin-echo attenuation appears to follow Eq. ( 5 ) with a mean Dzz)equal to one-third of the trace of the diffusivity D = i ( D , + D,, diffusion tensor (17,49). It is only this initial part, however, that is considered generally in PFG NMR experiments. Depending on the signal-to-noise ratio of the NMR signal and the magni, range of mean errors typical of self-diffusion meatudes of D ( r 2 ( t ) )the surements performed on zeolite systems is from 10% up to a factor of 2. All self-diffusion measurements reported in this paper have been carried out by means of the homemade NMR pulse spectrometer FEGRIS operating at a proton frequency of 60 MHz at the Department of Physics of the University of Leipzig (16-18).
+
B, SELF-DIFFUSION MEASUREMENTS BY THE NMR TRACER DESORPTION TECHNIQUE In general, for zeolitic self-diffusion at sufficiently high temperatures, the mean molecular displacements outside the crystal are much larger than those inside the zeolites; that is to say, long-range self-diffusion, D L ~ is . , much faster than intracrystalline self-diffusion, Din,,. For observation times comparable with the mean lifetimes of the adsorbed molecules in the individual crystallites, the spin-echo attenuation can be approximated by the superposition of two exponentials of the type of Eq. (6)
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where x ( t ) denotes the relative amount of molecules that have left their crystallites during the observation time, t. As a consequence of the initially assumed large difference between the intracrystalline and long-range mobilities, the root mean square (r.m.s.) displacement for long-range selfdiffusion, (r2(r))f!2,is much greater than that for intracrystalline migration, (r2(t)),',/&. Therefore, the quantity x ( t ) can be determined by a plot of In 4' versus (i3g)2.Moreover, by varying the time interval, t , between the two field gradient pulses, the complete time dependence of x (t) is available. This is the same information as that derived from traditional tracer desorption experiments. Therefore, this modification of pulsed-field gradient NMR has been termed tracer desorption (TD) NMR (50) (see also Refs. 3,16,17,51). There are two equivalent ways to achieve a quantitative analysis of the x ( t ) curves as obtained by TD NMR:
1. Comparison of mean intracrystalline lifetimes. For this kind of data evaluation, it is useful to introduce the first statistical moment
MI =
I-, [I
- x(t)I dt
= Tint,
(9)
as a measure of the mean lifetime, Tnntra, of the molecules inside the zeolite crystals. If the molecular exchange between the individual crystals of the sample/pellet is exclusively limited by intracrystalline self-diffusion (i.e., in the absence of surface barriers), for spherical particles of mean square radius (R') the molecular mean lifetime can be calculated from the crystallite size and the value of the intracrystalline self-diffusion coefficient, D,,,, (measured directly by PFG NMR): diff Tintra
=
~ d i f = f 1
(R2)/15Dmtm
(10)
If the calculated value of if if fa is equal to the measured intracrystalline lifetime, T ] . ~ , ~the , rate of molecular exchange between different crystals is controlled by the intracrystalline self-diffusion as the rate-limiting process. Any ~ ~ with T$Lindicates the existence of transport increase of T , in ~comparison resistances different from intracrystalline mass transport. Under the condithus these resistances can only be tions of TD NMR one has D I B D,,,,, brought about by surface barriers. The ratio Tmta/T$k represents, therefore, a direct measure of the influence of surface barriers on molecular transport. 2. Comparison of (effective) self-diffusion coefjcients. To give a clear idea of the adsorption/desorption retardation due to surface barriers, another means to achieve data evaluation from TD NMR experiments is the calculation of an effective self-diffusion coefficient, DeR.From the fractions x ( t ) of those molecules that have left the crystals during different observa-
HYDROCARBON MEASUREMENT IN ZEOLITES
357
tion times, t , by fitting corresponding solutions of Fick's law for diffusionlimited adsorption/desorption (52) to the x (t) curves, an effective selfdiffusion coefficient, Deff, can be determined. As an example, for x ( t ) = 0.5 (half of the molecules have left/entered the individual crystals of mean radius R during t ) , the relation D b 5 / R 2 = 0.03 (52) provides a rough estimate for the determination of D,B. Note that the sample is in sorption equilibrium; this means that the same amount of molecules that leave the crystals during t also enter them. The value of D,R as derived from TD NMR can be directly compared with Dint-as measured by PFG NMR. In the absence of a transport barrier near the outer crystal surface, the adsorption/desorption behavior is determined exclusively by the intracrystalline self-diffusion, consequently Deff-- Dint=.The presence of any surface barrier as an additional transport hindrance leads to a decisive retardation of the molecular exchange between the individual crystals of the sample. In this case, D,E < Dintra. C. APPLICATION OF PULSED-FIELD GRADIENT NMR TO ZEOLITEPELLETS One of the advantages of PFG NMR is its ability to provide direct information about the entirety of molecular transport phenomena in pelletized adsorbents and catalysts (316). As an example, Table I presents the transport parameters for methane in granulated zeolite NaCaA (16,53). Three quantities that have a key function for the understanding of mass transfer in granules are illustrated in Fig. 2: (i) the coefficients of intracrystalline self-diffusion, Dint=,and of (ii) long-range self-diffusion, as well as (iii) the molecular mean lifetime, n,lra. The coefficient of long-range self-difffusion is approximated by D1.r. =
Pinter
Dinter
(11)
where pinterand Dinterdenote the relative number and the self-diffusion coefficients of the molecules in the void space between the crystals. For sufficiently high molecular concentrations in the gas phase (2lo'* protons/ cm3), NMR provides an experimental access to both of these quantities: Pinter may be determined through the molecular concentration in the adsorbed (ca) and gaseous (cg) phases and the void fraction 7 = K n d (Knter + V,,,,) of the zeolite bed by the relation pinter =
c g Knter
Ca Kntra
+ c g Knter
-
7 7)+ cg7
cg
Ca(1 -
(12)
where cg and ca(l - 7)+ cg7 are directly obtained from the intensities of the NMR signal observed in the gas phase and in the zeolite bed.
I TABLETABLE I Molecular Transport Parameters for Methane in Granulated NaCa Zeolite" MolPrular Transpori Parameters for Meihane in Granulaied NaCu Zmliie" Quantity Quantity
SymbolSymbol
Intracrystalline self-diffusion coefficient Intracrystalline self-diffusion coefficient Molecular mean lifetime a crystal Molecular mean lifetime inside ainside crystal Molecular mean lifetime in a crystal Molecular mean lifetime in a crystal calculated under the assumption calculated under the assumption that that adsorption/desorption is diffusion adsorption/desorption is diffusion limitedlimited (absence of surface barriers) (absence of surface barriers) Long-range self-diffusion coefficient Long-range self-diffusion coefficient DI r of molecules of molecules in the in the RelativeRelative amountamount Pintcr intercrystalline of the granule intercrystalline space ofspace the granule Mean free path Mean free path Gas-phase self-diffusion coefficient Gas-phase self-diffusion coefficient Molecular mean lifetime in the intercryMolecular mean lifetime in the intercryof the granule stallinestalline space ofspace the granule Mean molecular diffusion Mean molecular diffusion path in path the in the intercrystalline of the granule intercrystalline space ofspace the granule
A
D,,,, T,nm Tdiff ,"Ira
MethodMethod of determination of determination
PFG for NMR for ( r 24( t(R2)IIZ ) ) ' /G 2 (R2)'12 PFG NMR (r2(t))1'2 Tracer desorption Tracer desorption NMR NMR Through D,.,,theand the crystal radius R, Through D,.,,and crystal radius R, Eq. (10) by Eq. by (10)
Value Value Xmz s-I m2 s-' 1.7 X 1.7 loA9 1.1 ms1.1 ms
0.2 ms0.2 ms
PFG for NMR for ( r 25,( tR2)'12 ) ) 1 / 2 R2)1/2 lo-' PFG NMR (r2(t))llZ 2.2 x 2.2 lo-' xm2 s-I m2 s-' Through the concentrations of methane 0.18 0.18 Through the concentrations of methane in the adsorbed gas phases (as in the adsorbed and gasand phases (as determined by NMR) the void determined by NMR) and theand void '1, by Eq. (12) 7,by Fq. (12) fractionfraction A Through the gas-phase concentration Through the gas-phase concentration and and 7.8 nm7.8 nm the collision cross section, Eq. (13) the collision cross section, by Eq.by (13) Dgas PFG NMR PFG applied NMR applied to the gas phase 3.4 x 3.4 xm2s-' m2s-' to the gas phase 240 ps240 p s Through the values P,.,~,,ofPp,.,,, , " , ~=P , " , ~= Through the of values 'T,n,er 1 -and P T,,~,, , and~by T,,, ~,, by ~(14) Eq. ~ (14) 1 - pnnIeC Eq. l,,,,, Through Through the values T ,~and D, ~ ,~ by 42 p m42 p m the values of T ,ofand ~ D, ,~~by Eq. (16) Eq. (16)
DI r
Pl"ler
" Temperature, K; six CH, molecules per cavity. From16 Refs. " Temperature, 293 K; 293 six CH, molecules per cavity. From Refs. and 16 53.and 53.
HYDROCARBON MEASUREMENT IN ZEOLITES
359
FIG.2. Mass transport parameters in zeolite pellets as determined by PFG NMR and TD NMR (42).
For molecular mean free paths much less than the mean free diameters of the intercrystalline void space in the zeolite bed, D,,,,is controlled by the same mechanism as in the gas phase, with a self-diffusion coefficient D,. Due to the steric confinement, D,,,, is reduced with respect to D, by a tortuosity factor, 7 6 , with values typically of the order of 2-3. The mean free path can be estimated through the relation A = kTaprra2 = 1/V%,mr2
(13)
where k denotes Boltzmann’s constant, T is the absolute temperature, p is the pressure, and m r 2 is the collision cross section. In the example considered in Table I, A is found to be clearly less than the mean free diameters within the zeolite bed, and comparison of D I, PinterDlnter with PlnterDg yields a tortuosity factor of Tb = D,/D,,te, -- 2.7. From the NMR tracer desorption and self-diffusion data (second and third S fa. In the example given, lines of Table I), one obtains the relation 7,ntra intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and highresolution electron microscopy studies (54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. It becomes obvious from the equilibrium condition pinter/Tinter = pintra/Tintra
(14)
that any enhancement of 7,ntra due to surface resistances leads to an enhance~ . mean distance covered by the molecules in the intercrysment of T , , , ~ ~The talline space before being captured again by a crystal follows from the cor-
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responding notation of Einstein’s equation, (liter)
=
(15)
6Dinter~inter
replacing the two quantities on the right-hand side by Eqs. (11) and (14), this relation can be written as (lfnter)
=
(16)
6D1.1. Tintralpintra
where both quantities D I . ~and , Tintraare directly accessible via the NMR experiments. In most cases, the relative number of molecules in the gas phase is negligible in comparison with the amounts adsorbed, so that pint,, pintra and consequently PinIra = 1. According to Table I, the mean diffusion path covered by the molecules in the intercrystalline space before being captured again by a zeolite crystal is one order of magnitude larger than the diameter of the crystals (3.8 pm). A parameter of some technical relevance is the ratio Tintra/Tgranule of the molecular mean lifetimes in the individual crystals and in the granulated particles. With Rgranule denoting the radius of a granulated particle, by analogy to Eq. (10) one has
*
Tgranule
L1
(R&mule)/
so that either of two quantities Tintraand
15Dl.r.
T~~~~~~~ can
(17)
be determined by NMR.
D. ON THE LIMITS OF APPLICATION OF PULSED-FIELD GRADIENT NMR FOR SELF-DIFFUSION MEASUREMENTS IN ZEOLITES The major limitations for an application of PFG NMR to self-diffusion studies can be summarized in four categories:
1. Most self-diffusion studies have been performed at low temperatures and high loadings characteristic of low temperatures. Due to collisional molecule-molecule interactions, often a drastic decrease of the selfdiffusion coefficient at high sorbate concentrations is found (see later, cf. Fig. 10). In the limit, molecular self-diffusion of small molecules in largepore zeolites can be described by diffusion models for liquids (e.g., diffusion of hydrocarbons in zeolite X by the so-called “free-volume model”; see Section V,B.). In contrast, typical catalytic operations work at temperatures above 275 K and, consequently, with sparse populations of molecules per zeolite cage. However, in the case of structure-related molecular selfdiffusion (as found for hydrocarbons in ZSM-5), the systematic study of molecular self-diffusion as a function of temperature and loading (at subcatalytic temperatures and concentrations usually higher than those in catalytic
HYDROCARBON MEASUREMENT IN ZEOLITES
36 1
reactions) provides a reliable basis for the extrapolation to catalytic conditions. On the other hand, by applying Fourier transform PFG NMR (this technique is described in Section VI,B,2), in recent PFG NMR studies (135) during the conversion of cyclopropane to propene on NaX at 473 K, the self-diffusion coefficients of the individual components involved in this reaction could be measured directly and simultaneously. Furthermore, the development of high-temperature probe heads for PFG NMR (which allowed measurement of the self-diffusion of n-paraffins in zeolite 5A at 625 K) (136) represents, again, substantial experimental progress toward catalytic conditions in PFG NMR. Another approach to determine diffusion coefficients under catalytic conditions can be achieved most effectively by studying the effectiveness factor in catalytic experiments on samples of different crystal size (the intrinsic reaction rate constant and the equilibrium constant must be known) as done by Haag et al. (55) for the cracking of n-hydrocarbons over HZSM-5. 2. The minimum self-diffusion coefficient measurable by PFG NMR depends significantly on the upper limit of the time interval t , which is limited by the damping of the NMR signal due to transverse nuclear magnetic relaxation. In general, t will be of the order of the transverse nuclear magnetic relaxation time, T 2 , or less (17,56). As an example, for benzene in ZSM-5 at 400 K , one has T2 = 0.5 ms and, assuming as characteristic values of t = 1 ms, 6 = 0.5 ms, and g = 10 T m-', only a self-diffusion coefficient D 2 cm2 s-' can be measured. This lower limit is about 3-4 orders of magnitude above the real diffusivity of benzene in ZSM-5 (cf. Fig. 17), i.e., there is only little hope to measure the benzene self-diffusion in ZSM5 by PFG NMR. However, by using partially deuterated compounds, the proton-proton interaction within one molecule can be reduced and as a result T2 can be prolonged, which gives the opportunity to apply larger t and 6 values (24,56).A further possibility to enhance the observation time t involves the application of the stimulated spin echo (3,17). In this case the spin-echo damping is controlled mainly by the longitudinal nuclear magnetic relaxation time, T I ,which may be considerably larger than T2. 3. In Ref. 56 it is shown that small amounts of highly mobile molecules adsorbed on the outer surface or within intracrystalline cracks will, in general, lead to an enhanced damping of the NMR signal that may be interpreted erroneously as a high overall mobility of the adsorbed molecules if the two-phase character of the signal is not taken into consideration. 4. The molecular root mean square displacement, (r2(t))1'2, of the diffusing molecules during the observation time, t , has to be much smaller than the crystal radius, R , in order to guarantee that the measured r.m.s. displacement reflects the undisturbed intracrystalline self-diffusion. Assuming
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a lower limit o f t = 0.5 ms and a crystal radius R = 1.5 p m , the diffusivities that can be measured amount to D < lop5cm2 s-l. However, this upper limit can be shifted to higher diffusivities if large zeolite crystals are available.
111.
Principles of NMR Techniques to Detect Molecular Reorientations
OF MOLECULAR REORIENTATIONS BY "c A. DETECTION NMR LINESHAPE ANALYSIS
In 13CNMR spectroscopy, deviations from a Lorentzian lineshape, which is usually obtained in liquids, can be caused by a chemical shift anisotropy (CSA). If a CSA is present, the position of the resonance line depends on the relative orientation of the molecule with respect to the direction of the magnetic field applied (21,22). The superposition of the individual resonance lines results in typical lineshape patterns that can be described by two parameters: the chemical shift anisotropy, As, and the asymmetry parameter, q , respectively. In the case of an axially symmetric CSA tensor, i.e., q = 0, the relation between the resonance frequency, w , and the orientation of the molecule is given by w =
wg
[
6i,"
-
1
A6 -j(3 cos26 - 1)
where wo = yBo denotes the Larmor frequency, 6iaois the isotropic chemical shift, and 6 is the angle between the magnetic field and the principal axis of the CSA tensor, thus describing the orientation of the molecule with respect to the magnetic field. Molecular motions can lead to an (at least partial) averaging of the CSA. The degree of averaging is determined by the type of motion as well as by the ratio of the correlation time, T,, and the value of A6 (21). Therefore, several types of molecular motions give rise to characteristic lineshape patterns. For
one has the spectrum of rigid molecules, i.e., molecules of a fixed orientation with respect to the magnetic field. In the case of a fast isotropic reorientation with
HYDROCARBON MEASUREMENT IN ZEOLITES
363
the CSA is completely removed and one obtains a Lorentzian line with a line width determined by the remaining interactions. In contrast to n-paraffins, which exhibit no or only a slight I3C NMR CSA, aromatics or hydrocarbons with double or triple bonds show a much larger anisotropy. Therefore, benzene (57) and 2-butyne (14) were chosen as suitable probe molecules to study molecular motions by 13C NMR lineshape analysis. Theoretical lineshapes for different motional states of benzene and 2-butyne molecules are depicted in Figs. 3 and 4. The protondecoupled I3C NMR spectra were recorded by means of the homemade NMR spectrometer UDRIS (University of Leipzig) and a BRUKER MSL 400 (Central Institute of Physical Chemistry, Berlin) at frequencies of 22.6 and 100.6 MHz (9,14,57).
h
A 0:
fast reorientation about F
fast aboutreorientation F
fast isotropic reorientations
,
I
I
Z O
200
150
100
6/ppm
-
I
I
50
0
FIG. 3. Theoretical I3C NMR lineshapes of benzene molecules for different types of motions (58).
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fast isotropic reorientation 200 150 100 50
b/ppm
-
0 -50
FIG.4. Theoretical "C NMR lineshapes of 2-butyne molecules for different types of motions (14). OF MOLECULAR REORIENTATIONS BY 'H B. OBSERVATION NMR LINESHAPE ANALYSIS
The *H NMR lineshape of solids is determined by the quadrupolar interaction, which can be described by two parameters: the quadrupole frequency, W Q , and the asymmetry parameter, 77 (19,20). The parameter W Q is determined by the electric quadrupole moment of the deuteron and the zz component of the electric field gradient at the deuteron site. For deuterons bonded to carbon atoms, the asymmetry parameter is approximately zero and the z axis is along the C-D bond. In this case, the dependence of the resonance frequency, W , from the orientation of the molecule with respect to the magnetic field applied is given by a relation similar to Eq. (18) (19). As long as the correlation time, r,, of a molecular motion is sufficiently large, i.e., TcWQ
%
1
(21)
the lineshape is not influenced by this motion. For faster motions, however, characteristic deviations occur, because-depending on the type of motion-at least a certain part of the quadrupolar interaction is averaged to zero (19,20). Depicted in Fig. 5 , are theoretical 'H NMR lineshape patterns of perdeuterated benzene for various motions. The 2H NMR spectra were
HYDROCARBON MEASUREMENT IN ZEOLITES
365
H&
fast reorientation about F
fast aboutF reorientation
fast isotropic reorientations
I
I
100
50
0
-50 -100
FIG. 5. Theoretical *H NMR lineshape patterns of perdeuterated benzene molecules undergoing various types of motions (7).
obtained with the quadrupole echo pulse sequence on the previously mentioned spectrometers at frequencies of 13.8 and 61.4 MHz, respectively (7,9).
c. ANALYSIS OF MOLECULAR TRANSLATIONS AND ROTATIONS BY COMBINED 'H NMR RELAXATION AND NMR SELF-DIFFUSION STUDIES The self-diffusion paths of guest molecules in an isotropic host lattice can be described by a sum of successive individual molecular jumps (5,9,25, 26,59,60),
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where D is the self-diffusion coefficient and ( r 2 ( t ) )and (Z2) denote, respectively, the long-range mean square displacement during an observation time, t , and the individual mean square jump length after a residence time, 7 , of the jumping molecule at a sorption site, respectively. In addition to QENS, the value of the mean residence time, 7 ,of a jumping molecule can also be estimated from 'H NMR relaxation analysis. The correlation time T~ of the longitudinal proton magnetic relaxation can be approximated by the reciprocal value of the proton magnetic resonance frequency at the temperature of the T I minimum, i.e., T~ -- w0' (5,23,24). The motional process that controls NMR relaxation is usually assumed to be a molecular reorientation together with or without a simultaneous translational motion. Consequently, depending on the dominating mechanism of magnetic interaction, one has T~ 5 T . Therefore, from combined PFG NMR self-diffusion and NMR relaxation studies, according to Eq. (22) a lower limit of molecular mean jump lengths can be given. The longitudinal and transverse ' H NMR relaxation times have been measured using the NMR spectrometer UDRIS. IV.
A.
Principles of Other Mobility Measurements (Comparison with NMR Data)
MOLECULAR TRANSLATIONS AND ROTATIONS BY QUASI-ELASTIC NEUTRON SCATTERING (QENS)
For hydrocarbons in zeolites, only incoherent scattering has to be considered because of the large incoherent cross section of hydrogen. The neutron intensity scattered follows the incoherent scattering law Sinc(Q,w ) , which is related to the self-motion of protons, where 6Q and fiw denote the neutron momentum transfer and the neutron energy transfer, respectively. Assuming for a molecular system the vibrational, rotational, and translational motions as uncoupled, the incoherent scattering law can be expressed as a convolution product of the individual scattering laws for each motion, which can be examined separately: Sinc(6,
0)
= SP:(~, w )
B S \ ; A ( ~w,) B S ; F < ~ w, )
(23)
For the quasi-elastic region ( 5 2 meV) that is of concern here, the vibrational motions affect only the elastic intensity through a Debye-Waller facis the mean square hydrogen amplitude in tor, exp(-Q2(u2)), where (2) the vibrational modes. The scattering law for rotations can be written as a sum of an elastic peak intensity and a quasi-elastic component:
SE(6,
W)
= Ao(&(w)
+ Sqei(6,
0)
(24)
HYDROCARBON MEASUREMENT IN ZEOLITES
367
The elastic peak intensity is governed by A o ( ~ )which , is kcown astJhe elastic incoherent structure factor (EISF). The variation of Ao(Q) with Q allows determination of the nature of the rotation (e.g., isotropic or uniaxial rotations). The dynapical behavior of protons is reflected by the quasi-elastic component, Sqel(Q,w ) . This term can be expressed as a superposition of Lorentzians whose widths are related to the average time between jumps. The simplest model of translational motions in three dimensions is the continuous random walk diffusion (Fick’s law) giving a Lorentzian-shaped scattering law, SiF(Q,
W)
1 =-
To2
DQ’
+ (DQ’)’
where D is the self-diffusion coefficient. This model can be applied quite well to simple liquids at small Q values. In zeolites, however, jump diffusion models (61-63) have been found more appropriate. The broadening values obtained for methane diffusion can be fitted to a molecular jump model with a Gaussian distribution of jump lengths (25,62). Thus, the scattering law becomes a Lorentzian,
whose half-width at half maximum (HWHM) 1 Aw(Q) = ;[l
-
1 exp(-Q2(12)/6)] = -[1 - exp(-Q’Dr)] 7
(27)
is determined by both the mean time, r , between two succeeding jumps, and the mean square jump length, (1’). At small Q values, the HWHM becomes equal to AW(Q) = DQ’ and D can be derived. At high Q values, the half-width approaches the mean jump rate, T-’.For systems with a different distribution of jump lengths, the broadening curves were fitted with another jump model (63). The shape of the quasi-elastic peak is still a Lorentzian, but the HWHM is given by (63)
This model was used for ethane and benzene in NaX. The QENS results were obtained at the Institute Laue-Langevin, Grenoble, using the time-of-flight spectrometers IN5 and IN6 (25-27). The time scale on which the motions can be observed by QENS is determined by the elastic energy resolution, which amounted to 20 and 100 p e V for the spectrometers IN5 and IN6, respectively. Based on an appropriate statistical
368
J. CARO et
al.
data evaluation, broadenings smaller than the resolution can be measured so that motions in the range 10-’o-10-’2 s can be followed. Consequently, diffusion coefficients of the order of 10-4-10-6 cm2 s-’ can be measured. Furthermore, by applying the backscattering technique, a better instrument resolution, of the order of lpeV, can be obtained.
B . DIFFUSION COEFFICIENTS FROM SORPTION KINETICS By fitting appropriate solutions of Fick’s diffusion law to the adsorption/ desorption curves, diffusion coefficients can be derived. Depending on the way the experiments are performed, variable boundary conditions have to be taken into account (52). However, as a rough estimate, one can approximate the initial part of the adsorption/desorption curves by the so-called law accounting for the changing boundary conditions (64):
d
where PO,p,, and pmdenote the pressures at the beginning of sorption, at actual time t , and at sorption equilibrium, respectively. A denotes the external surface area and V is the volume of the crystals. Other methods of data evaluation are provided by the method of statistical moments (32)or the full analysis of uptake curves for complex processes by means of the software ZEUS (Zeolite Uptake Simulator) (65). In contrast to all the other techniques considered in this paper, in sorption experiments molecular migration is observed under nonequilibrium sorption conditions. Therefore, instead of self-diffusivities, D, in this case transport diffusivities, D t , are derived. It is generally assumed (see, e.g., Refs. 366) that the “corrected” diffusivities, Do,
D O = D,d [In c ( p ) ] / d[In p ]
(30) with c (p) denoting the sorbate concentration in equilibrium with the sorbate pressure p, should be of the order of the self-diffusivity, D. In the following discussion, sorption experiments will be discussed only in terms of the “corrected” diffusivity, Do. Two experimental methods to follow sorption kinetics have been applied. In the single-step frequency-response method, the frequency-response system at Imperial College, London, has been used. Fast volume perturbations that cause stepwise-like pressure changes have been achieved by activating an electromagnet that has copper bellows attached (3031). In another sorption kinetics technique installed at
369
HYDROCARBON MEASUREMENT IN ZEOLITES
the Central Institute of Physical Chemistry, Berlin, the pressure changes are initiated by dosing via opening a valve (32). In this mode, adsorption/ desorption processes caused by the pressure jump are followed piezometrically in a constant volume system. V. Combined Application of Different Experimental Techniques to Study Molecular Translations and Rotations of Hydrocarbons in Zeolites
A. COMPARISON OF SELF-DIFFUSION COEFFICIENTS DETERMINED BY PULSED-FIELD GRADIENT NMR AND QUASI-ELASTIC NEUTRON SCATTERING 1 . Methane in ZSM-5
Figure 6 represents typical plots of the spin-echo intensity in PFG NMR experiments. Comparing the slopes of these representations with those of standard liquids, one obtains the mean self-diffusivities, which are found to decrease with increasing sorbate concentration (5,12,16,59,60). It appears from Fig. 6 that within the accuracy of the measurement no deviation from a single exponential decrease may be observed. A comparison of the experimental spin-echo attenuation (Fig. 6) with the results of numerical calcula-
100 80 ffl
TT
-h
!t
60
o
3-
t
2o 10 1
2
3
L
4
5
6
7
8
9
1
0
f g 2 6 2 ( t ) / rel-units
FIG.6. PFG NMR spin-echo attenuations due to self-diffusion of CHI in ZSM-5 at 250 K for the loadings (CH4 per u.c.): 0, 4; 0 , 8; and 0 , 12 (49). For calibration, neat water (0) and liquid ammonia (A) are included, with self-diffusion coefficients of 2.3 X lo-' cm2 s-' (67) and 1.5 X cm2 s-' (68).
370
J. CARO et
al.
tions (Fig. 1) shows that for methane in ZSM-5, the principal tensor elements differ from each other by less than a factor of 5-10 (49). This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x , y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those (42,43).For the self-diffusion of methane in ZSM-S/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). In the QENS experiment (Fig. 7), the broadening of the elastic peak as a function of Q 2 is found to deviate from a straight line, so that a jump diffusion model has to be considered. The mean jump lengths are found to be larger at small loading and high temperatures (12,25,69).For methane in ZSM-5, the mean jump lengths calculated from QENS for small and high loadings at 200 K amount to 1.04 and 0.87 nm, respectively. The selfdiffusion coefficients obtained from PFG NMR and QENS are presented in Table 11. These data yield an activation energy for the self-diffusion of methane in ZSM-5 of 4-5 kJ mol-’ both for PFG NMR and QENS (12,69). Furthermore, Table I1 presents diffusivities determined by sorption uptake/ desorption measurements (single-step frequency-response technique) (30). Table I1 shows that the self-diffusion coefficients measured independently by PFG NMR and QENS are in excellent agreement (12,69).Owing to the different time scales of the two methods, this finding is not trivial. Whereas in QENS, molecular translations are measured up to 6 nm, in PFG NMR the mean molecular displacement may amount to several micrometers. Thus it
.,
-
0.2
0.L
0.6
0.8
02/i3-2
FIG. 7. Elastic peak broadening versus Q’ for CH, in ZSM-5 at 200 K for the loadings (CHJ per u.c.): A, 2; 4;and V, 8 (12.25.69).
37 1
HYDROCARBON MEASUREMENT IN ZEOLITES
TABLE I1 Self-DiffusionCoef$cients of Methane in ZSM-5Measured by PFG NMR and QENS Compared with Sorption UptakeiDesorption Diffusiivities" At T = 200 K(x
Loading (CR/u.c. 1 1.5 2 2.8
4
8 12
DQENS
DNMR
-
-
2.8
-
-
-
2.5 2.9
3.7 2.8 2.5
-
cmZS K I )
DSVRP 0.6 0.5 -
cm2 s-')
At T = 250 K ( X DQENS
DNMR
5.0
-
5.9
-
-
-
-
6.3 5.2 4.5
NMR and QENS data from Refs. 12, 25, and 69; diffusivity data from Ref. 30.
turns out that the migration over both ranges of displacements is determined by the same mechanism of intracrystalline diffusion. The diffusion data obtained by sorption uptake/desorption are smaller by a factor of 5 than the directly measured self-diffusivities, which is a much better agreement than was stated previously in comparative studies of the same system (70,71), where discrepancies up to 5 orders of magnitude have been obtained. The remaining difference might be attributed to the fact that in sorption experiments a slowing down of uptake rate due to the finite rate of adsorption heat dissipation cannot be entirely excluded. With QENS, both the rotational and translational motions of CH4 can be observed. It was found that the rotational motion of CH4 in ZSM-5 can be described by an isotropic rotational diffusion model with a rotational diffusion time constant, D,(72). The values of D,for CH4 adsorbed at 250 K in ZSM-5 are of the order of 5 X 10'' s-'. In MD simulations at 400 K , D, was found to be of the order of 10l2 s-' (73). This difference is due to the fact that a radius of gyration of 0.15 nm was used in the computer fits of the QENS profiles. This radius is intermediate between a simple rotation model, with 0.11 nm for the distance between the protons and the center of mass of the methane molecule, and the radius of the channel in which the molecule performs oscillations.
2. Ethane in NaX Figure 8 shows a comparison of experimental and calculated energy spectra in the QENS experiments for ethane in NaX at different Q values. Table I11 contains the molecular mobility data determined by QENS. In Fig. 9 the self-diffusion coefficients obtained by QENS (cf. Table 111) are com-
;L
n
u 0 l
I
-0.4
-
-02
0
0.2 0.4 hw/rneV
0.6 0.8
FIG. 8. QENS energy spectra for ethane in NaX at different Q values (253 K , 4.3 C2H6per supercage) (69). TABLE 111 SeEf-DiffusionCoefficients, Mean Residence Times beween Jumps, and Root Mean Square Jump Lengths for Ethane in NaX" Loading (CzHs per supercage)
D cm2 s-')
(x
1.3 4.3 5.8
( x lo-" s)
(12)1'2 (nm)
1.36 1.48 2.22
0.66 0.41 0.44
7
5.4 2.5 L .5
" As determined by QENS at 253 K (69).
.
N
E u
t
A0
2-
n
I
I
1
2 3 1 5 6 loading/ C2H6 per supercage
7
FIG.9. Comparison of the self-diffusion coefficients of ethane in NaX at 253 K measured by PFG NMR (0) (59) and QENS (A) (69).
373
HYDROCARBON MEASUREMENT IN ZEOLITES
pared with the corresponding PFG NMR data (59). As for methane/ZSM-5, agreement is observed in both the absolute values and the concentration dependence. Furthermore, a very similar trend in the decrease of the mean molecular jump lengths with increasing sorbate concentration, as shown in Table I11 for ethane/NaX, has been found by NMR methods for propane/ NaX (5). All the QENS spectra were fitted both by means of the scattering law for isotropic rotation and a jump diffusion model (63) according to Q . (28). The radius of gyration was found to vary between 0.18 nm at high loading and 0.22 nm at low loading. As is the case for methane in ZSM-5, this finding is explained by the fact that the motion does not strictly correspond to a rotation about a fixed center of mass because the position of the center of mass changes during the oscillatory state. The rotational diffusion time constant, D,, was found to be of the order of 10” s-l at 253 K.
B. COMBINED ‘H NMR RELAXATION AND PULSED-FIELD GRADIENT NMR SELF-DIFFUSION STUDIES FOR PROPANE IN ZSM-5 AND NAX For CHJZSM-5 and C2HdNaX, as was previously discussed, the selfdiffusion coefficients decrease monotonically with increasing concentrations. Figure 10 shows that this holds true also for propane in both ZSM-5 and zeolite X. ZSM-5 and zeolite X show similar concentration dependencies of the molecular self-diffusion, so that-at first glance-one might expect them to be caused by identical microdynamic mechanisms. However, according to Eq. (22), the translational mobility can be reduced by both decreasing mean square jump lengths, (1*), and increasing time intervals, T , between succeeding jumps. In fact, the relaxation time measurements (Figs. 1 1 and 12) indicate a decisive difference in the molecular transport mechanisms: for NaX, with increasing sorbate concentration, the temperatures of the TI minima (and associated with it the value of the correlation time, T ~ , of molecular motions) remain unchanged (cf. Fig. l l ) , whereas in ZSM-5 the TI minima are drastically shifted to higher temperatures (cf. Fig. 12), thus indicating a significant decrease of the jump rate. Table IV shows that for ZSM-5 at small and medium pore filling, the mean jump lengths are found to be invariable and amount to 1 nm, which is of the order of the distances between adjacent channel intersections of the MFI framework. Consequently, the concentration dependence of the selfdiffusion coefficients in ZSM-5 has to be explained by structure-related jumps, with jumping rates decreasing at elevated loadings. In contrast, for zeolite NaX the reduction of the molecular translational mobility with increasing sorbate concentration is mainly due to the reduction of the jump lengths, with jump rates practically unaffected by concentration. For hydrocarbons in NaX, the jump lengths are found to be corre-
-
f
2
10-71 L -
2 -
J
lo-*:L
FIG. 10. Self-diffusion coefficients of propane in zeolites NaX
(a),CaA (O), and ZSM-5
(a)at 300 K (5) as a function of sorbate concentration expressed by the number of C3Hs per
24 (Si + Al) atoms (representing one large cavity in the cases of zeolities X and A or one channel intersection with the adjacent pore segments in the case of ZSM-5). Data recently obtained in neutron scattering experiments for ZSM-5 (v) (74) are included.
75 I
temperature/ O C c0 -50 -100 -150 I
r
1
I
A
42-
E".102 +-
I
L-
1011 , 2
,
,
,
,
,
,
,
3
4
5
6
7
8
9
FIG. 11. Longitudinal relaxation times (TJ of propane in NaX for 1.5 (A), 2 (o),4 (o), 5 (01, and 6.5 ( 0 )C3Hg molecules per large cavity measured at a proton resonance frequency of
90 MHz (5).
HYDROCARBON MEASUREMENT IN ZEOLITES temperature
75
I
1 2
I
3
0 -50
/OC-
-100
4 5 -IO~K/T
375
6
-150
L
7
I
0
/
9
FIG. 12. Longitudinal relaxation times ( T I )of propane in ZSM-5 for 1 ( A ) , 1.5 (A),2 (01, 2.5 (m), 3 (o), and 3.5 (0).C3Hx molecules per channel intersection measured at 90 MHz ( 5 ) .
TABLE IV Estimated Vulues for Minimum Meun Jump Lengths in ZSM-5 and NuX" Concentration
NMR
[molecules per 24 (Si + Al) atoms]
Temperature of the TI minimum (K)
0.4 I .o I .5 2.0 2.5 3.0 3.3
150 175 210 270 315 360
I .5 2.0 4.0 5.5 6.5
135 135 I35 135 135
QENS (1 *)I/>
D (X
lo-' cm2 s - ' )
(X
lo-' nm)
PropaneiZSM-5 13 12 13 14 6 5
11.7 11.3 11.7 12.2 8.0 7.3
PropanelNaX 5.8 4.0 2.5 0.6
7.8 6.5 5.1 2.5
0.1
-
(/ 2 ) 1/ 2 (X
10-I nm) 9.2 8.4 6.6
1.o
" Obtained at the temperature of the TI minimum according to Eq. (22) ( 5 ) in comparison with QENS data (74).
376
J. CARO et
al. p e q ~,bid
I b l volume compression- adsorption
2-butyne lsilicalite -I 323 K
Pequ.,reo.: Pstart
l'Lgly I
[a) volume expansion
0 0.1 0 2
,I
"
NS
>
I , , .
,
10 20 30"W 100
-desorption
01
a2
"
D in
t/S
30 "goim
FIG.13. Kinetics of desorption (a) and adsorption (b) of 2-butyne on silicalite-I recorded by the pressure response following the rapid square-wave volume expansion (a) and compression (b). Experimental conditions; 1.5 Torr of 2-butyne at 323 K; 0,without adsorbent; 0 , ZSM-5 present in the system (14).
lated with the molecular free volume, so that the reduction of mobility with increasing concentration may be explained by a modification of the freevolume theory (59).
c.
SORPTION KINETICS AND "cNMR LINESHAPE FOR 2-BUTYNE IN ZSM-5 ANALYSIS
The adsorption and desorption kinetics of 2-butyne on ZSM-5 following square-wave pressure changes are shown in Fig. 13. In contrast to the results obtained for n-butane (14), sorption kinetic curves of 2-butyne on ZSM-5 cannot be described by only a single diffusion coefficient (cf. Fig. 13). After a fast initial sorption process, further adsorption proceeds much more slowly. For 2-butyne the time constant of the succeeding process of comparatively slow adsorption/desorption kinetics is larger by at least one order of magnitude than that for the initial fast sorption process. Applying the V? law to this initial region of sorption kinetics [cf. Eq. (29)], the diffusion coefficient of 2-butyne was found to be larger than 3 X em's-'.
HYDROCARBON MEASUREMENT IN ZEOLITES
I
1
1
I
I
200 150 100 50 b/PPm
I
I
0 -50
377
1
FIG.14. I3C NMR spectrum of 2-butyne sorbed on silicalite-I (1.35 mmollg) at room temperature. The spectrum was obtained by single-pulse excitation (14).
This value is higher than the corresponding value of -0.7-2.5 X cm2s-‘ for n-butane (14) obtained by the same experimental technique.* Our results (14) indicate that the rate of penetration into the molecular sieve lattice is higher for the “stiff’ 2-butyne than for the “flexible” nbutane. Hence, sorption uptake of 2-butyne on ZSM-5 turns out to be a coupled diffusion-rearrangement process. In the initial part, the adsorption/ desorption rates are controlled by intracrystalline diffusion. The final part of the sorption process, leading to a higher sorbate density, is determined by the rate of molecular reorientation of the sorbed molecules finding their optimum sorption arrangement. For ZSM-5, the latter process is especially slow for the relatively stiff 2-butyne but is fast for the flexible n-butane. Similar experimental findings, wherein the sorption kinetic data could not be fitted by a simple diffusion model, have been observed e.g., in the case of xylene isomers (9,78) and picoline (79) on ZSM-5 as well as for benzene on NaX (80) and for p-xylene in microporous gallosilicate (141). Further information on the molecular transport of 2-butyne in ZSM-5 can be derived from l3C NMR lineshape analysis. A comparison of the measured I3C NMR spectrum (Fig. 14) with the theoretical ones (Fig. 4) leads to the following conclusions: 1. The spectrum of sorbed 2-butyne is quite different from the calculated spectrum for molecules fixed in space. This indicates that the directions of
* For comparison, in recent studies the self-diffusion coefficient of n-butane in ZSM-5 was found to be of the order of 10-s-10-6 cm2 s-I: 1.4 X cm2 S K I[two C4HI0per unit cell cm2 s-’ (two C4H10per u.c., 298 K) (1 u.c = 96 SitAL atoms), 353 K] by QENS (73, by PFG NMR (106), and I .7 X lo-’ cm2 S K I (one C4HIoper u.c., 298 K) by M D simulations (77).
378
J. C A R 0
et a / .
the molecular axes are not fixed, i.e., the angle between the axis of the molecule and the magnetic field is changed by molecular motions. Consequently, the motion of 2-butyne molecules is not restricted only to the straight channels of ZSM-5. = 77 ppm, one has to con2. Because there is no Lorentzian line at clude that the sorbed molecules do not perform fast isotropic rotations in the channel intersections, a situation also found for benzene in ZSM-5 (7,9,57,81). Obviously, energetic restrictions prevent such motion, which might have been considered for geometrical reasons. 3. A possible interpretation of the experimental results is a 90" flip motion of the 2-butyne molecules. In the fast limit, such a motion generates a pseudoaxially symmetric CSA tensor with the parameters 611 = 56 2 11 ppm and 6, = 157 2 6 ppm (14). The corresponding lineshape is included in Fig. 4. Considering the ZSM-5 framework, this 90" flip can be a molecular jump from a straight into a sinusoidal pore segment or vice versa. From Eq. (20) it follows that the values of the correlation time must be much less than 10 ps. 4. On the time scale of the NMR experiment, the sorbed 2-butyne molecules behave as a single phase. There are no molecules moving exclusively through the straight channel system and no molecules performing isotropic rotations in the channel intersections.
D. NMR LINESHAPE ANALYSIS, PULSED-FIELD GRADIENT NMR, QUASI-ELASTIC NEUTRON SCATTERING, AND SORPTION KINETICS ON AROMATICS IN ZSM-5 AND NAX 1. Benzene in ZSM-5 I3C NMR lineshapes of benzene molecules sorbed on ZSM-5 are shown in Fig. 15. For high sorbate concentrations and low temperatures, powder spectra are obtained; these spectra are characteristic of an axially symmetric shielding tensor. This lineshape is known to be generated by a fast motion of the benzene molecules about their C-6 axes (cf. Fig. 3). With increasing temperature and decreasing loading, the lineshape changes into a Lorentzian one, i.e., an additional molecular motion becomes fast enough to average out the CSA. For perdeuterated benzene in ZSM-5, the dependencies of the *H NMR lineshape on both temperature and loading are given in Fig. 16. From a comparison of the spectra for high sorbate concentration and low temperature with the theoretical lineshapes for different motional states (cf. Fig. 5), it has to be concluded that the sorbed benzene molecules perform fast reorientations about their C-6 axes, a conclusion identical with the findings from I3C NMR.
-
loading / & H e per
U.C.
6D
3.2
8.0
260 K
E3
e
e
e aI
0, c
t
FIG.15. I3C N M R spectra of benzene sorbed on ZSM-5for various temperatures and concentrations. The spectra at 200 K were taken using signal enhancement by cross-polarization (9,57). 16
-
loading/C6D6 per u c .
56
40
7.6
1"1
200 K
P
5
167K
125 K 0
35
70
-
0
35
70 "W-Wol/;
.d-.,
35 ] / kHz
70
I
,\35
70
FIG. 16. *H N M R spectra of perdeuterated benzene sorbed on ZSM-5for various concentrations and temperatures. The spectra were obtained using 3.5-ps7r/2 pulses and a 60-ps pulse spacing (7,9).
380
J. C A R 0 et
al.
As follows from Fig. 16, a reduction of the sorbate concentration causes an effect similar to that of a rise in temperature. From I3C and 'H NMR lineshape analyses of benzene sorbed on ZSM-5, the following conclusions can be drawn (7,9,57,58):
1. The sorbed benzene molecules perform fast reorientations about their C-6 axes. Even at 125 K , the correlation time of this motion is much shorter than 1 e s . 2. Superimposed on this C-6 reorientation, there are jumps of the benzene molecules between a limited number of sorption sites. These sites allow only distinct orientations of the hexad axis of the benzene molecule with respect to the crystal system. The mean residence time, T ~ between , two succeeding jumps decreases with increasing temperature and decreasing loading. The rotational motion of benzene in ZSM-5 has also been characterized by QENS (81). On the time scale of the QENS experiment (=IO-"s), which is much shorter than in NMR, the spatial distribution of the rotating hydrogen atoms is found to be temperature and loading dependent. At low temperatures (90 K), there is a progressive blocking of the rotational motion, a finding that suggests benzene-benzene interactions. A model of uniaxial rotation in an N-fold cosine potential has been used to interpret the low-temperature patterns. At high temperature (400 K) and low loading (three C6Hdu.c.), the rotational motion converges toward a uniaxial C-6 rotation, but it does not reach the spherical rotational model, i.e., the spatial distribution of the protons remains limited to a circle of a radius R = 0.25 nm and does not reach a sphere. The correlation time obtained at 300 K is 3.2 X lo-'' s, Le., as fast as in the liquid. Simulations of 13CNMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental I3C NMR lineshapes, a mean residence time T~ of 20 and 150 ps for a concentration of six molecules per U.C.at 250 and 200 K , respectively, was derived. Provided that these jumps detected in I3C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (1') = 6D7, is valid, where (Z2) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm.
38 1
HYDROCARBON MEASUREMENT IN ZEOLITES
With the above values for the mean residence time 7j and its activation energy E, = 17 2 4 kJ mol-I, from the I3C NMR data a self-difisivity D = 1-5 X lo-'' cm2 s-' can be predicted for a temperature of 303 K and a loading of six molecules per U.C.(9). It should be noted, however, that this procedure is only justified if the activation energies of the jumping frequency and of the self-diffusion coincide. Furthermore, from 13C NMR a decrease of the molecular mobility with increasing sorbate concentration has to be expected. The concentration patterns of Do obtained from sorption uptake experiments for two ZSM-5 samples are shown in Fig. 17 (9). The data are in satisfactory agreement with the I3C NMR estimates in the absolute values, in the activation energies, and in the concentration dependencies. Moreover, the activation energy data for benzene are found to agree with the results of computer simulations (87).
2 . Benzene in Zeolite X Accounting for the influences of external heat and mass transfer resistances in limiting the sorption rates, in many instances reasonable agreement between diffusion data from sorption experiments and PFG NMR may
lo-*
1
t
a.
10'~
A x
v* v c
Ll 10'10
A
8
N
E
I
* =
303K 274 K I
I
1
2
-
I
3
4
I
loading / C s H 6 per u.c
FIG. 17. Concentration dependence of the self-diffusion coefficient DOfor benzene in two ZSM-5 samples. Filled symbols, %/A1 135; crosses, Si/AI > loo0 (9). i=
382
J. CARO
et al.
be obtained (30,3f,91-94). However, there are also numerous welldocumented experimental studies showing differences of up to two orders of magnitude (95). An especially large number of investigations have been devoted to benzene in zeolite NaX. For this system, sorption uptake measurements by different research groups revealed both agreement (10,13,93) and disagreement (95,96) with the PFG NMR self-diffusion data. In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and *H NMR lineshape analysis. With neutron scattering, it has been found that the rotational motion of benzene in NaX corresponds to a uniaxial reorientation about the C-6 axis, with jumps of 60". The mean time between successive jumps about the C-6 axis at 458 K was found to be 1 . 3 X s.
1
0
0 1
-
-
9
2 3 4 5 loading/C6 H6 per supercage
1
FIG.18. Self-diffusion coefficients of benzene in NaX at 458 K: PFG NMR, 0 (97) and 0 (92); QENS, A (13);deduced from *H NMR lineshape analysis, 0 (10). Comparison with zerononequilibrium measurements: v, sorption uptake with piezometric control (93); length column method (96); n , frequency-response and single-step frequency-response technique (%). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.
+,
383
HYDROCARBON MEASUREMENT IN ZEOLITES
TABLE V Translational Mobility Data for Benzene in Zeolite NaX" Loading (CbH6per supercage)
(X
0.8 I .3 2.0 a
D cm2 s-')
(12)1'2
7
4 1.9
7
(nm)
( x to-" s)
0.46 0.35 0.24
5.0 5.1 5.0
Obtained at 458 K by QENS (69).
Results obtained by QENS for the translational motion are summarized in Table V. As is the case for light hydrocarbons, the decrease of the selfdiffusion coefficient for benzene in NaX with increasing sorbate concentration is mainly due to reduced mean jump lengths rather than to increasing mean residence times between succeeding jumps. The same conclusions as drawn from QENS data can be drawn from 'H NMR lineshape analysis. The temperature influence on the 2H NMR lineshape of benzene sorbed on NaX is shown in Fig. 19. As in the case of 250 K
222K
200 K
F
182 K
2
eaJ
c
E
167 K
aJ
c
t 0
35
70
-
-[~w-w,)/~I~I/
125 K
kHz
FIG. 19. Temperature dependence of the 2H NMR lineshape for perdeuterated benzene sorbed on NaX (loading: 4 C6D, per supercage) (7).
384
J. CARO et
al.
benzene sorbed on HZSM-5, there is clear evidence (cf. Fig. 5 ) for a fast C-6 reorientation of the sorbed molecules with a correlation time T~ 1 ps. On the other hand, our spectra show that on the time scale of the NMR experiment, the benzene molecules are fixed at their sorption sites. According to Eq. (21), for all motions that change the orientation of the hexad axes of the molecules (e.g., translational jumps between sorption sites), even at T = 200 K, the values of the correlation time, T,, are much larger than the reciprocal value of the quadrupole frequency, w Q , i.e., T~ % 1 ps. This may be caused by the interaction of benzene molecules with sodium ions via their 7~ electrons. In QENS investigations (99), the sorbed benzene molecules were found to interact in Na-mordenite predominantly with the sodium ions, resulting in a uniaxial C-6 reorientation with a correlation time T~ 5 2 ps at 300 K. The correlation time obtained by QENS for the C-6 reorientation of benzene in NaX is of the same order of magnitude. At temperatures above room temperature, Lorentzian 2H NMR lineshapes are observed for perdeuterated benzene in NaX (7). Therefore, in this range of temperature, the translational mobility of benzene in NaX is expected to be significantly higher than in HZSM-5. This expectation was fulfilled indeed in sorption kinetics measurements. The diffusion coefficient Do for benzene on NaX is -2 x lo-' cm2 s-' at 353 K (93),whereas under similar experimental conditions a value of the order of 10-l' cm2 s-' was obtained for benzene on ZSM-5 (100).
*
3. p-Xylene in ZSM-5 The 'H NMR spectrum of p-xylene-d4 (all ring protons are replaced by deuterons) sorbed on ZSM-5 is shown in Fig. 20. From the observed quadrupole splitting of about 140 kHz, it follows that for all molecular mo-
I . . . . I . . . . l . . I . I . . I . l . . I . I . . . . I . . I . I I . . . ,
100
0
- 100
-
[(w-w~)/ZX]/~HZ
FIG.20. *H NMR spectra of p-xylene-d4 sorbed on ZSM-5(7.2 C8D4H6 per u.c., T = 295 K) obtained by composite 7r/2 pulses (9,58).
385
HYDROCARBON MEASUREMENT IN ZEOLITES
tions at room temperature the correlation times are much larger than 1 ps. Taking into account the pulse interval and the duration of the composite 7r/2 pulses used [40 and 71 ps (9)], the lower limit of the correlation time, T,, of molecular motions that change the orientation of the molecular plane with respect to the magnetic field is estimated to be T~ > 100 ps. A fast rotation about the para axis of the molecule, as deduced from 13CNMR spectra at 310 K (101), can be excluded. Our findings are in accordance with those of a previous 2H NMR study (102). The additional intensity in the center of the spectrum in Fig. 20 can be caused by molecules in another motional state (e.g., molecules outside the pore system performing fast 180” flips) as well as by traces of methyl deuterons as impurities. Assuming for p-xylene a jump mechanism similar to that of benzene, the same procedure can be applied to derive an upper limit for the translational diffusivity. At high sorbate concentrations, the p-xylene molecules in ZSM-5 should be localized in the channel intersections and the pore segments of the sinusoidal channels, based on theoretical (103) and XRD (103,104) studies. With this arrangement of sorption sites and the derived lower limit for the mean residence time (T~2 100 ps), one can predict a diffusion coefficient D I lo-” cm2 s-’ at room temperature and maximum loading, which corresponds well with the uptake data shown in Fig. 21. As in the case for benzene in ZSM-5, the translational motion of p-xylene in ZSM-5 was too slow to be measured on the IN6 neutron spectrometer
A
N
lo-”
i
A
A
A A
1
.,
2 3 looding/C8HI0 per u.C.
L
FIG. 21. Concentration dependence of the diffusivity DO for p-xylene on three different 50; Si/AI = 135; T, Si/AI > 1000 (9).
ZSM-5samples at 363 K: A, Si/AI
i=
386
J.
CARO et
al.
within the temperature range 90-380 K (105). No change of rotational motions was observed for a loading of four molecules per U.C.On the time scale of the neutron experiment (=lo-’’ s), the aromatic ring appears to be immobile and only one of the two methyl groups is rotating. The other methyl group seems to be blocked, most likely due to interactions with the framework. Theoretical and structural studies (103,104) suggest that for a loading of four molecules per u.c., the p-xylene molecules occupy the channel intersections with the methyl groups parallel to the straight channel. In this case, both methyl groups would be equivalent. The neutron results indicate, however, that the molecules located in the channel intersections have to be slightly inclined, leading to different interactions of the two methyl groups of the same molecule with the framework. For concentrations greater than four molecules per u.c., p-xylene becomes highly immobile ( 9 ) . OF N-HEXANE IN ZSM-5 STUDIED BY E. DIFFUSION PULSED-FIELD GRADIENT NMR, QUASI-ELASTIC NEUTRON AND SELECTIVE SORPTION UPTAKEKINETICS SCATTERING,
For both QENS and PFG NMR spectroscopic methods, the measurement of the translational molecular self-diffusion of n-hexane in ZSM-5 represents the present limit of detection. A value of 4.5 X lop6cm2 s-l is obtained by QENS at 300 K (75); by PFG NMR (106) the value is cm2 s-’ . These self-diffusion coefficients are in reasonable agreement with the data from MD simulations, 1.6 X cm2 S K ’ (107), and with sorption uptake measurements, which indicate that D > 7 X loK6cm2 s-’ (108). However, a difference of three orders of magnitude is observed with the value extrapolated from the “zero-length column” technique (109); five to six orders of magnitude deviation occurs using sorption uptake and gas chromatographic data (110,111). Additional sorption uptake studies on oriented ZSM-5 crystals have been performed (112,113). For anisotropic diffusion systems, this newly developed technique measuring sorption uptake through certain crystal faces, termed “selective sorption uptake kinetics” (113), can be used to determine the tensor components of the diffusion coefficient. For this reason, large ZSM-5 crystals have been aligned in two ways: upright standing crystals, aligned by means of electric fields as shown in Fig. 22, and crystals aligned horizontally in a plane. After embedding the zeolite crystals thus oriented into a gas-tight matrix (e.g., glass, metal, epoxy resin), by careful abrasion selective crystal faces can be opened for selective sorption uptake kinetics. Abrasion of the crystal arrangement shown in Fig. 22 gives the sample shown in Fig. 23. The sorption uptake kinetics on this sample is exclusively controlled by the mobility in the length direction of the ZSM-5 crystal, Dzz.For ZSM-5 crystals hori-
FIG. 22. Large ZSM-5 crystals synthesized by J. Kornatowski (137. f38) and aligned by means of an electric field of strength 2.3 kV cm-I. Crystals are fixed in the upright position by a thin film of an epoxy resin (113).
FIG. 23. Crystal arrangement as shown in Fig. 22 after embedding the crystals into a thermally stable epoxy resin and abrading the top (113). In sorption uptake, this sample was used to measure selectively D,,.
388
J. CARO et
al.
FIG.24. Plane-oriented ZSM-5 crystals, embedded into a copper matrix (Cu deposition by sputtering). The [lo01 and [OlO] faces were selectively opened for adsorption by abrasion. Because of the random orientation of the crystals in the plane, the mean (Dxx 0,,)/2 is determined in sorption kinetics ( I 13).
+
zontally oriented in the plane, as shown in Fig. 24, the tensor component (Dxx+ Dyy)/2becomes accessible. The mean is a result of the random crystal orientation. Using large ZSM-5 crystals (110 X 110 X 310 pm3), the time, in an individual sorption uptake step, to reach 50% of the final amount adsorbed, for the crystal arrangement shown in Fig. 23, is about 15 times larger than for the crystals shown in Fig. 24. At 298 K , the diffusion coefficients amount to D , = 2.4 X lo-’ cm2 s-’ and D,, = 0.8 X lo-’ cm2 s-’ (113);this shows that for n-hexane in ZSM-5 the mass transport in the length direction of the crystal is about three times slower than in the plane perpendicular to this direction. However, these sorption uptake diffusivity values fall between the values from the spectroscopic methods and the other sorption uptake experiments. Possible reasons for these deviations from intracrystalline mass transport could be the internal twinning of the ZSM-5 crystals under study as well as the fact that abrasion could possibly mechanically damage a tiny surface layer (formation of an amorphous surface barrier).
389
HYDROCARBON MEASUREMENT IN ZEOLITES
VI. Structure-Related Molecular Self-Diffusion in Zeolites by Pulsed-Field Gradient NMR: Influence of Pore Diameter, W A I Ratio, and Concentrations of Internal OH Groups and Cations; Self-Diffusion of Mixtures
A. SINGLE-COMPONENT MEASUREMENTS As Fig. 25 shows, the intracrystalline self-diffusion coefficient of methane in ZSM-5 is between coefficients in zeolites NaCaA and NaX (5,7Z,lZ4,ZZ5,). This order can be interpreted in terms of the minimum apertures of the zeolite channels, which are approximately 0.45,0.55, and 0.75 nm for 5A, ZSM-5,and X-type zeolites. Due to the hydrophobic nature of Z S M - 5 , the mobility of water in ZSM-5 considerably exceeds the mobility in zeolites NaA and NaX. A change in the SiO2/AI2O3ratio of ZSM-5 does not alter the self-diffusion coefficient of methane. On the contrary, for water in ZSM-5 an increase in the self-diffusion coefficients with decreasing A1 concentrations in the framework is indicated.
$
CHblNaX
CHLI ZSM-5 A[
A
CHdNaCaA
I$
+
AA
['A
A
H201ZSM-5
A A HfllNaX
H201NaA
-Si02/A1203 4
1
10
lo2
I
lo3
FIG.25. Self-diffusion coefficients of methane (open symbols) and water (filled symbols) in zeolites NaCaA, NaX, and ZSM-5 (loading, approximately 1 CH4 or HzO molecule per 24 T atoms, 296 K) (5).
390
J. CARO
et al.
TABLE VI Influence of Hydrothermal Treatment on Sorption and Diffusion Properties of a Silicalite Specimen Si-OH concentration (number g - ' ) 8 . 4 X lozod 4.6 X 10''
Sorption capacity
Self-diffusion coefficient ( X lo-' m2 S K I )
(mmol g-') c,,,(n-CsHd
Csat(H2O)
D (CHdb
D (H?0)"
1.28 1.38
3.05 1.62
9.8 7.2
1.4 3.1
The silicalite specimen (121) has large concentrations of internal Si-OH groups; as measured by 'H MAS NMR (122,123). all measurements at 300 K . Loading -8CH4 per U . C . ' Loading -12Hr0 per U . C . Parent sample ' After steaming
Due to synthesis conditions, zeolites can contain remarkable concentrations of intracrystalline Si-OH groups (116-121). These groups represent defect sites in the form of nonintact Si-0-Si bonds inside the crystals. Because hydrothermal treatment is a suitable method to recombine zeolitic Si-0-Si bonds, a silicalite sample was held under steam at 1100 K for 5 days (121). In the parent sample, -8% of the framework Si atoms were present as Si-OH. As Table VI shows, during hydrothermal treatment algroups reacted and formed intact most 50% of the former Si-OH Si-0-Si units. As a result, the n-hexane sorption capacity increased by -7%. With water, the opposite effect has been observed. Owing to the increased hydrophobicity of the steamed sample, the former sorption capacity of water decreases by -50%. However, even this reduced amount of sorbed water is approximately three orders of magnitude larger than the amount necessary to produce monolayer coverage on the external surface of the zeolite crystals. With the drastic reduction in the number of silanol groups, the water self-diffusion coefficient increases. In light of these results, the significant scattering of the values of sorption capacity and diffusivity on zeolites as reported in the literature (70,71,92,95) could correlate also with structural defects such as nonintact Si-0-Si bonds. B . PULSED-FIELD GRADIENT NMR MULTICOMPONENT SELF-DIFFUSION During their technical application, molecular sieve catalysts are generally used under the conditions of multicomponent adsorption and diffusion. Selective measurement of the diffusivity of individual components is therefore of both theoretical and practical relevance. The traditional way to perform
HYDROCARBON MEASUREMENT IN ZEOLITES
39 1
self-diffusion studies in mixtures by PFG NMR is to use deuterated compounds or compounds without any hydrogen, so that the ‘ H NMR signal stems from only one of the mixture compounds (3, 42, 142). Unfortunately, selective diffusion measurement necessitates additional experimental preparations, because for the study of a system containing n components at least n various PFG NMR samples must be prepared, each of them with a different compound in the hydrogen form. A more straightforward possibility of selective self-diffusion measurements is provided by Fourier transform PFG NMR, as was discussed previously. Using this method, the total NMR signal is split up into separate signals due to different NMR chemical shifts. This procedure has been successfully applied to multicomponent liquids, where it was possible to measure simultaneously the diffusivity of up to eight different components (124). In adsorbate-adsorbent systems, however, such experiments are complicated by the reduction of molecular mobility. The linewidths must be small enough to allow resolution of the observed NMR spectra into the spectra of the individual components. 1. NMR SelfDiffusion in Binary Mixtures Using
Deuterated Compounds
a. Methanol and Water in HZSM-5. Figure 26 shows the self-diffusion coefficients of water and methanol in a methanollwater mixture absorbed in HZSM-5 for two different total loadings (125). For every mixture composition, the self-diffusion of the proton-containing component was measured selectively; the other mixture component was present in the deuterium form (for ‘ H NMR “invisible”). For a total loading of 35 mg (water plus methanol) per gram of ZSM-5, the mobility of the sorbed water was found to be enhanced with respect to pure liquid water. In contrast, the mobility of the sorbed methanol was slightly reduced. At a total loading of 50 mg per gram of ZSM-5, the self-diffusion coefficients of both adsorbed water and methanol were found to be lower than the values for the free liquids. For nonadsorbed liquid mixtures, a remarkable minimum of the selfdiffusivity was found (Fig. 26). In contrast, no mimima in the self-diffusion coefficients of the sorbed mixtures were obtained. Obviously, the sorption potential and /or the geometric constraints of the intracrystalline channel system prohibit the formation of highly structured methanol/water complexes, which are present in liquid methanol/water mixtures. These bulky complexes have been proposed to cause the mimima found in the diffusion coefficients of the liquid mixtures (126,127). b. C4 Hydrocarbons in the Presence of Water in NaX. Figure 27 shows that the self-diffusion behavior of paraffins and olefins may be influenced significantly by coadsorbed molecules ( 1 15). The self-diffusion coefficient
J. CARO et
392
al.
O
2.0 -
1.5-
n 1.0-
I
I
I
I
I
0
25
50
75
I I
100
mol % methanol
__c
FIG.26. Self-diffusion coefficients of methanol (squares) and water (circles) in their binary mixtures sorbed in HZSM-5 for two total loadings: 35 mg (HzO + CH3OH) g-' (open symbols) and 50 mg g-' (filled symbols) at 300 K (125). Comparison with the self-diffusivity in liquid methanol/water mixtures (126,127): dotted line, D(CH3OH); dashed lines, D(H20).
of n-butane in NaX decreases by up to three orders of magnitude with increasing amounts of coadsorbed water (D20). With a slight increase for small amounts of coadsorbed water, the self-diffusion coefficients of but- 1ene exhibit a different dependence. This effect is due to the specific interaction of but-1-ene with adsorption centers in NaX. These centers are blocked by water, thus leading to an increase in the mobility of the but-lene molecules. The presence of further water molecules leads to a steric hindrance of the but- 1-ene mobility similar to that of n-butane. As shown in Fig. 28, coadsorbed ammonia (ND3) affects the selfdiffusion behavior of n-butane and but- 1-ene in NaX in a manner similar to that seen in the coadsorption of water. In contrast to water and ammonia, the dependence of n-butane and but-1-ene diffusion on the number of coadsorbed C02 molecules is less pronounced.
2. Fourier Transform PFG NMR The first 'H PFG Fourier transform NMR experiments of adsorbed molecules have been carried out with an ethane/ethene mixture adsorbed on
I
-
number of D,O per cavity
in NaX as a function FIG.27. Self-diffusion coefficients of n-butane ( 0 )and but-I-ene (0) of coadsorbed water (0.8 C4 molecules per cavity, 293 K ) (115).
,
I
1
I
___)
I
5
I
I
I
I
I
10
I
I
I
J
number of cosorbed molecules per cavity
FIG. 28. Self-diffision coefficients of n-butane and but-I-ene in NaX (0.8. C, molecules per cavity, 293 K) in the presence of coadsorbed ND, and C02 (115): A, C4HI0+ ND3;0, C4HlU + CO; A , C4H8 ND,; 0, C~HR + COz.
+
394
J . CARO et
al.
ms
/
1 .d
0
/'
l.I-L__LLi_l
1
2
3
4
5
6
&* H/PPm
FIG.29. ' H PFG Fourier transform NMR spectra of an ethane-ethene mixture in NaX (1.5 CzH6plus 1 CzH4per supercage, 293 K ) for increasing values of the width (6) of the field gradient pulses. The pulse separation ( t ) and the field gradient intensity (g) are 4 ms and 2.8 T m-'. The chemical shifts S , , refer to TMS (128).
zeolite NaX (128). This system is especially suitable for such studies, because the spectra of both components consist of only one line and the mobility of both components is sufficiently high to guarantee line narrowing that allows separation of the two spectra. Considering a sorbate concentration of 1.5 molecules ethane and 1 molecule ethene per supercage, it follows from Fig. 29 that the ethene mobility remains the same as in the case of singlecomponent self-diffusion, D = 1.25 X lo-' m2 s-', whereas the selfm2 s-', is found to be reduced by a diffusivity of ethane, D = 4.6 X factor of about 2. Recently, this method has been applied to the in situ observation of the diffusivity of both the reactant and product molecules during the conversion of cyclopropane to propene in NaX catalysts (135).
VII. Location of Diffusion Obstacles Inside the ZSM-5 Framework by Pulsed-Field Gradient NMR For a number of adsorbate-adsorbent systems it has been found that the intracrystalline self-diffusion of a highly mobile component is drastically reduced by the presence of a second, strongly coadsorbed component. By combining these self-diffusion measurements with a computer simulation of
HYDROCARBON MEASUREMENT IN ZEOLITES
0
05
395
1a
number of coadsorbed benzene molecules per 1 / 4 U.C.
FIG. 30. Self-diffusion coefficient of methane adsorbed on ZSM-5 as a function of coadsorbed benzene (3 CH, per u.c., 293 K) (86).
the random walk (of the highly mobile molecule) in a zeolite framework that contains statistically blocked channels and/or channel intersections, information about the location of the strongly adsorbed component (diffusion obstacle) inside the zeolite framework is obtained. A. MOLECULAR SELF-DIFFUSION OF METHANE ADSORBED ON ZSM-5 CONTAINING COADSORBED BENZENE Figure 30 shows the self-diffusion coefficient of methane in ZSM-5 samples that contain different amounts of coadsorbed benzene (86). It can be seen that the benzene molecules significantly reduce the methane mobility. It is evident that the blocking effect of diffusion obstacles such as benzene should depend decisively on their position inside the channel network: (1) for benzene molecules located in pore segments (between the channel intersections), the passage through only these segments is prohibited; (2) a benzene occupation of the channel intersections should lead to a blocking of all four adjacent channel segments.
396
J. CARO et
al.
-
number of coad60rbed benzene molecules per 114 U.C.
1
\
0.01
-
b=0004
l . I . I I I I . I I
0
0.5
1.0
number of dlffusion obstacle8 a8SUmed In computer slmulatlon per 1/4 u.C.
FIG.31. Computer simulation of the random walk in a two-dimensional network with obstacles distributed statistically over the pore segments (dashed lines) and over the channel intersections (solid lines). Different transition probabilities b to pass the barrier are assumed: b = 0.004, 0.020, and 0.120. The experimental results of the methane self-diffusion in ZSM-5containing coadsorbed benzene (0, cf. Fig. 30) are included (86).
Figure 31 shows the results of a computer simulation of the random walk in a two-dimensional channel network with obstacles distributed statistically (1) over the pore segments and (2) over the channel intersections. As expected, the influence of the obstacles distributed over the channel intersections considerably exceeds the influence of the obstacles in the pore segments. The computer calculation shows that the shape of the individual plots of In D versus the amount N of obstacles is typical of the given type of obstacle distribution, i.e., there is no possibility of transferring the In D versus N plots of one case to another by simply changing the transition probability across the obstacles. One has to conclude, therefore, that for loadings <4 benzene/u.c. and room temperature, the benzene molecules have extended residence times in the channel intersections. In this way they cause a maximum hindrance for the self-diffusion of the methane molecules. The experimental data (Fig. 30) fit the curve calculated for diffusion obstacles located in the channel intersections, assuming a transition probability (blocking efficiency) of b = 0.004. This finding is in accordance with other experimental and theoretical studies discussed herein.
397
HYDROCARBON MEASUREMENT IN ZEOLITES
I
f
I
I
\
-
-+I$
-
I
0 Q
1
5-
OOQ 0 0
Q@
a@ .,
-
I
:8
1
8
0
0
2-
lo9
1
0
5-
2 -
1
I
FIG.32. Self-diffusion coefficients of methane (4 CH, per u.c., 293 K) in HZSM-5 specimens of different Si/AI ratios. Specimens contain chemisorbed N compounds (80% of the equivalent number of Bransted acid sites): (3, ammonia; 0 , pyridine. For comparison, the self-diffusivities in the parent HZSM-5 without any N bases (0) are included (129).
B. SELF-DIFFUSION IN HZSM-5 CONTAINING CHEMISORBED N BASES Figure 32 shows the self-diffusion coefficients of methane in HZSM-5 specimens (of different %/A1 ratios) that contain different amounts of chemisorbed N compounds (129). Before the self-diffusion measurements, the samples were modified by quantitative chemisorption of ammonia and pyridine, respectively, in the following way. After sample evacuation at 673 K, an amount of ammonia or pyridine corresponding to 80% of the equivalent number of Br@nstedacid protons [as determined by 'H magic angle spinning (MAS) NMR] (122,123)was added and chemisorbed on the activated zeolite. It was concluded from subsequent 'H MAS NMR that all of the N compounds introduced had reacted with the Brplnsted acid sites. Then the ZSM-5 samples of different Si/Al containing different amounts of chemisorbed N compounds were loaded with methane. Chemisorption of N compounds leads to a significant reduction of the self-diffusion coefficients of methane. This effect becomes more pronounced with increasing amounts of chemisorbed N bases. Obviously., with
J. CARO et
398
al.
chemisorbed molecules per 1 / 4 U.C. I
-
I 0
I
0.25 n u m b e r of
I
I
0.75 I 1 d i f f u s i o n obstacles 0.5
a s s u m e d in c o m p u t e r simulation p e r 1 / 4 U.C.
FIG.33. Comparison of the experimental values (Fig. 32) of methane self-diffusion in HZSM-5 containing ammonium ((3) and pyridinium ( 0 )ions with the results of the computer simulation of a random walk in a two-dimensional channel network with diffusion obstacles statistically distributed over the channel intersections (solid lines) and over the pore segments (dashed lines) (129). Different transition probabilities, b, to pass the obstacle are assumed.
respect to the highly mobile methane molecules, the chemisorbed N bases may be regarded as rigid obstacles inside the channel network of HZSM-5. As already discussed, for the partial blocking of ZSM-5 by benzene, the experimental data discussed herein will be compared with two cases of an obstacle distribution: (1) in the connecting pore segments or (2) in the channel intersections. Figure 33 compares the experimental results and the cornputer simulations. For pyridine, the self-diffusion data are in satisfactory agreement with the model for obstacles distributed over the channel intersections. One has to conclude, therefore, that the chemisorbed pyridine molecules and, thus, the Brgnsted acid sites, are localized near or even in the channel intersections. That is to say, all catalytically active centers are accessible for a reactant molecule in a channel intersection. A similarly strict conclusion cannot be drawn from the experimental data for chemisorbed ammonia, which give rise to a behavior intermediate between those of the two limiting cases. One should take into account, however, that due to its smaller size, an ammonium ion situated in a channel intersection does not lead to a simultaneous blockage of all four adjacent
HYDROCARBON MEASUREMENT IN ZEOLITES
399
channel segments. Thus, for ammonia, complete agreement with the computer simulations cannot be expected. VIII. Detection of Spatial Distributions of Diffusion Obstacles over the Crystal Size by Pulsed-Field Gradient NMR
Information on the distribution of diffusion obstacles such as coke, modifiers, or regions of framework damage can be derived from combined PFG NMR and TD NMR measurements. Limitations of the overall adsorption/desorption kinetics as followed by TD NMR can be caused by deposits inside the crystals and/or on their outer surfaces. In contrast, in PFG NMR only diffusion obstacles in the volume phase of the zeolite crystal are detected. Conclusions can be drawn from the following considerations: 1. A reduction of the intracrystalline self-diffusion coefficient, DLntTd, of a probe molecule (e.g., methane) as measured by PFG NMR has to be regarded as proof of the existence of coke, modifiers, etc. in the volume phase of the zeolite crystal. 2. The absence of additional diffusion barriers at the crystal surface (coke, modifiers, etc.) can be assumed if the experimentally determined ~~ by TD NMR), and the cormean intracrystalline lifetimes, T , ” ,(measured responding calculated data, .rdtf, [according to Eq. (lo)], coincide. The T?,% data are calculated by using the self-diffusion coefficients, Duma (measured by PFG NMR), and crystal radii, R , assuming the adsorption/desorption process to be diffusion controlled. 3 . If the values of the effective self-diffusion coefficients, Deft [calculated from the complete x ( t ) curves in TD NMR experiments, assuming diffusion-limited uptake (52)] are below the corresponding intracrys(measured directly by PFG NMR), the existence of additalline data, DIntra tional mass transfer resistances in a layer near or on the outer surface of the zeolite crystals is indicated. The second and third considerations are equivalent ways to prove the existence of transport barriers near the outer crystal surface. OF HZSM-5 IMPREGNATED WITH A. CHARACTERIZATION H,P04
Figure 34 shows that both the intracrystalline self-diffusivity Dintra(as measured by PFG NMR) and the effective self-diffusivity D,ff (as derived from TD NMR) decrease with increasing phosphorus content. The continu-
400
J. CARO
et al. I
r
30
I I
1 0
1
I
-mass
2
I
3
I
.
1
4
I
5
I
%P
FIG. 34. Intracrystalline self-diffusion coefficient Dinlra(A) and effective self-diffusion coefficient Dea (0) of methane in HZSM-5modified by impregnation with H3P04. The startm2 s-l (6 CH4 per u.c., 293 K) (130). ing self-diffusion coefficient is 8.9 X
ous decrease of Dint,has to be taken as proof that phosphoric acid can be progressively incorporated into the pore system of ZSM-5. Because Deff decreases more steeply than Dintra, it is concluded that with increasing amounts of phosphoric acid, additional diffusion obstacles near the crystal surface simultaneously arise, i.e., an enrichment of phosphorus species near the surface of the zeolite crystals takes place (130). This result is demonstrated in Fig. 3 5 , which shows the ratio Dintm/Deff as a function of the phosphorus content. For DintrJDeS = 1, a homogeneous distribution of the phosphorus > 1 indicates an enrichdeposits over the crystals is indicated. Dinrra/Deff ment of phosphorus species near the outer crystal surface. Figure 35 clearly shows that such enrichment occurs with increasing amounts of phorphorus deposits. Unfortunately, no information on the chemical nature of these transport resistances can be obtained from 'H NMR self-diffusion experiments. For this purpose, several MAS NMR methods have been applied successfully (130). Figure 36 shows the 31PMAS NMR spectrum of the HZSM-5 sample containing 2 wt% P. Three signals can be distinguished: (1) the signal at 1 ppm stems from monomeric [P04l3- groups like those in orthophosphoric acid; (2) the signal at -6 ppm is due to the P atoms in pyrophosphoric acid or due to the terminal [PO4I3- groups in polyphosphoric
HYDROCARBON MEASUREMENT IN ZEOLITES
-
0
1
I
I
2
3
4
5
40 1
I
mass YO P
for methane self-diffusion in HZSM-5 impregnated with H J P O ~ FIG. 35. Ratio Dinlra/Deff (experimental data from Fig. 34) (130).
I
20
I
0
I
-20 c -
1
-40
I
-60
6 1P/ppm
FIG.36. "P MAS NMR spectrum of HZSM-5 with 2% P brought about by H3PO4soaking and subsequent thermal treatment at 823 K (partial sample rehydration before the "P MAS NMR measurement at 293 K) (130).
species; (3) the signal at -30.7 ppm is attributed to aluminum phosphate. The intensity of the latter signal grows with increasing amounts of H3P04 added and indicates a progressive framework dealumination. Consequently, intracrystalline and /or surface deposits of polyphosphates and/or aluminium
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phosphates (the presence of which follows from the finding of 27Aland 31P MAS NMR) should cause the transport limitations observed in PFG NMR and TD NMR studies (130).
B. DETECTION OF THE HYDROTHERMAL CRYSTAL OF ZEOLITE A DAMAGE Table VII compares the measured intracrystalline mean lifetimes, T , " , ~of ~, methane and xenon in various zeolites with the values of ~ S f f .calculated ~, according to Eq. (10) from the self-diffusion coefficients and the mean crystal radii. It turns out that in the case of methane, for all three zeolite samples both quantities are in reasonable agreement; for xenon in NaCaA and HZSM-5 the mean residence time is drastically enhanced in comparison with the values expected from the intracrystalline mobility according to Eq. (10). This experimental finding may be correlated with the larger diameter of the xenon atoms (0.49 nm, in comparison with 0.41 nm for methane), making them more sensitive to a reduction in surface permeability of adsorbents with limiting free diameters of this order of magnitude (0.4-0.5 nm for NaCaA, -0.55 nm for HZSM-5). The surface regions of the crystal exhibit a transport resistance to some types of diffusants (e.g., xenon), while other diffusants (methane) may pass without any perceptible restriction; one can therefore conclude that the surface barrier is not brought about by a total blocking of a certain fraction of apertures in the interface, but by a pore narrowing in a surface layer (42,239). TABLE VII lntrucrystulline Mean Lifetimes of' Methane and Xenon in Zeolites NaCuA, NuX and HZSM- 5" Zeolites
Mean
Methane
crystal diameter (pm)
T,,l,(ms)
T%:,(rns)
Xenon Tdms)
T Lnrra(ms) ~'~'
NaCaA
CaL '
45% 63%
NaX
80%
HZSM-5 "
13 20 5 50 20 25
3*1 4 2 1 0.4 k 0.2 2+ 1 0.4 2 0.2 3 + 1
Obtained at 293 K . From Ref. 42
6 i 2 4 r 2 1 + 0.5 1 + 0.5 2 + 1 4?1
3+-1 4 2 1 0.4 0.2 8 1 2 1.5 C 0.5 11 2 3
*
80 + 20 45 + 10 25 + 8 15 lir 10 5 + 3 > 40
HYDROCARBON MEASUREMENT IN ZEOLITES
c. 1.
403
O N THE LOCATION OF COKE DEPOSITS IN/ON ZSM-5
CRYSTALS
Coke Deposition by n-Hexane Cracking
The reduction of molecular self-diffusion due to coking can be used to determine the distribution of coke deposits over the crystals. As an example, Fig. 37 shows the characteristic decrease of Dintraand DeRfor HZSM-5 (Si/ A1 = 70, crystal size -14 p m , coked by n-hexane cracking) as a function of coking times. For ZSM-5 samples with a time onstream <2 h, a similar reduction of both Dint=and Def for the methane self-diffusion was found, indicating the existence of homogeneously distributed intracrystalline coke. However, for samples coked longer than 2 h, the intracrystalline mobility, D,,,,, of the methane guest molecule remained practically constant. In contrast, De8 continued to slow down, indicating an increasing transport resistance near or on the external surface. Obviously, with extended times onstream, coke is preferentially deposited in the outer regions of the ZSM-5 crystals, blocking the mouths of pores. In accordance with Fig. 37, from Fig. 38 two periods of coke formation can be distinguished. In the first period, with the ratio Dint,/DeR = l , a homogeneous coke distribution over the whole crystal takes place. In a second period, Dintra/Defincreases, indicating an enrichment of coke in the surface region.
I
‘ 0
1
2
3
1
5
+
6 4 1 6
time onstreamlh
FIG. 37. NMR intracrystalline self-diffusion coefficient Dintra(A) and effective selfdiffusivity Deff(0) of methane in HZSM-5crystals that were coked for different times by nhexane cracking (131-133). Before loading with methane (9.2 CH, per u . ~ . ) , the coked ZSM-5crystals were carefully outgassed at 623 K and Pa. The remaining carbonaceous residues were defined as “coke.” Amounts of coke after different times on stream: 1 h, 0.8 wt% C; 2 h, 1.3 wt% C; 6 h, 3.2 wt% C; 16 h, 4.8 wt% C. The starting self-diffusion m2 s-’.. coefficient is 8.1 x
J. CARO et
404
al.
-I"
-
2.0
0
r
eme
1.5'
t
1.0 .
a'
I
0
I
I
I
I
2
3
4
-
mass % coke
as a function of the amount of coke deposited for three FIG.38. Ratio of Dintra/DeE HZSM-5 specimens (crystal type, as shown in Fig. 42, with mean equivalent diameters of 8.5 p m (A), 14 p m (n),and 28 p m (v) and an HZSM-5 plycrystalline grain (0;cf. Fig. 43) (131-133).
2. ~ e ~ d ~ f ~ins ZSM-5 i o n Coked by Mesitylene Cracking In contrast to HZSM-5 coked by n-hexane, for mesitylene-coked HZSM-5 (Fig. 39) the intracrystalline mobility, Dintra, of methane is nearly unaffected by coke deposits (42,131). On the other hand, the effective selfdiffusion coefficient, &, decreases continuously with increasing time onstream, i.e., Deff4 Dintra. The conclusion is that mesitylene coking leads to the pronounced formation of a surface barrier, i.e., from the beginning of
8
0 -time
16
24
onstreamlh
(v)and Dew (O), of FIG. 39. Intracrystalline and effective self-diffusion coefficients, Dintm methane (9 CH4 per u.c., 293 K) in HZSM-5 crystals coked by mesitylene cracking versus the time onstream (131). Amounts of coke after different times onstream: 8 h, 0.5 wt% C; 16 h, 0.9 wt% C; 24 h, 1.2 wt% C. The starting self-diffusion coefficient is 8.2 X mz s-I.
HYDROCARBON MEASUREMENT IN ZEOLITES
0
,
1
I
2
3
L
t
4
5
mass % coke
405
FIG. 40. Ratio Dinrra/DeR for coke from n-hexane (A) and mesitylene (v) cracking on
HZSM-5as a function of the coke content (131).
coking the carbonaceous residues are deposited onhear the outer surface of the zeolite crystals, because the mesitylene molecules are too large to penetrate into the ZSM-5 pores. The different coking behaviors of n-hexane and mesitylene on ZSM-5 can also be demonstrated by the ratios of Dintra/De# (Fig. 40). Because mesitylene coking produces mainly surface coke, the intracrystalline mobility of methane remains unchanged, i.e., Dintra/Des > 1. In the case of coke formation by n-hexane cracking, surface coke (Dintra/De~ > 1) is formed after an initial period of intracrystalline coke deposition (Dintra/Deff = 1). In Fig. 41, distinct differences in the amounts of chemisorbed pyridine can be seen for HZSM-5 samples coked by n-hexane and mesitylene cracking. Whereas coke from mesitylene only slightly inhibits the pyridine chemisorption, coke from n-hexane leads to a much stronger inhibiting effect. This result supports the model of controlled coke deposition derived
I
n
0
1 2 -mass
3
4
5
% coke
FIG.41. Pyridine chemisorption as a function of the coke content: A , n-hexane coke; V, mesitylene coke (131).
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from the self-diffusion studies discussed above. A homogeneous coke distribution inside the crystals blocks more acidic sites and, hence, inhibits pyridine chemisorption more strongly than the concentration of coke in a surface layer. IX. Self-Diffusion in ZSM-5 Particles of Different Crystal Morphology
Figures 42 and 43 show scanning electron micrographs of two ZSM-5 samples of different configurations: coffin-shaped crystals and polycrystalline grains. To emphasize the relationship between sample dimensions and diffusion paths followed during the PFG NMR experiment, magnifications are referenced against typical root mean square displacements for methane and propane molecules during typical PFG NMR observation times. Comparing the self-diffusion coefficients of short-chain alkanes in various coffin-shaped ZSM-5 crystals of different origins (crystal type, as shown in Fig. 42) with those in more than a dozen samples of polycrystalline grains (Fig. 43), it can be concluded that molecular mobility in ZSM-5 polycrystals is significantly higher than in polyhedral crystals. This experimental finding is explained by a promotion of molecular transport due to additional fast diffusion paths originating from the polycrystalline structure of the grain. Hence, the increase in diffusivity can simply be considered as a higher molecular mobility in the voids between the intergrown disks forming the substructure of the grain. Obviously, the interfacial voids between adjacent disks have the nature of transport pores (second-order pores). From this diffusion model for polycrystalline grains, an enhancement of molecular mobility with increasing diffusion time is to be expected. Results of corresponding experiments are shown in Fig. 44. For the uncoked sample, an increase of DinIra is observed with increasing observation time. This finding can be understood by the following mechanism. During short observation times, the majority of the propane molecules move preferentially within the substructure of the polycrystalline grain. With increasing time intervals allowed for self-diffusion, an increasing number of molecules will enter the interspace between the disks, a region of transport enhancement, and will travel there over longer distances. The self-diffusivity of propane in the coked polycrystalline grains unveils details of coke formation in polycrystalline particles. Figure 44 shows that coking reduces the translational mobility inside the grains. The effect of intracrystalline coke deposition on the translational mobility of propane is indicated in Fig. 43. After a coking time of 1 h, only a slight increase of Dint= with increasing observation times occurs. After 12 h, a decrease is ob-
FIG. 42. Comparison of the crystal morphology of ZSM-5 with the mean molecular displacements, (r' (t))!,{$, during the observation time of self-diffusion: (a) methane (t = 0.5 ms, 12 CH, per u.c., 298 K) and (b) propane (t = 1.5 ms, 10 C3Hs per u.c., 298 K). The m2 s-' for methane and 2.5 x lo-'' corresponding self-diffusion coefficients are 8 X m' s - ' for propane (134).
FIG. 43. Morphology of ZSM-5 polycrystalline grains compared with the mean diffusion path of (a) methane ( t = 0.5 ms) and (b) propane (t = 1.5 ms). The corresponding selfdiffusion coefficients are 1.4 X lo-' mz s-' for methane and 4 X lo-'' m2 s-' for propane. (For further explanation, see Fig. 42.) For propane, the reduction of the root mean square displacement due to deposition of n-hexane coke (4.3 wt% c) is indicated (134).
HYDROCARBON MEASUREMENT IN ZEOLITES
r :
I
5
a5
10
1.5
409
Oh
2.0
t/ms
RG.44. Self-diffusivity Dint, of propane (10 C,Hs per u.c., 293 K ) as a function of the observation time t of self-diffusion for the polycrystalline grains shown in Fig. 43 after different coking times by n-hexane cracking (132):0, starting ZSM-5; @1 h, 3.6 wt% C; 0 , 12 h, 4.3 wt% c.
served. This behavior indicates that now coke is preferentially incorporated in the second-order pores. This means that the interspaces between the disks progressively lose their transport-promoting character. Finally, the second-order pores, when filled up with coke, become a transport hindrance.
X. Conclusions It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffusivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. Analyzing the self-diffusion behavior of guest molecules in a microporous catalyst by the combined application of pulsed-field gradient NMR selfdiffusion techniques reveals the spatial distribution of transport resistances over the catalyst particles. In the case of coke deposits on ZSM-5, the distribution of carbonaceous residues over the crystal was found to be a function of the crystal morphology, the time onstream, and the chemical nature of the coke-producing reactant. In the case of ZSM-5 modified by H3P04, the spatial distribution of the P compounds over the ZSM-5 crystals can be determined by self-diffusion measurements. Location of transport hindrances in a zeolite framework is based on self-diffusion measurements, in
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al.
comparison with using the computer-simulated random walk in considering the influence of diffusion obstacles. In this way, physisorbed benzene and chemisorbed pyridyne were found to have extended residence times near the channel intersections, compared with the pore segments of ZSM-5. Furthermore, nonintact Si-0-Si bonds and the Si/AI ratio of the zeolite framework significantly alter the diffusion patterns of polar molecules such as water and methanol. In polycrystalline aggregates the self-diffusion coefficients of light hydrocarbons were found to be enhanced compared with the diffusion in an undisturbed crystal structure. Detailed information on the complex nature of mass transport in both the intra- and intercrystalline space of catalyst pellets can thus be obtained for both single and multicomponent systems. ACKNOWLEDGMENTS The authors want to express deep appreciation to Prof. H. Pfeifer (Leipzig), Prof. W. Schirmer (Berlin), and Prof. M. Bet: (St. Martin d’Heres) for their fruitful and friendly cooperation during the past decade. The authors thank Prof. L. V. C. Rees (London) for stimulating discussions and for joint single-step frequency-response measurements on the frequencyresponse apparatus at Imperial College. We thank Dr. G. J. Kearley (Grenoble) for help in performing the neutron experiment at the lnstitut Laue-Langevin, Grenoble; Dr. W. Heink (Leipzig), for the development of the NMR spectrometer FEGRIS; Dr. M. Noack (Berlin), for the measurement of selective sorption uptake kinetics; Dr. J. Volter (Berlin), for the joint coking investigations; Mr. J. Richter-Mendau (Berlin), for the REM; Prof. S. P. Zhdanov (St. Petersburg) and Dr. J. Kornatowski (Torun), for the zeolite synthesis. REFERENCES I . Weisz, P. B., CHEMTECH 3, 498 (1973). 2. Post, M. F. M., in “Studies in Surface Science and Catalysis. Vol. 58: Introduction to Zeolite Science and Practice”. (H. van Bekkum, E. M. Flanigen, and J . C. Jansen, eds.), p. 391. Elsevier, Amsterdam, 1991. 3. Karger, J., and Ruthven, D. M., “Diffusion in Zeolites and Other Microporous Solids.” Wiley, New York, 1992. 4. Garcia, S. F., and Weisz, P. B., J. Catal. 121, 294 (1990). 5. Caro, J., Biilow, M., Schirmer, W., Karger, J., Heink, W., Pfeifer, H . , and Zhdanov, S . P., J.C.S. Faraday I 81, 254 1 (1 985). 6. Eckman, R. R., and Vega, A. J., J. fhys. Chem. 90,4679 (1986). 7. Zibrowius, B., Caro, J., and Pfeifer, H., J.C.S. Faraday I 84, 2347 (1988). 8. Reischmann, P. T., Schmitt, K. D., and Olson, D. H., J . fhys. Chem. 92, 5165 (1988). 9. Biilow, M., Caro, J., Rohl-Kuhn, B . , and Zibrowius, B., in “Studies in Surface Science and Catalysis. Vol. 46: Zeolites as Catalysts, Sorbents and Detergent Builders” H. G. Karge and J. Weitkamp, eds.), p. 505. Elsevier, Amsterdam, 1989. 10. Boddenberg, B., and Burmeister, R., Zeolites 8, 488 (1988). 11. Silbernagel, B. G., Garcia, A. R., Newsam, J. M., and Hulme, R., J . Phys. Chem. 93, 6506 (1989). 12. Jobic, H . , Bee, M., Caro, J. Biilow, M., and Karger, J., J.C.S. Faraday 1 8 5 , 4201 ( I 989).
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Biilow, M., Karger, J., Koi-iiik M., and Voloshchuk, A. M., Z . Chem. 21, 175 (1981). Karger, J., and Ruthven, D. M., J.C.S. Furaduy 177, 1485 (1981). Biilow, M., Mietk, W., Struve P., and Lorenz, P., J.C.S. Faraday I 79, 2457 (1983). Biilow, M., Lorenz, P., Mietk, W., Struve, P., and Samulevich, N. N., J.C.S. Faraduy 179, 1099 (1983). Karger, J., and Ruthven, D. M., Zeolites 9, 267 (1989). Eic, M., Goddard, N. V., and Ruthven, D. M., Zeolites 8 , 327 (1988). Germanus, A., Karger, J., Heifer, H., Samulevich, N. N., and Zhdanov, S. P., 20lites 5, 91 (1985). Shen, D., and Rees, L. V. C., unpublished results. Jobic, H., Bee, M., and Renouprez, A., Surf. Sci. 140, 307 (1984). Zikanova, A., Biilow, M., and Schlodder, H., Zeolites 7 , 115 (1987). Nagy, J. B., Derouane, E. G., Resing, H. A., and Hiller, G. R., J. Phys. Chem. 87, 833 (1983).
Eckman, R. R., and Vega, A. J., J. Am. Chem. SOC. 105,4841 (1983). Reischmann, P. T., Schmitt, K. D., and Olson, D. H., J. Phys. Chem. 92,5165 (1988). Mentzen, B. F., Bosselet F., and Bouix, J., C. R. Acad. Sci., Ser. 2 305, 581 (1987). Czjzek, M., Jobic, H., and Bee, M., J.C.S. Furuduy 87, 3455 (1991). Heink, W., Karger, J., Heifer, H., Datema, K. P., and Nowak, A., J.C.S. Furuduy (in press). June, R. L., Bell, A. T., and Theodorou, D. N., J. Phys. Chem. 86, 1051 (1992). Beschmann, K., Fuchs, S., and Riekert, L., Zeolites 10, 798 (1990). Eic, M., and Ruthven, D. M., in “Studies in Surface Science and Catalysis. Vol. 49: Zeolites: Facts, Figures, Future” (P. A. Jacobs and R. A. van Santen, eds.), p. 897. Elsevier, Amsterdam, 1989. Wu, P., and Ma, Y.H., Proc. Int. Zeolite Conf., 6th p. 251 (1984). Ma, Y.H., Proc. Inr. Zeolite Conf., 7th Tokyo p. 531 (1986). Caro, J., Finger, G., Kornatowski, J., Richter-Mendau, J., Werner, L., and Zibrowius, B., Adv. Mater. 4, 273 (1992). Caro, J., Finger, G., Jahn, E., Kornatowski, J., Marlow, F., Naack, M., Werner, L., and Zibrowius, B., Int. Zeolite Conf., 9th. Montreal in press (1992). Caro, J., Hocevar, S., Karger, J., and Riekert, L., Zeolites 6, 213 (1986). Heifer, H., Karger, J., Germanus, A., Schirmer, W., Biilow, M., and Caro, J., Adv. Sci. Technol. 2, 299 (1985). Datka, J., and Tuznik, E., Zeolites 5, 230 (1985). Engelhardt, G., Fahike, B., Magi, M., and Lippmaa, E., Z . Phys. Chem. (Leipzig) 266, 239 (1985).
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Molecular Mobility Measurement of Hydrocarbons in Zeolites by NMR Techniques J. CAR0
H . JOBIC
Zentrum f u r Heterogene Katalyse D-I199 Berlin-Adlershof, Germany
Institut de Recherches sur la Catalyse 69626 Villeurbanne, France
M. BULOW
J. KARGER
The BOC Group Murray Hill, New Jersey 07974, U . S . A .
Fachbereich Physik der Universitat Leipzig 0-7010 Leipzig, Germany AND
B. ZIBROWIUS Department of Chemistry University of Manchester Institute of Science and Technology Manchester M601QD, England
1.
introduction
This article provides a review of the most relevant experimental methods to follow molecular translations and/or reorientations of guest molecules in zeolite pores. The benefit of combining these techniques is illustrated by a
35 1 Copyright 0 1993 by Academic Press, Inc. All rights of reproduction in any form reserved.
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series of diffusion studies of hydrocarbons adsorbed in zeolite catalysts. Because of the key role of structure-related diffusion processes in shapeselective catalysis and the unique possibilities of the NMR self-diffusion techniques to investigate such processes, the fundamentals of the NMR selfdiffusion techniques are presented in more detail and examples are given of their application to characterize zeolite catalysts. Zeolitic molecular sieves ex hibit remarkable properties that have made them an interesting topic of both fundamental research and industrial application. In shape-selective catalysis, the correspondence between the diameters of typical reactantlproduct molecules and those of the zeolite channels leads to an intense interplay between the host framework and the guest molecule. Therefore, Weisz introduced the term “configurational diffusion” to describe this special kind of molecular mass transport in zeolites ( I ) . Consequently, slight differences in the structure of the guest molecules can lead to a strong variation in their diffusivities. And vice versa, small changes in the zeolite pore structure (e.g., lattice imperfections such as structural defects, stacking faults, and intergrowths of different zeolite types) can significantly modify the diffusion and adsorption patterns. Recent reviews on mass transport in zeolites are given in Refs. 2 and .?. To understand the principles of shape-selective adsorption and catalysis, a detailed knowledge of the microdynamics of the molecules inside the zeolitic pore system is required. Garcia and Weisz ( 4 ) pointed out the relevance of NMR methods to yield a unifying picture for the phenomena, mechanisms, and magnitudes of “diffusivities.” In the past few years, a deeper insight into molecular motions in zeolites has been achieved, especially by combining investigations of molecular translation with studies of reorientation processes on different time scales (5-14). First we will review the relevant NMR techniques and their most recent developments: (1) pulsed-field gradient (PFG) NMR (315-18) for the measurement of translational molecular self-diffusion and (2) ’H (6,7,lO,19,20) and I3C (9,21,22)NMR lineshape analysis as well as ‘ H NMR relaxation analysis (5,23,24)for the study of molecular reorientation. For selected adsorbateladsorbent systems, we demonstrate the benefit of combining these experimental methods to reveal complex molecular transport phenomena. The results of these NMR methods will be compared with those of other experimental techniques, such as quasi-elastic neutron scattering (QENS) (12,13,25-27), the frequency-response technique (28,29) in its singlestep mode (14.30,31), and sophisticated sorption uptake experiments (39,32,33,113) as well as recent molecular dynamics (MD) calculations (34-41).
353
HYDROCARBON MEASUREMENT IN ZEOLITES
II. Basic Principles of NMR Self-Diffusion Studies A. SELF-DIFFUSION MEASUREMENT BY PULSED-FIELD GRADIENT NMR In a magnetic field of strength B, the resonating nuclear spins precess with the Larmor frequency W = -yB (1) about the direction of the magnetic field, where y denotes the gyromagnetic ratio of the resonating nuclei. In NMR diffusion measurements (15-18,23, 24,42,43), this magnetic field consists of a strong time- and spaceindependent component (Bo)and a superimposed field (ABo)that is assumed to increase linearly in the z direction (i.e., ABo = gz). Consequently, the Larmor frequency becomes a function of the space coordinate ( z ) determined by the direction of the field gradient ( g ) . In PFG NMR, the magnetic field gradient is only applied during two short time intervals of identical duration (6) (“field gradient pulses”) and separation ( t ) . By applying an appropriate radio-frequency pulse sequence (a r / 2 - r sequence for generating the “primary” spin echo or a 7r/2-7r/2-7~/2 sequence for generating the “stimulated’ echo), one can observe the transverse nuclear magnetization, i.e., the component of the total magnetization perpendicular to the constant magnetic field, developing under the influence of these two gradient pulses. In order to calculate the vector sum of the total magnetization, one has to determine the difference A$(i) between the average phase and the actual phase for each of the spins after the second gradient pulse. Denoting the z coordinates for the ith spin during the first and second gradient pulses by zI“ and z!’, one obtains from Eq. (1) in the generally considered limiting case of sufficiently short field gradient pulses
A+(d =
I
I
~ d t -
2nd gradient pulse
o dt =
1st gradient
y6g(Zy’ -
zY)
(2)
pulse
Because each spin contributes to the total transverse magnetization via the cosine of the phase difference A+(’),the quantity observed in PFG NMR is given by the relation *(6g, t ) = M J M , ,
=
CoS”)‘@(Zi
-
ZZ)]P(ZI) P(Z2, Z I , t ) dZi dZ2(3)
where M, and M , denote the magnitudes of the total transverse magnetizations with and without field gradients, respectively, p ( z J dzl is the prob-
354
J. CAR0
et a/.
ability of finding a molecule in a position with a z coordinate between z I and z1 + dz, and P (z2, z l , t ) dz2 denotes the conditional probability that a molecule that starts at the time of the first gradient pulse from position z I has reached a position between z2 and z2 + dz2 after the time t. For molecular self-diffusion in a homogeneous medium, one has P ( Z , zl, t) = ( 4 n ~ t ) - I ’exp[-(z ~ - zJ2/4 Dt)
(4)
Equation (4)corresponds to the solution of Fick’s second law in an infinite space for the initial condition c*(z, 0) = S(z - z1). With Eq. (4), Eq. (3) simplifies to *(Sg, t ) = exp{-y262g2Dt}
(5)
or, using the Einstein relation D = (r2(t))/6t, we can write *(Sg, t ) = e ~ p { - y ~ 6 ~ g ~ ( r ~ ( t ) ) / 6 }
(4)
with ( r 2 ( t ) )denoting the mean square displacement during the time interval t . According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal T versus (Sg)*. The “observation” time of self-diffusion is the separation between the two field gradient pulses, t . Owing to their relatively large gyromagnetic ratio and to their natural abundance of = 1, protons provide very suitable conditions for N M R self-diffusion studies, but I3C (44), 19F ( 4 3 , and 129Xe(46-48) resonances have also been used successfully in recent PFG N M R studies of zeolites. For diffusion in anisotropic systems such as the MFI structure (ZSM-5/ silicalite-I), Eq. ( 5 ) has to be replaced (3,17,42,49)by *(gJ,A) +
= exp[-y2S2
-
ZEZt]
(7)
with 5 and 2 denoting the diffusion tensor and the field gradient vector, respectively, instead of the scalar quantities D and g. Thus, in macroscopically oriented systems the principal elements of the diffusion tensor may be determined by varying the direction of the field gradient. In powder systems such as beds of zeolite crystallites, one has to integrate over all possible directions and, strictly speaking, the spin-echo attenuation is no longer exponential. For a diffusion tensor of axial symmetry with Dli > D,,Fig. 1 shows the influence of a diffusion anisotropy on the PFG N M R spin-echo attenuation as simulated in numerical calculations (49). The quantitative analysis shows, however, that for principal tensor elements not too different from each other (i.e., for tensor elements within one order of magnitude), the ini-
355
HYDROCARBON MEASUREMENT IN ZEOLITES
C
-
Dn,703
9
3-
10
5 1
10-
I
,
1
2
, 3
-
,
,
,
,
,
,
,
4
5
6
7
8
9
10
Y*g26*
(!I/
re( units
FIG. 1. Parameter calculations for the PFG NMR spin-echo attenuation due to anisotropic self-diffusion in a diffusion system of axial symmetry with Dll > D I (49).
tial part of the spin-echo attenuation appears to follow Eq. ( 5 ) with a mean Dzz)equal to one-third of the trace of the diffusivity D = i ( D , + D,, diffusion tensor (17,49). It is only this initial part, however, that is considered generally in PFG NMR experiments. Depending on the signal-to-noise ratio of the NMR signal and the magni, range of mean errors typical of self-diffusion meatudes of D ( r 2 ( t ) )the surements performed on zeolite systems is from 10% up to a factor of 2. All self-diffusion measurements reported in this paper have been carried out by means of the homemade NMR pulse spectrometer FEGRIS operating at a proton frequency of 60 MHz at the Department of Physics of the University of Leipzig (16-18).
+
B, SELF-DIFFUSION MEASUREMENTS BY THE NMR TRACER DESORPTION TECHNIQUE In general, for zeolitic self-diffusion at sufficiently high temperatures, the mean molecular displacements outside the crystal are much larger than those inside the zeolites; that is to say, long-range self-diffusion, D L ~ is . , much faster than intracrystalline self-diffusion, Din,,. For observation times comparable with the mean lifetimes of the adsorbed molecules in the individual crystallites, the spin-echo attenuation can be approximated by the superposition of two exponentials of the type of Eq. (6)
356
J. CAW
et al.
where x ( t ) denotes the relative amount of molecules that have left their crystallites during the observation time, t. As a consequence of the initially assumed large difference between the intracrystalline and long-range mobilities, the root mean square (r.m.s.) displacement for long-range selfdiffusion, (r2(r))f!2,is much greater than that for intracrystalline migration, (r2(t)),',/&. Therefore, the quantity x ( t ) can be determined by a plot of In 4' versus (i3g)2.Moreover, by varying the time interval, t , between the two field gradient pulses, the complete time dependence of x (t) is available. This is the same information as that derived from traditional tracer desorption experiments. Therefore, this modification of pulsed-field gradient NMR has been termed tracer desorption (TD) NMR (50) (see also Refs. 3,16,17,51). There are two equivalent ways to achieve a quantitative analysis of the x ( t ) curves as obtained by TD NMR:
1. Comparison of mean intracrystalline lifetimes. For this kind of data evaluation, it is useful to introduce the first statistical moment
MI =
I-, [I
- x(t)I dt
= Tint,
(9)
as a measure of the mean lifetime, Tnntra, of the molecules inside the zeolite crystals. If the molecular exchange between the individual crystals of the sample/pellet is exclusively limited by intracrystalline self-diffusion (i.e., in the absence of surface barriers), for spherical particles of mean square radius (R') the molecular mean lifetime can be calculated from the crystallite size and the value of the intracrystalline self-diffusion coefficient, D,,,, (measured directly by PFG NMR): diff Tintra
=
~ d i f = f 1
(R2)/15Dmtm
(10)
If the calculated value of if if fa is equal to the measured intracrystalline lifetime, T ] . ~ , ~the , rate of molecular exchange between different crystals is controlled by the intracrystalline self-diffusion as the rate-limiting process. Any ~ ~ with T$Lindicates the existence of transport increase of T , in ~comparison resistances different from intracrystalline mass transport. Under the condithus these resistances can only be tions of TD NMR one has D I B D,,,,, brought about by surface barriers. The ratio Tmta/T$k represents, therefore, a direct measure of the influence of surface barriers on molecular transport. 2. Comparison of (effective) self-diffusion coefjcients. To give a clear idea of the adsorption/desorption retardation due to surface barriers, another means to achieve data evaluation from TD NMR experiments is the calculation of an effective self-diffusion coefficient, DeR.From the fractions x ( t ) of those molecules that have left the crystals during different observa-
HYDROCARBON MEASUREMENT IN ZEOLITES
357
tion times, t , by fitting corresponding solutions of Fick's law for diffusionlimited adsorption/desorption (52) to the x (t) curves, an effective selfdiffusion coefficient, Deff, can be determined. As an example, for x ( t ) = 0.5 (half of the molecules have left/entered the individual crystals of mean radius R during t ) , the relation D b 5 / R 2 = 0.03 (52) provides a rough estimate for the determination of D,B. Note that the sample is in sorption equilibrium; this means that the same amount of molecules that leave the crystals during t also enter them. The value of D,R as derived from TD NMR can be directly compared with Dint-as measured by PFG NMR. In the absence of a transport barrier near the outer crystal surface, the adsorption/desorption behavior is determined exclusively by the intracrystalline self-diffusion, consequently Deff-- Dint=.The presence of any surface barrier as an additional transport hindrance leads to a decisive retardation of the molecular exchange between the individual crystals of the sample. In this case, D,E < Dintra. C. APPLICATION OF PULSED-FIELD GRADIENT NMR TO ZEOLITEPELLETS One of the advantages of PFG NMR is its ability to provide direct information about the entirety of molecular transport phenomena in pelletized adsorbents and catalysts (316). As an example, Table I presents the transport parameters for methane in granulated zeolite NaCaA (16,53). Three quantities that have a key function for the understanding of mass transfer in granules are illustrated in Fig. 2: (i) the coefficients of intracrystalline self-diffusion, Dint=,and of (ii) long-range self-diffusion, as well as (iii) the molecular mean lifetime, n,lra. The coefficient of long-range self-difffusion is approximated by D1.r. =
Pinter
Dinter
(11)
where pinterand Dinterdenote the relative number and the self-diffusion coefficients of the molecules in the void space between the crystals. For sufficiently high molecular concentrations in the gas phase (2lo'* protons/ cm3), NMR provides an experimental access to both of these quantities: Pinter may be determined through the molecular concentration in the adsorbed (ca) and gaseous (cg) phases and the void fraction 7 = K n d (Knter + V,,,,) of the zeolite bed by the relation pinter =
c g Knter
Ca Kntra
+ c g Knter
-
7 7)+ cg7
cg
Ca(1 -
(12)
where cg and ca(l - 7)+ cg7 are directly obtained from the intensities of the NMR signal observed in the gas phase and in the zeolite bed.
I TABLETABLE I Molecular Transport Parameters for Methane in Granulated NaCa Zeolite" MolPrular Transpori Parameters for Meihane in Granulaied NaCu Zmliie" Quantity Quantity
SymbolSymbol
Intracrystalline self-diffusion coefficient Intracrystalline self-diffusion coefficient Molecular mean lifetime a crystal Molecular mean lifetime inside ainside crystal Molecular mean lifetime in a crystal Molecular mean lifetime in a crystal calculated under the assumption calculated under the assumption that that adsorption/desorption is diffusion adsorption/desorption is diffusion limitedlimited (absence of surface barriers) (absence of surface barriers) Long-range self-diffusion coefficient Long-range self-diffusion coefficient DI r of molecules of molecules in the in the RelativeRelative amountamount Pintcr intercrystalline of the granule intercrystalline space ofspace the granule Mean free path Mean free path Gas-phase self-diffusion coefficient Gas-phase self-diffusion coefficient Molecular mean lifetime in the intercryMolecular mean lifetime in the intercryof the granule stallinestalline space ofspace the granule Mean molecular diffusion Mean molecular diffusion path in path the in the intercrystalline of the granule intercrystalline space ofspace the granule
A
D,,,, T,nm Tdiff ,"Ira
MethodMethod of determination of determination
PFG for NMR for ( r 24( t(R2)IIZ ) ) ' /G 2 (R2)'12 PFG NMR (r2(t))1'2 Tracer desorption Tracer desorption NMR NMR Through D,.,,theand the crystal radius R, Through D,.,,and crystal radius R, Eq. (10) by Eq. by (10)
Value Value Xmz s-I m2 s-' 1.7 X 1.7 loA9 1.1 ms1.1 ms
0.2 ms0.2 ms
PFG for NMR for ( r 25,( tR2)'12 ) ) 1 / 2 R2)1/2 lo-' PFG NMR (r2(t))llZ 2.2 x 2.2 lo-' xm2 s-I m2 s-' Through the concentrations of methane 0.18 0.18 Through the concentrations of methane in the adsorbed gas phases (as in the adsorbed and gasand phases (as determined by NMR) the void determined by NMR) and theand void '1, by Eq. (12) 7,by Fq. (12) fractionfraction A Through the gas-phase concentration Through the gas-phase concentration and and 7.8 nm7.8 nm the collision cross section, Eq. (13) the collision cross section, by Eq.by (13) Dgas PFG NMR PFG applied NMR applied to the gas phase 3.4 x 3.4 xm2s-' m2s-' to the gas phase 240 ps240 p s Through the values P,.,~,,ofPp,.,,, , " , ~=P , " , ~= Through the of values 'T,n,er 1 -and P T,,~,, , and~by T,,, ~,, by ~(14) Eq. ~ (14) 1 - pnnIeC Eq. l,,,,, Through Through the values T ,~and D, ~ ,~ by 42 p m42 p m the values of T ,ofand ~ D, ,~~by Eq. (16) Eq. (16)
DI r
Pl"ler
" Temperature, K; six CH, molecules per cavity. From16 Refs. " Temperature, 293 K; 293 six CH, molecules per cavity. From Refs. and 16 53.and 53.
HYDROCARBON MEASUREMENT IN ZEOLITES
359
FIG.2. Mass transport parameters in zeolite pellets as determined by PFG NMR and TD NMR (42).
For molecular mean free paths much less than the mean free diameters of the intercrystalline void space in the zeolite bed, D,,,,is controlled by the same mechanism as in the gas phase, with a self-diffusion coefficient D,. Due to the steric confinement, D,,,, is reduced with respect to D, by a tortuosity factor, 7 6 , with values typically of the order of 2-3. The mean free path can be estimated through the relation A = kTaprra2 = 1/V%,mr2
(13)
where k denotes Boltzmann’s constant, T is the absolute temperature, p is the pressure, and m r 2 is the collision cross section. In the example considered in Table I, A is found to be clearly less than the mean free diameters within the zeolite bed, and comparison of D I, PinterDlnter with PlnterDg yields a tortuosity factor of Tb = D,/D,,te, -- 2.7. From the NMR tracer desorption and self-diffusion data (second and third S fa. In the example given, lines of Table I), one obtains the relation 7,ntra intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and highresolution electron microscopy studies (54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. It becomes obvious from the equilibrium condition pinter/Tinter = pintra/Tintra
(14)
that any enhancement of 7,ntra due to surface resistances leads to an enhance~ . mean distance covered by the molecules in the intercrysment of T , , , ~ ~The talline space before being captured again by a crystal follows from the cor-
360
J. CARO et
al.
responding notation of Einstein’s equation, (liter)
=
(15)
6Dinter~inter
replacing the two quantities on the right-hand side by Eqs. (11) and (14), this relation can be written as (lfnter)
=
(16)
6D1.1. Tintralpintra
where both quantities D I . ~and , Tintraare directly accessible via the NMR experiments. In most cases, the relative number of molecules in the gas phase is negligible in comparison with the amounts adsorbed, so that pint,, pintra and consequently PinIra = 1. According to Table I, the mean diffusion path covered by the molecules in the intercrystalline space before being captured again by a zeolite crystal is one order of magnitude larger than the diameter of the crystals (3.8 pm). A parameter of some technical relevance is the ratio Tintra/Tgranule of the molecular mean lifetimes in the individual crystals and in the granulated particles. With Rgranule denoting the radius of a granulated particle, by analogy to Eq. (10) one has
*
Tgranule
L1
(R&mule)/
so that either of two quantities Tintraand
15Dl.r.
T~~~~~~~ can
(17)
be determined by NMR.
D. ON THE LIMITS OF APPLICATION OF PULSED-FIELD GRADIENT NMR FOR SELF-DIFFUSION MEASUREMENTS IN ZEOLITES The major limitations for an application of PFG NMR to self-diffusion studies can be summarized in four categories:
1. Most self-diffusion studies have been performed at low temperatures and high loadings characteristic of low temperatures. Due to collisional molecule-molecule interactions, often a drastic decrease of the selfdiffusion coefficient at high sorbate concentrations is found (see later, cf. Fig. 10). In the limit, molecular self-diffusion of small molecules in largepore zeolites can be described by diffusion models for liquids (e.g., diffusion of hydrocarbons in zeolite X by the so-called “free-volume model”; see Section V,B.). In contrast, typical catalytic operations work at temperatures above 275 K and, consequently, with sparse populations of molecules per zeolite cage. However, in the case of structure-related molecular selfdiffusion (as found for hydrocarbons in ZSM-5), the systematic study of molecular self-diffusion as a function of temperature and loading (at subcatalytic temperatures and concentrations usually higher than those in catalytic
HYDROCARBON MEASUREMENT IN ZEOLITES
36 1
reactions) provides a reliable basis for the extrapolation to catalytic conditions. On the other hand, by applying Fourier transform PFG NMR (this technique is described in Section VI,B,2), in recent PFG NMR studies (135) during the conversion of cyclopropane to propene on NaX at 473 K, the self-diffusion coefficients of the individual components involved in this reaction could be measured directly and simultaneously. Furthermore, the development of high-temperature probe heads for PFG NMR (which allowed measurement of the self-diffusion of n-paraffins in zeolite 5A at 625 K) (136) represents, again, substantial experimental progress toward catalytic conditions in PFG NMR. Another approach to determine diffusion coefficients under catalytic conditions can be achieved most effectively by studying the effectiveness factor in catalytic experiments on samples of different crystal size (the intrinsic reaction rate constant and the equilibrium constant must be known) as done by Haag et al. (55) for the cracking of n-hydrocarbons over HZSM-5. 2. The minimum self-diffusion coefficient measurable by PFG NMR depends significantly on the upper limit of the time interval t , which is limited by the damping of the NMR signal due to transverse nuclear magnetic relaxation. In general, t will be of the order of the transverse nuclear magnetic relaxation time, T 2 , or less (17,56). As an example, for benzene in ZSM-5 at 400 K , one has T2 = 0.5 ms and, assuming as characteristic values of t = 1 ms, 6 = 0.5 ms, and g = 10 T m-', only a self-diffusion coefficient D 2 cm2 s-' can be measured. This lower limit is about 3-4 orders of magnitude above the real diffusivity of benzene in ZSM-5 (cf. Fig. 17), i.e., there is only little hope to measure the benzene self-diffusion in ZSM5 by PFG NMR. However, by using partially deuterated compounds, the proton-proton interaction within one molecule can be reduced and as a result T2 can be prolonged, which gives the opportunity to apply larger t and 6 values (24,56).A further possibility to enhance the observation time t involves the application of the stimulated spin echo (3,17). In this case the spin-echo damping is controlled mainly by the longitudinal nuclear magnetic relaxation time, T I ,which may be considerably larger than T2. 3. In Ref. 56 it is shown that small amounts of highly mobile molecules adsorbed on the outer surface or within intracrystalline cracks will, in general, lead to an enhanced damping of the NMR signal that may be interpreted erroneously as a high overall mobility of the adsorbed molecules if the two-phase character of the signal is not taken into consideration. 4. The molecular root mean square displacement, (r2(t))1'2, of the diffusing molecules during the observation time, t , has to be much smaller than the crystal radius, R , in order to guarantee that the measured r.m.s. displacement reflects the undisturbed intracrystalline self-diffusion. Assuming
362
J. C A R 0 el al.
a lower limit o f t = 0.5 ms and a crystal radius R = 1.5 p m , the diffusivities that can be measured amount to D < lop5cm2 s-l. However, this upper limit can be shifted to higher diffusivities if large zeolite crystals are available.
111.
Principles of NMR Techniques to Detect Molecular Reorientations
OF MOLECULAR REORIENTATIONS BY "c A. DETECTION NMR LINESHAPE ANALYSIS
In 13CNMR spectroscopy, deviations from a Lorentzian lineshape, which is usually obtained in liquids, can be caused by a chemical shift anisotropy (CSA). If a CSA is present, the position of the resonance line depends on the relative orientation of the molecule with respect to the direction of the magnetic field applied (21,22). The superposition of the individual resonance lines results in typical lineshape patterns that can be described by two parameters: the chemical shift anisotropy, As, and the asymmetry parameter, q , respectively. In the case of an axially symmetric CSA tensor, i.e., q = 0, the relation between the resonance frequency, w , and the orientation of the molecule is given by w =
wg
[
6i,"
-
1
A6 -j(3 cos26 - 1)
where wo = yBo denotes the Larmor frequency, 6iaois the isotropic chemical shift, and 6 is the angle between the magnetic field and the principal axis of the CSA tensor, thus describing the orientation of the molecule with respect to the magnetic field. Molecular motions can lead to an (at least partial) averaging of the CSA. The degree of averaging is determined by the type of motion as well as by the ratio of the correlation time, T,, and the value of A6 (21). Therefore, several types of molecular motions give rise to characteristic lineshape patterns. For
one has the spectrum of rigid molecules, i.e., molecules of a fixed orientation with respect to the magnetic field. In the case of a fast isotropic reorientation with
HYDROCARBON MEASUREMENT IN ZEOLITES
363
the CSA is completely removed and one obtains a Lorentzian line with a line width determined by the remaining interactions. In contrast to n-paraffins, which exhibit no or only a slight I3C NMR CSA, aromatics or hydrocarbons with double or triple bonds show a much larger anisotropy. Therefore, benzene (57) and 2-butyne (14) were chosen as suitable probe molecules to study molecular motions by 13C NMR lineshape analysis. Theoretical lineshapes for different motional states of benzene and 2-butyne molecules are depicted in Figs. 3 and 4. The protondecoupled I3C NMR spectra were recorded by means of the homemade NMR spectrometer UDRIS (University of Leipzig) and a BRUKER MSL 400 (Central Institute of Physical Chemistry, Berlin) at frequencies of 22.6 and 100.6 MHz (9,14,57).
h
A 0:
fast reorientation about F
fast aboutreorientation F
fast isotropic reorientations
,
I
I
Z O
200
150
100
6/ppm
-
I
I
50
0
FIG. 3. Theoretical I3C NMR lineshapes of benzene molecules for different types of motions (58).
364
J.
CARO et
a/.
fast isotropic reorientation 200 150 100 50
b/ppm
-
0 -50
FIG.4. Theoretical "C NMR lineshapes of 2-butyne molecules for different types of motions (14). OF MOLECULAR REORIENTATIONS BY 'H B. OBSERVATION NMR LINESHAPE ANALYSIS
The *H NMR lineshape of solids is determined by the quadrupolar interaction, which can be described by two parameters: the quadrupole frequency, W Q , and the asymmetry parameter, 77 (19,20). The parameter W Q is determined by the electric quadrupole moment of the deuteron and the zz component of the electric field gradient at the deuteron site. For deuterons bonded to carbon atoms, the asymmetry parameter is approximately zero and the z axis is along the C-D bond. In this case, the dependence of the resonance frequency, W , from the orientation of the molecule with respect to the magnetic field applied is given by a relation similar to Eq. (18) (19). As long as the correlation time, r,, of a molecular motion is sufficiently large, i.e., TcWQ
%
1
(21)
the lineshape is not influenced by this motion. For faster motions, however, characteristic deviations occur, because-depending on the type of motion-at least a certain part of the quadrupolar interaction is averaged to zero (19,20). Depicted in Fig. 5 , are theoretical 'H NMR lineshape patterns of perdeuterated benzene for various motions. The 2H NMR spectra were
HYDROCARBON MEASUREMENT IN ZEOLITES
365
H&
fast reorientation about F
fast aboutF reorientation
fast isotropic reorientations
I
I
100
50
0
-50 -100
FIG. 5. Theoretical *H NMR lineshape patterns of perdeuterated benzene molecules undergoing various types of motions (7).
obtained with the quadrupole echo pulse sequence on the previously mentioned spectrometers at frequencies of 13.8 and 61.4 MHz, respectively (7,9).
c. ANALYSIS OF MOLECULAR TRANSLATIONS AND ROTATIONS BY COMBINED 'H NMR RELAXATION AND NMR SELF-DIFFUSION STUDIES The self-diffusion paths of guest molecules in an isotropic host lattice can be described by a sum of successive individual molecular jumps (5,9,25, 26,59,60),
366
J. CARO et
al.
where D is the self-diffusion coefficient and ( r 2 ( t ) )and (Z2) denote, respectively, the long-range mean square displacement during an observation time, t , and the individual mean square jump length after a residence time, 7 , of the jumping molecule at a sorption site, respectively. In addition to QENS, the value of the mean residence time, 7 ,of a jumping molecule can also be estimated from 'H NMR relaxation analysis. The correlation time T~ of the longitudinal proton magnetic relaxation can be approximated by the reciprocal value of the proton magnetic resonance frequency at the temperature of the T I minimum, i.e., T~ -- w0' (5,23,24). The motional process that controls NMR relaxation is usually assumed to be a molecular reorientation together with or without a simultaneous translational motion. Consequently, depending on the dominating mechanism of magnetic interaction, one has T~ 5 T . Therefore, from combined PFG NMR self-diffusion and NMR relaxation studies, according to Eq. (22) a lower limit of molecular mean jump lengths can be given. The longitudinal and transverse ' H NMR relaxation times have been measured using the NMR spectrometer UDRIS. IV.
A.
Principles of Other Mobility Measurements (Comparison with NMR Data)
MOLECULAR TRANSLATIONS AND ROTATIONS BY QUASI-ELASTIC NEUTRON SCATTERING (QENS)
For hydrocarbons in zeolites, only incoherent scattering has to be considered because of the large incoherent cross section of hydrogen. The neutron intensity scattered follows the incoherent scattering law Sinc(Q,w ) , which is related to the self-motion of protons, where 6Q and fiw denote the neutron momentum transfer and the neutron energy transfer, respectively. Assuming for a molecular system the vibrational, rotational, and translational motions as uncoupled, the incoherent scattering law can be expressed as a convolution product of the individual scattering laws for each motion, which can be examined separately: Sinc(6,
0)
= SP:(~, w )
B S \ ; A ( ~w,) B S ; F < ~ w, )
(23)
For the quasi-elastic region ( 5 2 meV) that is of concern here, the vibrational motions affect only the elastic intensity through a Debye-Waller facis the mean square hydrogen amplitude in tor, exp(-Q2(u2)), where (2) the vibrational modes. The scattering law for rotations can be written as a sum of an elastic peak intensity and a quasi-elastic component:
SE(6,
W)
= Ao(&(w)
+ Sqei(6,
0)
(24)
HYDROCARBON MEASUREMENT IN ZEOLITES
367
The elastic peak intensity is governed by A o ( ~ )which , is kcown astJhe elastic incoherent structure factor (EISF). The variation of Ao(Q) with Q allows determination of the nature of the rotation (e.g., isotropic or uniaxial rotations). The dynapical behavior of protons is reflected by the quasi-elastic component, Sqel(Q,w ) . This term can be expressed as a superposition of Lorentzians whose widths are related to the average time between jumps. The simplest model of translational motions in three dimensions is the continuous random walk diffusion (Fick’s law) giving a Lorentzian-shaped scattering law, SiF(Q,
W)
1 =-
To2
DQ’
+ (DQ’)’
where D is the self-diffusion coefficient. This model can be applied quite well to simple liquids at small Q values. In zeolites, however, jump diffusion models (61-63) have been found more appropriate. The broadening values obtained for methane diffusion can be fitted to a molecular jump model with a Gaussian distribution of jump lengths (25,62). Thus, the scattering law becomes a Lorentzian,
whose half-width at half maximum (HWHM) 1 Aw(Q) = ;[l
-
1 exp(-Q2(12)/6)] = -[1 - exp(-Q’Dr)] 7
(27)
is determined by both the mean time, r , between two succeeding jumps, and the mean square jump length, (1’). At small Q values, the HWHM becomes equal to AW(Q) = DQ’ and D can be derived. At high Q values, the half-width approaches the mean jump rate, T-’.For systems with a different distribution of jump lengths, the broadening curves were fitted with another jump model (63). The shape of the quasi-elastic peak is still a Lorentzian, but the HWHM is given by (63)
This model was used for ethane and benzene in NaX. The QENS results were obtained at the Institute Laue-Langevin, Grenoble, using the time-of-flight spectrometers IN5 and IN6 (25-27). The time scale on which the motions can be observed by QENS is determined by the elastic energy resolution, which amounted to 20 and 100 p e V for the spectrometers IN5 and IN6, respectively. Based on an appropriate statistical
368
J. CARO et
al.
data evaluation, broadenings smaller than the resolution can be measured so that motions in the range 10-’o-10-’2 s can be followed. Consequently, diffusion coefficients of the order of 10-4-10-6 cm2 s-’ can be measured. Furthermore, by applying the backscattering technique, a better instrument resolution, of the order of lpeV, can be obtained.
B . DIFFUSION COEFFICIENTS FROM SORPTION KINETICS By fitting appropriate solutions of Fick’s diffusion law to the adsorption/ desorption curves, diffusion coefficients can be derived. Depending on the way the experiments are performed, variable boundary conditions have to be taken into account (52). However, as a rough estimate, one can approximate the initial part of the adsorption/desorption curves by the so-called law accounting for the changing boundary conditions (64):
d
where PO,p,, and pmdenote the pressures at the beginning of sorption, at actual time t , and at sorption equilibrium, respectively. A denotes the external surface area and V is the volume of the crystals. Other methods of data evaluation are provided by the method of statistical moments (32)or the full analysis of uptake curves for complex processes by means of the software ZEUS (Zeolite Uptake Simulator) (65). In contrast to all the other techniques considered in this paper, in sorption experiments molecular migration is observed under nonequilibrium sorption conditions. Therefore, instead of self-diffusivities, D, in this case transport diffusivities, D t , are derived. It is generally assumed (see, e.g., Refs. 366) that the “corrected” diffusivities, Do,
D O = D,d [In c ( p ) ] / d[In p ]
(30) with c (p) denoting the sorbate concentration in equilibrium with the sorbate pressure p, should be of the order of the self-diffusivity, D. In the following discussion, sorption experiments will be discussed only in terms of the “corrected” diffusivity, Do. Two experimental methods to follow sorption kinetics have been applied. In the single-step frequency-response method, the frequency-response system at Imperial College, London, has been used. Fast volume perturbations that cause stepwise-like pressure changes have been achieved by activating an electromagnet that has copper bellows attached (3031). In another sorption kinetics technique installed at
369
HYDROCARBON MEASUREMENT IN ZEOLITES
the Central Institute of Physical Chemistry, Berlin, the pressure changes are initiated by dosing via opening a valve (32). In this mode, adsorption/ desorption processes caused by the pressure jump are followed piezometrically in a constant volume system. V. Combined Application of Different Experimental Techniques to Study Molecular Translations and Rotations of Hydrocarbons in Zeolites
A. COMPARISON OF SELF-DIFFUSION COEFFICIENTS DETERMINED BY PULSED-FIELD GRADIENT NMR AND QUASI-ELASTIC NEUTRON SCATTERING 1 . Methane in ZSM-5
Figure 6 represents typical plots of the spin-echo intensity in PFG NMR experiments. Comparing the slopes of these representations with those of standard liquids, one obtains the mean self-diffusivities, which are found to decrease with increasing sorbate concentration (5,12,16,59,60). It appears from Fig. 6 that within the accuracy of the measurement no deviation from a single exponential decrease may be observed. A comparison of the experimental spin-echo attenuation (Fig. 6) with the results of numerical calcula-
100 80 ffl
TT
-h
!t
60
o
3-
t
2o 10 1
2
3
L
4
5
6
7
8
9
1
0
f g 2 6 2 ( t ) / rel-units
FIG.6. PFG NMR spin-echo attenuations due to self-diffusion of CHI in ZSM-5 at 250 K for the loadings (CH4 per u.c.): 0, 4; 0 , 8; and 0 , 12 (49). For calibration, neat water (0) and liquid ammonia (A) are included, with self-diffusion coefficients of 2.3 X lo-' cm2 s-' (67) and 1.5 X cm2 s-' (68).
370
J. CARO et
al.
tions (Fig. 1) shows that for methane in ZSM-5, the principal tensor elements differ from each other by less than a factor of 5-10 (49). This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x , y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those (42,43).For the self-diffusion of methane in ZSM-S/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). In the QENS experiment (Fig. 7), the broadening of the elastic peak as a function of Q 2 is found to deviate from a straight line, so that a jump diffusion model has to be considered. The mean jump lengths are found to be larger at small loading and high temperatures (12,25,69).For methane in ZSM-5, the mean jump lengths calculated from QENS for small and high loadings at 200 K amount to 1.04 and 0.87 nm, respectively. The selfdiffusion coefficients obtained from PFG NMR and QENS are presented in Table 11. These data yield an activation energy for the self-diffusion of methane in ZSM-5 of 4-5 kJ mol-’ both for PFG NMR and QENS (12,69). Furthermore, Table I1 presents diffusivities determined by sorption uptake/ desorption measurements (single-step frequency-response technique) (30). Table I1 shows that the self-diffusion coefficients measured independently by PFG NMR and QENS are in excellent agreement (12,69).Owing to the different time scales of the two methods, this finding is not trivial. Whereas in QENS, molecular translations are measured up to 6 nm, in PFG NMR the mean molecular displacement may amount to several micrometers. Thus it
.,
-
0.2
0.L
0.6
0.8
02/i3-2
FIG. 7. Elastic peak broadening versus Q’ for CH, in ZSM-5 at 200 K for the loadings (CHJ per u.c.): A, 2; 4;and V, 8 (12.25.69).
37 1
HYDROCARBON MEASUREMENT IN ZEOLITES
TABLE I1 Self-DiffusionCoef$cients of Methane in ZSM-5Measured by PFG NMR and QENS Compared with Sorption UptakeiDesorption Diffusiivities" At T = 200 K(x
Loading (CR/u.c. 1 1.5 2 2.8
4
8 12
DQENS
DNMR
-
-
2.8
-
-
-
2.5 2.9
3.7 2.8 2.5
-
cmZS K I )
DSVRP 0.6 0.5 -
cm2 s-')
At T = 250 K ( X DQENS
DNMR
5.0
-
5.9
-
-
-
-
6.3 5.2 4.5
NMR and QENS data from Refs. 12, 25, and 69; diffusivity data from Ref. 30.
turns out that the migration over both ranges of displacements is determined by the same mechanism of intracrystalline diffusion. The diffusion data obtained by sorption uptake/desorption are smaller by a factor of 5 than the directly measured self-diffusivities, which is a much better agreement than was stated previously in comparative studies of the same system (70,71), where discrepancies up to 5 orders of magnitude have been obtained. The remaining difference might be attributed to the fact that in sorption experiments a slowing down of uptake rate due to the finite rate of adsorption heat dissipation cannot be entirely excluded. With QENS, both the rotational and translational motions of CH4 can be observed. It was found that the rotational motion of CH4 in ZSM-5 can be described by an isotropic rotational diffusion model with a rotational diffusion time constant, D,(72). The values of D,for CH4 adsorbed at 250 K in ZSM-5 are of the order of 5 X 10'' s-'. In MD simulations at 400 K , D, was found to be of the order of 10l2 s-' (73). This difference is due to the fact that a radius of gyration of 0.15 nm was used in the computer fits of the QENS profiles. This radius is intermediate between a simple rotation model, with 0.11 nm for the distance between the protons and the center of mass of the methane molecule, and the radius of the channel in which the molecule performs oscillations.
2. Ethane in NaX Figure 8 shows a comparison of experimental and calculated energy spectra in the QENS experiments for ethane in NaX at different Q values. Table I11 contains the molecular mobility data determined by QENS. In Fig. 9 the self-diffusion coefficients obtained by QENS (cf. Table 111) are com-
;L
n
u 0 l
I
-0.4
-
-02
0
0.2 0.4 hw/rneV
0.6 0.8
FIG. 8. QENS energy spectra for ethane in NaX at different Q values (253 K , 4.3 C2H6per supercage) (69). TABLE 111 SeEf-DiffusionCoefficients, Mean Residence Times beween Jumps, and Root Mean Square Jump Lengths for Ethane in NaX" Loading (CzHs per supercage)
D cm2 s-')
(x
1.3 4.3 5.8
( x lo-" s)
(12)1'2 (nm)
1.36 1.48 2.22
0.66 0.41 0.44
7
5.4 2.5 L .5
" As determined by QENS at 253 K (69).
.
N
E u
t
A0
2-
n
I
I
1
2 3 1 5 6 loading/ C2H6 per supercage
7
FIG.9. Comparison of the self-diffusion coefficients of ethane in NaX at 253 K measured by PFG NMR (0) (59) and QENS (A) (69).
373
HYDROCARBON MEASUREMENT IN ZEOLITES
pared with the corresponding PFG NMR data (59). As for methane/ZSM-5, agreement is observed in both the absolute values and the concentration dependence. Furthermore, a very similar trend in the decrease of the mean molecular jump lengths with increasing sorbate concentration, as shown in Table I11 for ethane/NaX, has been found by NMR methods for propane/ NaX (5). All the QENS spectra were fitted both by means of the scattering law for isotropic rotation and a jump diffusion model (63) according to Q . (28). The radius of gyration was found to vary between 0.18 nm at high loading and 0.22 nm at low loading. As is the case for methane in ZSM-5, this finding is explained by the fact that the motion does not strictly correspond to a rotation about a fixed center of mass because the position of the center of mass changes during the oscillatory state. The rotational diffusion time constant, D,, was found to be of the order of 10” s-l at 253 K.
B. COMBINED ‘H NMR RELAXATION AND PULSED-FIELD GRADIENT NMR SELF-DIFFUSION STUDIES FOR PROPANE IN ZSM-5 AND NAX For CHJZSM-5 and C2HdNaX, as was previously discussed, the selfdiffusion coefficients decrease monotonically with increasing concentrations. Figure 10 shows that this holds true also for propane in both ZSM-5 and zeolite X. ZSM-5 and zeolite X show similar concentration dependencies of the molecular self-diffusion, so that-at first glance-one might expect them to be caused by identical microdynamic mechanisms. However, according to Eq. (22), the translational mobility can be reduced by both decreasing mean square jump lengths, (1*), and increasing time intervals, T , between succeeding jumps. In fact, the relaxation time measurements (Figs. 1 1 and 12) indicate a decisive difference in the molecular transport mechanisms: for NaX, with increasing sorbate concentration, the temperatures of the TI minima (and associated with it the value of the correlation time, T ~ , of molecular motions) remain unchanged (cf. Fig. l l ) , whereas in ZSM-5 the TI minima are drastically shifted to higher temperatures (cf. Fig. 12), thus indicating a significant decrease of the jump rate. Table IV shows that for ZSM-5 at small and medium pore filling, the mean jump lengths are found to be invariable and amount to 1 nm, which is of the order of the distances between adjacent channel intersections of the MFI framework. Consequently, the concentration dependence of the selfdiffusion coefficients in ZSM-5 has to be explained by structure-related jumps, with jumping rates decreasing at elevated loadings. In contrast, for zeolite NaX the reduction of the molecular translational mobility with increasing sorbate concentration is mainly due to the reduction of the jump lengths, with jump rates practically unaffected by concentration. For hydrocarbons in NaX, the jump lengths are found to be corre-
-
f
2
10-71 L -
2 -
J
lo-*:L
FIG. 10. Self-diffusion coefficients of propane in zeolites NaX
(a),CaA (O), and ZSM-5
(a)at 300 K (5) as a function of sorbate concentration expressed by the number of C3Hs per
24 (Si + Al) atoms (representing one large cavity in the cases of zeolities X and A or one channel intersection with the adjacent pore segments in the case of ZSM-5). Data recently obtained in neutron scattering experiments for ZSM-5 (v) (74) are included.
75 I
temperature/ O C c0 -50 -100 -150 I
r
1
I
A
42-
E".102 +-
I
L-
1011 , 2
,
,
,
,
,
,
,
3
4
5
6
7
8
9
FIG. 11. Longitudinal relaxation times (TJ of propane in NaX for 1.5 (A), 2 (o),4 (o), 5 (01, and 6.5 ( 0 )C3Hg molecules per large cavity measured at a proton resonance frequency of
90 MHz (5).
HYDROCARBON MEASUREMENT IN ZEOLITES temperature
75
I
1 2
I
3
0 -50
/OC-
-100
4 5 -IO~K/T
375
6
-150
L
7
I
0
/
9
FIG. 12. Longitudinal relaxation times ( T I )of propane in ZSM-5 for 1 ( A ) , 1.5 (A),2 (01, 2.5 (m), 3 (o), and 3.5 (0).C3Hx molecules per channel intersection measured at 90 MHz ( 5 ) .
TABLE IV Estimated Vulues for Minimum Meun Jump Lengths in ZSM-5 and NuX" Concentration
NMR
[molecules per 24 (Si + Al) atoms]
Temperature of the TI minimum (K)
0.4 I .o I .5 2.0 2.5 3.0 3.3
150 175 210 270 315 360
I .5 2.0 4.0 5.5 6.5
135 135 I35 135 135
QENS (1 *)I/>
D (X
lo-' cm2 s - ' )
(X
lo-' nm)
PropaneiZSM-5 13 12 13 14 6 5
11.7 11.3 11.7 12.2 8.0 7.3
PropanelNaX 5.8 4.0 2.5 0.6
7.8 6.5 5.1 2.5
0.1
-
(/ 2 ) 1/ 2 (X
10-I nm) 9.2 8.4 6.6
1.o
" Obtained at the temperature of the TI minimum according to Eq. (22) ( 5 ) in comparison with QENS data (74).
376
J. CARO et
al. p e q ~,bid
I b l volume compression- adsorption
2-butyne lsilicalite -I 323 K
Pequ.,reo.: Pstart
l'Lgly I
[a) volume expansion
0 0.1 0 2
,I
"
NS
>
I , , .
,
10 20 30"W 100
-desorption
01
a2
"
D in
t/S
30 "goim
FIG.13. Kinetics of desorption (a) and adsorption (b) of 2-butyne on silicalite-I recorded by the pressure response following the rapid square-wave volume expansion (a) and compression (b). Experimental conditions; 1.5 Torr of 2-butyne at 323 K; 0,without adsorbent; 0 , ZSM-5 present in the system (14).
lated with the molecular free volume, so that the reduction of mobility with increasing concentration may be explained by a modification of the freevolume theory (59).
c.
SORPTION KINETICS AND "cNMR LINESHAPE FOR 2-BUTYNE IN ZSM-5 ANALYSIS
The adsorption and desorption kinetics of 2-butyne on ZSM-5 following square-wave pressure changes are shown in Fig. 13. In contrast to the results obtained for n-butane (14), sorption kinetic curves of 2-butyne on ZSM-5 cannot be described by only a single diffusion coefficient (cf. Fig. 13). After a fast initial sorption process, further adsorption proceeds much more slowly. For 2-butyne the time constant of the succeeding process of comparatively slow adsorption/desorption kinetics is larger by at least one order of magnitude than that for the initial fast sorption process. Applying the V? law to this initial region of sorption kinetics [cf. Eq. (29)], the diffusion coefficient of 2-butyne was found to be larger than 3 X em's-'.
HYDROCARBON MEASUREMENT IN ZEOLITES
I
1
1
I
I
200 150 100 50 b/PPm
I
I
0 -50
377
1
FIG.14. I3C NMR spectrum of 2-butyne sorbed on silicalite-I (1.35 mmollg) at room temperature. The spectrum was obtained by single-pulse excitation (14).
This value is higher than the corresponding value of -0.7-2.5 X cm2s-‘ for n-butane (14) obtained by the same experimental technique.* Our results (14) indicate that the rate of penetration into the molecular sieve lattice is higher for the “stiff’ 2-butyne than for the “flexible” nbutane. Hence, sorption uptake of 2-butyne on ZSM-5 turns out to be a coupled diffusion-rearrangement process. In the initial part, the adsorption/ desorption rates are controlled by intracrystalline diffusion. The final part of the sorption process, leading to a higher sorbate density, is determined by the rate of molecular reorientation of the sorbed molecules finding their optimum sorption arrangement. For ZSM-5, the latter process is especially slow for the relatively stiff 2-butyne but is fast for the flexible n-butane. Similar experimental findings, wherein the sorption kinetic data could not be fitted by a simple diffusion model, have been observed e.g., in the case of xylene isomers (9,78) and picoline (79) on ZSM-5 as well as for benzene on NaX (80) and for p-xylene in microporous gallosilicate (141). Further information on the molecular transport of 2-butyne in ZSM-5 can be derived from l3C NMR lineshape analysis. A comparison of the measured I3C NMR spectrum (Fig. 14) with the theoretical ones (Fig. 4) leads to the following conclusions: 1. The spectrum of sorbed 2-butyne is quite different from the calculated spectrum for molecules fixed in space. This indicates that the directions of
* For comparison, in recent studies the self-diffusion coefficient of n-butane in ZSM-5 was found to be of the order of 10-s-10-6 cm2 s-I: 1.4 X cm2 S K I[two C4HI0per unit cell cm2 s-’ (two C4H10per u.c., 298 K) (1 u.c = 96 SitAL atoms), 353 K] by QENS (73, by PFG NMR (106), and I .7 X lo-’ cm2 S K I (one C4HIoper u.c., 298 K) by M D simulations (77).
378
J. C A R 0
et a / .
the molecular axes are not fixed, i.e., the angle between the axis of the molecule and the magnetic field is changed by molecular motions. Consequently, the motion of 2-butyne molecules is not restricted only to the straight channels of ZSM-5. = 77 ppm, one has to con2. Because there is no Lorentzian line at clude that the sorbed molecules do not perform fast isotropic rotations in the channel intersections, a situation also found for benzene in ZSM-5 (7,9,57,81). Obviously, energetic restrictions prevent such motion, which might have been considered for geometrical reasons. 3. A possible interpretation of the experimental results is a 90" flip motion of the 2-butyne molecules. In the fast limit, such a motion generates a pseudoaxially symmetric CSA tensor with the parameters 611 = 56 2 11 ppm and 6, = 157 2 6 ppm (14). The corresponding lineshape is included in Fig. 4. Considering the ZSM-5 framework, this 90" flip can be a molecular jump from a straight into a sinusoidal pore segment or vice versa. From Eq. (20) it follows that the values of the correlation time must be much less than 10 ps. 4. On the time scale of the NMR experiment, the sorbed 2-butyne molecules behave as a single phase. There are no molecules moving exclusively through the straight channel system and no molecules performing isotropic rotations in the channel intersections.
D. NMR LINESHAPE ANALYSIS, PULSED-FIELD GRADIENT NMR, QUASI-ELASTIC NEUTRON SCATTERING, AND SORPTION KINETICS ON AROMATICS IN ZSM-5 AND NAX 1. Benzene in ZSM-5 I3C NMR lineshapes of benzene molecules sorbed on ZSM-5 are shown in Fig. 15. For high sorbate concentrations and low temperatures, powder spectra are obtained; these spectra are characteristic of an axially symmetric shielding tensor. This lineshape is known to be generated by a fast motion of the benzene molecules about their C-6 axes (cf. Fig. 3). With increasing temperature and decreasing loading, the lineshape changes into a Lorentzian one, i.e., an additional molecular motion becomes fast enough to average out the CSA. For perdeuterated benzene in ZSM-5, the dependencies of the *H NMR lineshape on both temperature and loading are given in Fig. 16. From a comparison of the spectra for high sorbate concentration and low temperature with the theoretical lineshapes for different motional states (cf. Fig. 5), it has to be concluded that the sorbed benzene molecules perform fast reorientations about their C-6 axes, a conclusion identical with the findings from I3C NMR.
-
loading / & H e per
U.C.
6D
3.2
8.0
260 K
E3
e
e
e aI
0, c
t
FIG.15. I3C N M R spectra of benzene sorbed on ZSM-5for various temperatures and concentrations. The spectra at 200 K were taken using signal enhancement by cross-polarization (9,57). 16
-
loading/C6D6 per u c .
56
40
7.6
1"1
200 K
P
5
167K
125 K 0
35
70
-
0
35
70 "W-Wol/;
.d-.,
35 ] / kHz
70
I
,\35
70
FIG. 16. *H N M R spectra of perdeuterated benzene sorbed on ZSM-5for various concentrations and temperatures. The spectra were obtained using 3.5-ps7r/2 pulses and a 60-ps pulse spacing (7,9).
380
J. C A R 0 et
al.
As follows from Fig. 16, a reduction of the sorbate concentration causes an effect similar to that of a rise in temperature. From I3C and 'H NMR lineshape analyses of benzene sorbed on ZSM-5, the following conclusions can be drawn (7,9,57,58):
1. The sorbed benzene molecules perform fast reorientations about their C-6 axes. Even at 125 K , the correlation time of this motion is much shorter than 1 e s . 2. Superimposed on this C-6 reorientation, there are jumps of the benzene molecules between a limited number of sorption sites. These sites allow only distinct orientations of the hexad axis of the benzene molecule with respect to the crystal system. The mean residence time, T ~ between , two succeeding jumps decreases with increasing temperature and decreasing loading. The rotational motion of benzene in ZSM-5 has also been characterized by QENS (81). On the time scale of the QENS experiment (=IO-"s), which is much shorter than in NMR, the spatial distribution of the rotating hydrogen atoms is found to be temperature and loading dependent. At low temperatures (90 K), there is a progressive blocking of the rotational motion, a finding that suggests benzene-benzene interactions. A model of uniaxial rotation in an N-fold cosine potential has been used to interpret the low-temperature patterns. At high temperature (400 K) and low loading (three C6Hdu.c.), the rotational motion converges toward a uniaxial C-6 rotation, but it does not reach the spherical rotational model, i.e., the spatial distribution of the protons remains limited to a circle of a radius R = 0.25 nm and does not reach a sphere. The correlation time obtained at 300 K is 3.2 X lo-'' s, Le., as fast as in the liquid. Simulations of 13CNMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental I3C NMR lineshapes, a mean residence time T~ of 20 and 150 ps for a concentration of six molecules per U.C.at 250 and 200 K , respectively, was derived. Provided that these jumps detected in I3C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (1') = 6D7, is valid, where (Z2) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm.
38 1
HYDROCARBON MEASUREMENT IN ZEOLITES
With the above values for the mean residence time 7j and its activation energy E, = 17 2 4 kJ mol-I, from the I3C NMR data a self-difisivity D = 1-5 X lo-'' cm2 s-' can be predicted for a temperature of 303 K and a loading of six molecules per U.C.(9). It should be noted, however, that this procedure is only justified if the activation energies of the jumping frequency and of the self-diffusion coincide. Furthermore, from 13C NMR a decrease of the molecular mobility with increasing sorbate concentration has to be expected. The concentration patterns of Do obtained from sorption uptake experiments for two ZSM-5 samples are shown in Fig. 17 (9). The data are in satisfactory agreement with the I3C NMR estimates in the absolute values, in the activation energies, and in the concentration dependencies. Moreover, the activation energy data for benzene are found to agree with the results of computer simulations (87).
2 . Benzene in Zeolite X Accounting for the influences of external heat and mass transfer resistances in limiting the sorption rates, in many instances reasonable agreement between diffusion data from sorption experiments and PFG NMR may
lo-*
1
t
a.
10'~
A x
v* v c
Ll 10'10
A
8
N
E
I
* =
303K 274 K I
I
1
2
-
I
3
4
I
loading / C s H 6 per u.c
FIG. 17. Concentration dependence of the self-diffusion coefficient DOfor benzene in two ZSM-5 samples. Filled symbols, %/A1 135; crosses, Si/AI > loo0 (9). i=
382
J. CARO
et al.
be obtained (30,3f,91-94). However, there are also numerous welldocumented experimental studies showing differences of up to two orders of magnitude (95). An especially large number of investigations have been devoted to benzene in zeolite NaX. For this system, sorption uptake measurements by different research groups revealed both agreement (10,13,93) and disagreement (95,96) with the PFG NMR self-diffusion data. In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and *H NMR lineshape analysis. With neutron scattering, it has been found that the rotational motion of benzene in NaX corresponds to a uniaxial reorientation about the C-6 axis, with jumps of 60". The mean time between successive jumps about the C-6 axis at 458 K was found to be 1 . 3 X s.
1
0
0 1
-
-
9
2 3 4 5 loading/C6 H6 per supercage
1
FIG.18. Self-diffusion coefficients of benzene in NaX at 458 K: PFG NMR, 0 (97) and 0 (92); QENS, A (13);deduced from *H NMR lineshape analysis, 0 (10). Comparison with zerononequilibrium measurements: v, sorption uptake with piezometric control (93); length column method (96); n , frequency-response and single-step frequency-response technique (%). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.
+,
383
HYDROCARBON MEASUREMENT IN ZEOLITES
TABLE V Translational Mobility Data for Benzene in Zeolite NaX" Loading (CbH6per supercage)
(X
0.8 I .3 2.0 a
D cm2 s-')
(12)1'2
7
4 1.9
7
(nm)
( x to-" s)
0.46 0.35 0.24
5.0 5.1 5.0
Obtained at 458 K by QENS (69).
Results obtained by QENS for the translational motion are summarized in Table V. As is the case for light hydrocarbons, the decrease of the selfdiffusion coefficient for benzene in NaX with increasing sorbate concentration is mainly due to reduced mean jump lengths rather than to increasing mean residence times between succeeding jumps. The same conclusions as drawn from QENS data can be drawn from 'H NMR lineshape analysis. The temperature influence on the 2H NMR lineshape of benzene sorbed on NaX is shown in Fig. 19. As in the case of 250 K
222K
200 K
F
182 K
2
eaJ
c
E
167 K
aJ
c
t 0
35
70
-
-[~w-w,)/~I~I/
125 K
kHz
FIG. 19. Temperature dependence of the 2H NMR lineshape for perdeuterated benzene sorbed on NaX (loading: 4 C6D, per supercage) (7).
384
J. CARO et
al.
benzene sorbed on HZSM-5, there is clear evidence (cf. Fig. 5 ) for a fast C-6 reorientation of the sorbed molecules with a correlation time T~ 1 ps. On the other hand, our spectra show that on the time scale of the NMR experiment, the benzene molecules are fixed at their sorption sites. According to Eq. (21), for all motions that change the orientation of the hexad axes of the molecules (e.g., translational jumps between sorption sites), even at T = 200 K, the values of the correlation time, T,, are much larger than the reciprocal value of the quadrupole frequency, w Q , i.e., T~ % 1 ps. This may be caused by the interaction of benzene molecules with sodium ions via their 7~ electrons. In QENS investigations (99), the sorbed benzene molecules were found to interact in Na-mordenite predominantly with the sodium ions, resulting in a uniaxial C-6 reorientation with a correlation time T~ 5 2 ps at 300 K. The correlation time obtained by QENS for the C-6 reorientation of benzene in NaX is of the same order of magnitude. At temperatures above room temperature, Lorentzian 2H NMR lineshapes are observed for perdeuterated benzene in NaX (7). Therefore, in this range of temperature, the translational mobility of benzene in NaX is expected to be significantly higher than in HZSM-5. This expectation was fulfilled indeed in sorption kinetics measurements. The diffusion coefficient Do for benzene on NaX is -2 x lo-' cm2 s-' at 353 K (93),whereas under similar experimental conditions a value of the order of 10-l' cm2 s-' was obtained for benzene on ZSM-5 (100).
*
3. p-Xylene in ZSM-5 The 'H NMR spectrum of p-xylene-d4 (all ring protons are replaced by deuterons) sorbed on ZSM-5 is shown in Fig. 20. From the observed quadrupole splitting of about 140 kHz, it follows that for all molecular mo-
I . . . . I . . . . l . . I . I . . I . l . . I . I . . . . I . . I . I I . . . ,
100
0
- 100
-
[(w-w~)/ZX]/~HZ
FIG.20. *H NMR spectra of p-xylene-d4 sorbed on ZSM-5(7.2 C8D4H6 per u.c., T = 295 K) obtained by composite 7r/2 pulses (9,58).
385
HYDROCARBON MEASUREMENT IN ZEOLITES
tions at room temperature the correlation times are much larger than 1 ps. Taking into account the pulse interval and the duration of the composite 7r/2 pulses used [40 and 71 ps (9)], the lower limit of the correlation time, T,, of molecular motions that change the orientation of the molecular plane with respect to the magnetic field is estimated to be T~ > 100 ps. A fast rotation about the para axis of the molecule, as deduced from 13CNMR spectra at 310 K (101), can be excluded. Our findings are in accordance with those of a previous 2H NMR study (102). The additional intensity in the center of the spectrum in Fig. 20 can be caused by molecules in another motional state (e.g., molecules outside the pore system performing fast 180” flips) as well as by traces of methyl deuterons as impurities. Assuming for p-xylene a jump mechanism similar to that of benzene, the same procedure can be applied to derive an upper limit for the translational diffusivity. At high sorbate concentrations, the p-xylene molecules in ZSM-5 should be localized in the channel intersections and the pore segments of the sinusoidal channels, based on theoretical (103) and XRD (103,104) studies. With this arrangement of sorption sites and the derived lower limit for the mean residence time (T~2 100 ps), one can predict a diffusion coefficient D I lo-” cm2 s-’ at room temperature and maximum loading, which corresponds well with the uptake data shown in Fig. 21. As in the case for benzene in ZSM-5, the translational motion of p-xylene in ZSM-5 was too slow to be measured on the IN6 neutron spectrometer
A
N
lo-”
i
A
A
A A
1
.,
2 3 looding/C8HI0 per u.C.
L
FIG. 21. Concentration dependence of the diffusivity DO for p-xylene on three different 50; Si/AI = 135; T, Si/AI > 1000 (9).
ZSM-5samples at 363 K: A, Si/AI
i=
386
J.
CARO et
al.
within the temperature range 90-380 K (105). No change of rotational motions was observed for a loading of four molecules per U.C.On the time scale of the neutron experiment (=lo-’’ s), the aromatic ring appears to be immobile and only one of the two methyl groups is rotating. The other methyl group seems to be blocked, most likely due to interactions with the framework. Theoretical and structural studies (103,104) suggest that for a loading of four molecules per u.c., the p-xylene molecules occupy the channel intersections with the methyl groups parallel to the straight channel. In this case, both methyl groups would be equivalent. The neutron results indicate, however, that the molecules located in the channel intersections have to be slightly inclined, leading to different interactions of the two methyl groups of the same molecule with the framework. For concentrations greater than four molecules per u.c., p-xylene becomes highly immobile ( 9 ) . OF N-HEXANE IN ZSM-5 STUDIED BY E. DIFFUSION PULSED-FIELD GRADIENT NMR, QUASI-ELASTIC NEUTRON AND SELECTIVE SORPTION UPTAKEKINETICS SCATTERING,
For both QENS and PFG NMR spectroscopic methods, the measurement of the translational molecular self-diffusion of n-hexane in ZSM-5 represents the present limit of detection. A value of 4.5 X lop6cm2 s-l is obtained by QENS at 300 K (75); by PFG NMR (106) the value is cm2 s-’ . These self-diffusion coefficients are in reasonable agreement with the data from MD simulations, 1.6 X cm2 S K ’ (107), and with sorption uptake measurements, which indicate that D > 7 X loK6cm2 s-’ (108). However, a difference of three orders of magnitude is observed with the value extrapolated from the “zero-length column” technique (109); five to six orders of magnitude deviation occurs using sorption uptake and gas chromatographic data (110,111). Additional sorption uptake studies on oriented ZSM-5 crystals have been performed (112,113). For anisotropic diffusion systems, this newly developed technique measuring sorption uptake through certain crystal faces, termed “selective sorption uptake kinetics” (113), can be used to determine the tensor components of the diffusion coefficient. For this reason, large ZSM-5 crystals have been aligned in two ways: upright standing crystals, aligned by means of electric fields as shown in Fig. 22, and crystals aligned horizontally in a plane. After embedding the zeolite crystals thus oriented into a gas-tight matrix (e.g., glass, metal, epoxy resin), by careful abrasion selective crystal faces can be opened for selective sorption uptake kinetics. Abrasion of the crystal arrangement shown in Fig. 22 gives the sample shown in Fig. 23. The sorption uptake kinetics on this sample is exclusively controlled by the mobility in the length direction of the ZSM-5 crystal, Dzz.For ZSM-5 crystals hori-
FIG. 22. Large ZSM-5 crystals synthesized by J. Kornatowski (137. f38) and aligned by means of an electric field of strength 2.3 kV cm-I. Crystals are fixed in the upright position by a thin film of an epoxy resin (113).
FIG. 23. Crystal arrangement as shown in Fig. 22 after embedding the crystals into a thermally stable epoxy resin and abrading the top (113). In sorption uptake, this sample was used to measure selectively D,,.
388
J. CARO et
al.
FIG.24. Plane-oriented ZSM-5 crystals, embedded into a copper matrix (Cu deposition by sputtering). The [lo01 and [OlO] faces were selectively opened for adsorption by abrasion. Because of the random orientation of the crystals in the plane, the mean (Dxx 0,,)/2 is determined in sorption kinetics ( I 13).
+
zontally oriented in the plane, as shown in Fig. 24, the tensor component (Dxx+ Dyy)/2becomes accessible. The mean is a result of the random crystal orientation. Using large ZSM-5 crystals (110 X 110 X 310 pm3), the time, in an individual sorption uptake step, to reach 50% of the final amount adsorbed, for the crystal arrangement shown in Fig. 23, is about 15 times larger than for the crystals shown in Fig. 24. At 298 K , the diffusion coefficients amount to D , = 2.4 X lo-’ cm2 s-’ and D,, = 0.8 X lo-’ cm2 s-’ (113);this shows that for n-hexane in ZSM-5 the mass transport in the length direction of the crystal is about three times slower than in the plane perpendicular to this direction. However, these sorption uptake diffusivity values fall between the values from the spectroscopic methods and the other sorption uptake experiments. Possible reasons for these deviations from intracrystalline mass transport could be the internal twinning of the ZSM-5 crystals under study as well as the fact that abrasion could possibly mechanically damage a tiny surface layer (formation of an amorphous surface barrier).
389
HYDROCARBON MEASUREMENT IN ZEOLITES
VI. Structure-Related Molecular Self-Diffusion in Zeolites by Pulsed-Field Gradient NMR: Influence of Pore Diameter, W A I Ratio, and Concentrations of Internal OH Groups and Cations; Self-Diffusion of Mixtures
A. SINGLE-COMPONENT MEASUREMENTS As Fig. 25 shows, the intracrystalline self-diffusion coefficient of methane in ZSM-5 is between coefficients in zeolites NaCaA and NaX (5,7Z,lZ4,ZZ5,). This order can be interpreted in terms of the minimum apertures of the zeolite channels, which are approximately 0.45,0.55, and 0.75 nm for 5A, ZSM-5,and X-type zeolites. Due to the hydrophobic nature of Z S M - 5 , the mobility of water in ZSM-5 considerably exceeds the mobility in zeolites NaA and NaX. A change in the SiO2/AI2O3ratio of ZSM-5 does not alter the self-diffusion coefficient of methane. On the contrary, for water in ZSM-5 an increase in the self-diffusion coefficients with decreasing A1 concentrations in the framework is indicated.
$
CHblNaX
CHLI ZSM-5 A[
A
CHdNaCaA
I$
+
AA
['A
A
H201ZSM-5
A A HfllNaX
H201NaA
-Si02/A1203 4
1
10
lo2
I
lo3
FIG.25. Self-diffusion coefficients of methane (open symbols) and water (filled symbols) in zeolites NaCaA, NaX, and ZSM-5 (loading, approximately 1 CH4 or HzO molecule per 24 T atoms, 296 K) (5).
390
J. CARO
et al.
TABLE VI Influence of Hydrothermal Treatment on Sorption and Diffusion Properties of a Silicalite Specimen Si-OH concentration (number g - ' ) 8 . 4 X lozod 4.6 X 10''
Sorption capacity
Self-diffusion coefficient ( X lo-' m2 S K I )
(mmol g-') c,,,(n-CsHd
Csat(H2O)
D (CHdb
D (H?0)"
1.28 1.38
3.05 1.62
9.8 7.2
1.4 3.1
The silicalite specimen (121) has large concentrations of internal Si-OH groups; as measured by 'H MAS NMR (122,123). all measurements at 300 K . Loading -8CH4 per U . C . ' Loading -12Hr0 per U . C . Parent sample ' After steaming
Due to synthesis conditions, zeolites can contain remarkable concentrations of intracrystalline Si-OH groups (116-121). These groups represent defect sites in the form of nonintact Si-0-Si bonds inside the crystals. Because hydrothermal treatment is a suitable method to recombine zeolitic Si-0-Si bonds, a silicalite sample was held under steam at 1100 K for 5 days (121). In the parent sample, -8% of the framework Si atoms were present as Si-OH. As Table VI shows, during hydrothermal treatment algroups reacted and formed intact most 50% of the former Si-OH Si-0-Si units. As a result, the n-hexane sorption capacity increased by -7%. With water, the opposite effect has been observed. Owing to the increased hydrophobicity of the steamed sample, the former sorption capacity of water decreases by -50%. However, even this reduced amount of sorbed water is approximately three orders of magnitude larger than the amount necessary to produce monolayer coverage on the external surface of the zeolite crystals. With the drastic reduction in the number of silanol groups, the water self-diffusion coefficient increases. In light of these results, the significant scattering of the values of sorption capacity and diffusivity on zeolites as reported in the literature (70,71,92,95) could correlate also with structural defects such as nonintact Si-0-Si bonds. B . PULSED-FIELD GRADIENT NMR MULTICOMPONENT SELF-DIFFUSION During their technical application, molecular sieve catalysts are generally used under the conditions of multicomponent adsorption and diffusion. Selective measurement of the diffusivity of individual components is therefore of both theoretical and practical relevance. The traditional way to perform
HYDROCARBON MEASUREMENT IN ZEOLITES
39 1
self-diffusion studies in mixtures by PFG NMR is to use deuterated compounds or compounds without any hydrogen, so that the ‘ H NMR signal stems from only one of the mixture compounds (3, 42, 142). Unfortunately, selective diffusion measurement necessitates additional experimental preparations, because for the study of a system containing n components at least n various PFG NMR samples must be prepared, each of them with a different compound in the hydrogen form. A more straightforward possibility of selective self-diffusion measurements is provided by Fourier transform PFG NMR, as was discussed previously. Using this method, the total NMR signal is split up into separate signals due to different NMR chemical shifts. This procedure has been successfully applied to multicomponent liquids, where it was possible to measure simultaneously the diffusivity of up to eight different components (124). In adsorbate-adsorbent systems, however, such experiments are complicated by the reduction of molecular mobility. The linewidths must be small enough to allow resolution of the observed NMR spectra into the spectra of the individual components. 1. NMR SelfDiffusion in Binary Mixtures Using
Deuterated Compounds
a. Methanol and Water in HZSM-5. Figure 26 shows the self-diffusion coefficients of water and methanol in a methanollwater mixture absorbed in HZSM-5 for two different total loadings (125). For every mixture composition, the self-diffusion of the proton-containing component was measured selectively; the other mixture component was present in the deuterium form (for ‘ H NMR “invisible”). For a total loading of 35 mg (water plus methanol) per gram of ZSM-5, the mobility of the sorbed water was found to be enhanced with respect to pure liquid water. In contrast, the mobility of the sorbed methanol was slightly reduced. At a total loading of 50 mg per gram of ZSM-5, the self-diffusion coefficients of both adsorbed water and methanol were found to be lower than the values for the free liquids. For nonadsorbed liquid mixtures, a remarkable minimum of the selfdiffusivity was found (Fig. 26). In contrast, no mimima in the self-diffusion coefficients of the sorbed mixtures were obtained. Obviously, the sorption potential and /or the geometric constraints of the intracrystalline channel system prohibit the formation of highly structured methanol/water complexes, which are present in liquid methanol/water mixtures. These bulky complexes have been proposed to cause the mimima found in the diffusion coefficients of the liquid mixtures (126,127). b. C4 Hydrocarbons in the Presence of Water in NaX. Figure 27 shows that the self-diffusion behavior of paraffins and olefins may be influenced significantly by coadsorbed molecules ( 1 15). The self-diffusion coefficient
J. CARO et
392
al.
O
2.0 -
1.5-
n 1.0-
I
I
I
I
I
0
25
50
75
I I
100
mol % methanol
__c
FIG.26. Self-diffusion coefficients of methanol (squares) and water (circles) in their binary mixtures sorbed in HZSM-5 for two total loadings: 35 mg (HzO + CH3OH) g-' (open symbols) and 50 mg g-' (filled symbols) at 300 K (125). Comparison with the self-diffusivity in liquid methanol/water mixtures (126,127): dotted line, D(CH3OH); dashed lines, D(H20).
of n-butane in NaX decreases by up to three orders of magnitude with increasing amounts of coadsorbed water (D20). With a slight increase for small amounts of coadsorbed water, the self-diffusion coefficients of but- 1ene exhibit a different dependence. This effect is due to the specific interaction of but-1-ene with adsorption centers in NaX. These centers are blocked by water, thus leading to an increase in the mobility of the but-lene molecules. The presence of further water molecules leads to a steric hindrance of the but- 1-ene mobility similar to that of n-butane. As shown in Fig. 28, coadsorbed ammonia (ND3) affects the selfdiffusion behavior of n-butane and but- 1-ene in NaX in a manner similar to that seen in the coadsorption of water. In contrast to water and ammonia, the dependence of n-butane and but-1-ene diffusion on the number of coadsorbed C02 molecules is less pronounced.
2. Fourier Transform PFG NMR The first 'H PFG Fourier transform NMR experiments of adsorbed molecules have been carried out with an ethane/ethene mixture adsorbed on
I
-
number of D,O per cavity
in NaX as a function FIG.27. Self-diffusion coefficients of n-butane ( 0 )and but-I-ene (0) of coadsorbed water (0.8 C4 molecules per cavity, 293 K ) (115).
,
I
1
I
___)
I
5
I
I
I
I
I
10
I
I
I
J
number of cosorbed molecules per cavity
FIG. 28. Self-diffision coefficients of n-butane and but-I-ene in NaX (0.8. C, molecules per cavity, 293 K) in the presence of coadsorbed ND, and C02 (115): A, C4HI0+ ND3;0, C4HlU + CO; A , C4H8 ND,; 0, C~HR + COz.
+
394
J . CARO et
al.
ms
/
1 .d
0
/'
l.I-L__LLi_l
1
2
3
4
5
6
&* H/PPm
FIG.29. ' H PFG Fourier transform NMR spectra of an ethane-ethene mixture in NaX (1.5 CzH6plus 1 CzH4per supercage, 293 K ) for increasing values of the width (6) of the field gradient pulses. The pulse separation ( t ) and the field gradient intensity (g) are 4 ms and 2.8 T m-'. The chemical shifts S , , refer to TMS (128).
zeolite NaX (128). This system is especially suitable for such studies, because the spectra of both components consist of only one line and the mobility of both components is sufficiently high to guarantee line narrowing that allows separation of the two spectra. Considering a sorbate concentration of 1.5 molecules ethane and 1 molecule ethene per supercage, it follows from Fig. 29 that the ethene mobility remains the same as in the case of singlecomponent self-diffusion, D = 1.25 X lo-' m2 s-', whereas the selfm2 s-', is found to be reduced by a diffusivity of ethane, D = 4.6 X factor of about 2. Recently, this method has been applied to the in situ observation of the diffusivity of both the reactant and product molecules during the conversion of cyclopropane to propene in NaX catalysts (135).
VII. Location of Diffusion Obstacles Inside the ZSM-5 Framework by Pulsed-Field Gradient NMR For a number of adsorbate-adsorbent systems it has been found that the intracrystalline self-diffusion of a highly mobile component is drastically reduced by the presence of a second, strongly coadsorbed component. By combining these self-diffusion measurements with a computer simulation of
HYDROCARBON MEASUREMENT IN ZEOLITES
0
05
395
1a
number of coadsorbed benzene molecules per 1 / 4 U.C.
FIG. 30. Self-diffusion coefficient of methane adsorbed on ZSM-5 as a function of coadsorbed benzene (3 CH, per u.c., 293 K) (86).
the random walk (of the highly mobile molecule) in a zeolite framework that contains statistically blocked channels and/or channel intersections, information about the location of the strongly adsorbed component (diffusion obstacle) inside the zeolite framework is obtained. A. MOLECULAR SELF-DIFFUSION OF METHANE ADSORBED ON ZSM-5 CONTAINING COADSORBED BENZENE Figure 30 shows the self-diffusion coefficient of methane in ZSM-5 samples that contain different amounts of coadsorbed benzene (86). It can be seen that the benzene molecules significantly reduce the methane mobility. It is evident that the blocking effect of diffusion obstacles such as benzene should depend decisively on their position inside the channel network: (1) for benzene molecules located in pore segments (between the channel intersections), the passage through only these segments is prohibited; (2) a benzene occupation of the channel intersections should lead to a blocking of all four adjacent channel segments.
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-
number of coad60rbed benzene molecules per 114 U.C.
1
\
0.01
-
b=0004
l . I . I I I I . I I
0
0.5
1.0
number of dlffusion obstacle8 a8SUmed In computer slmulatlon per 1/4 u.C.
FIG.31. Computer simulation of the random walk in a two-dimensional network with obstacles distributed statistically over the pore segments (dashed lines) and over the channel intersections (solid lines). Different transition probabilities b to pass the barrier are assumed: b = 0.004, 0.020, and 0.120. The experimental results of the methane self-diffusion in ZSM-5containing coadsorbed benzene (0, cf. Fig. 30) are included (86).
Figure 31 shows the results of a computer simulation of the random walk in a two-dimensional channel network with obstacles distributed statistically (1) over the pore segments and (2) over the channel intersections. As expected, the influence of the obstacles distributed over the channel intersections considerably exceeds the influence of the obstacles in the pore segments. The computer calculation shows that the shape of the individual plots of In D versus the amount N of obstacles is typical of the given type of obstacle distribution, i.e., there is no possibility of transferring the In D versus N plots of one case to another by simply changing the transition probability across the obstacles. One has to conclude, therefore, that for loadings <4 benzene/u.c. and room temperature, the benzene molecules have extended residence times in the channel intersections. In this way they cause a maximum hindrance for the self-diffusion of the methane molecules. The experimental data (Fig. 30) fit the curve calculated for diffusion obstacles located in the channel intersections, assuming a transition probability (blocking efficiency) of b = 0.004. This finding is in accordance with other experimental and theoretical studies discussed herein.
397
HYDROCARBON MEASUREMENT IN ZEOLITES
I
f
I
I
\
-
-+I$
-
I
0 Q
1
5-
OOQ 0 0
Q@
a@ .,
-
I
:8
1
8
0
0
2-
lo9
1
0
5-
2 -
1
I
FIG.32. Self-diffusion coefficients of methane (4 CH, per u.c., 293 K) in HZSM-5 specimens of different Si/AI ratios. Specimens contain chemisorbed N compounds (80% of the equivalent number of Bransted acid sites): (3, ammonia; 0 , pyridine. For comparison, the self-diffusivities in the parent HZSM-5 without any N bases (0) are included (129).
B. SELF-DIFFUSION IN HZSM-5 CONTAINING CHEMISORBED N BASES Figure 32 shows the self-diffusion coefficients of methane in HZSM-5 specimens (of different %/A1 ratios) that contain different amounts of chemisorbed N compounds (129). Before the self-diffusion measurements, the samples were modified by quantitative chemisorption of ammonia and pyridine, respectively, in the following way. After sample evacuation at 673 K, an amount of ammonia or pyridine corresponding to 80% of the equivalent number of Br@nstedacid protons [as determined by 'H magic angle spinning (MAS) NMR] (122,123)was added and chemisorbed on the activated zeolite. It was concluded from subsequent 'H MAS NMR that all of the N compounds introduced had reacted with the Brplnsted acid sites. Then the ZSM-5 samples of different Si/Al containing different amounts of chemisorbed N compounds were loaded with methane. Chemisorption of N compounds leads to a significant reduction of the self-diffusion coefficients of methane. This effect becomes more pronounced with increasing amounts of chemisorbed N bases. Obviously., with
J. CARO et
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al.
chemisorbed molecules per 1 / 4 U.C. I
-
I 0
I
0.25 n u m b e r of
I
I
0.75 I 1 d i f f u s i o n obstacles 0.5
a s s u m e d in c o m p u t e r simulation p e r 1 / 4 U.C.
FIG.33. Comparison of the experimental values (Fig. 32) of methane self-diffusion in HZSM-5 containing ammonium ((3) and pyridinium ( 0 )ions with the results of the computer simulation of a random walk in a two-dimensional channel network with diffusion obstacles statistically distributed over the channel intersections (solid lines) and over the pore segments (dashed lines) (129). Different transition probabilities, b, to pass the obstacle are assumed.
respect to the highly mobile methane molecules, the chemisorbed N bases may be regarded as rigid obstacles inside the channel network of HZSM-5. As already discussed, for the partial blocking of ZSM-5 by benzene, the experimental data discussed herein will be compared with two cases of an obstacle distribution: (1) in the connecting pore segments or (2) in the channel intersections. Figure 33 compares the experimental results and the cornputer simulations. For pyridine, the self-diffusion data are in satisfactory agreement with the model for obstacles distributed over the channel intersections. One has to conclude, therefore, that the chemisorbed pyridine molecules and, thus, the Brgnsted acid sites, are localized near or even in the channel intersections. That is to say, all catalytically active centers are accessible for a reactant molecule in a channel intersection. A similarly strict conclusion cannot be drawn from the experimental data for chemisorbed ammonia, which give rise to a behavior intermediate between those of the two limiting cases. One should take into account, however, that due to its smaller size, an ammonium ion situated in a channel intersection does not lead to a simultaneous blockage of all four adjacent
HYDROCARBON MEASUREMENT IN ZEOLITES
399
channel segments. Thus, for ammonia, complete agreement with the computer simulations cannot be expected. VIII. Detection of Spatial Distributions of Diffusion Obstacles over the Crystal Size by Pulsed-Field Gradient NMR
Information on the distribution of diffusion obstacles such as coke, modifiers, or regions of framework damage can be derived from combined PFG NMR and TD NMR measurements. Limitations of the overall adsorption/desorption kinetics as followed by TD NMR can be caused by deposits inside the crystals and/or on their outer surfaces. In contrast, in PFG NMR only diffusion obstacles in the volume phase of the zeolite crystal are detected. Conclusions can be drawn from the following considerations: 1. A reduction of the intracrystalline self-diffusion coefficient, DLntTd, of a probe molecule (e.g., methane) as measured by PFG NMR has to be regarded as proof of the existence of coke, modifiers, etc. in the volume phase of the zeolite crystal. 2. The absence of additional diffusion barriers at the crystal surface (coke, modifiers, etc.) can be assumed if the experimentally determined ~~ by TD NMR), and the cormean intracrystalline lifetimes, T , ” ,(measured responding calculated data, .rdtf, [according to Eq. (lo)], coincide. The T?,% data are calculated by using the self-diffusion coefficients, Duma (measured by PFG NMR), and crystal radii, R , assuming the adsorption/desorption process to be diffusion controlled. 3 . If the values of the effective self-diffusion coefficients, Deft [calculated from the complete x ( t ) curves in TD NMR experiments, assuming diffusion-limited uptake (52)] are below the corresponding intracrys(measured directly by PFG NMR), the existence of additalline data, DIntra tional mass transfer resistances in a layer near or on the outer surface of the zeolite crystals is indicated. The second and third considerations are equivalent ways to prove the existence of transport barriers near the outer crystal surface. OF HZSM-5 IMPREGNATED WITH A. CHARACTERIZATION H,P04
Figure 34 shows that both the intracrystalline self-diffusivity Dintra(as measured by PFG NMR) and the effective self-diffusivity D,ff (as derived from TD NMR) decrease with increasing phosphorus content. The continu-
400
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et al. I
r
30
I I
1 0
1
I
-mass
2
I
3
I
.
1
4
I
5
I
%P
FIG. 34. Intracrystalline self-diffusion coefficient Dinlra(A) and effective self-diffusion coefficient Dea (0) of methane in HZSM-5modified by impregnation with H3P04. The startm2 s-l (6 CH4 per u.c., 293 K) (130). ing self-diffusion coefficient is 8.9 X
ous decrease of Dint,has to be taken as proof that phosphoric acid can be progressively incorporated into the pore system of ZSM-5. Because Deff decreases more steeply than Dintra, it is concluded that with increasing amounts of phosphoric acid, additional diffusion obstacles near the crystal surface simultaneously arise, i.e., an enrichment of phosphorus species near the surface of the zeolite crystals takes place (130). This result is demonstrated in Fig. 3 5 , which shows the ratio Dintm/Deff as a function of the phosphorus content. For DintrJDeS = 1, a homogeneous distribution of the phosphorus > 1 indicates an enrichdeposits over the crystals is indicated. Dinrra/Deff ment of phosphorus species near the outer crystal surface. Figure 35 clearly shows that such enrichment occurs with increasing amounts of phorphorus deposits. Unfortunately, no information on the chemical nature of these transport resistances can be obtained from 'H NMR self-diffusion experiments. For this purpose, several MAS NMR methods have been applied successfully (130). Figure 36 shows the 31PMAS NMR spectrum of the HZSM-5 sample containing 2 wt% P. Three signals can be distinguished: (1) the signal at 1 ppm stems from monomeric [P04l3- groups like those in orthophosphoric acid; (2) the signal at -6 ppm is due to the P atoms in pyrophosphoric acid or due to the terminal [PO4I3- groups in polyphosphoric
HYDROCARBON MEASUREMENT IN ZEOLITES
-
0
1
I
I
2
3
4
5
40 1
I
mass YO P
for methane self-diffusion in HZSM-5 impregnated with H J P O ~ FIG. 35. Ratio Dinlra/Deff (experimental data from Fig. 34) (130).
I
20
I
0
I
-20 c -
1
-40
I
-60
6 1P/ppm
FIG.36. "P MAS NMR spectrum of HZSM-5 with 2% P brought about by H3PO4soaking and subsequent thermal treatment at 823 K (partial sample rehydration before the "P MAS NMR measurement at 293 K) (130).
species; (3) the signal at -30.7 ppm is attributed to aluminum phosphate. The intensity of the latter signal grows with increasing amounts of H3P04 added and indicates a progressive framework dealumination. Consequently, intracrystalline and /or surface deposits of polyphosphates and/or aluminium
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phosphates (the presence of which follows from the finding of 27Aland 31P MAS NMR) should cause the transport limitations observed in PFG NMR and TD NMR studies (130).
B. DETECTION OF THE HYDROTHERMAL CRYSTAL OF ZEOLITE A DAMAGE Table VII compares the measured intracrystalline mean lifetimes, T , " , ~of ~, methane and xenon in various zeolites with the values of ~ S f f .calculated ~, according to Eq. (10) from the self-diffusion coefficients and the mean crystal radii. It turns out that in the case of methane, for all three zeolite samples both quantities are in reasonable agreement; for xenon in NaCaA and HZSM-5 the mean residence time is drastically enhanced in comparison with the values expected from the intracrystalline mobility according to Eq. (10). This experimental finding may be correlated with the larger diameter of the xenon atoms (0.49 nm, in comparison with 0.41 nm for methane), making them more sensitive to a reduction in surface permeability of adsorbents with limiting free diameters of this order of magnitude (0.4-0.5 nm for NaCaA, -0.55 nm for HZSM-5). The surface regions of the crystal exhibit a transport resistance to some types of diffusants (e.g., xenon), while other diffusants (methane) may pass without any perceptible restriction; one can therefore conclude that the surface barrier is not brought about by a total blocking of a certain fraction of apertures in the interface, but by a pore narrowing in a surface layer (42,239). TABLE VII lntrucrystulline Mean Lifetimes of' Methane and Xenon in Zeolites NaCuA, NuX and HZSM- 5" Zeolites
Mean
Methane
crystal diameter (pm)
T,,l,(ms)
T%:,(rns)
Xenon Tdms)
T Lnrra(ms) ~'~'
NaCaA
CaL '
45% 63%
NaX
80%
HZSM-5 "
13 20 5 50 20 25
3*1 4 2 1 0.4 k 0.2 2+ 1 0.4 2 0.2 3 + 1
Obtained at 293 K . From Ref. 42
6 i 2 4 r 2 1 + 0.5 1 + 0.5 2 + 1 4?1
3+-1 4 2 1 0.4 0.2 8 1 2 1.5 C 0.5 11 2 3
*
80 + 20 45 + 10 25 + 8 15 lir 10 5 + 3 > 40
HYDROCARBON MEASUREMENT IN ZEOLITES
c. 1.
403
O N THE LOCATION OF COKE DEPOSITS IN/ON ZSM-5
CRYSTALS
Coke Deposition by n-Hexane Cracking
The reduction of molecular self-diffusion due to coking can be used to determine the distribution of coke deposits over the crystals. As an example, Fig. 37 shows the characteristic decrease of Dintraand DeRfor HZSM-5 (Si/ A1 = 70, crystal size -14 p m , coked by n-hexane cracking) as a function of coking times. For ZSM-5 samples with a time onstream <2 h, a similar reduction of both Dint=and Def for the methane self-diffusion was found, indicating the existence of homogeneously distributed intracrystalline coke. However, for samples coked longer than 2 h, the intracrystalline mobility, D,,,,, of the methane guest molecule remained practically constant. In contrast, De8 continued to slow down, indicating an increasing transport resistance near or on the external surface. Obviously, with extended times onstream, coke is preferentially deposited in the outer regions of the ZSM-5 crystals, blocking the mouths of pores. In accordance with Fig. 37, from Fig. 38 two periods of coke formation can be distinguished. In the first period, with the ratio Dint,/DeR = l , a homogeneous coke distribution over the whole crystal takes place. In a second period, Dintra/Defincreases, indicating an enrichment of coke in the surface region.
I
‘ 0
1
2
3
1
5
+
6 4 1 6
time onstreamlh
FIG. 37. NMR intracrystalline self-diffusion coefficient Dintra(A) and effective selfdiffusivity Deff(0) of methane in HZSM-5crystals that were coked for different times by nhexane cracking (131-133). Before loading with methane (9.2 CH, per u . ~ . ) , the coked ZSM-5crystals were carefully outgassed at 623 K and Pa. The remaining carbonaceous residues were defined as “coke.” Amounts of coke after different times on stream: 1 h, 0.8 wt% C; 2 h, 1.3 wt% C; 6 h, 3.2 wt% C; 16 h, 4.8 wt% C. The starting self-diffusion m2 s-’.. coefficient is 8.1 x
J. CARO et
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al.
-I"
-
2.0
0
r
eme
1.5'
t
1.0 .
a'
I
0
I
I
I
I
2
3
4
-
mass % coke
as a function of the amount of coke deposited for three FIG.38. Ratio of Dintra/DeE HZSM-5 specimens (crystal type, as shown in Fig. 42, with mean equivalent diameters of 8.5 p m (A), 14 p m (n),and 28 p m (v) and an HZSM-5 plycrystalline grain (0;cf. Fig. 43) (131-133).
2. ~ e ~ d ~ f ~ins ZSM-5 i o n Coked by Mesitylene Cracking In contrast to HZSM-5 coked by n-hexane, for mesitylene-coked HZSM-5 (Fig. 39) the intracrystalline mobility, Dintra, of methane is nearly unaffected by coke deposits (42,131). On the other hand, the effective selfdiffusion coefficient, &, decreases continuously with increasing time onstream, i.e., Deff4 Dintra. The conclusion is that mesitylene coking leads to the pronounced formation of a surface barrier, i.e., from the beginning of
8
0 -time
16
24
onstreamlh
(v)and Dew (O), of FIG. 39. Intracrystalline and effective self-diffusion coefficients, Dintm methane (9 CH4 per u.c., 293 K) in HZSM-5 crystals coked by mesitylene cracking versus the time onstream (131). Amounts of coke after different times onstream: 8 h, 0.5 wt% C; 16 h, 0.9 wt% C; 24 h, 1.2 wt% C. The starting self-diffusion coefficient is 8.2 X mz s-I.
HYDROCARBON MEASUREMENT IN ZEOLITES
0
,
1
I
2
3
L
t
4
5
mass % coke
405
FIG. 40. Ratio Dinrra/DeR for coke from n-hexane (A) and mesitylene (v) cracking on
HZSM-5as a function of the coke content (131).
coking the carbonaceous residues are deposited onhear the outer surface of the zeolite crystals, because the mesitylene molecules are too large to penetrate into the ZSM-5 pores. The different coking behaviors of n-hexane and mesitylene on ZSM-5 can also be demonstrated by the ratios of Dintra/De# (Fig. 40). Because mesitylene coking produces mainly surface coke, the intracrystalline mobility of methane remains unchanged, i.e., Dintra/Des > 1. In the case of coke formation by n-hexane cracking, surface coke (Dintra/De~ > 1) is formed after an initial period of intracrystalline coke deposition (Dintra/Deff = 1). In Fig. 41, distinct differences in the amounts of chemisorbed pyridine can be seen for HZSM-5 samples coked by n-hexane and mesitylene cracking. Whereas coke from mesitylene only slightly inhibits the pyridine chemisorption, coke from n-hexane leads to a much stronger inhibiting effect. This result supports the model of controlled coke deposition derived
I
n
0
1 2 -mass
3
4
5
% coke
FIG.41. Pyridine chemisorption as a function of the coke content: A , n-hexane coke; V, mesitylene coke (131).
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al.
from the self-diffusion studies discussed above. A homogeneous coke distribution inside the crystals blocks more acidic sites and, hence, inhibits pyridine chemisorption more strongly than the concentration of coke in a surface layer. IX. Self-Diffusion in ZSM-5 Particles of Different Crystal Morphology
Figures 42 and 43 show scanning electron micrographs of two ZSM-5 samples of different configurations: coffin-shaped crystals and polycrystalline grains. To emphasize the relationship between sample dimensions and diffusion paths followed during the PFG NMR experiment, magnifications are referenced against typical root mean square displacements for methane and propane molecules during typical PFG NMR observation times. Comparing the self-diffusion coefficients of short-chain alkanes in various coffin-shaped ZSM-5 crystals of different origins (crystal type, as shown in Fig. 42) with those in more than a dozen samples of polycrystalline grains (Fig. 43), it can be concluded that molecular mobility in ZSM-5 polycrystals is significantly higher than in polyhedral crystals. This experimental finding is explained by a promotion of molecular transport due to additional fast diffusion paths originating from the polycrystalline structure of the grain. Hence, the increase in diffusivity can simply be considered as a higher molecular mobility in the voids between the intergrown disks forming the substructure of the grain. Obviously, the interfacial voids between adjacent disks have the nature of transport pores (second-order pores). From this diffusion model for polycrystalline grains, an enhancement of molecular mobility with increasing diffusion time is to be expected. Results of corresponding experiments are shown in Fig. 44. For the uncoked sample, an increase of DinIra is observed with increasing observation time. This finding can be understood by the following mechanism. During short observation times, the majority of the propane molecules move preferentially within the substructure of the polycrystalline grain. With increasing time intervals allowed for self-diffusion, an increasing number of molecules will enter the interspace between the disks, a region of transport enhancement, and will travel there over longer distances. The self-diffusivity of propane in the coked polycrystalline grains unveils details of coke formation in polycrystalline particles. Figure 44 shows that coking reduces the translational mobility inside the grains. The effect of intracrystalline coke deposition on the translational mobility of propane is indicated in Fig. 43. After a coking time of 1 h, only a slight increase of Dint= with increasing observation times occurs. After 12 h, a decrease is ob-
FIG. 42. Comparison of the crystal morphology of ZSM-5 with the mean molecular displacements, (r' (t))!,{$, during the observation time of self-diffusion: (a) methane (t = 0.5 ms, 12 CH, per u.c., 298 K) and (b) propane (t = 1.5 ms, 10 C3Hs per u.c., 298 K). The m2 s-' for methane and 2.5 x lo-'' corresponding self-diffusion coefficients are 8 X m' s - ' for propane (134).
FIG. 43. Morphology of ZSM-5 polycrystalline grains compared with the mean diffusion path of (a) methane ( t = 0.5 ms) and (b) propane (t = 1.5 ms). The corresponding selfdiffusion coefficients are 1.4 X lo-' mz s-' for methane and 4 X lo-'' m2 s-' for propane. (For further explanation, see Fig. 42.) For propane, the reduction of the root mean square displacement due to deposition of n-hexane coke (4.3 wt% c) is indicated (134).
HYDROCARBON MEASUREMENT IN ZEOLITES
r :
I
5
a5
10
1.5
409
Oh
2.0
t/ms
RG.44. Self-diffusivity Dint, of propane (10 C,Hs per u.c., 293 K ) as a function of the observation time t of self-diffusion for the polycrystalline grains shown in Fig. 43 after different coking times by n-hexane cracking (132):0, starting ZSM-5; @1 h, 3.6 wt% C; 0 , 12 h, 4.3 wt% c.
served. This behavior indicates that now coke is preferentially incorporated in the second-order pores. This means that the interspaces between the disks progressively lose their transport-promoting character. Finally, the second-order pores, when filled up with coke, become a transport hindrance.
X. Conclusions It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffusivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. Analyzing the self-diffusion behavior of guest molecules in a microporous catalyst by the combined application of pulsed-field gradient NMR selfdiffusion techniques reveals the spatial distribution of transport resistances over the catalyst particles. In the case of coke deposits on ZSM-5, the distribution of carbonaceous residues over the crystal was found to be a function of the crystal morphology, the time onstream, and the chemical nature of the coke-producing reactant. In the case of ZSM-5 modified by H3P04, the spatial distribution of the P compounds over the ZSM-5 crystals can be determined by self-diffusion measurements. Location of transport hindrances in a zeolite framework is based on self-diffusion measurements, in
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al.
comparison with using the computer-simulated random walk in considering the influence of diffusion obstacles. In this way, physisorbed benzene and chemisorbed pyridyne were found to have extended residence times near the channel intersections, compared with the pore segments of ZSM-5. Furthermore, nonintact Si-0-Si bonds and the Si/AI ratio of the zeolite framework significantly alter the diffusion patterns of polar molecules such as water and methanol. In polycrystalline aggregates the self-diffusion coefficients of light hydrocarbons were found to be enhanced compared with the diffusion in an undisturbed crystal structure. Detailed information on the complex nature of mass transport in both the intra- and intercrystalline space of catalyst pellets can thus be obtained for both single and multicomponent systems. ACKNOWLEDGMENTS The authors want to express deep appreciation to Prof. H. Pfeifer (Leipzig), Prof. W. Schirmer (Berlin), and Prof. M. Bet: (St. Martin d’Heres) for their fruitful and friendly cooperation during the past decade. The authors thank Prof. L. V. C. Rees (London) for stimulating discussions and for joint single-step frequency-response measurements on the frequencyresponse apparatus at Imperial College. We thank Dr. G. J. Kearley (Grenoble) for help in performing the neutron experiment at the lnstitut Laue-Langevin, Grenoble; Dr. W. Heink (Leipzig), for the development of the NMR spectrometer FEGRIS; Dr. M. Noack (Berlin), for the measurement of selective sorption uptake kinetics; Dr. J. Volter (Berlin), for the joint coking investigations; Mr. J. Richter-Mendau (Berlin), for the REM; Prof. S. P. Zhdanov (St. Petersburg) and Dr. J. Kornatowski (Torun), for the zeolite synthesis. REFERENCES I . Weisz, P. B., CHEMTECH 3, 498 (1973). 2. Post, M. F. M., in “Studies in Surface Science and Catalysis. Vol. 58: Introduction to Zeolite Science and Practice”. (H. van Bekkum, E. M. Flanigen, and J . C. Jansen, eds.), p. 391. Elsevier, Amsterdam, 1991. 3. Karger, J., and Ruthven, D. M., “Diffusion in Zeolites and Other Microporous Solids.” Wiley, New York, 1992. 4. Garcia, S. F., and Weisz, P. B., J. Catal. 121, 294 (1990). 5. Caro, J., Biilow, M., Schirmer, W., Karger, J., Heink, W., Pfeifer, H . , and Zhdanov, S . P., J.C.S. Faraday I 81, 254 1 (1 985). 6. Eckman, R. R., and Vega, A. J., J. fhys. Chem. 90,4679 (1986). 7. Zibrowius, B., Caro, J., and Pfeifer, H., J.C.S. Faraday I 84, 2347 (1988). 8. Reischmann, P. T., Schmitt, K. D., and Olson, D. H., J . fhys. Chem. 92, 5165 (1988). 9. Biilow, M., Caro, J., Rohl-Kuhn, B . , and Zibrowius, B., in “Studies in Surface Science and Catalysis. Vol. 46: Zeolites as Catalysts, Sorbents and Detergent Builders” H. G. Karge and J. Weitkamp, eds.), p. 505. Elsevier, Amsterdam, 1989. 10. Boddenberg, B., and Burmeister, R., Zeolites 8, 488 (1988). 11. Silbernagel, B. G., Garcia, A. R., Newsam, J. M., and Hulme, R., J . Phys. Chem. 93, 6506 (1989). 12. Jobic, H . , Bee, M., Caro, J. Biilow, M., and Karger, J., J.C.S. Faraday 1 8 5 , 4201 ( I 989).
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