Bergaya F. Handbook of Clay Science

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12.5.2. SAS BY CLAY MINERALS

There are two sets of publications dealing with the characterization of clay dis-

persions us ing SAS techniques.

The ﬁrst set focuses on the hydration mechanisms by which a powder of smectite is

transformed into a concentrated gel or a paste. The SAS investigations consist of

observing the shift in diffraction peaks that occurs during clay mineral hydration, i.e.,

monitoring the proﬁle change of the (001) reﬂections from the dry state (corresponding

to dE1 nm) to the gel state. During this process, the interlayer distances can increase to

several tens or even several hundreds of nanometers. This evolution was followed as a

function of various parameters such as clay concentration, nature of interlayer cation,

ionic strength, external pressure or temperature. As already mentioned, most inves-

tigations are concerned with natural di- and tri-octahedral smectites and vermiculites.

The second set relates to the relatively recent development of powerful SAS de-

vices, such as ultra SAS of neutrons and X-rays. These investigations focus on the

sol–gel transition mechanisms, the relationship between gel structure and rheological

behaviour and thermodynamic models of the swelling clay dispersions. In order to

minimize experimental difﬁculties associated with earlier studies, most of the second-

generation researchers used Laponite (synthetic hectorite) as the clay mineral. The

small diameter of Laponite platelets, in comparison with natural smectites, allows

interparticle interactions to be simpliﬁed. Laponite particles also have a narrow par-

ticle size distribution, and hence a ‘mean’ size may be used. The diameter of Laponite

platelets is much smaller than the size that is accessible to SAS techniques. In case of

Montmorillonite, even ultra SAS of X-rays or neutrons cannot include the whole

range of Montmorillonite particle diameters. Unlike montmorillonite, the structure

and behaviour of Laponite dispersions can be thoroughly studied. The light scattering

scale could be suitable, even if it is generally available for highly dilute dispersions.

A. Initial Hydration Stages and Osmotic Transition

SAS Analysis by Fourier Transform of Intensity

Rausell-Colom and Norrish (1962) and Norrish and Rausell-Colom (1963) have used

SAXS to investigate the swelling in salt-water solutions of orientated ﬂakes of Na

montmorillonite (Wyoming) and single crystals of Li

-vermiculite (Kenya). The in-

crease in interlayer spacing was studied as a function of the ionic strength. The

scattering intensity was recorded along the direction perpendicular to the ﬂake (or

single crystal) plane using a low-angle diffractometer and within an angular range

that allows interlayer distances to be measured just after the transition to ‘osmotic’

swelling, that is, from 3 to 50 nm. The scattered intensity can be expressed by Eq. (10),

in which the q vector is replaced by its component q

perpendicular to the ﬂakes.

Iðq

Þ/F

ðq

ÞGðq

Þð12Þ

Chapter 12.5: Small-Angle Scattering Techniques886

The one-dimensional Fourier transform of G(q

) is given by:

WðrÞ1 ¼

Gðq

Þcosðrq

Þ dq

ð13Þ

In this case, W(r) is the one-dimensional distance distribution. The most probable

basal distance d corresponds to the maximum of W(r). Because the structure of

these clay mineral-water systems is heterogeneous and disordered, W(r) gave poor

information. Nevertheless, the following conclusions can be made. Interlayer

(‘crystalline’) swelling occurs by a process that is highly dependent on the hydration

energy of the interlayer cations. With some monovalent interlayer cations such as

and Li

, the interlayer distance ‘jumps’ at a high water content. Gel formation

can be explained in terms of repulsive osmotic forces resulting from the entry of

water into the interlayer space and the development of ionic double layers. After

passing the osmotic transition threshold, the increase in interlayer distance is

proportional to the water content, as is the case for swelling in pure water. In

salt solutions, the interlayer distance increases linearly with C

1/2

, where C is the

electrolyte concentration.

Andrews et al. (1967) carried out the same analysis with a SAS device that can

extend to smaller scattering angles, i.e., much larger parti cle size than in the above

experiment (about 100 nm). In agreement with Rausell-Colom and Norrish (1962)

and Norrish and Rausell-Colom (1963), they point out the inaccuracy of using a

direct Fourier transform for such samples.

Geometrical Simulation of SAS

The description of the gel structure can be improved by simulation of the scattering

curves. Experiments performed wi th standard laboratory SAS are not easy to model,

because a punctual collimation of X-ray sources is impossible to realize while main-

taining the intensity of scattering. It is then necessary to correct the experimental

data by using a heavy desmearing method or to introduce a complex optical transfer

function in the spectra simulation. This problem was overcome by using radiation

supplied by a synchrotron, allowing pinpoint collimat ion with a high intensity to be

achieved.

Pons et al. (1981, 1982a) performed small-angle X-ray experiments with a syn-

chrotron beam of the Laboratoire d’Utilisation du Rayonnement Synchrotron

(LURE, Orsay, France). They studied the swelling of Wyoming Na

-montmorillo-

nite and Li

-saponite in pure water, starting from a gel containing 17%, (w/w) clay.

The scattering evolution was observed in the course of alternate freezing at 70 1C

followed by slow warming up to room temperature. The time-resolved diffraction

patterns were recorded during temperature increase. The theoretical spectra were

simulated using the methods previous ly e laborated for the simulation of 00l reﬂec-

tions from disordered or interstratiﬁed layer stacking systems (see Section 12.5.1).

The simulation model of the dispersion consists of particles (layer stackings) that are

12.5.2. SAS by Clay Minerals 887

disoriented from each other. The intensity is given by:

IðqÞ¼

ðqÞ

aðMÞGðq; M; p

; d

Þð14Þ

where O is the unit cell area, F

(q) the structure factor of the unit layer along the 00l

direction, q the vector modulus, M, the number of layers in a particle, a(M), the

weight distribution of particles containing M layers, and G(q, M, p

, d

) is the inter-

ference function (or modulation function) that depends on M and on the interlayer

distance, d

with their respective probabilities, p

The spectra conﬁrmed the increa se of basal spacing from 2 to more than 3 nm at

the osmotic transition threshold, and the reversibility of this transition. But the

primary aim of the study was to compare the scattering evolution between 0 1C and

room temperature (Fig. 12.5.2).

The peak position was the same at both temperatures, but the narrow peak at 0 1C

transformed into a diffuse modulation at room temperature, indicating that swelling

Fig. 12.5.2. Time-resolved experiments showing the evolution of experimental SAXS inten-

sity I(s) vs. basal distance d or S ¼ 1=d, of a gel after freezing at –70 1C and then slowly heated

to room temperature. From Pons (1980) and Calas et al. (1984).

Chapter 12.5: Small-Angle Scattering Techniques888

was not impeded at 0 1C. At this temperature, the system was constrained by the

presence of residual ice in equilibrium with water. At room temperature, a large

disorder in layer stacking took place but with the same most probable basal distance.

This would indicate that the energy spent in establishing a swelling equilibrium

contains an entropy term inducing a dispersion of unit layers and the form ation of

smaller particles (stacked layers) that are disoriented from each other.

Comparison of experimental and theoretical scattering curves showed that the

-montmorillonite gel at 17% (w/w) formed at room temperature, consists of

particles containing between 1 and 8 parallel layers with interlayer distances of

4–20 nm, giving an average value of 10 nm. The particles themselves are completely

disoriented from each other. The proposed structural model was checked by high

resolution transmission electron microscopy (Pons et al., 1982b). Because of the high

clay concentration, other explanations may be proposed such as the formation of

nematic structures (see below).

The same simulation and ﬁtting method was used by Rausell-Colom et al. (1989)

to analyse the swelling of single crystals of Santa Olalla vermiculite in aqueous

solutions of

L-ornithine hydrochloride. They compared the basal spacing distribu-

tions obtained from SAS wi th those derived from the DLVO theory, taking into

account a Boltzmann distance distribution and a layer of water molecule on the clay

mineral surface (Cebula et al., 1980). Fig. 12.5.3 illustrates the ﬁt between the two

types of plots for different ionic concentrations of the swelling solution.

Following Callaghan and Ottewill (1974), Ben Rhaiem et al. (1987) studied the

hydration–dehydration behaviour of Na

- and Ca

-montmorillonite in 10

3

Fig. 12.5.3. Vermiculite wafer swelling. Comparison of basal spacing distributions computed

from diffuse double-layer interaction (broken line) and inferred from XRD data (continuous

line). c, ionic concentration of solvent; p, pressure applied on the wafer to balance the swelling

pressure. From Rausell-Colom et al. (1989).

12.5.2. SAS by Clay Minerals 889

NaCl and CaCl

by synchrotron SAS. The samples wer e examined during drying and

rewetting in an ultraﬁltration cell by varying the suction. Their results again conﬁrm

an osmotic transition and its reversibility for Na

-montmorillonite but not for

-montmorillonite. They further show that the gel, at least at high clay contents,

is formed by stackings of expanded layers as in nematic domains with variable

interlayer distances that are disoriented from each other. These gel domains alternate

with pores whose hierarchical size distribution can be determined by comparing SAS

spectra and permeability results of pressure experiments.

Keren and Klein (1995) used SALS to determine the clay concentration in aque-

ous dispersions of bi-ionic Na

/Ca

-montmorillonite. The samples were carefully

prepared by selecting particle size and stirring the two homoionic clay mineral dis-

persions for long periods. From experiments with various Na

/Ca

ratios and a

0.1% clay concentration, they concluded that the SALS technique is not appropriate

for such systems because of the broad particle-size heterogeneity. A theory for mix-

tures is required to take into account the scattering of particles with different sizes

(cf. the light scattering theories in Table 12.5.1).

Indeed, it is always perilo us to analyse heterogeneous media without any pos-

sibility to perform contrast matching in SAS experiment. As described below, there

are techniques that can be used for particular cases.

B. Anomalous Small Angle X-ray Scattering

Anomalous small-angle X-ray scattering (ASAXS) refers to an extension of standard

SAXS experiments in which the energy of the probing X-rays are tun ed near the K, L

or M absorption edges of an element in the sample. By performing SAXS exper-

iments near one of the characteristic absorption edges of any given atom, it is

possible to vary the scattering contrast of that atom. This systematic variation in

contrast yields the partial scattering functions of the speciﬁc atomic species. In

general, the atomic scattering can be expressed as

f ðq; EÞ¼f

ðqÞþf

ðq; EÞþif

ðq; EÞð15Þ

where E is the energy of the probing X-rays and f

and f

the real and imaginary parts

of anomalous scattering. The variation of f

is responsible for the change in contrast

seen in the ASAXS signals.

Near the absorption edge the scattering intensity is given by

Iðq; lÞ¼I

ðqÞþf

ðlÞI

ðq; lÞþðf

ðlÞþf

ðlÞÞI

ðqÞð16Þ

Here I

(q) is the normal non-resonant scattering, I

is a cross term reﬂecting scat-

tering between the speciﬁc element of interest and the remainder of material and I

corresponds to the distance correlations of the resonant scattering centres.

Chapter 12.5: Small-Angle Scattering Techniques890

This matching method is easily accessible to elements having Z values between 20

and 36 for K edges, and between 50 and 82 for L edges. Since f

and f

are sharply

varying functions near the edge, these experiments require the highest possible en-

ergy resolution (Dl /lE 10

4

). To resolve Eq. (16) it is necessary to perform several

measurements with different wavelengths far and near the edge. Such a technique

can reveal the distribution of speciﬁc species within a multicomponent matrix.

Carrado et al. (1998) exploited ASAXS to monitor the solvation behaviour of

transition metal and lanthanide ions within the interlayer space of montmorillonite.

The experiments were performed a t the Stanford Synchrotron Radiation Laboratory

(SSRL, USA). The variations of scattering intensities, as a function of the absorption

energy were monitored for Cu

-, Er

- and Yb

- montmorillonites as a functi on

of hydration.

C. Gel Structure and Sol– Gel Transition

The second series of investigations, using an ultra-small-angle X-ray scattering

(USAXS), neutrons and light scattering were devoted to study the structure of clay

gels and the sol–gel transition.

Gel Structure in Natural Smectite Dispersions

Cebula et al. (1980) performed SANS experiments at the Institute Laue-Langevin

(ILL) in Grenoble, France on aqueous dispersions, comparing the effect of ex-

changeble Li

and Cs

cations on the structure of dilute montmorillonite sols

(0.8%, w/w).

Fig. 12.5.4 illustrates the Guinier plots: ln (q

I) vs. q

. The particle thickness may

be derived from the slope of the linear part of each curve, using Eq. (8a). The

extrapolation of these straight lines to q ¼ 0 gives (Iq

)

. This last value was used to

control the exchange H

O - D

O. By changing the relative proportions between

O and D

O, it was possible to reach the condition ðIq

¼ 0 when the contrast

disappears. Matching allows even a very low exchange between D

O and H

O layers

at the clay mineral surface to be detected, and compared with the free H

O molecules

of the bulk solvent. Matching enhances the scattering contribution of these water

layers and allows their thickness (of about two water layers) to be evaluated. The

measurement of particle thickness, using the plots of Fig. 12.5.4, showed that Li

montmorillonite was completely de laminated with a layer thickness of ca. 1.10 nm

including the water layers. In K

-montmorillonite the average particle thickness was

ca. 2.6 nm, corresponding to two parallel clay miner al layers. In Cs

-montmorillo-

nite aggregation was more pronounced with a broad distribution of particles around

a thickness of about 4.2 nm corresponding to three associated layers with their hy-

dration layers. Matching of the particle–solvent scattering length contrast was ob-

tained with a solvent containing 65% D

O. This experimental deﬁned amount of

O cannot be obtained theoretically by only considering the scattering length of the

clay mineral and of the solvent. This experimental value also depends on the very low

12.5.2. SAS by Clay Minerals 891

exchange rate between hydrogen and deuterium in water within the interlayer space,

even if this water is very mobile (self-diffusion coefﬁcient E10

–10

/s).

Pinnavaia et al. (1984) used SANS (ILL, Grenoble) to study particle aggregation

and particle–pore distribution of Spur homoionic montmorillonites (in the Li

,Na

or Cs

forms). For 1% (w/w) dispersions, Li

-montmorillonite obeyed

Guinier’s law, while Cs

-montmorillonite followed Porod’s law (I(q)pq

4

), indi-

cating particle aggregation in the presence of Cs

ions. Na

-montmorillonite disper-

sions showed some aggregation of clay minerals layers, while K

-montmorillonite

gave a pattern similar to Cs

-montmorillonite. The dynamics of water and other

intercalated molecules were also investigated by quasi-elastic neutron scattering.

Comparing Montmorillonite with Laponite

Morvan et al. (1994) performed USAXS and SAXS experiments (CEA, Saclay,

France) on Laponite in pure water and in salt solutions. Fig. 12.5.5 shows the

log–log plots of scattering curves at 1.8, 3.5 and 10% (w/w).

The 1.8 and 3.5% (w/w) samples give curves that are typical for ideally dispersed

disk-like particles. Their proﬁle was simulated using the i(q) intensity expression of

Eq. (7) for randomly oriented cylinders of axial length 2H an d cross-sectional radius

R, and Eq. (3) taking into account the scattering length contrast. A plateau is

observed for the Guinier plot domain. Thus, the Laponite layers scatter independ-

ently without any interactions. For the 10% (w/w) concentration, the increase in

intensity at small q values has an exponent a ¼3 :1 indicative of a heterogeneous

medium.

Fig. 12.5.6 shows USAXS curves for a 4% (w/w) montmorillonite dispersions in

0.1 M NaCl. (Faisandier-Cauchois et al., 1995; Faisandier et al., 1998 ). Both plots

(Å

-2

)

ln (q

Fig. 12.5.4. Guinier plots obtained from SANS experiments for aqueous dispersions of Li

montmorillonite (&). K

-montmorillonite (K) and Cs

-montmorillonite (

). Clay mineral

concentration was 0.8% (w/w). From Cebula et al. (1980).

Chapter 12.5: Small-Angle Scattering Techniques892

are typical of well-dispersed montmorillonites obeying scaling laws over the whole

q-range. Such behaviour is also typical of scattering by non-interfering very large

membranes with a diameter D ¼ p/q

E1 mm (where q

is the lowest experimental

q value), and a thickness of ca. 1 nm. This diameter is clearly larger than the usual

Fig. 12.5.5. Experimental USAXS intensity I(q) vs. the modulus of scattering vector q of

aqueous Laponite dispersions, presented as a log–log plot. The corresponding clay concen-

trations were (’’’) 1.8% (w/w); (—) 3.5% (w/w) and (&&&) 10% (w/w). From Morvan

et al. (1994).

q(Å

-1

)

I(q)

1E-04 1E-03 1E-02 1E-01 1E-00

1E+10

1E+09

1E+08

1E+07

1E+06

1E+05

1E+04

1E+03

1E+02

1E+01

Fig. 12.5.6. Experimental USAXS intensity I(q) vs. the modulus of scattering vector q of

aqueous montmorillonite dispersions in 0.1 M NaCl, presented as a log–log plot. Clay mineral

concentration is 4% (w/w). From Faisandier-Cauchois et al. (1995). The slope values (2.15,

2, 4) represent scale laws characteristic of the different structures.

12.5.2. SAS by Clay Minerals 893

diameter of one montmorillon ite unit layer. For the sample prepared at room tem-

perature the exponent 2.15 indicates that some layers are parallel. For the sample

under pressure (in sealed ampoules at 200 1C), the slope is 2 as expected for ideally

dispersed layers. These results show that at this clay concentration and ionic

strength, the unit layers form large bands by edge-to-edge contacts, as mentioned by

Low (1991).

Ramsay et al. (1990) compared neutron diffraction and SANS (PLUTO Harwell,

UK) data for Laponite RD and Wyoming montmorillonite in D

O. The structural

changes investigated concerned samples in which the clay platelets were initially

aligned in the dry state. The authors followed the development of orientational

disorder and eventually a randomly oriented isotropic structure, over a wide range of

O concentration (D

O/clay ratio. x ¼ 0:2 to 31 (w/w)).

The Por od’s part of the SAS curves followed a Q

law with same exponent for

both clays. As the heavy water concentration increased, the exponent varied from 4

in the compacted system to 2 for the highly dilute dispersions.

Because of the small size of Laponite particles (in comparison with montmo-

rillonite), the SAS in the lowest q-range allows particle diameters (25–30 nm) to be

determined, using Eqs. (8a) and (8b).

SANS Studies under Shear

Using SANS (ILL, Grenoble), Ramsay and Lindner (1993) compared the in situ

scattering of Laponite and montmorillonite dispersions under static conditions and

during shearing in a Couette-type cell. The patterns were recorded with a 2D

detector. The range of clay contents was chosen within 0.5–6.5% (w/w) where

time-dependent gelation and thixotropic behaviour occur. Spatial and orientation

correlations between the particles developed in dispersions of low ionic strength

(o10

3

mol/L). Such self-organized structures are limited to domains of restricted

size, as indicated by the anisotropic scattering behaviour, and are inﬂuenced by the

clay mineral concentration, particle size and particle shape (Fig. 12.5.7).

Orientational correlations were more extensive for the relatively large montmo-

rillonite particles. Some preferential alignment was observed at distances b10

under equilibrium conditions. The effect of shear on structures was indicated by the

anisotropic SANS patterns. At low rates of shear, montmorillonite dispersions showed

preferential alignment of particles in the direction of ﬂow, but spatial correlations also

persisted. At high shear rates (ca. 10

1

) the three-dimensional structure broke down

and only the preferential alignment was observed. The time-resolved SANS studies of

montmorillonite dispersions showed a high degree of thixotropy.

Similarly, Hanley et al. (1994) carried out a SANS study of a 1% (w/w) dispersion

of Na

-montmorillonite using the instrument at CNR (Cold Neutron Research)

facility of the National Institute of Science and Technology (NIST), USA. The

spectra were recorded on a two-dimensional detector. At equilibrium, the plot of log

I vs. log q showed the classical scaling law with a slope of 2.2 indicating a

high degree of dispersion with scarcely detectable an isotropy. The behaviour of the

Chapter 12.5: Small-Angle Scattering Techniques894

dispersion under shear was as expected for disk-shaped particles. The disks aligned

under shear with the normal parallel to the velocity gradient.

Small-angle Light Scattering and Dynamic Light Scattering

Avery and Ramsay (1986) investigated a Na

-Laponite dispersion (p10 g/L) at low

ionic strength ([Na]E10

–3

mol/L) by static SALS, dynamic light scattering (DLS)

and SANS (PLUTO, AERE, Harwell, UK). This will be discussed below.

SALS. The data were evaluated using the scattering equation based on the Ray-

leigh–Debye theory: because of the difﬁculty in measuring absolute intensities, the

Rayleigh ratio, R

, is generally used with R

¼ I

, where I

and I

are the in-

tensity of the incident and scattered beam, respectively.





¼ M

PðqÞ

1



þ 2Bc ð17Þ

Here c is the particle number density, qð¼ 4p sin y=

nlÞ the scattering vector, and

P(q) the particle scattering factor. Taking into account the size of the particle in

Ln q(Å

-1

)

Ln I(q)

Fig. 12.5.7. SANS curves for aqueous Laponite dispersions: (a) static, (b) sheared. For

montmorillonite dispersions: (c) static, (d) sheared. Clay mineral concentration, 0.05 g/cm

;

shear rate, g ¼ 1.2 10

–1

. Data are radially averaged. From Ramsay and Lindner (1993).

12.5.2. SAS by Clay Minerals 895