A diffusion study of small hydrocarbons in DDR zeolites by micro-imaging

Microporous and Mesoporous Materials 180 (2013) 219–228

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A diffusion study of small hydrocarbons in DDR zeolites by micro-imaging Tomas Binder a, Christian Chmelik a, Jörg Kärger a,⇑, Alberto Martinez-Joaristi b, Jorge Gascon b, Freek Kapteijn b, Douglas Ruthven c a b c

Department of Interface Physics, University of Leipzig, Leipzig, Germany Catalysis Engineering, Delft University of Technology, Delft, The Netherlands Department of Chemical and Biological Engineering, University of Maine, Orono, ME, USA

a r t i c l e

i n f o

Article history: Received 14 February 2013 Received in revised form 3 June 2013 Accepted 27 June 2013 Available online 6 July 2013 Keywords: Diffusion DDR Olefins Paraffins Sorption

a b s t r a c t Intracrystalline diffusion of the light hydrocarbons methane, ethane, ethylene and propylene in three different species of zeolite DDR has been investigated by recording the transient concentration profiles during uptake and release. The measured profiles approximate the form of the appropriate solution of the diffusion equation for radial diffusion in an infinite cylinder. This is as expected since, for an ideal DDR crystal with its 2D pore structure, there should be no flux in the axial direction. Over the range of guest molecules considered, the diffusivities are found to decrease, with increasing critical molecular diameter, over more than three orders of magnitude, i.e. over about one order of magnitude on comparing ethane, ethylene and ethane, and over, additionally, more than two orders of magnitude for propylene. The observed diffusivities are found to be in reasonable agreement (with differences of up to a factor of three) between the three different DDR specimens as well as with values from the literature, obtained mainly from transient macroscopic measurement or microscopic PFG NMR self-diffusion measurements. In the present study, all measurements were performed by the same experimental technique (micro-imaging by interference microscopy), and the derived diffusivities provide a coherent picture of the diffusion process. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The rate of mass transport of guest molecules in the interior of nanoporous solids is often crucial for the technological application of these materials in applications ranging from separation [1–3] to catalysis [3–5]. Over the last twenty years, the influence of deviations from structural ideality leading to transport resistances on the external crystal surface [6,7] and in the pore bulk phase [8– 13] have been found to compete with (or often to even exceed) the diffusion resistance of the genuine pore network, as shown by diffraction studies [14,15]. From the scientific perspective, these findings demonstrate the importance of short range diffusion measurements with molecular displacements covering a couple of unit cells (for example by Quasi-Elastic Neutron Scattering (QENS)) since it is only at such scales that diffusion in a real crystal (with structural defects) can be expected to replicate the behavior predicted for an ideal structure. ⇑ Corresponding author. Address: Faculty of Physics and Geosciences, University of Leipzig, Linnestrasse 5, 04103 Leipzig, Germany. Tel.: +49 341 9732502; fax: +49 341 9732549. E-mail address: [email protected] (J. Kärger). 1387-1811/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.micromeso.2013.06.038

The scale of the measurements should be large enough to ensure a diffusional process, but still sufficiently small that the fraction of the molecules affected by these additional resistances is negligibly small [16]. There is indeed an impressive series of QENS studies in which the diffusivities obtained experimentally under such conditions were found to be in good agreement with the predictions of molecular modeling (assuming structurally ideal host crystal) [17– 20]. However, from a practical perspective, following the same line of argument, the value of the information derived from this type of measurement is evidently somewhat limited, since, if the rate of mass transfer between the interior of the nanoporous material and the surrounding fluid phase is controlled by additional intracrystalline or surface barriers, the adsorption/desorption rates will not reflect diffusion in the ideal pore network. The detection of such resistances and their quantitative assessment requires diffusion measurements in which molecular trajectories can be followed over the range of micrometers. The earliest measurements of this kind were made by the pulsed field gradient (PFG) technique of NMR [3,21–24]. This technique generally operates with closed sample tubes containing the equilibrated nanoporous host–guest system and yields the probability distribution of the displacements of the guest molecules within the sample

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(typically micrometers) during the observation time of the PFG NMR experiment (typically milliseconds). This is commonly referred to as the mean propagator [24,25]. Transport resistances acting in addition to the genuine pore system appear as a retardation of the rate of propagation as soon as the mean displacements attain the order of magnitude of the spatial separation between these resistances. It is, however, impossible to specify the location of these resistances since the measurements are averages over the pore space within each individual crystal and over all crystals within the sample. This limitation has now been overcome by the use of micro-imaging techniques to record the transient concentration profiles during molecular uptake and release [26]. For this purpose, both IR microscopy [27–29] and interference microscopy [30,31] have been successfully applied. Micro-imaging by IR microscopy offers the advantage of allowing simultaneous monitoring of the concentration profiles of different molecular species, including the option of selective diffusion measurements during mass separation and conversion [26]. However, single-component diffusion studies by micro-imaging have the critical advantage of the much better spatial resolution of interference microscopy (<1 lm compared with about 5 lm for IR microscopy). The present paper reports the application of micro-imaging by interference microscopy to an in-depth study of the intrinsic transport properties of various specimens of zeolite DDR [32] first synthesized by Gies [33], using various small hydrocarbons as probe molecules. There are at least three reasons that make zeolite DDR a particularly attractive host system for such studies: (i) In contrast to the ‘‘8-ring’’ zeolites (with effective pore diameters from about 0.35 to 0.45 nm) such as natural chabazite and zeolite A which have been commonly applied as host systems in kinetic separation processes [3,12], all silica DDR-type zeolites are free of cations. The decreased hydrophilicity and catalytic activity make cation free structures promising adsorbents for practical applications. In particular, the separation of CO2/CH4 and olefin/paraffin mixtures over DDR and other high silica zeolites [34–38] has attracted substantial interest over the past few years [39–44]. (ii) The prior literature provides a useful review of the results of both experimental studies and molecular simulations of diffusion in zeolite DDR, including the investigations reported in Refs. [3,35,38,43,45–48] to which we refer in more detail in the discussion of the results of the present study. In addition, the micro-imaging studies reported in the present paper have been performed with the same materials as have been investigated in Refs. [45,47] thus allowing a direct comparison of the diffusivities measured by different techniques. (iii) The procedure commonly applied in tomography is to reconstruct the complete three-dimensional (3D) structure of an object (in our case: the distribution of the guest molecules within the host lattice) from the 2D plots determined from different directions of observation [49,50]. However, the nature of the process of interest (the evolution of the distribution of guest molecules with increasing time) together with the sensitivity of the measurements complicates the application of this approach. Some progress has been achieved but the required procedures are complex involving, for example, rotation of the host crystal in the cuvette of the microscope before repeating the uptake or release process [51,52], see also Section 12.3.1 in [3]. Owing to their hexagonal symmetry, such complications do not exist with DDRtype zeolites, provided that the c-axis (axis of hexagonal symmetry) is aligned in the direction of observation. For a perfect DDR crystal structure transport in the axial direction should be negligible since it can only occur through 6-rings

with pore apertures of about 0.26 nm. The local sorbate concentration should therefore be a function only of the x–y coordinates and independent of the z coordinate. The quantity measured, namely the concentration integral in the c (or z) direction at a certain position x–y in the plane of observation should therefore be directly proportional to the local concentration c(x, y) at any position within the crystal. It may also be shown that, on propagating toward the central axis, the concentration front rapidly approaches cylindrical symmetry so that the spatial dependence of concentration pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi may be noted as cðr ¼ x2 þ y2 Þ. A second advantage of the particular shape of the DDR crystals is that data accuracy may thus be notably enhanced by considering the average overpall local concentration integrals at identical distances ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ x2 þ y2 from the axis [53]. 2. Experimental 2.1. The zeolite specimens under study Our experiments were carried out using two samples which were used in previous diffusion studies by the zero-length column (ZLC) technique [45,47] and a third sample which was synthesized for this work. In this synthesis, methyltropinium iodide (MTI) has been used as a structure-directing agent. It was prepared by adding 25.1 g methyl iodide (99 wt.%) dropwise to a solution of 25.0 g tropine (98 wt.%) in 100 g ethanol at 273 K under stirring and keeping the suspension under reflux for 72 h. After cooling and filtration, the resulting crystalline MTI was washed with 100 g ethanol and dried at 353 K [54]. The molar ratio of the synthesis mixture was MTI:SiO2:Na2O:H2O = 17.5:70:11.5:2800. It was prepared as follows: 10 g of Ludox HS-40 was added to a solution of 4.7 g MTI and 8.7 g demineralised H2O and stand overnight while stirring (solution A). 0.78 g sodium hydroxide were dissolved in 33.3 g H2O (solution B) [55]. The resulting solution (A + B) is stirred for 30 min, placed in a Teflon-lined autoclave and heated under hydrothermal conditions (autogenous pressure) to 433 K for 6 days. The as-synthesized materials were calcined (0.5 K/min) at 973 K for 10 h in a static oven. The calcined material displayed a surface area (as calculated from N2 adsorption at 77 K) of 372 m2g1. A summary of the data for crystal characterization of the three specimens available for this study is provided in Table 1. The crystals of all samples are of hexagonal prismatic shape. Their crystallographic structure was confirmed to coincide with the genuine structure of zeolite DDR, in this case the all-silica analogue of ZSM-58. 2.2. Micro-imaging by interference microscopy (IFM) In interference microscopy (IFM), the determination of the concentration integral is based on the measurement of the phase shift DuL between the light beams passing through the crystal and the corresponding beams through the surrounding atmosphere. Changes D(DuL) in this difference (which appear in corresponding changes of the interference patterns [26,56]) are caused by changes Dn of the refractive index which, in turn, are a consequence of changes Dc in the host concentration. In linear approximation one thus obtains:

DðD/L ðtÞÞ /

Z 0

L

DnðtÞ dz /

Z

L

Dcðx; y; z; tÞ dz

ð1Þ

0

with L denoting the crystal height in axial (in our case z-) direction (see Table 1). As indicated by the signs of proportionality, interference microscopy is unable to provide absolute concentration data.

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Table 1 Details of the different DDR samples under study. DDR I Mean crystal extensions (lm) In radial direction (2R) 52 In axial direction (L) 14 Si/Al ratio – 2 BET (m /g) 375 Crystal geometry Hexagonal prism Surface Clean

DDR II

DDR IIIa

37 20 1662 – Hexagonal prism, side faces like truncated octahedron Speckled

23 13 950 365 Hexagonal prism, side faces like truncated octahedron Clean

a Samples DDR I and DDR II have been employed in Ref. [53] under the same notation. To avoid confusion, the third sample considered in the present study is therefore referred to as DDR III (rather than DDR I which was the name of this sample in Refs. [45,47]).

This information must be obtained from comparison with conventional (macroscopic) sorption measurements at the same pressure. The IFM measurements were performed using a Carl-Zeiss JENAPOL interference microscope with a Mach-Zender type interferometer [57]. The concentration integrals thus obtained have a spatial resolution of Dx  Dy = 0.5 lm  0.5 lm. The minimum temporal separation between two subsequent concentration profiles presently accessible is 10 s, but there are no inherent limitations prohibiting smaller time intervals of observation. All measurements were carried out at room temperature. IFM measurements up to temperatures of 100 °C have recently become possible [7]. However, the long waiting periods required to establish thermal equilibrium between the dosing volume and the cuvette containing the crystal make this type of measurement rather time consuming and, hence, inappropriate for comparative studies involving a variation of both the host systems and guest molecules, which was the focus of the present study.

2.3. Data analysis In contrast to diffusion in isotropic homogeneous systems, which is completely described by a single diffusivity, molecular diffusion in nanoporous crystals of non-cubic symmetry can only be properly described by a diffusion tensor, i.e. an entity of three parameters. These parameters are the principal elements of the diffusion tensor, which may, intuitively, be understood as the diffusivities in three mutually orthogonal directions [3,58]. For the DDR-type zeolites considered in this study the diffusion tensor assumes a particularly simple form. As a consequence of the hexagonal symmetry, the diffusivities in all planes perpendicular to the axis of symmetry must coincide; this is referred to as the radial diffusivity D. Since the apertures between the cages in axial direction (0.26 nm) are too small to allow any passage for the molecules under study, the diffusivity in axial direction is equal to zero. In our IFM experiments, the crystals have been placed with their symmetry axis parallel to observation direction. In this way, due to the vanishing diffusivities in axial direction, any essential mass transfer in this direction (and, hence, in observation direction) can be excluded, so that the concentration change Dc can be expected to be invariant in the observation direction (i.e. in c). The concentration integrals appearing on the right hand side of Eq. (1) as the primary data of the measurement are thus seen to degenerate to a simple product of the crystal length L and the local concentration c(x, y), so that the spatial and temporal dependences of the guest concentration are directly accessible from the measurement. An example of the data obtained in this way is shown in Fig. 1, which displays the evolution of the local concentration of ethylene in DDR II initiated by a pressure step from 0 to 210 mbar in the surrounding atmosphere.

In principle, the diffusivities D(c) can be determined by locally applying Fick’s second law

@c ¼ divðDðcðx; yÞÞgrad cðx; yÞÞ @t

ð2Þ

to such profiles. However, since the individual concentration data points can be determined only with limited accuracy, data analysis based directly on Eq. (2) would lead to errors, which can be avoided by analysing, instead, selected combinations of data points. Ref. [53] provides a detailed description of these options. They all benefit from the observation that, for the host systems under study and the guest molecules considered, any essential influence of transport resistances on the surface of the individual crystals may be excluded. The decision about which of the possible options is used for analysis depends on the experimental conditions, notably on the accuracy of the primary data and the time interval over which molecular uptake and/or release are followed. They include: 2.3.1. Short-time analysis Evolution of the concentration profiles is only considered over the initial time of molecular uptake (or molecular release), during which the diffusion fronts from different crystal faces have not yet converged. In this case, the crystal may be considered to be of infinite extent. This allows application of the Boltzmann–Matano method, by which the diffusivity and its concentration dependence may be determined directly from a plot of the concentration profiles in the reduced coordinates x/t1/2 [53,58,60]. Moreover, the exploitation of analytical expressions available for certain models of concentration dependence may further facilitate the analysis. This includes, in particular, the constant diffusivity case as well as the Fujita model [61]

D¼

Dðc ¼ c0 Þ 1  kc=cmax

ð3Þ

as an approach for diffusivities that increase monotonically with increasing concentration over the interval c0. . .cmax. With k = cmax/ csat, this expression corresponds to the form of concentration dependence expected for an ideal Langmuirian system with constant intrinsic mobility, in which the concentration dependence of the diffusivity arises only from the thermodynamic correction factor [olnp/olnc = (1  c/csat)1]. 2.3.2. Center-line analysis The center-line analysis is focused on the inverse of the situation in which the short-time analysis is valid, i.e. the situation at longer times when the diffusion fronts penetrating the crystal from all its faces have fully merged. Under cylindrical symmetry, Eq. (2) may be simplified to yield, for the evolution of concentration at the crystal center (r = 0), the expression [53]

@c @2c ¼ 2D 2 : @t @r

ð4Þ

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(b)

(a)

(c)

Fig. 1. SEM picture of a typical crystal of zeolite DDR considered in this study (DDR II, (a)) and example of a 2D-plot of the intracrystalline concentration during molecular uptake (b). The transient profiles shown in (c) are data columns taken in the vertical direction through the crystal center ((b), x = 25 lm) at subsequent instants of time following an adsorption step of 0 to 210 mbar ethylene in the surrounding atmosphere (corresponding to a final loading of 3.47 molecules per unit cell [59]). The 2D-plot shown in (b) gave rise to the profile at t = 160 s.

Both the increase in concentration ð@c Þ and the curvature of the @t 2 concentration profile ð@@r2cÞ in the crystal center are directly accessible from the experimental data, so that, for each of the concentrations attained in the crystal center, Eq. (4) yields the corresponding diffusivity. 2.3.3. Full-profile fitting Assuming cylindrical symmetry (in a cylinder of radius R) and a constant diffusivity D over the concentration range c0. . .cmax considered in an uptake experiment, as a solution of Eq. (2) the guest concentration c(r, t) at distance r from the crystal axis and time t can be determined to follow the relation [53,61] 1 cðr; tÞ  c0 2X expðDa2n tÞJ 0 ðr an Þ ¼1 ; R n¼1 cmax  c0 an J1 ðRan Þ

ð5Þ

where Ji(x) denotes the Bessel function of order i and the ans are the positive roots of

J 0 ðRan Þ ¼ 0:

ð6Þ

This method is applicable to systems in which the diffusivity is constant, i.e. in cases where other methods of data analysis already indicate that the diffusivity is not concentration-dependent. However, by numerical calculation it is also possible to perform full profile fitting using concentration-dependent diffusivities and

thereby introducing a second fit parameter besides D, namely k from the Fujita model Eq. (3) corresponding to the strength of the D(c) dependence [53]. This procedure leads to satisfactory fitting results for systems in which the concentration-dependence of D is strong, for which the simplified approach of Eq. (5) would not be successful. 2.3.4. Fitting of integral uptake Summing (‘‘integrating’’) over all pixels of the IFM 2D-concentration plots (Fig. 1b), the attained information corresponds to the measurements provided by conventional uptake (or release) experiments. Under the conditions of cylindrical symmetry with no mass transfer in the axial direction (i.e. for the local concentrations as given by Eq. (5)), overall molecular uptake mt is known to obey the relation [3,61] 1 X mt 1 ¼14 expða2n DtÞ 2 2 m1 n¼1 R an

ð7Þ

with m1 denoting the equilibrium uptake after infinite time and the

an as defined by Eq.(6). The first statistical moment of molecular uptake [3,62]

M1 ¼

Z 0

1

ð1 

mt Þdt m1

ð8Þ

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is a common measure for the time constant of molecular uptake and release. For host particles of cylindrical symmetry, with Eq. (7) it is given by [62]

M 1 ¼ R2 =8D:

ð9Þ

Numerical calculations based on Eq. (7) also yield the half-time (t1/2) after which the single crystal under study has reached half of the saturation loading for the given pressure step as

t 1=2 

1 M 1 ¼ R2 =16D: 2

Table 2 Ethane diffusivity data deduced from transient ethane profiles during molecular uptake by the different specimens of zeolite DDR, following a pressure step in the surrounding atmosphere from 0 to 210 mbar, corresponding to an equilibrium loading of 3.50 molecules per unit cell [59]. The concentration-dependent diffusivities were determined by applying the Fujita model [63] D(c) = D0/(1  kc/cmax). The different methods of data analysis applied (see Section 2.3) are (i) short-time analysis, (ii) center-line analysis, (iii) full-profile fitting and (iv) fitting of the integral uptake curve, the latter providing concentration-independent diffusivities (k = 0). D0 (m2/s) DDR I

ð10Þ

DDR II

3. Results and discussion DDR III

3.1. Comparison between different DDR host materials with ethane as probe molecule With time constants for molecular uptake and release in the range of a couple of minutes and giving rise to changes in the refractive index of the host materials, which, for moderate pressure steps in the surrounding atmosphere, could be recorded by IFM with satisfactory accuracy, ethane provided the best conditions for a comparison of the different DDR host materials considered in this study. Fig. 2 shows the transient concentration profiles observed by IFM in the three different host materials for a pressure step from 0 to 210 mbar ethane in the surrounding atmosphere. The results of data analysis with theses profiles are summarized in Table 2, and Fig. 3 provides an example of such a comparison.

(a)

k 13

(i) 1.8  10 (ii) 1.56  1013 (iii) 1.6  1013 (iv) 2.5  1013 (ii) 5.0  1014 (iii) 6.1  1014 (iv) 1.5  1013 (ii) 3.5  1014 (iv) 6.3  1014

0.87 0.95 0.87 0 0.67 0.71 0 0.80 0

The data shown in Table 2 for data analysis with the simplifying assumption of a constant diffusivity (fitting of integral uptake to the analytical expression (Eq. (7)) provides a reasonable first approximation for quantification of the diffusion behavior. It is interesting to note that, in the more specific analysis with a concentration dependent diffusivity following the Fujita approach, the concentration parameter k (see Eq. (3)) is found to be of the same order for all samples considered. This is evident from the similarity of the concentration dependences for the different samples shown in Fig. 3.

(b)

(c)

Fig. 2. Comparison of the transient concentration profiles for ethane in DDR I (a), II (b) and III (c) for a pressure step from 0 to 210 mbar corresponding to a concentration step from zero to cmax (=c210 mbar) = 3.50 molecules per unit cell [59]. The ‘‘half-filled’’ profiles, i.e. profiles taken at time t1/2 (see Eq. (10)), are shown in bold blue. In each case, the outer shell with about 20% capacity of the crystal cannot be accessed by interference microscopy. The order of lines in the figure’s legend corresponds to that of the profiles, i.e. from t = 0 s at the bottom to equilibrium at the top. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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DDR II and III the concentration in the crystal center (i. e. for x = r = 0) is seen to increase already at relatively short times at which the concentration increase due to molecular fluxes in the radial direction should be negligibly small.

Fig. 3. Concentration dependence of ethane diffusivity for the three different specimens DDR I, II and III, corresponding to the data of Table 2.

Table 3 Guest concentration (c(r = 0, texp.) = ccenter) in the crystal center recorded at that time (texp.) which was closest to the time t1/2 of crystal half filling (subsequently calculated via Eq. (10) using R and D from Tabs. 1 and 2.

DDR I DDR II DDR III

Calculated t1/2 / s

texp./s

c(r = 0, texp.) = ccenter

144 167 99

160 160 100

0.02 0.12 0.06

The D0 data of Table 2 determined by procedures (i)–(iii) represented the lowest diffusivities in the concentration intervals covered in the respective uptake and release experiments, namely those for the smallest concentration. It is easily understandable, therefore, that, by striving to approach the whole of the uptake and release curves by a single diffusivity D0, procedure (iv) leads to systematically larger values. On comparing the diffusion properties of the different samples, the behavior of sample DDR I differs from that of DDR II and DDR III in two ways: (i) From Table 2 and Fig. 3 the diffusivity of ethane in DDR I is seen to exceed the diffusivity in the other two samples by a factor of about 2 to 3, (ii) From Fig. 2, it is evident that the transient guest profiles in DDR I nicely follow the behavior expected for molecular uptake due entirely to radial diffusion, while in zeolites

The latter situation is substantiated by the data presented in Table 3. These data characterize the situation for ‘‘half-filled’’ host systems, i.e. when the actual uptake mt has attained one half of its final value m1. With Eqs. (5) and (6), c(r = 0) at this instant of time is calculated to be 0.035. Within the limits of accuracy of the measurement, this value is seen to be in good agreement with the concentration in the crystal center of DDR I as determined experimentally. The much larger values for DDR II and III suggest that, contrary to our initial assumption, mass transfer must also occur to a small but significant extent in the axial direction, leading to additional molecular uptake through the top and bottom faces of the crystal. Since IFM integrates over the total crystal in axial direction, this uptake appears as a base line shift and, hence, as an increase in the concentration in the central region of the observed profiles, well before this increase can be caused by uptake in radial direction. Since the actual structures of nanoporous materials often deviate from the ideal crystal structure [8–11,14,15], the observed mass transfer in the axial direction may be reasonably ascribed to the occurrence of structural defects in samples DDR II and DDR III. Structural defects may also give rise to the formation of additional diffusion resistances acting in conjunction with the diffusion resistance of the ideal pore network. This could explain why the diffusivities in the radial direction in DDR II and III are found to be reduced in comparison with zeolite DDR I. For a number of zeolite structure types, including zeolite LTA [12] and MFI [64], differences in zeolitic diffusivities over orders of magnitude are not uncommon. Such differences are generally attributed to structural differences in the host materials under study, which remain invisible in conventional structural analysis [3,14]. The outcome of the present study with different samples of zeolite DDR of different origin with, most likely, substantial differences in both synthesis and pretreatment is thus not unexpected. In fact, in view of the moderate variation, the ethane diffusivities observed in this series of experiments will, in the next two sections, be shown to provide a sound basis for comparison with the diffusivities of other guest molecules as well as with diffusion results for DDR-type zeolites reported in the literature.

Table 4 Comparison of the limiting diffusivities (D0) for small hydrocarbons in DDR I and DDR II (at 298 K) obtained by interference microscopy and various literature data. The different methods of data analysis applied (see Section 2.3) are (i) short time analysis, (ii) center-line analysis, (iii) full-profile fitting and (iv) fitting of the integral uptake curve, the latter providing concentration-independent diffusivities (k = 0). DDR I

DDR II

Literature

D0/m2 s1

k

D0/m2 s1

k

D0/m2 s1

Methane

(iv) 1.1  1012

0

(ii) 5.5  1013 (iii) 9.6  1013 (iv) 1.1  1012

0.50 0 0

2.3  1012 ZLC, [45] 1.7  1012 FR, [3] 2  1012 MD-Sim., [38] 1.6  1012 PFG-NMR, [46] 7.6  1014 Membrane, [35]

Ethylene

(ii) 2.6  1013 (iv) 3.3  1013 (Desorption) (iv) 5.1  1013 (Adsorption)

0.57 0 0

(ii) 1.0  1013 (iv) 3.0  1013

0.95 0

1.0  1013 ZLC, [47] 1.5  1013 PFG-NMR, [46]

Ethane

(i) 1.8  1013 (ii) 1.56  1013 (iii) 1.6  1013 (iv) 2.5  1013

0.87 0.95 0.87 0

(ii) 5.0  1014 (iii) 6.1  1014 (iv) 1.5  1013

0.67 0.71 0

2.5  1013 ZLC, [47]

Propylene

(i) 6.5  1016 (iv) 1.4  1015

0.9 0

(iv) 3.0  1016 (Desorption) (iv) 1.0  1015 (Adsorption)

0 0

5.0  1016 Gravimetr., [48] 2.4  1016 to 1.6  1015 Breakthrough, [43]

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the most appropriate approach to data analysis varies with the guest molecule under study. We shall refer to this aspect in more detail in the following sub-sections.

Fig. 4. Uptake curves for methane in DDR II after a pressure step from 0 to 800 mbar, corresponding to an equilibrium loading of 2.89 molecules per unit cell [35], showing convergence to the diffusion model at longer times. The ‘‘corrected’’ data points were calculated allowing for the fact that only the middle 80% of the crystal is seen by interference microscopy. The symbols’ error bars are within the size of the symbols except for the two first instances of time at t1/2 = 3.2 s1/2 and 5 s1/2, respectively.

Fig. 5. Concentration dependent diffusivities for ethylene in DDR II after a pressure step from 0 to 210 mbar, corresponding to an equilibrium loading of 3.47 molecules per unit cell [59].

3.2. Comparison between different guest molecules in the zeolite specimen DDR II The previous section was focused on the analysis of intracrystalline transient concentration profiles during molecular uptake and release on the three different specimens of zeolite DDR, with ethane as a probe molecule. Although with differences of up to a factor of about three in the absolute values of the diffusivities, the general patterns of mass transport (e.g. the concentration dependence) were found to be essentially the same for all three samples. In order to investigate the influence of the nature of the guest molecule on its diffusion properties in zeolite DDR, we have therefore restricted ourselves to considering just one of these three samples (DDR II). Comparisons of the diffusivities from the present study with literature data, including the results obtained with the other specimens considered in this study are summarized in Table 4 and discussed in Section 3.3. The ratio of the highest and lowest diffusivities for the various guest molecules considered in this study is three orders of magnitude; greatly exceeding the quite moderate factor of 3 reported in the previous section for the diffusivity ratio between the three different DDR samples. The huge differences in the diffusivities between the different probe molecules lead to correspondingly large differences in the time scales of uptake and release, so that

3.2.1. Methane Methane is only weakly adsorbed in DDR. According to the isotherms of van den Bergh [35], under the experimental conditions (T = 298 K, p = 800 mbar), the equilibrium loading is about 2.9 molecules per unit cell (0.48 molecule/cage) which is only just beyond the Henry’s law regime. The diffusivity should therefore be essentially independent of loading and the transient profiles should conform to the constant diffusivity model. The experimental data show the expected behavior, although, as a consequence of the weak adsorption and relatively rapid diffusion, the accuracy of the data is limited. The diffusional time constant is of the same order as the IFM accumulation time. As a consequence, in contrast to the situation for ethane (shown in Fig. 2), during molecular uptake only a very limited number of concentration profiles could be recorded. Local concentrations therefore vary during the recording process so that the resulting profile and its attribution to the mean of the time interval of recording must be considered to be only an approximation. This approximation is obviously most critical in the initial stage of the uptake or release when the most rapid changes in local concentration occur. The accuracy of the concentration data is also impaired by the fact that methane is much less strongly adsorbed than the other guest molecules considered, so that the changes in the refractive index during a sorption experiment are rather small. With the center-line analysis (see (ii) in Section 2.3), the recorded concentration profiles [65] yield a value of 5.5  1013 m2 s1 for the methane diffusivity with an essentially negligible concentration dependence. Fitting of the integral uptake curve ((iv) in Section 2.3) considers the average over many more data points and can therefore be expected to yield diffusivities with higher accuracy. Fig. 4 presents the data points for both uptake (filled symbols) and release (open symbols) experiments as obtained by integrating over the recorded intra-crystalline concentrations, together with the theoretical curve derived from Eq. (7). The primary data (diamonds) are seen to deviate from the expected behavior. These differences are, however, seen to be corrected (squares) if it is assumed that (as a consequence of imperfections in the crystal faces and in crystal positioning) IFM fails to monitor

Fig. 6. Concentration profiles for propylene in DDR II after a pressure increase from 0 to 25 mbar, corresponding to an equilibrium loading of 3.46 molecules per unit cell [59]. The ‘‘half-filled’’ profile, i.e. the profile taken at time t1/2 (see Eq. (10)), is indicated bold blue. The order of lines in the figure’s legend corresponds to that of the profiles, i.e. from t = 0 s at the bottom to (almost) equilibrium at the top. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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of the profiles along mutually perpendicular directions (see Fig. 1b) recorded during one and the same run, as well as on a second run.

Fig. 7. Limiting diffusivities (D0) for small hydrocarbons in zeolite DDR at 295 K as determined by micro-imaging (this study) and comparison with literature data, plotted as a function of the critical molecular diameter. A complete list of the data and their specification is given in Table 4. The symbols’ error bars are within the size of the symbols.

the concentration in an outer shell with 20% of the total adsorption capacity and that, when the first concentration profile is recorded, this part of the crystal is already filled. In this case, a value of 1.1  1012 m2 s1 would result. Given the above mentioned limitations, this is in fair agreement with the result of the center-line analysis. Moreover, the agreement between the curves of molecular uptake and release also confirms the message of the center-line analysis that, over the considered concentration range, the diffusivity shows no significant concentration dependence. Finally, for both adsorption and desorption full-profile fitting (Eq. (5), option (iii) of data analysis) with a value of D = 0.96  1012 m2 s1 yields good agreement between the calculated and measured concentrations profiles, in excellent agreement with the diffusivity derived from the overall uptake curves shown in Fig. 4. 3.2.2. Ethane In Section 3.1, ethane was chosen as a probe molecule for a comparative diffusion study including all specimens under discussion, with the diffusivity data for DDR II which are also given in this section (Table 2 and Fig. 3). For DDR II, uptake was also observed to occur in the axial direction, suggesting imperfections in the crystal structure which are known to be common with nanoporous materials. In the present context, it is important to realize that this uptake, occurring through the top and bottom faces of the crystal, is much smaller than the uptake through the six side faces which is the primary source of the observed profiles. Although clearly contributing to the uncertainty in the determined diffusivities, this spurious flux is sufficiently small that it does not affect the order of magnitude of the derived diffusivities. 3.2.3. Ethylene For transient sorption experiments with pressure steps between 0 and 210 mbar (corresponding to loadings between 0 and 3.47 molecules per unit cell [59]), uptake curve fitting to Eq. (7) yielded diffusivities D = 3.6  1013 m2 s1 for uptake and 2.3  1013 m2 s1 for release [65]. Differences in the fitting parameters for molecular uptake and release are well known to be an indication of concentration-dependent diffusivities [3], where diffusivities increasing with concentration give rise to higher values for the uptake measurements than for molecular release, as observed in the present experiments. This quite general message is nicely confirmed by the results from the center-line analysis of the transient concentration profiles shown in Fig. 5. The data analysis has been based on the evolution

3.2.4. Propylene In comparison with ethane and ethylene, the uptake and release time constants for propylene are found to be increased by at least two further orders of magnitude. As a result, for this system, the time required for complete equilibration of the host system with the surrounding atmosphere during molecular uptake and release is too large to be reached during an experimentally reasonable time. This is exemplified by the transient concentration profiles for molecular uptake shown in Fig. 6, where, after as long as 42 h, the concentration profiles are seen still to deviate significantly from their equilibrium values. As already observed with ethane (see Fig. 2b), there is a pronounced increase in the concentration in the central region of the crystal, i.e. close to the crystal axis, which cannot be attributed to the molecular fluxes originating from the side faces and has therefore to be interpreted as arising from a spurious additional flux in the axial direction entering through the top and bottom faces, due to crystal imperfections. The value of 0.14 for relative uptake in the crystal center at crystal half filling is very similar to the corresponding value for ethane (0.12, see Table 3). This is consistent with the proposed explanation, since the ratio of the radial to axial fluxes should be determined only by the defect structure and should not depend on the nature of the probe molecule. Given the rather substantial expenditure of time, we have limited ourselves to analyzing the integral uptake during the initial stages of our transient sorption experiments, yielding diffusivities D = 1.0  1015 m2 s1 and 3.0  1016 m2 s1 for uptake and release, respectively. Not unexpectedly, we have thus recognized the situation typical of diffusivities increasing with concentration, as already observed for ethane and ethylene. Under the conditions of our experiments, the concentrations of methane were too small to give rise to any significant mutual interaction of the guest molecules which may easily recognized as the origin of concentration dependent diffusivities [3,66–69]. The guest diffusivities in DDR II reported in this section are plotted in Fig. 7 as a function of the critical diameter of the probe molecule, defined as the diameter of the smallest cylinder that can circumscribe the molecule in its most favorable equilibrium conformation and calculated from the well-known bond lengths and bond angles, implying (as one option among other possibilities [70]) an effective hydrogen diameter of 0.166 nm [59]. In this representation, the diffusivity data are nicely seen to drop over more than two orders of magnitude as soon as the critical molecular diameters approach the principal diameters of about 0.36 nm and 0.44 nm of the elliptically shaped windows between the adjacent cavities in DDR-type zeolites [32]. Also shown in Fig. 7 are data points taken from the literature, where this trend has already been presented and discussed in some detail. However, in the present study, this dependency has been demonstrated with the same host material and the same direct measuring technique (IFM). A complete list of these data, with their specification and references, is given in Table 4. 3.3. Comparison between different DDR host materials and with literature data Stimulated by their relevance for mass separation, over the last few years, diffusion studies of light hydrocarbons in DDR-type zeolites have become a popular topic for both experimental diffusion measurements and molecular simulations. This is demonstrated by the selected literature data summarized in Table 4. Also included are results obtained in the present study with specimen DDR I, which were not discussed in the previous section. The data

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presented in Table 4 refer to both transport diffusivities (i.e. to transient sorption experiments as considered in this study) and self-diffusivities, i.e., molecular diffusivities determined under equilibrium conditions. For the low loadings considered in this table, transport and self-diffusion are known to coincide [3], so that their direct comparison is justified. Similarly, as already observed in the comparative measurements with the three specimens considered in this study using ethane as a probe molecule, the literature data for zeolite DDR are remarkably consistent. Since for other types of zeolites, including LTA, MFI and FAU, diffusivity data in the literature often reveal significant discrepancies, the observed agreement may be taken as an indication of the robustness and structural stability of structure type DDR. Surprisingly, in only one case (membrane permeation studies with methane) [35], deviations of slightly more than an order of magnitude have been observed. Given the unavoidable uncertainty in the diffusivity values derived from membrane permeation measurements, such a deviation is certainly not surprising [71–73].

4. Conclusions Micro-imaging by interference microscopy (IFM) has been applied to record transient concentration profiles during molecular uptake and release of small hydrocarbons in three different specimens of zeolite DDR. The wealth of kinetic information thus attainable opens various routes for data analysis, including recording of the overall uptake as in conventional transient sorption experiments, analysis of the concentration profile in the initial and final stages of uptake or release and full-profile fitting. The applicability and accuracy of each of these techniques depends on the sorbate (strength of adsorption) and the experimental conditions. For many of the systems studied, several techniques could be applied. The derived diffusivity values showed good agreement (variation in the absolute values of typically less than 20%), thus confirming both the consistency of the experimental data and the validity of the diffusion model for mass transfer in this important class of 8membered ring molecular sieves. The diffusivities of the fastest and slowest molecules considered in this study (methane and propylene) were found to differ by more than three orders of magnitude, while, for a given guest molecule, the diffusivities for the different DDR samples varied only by a factor of about three. The diffusivity increase with increasing loading (attaining, e.g., for ethane one order of magnitude in the considered concentration range) was essentially identical for all three DDR samples. Two of the specimens showed clear evidence of a small but clearly perceptible diffusive flux in axial direction (yielding no more than 10% of total uptake). Since, for the molecules studied, diffusion in the axial direction is prohibited in the ideal crystal structure, this observation strongly suggests the presence of crystal defects, which would also explain the (small) differences in diffusivity between the three samples. Remarkably, on comparing the present results with the extensive literature data, similarly satisfactory agreement is observed. This result is far from common for diffusion studies with nanoporous materials and may be interpreted as an indication of the robustness of the (cation free) DDR structure. Since it records directly the evolution of intracrystalline concentration profiles, micro-imaging by IFM provides unequivocal evidence that the transport properties determined in this way refer exclusively to the rate of intracrystalline mass transfer – confirming convincingly the conclusions and diffusivity values from previous sorption rate measurements, in which overall uptake and release rates were assumed (but not proved) to be controlled by intracrystalline diffusion.

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