Neutron diffraction and inelastic scattering from adsorbed molecules

Surface Science 76 (1978) 13-49 0 North-Holland Publishing Company

NEUTRON DIFFRACTION

AND INELASTIC SCATTERING

FROM ADSORBED

MOLECULES

J.W. WHITE Institut Laue-Langevin,

156X Centre de Tri, F-38042

Grenoble, France

R.K. THOMAS, T. TREWERN and I. MARLOW Physical Chemistry Laboratory,

Oxford University, Oxford, UK

and G. BOMCHIL Institut Laue-Langevin, 156X Centre de Tri’, F-38042 Grenoble, France and DRF, Centre d ‘Etudes Nuclkaires, F-38042 Grenoble, France

Neutron scattering measurements on the structure and dynamics of adsorbed phases at the gas solid interface have proliferated in the last five years and this paper reports some recently obtained results for the systems methane-graphite and ammonia-graphite, which show BET type I and type III isotherms respectively. These systems clearly illustrate the differences in both structure and dynamics to be expected in other examples where either wetting of the surface or non-wetting behaviour occurs upon adsorption. Evidence for phase transitions in both types of system coming from diffraction is reported, and this is substantiated by measurements using inelastic scattering to follow the molecular dynamics. The neutron inelastic scattering from molecules adsorbed on platinum black and in zeolites reveals some of the virtues of neutron inelastic scattering for the study of chemisorbed species. Finally, some preliminary experiments on neutron small angle scattering at the solid liquid interface in polystyrene latex-water sols are reported.

1. Introduction During the last 15 years neutron diffraction and inelastic scattering have played a key role in our understanding of the structures of three dimensional crystals and, at a microscopic level, the forces between atoms and molecules responsible for those structures. Through the determination of phonon dispersion curves, it has been possible with neutrons to determine both the range and magnitude of the inter-atomic forces within the crystal. Before neutron scattering methods were used to determine the phonon dispersion curves, one of the chief sources of information about solid state dynamics lay in the interpretation of the very large mass of specific heat and other thermodynamic data in terms of models such as the Born-von Karman model. In many ways a similar situation exists today in respect of the 13

14

J. W. White et al. /Neutron

diffraction and inelastic scattering

structure and dynamics of adsorbed species. A large body of thermodynamic data - chiefly adsorption isotherms -exists, and the problem, as with three dimensional matter, is to find adequate models of the surface and intermolecular potentials to explain the phenomenological observations. In this area it is clear that there are two complementary projects - the one involving ultra high vacuum techniques and highly cleaned single crystal surfaces, whilst the other is concerned with the study of fine powders and so is, in some senses, rather more closely related to practical experiments of catalysis. It is in this second area that neutron scattering, at the moment, has a role to play, and we rely upon all of the careful developments of materials that have been made for the thermodynamic studies [1,2]. Using advanced preparative methods and efficient out-gassing and cleaning of the surface for small samples, reproducible surface areas and surface homogeneity have been obtained, as measured by the differential heats of adsorption as a function of coverage. Some of the advantages of neutron scattering for surface studies naturally allow qualitative experiments on less well prepared surfaces to be done with ease, but at present the main attention is centred on the use of highly characterised materials to study the surface potential in physisorption and chemisorption. In this review some typical experiments for the gas solid interface, embracing not only the structure of the adsorbed phase but also its dynamics, will be treated, and to a large extent only new material supplementary to a recent review will be discussed [3]. In addition, the considerable potential of neutron scattering for studying the solid-liquid interface will be briefly treated, as well as a typical application of neutron scattering combined with optical spectroscopy to study the adsorption of water and swelling of the highly important natural connective tissue, collagen. Table 1 Information available from neutron tion of adsorption potential energies (1)

Two-dimensional structures (a) sub-monolayers (b) monolayers (c) multilayers In principle, it is possible ascertain phase boundaries, effects at low coverages

diffraction

of adsorbed

scattering

relevant

to determina-

phases for:

to determine whether the layers are atomic or molecular, to to study defect structures due to impurities and nucleation

(2)

The surface-molecular (atomic) distance (a) an unmodified surface structure (b) a modified surface layer

(3)

The surface dynamics (a) monolayers (b) multilayers

(4)

The lattice

dynamics

and inelastic

in particular

for a model

vibration

of very small particles

of:

and diffusional

modes for:

J. W. Whiteet al. /Neutron diffraction and inelastic scattering

15

The sources of evidence on the surface potential, which can be reached by neutron scattering measurements, are listed in table 1. For the liquid interface, similar questions can be posed, but an important additional variable (to be discussed below) is that the scattering contrast between the solvent and the adsorbent particle can be varied at will using isotopic substitution, whilst retaining a constant adsorbant, and just as this technique has been of great value in determining the structure of biological macromolecules, it might well be the key to certain long-standing questions for the solid liquid interface [4,5].

2. Neutron

scattering

In the classical neutron scattering experiment a monochromatic beam of neutron typically of wave-lengths between 1 and 8 A, as determined by selection through Bragg diffraction at a monochromator crystal, or by time-of-flight analysis, is extracted from a nuclear reactor or from an accelerator source of neutrons. Neutrons of this wave-length have energies of the order of a few milli-electron volts (approximately 30 optical wave numbers) and so it is convenient to measure not only their diffraction from repeating structures but also any changes in energy that they may receive from inelastic events [6,7]. The diffraction aspect of neutron scattering is essentially the same experiment as X-ray diffraction, but the neutron method has certain distinct advantages. Cryostats and furnaces, as well as high pressure, may be used around the sample container with ease because neutrons easily penetrate these vessels without producing unacceptably high levels of background, thus experiments can readily be done from a few degrees of kelvin or up to 1 SO0 K. More importantly, though, the strength of neutron scattering is determined by the neutron scattering length b, which varies in a pseudo-random way throughout the periodic table, and in many cases provides good contrast between the adsorbed atom or molecule and the substrate. As will be explained below, this is especially valuable in studying the substrate-molecular distance effects. The scattering lengths for a number of atoms and mean scattering lengths for a number of molecules, compared to some typical adsorbants, are listed in table 2. When only the lowest orders of diffraction are observed from two-dimensional layers of molecules, the resolution of the diffraction experiment is not such as to warrant treating each atom in the molecule separately. Under these conditions a mean scattering length for the whole molecule can be defined, as shown in the second column of table 2. However, because of the distribution of scattering centres throughout the molecule, it is necessary to multiply this mean scattering cross-section by a form factor which is given by the zero order Bessel function &Qr,-J, as shown in the fourth column. In addition to the coherent scattering cross-section, which determines the intensity of the diffraction pattern, many nuclei also scatter incoherently and, in particular, the incoherent scattering cross-section for hydrogen is at least of an order of magnitude greater than for any other element. This is particularly useful for looking at

16

J. W. White et al. /Neutron

diffraction and ine~ansticscattering

Table 2 Neutron scattering and capture cross-sections ments have been done or are in progress

of some gases and substrates for which measure-

Coherent scattering Gas

47r (Z&Q2 (X 10-28 m’)

Radius of gyration 'd

(X lop9 m) 4He Ne =A Kr Xe H2 D2 N2 02 Ch CD4 CW4 ND3

NH3

1.13 2.66 74.20 6.88 2.90 7.03 22.34 44.41 16.90 46.13 139.6 8.68 108.7 0.42 46.0

Hz0

Neopentane (dl2) Neopentane (hl2)

0.36

1612.8 17.0

0.037 0.037 0.0547 0.0604 0.0994 0.109 0.109 0.094 0.038 0.094 0.038 0.076 0.059 0.094 0.076 0.059 0.096 0.24 0.24

Incoherent scattering .-______

4x (%&)2 i; (&d)

-28

2 111 3

(xdoinc

IX lo-$8

(X10-2Sm2)

d

m2)

(Q = I-71 A-1) 1.13 2.66 74.20 6.88 2.90 6.13 19.49 32.75 11.64 15.47 36.3 43.1 93.0 25.8 34.4 16.0 -

0.032 0.005 25.0 24.5 0.66 19.49 3.7 0.001 66.0 0.002 1.32 1.85

159.4 4.02 0.6 0.2 6.84 8.0 318 4.33

2.8

239.4

0.002 0.66

0.24

_

4.03 159.5

24.4

61.32

950

0.64

Substrate

471(c&)2 (x 1O-28 m2)

Lattice parameters

Surface area per gram (m2)

Ed %x,d (X lO-28 m2)

Graphite, C MgRrz Fe12 Pb12 SiOz

5.56 44.4 50.76 50.3 31.4

a = 0.247 nm, c = 0.693 nm

A&203

74.8

20-90 -10 -4 -7 20-500 ca. 200

0.9 1.0 0.84 -

Zeolite 13X Ni Pt TiO2 (rutile) _-

13.33 11.34 8.45

ca. 1000 ca. 200 ca. 200 a = 0.459 nm, c = 0.296 nm

4.7 0.6 3.0

J. W. White et al. /Neutron

diffraction and inelastic scattering

17

the inelastic scattering from adsorbed hydrygenous molecules, since it provides good contrast against the scattering from the substrate. With present neutron intensities, observation of coherent inelastic scattering is limited to a few favourable cases where the incoherent scattering is very weak and where the coherent scattering cross-section is large, for example 36Ar [21]. Neutron scattering technique involving analysis of the neutron spin polarisation are being developed which will allow the separation of coherent and incoherent scattering, and coupled with the future availability of intense pulsed sources, could lead to a great extension of the coherent scattering studies of surface excitations. Related to diffraction experiments are studies using neutron small angle scattering. Again, there is a comparable X-ray technique, but the neutrons have a distinct advantage, when the neutron wave length is long enough, so that the Bragg scattering condition cannot be satisfied for any set of planes within the crystal. Under these conditions, all interference with the low angle pattern from multiple Bragg effects is eliminated. This fact alone has led to the great increase in use of neutron small angle scattering in recent years [8,9]. An equally important feature of neutron small angle scattering is the use of contrast variation between a particle and its surrounding material. This increases the number of observables available from a small angle scattering experiment and allows not only the radius of gyration of a particle to be determined but also the mean scattering length density of the particle and, in the case of isolated particles, the internal structure of the particle. Because of the importance of this technique for characterising the adsorbant in experiments at the gas-solid interface, as well as for studies of the liquid solid interface, we will produce here some of the essential theory for this experiment. For a certain range of small angles the intensity of scattering from isolated particles as a function of the momentum transfer Q = (417 sin 0)/h, where 28 is the scattering angle and h the neutron wavelength, can be expressed by the Guinier approximation [ 101

z(Q) = 10 exp(-Q2R~/3) , where I, is the scattered intensity particle defined as

R;= yR4p(R)dR 0

at 0 = 0, and

R, is the “radius of gyration” of the

yR'p(R)dR, I

0

which for a sphere gives

R, = m

X actual radius

From (1) a plot of In Z(Q) against Q2 gives a straight line of slope -RE/3. For macromolecules in solution, or in our case a colloidal solution, the scattered intensity depends upon the contrast - the coherent scattering length density difference

18

J. W. White et al. J’ Neutron diffraction and inelastic scattering

between the surrounding liquid and the solute or colloidal particle. As hydrogen and deuterium have neutron scattering lengths of -0.38 X IO-t2 cm and f 0.65 X lo-l2 cm respectively, a large range of values of ps, the mean-scattering length density of the solvent, may be obtained by changing the relative H-D content. For example, 8% Da0 in H20 has ps = 0 and the small angle scattering from suspended particles is equivalent to their in vacua scattering. Stuhrmann [I l] has shown that, by using dilute solutions to eliminate inter-particle effects, the scattered intensity may be written as

(2) where V is the particle colume, pm is the mean scattering length density of the particle, and

(3)

FF(Q) =

k sext$iQ

- R) dR .

(4)

’ v The distribution mean is given by

of scattering

length density within the particle relative to the

b(R) - ~rnl. From (2) the square root of the scattered intensity extrapolated to zero angle should be linearly related to ,cs and will be zero when pm and ps are equal. With intensities measured in absolute units, the gradient gives Y, the particle volume. The value of the radius of giration at infinite contrast derives from the particle shape and the variation of Rz with (pm - ps)-’ reveals inhomogeneities in the internal distribution of scattering density. For no exchange or penetration of solvent into the scattering particle [ 1 l] the slope of the plot of Ri versus (p, - p&-l shows qualitatively whether the density gradient from the particle centre is positive or negative [ 11,121. Determination of these quantities may be of considerable interest in the study of ~croporicity [13]. Using the procedure described by Zimm [14,1.5], the concentration dependence of the scattering may be incorporated into (1) giving, for low concentration, and

Q&s KC

1 1

rce,c> =M exp(-Q2R$)

’ 2A2C ’

(5)

J. W. Whiteet al. /Neutron diffraction and inelastic scattering

19

which becomes

where K is a constant proportional to contrast, M is the molecular weight of the scattering particles, C is the concentration, and Az is the second virial coefficient. Simultaneously plotting C/ZQ against Q* and C at infinite contrast and extrapolating to zero angle and concentration gives a line of intercept l/M and initial gradient AZ. Thus the physical characteristics of particles - radius of gyration, volume and mean scattering length density - are derived as well as the second virial coefficient, and may be used to test theories of the colloid stability. Because the incident energy of neutrons which satisfy the Bragg scattering conditions for crystals is itself of the order of the energies of the interatomic and intermolecular vibrations in solids, changes in the neutron energy from inelastic scattering events can be readily measured by a re-determination of the neutrons wavelength (using a single Bragg analysing crystal) or by a measurement of the scattered neutron’s time-of-flight [ 161. In the time-of-flight method of neutron spectroscopy, which is most commonly used for incoherent neutron scattering experiments, a beam of almost monoenergetic neutrons, produced by a rotating velocity selector, is scattered by the sample into an array of neutron detectors arranged at different scattering angles (0) to the incident beam direction. The energy spectrum of the scattered neutrons is analysed by measuring the scattered neutron time-of-flight and gives the spectrum of excitations available in the sample. If the incident and scattered neutron wave vectors are k, and k’ then the momentum transfer in the collision is k’,

Q=k,-

(7)

which clearly depends on the scattering energy transfer, fiw, is Aw =

&

[k; -(k’)2]

angle between k,, k’. The corresponding

,

(8)

where m is the neutron mass. The scattered intensity from a monoatomic system for given energy and momentum transfers per unit solid angle and energy transfer is the differential scattering cross-section

-

bi2k’

2~ ko “u

exp [i(Q

. r -or)]

G(r, t) dr dt

(9)

(10)

20

J. W. White et al. /Neutron

diffraction and inelastic scattering

where G(r, t), S(Q, o) are the correlation function and scattering law for the motion of the atom i of effective scattering length bj [17]. The correlation function and its Fourier transform describes the full dynamics of the molecular and intermolecular motion for the system. In the case where incoherent scattering from a hydrogenous molecule is being observed, the correlation function becomes the selfcorrelation function of the hydrogen atom motion to a good approximation and for molecules whose centre of mass is fixed and which are not free to rotate (as in many molecular crystals), expansion of the scattering law retaining only the onephonon harmonic terms is a good approximation 1181, in which case the differential cross-section becomes

X csch $$

(

1

S(w, - w) ,

where the ~bye-Wailer

exponent

(11) wj is given by

Here Cy is the displacement of the jth atom in the mode it and Mi is the mass of the jth atom. The total molecular spectrum is made up of a series of delta functions like eq. (1 l), one for each mode. In eq. (1 I) the spectrum is strongly weighted by the thermal population factor (III) and by the sums over mass-normalised mode eigenvectars (II) and scattering lengths for the atoms j (I). When hydrogen atoms are present in the mokcule, the very large values of (b&.)H and l/MH make their scattering do~nant in the observed energy spectrum. A similar expression to eq. (11) can be written for the phonon spectrum [ 191 and it has been shown that the hydrogen amplitude weighting of the density of phonon states does not lead to great changes in the positions of the Van Hove singularities [19]. Because of the smaller dispersion of molecular modes, this happy state can be expected to persist for molecular scattering, although some singularities may be suppressed because of the stronger mass wei~ting effects in molecular modes where many of the heavier atoms may not be displaced in a particular normal vibration. Coherent inelastic scattering experiments are usually best done using the 3-axis spectrometer [20] and an example is a recent work on 36Ar [21]. In favourable cases, where there is a layer lattice, the time-of-flight method can be expected to give at least average phonon frequencies and an average dispersion curve for longitudinal phonons f22] .

J. W. White et al. f Neutron diffraction and inelastic scattering

3. The gas-solid

21

interface

The variety of adsorption behaviour shown by powder the five BET types of adsorption isotherms shown in fig. experiments have now been done from systems showing and III, and we look in some detail here at the case of and argon on the basal plane of graphite (nearly type drogen on platinum black (nearly type I), and adsorption plane of graphite (nearly type III).

P Fig. 1. Brunauer’s

.c

I

I

I

*

(IO)

I

(Adamson

I

I

I

[23]).

I

36A on grafoil V ADS = 454

Cm3

STP

.

&-

.

z

(I I)

(20)

+ :

+

. .

:4-

. :

,”

I_.~~‘~.

.

30

7:_.“. I

* ‘“&

50

diffraction

pattern

t ... . :*

. * . *.. . ty# . *

_ .

+uQp I 90

70

SCATTERING Fig. 2. Neutron

PO

isotherms

I

.

?8z 1

g2m c

P

five types of adsorption

E

20 iti

PO

samples is summarised by 1 [23]. Neutron scattering isotherms like types I, II physisorption of methane l), chemisorption of hyof ammonia on the basal

ANGLE

28

I

. I 110

(degrees)

from 36 Ar on grafoil

at 5 K (Taub et al. [21]).

22

J. W. White et al. /Neutron diffraction and inelastic scattering

NEOPENTANEd,2 on

TITANIUM

ONXloE

8)K

A =1.365A

COUNTS ,103 -*o

Fig. 3. Neutron diffraction [551).

pattern from neopentane

d12 on titanium dioxide at 80 K (Marlow

The characteristic shape of neutron diffraction from monolayer films is illustrated in figs. 2 and 3. Fig. 2 shows the diffraction pattern from the highly coherent scattering 36Ar adsorbed on graphite at 5 K after subtraction of the background from the substrate. The peaks show a characteristic asymmetry first described by Warren [24] for a layer lattice of small dimensions. The peaks for the adsorbate diffraction always have a long tail towards higher values of 20 (the scattering angle) and Warren showed that, for incident wavelength X, the diffraction pattern from randomly oriented lamellae is given by

NW&

112

lFhkl*exp[-2W]

F(a) ,

Ihk-

(13)

where L is the “size” of, the array in the direction (Irk), 20 is the scattering angle, mhk the multiplicity of the hk-th reflection and exp[-2W] a two-dimensional Debye-Waller factor. The function F(a) is defined by F(a) = 1

exp[-(x2

- a)*] dx ,

(14)

0 where a = 2n”*L/X tion dhk is (2&)-l

Ihk-N

mhk lFhki*

(sin 0 - sin 8,&) and the 2D plane spacing for the hk-th reflec-

= (sin &k)/?!. If a is large, eq. (13) reduces to a simpler form

f2ce)exp(-2W)

sin8(sin28 - sin%hk)

The molecular

l/2

.

form factor f(O) has been introduced

(15) to cover the case of a molec-

J. W. White et al. f Neutron diffraction and inelastic scattering

23

ular layer and is given by the spherical Bessel function,

whose argument is the product of the molecular radius of gyration,r, and the momentum transfer, Q, defined by Q = (4n sin 0)/X. It can readily be seen that eq. (15) leads to an asymmetric line shape whose width is governed by the parameter (I and hence the layer lattice extent. Kjems et al. [25] have shown how the effects of preferred orientation may be included in the treatment above. By studying the peak shape the size of the two dimensional crystalline rafts may be determined as a function of temperature and coverage for different crystallographic phases on the surface. In the case of Kr a simple registered 43 Xd3 lattice is formed but for molecular adsorbants considerably greater complexity arises 131. Fig. 3 shows another example of layer lattice diffraction from less than one monolayer of the approximately spherical molecule neopentane (dl2) adsorbed on titanium dioxide at 80 K. This case illustrates the very high coherent scattering power available when the approximation of a mean scattering length for the whole molecule is constructed according to the method used in table 1, and shows that, on more polar substrates, a high degree of crystalline order in the two dimensional phase results. In this figure the unindexed peaks come from the titanium dioxide substrate. For this substance the intensities of diffraction compared to background arc almost as great as those for 36Ar and, therefore, it can be hoped that at least average phonon dispersion curves will be forthcoming from experiments done in progress for more than one crystallographic direction. 3.1. Determination face

ofthe distance betweert the adsorbed monolayer and the sur-

In diffraction experiments information about the adsorbent packing on the surface not only comes from the two-dimensional diffraction peaks of the adsorbate but also from changes of intensity within diffraction peaks of the adsorbent. This is particularly marked for adsorbents like grafoil (an exfoliated graphite) or graphon (a highly crystalline graphite of very small particle size), where there may be only several tens of layers for each adsorbent particle or sheet. The presence of the adsorbed molecular layer thus constitutes a scattering length discontinuity or interface between the densely diffracting medium of the adsorbant and the weakly scattering dense gas surrounding the system. The effect has been treated quantitatively [26,27]. A brief summary of the treatment by Thorel et al. is given here for convenience. In order to calculate the intensity of diffraction, it is necessary to develop the structure factor for the combined system of lattice and adsorbed layers. Consider a monocrystalline sheet of graphite onto which is adsorbed a monolayer or multi-

24

J. W. White et al. /Neutron

diffraction and inelastic scattering

layers of a rare gas, for example. If we label the reciprocal lattice for the graphite and for the rare gas layers hkl and h’k’l respectively, then for a scattering vector Q, the scattering amplitude can be written in terms of the sum A =G

+ c m’

q

T

c

b[ x exp(iQu,)] o(

exp [2in(hm + kn t lp)]

a [ ;r) exp(iQus>] exp [2in(h’na’ + h’s’)]

n’

,

S

(17)

where b and a are the coherent scattering lengths for graphite and the adsorbed atom respectively, U, and U, are the reduced position of the ar-th substrate atom and the s-th surface atom respectively, and mnp is the running label of the unit cell for the substrate, rn’n’ is the running label of the two-d~ension~ cell of the adsorbate. By using the c-plane of the graphite surface as the origin for the z coordinate, and summing over all cells, it can be shown that the scattering amplitude A is given by eq. (18): sin nMh sin nNk sin sin nM'h' sin rrN’h’ - rrPle-inn bA + ____ -----ar, sin ?rh sin nk sin nl sin nh’ sin rib’

&f=---__

where A = c exp(iku,) a

,

I’ = c exp(iku,) s

.

(18)

The scattered intensity I=AA* has two kinds of maxima, those of graphite and those of the sorbed layer. But in the case of registry, and only in this case, crossinterference results in a modification of the graphite peaks (the OOn peaks can be affected even in the case of non-registry). A superstructure peak appears as a result of the second term. To calculate excatly the scattered intensity we must take into account: (a) the resolution of the apparatus; (b) the “powder average 21) line shape F(B) = [sin 0 (sin 26 - sin’ 0h~k))1’2]-1 ; (c) the angular distribution of the c-axis of the graphite used for the experiment. In spite of this, the final result depends mainly on the term AA*, which is proportional to 12 ]exp(izls,)]2 for a monolayer where sr is the reduced distance between the graphite surface and the adsorbed layer. In the case of a monocrystalline bilayer I rp = 2 - cos 2lrlsrs ) where

(19)

s12 = sz - sr is the distance between the two adsorbed layers. To determine the variation of graphite peak intensity as a function of sr, consider the registered case (43 X t/3 X 30”). The variation of intensity I is propor-

J. W. White et al. /Neutron

diffraction and inelastic scattering

25

tional to:

le- inpI ab Ar + Compl. Conj. 1. For krypton

on graphite, as treated by Thorel et al., and for the (100) peak:

(h’ = 1 ) k’ = 2 ,1= 0) . A=3j2

G3=+1)

If the first krypton atoms sit on the centre of carbon hexagon, I’r = 1; r2 = 2 independently of A or B location in the second layer. Other positions of krypton on graphite would have given other results: Ala

I Al I rl cos(Arg A - Arg r) ,

Ml cc-32,

AI,a-3,

i.e. there is a decrease in the intensity proportional to coverage and this is the observed result [26]. Variations of the graphite peak have also been seen for methane on graphite [28] i for deuterium on graphite [27], and for ammonia on graphite [29]. A typical result is that for deuterium adsorbed on grafoil. Warming, McTague and Nielsen studied the 002 reflection for the graphite with and without the adsorbed Since only a very small fraction of the scattering onto the &bstrate peak is coming from the adsorbed monolayer, very good counting statistics have to be obtained so that an adequate subtraction of the peak with and without adsorbant can be made. SCATTERING

I-=-=-? a

ANGLE (degrees) 71 70

82 +LOa

(II 8

0‘

if 5 -LOO g +a0

-400

1.80 WAVE Fig.

VECTOR

.

.

w Y aw OW k s

1.90

(A-‘)

4. (a) 0-28 scan through the (002) reflection of graphite in grafoil; the full line is a Gaussian fit. (b) The difference at 4.2 K between the (002) reflection measured with a full monolayer of Dz and the (002) reflection of the empty substrate. (c) The same difference as in (b) calculated for a substrate thickness of 30 layers (the parameter e is defined in the text) (Warming et al. [ 271).

26

J. W. White et al. /Neutron

diffraction and inelastic scattering

The original peak for graphite and the subtracted spectrum compared to a computer calcuIation for various valuations of the parameter E are shown in fig. 4. The parameter E is equal to s1 - d, where sr is the height above the substrate surface of the first adsorbed layer, as defined above, and d is the distance between neighbouring substrate layers. 3.2. The graphite-methane

system (BET type I/II isotherms)

The isotherms for methane adsorbed on exfoliated graphite have been studied with great care and precision by Thorny and Duval [30,31]. Figs. 5 and 6 show the full isotherms up to a p/p0 of 1 .O and in the very low pressure region below p/p0 of 3 X 10P3. Here p. is the saturation vapour pressure of the adsorbant at the mea-

01

Fig. 5. Adsorption isotherm (Thorny and Duval [30]).

a2

0.3

for methane

0.4

a5

0.6

on exfoliated

a7

08

oe9

1

graphite at 77.3 K @o = 9.4 Torr)

J. W. White et al. /Neutron

0

5

10

diffraction and inelastic scattering

15

20

25

Fig. 6. Adsorption isotherms for methane on exfoliated graphite showing the formation of the first layer at low pressures (1) 77.3 K; (2) 80 K; (3) 80.9 K; (4) 82.3 L; (5) 83.5 K; (6) 90.1 K (Thorny and Duval [31]).

temperature. It can be seen that the adsorption obeys an almost type I BET isotherm with the formation of a single monolayer at very low pressures for a temperature of 77.3 K. By using deuterated methane, a sample with a strong contrast between the adsorbed layer and the substrate can be obtained for coherent scattering measurements, and some obvious points of interest are to explore the temperature dependence of the structures of both the monolayer and multilayer films shown in fig. 5, the nature of the critical points between phases shown in fig. 6 at low pressures, and the molecular and lattice dynamics of these phases, with the objective of constructing a suitable molecule-molecule and molecule-surface potentital. As concerns the methane-methane potential, there already exist some neutron scattering studies on solid methane which can be of help [32]. Neutron diffraction experiments on deuterated methane adsorbed on graphon [2] were performed on the CURRAN diffractometer at AERE, Harwell, for a number of coverages and temperatures. The patterns for a coverage of 0.7 monolayers on Vulcan III between temperatures of 10 and 70 K are shown in fig. 7. They were obtained by the direct subtraction of the substrate pattern from the pattern obtained after adsorbing methane, the sample having not been moved in any way in between time. In these experiments the sample was also sufficiently small that there suring

28

J. W. White et al. /Neutron

diffraction and inelastic scattering

CD4

ON GRAPHON

40 K I

r

:

..

_..* J 8 ..**.... *..a.....*.._..*.**: 60K

*a:.

,..* I* .2_

..

. I .... ....-....“L”‘_\i ..:*, -. .*.*.‘.............

Fig. 7. Neutron diffraction from diffraction pattern. The coverage tion pattern (Marlow et al. [28]).

*. -‘&...‘*_ * . ..*.*a.**-. .

CD4 adsorbed on graphon after subtraction of the graphon was 0.7 monolayers and error bars are given on each diffrac-

would be no errors in the subtraction due to self-shielding or to small angle scattering effects. Some systematic errors do occur in the difference pattern at 70 K because all of the patterns in fig. 1 were obtained by subtrating 30” from the substrate pattern. As a result of the high coefficient of thermal expansion for graphite, there is a dip in the difference pattern at 70 K near 2P = 42”. This is also the reason for the artificially sharp separation of the two peaks in the 10 K pattern where the dip occurs at about 26 = 39”. The low temperature patterns contain two peaks, an intense peak at 28 = 41 S” (X = 2.4 A) coming from the 002 reflection of graphite whose intensity was increased by about 3% upon the adsorption of deuteromethane; the second peak centered at 20 = 38” is a two-dimensional lattice reflection from the methane monolayer. The methane peak position indicates that the methane is in registry with the graphite

J. W. White et al. /Neutron

diffraction and inelastic scattering

29

substrate and is packed in a 43 X 43 structure, in agreement with what has already been found for nitrogen [25] and krypton [26] on exfoliated graphite. At temperatures between 60 and 70 K the two-dimensional peak is replaced by a broader more symmetrical peak at lower values of 20. This behaviour is very reminiscent of that found for adsorbed nitrogen on graphite [25], where the crystalline two-dimensional layer was thought to melt to a two-dimensional liquid of rather low density. At 50 K there is evidence of a mixture between the twodimensional liquid and solid phases which perhaps indicates that, on this microcrystalline graphite, the phase transition is not as sharp as had been found by Thorny and Duval for exfoliated graphite. As part of our programme to systematically change the surface potential for adsorption at graphite surfaces, and also as a trick to avoid the contamination of the rather broad peaks from adsorbants like methane by the graphite substrate, we have used the idea of intercalation by graphite. Stable compounds are formed between graphon or Vulcan III and the alkali metals as well as the halogens and hence a wide variety of electronegativities is available with the same surface quality. CD4 ON K-

GRAPHON

f

Fig. 8. Neutron diffraction patterns between 10 and 80 K of adsorbed CD4 on potassium intercalated graphon. The coverage was 0.7 monolayers and the background has been subtracted. C&K and CgK peaks are marked in the lowest diagram (Marlow et al. [ 281).

30

J. W. White et al. / Neutrorz diffraction and inelastic watt&g

ADSORBENT: GRAPHON ADSORBATE : CH 4 I

115°K 6J = 0.5 1

2

400

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This idea works equally well for exfoliated graphites. By these means we have been able to remove the interference due to substrate peaks in the diffraction pattern from adsorbed deutero-methane. The intercalating agent used was potassium, which forms a stage I compound where a c-axis spacing has been effectively increased from 3.35 to 5.4 A, and a stage II compound with an effect layer spacing of 4.4 a (&K). A similar series of diffraction patterns to those for pure Vulcan III with deutero-methane is shown for the Stage I compound (CsK)-CD, adsorption in fig. 8. The methane diffraction peak can now be seen very clearly with its characteristic asymmetric shape almost free of any interference from the diffraction pattern of carbon or from the intercalation compounds. Also at 60 and 80 K can be seen the

J. W. White et al. /Neutron

diffraction and inelastic scattering

ADSORBENT: GRAPHON ADSORBATE: CH 4

if

31

140 K 8 = 0.5

z

YzIL z

bJO

z

72’

2

2

f .. .

.

f

::

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400

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pronounced dip in the spectrum due to the fact that adsorption of CD, is expected to reduce in intensity the 004 and 008 reflections of C24K and CsK. From the theory outlined above these changes of intensity have been used to show that the methane-carbon distance in these compounds may be between 3.6 and 3.3 A, and possibly as low as the latter. The value of 3.6 A would be consistent with a distance calculated using LennardJones parameters given by Steele [33]. These diffraction measurements for adsorbed methane are still in an early stage of development and have not yet been carried out with the high fluxes and multidetector arrangements available at the Institut Laue-Langvin in Grenoble, where further factors of 20-100 and signal to noise could be expected. 3.2.1. Inelastic scattering The intensity of coherent scattering from deutero-methane adsorbed on graphite is not sufficiently great to allow phonon measurements of the type performed for 36Ar [21] to be performed. However, with four hydrogen atoms per molecule the incoherent inelastic scattering cross-section for methane compared to that from the

32

J. W. White et al. /Neutron

diffraction and inelastic scattering

ADSORBENTGRAPHON ADSORBATE CH 4

400

800

1200

176 K @=0.2

1600 2000

TIME OF FLIGHT (psrn’l 1’1’1

1000’%05025

’

0

ENERGY (cm“)

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9c Fig. 9. (a) Neutron incoherent inelastic scattering spectra at six angles of scattering to the incident beam direction for 0.5 monolayers of CHQ adsorbed on graphon at 115 K. (b) Spectra at four scattering angles for 0.4 monolayers of CHq adsorbed on graphon at 140 K. (c) Scattering spectra for six scattering angles of methane adsorbed on graphon and 0.2 monolayers coverage at 176 K (Gamlen 1561).

carbon substrate is very large. The spectra for adsorbed methane as a function of coverage and temperature, on graphon and Vulcan III, have been measured by timeof-flight spectrometry, both at AERE, Harwell and at the Institut Laue-Langevin at Grenoble, where much higher resolution is available. Fig. 9 shows the time-offlight spectrum from methane on graphon at 115 k and with a surface coverage of 0.5 monolayers. This spectrum is taken approximately 5” above the normal boiling

J. W. Whiteet ad. / ~eur~o~ diffrar~~o~and inelastic scattering

33

point of liquid methane and it shows clear evidence of inelastic scattering from rotational motions of the methane (at energy transfers greater than about 25 wave numbers and up to about 1 SO cm-‘), as well as quasielastic broadening around the zero energy transfer position 1341. Even at a temperature of 176 K with coverage of 0.2 monolayers, a clear inelastic signal can still be detected as well as evidence of residual quasi-elastic scattering. These experiments were done at an incident energy resolution of the order of 300 PeV (2.4 optical wave numbers) and have been fitted by a model of a rotating and two dimensional diffusing dense gas on the graphite surface. The quality of fit is limited by the fact that, in the quasi-eleastic region, there are almost certainly two separate components which have recently been resolved with the high resolution (30 PeV) available at Grenoble. However, the shape of the quasi-elastic peak is not Lorentzian and seems best approximated by the convoluted logarithmic singularity expected for two-dimensional motion [35]. Clearly, the experiments described here only give a general outline of some qualitative points for the diverse structures and phases of methane on carbon between the temperatures of appro~mately 4 and 180 K where the signal-to-noise becomes low. They do, however, show that the neutron scattering technique will, in principle, be able to give detailed microscopic parameters of the phases with a good chance of testing models for the surface molecular physisorption potential over a wide range of surface densities for the adsorbant. The general outlines of the behaviour as described here are also qualitatively different from those which are now emerging from comparable studies on ammonia adsorbed on graphite where the molecule surface interaction is “hydrophobic” and where approximately type III BET isotherms prevail. 3.3. The graphite ammonia system (BET Type III/II isotherms) Adsorption isotherms for dry ammonia on Vulcan III and graphon, which have been outgassed at temperatures up to 5OO”C, have been determined [36] by gas microbalance methods, between the temperatures of 160 and 215 K. The normal melting point of ammonia (NHs) is 195.3 K, and of deutero-ammonia (ND,) is 199 K. The boiling points of NH, and ND, respectively are 239.65 and 242.1K. In the adsorption isotherm measurements, extreme care to achieve temperature and adsorption equilib~um was necessary, especially at temperatures between 200 and 215 K where equilibration times were very long. It was also found that, above temperatures of 200 K there was approximately 0.2 of a monolayer of ammonia irreversibly bound after adsorption measurements. This could only be removed by out-gassing at temperatures above 200°C. Corrections for buoyancy etc. were made at low gas densities by assuming an ideal gas behaviour. The adsorption isotherms for the ammonia Vulcan III system are shown in fig. 10 and it can be seen that they are closely of the type III BET form except for a possible knee at very low partial pressures of ammonia and low temperatures, At high partial pressures of ammonia, no evidence for decrease in slope of the isotherm

34

J. W. White et al. /Neutron

ADSXPTION r

11

diffraction and inelastic scattering

ISOTHERMS VULCAN

11

11

1111NH 3

11

1

NE STATISTICAL MONOLAYER -------NH3 Mol.Area 16 8 j 71.3 d

, = 0 RELATIVE

Fig. 10. Adsorption et al. [ 361).

0.5 PRESSURE

U P/po

isotherms for ammonia on graphon at a number of temperatures

(Bomchil

was found, and, hence, up to the highest pressures used for neutron measurements no evidence was found for capillary condensation effects in our sample. The surface area determined for the graphon was 86 m2 g-’ using nitrogen adsorption isotherms as described in the literature [37]. Other points about the isotherms are that, below about 190 K, the amount adsorbed actually decreases as the temperatures is lowered. Thermodynamic parameters for the adsorption process have been calculated from these adsorption isotherms. Below 180 K the value of the isosteric enthalpies of adsorption indicate that the adsorption process is closely related to that of melting. The enthalpy of adsorption is less than 7 kcal/mol, whilst the heat of sublimation from the vapour to the solid is 7 kcal. In contradiction to other published work, we found for our sample of graphite very little variation of the isosteric heat of adsorption as a function of “coverage”. The coverage meant here is the theoretical coverage assuming that the ammonia was forming a uniform mono-

.J. W. White et al. /Neutron

35

d~ff~acti~~ and ~~~last~cscattering

and given the nitrogen surface area. A study of the neutron diffraction at different points along an isotherm, and at different temperatures, indicates quite clearly that this concept of coverage is not at all accurate as opposed to the situation for methane on graphite where wetting of the graphite surface by the methane occurs. The nature of the adsorption of ammonia onto graphon has been followed by measuring the neutron diffraction patterns from adsorbed deutero-ammonia as a function of temperature and vapour pressure. Approximately one gram of graphon was needed for these experiments and was enclosed in a welded aluminium sample container within a normal neutron diffraction cryostat. The coverage was determined by volumetric adsorption and desorpt~on experiments with the vacuum line connected to the sample and checked against the previously measured adsorption isotherms. When less than a monolayer of deutero-ammonia is adsorbed on graphon at temperatures of the order of 215 K, and the whole sample then cooled to much lower temperatures (90 K), strong diffraction peaks, whose positions and intensities correspond to bulk ammonia (ND,) are observed, even down to coverages as tow as one-quarter of a statistical monolayer (monolayer here being used in the sense that coverage was defined above - namely on the assumption of uniform spread of the ammonia molecules over the surface). In particular, the 111 and 200 peaks from the ammonia are completely clear of substrate reflections and can be used to monitor the amount of c~st~line ammonia present in the sample as a function of temperature and pressure of adsorption, The dependence of the intensities of these peaks, as well as their widths (for a determination of crystallite size), upon temperatures for a given statistical coverage

layer

ND3

80

100

120

ON GRAPHON

140

160

I80

T/K

Fig. 11. Dependence of the intensity of (111) ND3 diffraction peaks on temperature for a coverage of: (a) 6 statistical monolayers; (b) 2.4 statistical monolayers; (c) 1 statistical monolayer; (d) 0.5 statistical monolayer (Marlow et al. [ 281).

36

J. W. White et al. /Neutron

diffraction and inelastic scattering

of the surface, has been studied, and the results are shown in fig. 11. The peak intensity decreases slowly at temperatures between 80’ and approximately 140”, and after that rapidly drops as the temperature approaches the bulk melting point. The temperature at which the peaks completely disappear varies With coverage, apperaring to approach a limiting value of about 180 K, but at high coverage, persisting up to the bulk melting point value. The absolute intensities of the curves in fig. 11 are not to scale but the curves show the “coverage” dependence of the melting behaviour of solid ammonia in contact with graphon. The curves show no hysteresis of cooling or heating and are, therefore, equilibrium curves. At the lowest coverages some peak broadening has been detected and indicates that a lower limit for the crystalline size involved in this diffraction is of the order of 4000 a, as estimated using the Scherrer formula [38]. A provisional interpretation of these data, which will be discussed more below, is that the curves arise from the equilibrium between ammonia crystallites and a mobile ammonia phase on the surface. An experiment to test the delicacy of the thermodynamic balance between these two phases is illustrated in fig. 12. Since it has been shown that methane is exothermically adsorbed on graphite, and wets the surface, it can be expected that the adsorption of ammonia followed by methane, in a temperature region where the disordered phase of ammonia in equilibrium with ammonia crystallites was mobile (e.g. between 160 and 190 K), would lead to compression of the mobile ammonia film by the preferential adsorption of a monolayer of methane. Accordingly, methane was added to the adsorbed ammonia system at a temperature above the melting point, as defined by the melting point curves of fig. 11. The immediate effect of this addition of methane was to increase somewhat the intensities of the crystalline ammonia diffraction peaks and to modify the shape

Fig. 12. Dependence of the [.l’l l] diffraction peak intensity from ND3 adsorbed by graphon on temperature in the presence of a layer of methane: (a) 1.0 statistical monolayer of ND3 only. (b) ND3 coverage: 0.5 statistical monolayer; CH4 coverage: 1.0 statistical monolayer. (c) ND3 coverage: 0.5 monolayer CH4 coverage: zero monolayer (Marlow et al. [28]).

J. W. White et al. /Neutron diffraction and itlelastic scattering

37

of the melting point curves so that melting occurred at higher temperatures than in the absence of methane. The working hypothesis drawn from these experiments is that crystallites of bulk ammonia are formed probably by nucleation at “hydroph~ic sites”. At temperatures between 160 and 180 K, depending upon the statistical coverage, a thermodynamic equilibirum is established between these crystallites, ammonia in the vapour (normally the vapour pressure is very low, typically less than 0.1 Torr at this temperature), and a mobile dense phase on the surface. By far the largest part of the ammonia mass is tied up in the equilibrium between the crystallites and the dense phase until within about 10” of the bulk melting point.

The existence of this equilibrium between the crystalline and dense mobile phase of ammonia has been strongly supported by neutron quasi-electric scattering studies on hydrogenous ammonia adsorbed by the same adsorbent. The same problem has been attacked using nuclear magnetic resonance spin lattice and spin spin relaxation measurements [39]. It turns out that the two techniques are complementary, the nuclear magnetic resonance measurements showing the equilibrium between the vapour and the adsorbed phase at high coverages very well, and the very high resolution nuclear quasi-elastic measurements resolving the different dynamics of the solid particles and the surrounding mobile phase. Fig. 13 shows the spectra taken at the IN5 high resolution time-of-flight spec-

(a)

’

T=130K f&l.1 A-’

** ._

Cd) Q=0.9K1

” -.

(b) T=163 K

(cl T=185K

(e)

Fig. 13. Incoherent quasielastic scattering spectra for NH3 adsorbed on graphon. Measurements were made at two values of the momentum transfer: Q = 1.1 A-’ (a, b, c), Q = 0.9 A-’ (d, e, f); and at temperatures of: 130 K (a, d), 163 K (b, e), 185 K (c, f) (Marlow et al. [28]).

38

J. W. White et al. /Neutron

diffraction and inelastic scattering

trometer at Grenoble (energy resolution 30 PeV) at temperatures of 130, 163 and 185 K for one statistical monolayer of NH, on graphon with the background subtracted and at momentum transfers of 1.1 and 0.9 A-‘. At 130 K a.sharp elastic scattering is observed for both momentum transfers (figs. 13a and d), whose width is determined by the energy resolution of the spectrometer. At 163 K extensive wings can be seen in addition to the presence of a narrow centre peak which again has the elastic resolution, and at 185 K much of the central elastic peak has disappeared and the intensity gone into the wide quasi-elastic wings. The central peak comes from the solid ammonia crystallites and the intensity of this peak extrapolated to zero momentum transfer is proportional to the concentration of ammonia held in this phase (strictly speaking this peak comprehends all of the scattering from ammonia molecules whose frequency of motion (translational or rotational) is at lower frequencies than approximately 10 GHz. There is strong evidence that the ammonia molecules in the crystallites are tumbling at least at temperatures above 160 K, but further experiments and analysis of the momentum dependence of the scattering are needed to resolve this. The broad quasielastic feature can be associated with mobile ammonia and has been fitted to the scattering law accepted for a two-dimensional liquid to give values of the two-dimensional diffusion coefficients for the ammonia. These diffusion coefficients are much greater than the values found for b&liquid ammonia just above the melting point, and so it is provisionally concluded that the ammonia in the two-dimensional phase does not benefit from the three-dimensional hydrogen bonding of a normal liquid [28]. This behaviour is also strongly dependent upon the degree of coverage as already indicated in the melting point curves. A final factor which cannot be discounted from analysis of these data is the contribution of rotational diffusion of the adsorbed ammonia molecules in the mobile phase. Only a limited range of momentum transfer 0 is available in the experiments because of extensive small angle scattering, but experiments are under way to distinguish this coherent small angle scattering from the incoherent inelastic scattering and thereby provide a more precise model for the dynamics of the fluid phase. 3.3.2. Small angle scattering measurements In so far as our model for the adsorption of ammonia on graphon implies the existence of hydropholic nucleating sites, it is conceivable that the distribution of these sites could be studied by small angle neutron scattering. Two attempts at such a study have been made but with some ambiguous results so far. The first attempt exploited the strong scattering length difference betweeen ordinary ammonia and the carbon substrate. If we are to assume that the tightly bound ammonia revealed by the adsorption isotherm studies above 200 K is in fact ammonia attached strongly to the “hydrophilic sites”, then we may decorate these sites with NH, molecules up to an effective coverage of about 0.2 monolayers. By adding slightly more ammonia the crystallites about these nuclei should be allowed to grow so that their dimensions were of the order of several angstroms, and their approximate

J. W. White et al. 1 Neutron diffraction and inelastic scattering

39

spacing up to 10 or 20 A. By cooling such a substrate to the point where no further mobility about the sites existed, and to a point where the mobile phase had condensed onto the nuclei, it might be possible to observe the small angle scattering pattern from this distribution of differently scattering sites. The difficulty with this is that the small angle scattering pattern from the voids between carbon particles in the sample was also comparatively large. An attempt was made to get round this problem by a second adsorption of a mixture of NH3 and ND3 whose mean scattering length corresponded to that of the carbon. By adding enough of this mixture, so that all voids in the structure were filled, but at a low enough temperature to avoid substantial exchange between these mixtures and the sites decorated with NH3 molecules, a maxtrix of unfirom scattering length composed of carbon and the mixture, in which is dispersed the decorated sites can, in principle, be produced. Some excess scattering was seen in this experiment but the experimental difficulty of avoiding any exchange between the decorated sites of the surrounding matrix led to considerable non-reproducibility and hence an ambiguous result. A better idea is now being tried. Chemical methods for decorating the sites with large hydrogenous molecules to form a chemical bond to the surface, are used instead of decoration by NH, molecules. The rest of the experiment is the same, but as yet no positive results have emerged.

4. Chemisorption In most cases where chemisorption experiments are done using fine powders, the problem of defining the role of the surface as opposed to the role of bulk adsorption in any catalytic process is often quite intractable. Nevertheless, neutron diffraction experiments can contribute to definition of the structure of non-stoichiometric phases such as Pd-H or Pt-H systems, and the same types of experiment are possible as for physisorption in cases where extensive surface areas and homogenious surface are present. Usually, though, for materials like platinum black, Rainey nickel, and other fine metallic powders, the powder is highly dispersed and, therefore, any layer formation on it gives as broad diffraction peaks as those from the powder itself. The problems of defining the structure of adsorbed molecules then rather resemble those encountered in neutron diffuse scattering from defect and non-stoichiometric solids. Very little work on diffraction has been done for these types of materials and it can be expected that the extensively developed techniques for studying precipitation in alloys etc. will come to be applied to the study of chemisorption. By contrast, there have been a large number of preliminary experiments and some definitive ones using neutron incoherent inelastic scattering where the effective transparency of the metal substrates to neutrons compared to the strong scattering from hydrogenous adsorbates has been exploited [4,41-431. We given three examples to illustrate the phenomena that have been observed so far; hydrogen on Rainey

J. W. White et al. /Neutron

40

diffraction and inelastic scattering

nickel, hydrogen on platinum black, and ethylene adsorbed in silver substituted type Z zeolites. Rainey nickel is supposed to be made of crystallites whose linear dimensions are between 50 and 70 A, which are connected in a sponge-like form. The material has pores 10-l 5 A in diameter, which are accessible to hydrogen, and the properties of adsorbed hydrogen up to fillings of between 30 and 40 ml/g of nickel have been studied by neutron inelastic scattering within the energy transfer range O-200 meV (o-1600 optical wave numbers) [41]. Three different types of information come from these measurements. In the region around zero energy transfer the incoherent quasi elastic scattering had a width, the accuracy of whose measurement was limited by the resolution function of the spectrometer (0.07 meV). At room temperature this sets an upper limit for the three dimensional diffusion constant of the protons at 5 X lo-’ cm’ set-‘. The measurement with higher resolution spectrometers, and at higher temperatures, would allow the activation energy and other parameters of diffusion phenomena to be studied in more detail. In the region between 5-40 meV, an intense spectrum was found for the frequency distribution in hydrogenated Rainey nickel, which was almost the same as that for deuterated Rainey nickel. In fact, in this region the hydrogen can be treated as moving in phase with the surface atoms to which it is absorbed, and the hydrogenous motions, therefore, reflect the density of states for the lattice as a whole, as has been found in the past for intercalated and clathrated molecules [40,44]. At frequencies above 70 millivolts energy transfer there is a

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[421).

J. W. White et al. /Neutron

diffraction and inelastic scattering

41

broad excitation centring upon about 150 meV transfer for Rainey nickel-hydrogen (1120 cm-‘) and 800 cm-’ in the case of deuterium. This mode is attributed to the motions of hydrogen atoms relative to the nickel surface and it has been found that the mean scattering amplitude of the bound proton exceeds that of the nickel atom vibrations by 0.04 f 0.02 A2. In the case of the hydrogen adsorbed by platinum powder [42], the platinum was cleaned at 10e6 Torr by repeated adsorption and desorption of high purity hydrogen at 200°C. The spectrum recorded at ambient temperature is shown in fig. 14, as recorded by time-of-flight up-scattering using incident -4.2 A neutrons. The three prominent peaks found in the spectrum can be attributed to a mode at the highest energies due to the relative motion of hydrogen with respect to the platinum surface, of the same kind as seen with the Rainey nickel described above. The ENERGY TRANSFER cm-1 200 CO 50 25 I I I1 1

300

600

900

NEUTRON TIME OF FLIGHT JJ.s~-~

200

250

300 350 400 L50 INCIDENT ENERGY/cm-r

500

550

Fig. 15. Neutron time-of-flight spectra of (a) ethylene adsorbed on silver-13X zeolites at low pressure; (b) ethylene absorbed on silver-l 3X zeolites at a pressure of 500 Torr; (c) spectrum of silver-l 3X zeolites alone (Howard et al. [43]). Fig. 16. High energy neutron incoherent scattering spectra for ethylene absorbed on silver substituted 13X zeolites: (a) trans CZDZH~ with no background subtracted and at low coverage; (b) trans CzD2Hz low coverage, background subtracted; (c) silver-13X zeolites plus silica container plus background (Howard et al. [46]).

42

J. W. White et al. f Neutron diffraction and inelastic scattering

two lower peaks correspond very well to the lowest energy maxima in the phonon density of states spectrum for bulk platinum. It is thought that the hydrogen vibrations see, probably correspond to hydrogen in the so-called delta state which desorbs from plat~um at temperatures above 200°C and which is infrared and active. This vibration occurs at 50 + 2.5 mV (400 It 20 cm-‘) and is, therefore, of considerably lower frequency than the mode observed for Rainey nickel. Just as the contrast between the scattering from hydrogen and the metal atoms of plat~um and nickel catalyst substrates allows inelastic scattering to be observed, so also may the molecular and torsional modes of ethylene and acetylene adsorbed by silver exchanged type 13 X zeolites be studied [45,46]. For ethylene, a large number of model studies on such compounds as Zeise’s salt and similar materials have been carried out by neutron inelastic scattering to allow an interpretation of the spectrum of frequencies observed by adsorption in the molecular sieve. For this system modes have been observed at approximately 40 cm-’ corresponding to the libration of the ethylene molecule about an axis from the silver atom perpendicularly through the double bond. The frequency is a sensitive function of the degree filling indicating that a number of different sites are available and the spectrum may be interpreted in terms of a libration frequency of type 2 sites occurring at 22 wave numbers energy transfer, whilst that on the more strongly bound type 3 sites occurs at 56 cm-‘. The spectra as a function of filling are shdwn in fig. 15. Measurements at higher energy transfers reveal the existence of further bands in the case of adsorbed ethylene on silver exchanged zeolite at 285 + 2 1 wave numbers and 4 18 + 28 wave numbers, which could be assigned as the torsional motions about the other two axes through the molecule. These spectra are shown in fig. 16. However, as yet the agreement between predicted and experimental values of the deuterium shifts for these assignments are only fair for the higher frequency excitation, which may be of a rather more complex nature. 4. I. Metal cluster compounds To some extent the dyna~cs and structure of che~sorbed species at single metal atom sites in zeolites, and on the surfaces of bulk metal, represent extreme cases as models for catalytic sites. In a large number of catalysts, it may be supposed that the catalytic particles or the sites are composed of a fairly small number of atoms including the adsorbed species. In such cases the catalyst may be more properly represented by the properties of metal cluster compounds, which have been extensively studied in connection with homogenious catalysis. It is well known that very small clusters of metal atoms have rather different properties from the bulk metal and, therefore, the study of cluster compounds themselves is relevant to an understanding of the chemisorption on finely divided metaIs in other materials . Neutron inelastic scattering has contributed to an understand~g of the dynamics of small metal clusters, particularly because of the emphasis, given to the dynamics

J. W. White et al. /Neutron

diffraction and inelastic scattering

43

of hydrogen and other light atoms by their small mass and high vibration amplitudes, compared to the spectra that one obtains when using infrared or other optical methods [47-491. Typical of the cluster compounds studied HFeCOs(CO)r2 and HsMn4(CO)r2, for which it has been possible to identify separately the hydrogen atom motions as well as the vibrations of the metals atoms in the cluster.

5. The solid-liquid

interface

Adsorption at the solid liquid interface is more complicated than at the gas solid interface because there is normally a third component, namely the solvent in which the adsorbant is dissolved. At low concentrations of adsorbant, the adsorption isotherms resemble those for the gas-solid interface and it can be expected that many of the techniques already discussed will be carried over to the liquid-solid interface in due time. For example, it is obvious that studies of the clustering of adsorbed molecules could be followed by small angle scattering measurements by using an adsorbent and a solvent of the same mean scattering length density, giving good contrast for an adsorbant of quite different density. The adsorption isotherms at the solid-liquid interface vary from the most simple types, reminiscent of the gassolid interface, to very complex isotherms which show up the effect of non-ideality in the solvent-solute interaction. Interpretation of the isotherms also is subject to considerable speculation, and in particular there is strong evidence against the simple model of a monomolecular adsorbant layer on the adsorbate in some systems. With polar molecules, bilayers are clearly likely structures and in other systems, for example for polymeric adsorption, it is quite conceivable that extended structures from the surface exist. A detailed study of these structures, as a function of temperature and the concentration of the solute, is feasible by a combination of neutron methods. Moreover, for colloidal dispersions, the diffusive motions of the colloid particles are likely to occur on a time-scale many orders of magnitude slower than the rotational and fluxional motions of the adsorbed molecules, and so it would appear that, by the use of neutron inelastic scattering, these motions could be separated. This opens up the possibility of studying the actual kinetic steps for the adsorption and desorption process, as well as the diffusive motions of the adsorbed molecules on the surface of finely divided or colloidal particles suspended in weakly scattering liquids (such as fully deuterated solvents). One of the most promising ways of studying adsorption at the solid liquid interface is to study adsorption on colloidal dispersions. Very little neutron scattering work has been done in this area so here we take two separate examples of recent work to illustrate the effect of polydispersity upon small angle scattering measurements in colloidal dispersions [50] and, to our knowledge, no published work on high angle neutron diffraction from adsorbed molecules on colloids, or of inelastic scattering from adsorbed molecules on colloids, exists. Polystyrene latices containing a single ionogenic surface species (carboxylic acid

44

J. W. White et al. /Neutron

diffraction and inelastic scattering

group), and with a very small coefficient of variation in the particle size (typically less than a few percent), have been prepared by Ottewill and his collaborators [.51,521 and form an elegant system for defining the precision of neutron small angle scattering measurements of adsorption on colloidal dispersions. Samples of this material in stabilised dispersed form at 0.2% weight per volume were used for a series of small angle scattering measurements on the Dll small angle scattering camera of the Institut Laue-Langevin in Grenoble. At this instrument the incident neutron wavelength may be selected between 4 and 16 8, and the camera length can be varied from 60 cm to 40 m. It is, therefore, possible to observe the small angle scattering patterns from highly dispersed colloids where the particle size ranges from a few angstroms to about 40,000 A. In a preliminary experiment the mean scattering length density of the polystyrene latex was determined by contrast variation using H20-D20 mixtures as the supporting solution and the radius of gyration was found by the Guinier method [lo]. Fig. 17 shows the Guinier plots of the logarithm of the scattered intensity as a function of the squared momentum transfer for a range of D,O concentrations. The scattering intensity is extremely weak for the 25% D,O colloidal solution and the contrast match-point is at approximately 39% D,O : 71% HzO. The good straight lines obtained for the Guinier plots between the squared momentum transfers of 10 and 110 X 10V6 A-’ allow accurate values of the radius of gyration for the particle to be determined. The value found for (Ri) was 172 8, giving for the particle diameter 440 A in close agreement with the value of about 500 A found from electron microscope counts. Slight curvature of the Guinier plots at the very lowest momentum transfers may indicate a tendency towards a small fraction of particles with rather larger radii. Ln (Scattered

Intensity)

t

,_

OoDO

00 0

0

I 10

I 20

I 30

Qo

I 40

o I 50

0 25% D20

0

I 60

II 70

60

110. 90 100

(momentum transfer?.

Fig. 17. Logarithm (scattered intensity) versus squared angle scattering patterns of mono-dispersed polystyrene and D20 (Harris et al. [SO]).

110

C? lob, X2

momentum transfer, Q2, for the low latex in various concentrations of Hz0

45

J. W. White et al. f Neutron diffraction and inelastic scattering A

fro 4

(IO= Intensity

at Q=Oj

-

30 20 10 -

40 -' -05 1

I

I

I

I

I

!

I

I)

0

cl5

I

1.5

2

25

3

3.5

length

density

cm-2x10’o

Scattering

Fig. 18. The square root of the extrapolated intensity at zero scattering angle (square root of 10) as a function of the dispersent scattering length density for polystyrene latex in HzO/DzO mixtures (Harris et al. [50]).

The intensity at zero scattering angle for neutrons is closely related to the neutron refractive index difference between the dispersed material and the dispersant. Fig. 18 shows a plot of the square root of the intensity extrapolated to zero Q as a function of the volume per centage D,O. Immediately the contrast matching point is seen, which gives a mean scattering length density for the polystyrene particles of 1.37 f 0.1 X 10” cmm2, hence the particle density of 1.03 -I 0.0 g/cm3 compared to the expected value of 1.057 g/cm3. At each value of the contrast indicated on fig. 18, the radius of gyration was measured from fig. 17. To within the accuracy of the experiment, all radii of gyration were the same and this indicates that the profile of the particle has uniform scattering density [5]. Experiments at present in progress are concerned with the neutron small angle scattering from anionic and neutral surfactants adsorbed at the polystyrene latex surface. By using deuterated surfactants and H20/D20 concentrations of the same scattering power as the polystyrene latex, only the scattering from the shell of the surfactant around the polystyrene latex particle is observed. For latices with the weight per volume density used in these experiments, the scattering power from such a monomolecular shell is quite sufficient to be observable with counting times of the order of about 2 h at the Dl 1 instrument at Grenoble. An experiment which illustrates the effect of the addition of surfactants, and at the same time the effect of polydispersity in the colloid, is a recent study on the adsorption of sodium dodecyl-sulphate by ultrasonically dispersed graphon in

46

J. W. White et al. /Neutron

diffraction and irlelastic scattering

6 5o%D20-6

l

-

.

80%

D20

l

100%

D20 -

5

000 N

Oooo . .

00

n=.

00

-1 O”oo

l

m

.

0 .

hand conzIst _ (right sale) /. In negative

.

.

’

0

100

200

300

o 0 -0

0 0 .

’ ’

.

@lGMENTUM TRANSFB?~ Fig. 19. Guinier plots for the low angle scattering mixtures peptised with sodium dodecyl sulphate. persity of the colloid (Harris er al. [SO]).

00

’ ’ ’ .

I

0

0

.

LOO

--1

. .

500

b-2,10-7]

from a 2% Vulcan III solution in HzO/D,O The marked curvature is due to the polydis-

water. The actual graphon used was Vulcan III (Batch No. 2A/29) whose surface area determined on krypton adsorption was 71 m2/g [2]. Dispersions with concentrations of between 0.2 up to 10 wt% of carbon were sonicated for 90 set using an ultrasonic finger in direct contact with the solution. This time was rather lees than the S min specified by Medalia and Heckman for complete dispersion of the graphon aggregates [.53]. Experiments were done on samples without the addition of peptising sodium dodecyl sulphate and on samples to which 35 mg of SDS have been added for each 100 mg of carbon. This is equivalent to approximately five monolayers of the surfactant if the surfactant molecules occupy an area of 50 A2 [2]. This SDS concentration ratio was kept constant. The peptised samples were noticeably more stable than dispersions in water and remained apparently dispersed for several months. Fig. 19 shows the Guinier plots for 2 wt% Vulcan III dispersed in various H20/ D20 mixtures with SDS as the peptising agent. The plots are markedly curved at low angles but a straight line may be drawn through the high angle region giving values for the apparent radius of gyration, CR,), and by extrapolation the scattered intensity at zero angle, IO. The intensities have all been corrected for self absorption, which is not negligible for samples of the order of several millimetres thick, and for high H,O concentrations. Polydispersity of this colloid is immediately obvious from the curved nature of the Guinier plots. If measurements were to be made over a much larger range of the momentum transfer, Q, then models for the polydispersity could be fitted to the observed curves with the idea of extracting the particle size distribution function. This has not been done here since the experiments were essentially demonstrative. It can also be seen that, within the approxi-

J. W. White et al. /Neutron

41

diffraction and inelastic scattering

mation used for analysing the curves, the radius of gyration was constant and independent of the contrast. As with the polystyrene latices, a plot of the square root of 1, as a function of the mean scattering length density of the solvent was made, and as predicted a linear relationship was observed. For the unpeptised samples this gave a contrast matching point near 100% D,O. The value for the peptised samples was considerably less (near 80% DaO). The corresponding mean scattering length densities for carbon without the presence of the surfactant was 6.5 + 0.7 X 10” cmP2, and for the peptised dispersion 5.7 + 0.5 X 10” cm-2. Since sodium dodecyl sulphate has a rather lower mean scattering length density than carbon, the in between scattering length density of the peptised colloidal particle is necesarily smaller than that for carbon alone. This is clearly reflected in the mean scattering length densities determined and it is clear, therefore, that, even for polydispersed samples, the liquid sensitivity to detect a few monolayers from neutron small angle scattering.

5.1. Conclusions For monodispersed colloids it is concluded that measurements of the radius of gyration, the particle mean scattering length density, and the intensities at zero scattering angle, by neutron small angle scattering, are effective methods of studying adsorption at the liquid-solid interface with techniques now available. The technique has adequate sensitivity to study the packing of the adsorbate over a large of the adsorption isotherm and, when used in conjunction with contrast variation, could be used to determine the conformation of complex or polymeric adsorbates. For monodispersed systems at high concentration, where long-range particle ordering has been observed, it is even conceivable that three-dimensional information on the colloid particle and surfactant packing could be obtained in the same way as has recently been found for virus crystals [54]. For polydispersed systems the measurements are rather harder than for monodispersed material, but provided measurements are made over a large enough range of momentum transfer, and the model for the particle size distribution can be fitted, similar information is available as for monodispersed systems. It is clear that these types of measurement have considerable potential for applications to such problems as the study of flocculation of colloids, surface structure of adsorbed polymers, wetting and lubrication and adhesion.

References [l] A. Thorny and X. Duval, J. Chim. Phys. 66 (1969) 1966. [2] D.H. Everett, G.D. Parfitt, K.S.W. Sing and R. Wilson, (1974) 199. [3] J.W. White, Dynamics of Solids and Liquids by Neutron

J. Appl. Scattering,

Chem.

Biotechnol.

24

in: Topics in Current

48

[4] [5] [6] [7] [8] [9]

[lo] [ 11) [12] [ 131 [14] [15] [ 161 [17]

[ 181 [19]

[ 201 [21] [22] [23] [24] [25] [26]

[27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

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Physics, Eds. S.W. Lovesey and T. Springer (Springer, Berlin, 1977) ch. IV. K. Ibel and H.B. Stuhrmann, J. Mol. Biol. 93 (1975) 255. B. Jacrot, Rept. Progr. Phys. 39 (1976) 911. G.E. Bacon, in: Thermal Neutron Diffraction (Oxford University Press, 1976). W. Marshall and S.W. Lovesey, in: Theory of Thermal Neutron Scattering (Oxford University Press, 1971). W. Schmatz, T. Springer, J. Schelten and K. Ibel, J. Appl. Cryst. 1 (1974) 96. Proc. Conf. on Neutron Scattering, Gatlinburg, Tennessee, 1976; Oak Ridge National Laboratory Conf.-760601-Pl (National Technical Information Services, US Department of Commerce, Springfield, Virginia, 22161). A. Guinier and G. Fournet (Wiley, New York, 1955) p. 25. K. Ibel and H.B. Stuhrman, J. Mol. Biol. 93 (1975) 255. B. Jacrot, Rept. Progr. Phys. 39 (1976) 911. See, for example, S.J. Gregg, in: Surface Chemistry and Colloids, Vol. 7, Ed. M. Kerker (Butterworths, London, 1972) p, 189. B.H. Zimm, J. Chem. Phys. 16 (1948) 1093. B.H. Zimm, J. Chem. Phys. 16 (1948) 1099. G.C. Stirling, in: Chemical Applications of Neutron Scattering, Ed. B.T.M. Willis (Oxford University Press, 1970). W.M. Lomer and G.G.E. Low, in: Thermal Neutron Scattering, Ed. P.A. Egelstaff (Academic Press, New York 1965) ch. I. 1.1. Gurevich and L.V. Tarasov, Low Energy Neutron Physics (North-Holland, Amsterdam, 1968). G.S. Pawley, P.A. Reynolds, J.K. Kjems and J.W. White, Solid State Commun. 9 (1971) 1353. H.G. Smith and M. Wakabayashi, in: Dynamics of Solids and Liquids by Neutron Scattering, Eds. S.W. Lovesey and T. Springer (Springer, Berlin, 1972) ch. II. H. Taub, L. Passell, J.K. Kjems, K. Carneiro, J.P. McTague and J.G. Dash, Phys. Rev. Letters 34 (1975) 654. P.H. Gamlen and J.W. White, Faraday Trans. Chem. Sot. 2 (1976) 446. A.W. Adamson, Physics and Chemistry of Surfaces (Interscience, New York, 1967) p. 584. B.E. Warren, Phys. Rev. 59 (1941) 693. J.K. Kjems, L. Passell, H. Taub, J.G. Dash and A.N. Novaco, Phys. Rev. 13 (1976) 1446. P. Thorel, B. Croset, C. Marti and J.P. Coulomb, in: Proc. Gatlinburg Conf. on Neutron Scattering (1976) Vol. 1, p. 85, Oak Ridge National Laboratory Conf.-760601-Pl (National Technical Information Services, U.S. Department of Commerce, Springfield, Va. 22161). E. Warming, J.P. McTague and M. Nielsen, Physics Department, Annual Progress Report, A.E.K. (Ris# Report No. 352) (1976) p. 40. I. Marlow, R.K. Thomas, T.D. Trewern and J.W. White, in: Proc. Marseilles Conf. on the State of Physisorption by Diffraction Techniques, to be published in J. Phys. (Paris). J.W. White, R.K. Thomas, G. Bomchil and T. Trewern, to be published. A. Thorny and X. Duval, J. Chim. Phys. 67 (1970) 287. A. Thorny and X. Duval, J. Chim. Phys. 67 (1970) 1101. H. Kapulla and W. Glaser, in: Neutron Inelastic Scattering, Proc. IAEA, Vienna, 1972, p. 841. W.A. Steele, Interaction of Gases with Solid Surfaces (Pergamon, Oxford, 1974). P.H. Gamlen, Thesis, Oxford University (1977). H. Stockmeyer, J. Stortnik and H.M. Conrad, in ref. [9], Vol. I, p. 303. G. Bomchil, R.K. Thomas and J.W. White, to be published. S.G. Ash and G.H. Findenegg, Special Discussions of the Faraday Society on Thin Liquid Films and Boundary Layers (I 97 1).

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diffraction and inelastic scattering

49

(Freeman, San Francisco, 1963). J. Tabony, R.K. Thomas and J.W. White, to be published. J.W. White in Neutron Inelastic Scattering (IAEA, Vienna, 1972) p. 315. R. Stockmeyer, H.M. Conrad, A. Renouprez and P. Fouilloux, Surface Sci. 49 (1975) 549. J. Howard, T.C. Waddington, C.J. Wright, J. Chem. Phys. 64 (1976) 3897. J. Howard, T.C. Waddington and C.J. Wright, J. Chem. Sot. Chem. Commun. (1975) 775. J.S. Downs, J.W. White, P.A. Egelstaff and V. Rainey,Phys. Rev. Letters 17 (1966) 533. J. Howard and T.C. Waddington, Surface Sci. 68 (1977) 86. J. Howard, T.C. Waddington and C.J. Wright, J. Chem. Sot., Faraday 2 (1977) 1768. J.W. White and C.J. Wright, Chem. Commun. (1970) 970. J.W. White and C.J. Wright, Chem. Commun. (1970) 971. J.W. White and C.J. Wright, J. Chem. Sot., Section A (1971) 2803. N.M. Harris, J. Tabony and J.W. White, Neutron Scattering in Applied Research (IAEA, 1977) p. 204. J.N. Shaw and R.H. OttewiIl, Nature 208 (1965) 681. R.H. Ottewill and J.N. Shaw, Discussions Faraday Sot. 42 (1966) 154. AI. Medalia and F.A. Heckman, Carbon 7 (1969) 567. A. Lewit, P.A. Timmins, G. Bentley, B. Jacrot and J. Witz, 4th European Crystallographic Meeting, Oxford, 1977. I. Marlow, Part II Thesis, Oxford University (1977). P.H. Gamlen, D. Phil Thesis, Oxford University (1978)