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ABSTRACT
PATHWAYS OF CATIONIC DIFFUSION IN CLAY MINERALS

by Tung-Ming Lai

In order to study the pathways of cationic diffusion
in clay minerals, models of homogeneous and heterogeneous
cationic diffusion systems were applied to these minerals
and the effects of mineral orientation on diffusion were
determined.

The diffusion of Na and.Cs ions in expanded Na—ver-
miculite, which has both internal and external surfaces
available for cationic diffusion, decreased with increasing
diffusion time, a characteristic of heterogeneous systems.
Diffusion of those ions remained essentially constant in
collapsed K-vermiculite which has only external surface
available for diffusion and can thus be described as homo-
geneous. The property of homogeneity was further confirmed
with cationic diffusion in the vermiculite whose exchange
sites were clogged by pfphenylenediamine cation, and in Na-
and K-kaolinite which have external surfaces only; while
the heterogeneous property was observed to Na- and K—bentoe
nite which have both external and internal surfaces.

The diffusion of Na ion in Na—vermiculite was related
to a model originally derived for mathematical analysis of
grain boundary problems. The evaluation of diffusion coef-
ficients of external surface (De) and of interlayer surface
(Di) was made, and De of Na ion in Na-vermiculite was found

to be about 5 times larger than that of Di'

Tung-Ming Lai

Pellet Specimens were prepared by pressing freeze-
dried vermiculite in a cylindrical die, with the result
that the flakes of vermiculite were highly oriented with
the c axis of the minerals parallel with the axis of the
cylindrical pellet. It was possible to prepare different
angles of specimen orientation with respect to the surface
where diffusion was initiated, and the orientation effects
were studied. Mathematical relationships of orientation
angles, axial ratio of the platelets, and diffusion coef-
ficient were developed. The experimental results on the
diffusion of Na ion in vermiculite were shown to obey the
prOposed mathematical equations in the case of homogeneous
system (K-vermiculite), but not in the case of heterogen-
eous system (Na-vermiculite).

Based on the orientation effects, an effective area
factor was utilized in attempts to calculate the "true"

diffusion coefficient.

The importance of considering the homo— and heterogen-".

eity of the system in the study of cationic diffusion in

clay minerals is suggested.

PATHWAYS OF CATIONIC DIFFUSION IN CLAY MINERALS

BY

Tung-Ming Lai

AsTHESIS

.Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Soil Science

1967

ACKNOWLEDGMENTS

The author wishes to express his sincere gratitude to
Dr. M. M. Mortland for his guidance, suggestions, encourage—
ment, and enthusiasm in this study.

He expresses his sincere appreciation to Dr. R. L. Cook
for arranging his financial support by the Michigan State
University and for other related administrative help, which
alone enabled the author to pursue and complete this in-
vestigation.

The author would also like to thank Drs. R. S. Bandurski,
B. G. Ellis, R. J. Kunze, and A. Timnick for their helpful
suggestions concerning the course work program and research
program.

He wishes to thank Dr. K. V. Raman for his helpful dis-
cussions of this study.

His thanks also go to his wife, Chin-Yu, whose unusual
ability to manage the family, enabled him to devote his

energy and time to carrying on this work.

ii

TABLE OF CONTENTS

CHAPTER Page
I. INTRODUCTION . . . . . . . . . . . . . . . . 1

II. LITERATURE REVIEW . . . . . . . . . . . . . 5
Measurement of Diffusion Coefficients . . 5

Nature of Cationic Diffusion . . . . . . . 10
Effect of Soil Properties on Ionic Dife

fusion . . . . . . . . . . . . . . . . . 13
Ionic Diffusion Relating to Other
Processes in the Soil . . . . . . . . . 16

III. EXPERIMENTAL METHODS . . . . . . . . . . . . 19

Preparation of Sample . . . . . . . . . . 19
Preparation of Diffusion Specimen . . . . 20
Diffusion Measurement . . . . . . . . . . 23

IV. HOMOGENEOUS AND HETEROGENEOUS SYSTEMS. . . . 28

Theoretical Background . . . . . . . . . . 28
Homogeneous and Heterogeneous Systems . . 31
The Diffusion Model . . . . . . . . . . . 39
Evaluation of Diffusion Coefficients in

the Heterogeneous System“. . . . . . . . 45

V. ORIENTATION EFFECTS . . . . . . . . . . . . 50
Theoretical Considerations . . . . . . . . 50
Effect of Orientation on Diffusion . . . . 53
Orientation Effects in Heterogeneous

System . . . . . . . . . . . . . . . . . 56
Evaluation of True Diffusion Coefficient . 58

VI. CONCLUSIONS . . . . . . . . . . . . . . . . 68

LITERATURE CITED . . . . . . . . . . . . . . . . . . 70

iii

TABLE

1.

LIST OF TABLES

Page

Observed diffusion coefficients of Na ion in
K-vermiculite oriented at angle 6 = 90° (D )

and 0° (D ) with reSpect to the diffusion flux
and calchated results at various intermediate
values of a . . . . . . . . . . . . . . . . . 57

Observed diffusion coefficients of Na ion in
Na-vermiculite oriented at angle 6 = 90° (D )

and 0° (D ) with respect to the diffusion.

flux and calculated results at various inter—
mediate values of e . . . . . . . . . . . . . 60

Values of width:height ratio, effective area
factor, observed and "true" diffusion coef-
ficients of specimens oriented at angle 9 = 0°
and 90° with respect to the diffusion flux

of Na ion in two different particle sizes and
apparent densities of K-vermiculite pellets . 66

iv

FIGURE

1.
2.

10.

11.

LIST OF FIGURES

Page
Heterogeneous and homogeneous diffusion systems 2

Schematic drawing of vermiculite pellet mounted

on a plexiglas rod designed to give a plane of
angle 9 of orientation with respect to the
diffusion flux . . . . . . . . . . . . . . . . 22

Model used for grain boundary diffusion ‘ .
analysis . . . . . . . . . . . . . . . . . . . 30

Relationship of diffusion time with the dif-
fusion coefficient of Na ion in vermiculite

on samples equilibrated at 81.0% relative

humidity (20°C) . . . . . . . . . . . . . . . 32

Relationship of diffusion time with the dif-
fusion coefficient of Cs ion in vermiculite

on samples equilibrated at 81.0% relative

humidity (20°c) . . . . . . . . . . . . . . . 34

Relationship of diffusion time with the dif-
fusion coefficients of Cs and Na ions in pro-
tonated pfphenylenediamine saturated vermicu-

lite on samples equilibrated at 81. 0% rela-

tive humidity (20°C) . . . . . . . . . . . . 36

Relationship of diffusion time with the dif-
fusion coefficient of Na ion in kaolinite and
bentonite equilibrated at 81.0% relative

humidity (20°C) . . . . . . . . . . . . . . . 37

Specific activity of 22Na versus penetration
distance for the diffusion of Na ion in Na-
vermiculite at 4 and 24 hours. . . . . . . . . 42

Model used for analysis of diffusion pathways

on the surface of a platy particle seen edge-

wise and oriented at an angle 9 with respect

to the diffusion flux . . . . . . . . . . . . 51

Relationship of cos2 6 and cosz(Q - o) with the
diffusion coefficient of Na ion in K-vermiculite
oriented at various angles of 6 with reSpect to
the diffusion flux and equilibrated at 81.0%
relative humidity (20°C) . . . . . . . . . . . 54

Relationship of cos2 9 with the diffusion coef-

ficient of Na ion in Na-vermiculite oriented at

various angles of 9 with respect to the diffu-

sion flux and equilibrated at 81.0% relative

humidity (20°C) . . . . . . . . . . . . . . . 59
v

I. INTRODUCTION

.Cationic diffusion has been of interest in basic studies
of cation exchange and nutrient supply in soils in recent
years. However, the mechanism of this process in soils is
still not completely established. Diffusion is primarily a
random movement of particles. The diffusion in solids has
been treated with the mathematics of the random-walk prob-
lem in relating diffusion coefficient to the jump frequen-
cies and jump distances of the diffusing atoms (72). As
far as the pathways of cationic diffusion in clay minerals
are concerned, it has been suggested that cationic diffusion
in salt free systems results from movement from exchange
site to exchange site on the mineral surface (38,78).

The surface of clay minerals can be subdivided into
external and internal surfaces as far as the structure and
ion exchange processes are concerned. Ion exchange can
occur only on external surface of non-swelling clay minerals.
For expanded 2:1 clay minerals exchangeable ions are bonded
both on external and interlayer surfaces. Since in salt
free systems cations diffuse from one exchange site to an-
other, it is likely that there are at least two diffusion
pathways in expanded 2:1 clay minerals: on the external
surface and through the interlayer surface as shown in
A Fig. 1. For 1&1 clays or collapsed 2:1 minerals, only
the external surface is available for cationic diffusion

(B, Fig. 1).

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diffusion systems.

3

Because of the different properties of external and
interlayer surfaces, the magnitude of the external diffusion
coefficient (De) may differ from that of the interlayer dif-
fusion coefficient (Di)° Accordingly, the clay system with
both internal and external surfaces as shown in Fig. 1A is
heterogeneous as far as the diffusion is concerned, and the
type of clay where only external surface is available in
Fig. 1B, is considered a homogeneous system.

Furthermore, both isotropy and anisotropy for the dif-
fusion process have been found in noncubic materials (72).
Clay minerals generally have a pronounced platy or fibrous
structure. Walker (78) showed that the cationic movement
was isotropic within the plane of the silicate layers of
vermiculite flakes. The question may be raised as to whether
the diffusion coefficient will be constant or variable a-
long different axes in these minerals.

Most experimentally observed diffusion coefficients
are apparent values, in which three main factors are invol-
ved, namely, tortuosity of pathways, interactions of the_
diffusing ions with the clay minerals, and nature of the
ion itself. In a highly oriented clay system, physical
tortuosity effects could be studied by determination of ap-
parent diffusion coefficients at various angles of orienta-
tion with respect to the direction of diffusion flux. From
these results, diffusion coefficients which may reflect only
the properties of the diffusing species and the matrix

through which movement occurs, could be evaluated.

4
The investigation was designed to study the pathways
of cationic diffusion in clay minerals with the following
objectives in mind: (1) to test the hypothesis of homo—
geneous and heterogeneous diffusion systems, and (2) to

study the effects of clay mineral orientation on diffusion.

II. LITERATURE REVIEW

Measurement of Diffusion Coefficients

I

For the determination of diffusion coefficients one
ordinarily utilizes Fick's law of diffusion. An excellent
summary of earlier works on the diffusion in and through
solids has been given by Barrer (4). In Jost's book (34)
_the diffusion theories are fairly well integrated. There
are varieties of boundary conditions of Fiokls second law,
and Crank's book (15) is invaluable for the solution of the
differential equations of the diffusion type. Shewman's
(72) and Girifalco's (28)volumes give a modern treatment of
the diffusion in solids.

The development of accurate methods for the measurement
of ion diffusion coefficients in soils has received atten—
tion for more than a decade. Various methods have been
developed at different laboratories to meet the requirements
of different boundary conditions of Fick's law. In 1957,
Bloksma (6) published a procedure measuring the self-dif-
fusion coefficients of sodium and iodide ions in bentonite
and kaolinite pastes by means of layer analysis and use of
radioisotopes in a diffusion apparatus. With this apparatus
Fletcher and Slabaugh (26) were able to determine the self-
diffusion of Ca ion in a Wyoming bentonite gel. Attempting
to obtain more accurate data with Bloksma's method, Gast

(27) applied Longsworth's zero—time correction equation (46)

6

to this method. However, he found some anomalous results
in measurement of cationic diffusivity in bentonite pastes.

In Bloksma's method a layer of soil or clay mineral
containing radioactive tracer of the ion under investigation
is placed in contact with a similar layer without tracer,-
and then allowing diffusion to proceed for a certain definite
period of time. After measuring radioactivity in the layers,
the apparent diffusion coefficient is evaluated on the
basis of Fick's law. In order to solve some technical
problems in the measurement, Schofield and Graham-Bryce (71)
and Graham-Bryce (30) used a thin permeable ion-exchange
membrane (Permaplex supplied by the Permutit Co., Ltd.),
which was previously prepared in equilibrium with half the
initial tracer concentration in the radioactive section,
to separate the two layers and after a given time the dif-
fusion of Rh, I, or P ions in the soil was determined. In—
stead of a membrane, a thin, coarse, nylon-mesh cloth was
placed between the layers to facilitate a later separation
of the samples at the interface as reported by Olsen et al.
'(59) in the measurement of self-diffusion of P in soils.
However, Lewis and Quirk (44) found that, in the measure-
ment of diffusion of P in soils, no membrane was needed to
separate the two layers although a number of membranes were
tried and discarded. For the purpose of avoiding the sep-
aration procedure in the determination of radioactivity dis-
tribution in the layers, Evans and Barber (22) took several

autoradiographs at approximately 1-week intervals during

7
the course of the experiments to follow the movement of
§°Rb in the samples. Enlarged densitometer tracings were
made across the boundary between labeled and unlabeled
samples on the autoradiographs and the diffusion coeffici—
ent was calculated. On the other hand, Brown eg_gl. (11)
applied a quick-freezing technique in order to section the
layers into 50u segments with a refrigerated microtome,
after radioisotopes diffused from the labeled layer of
soil- or clay mineral-water system to the unlabeled system.
The radioactivity of the Son sections was determined and
the diffusion coefficient was then evaluated. With the
same principle of a one-dimensional closed finite diffusion
system, but with some difference in the technique of measur-
ing concentration of diffusing ions, Klute and Letey (35)
described a method measuring the self-diffusion coefficient
of 86RbCl in glass beads. Porter eg_§l. (66) measured
chloride diffusion in soils.

In an earlier paper Thomas (73) developed another type
of method to measure the self-diffusion coefficients of ions
in agar gels. In his method, coefficients of ions traceable
by y-ray can be deduced from determinations of the total
activity of a "short rod" of the material from which the
diffusion takes place through a thin membrane into a rapidly
stirred bath at zero activity. After some modifications
were made (1), this method was used to measure the self-dif-
fusion of the Na ion in a montmorillonite suspension by

Cremers and Thomas (16).

8

A thin-film boundary condition of Fick's law which is
often used in the study of diffusion in solids, was applied
by Lai and Mortland (38) for measuring diffusion coeffici-
ents in clay plugs. After depositing a thin film of radio-
active tracer on the surface of the plug, thin sections were
removed after a given time and radioactivity measurements
made on the portion of the plug remaining. The coefficient
was evaluated by a graphical method from the solution of
Fick's law at this special boundary condition.

Using Amberlite ion exchange paper as a sink maintaining
zero concentration of the diffusate at the soil surface,
Vaidyanathan and Nye (74) developed another kind of method
measuring ionic diffusion in soild. The method was based
on the principle that the quantity of ions diffusing from
the soil of semi—infinite thickness was directly propor—
tional to the square root of the diffusion time until about
half the counter-ions originally on the resin were changed.
Values of average diffusion coefficients were calculated
using this porportionality constant and the concentration
of total exchangeable ions.

With a single piece of vermiculite flake of thickness
about 0.1 mm and lateral dimensions of 1 to 2 mm, Walker
(78) was able to measure the diffusion of Sr ion in Mg-
vermiculite with an optical method by determining the rate
of the moving boundary.

Transient and steady-state systems are the two main

types used to measure diffusion coefficients in soils

9

and clays. All of the previously mentioned methods are con-
sidered as transient systems. In 1954, Husted and Low (33)
determined the steady-state counterdiffusion of K-H, K-NH4.
K-Na, and K-Li ions systems through bentonite gels. Their
counterdiffusion assembly was mainly constructed with a
diffusion chamber containing the bentonite gel and two
flow chambers connecting to both ends of the diffusion cham-
ber. The flow rate of the flowates in both chambers were
the same, and the concentrations of the flowates were de-
termined. Later on, Dutt and Low (21) constructed another
diffusion cell from which solutions of different salt con-
centrations could be brought into contact with opposite
ends of a clay-water paste confined at both ends by means
of Millipore filters in a plastic compartment, and diffusion
coefficients for the steady-state diffusion of LiCl and
NaCl in bentonite-water paste were determined. Very recent-
ly, Mokady and Low (52) designed a more complicated diffu-
sion apparatus with the objective that the simultaneous
diffusion of water, NaCl and its component ions through
Na-bentonite could be made. Olsen eE_§l. (59) also measured
the steady—state self-diffusion of P in soils by means of
a diffusion cell with the soil sample in the central com-
partment confined with two porous steel plates on both ends
of the sample.

According to the Nernst-Einstein equation, the ionic
diffusion coefficient may be calculated from the mobility

which may be measured electrically or electro—chemically.

10
Cremers and Laudelout (17) calculated the diffusion coef-
ficients from the results of conductivity of Na, K, Rb, and
Cs ions in bentonite ahd kaolinite with the correction for
formation factors. They found that their calculated values
agreed quite well with the results of Lai and Mortland (37,
38) obtained by a tracer technique based on Fick's law.
Mokady and Low (51) determined the transference number of
LiCl or NaCl in the montmorillonite pastes from the emf's
of the cell using Beckman electrodes with which Li and Na
activities were measured. The diffusion coefficients of
LiCl and NaCl in two kinds of bentonite-water systems were

then calculated from the results of transference number.
Nature of Cationic Diffusion

The cationic diffusion in soil or clay systems differs
from that in water, mainly because of interactions of dif—
fusing ions with the media and tortuosity effects. Walker
(78) has suggested that cations diffuse along exchange sites
of vermiculite. By means of dzNa and 35S double—labelled
Na2804 tracer techniques, Lai and Mortland (38) demonstrated
that Na ion migrated along the negatively charged matrix
of the bentonite gel and 504 ion moved through the middle
of the "channel" of the matrix. In the same paper, an
analogy of cationic diffusion in clay minerals to de Boer's
"hopping" mechanism of gas adsorption (20) has been pro-
posed by them. Recently, Cremers and Laudelout (17) also

adapted the same idea in their studies on surface mobilities

11
of cations in clays. On the other hand, the idea of "jump"
distance and jump frequency have been well established in
the mechanism of diffusion in solids (72). Based on the
results of the effect of salt concentrations on cationic
diffusion in soils, Graham-Bryce (29) has also suggested
that cations diffuse in the exchange phase of soils. Further-
more, Cremers and Thomas (16) developed a procedure to eval-
uate the surface diffusion coefficient of Na ion in bentonite
gel for the observed apparent coefficient. They presumed
that the surface diffusion coefficient depended directly on
the fraction of ions counted as belonging to the surface,
and this fraction was defined in terms of the base exchange
capacity of the suspended mineral. Nye (57) proposed to
separate the diffusion of exchangeable ions in soil along
the liquid pathway from the solid path in which the move-
ment is associated with the surface of the solid by using
mathematical equations.

Almost all of the values of apparent ionic diffusion
coefficients in soil. and clay systems measured were smaller
than that of the same ion in water. As far as the relative
order of diffusion rate of various ions is concerned, Husted
and Low (33) found that the counterdiffusion rate of K ion
through bentonite gels in steady-state depended on the
diffusion rate of the counterdiffusing ions which were in
the order NH4 > Na > Li, which is the same as that for
those ions in solution. With a transient system, Lai and

Mortland (37) also found that as far as the ion species

12
used to saturate the bentonite gels are concerned, the
diffusion rate of Na, Rb, Cs, Ca, and 804 ions in bentonite
systems varied with various kinds of homoionic clays, and
that these 5 ions followed the same order, namely, K-clay >
Na-clay > Li-clay. However, as far as the diffusion rate
of diffusing ions themselves is concerned, in the 3 homo-
ionic systems (K—, Na-, and Li-bentonite) their rates were
in the relative order 804 > Na > Rb > Ca > Cs which differs
from that in the order Cs > Rb > Na'> $04 > Ca in water.
The difference in the relative order of the rate of dif-
fusing ions between the clay and water systems suggested an
important influence of the clay structure on the diffusion
of ions. With vermiculite, it was also found that the
relative diffusion rate of Na ion was larger than that of
Cs ion in both Na- and Cs-clays (37).

To evaluate the tortuosity effects, there is a well-
written volume on the earlier works, which is reviewed by
Carman (12). For modern treatment on this subject, one may
refer to Meredith and Tobias's paper (49). Some mathemati-
cal equations have been worked out to solve the tortuosity
problems in unconsolidated systems (18,40,50). Cremers and
Thomas (16) applied a "formation factor" equation in the
study of self-diffusion of Na ion in montmorillonite gel,
and Cremers and Laudelout (17) used the same equation in
measuring surface mobilities of several cations in bentonite

gels.

13

Some workers used anions, such as chloride (35,66) and
iodide (6), and urea (6) to evaluate the tortuosity effects
on the basis of the assumption that those anions and urea
may not react with clays. However, Mokady and Low (53)
found that the average activity coefficient of Cl ion was
larger than unity during the steady-state diffusion of NaCl
through Na-bentonites. In fact, Lai and Mortland (37)
demonstrated that the diffusion of 804 ion in Na-bentonite
gel at low clay contents (less than 9% by weight) was even
higher than that in water. As far as urea is concerned,
based on the infrared absorption studies Mortland (55) has
observed the formation of urea complexes with montmorillonte
and its exchangeable cations.

Low (47) has suggested that the viscosity of water
increases towards the clay mineral surfaces, and thus the
greater viscosity in the vicinity of clay surfaces is also
one of the factors influencing cationic diffusion in clay
(55). Also, Chaussidon (13) suggested that at very low
moisture content, the structure of water is a very important

factor affecting cationic mobility in soils and clays.
Effect of Soil Properties on Ionic Diffusion

From the previous section on review of the nature of
cationic diffusion in soil and clay systems, the effects
of clay structure and kinds of exchangeable ions on ionic
diffusion in soils are obvious (36,37,62). In addition to
these, the effects of some other soil properties on ionic

diffusion have been studied.

14

The effect of moisture contents on ionic diffusion
has been demonstrated by several workers. Their results
showed that the diffusion of Na(38), Rb (31,61,65), Sr
(36,67), and Cl (66) ions in soils and clays increased
with increasing moisture contents. The quantitative rela-
tionship between moisture content and ionic diffusion still
has not been established. Graham-Bryce (31) found a rapid
rise in Rb ion diffusion taking place between 5 and 10%
moisture contents in a soil, that may correspond with the
establishment of a continuous aqueous diffusion system.

The number of exchange sites present per unit volume
should affect the diffusion rate. Increasing the clay
content will increase the number of exchange sites, there-
by increasing the frequency of exchanges an ion makes in
a given distance. This should result in a decrease in the
diffusion coefficient. Changes in tortuosity of the dif-
fusion path also could change with clay concentration.
These could account for the observations of Lai and Mortland
(38) who found that the diffusion coefficients of Na, Cs.
and Ca ions in bentonite gels decreased with increasing
clay contents. Evans and Barber (22) used agar as a medium
to dilute a soil and a kaolinite, and noted that the dif-
fusion of Rb decreased with increasing percentage of soil
and clay. On the other hand, when the "true" diffusion co-
efficient of P in soils was evaluated by a factor obtained
by chloride diffusion, Olsen and Watanabe (60) found that

the “true" coefficient increased with increasing clay contents.

15

When the clay content reaches a certain point and the
jump from particle to particle becomes the rate-limiting
process, then the diffusion could increase with increasing
clay content. In fact, Graham-Bryce (32) and Phillips and
Brown (63,64) found that the cationic diffusion coeffici-
ents increased with increasing bulk density. Their work is
based on the results of "hopping distance" as reported by
Lai and Mortland (37,38) in which the "hopping distance"
between clay particles became smaller as the clay content
increased.

Humus has a high ion exchange capacity, and thus the
results of Prokhorov (67) and Prokhorov and Frid (68) that
the diffusion of Sr-90 in quartz sand and soils decreased
with increasing humus content are understandable.

For cationic diffusion relating to the ion exchange
properties in soils, it is easy to understand the results
of the effects of cation exchange capacity and surface area
on the diffusion coefficients of Rb and Sr ions in kaolinite
and soils as reported by Evans and Barber (22) and Prokhorov
(57).

The diffusion coefficients of Rh ion in different
types of soils were determined by Evans and Barber (22)
and Graham-Bryce (31,32). Both results indicated the vari-
ation of the coefficients in the different soils. The cor-
relation of these coefficients with soil properties, such
as pH, cation exchange capacity, exchangeable K, clay

content and moisture content was tested by Graham-Bryce (32),

16
but no simple relationship was found. This is not sur-
prising because the diffusion coefficient is controlled
by both electro-chemical and geometrical factors for which

there can be no simple parameter.
Ionic Diffusion Relating to Other Processes in the Soil

The extensive work on ionic diffusion by Boyd and his
co~workers (8,9) has thrown light on the mechanisms of ion
exchange in resins. The results obtained by Mortland and
Ellis (56) have indicated that the release of fixed K from
vermiculite is a diffusion-controlled process. Walker (78)
has also shown that the Sr-Mg exchange reaction in vermicu-
lite is a diffusion proces3s Since then, the concept of
the diffusion of cations plays an important role in cation
exchange and has been accepted in the field of soil chem—
istry (5). For example, a study of kinetics of Cs sorption
by clay minerals was conducted by Sawhney (70) who found
that the Cs sorbed by Ca-montmorillonite reached equilibrium
quickly and, in contrast to that, Ca-vermiculite continued
to sorb Cs and the equilibrium was not attained even after
500 hours. He explained that whereas Cs diffuses into Ca-
vermiculite interlayers, which is a slow process, it does
not diffuse into Ca-montmorillonite interlayers.

The double layer theory as related to ionic diffusion
has been applied by Lai and Mortland (37) in order to ex-
plain the effects of exchangeable cations on the diffusion

of Na and Cs ions in the bentonite gels. Furthermore, based

17
on the diffusion studies, the fractions of the exchangeable
cations in the diffuse layer were estimated by van Schaik,
{Kemper, and Olsen (75). They calculated that approximately
70% of exchangeable Na ion and 25% of Ca ion were mobile,
and participated in ionic diffusion in a bentonite system.

In a practical sense, the movement of some nutrient
ions in soils is to be considered as being controlled by
the diffusion process, and rather extensive studies on the
nutrient uptake relating to the ionic diffusion in soils
have been made.

In 1954 Bray (10) proposed the nutrient mobility con-
cept in which he separated the nutrients into two groups
based on mobility in the soil: mobile nutrients such as
N03, Cl, and $04 ions, and relatively immobile nutrients
such as P, K, Ca, and Mg ions. He drew a picture of a
"hypothetical" narrow root surface sorption zone for supply
of relatively immobile nutrients in the soil. Several
years later after Bray's publication Walker and Barber (79)
were able to show by radioautography with 32P and 86Rb that
there was "actually" such a zone present in the soil. Further-
more, Lai, Fang, and Shieh (39) measured the root surface
sorption zone of Rb ion in two soils and calculated the dis-
tribution of Rb ion in the absorption zone from which it
was shown to follow Fick's law of diffusion.

At the low concentration of P ion usually observed in
the soil, diffusion is the main process of tranSport to the

plant roots as reported by several investigators (2,7,45,58).

18

Olsen and Watanabe (60) studied the relationship between
the diffusion and uptake of P by corn seedlings, and showed
that the observed results were close to the calculated ones
based on their proposed diffusion equation. Lewis and Quirk
(43) conducted a pot eXperiment with wheat to correlate
the plant growth with the diffusion coefficient of P. The
optimum coefficient of P for wheat growth in that particular
soil was 5 x 10-9 cm2 sec-1

Barber and his associates (23,65,76) have published
several papers on the diffusion and uptake of Rb. They
found that diffusion coefficient of Rb ion in soils cor-
related very well with the uptake by plants. For practical
purposes, Barber et al. (3) suggested that diffusion should

be one of the main processes to be considered in the develop-

ment of soil tests for available nutrients.

III. EXPERIMENTAL METHODS
Preparation of Sample

Vermiculite. The vermiculite used in this work was
from Libby, Montana and supplied by Ward's Natural Science
Establishment, Inc., Rochester, New York. Because the Mon-
V tana vermiculite contained some micaceous material, the clay
fraction (< 2n) was continuously leached with 2N NaCl
solution until the X-ray diffraction pattern showed the
disappearance of the 10A spacing (it required about 40
liters of 2N NaCl solution for 100 g clay with continuous
leaching for one week). After most of the excess NaCl was
washed out with water by a centrifugation procedure, the
suspension of Na-vermiculite was passed through the follow-
ing sequence of Amberlite synthetic resin (supplied by
Rohm & Haas Company, Philadelphia, Pennsylvania) columns:
OH-IR-45 -—> H-IRC-50 —> Na-IRc-so (OH-IR-45 is a weak amine
type anion exchange resin in hydroxy form, H-IRC-50 a
weakly carboxylic acid type cation exchange resin in hydro-
gen form, and Na-IRC-50 that in sodium salt form). This
product was a salt-free, Na-saturated vermiculite. The
homoionic K-vermiculite was prepared the same way except
using K-IRC-50 column instead of Na—resin in the final
columning process. For the study of effects of orientation,
the 2-5u particles of.K—vermiculite were also separated by
ordinary decantation procedures.

19

20
Kaolinite and Bentonite. These clays were American
Petroleum Institute Clay Mineral Standards Project No. 49
reference clay minerals H-5 and H—25 (also supplied by
Ward's Natural Science Establishment, Inc.) respectively.
The homoionic clay samples were prepared by washing the
< 2n fraction with NaCl or KCl solutions and rendering

them salt-free.

Preparation of Diffusion Specimen

 

In order to obtain diffusion specimens oriented as
shown in Fig. 1, the clay suspension was freeze dried, and
was pressed in a cylindrical die under 1,000 pounds per
square inch pressure to make a pellet as described by Cloos
and Mortland (14). The result of this method of pellet
preparation was to create highly oriented systems in which
the c axis of the clay particles was parallel to the axis
of the cylindrical clay pellet. The highly oriented condi-
tion of the clay resulted in a platy structure easily ob-
served under the microscope as shown in Plate 1.

In order to study orientation effects, it was neces-
sary that measurement be made of apparent diffusion coef-
ficients at various angles of orientation with respect to
the direction of diffusion flux. The vermiculite pellet
was cut and mounted as follows:

The pellet was affixed with paraffin to a plexiglas;
rod with a surface of angle ¢ as shown in Fig. 2. The dashed

lines show the orientation of vermiculite flakes. The

21

 

Plate 1. Microscope photograph of longitudinal
section of K-vermiculite pellet (x25).

Figure 2.

 

22

VERMICULITE
PELLET

 

 

PLEXIGLAS
ROD

 

 

 

Schematic drawing of a vermiculite pellet
mounted on a plexiglas rod designed to
give a plane of angle 9 of orientation
with respect to the diffusion flux.

 

23
final diffusion specimen was cut into ABDC as shown in
Fig. 2. AB is the surface on which the diffusion was
initiated in direction y in Fig. 2 and which was formed
by carefully slicing with a microtome. 9 is the angle of
vermiculite platelets oriented with respect to the dif-
fusion flux and has the value of 90° 7 ¢. The diffusion
studies at various angles of 6 were performed. Pellets
of kaolinite and bentonite were also tried, but were not
rigid enough to be cut into various angles as described
with vermiculite. Because of this experimental difficulty,

only vermiculite was used in the orientation studies.
Diffusion Measurement

Fundamentally the same radioactive tracer technique
‘developed by Lai and Mortland (38) was used for measuring
apparent diffusion coefficients. Their method was based
on the following equation of a thin-film boundary condition
of Fick's law of diffusion:
Cx = -——-Q——-exp (—x2/4Dt) (1)
th - .
Where Cx is the concentration of the diffusing substance
at time t at distance x from the initial boundary, Q
is the quantity of the substance deposited as a uniform and
thin layer on the surface and allowed to diffuse into a
semi-infinite medium, and D is the diffusion coefficient.
They(38) deve10ped a special experimental technique utiliz-

ing the equation [1]. -After depositing a thin film of

24
radioactive tracer on the surface of the clay plug, thin
slices were removed after a given time and radioactivity
measurements made on the remaining portion of the plug.
The coefficient was evaluated by a graphical method from
the solution of Fick's law at this boundary condition (38).
For its application to solid pellet specimens and to measure
the coefficients within short diffusion times, some modi-
fications were made.

A micrometer system was used instead of the hypo-
dermic syringe which was used in the original method (38)
for the purpose in cutting thin slices from the clay pel-
lets. With this technique a very thin slice accurate to
0.02 mm could be made, and the diffusion time out down to
several hours with the coefficient as low as 10-8 cm2
sec-1.

Theoretically, the diffusion coefficient is evaluated
from the slope of ln Cx versus x9, according to equation
[1] this lepe has the value of x3/4Dt. If’an accurate
value of the slope of ln-Cx versus x2 is to be Obtained,
it is necessary to have several slices from the pellet
specimen. -These slices should vary over a concentration
range of an order of magnitude (72). This means that slices
should be taken to a depth of x3/4Dt g 2.3 or x :3-VTD—t).
The minimum slice depth which can be taken in this eXperi-
mental technique is 0.02 mm or 2 x10_3 cm, so that for
10 slices, which are needed for this procedure, the minimum

value of x will be about 2 x 10.2 cm. If D is i

25

10-8 cm2 sec-1, then it should be possible to make an ac-
curate determination of D after a diffusion time t;:

(2 x 10‘3/3 x 10‘“)2 a: 104 sec 2 2.5 hr. In practice, it
required several minutes to take the diffusion specimen
from the constant temperature bath where the diffusion pro-
ceeded and to put it under the NaI(T1) crystal for radio-
activity measurements. To minimize the percentage error

of this time interval in the total diffusion time, it was
preferable to work at diffusion times no shorter than 4 hours.

The moisture content of sample, conditions for making
pellet, and diffusion temperature were controlled. After
the freeze dried sample was equilibrated in a desiccator
containing saturated (NH4)ZSO4 solution (81.0% relative
humidity at 20°C), 500 mg of sample was weighed and a pel-
let made in the stainless steel die. The pellet was stored
again in the same conditions for at least one day before
the diffusion measurement was made, and identical condi-
tions were maintained during diffusion experiments.

To insure that the diffusing source conformed to the
thin-film boundary condition of Fick's law, the 134Cs-IR-120
(strongly acidic type Amberlite cation exchange resin ab-
sorbed with 134Cs ion), and 134Cs-IRC-50 (weakly acidic
type resin absorbed with 134Cs ion) resin loaded papers
(supplied by H. Reeve Angel, Clifton, New Jersey), and 3n
pore size cellulose ester type Millipore filter (supplied
by Millipore Corporation, Bedford, Massachusetts) soaked

with very high specific acitivfiw'134CsCl (22.7 uC/mg), were

26
compared as radioactive sources. The following results

were obtained.

A Le Observed Diffusion Coefficient of
Radioactive Source Cs ion iva-vermiculite at 20°C
(cm2 sec 1 x 101°)
Experiment 1 Experiment 2
134Cs—IRc-50 paper 1.69 1.83
134cS-IR-120 paper 1.86 1.66
134CsCl-Millipore filter 1.84 1.98

It shows that these 3 different diffusion sources give
practically the same results. All eXperimental results
were in obedience to Fick's law as tested by the original
Lai and Mortland method (38). Because of better mechani—
cal strength and easy handling, the Millipore filter was
used throughout this investigation.

The carrier-free 22Na and 134C8 of very high Specific
activity in chloride form were used as diffusing ions.
About 0.5 uC of radioactive material was used for each
measurement. A Millipore filter was cut into small discs
the same size of the clay pellet (about 1 cm in diameter),
then soaked in radioactive solution and dried. This was
used as the radioactive diffusing source. After the radio-
active Millipore disc was equilibrated under the same con-
dition as that of the clay pellet, it was kept firmly in
contact with the surface of the clay by a coil spring during
the process of diffusion. After the preselected diffusing

time, the Millipore disc was taken off, and the radioactivity

27
of the pellet at different distances from the surface was
measured with a single channel pulse height analyzer.

The diffusion experiments were conducted in duplicate,
and the apparent diffusion coefficients reported are the
average between duplicates. In certain figures (Figs. 4,
5, 6, and 7) the average of duplicates are the centers of
the circles appearing in the graphs, and the deviation be-
tween duplicates is represented by the diameter of the

circles.

IV. HOMOGENEOUS AND HETEROGENCEOUS SYSTEMS
Theoretical Background

A grain boundary exists between crystal lattices in
polycrystalline forms of some metals. The grain boundary
diffusion (Db) and lattice diffusion (D3) are well estab-
lished (28,72). This kind of diffusion has been put on a
quantitative basis by Fisher (25). His work was followed
by other workers proposing modification (41).

Fisher's model was based on an intuitive picture of
grain boundary diffusion which is diffusion along a thin
layer of high diffusivity substance sandwiched between a
large volume of low diffusivity material. When Db/Dg is
large enough, he assumed that diffusion outside the grain
boundary slab was primarily normal to the slab at larger
penetrations. After material has diffused into the solid
through the surface, the concentration of diffusing material
(c) is measured at various distances (y) below the surface.
According to Fisher's solution a plot of log c versus y

then should give a straight line of slope

 

 

“’5 <2)
4.!wasz ~/(6Db/D£)
where D2 = lattice diffusion coefficient
Db = grain boundary diffusion coefficient
t = diffusion time
o -= thickness of the grain boundary slab.

28

29
Fisher's solution is limited to certain simple cases,
which Whipple (81) extended and published in his solution
with fewer limitations. With his more complex solution,
the grain boundary concentration contours can be calculated
at different conditions. Fig. 3 is adapted from Whipple

and shows concentration contours changing with 6, and

 

 

Pbé
e = — <3)
2 DZ «1 "Dflt

It is seen that with small values for B, the preferential
penetration down the grain boundary is small. Contrari-
wise, great preferential penetration down the grain boundary
exists when values for B are large. Therefore, the degree
of discrimination of grain boundary from lattice diffusion
can be varied with the variation of B. From equation [3],
it follows that with varying either Db/Dz ratio or diffusion
time (t), the magnitude of B should be changed. Experi-
mentally, it has been demonstrated that the contribution
of grain boundary diffusion or lattice diffusion to the ob-
served apparent diffusion (including both Db and D3) in poly-
crystalline zinc, varied with different diffusion tempera-
tures (77). With polycrystalline cadmium it was also found
that the observed diffusion coefficients decreased with
increasing diffusion time (48).

Although Fisher's and Whipple's solutions were origin-
ally derived for solving grain boundary problems, basically

it can be applied to the problem of heterogeneous diffusion

30

 

 

 

 

 

 

Figure 3. Model used for grain boundary diffusion
analysis. ‘

31
systems with high—diffusivity pathways. Consequently, it
is possible to distinguish the high-diffusivity path dif-
fusion from lattice diffusion in heterogeneous systems by

varying diffusion time according to equation [3].
Homogeneous and Heterogeneous Syetems

Figure 4 shows the apparent diffusion coefficients of
Na ions into Na- and K-vermiculite pellets at 20°C under
81.0% relative humidity. The moisture content was 18.1%
by weight for Na-vermiculite, and 3.6% for K-vermiculite
(105°C).

It shows very clearly that the apparent diffusion co—
efficients of Na ion in Na-vermiculite decrease with increas—
ing diffusion time, while remaining essentially constant in
K-vermiculite. From.X-ray diffraction results, the 15A
spacing of Na-vermiculite indicates an expansion that will
allow the Na ion to move into its interlayer regions. The
10A spacing of K-vermiculite means a collapsed structure,
with the result that only external surface is available for
cationic diffusion. If one compares the results in Fig.‘4
with the self-diffusion of cadmium by Mahmoud and.Kamel (48),
it is easy to see the following analogies: (1) the change
of the apparent diffusion coefficient with diffusion time
for Na-vermiculite and polycrystalline Cd, and (2) the uni-
formity of diffusion coefficient with time for both K-vermic—
ulite and monocrystalline Cd. In the former both grain

boundary and lattice diffusion occur, in the latter only

D X |09 cm2 sec-l

Figure 4.

32

60-

 

. A K—ve miculite

% No-K—vermiculii‘e
. m
V o

40r

 

20

 

‘W‘ I

I

l 2

 

[to—vermiculite

  

 

I J

l l
5 IO I5 20 25
' DIFFUSION TIME, hrs.

Relationship of diffusion time with the diffusion
coefficient of Na ion in vermiculite on samples
equilibrated at.81.0% relative humidity (20 C). The
moisture contents of K-, Na-K-, and Na-vermiculite
were 3.6, 6.8, and 18.1% by weight respectively
(105°C).

33

lattice diffusion for monocrystalline Cd and only grain
boundary diffusion for.K-vermiculite. It seems obvious
that both Na-vermiculite and polycrystalline Cd are hetero-
geneous diffusion systems with at least two coefficients,
De and Di in Na-clay and Db and DE in polycrystalline Cd
reSpectively; and homogeneous systems describe the cases
of K-vermiculite and monocrystalline Cd with only one dif-
fusion coefficient. Theoretically, it has been pointed out
that the value of 5 (equation [3]) is inversely prOportional
to time t. When time is short, 6, is large, the diffusion
in the high-diffusivity path (Db in equation [3]) predom-
inates in the over—all process. When time becomes longer,
the opposite is true. Therefore, the observed diffusion
coefficient in heterogeneous systems decreases with increas—
ing time. Under the experimental conditions in this study,
the diffusion coefficients obtained were observed values,
and thus only apparent coefficients. It can be observed,
however, that Na-vermiculite conforms to effects expected
of a heterogeneous diffusion system and K-vermiculite to
homogeneous diffusion. It is also apparent that the external
surface diffusion coefficient is larger than interlayer dif-
fusion coefficient.

The results of diffusion of Cs ions in Na- and K-ver-
miculite as shown in Fig. 5 also demonstrate the different
behavior of diffusion in these two systems.’ For Cs ion dif—

fusion,the eXpanded Na-clay is still a heterogeneous system,

and that of the collapsed K-system, homogeneous.

D X IO'O cm2 sec"

D X l0”cm2 sec"

N

 

 

34

K-vermiculite

‘GO Go

 

 
   
 

No-vermiculite

I5 20 5
DIFFUSION I'll-IE

Figure 5. Relationship of diffusion time with the

diffusion coefficient of Cs ion in
vermiculite on samples e uilibrated at
81.0% relative humidity 20°C).

35

Mortland (54) found some organic salts, such as p-phenyl-
enediamine dihydrochloride, effectively prevented K absorp-
tion on vermiculite, even though the vermiculite was expanded.
He proposed that the cation exchange sites were"clogged'
with those organic cations which K could not displace, with
the result that the K was unable to enter the internal ver-
miculite surface. If this is true, after the vermiculite
is saturated with those organic cations, it should act as
a homogeneous diffusion system. Figure 6 indicates that
with reSpect to both Na and Cs ions, the observed diffusion
coefficient remains unchanged with diffusion time thus ful-
filling the above prediction.

Regardless of Na or K saturation the kaolinite has only
external surface. Figure 7 proves that both Na— and K-
kaolinite are homogeneous systems with respect to the dif-
fusion of Na ion. There is no change in apparent diffusion
coefficient with time. Bentonite will not be completely
collapsed by K ion saturation, thus Figure 7 shows the ob—
served diffusion coefficients of Na ion in K-bentonite de—
creases with increasing time, suggesting that both external
and internal surface diffusion occur. The expanded Na-
bentonite certainly shows the heterogeneous property.

Graham-Bryce (32) noted that several investigators have
found that ionic diffusion in soils decreased with time.

Gast (27) also reported some anomalous results in measurement
of cationic diffusivity in bentonite pastes. He suggested

that multiple rate processes contributed from the diffuse

(O

D X IO'Icmzsec'l

D X IO9 cmzsec”I

Figure 60

 

36

~ Cs-diffusion

 

.(:> (g) (1.

 

 

L I W
I2 24 96
DIFFUSION TII.‘.E, hrs.

MCI—diffusion

M—{h 0-

 

 

5 IO IS 20 45 5
DIFFUSION TIME, hrs.

Relationship of diffusion time with

the diffusion coefficients of Cs and

Na ions in protonated p-phenylenediamine
saturated vermiculite on samples
equilibrated at 81.0% relative humidity
(20°C). The moisture content of the
sample was 7.4% by.weight.

Figure 7.

37

Relationship of diffusion time with the diffusion
coefficient of Na ion in kaolinite and bentonite
equilibrated at 81.0% relative humidity (20°C).
The moisture contents were 1.3% in K-kaolinite,
1.7% in Na-kaolinite, 6.7% in K—bentonite, and
20.2% in Na-bentonite by weight respectively ;
(1050c).

' D X IO8 cmzeec-I

38'

 

 

 

 

 

 

   

 

    

 

 

 

9._ No-Izoolinite
o O O o—
8%-
4”“ K-- kaolinite
0—0 0 O‘-
3‘...
§
ll-
Ito-bentonite
O
9?-
4L
K—bentonite
~o
2 ..
J L I I _J
5 IO I5 20 25

DIFFUSIOF.‘ TIIJE, hrs,

Figure 7

39
layer and true solution ions and the Stern layer ions were
responsible. Meanwhile he also showed the observed dif—
fusion coefficients of Na, Ba, and Ce decreased with time.
It may be that these results can be explained as resulting

from heterogeneous systems as described here.
The Diffusion Model

Several alterations of the Fisher model have been pub-
lished which basically follow his idea. The grain boundary
is considered as a "sink" from which the diffusant moves
normally to the lattice of the polycrystalline body although
in a very thin region near the exposed surface the ordinary
lattice diffusion is dominant. —At larger penetrations of
the polycrystalline material, the lattice diffusion is no
longer influenced by the exposed surface and the "boundary
sinks" play the crucial role. This is the region of ex-
perimental interest in grain boundary diffusion studies. If
one compares the clay system of Fig.1;A with Fisher's orig-
inal idea, it may be seen that there is a possibility of
adapting this model of a heterogeneous diffusion system to
clay minerals. Even in the very thin region near the exposed
surface, where the proposed mathematical analysis for grain
boundary can not be applied, it is possible to adapt in the
clay system because the diffusant in the interlayers comes
normally from the "sink" of the external surface "channel"
as shown in Fig. 1 A. It is impossible to have the cation

penetrate directly from the exposed surface through the

40
crystal layer into the interlayer space under ordinary tem-
perature conditions. Furthermore, it is seen in grain
boundary diffusion that there is no significant additional
penetration along the grain until B (equation [3]) > 1.
Since the thickness of 6 (equation [3]) of polycrystalline
metals is usually very small, of the order of A, the value
of Db/D£ should be large enough so that B is large in order
that the grain boundary diffusion can be observed. In the
case of clay minerals, 6 is equivalent to the thickness of
the channel formed by the external surfaces as shown in
Fig. 1 A. The value of 6 of clay system in ordinary condi-
tions should be much larger than that of polycrystalline
metals. With the comparison between the heterogeneous sys-
tem of clays and polycrystalline metals, it seems reasonable
to assume that the value of De/Di in clays should be much
less than that of Db/Dz in metals. Because of the larger
value of 6 and with the short time, the heterogeneous dif-
fusion in clay systems is observed as shown in Figs. 4, 5,
and 7.

In 1960 Levine and MacCallum (42) published their modi-
fication of Fisher's model mainly introducing a suitable
empirical function to describe the loss of diffusant from
the high diffusivity "sinks" into the lattice of the poly-
crystalline body. It was based on the observation that, in
the penetration range most Commonly covered in polycrystal-
line diffusion experiments, the log of the average concen-

tration varied as the 6/5 power of penetration depth. A

41
few years later Le Claire (41) rearranged Levine and Mac-
Callum's solution in order to put it in more practical form.
If D6 and Di of clay systems are equivalent to Db and DE

of polycrystalline metals respectively, the following equa-

tion is adapted from Le Claire's report (41)

—5/3 4Di 1/2

_ d 1 d 1 5/3
- gee-o <—-.—> (were an

 

where De = external diffusion coefficient
Di = interlayer diffusion coefficient
c = concentration of diffusing ion

y - penetration depth

t = diffusion time

6 = thickness of the channel formed by the external
surfaces of clay particles

o = Y/(Dit)1/2

B (Deé)/[201(Dit)1/21

According to equation [4], the log of average concentration
varies linearly with the 6/5 power of penetration depth y,
in contrast with the linear correlation with y2 in ordinary
homogeneous systems at a thin-film boundary condition of
Fick's law. For the purpose of verifying heterogeneous dif-
fusion of Na in Na-vermiculite with Levine and MacCallum's
equation, the pellet was sectioned with a microtome at the
accuracy of Sn, and the specific radioactivity of 22Na of
each slice was measured after a given time t was allowed

for diffusion. Figure 8 shows results of comparing the plot

42

Figure 8. Specific activity of 22Na versus penetration
distance (y) for the diffusion of Na ion in
Na-vermiculite at 4 and 24 hours.

SPECIFIC ACTIVITY (spm lmgi

y2 X l03cm.2
I.0 |.5 2.0
I

 

 
   

 

   
 

 

 

3,000 ‘ ‘
2,000r-
_ A. Diffusion
'3000 “met 4- hrs.
500‘-
IOO 1 ‘ '
l.0 l.5 2.0
y6/5 X IO2 cm.
yz. X I03cm.2
0.5 I0 I.5
r I ' I

3,000
2,000

I,OOO‘

500

200

 

  
   

B. Diffusion
time: 24 hrs.

I

 

0.5 l.0 |.5 2.0
y5/5X I02 cm.
Figure 8

44
of log of specific activity of 22Na versus yfi/5 and y2 at
a diffusion time of 4 hours. The linearity of log c versus
ya/£5 reveals the possibility of Levine and MacCallum's
modified model applying to clay systems. By the time of
24 hours for the diffusion of Na ion in Na-vermiculite un-
der these experimental conditions, B becomes so small that
the ordinary homogeneous diffusion plays the dominant role.
Therefore, experimental results as plotted in Fig. 8 indi—
cate that at 24 hours diffusion time, log c varies linearly
with yz, not y6/5. Results obtained at 10 hours diffusion
time indicated lack of complete linearity for both y°/5 and
Y2-

If any two values of De’ Di' and 6 are known, the third
value can be calculated from equation [4], because dlog c/
dye/5 is the slope of a plot of log c ~y6/5 at a certain
time t. To the authorfs knowledge none of the 3 values for
clay systems are available. However, given a certain clay
system under uniform conditions the 3 values, De, Di’ and 6
should be constant. In addition Le Claire (41) has reported

that for practical purposes, when Bvis large (2-10), dlog c/

d(qB_'1/2)6/5 approaches a constant value of 0.78. Then, if B

is in the range of 2-10, equation [4] is written as follows

De6/Di1/2 = (o.78)5/3(§i%§;9)

Diffusion time is the only factor necessary to change in

Wad->1” (5)

order to test the constancy of B under the experimental condi-

tion in this study. If B is constant, then the value of

45
1/2 . . . . .
De6/Di should not change With various diffu51on times.
Following are the experimental results obtained by finding
the slopes of log c ~y6/5 at various diffusion times and

then calculated according to equation [5]

Diffusion time, Hr. De6/Di1/2 x 105
4 1.59 i .18
6 1.61 i .05
8 1.80 i .16

It is seen that for the varying diffusion times above
for Na ion diffusing into Na-vermiculite the constancy of

De' Di’ 6 and B are as described in equation [5].

Evaluation of Diffusion Coefficients in the
Heterogeneous System

As the observed diffusion of Na ion into Na-vermiculite
consists of external and interlayer surface diffusion, the
observed apparent coefficient (Do) is the average contri-
bution from De and Di‘ It is of interest to attempt to eval-
uate those two coefficients in the heterogeneous system. In
a heterogeneous system the observed flux of diffusant along
the concentration gradient is the sum of the flux of the
external surface channel and of the interlayer pathway, and
for the homogeneous system the observed flux is that of ex—
ternal diffusion only. When the heterogeneous clay system
is oriented such that the observed flux is parallel to the

external surface channel as shown in Fig. 1 A, it is less

46

than that in the homogeneous situation because of leakage
perpendicularly to the interlayer positions. As shown pre-
viously De is larger than Di’ the flux in the external sur-
face channel should be larger than that in the interlayer
space. Therefore, in this particular case the observed flux
in the heterogeneous system is the result of movement through
the external pathway modified by leakage to the internal

pathway. For

_ is
Flux - —D dy (6)

where c is the concentration of diffusing ion, y is
the penetration depth and D is the diffusion coefficient,
since only the absolute value of the flux is of interest in

this case, the following equation should be true

dco dce dci ( )
D—=D—--D.—— 7
o dyo e dye 1 dyi

where the subscripts o, e, and i stand for observed, ex-
ternal, and interlayer respectively. For diffusion of Na
ion in Naevermiculite, values of Do’ doc, and dyo can be ob-
tained experimentally. In order to get the values for the
external surface diffusion in the Na-vermiculite system,

the author: prepared a vermiculite system which is collapsed
by K ion yet saturated with Na ion on the exchange sites of
the external surface. The purpose of this was to study Na
diffusion in Na-vermiculite where internal surface had been
eliminated as a diffusion pathway. The Na-K-vermiculite

system was prepared by using the K-vermiculite previously

47

described in this study, and then passing the suspension
of K-clay through a Na-IRC-50 resin column. After column-
ing, the Na-K-vermiculite suspension was freeze dried im-
mediately. The X-ray pattern of this Na-K-clay showed the
spacing of 10.4A.with a little broader peak than that of
K-system. The behavior of homogeneity in diffusion of Na
ion of the Na-K—system was also tested as shown in Fig. 4.
It indicates that it is characterized pretty well as a
homogeneous diffusion system since the Na ion showed little
change in diffusion coefficient with time. An indirect
method was utilized to calculate dci and dyi of equation
[7] and is described in the following section.

N-Methylacetamide (NMA) is a high dielectric constant
organic solvent (165 at 40°C, 19) in which many inorganic
salts are quite soluble, and in which clay minerals can be
suspended as well as in water. After freeze dried Na-ver-
miculite was dehydrated as much as possible by vacuum
pumping, it was suspended in NMA at 40°C (the freezing point
of NMA is 30.6°C) over-night. The Na-vermiculite was found
to be collapsed as indicated by the spacing of 10.1A, al—
though upon exposure to the atmosphere this system gradually
reexpanded as water was absorbed. The radioisotope dilution
method was applied to measure the total exchangeable Na ion
in Na-vermiculite in water suspension with a value found of
141.4 m.e./100 g (the cation exchange capacity of the same
sample measured by ordinary CaClz saturation method was

150.0 m.e /100 g). The same technique was used to measure

48
the amount of Na ion of Na-vermiculite in NMA, it was only
16.6 m.e./100 9. For the purpose of comparing chemical be-
havior of vermiculite in NMA and in water, the absorption
of Cs ion by different systems in those two solvents was
measured by 134Cs tracer technique. The following results

were found.

Absorption of Cs ion at 40°C

m.e./100 g
K-vermiculite in water 26.7
K-vermiculite in NMA 28.6
Na-vermiculite in water 121.5
Na-vermiculite in NMA 29.2

It shows clearly that in K—clay the difference in absorption
of Cs ion between these two solvents is very small. The
great difference between the two solvents for.the Na—system
is due to the fact that Na-vermiculite is collapsed in NMA.
so that the absorption of Cs ion is limited mainly to ex-
ternal surface, and behaves in a manner similar to the col—
lapsed K-system. The value of 141.4 m.e./100 g is considered
as total exchangeable Na ion for Na—vermiculite, and that
of 16.6 suggested as the amount of Na ion on the external
surface only. The percentage of exchange sites for Na ion
in the interlayer space of Na-vermiculite can then be calcu-
lated as [(141.4 - 16.6)/141.4] x 100 - 88.3%.

After the diffusion of Na ion proceeded for 6 hours,

Specimens of Na-vermiculite and of Na-K-vermiculite were

49

sectioned and specific activity of 22Na was determined as
described previously. The values of Do and De were measured
from Na- and Na-K-clays respectively, and the values of dco,
dyo, dce, and dye were read from the plots of log c versus
penetration depth. The value of dci was calculated from
dcO based on the value of 88.3% of interlayer exchange sites
in comparison with the total sites of the system. It was
assumed that at any point in the system, the diffusing Na
was distributed between the external and internal exchange
sites in proportion to the relative distribution of external

and internal exchange sites. All the experimental and

calculated values were then put into equation [7] as follows

 

-a 85.§ a -s 45.3 _ 75.3
1.10 x 10 x 0.03 3.01 x 10 x 0.03 Di x 0.03 (8)

- -1

The value found for Di was 0.57 x 10 8 cm2 sec . For
diffusion of Na ion in Na-vermiculite in these experimental
conditions, the ratio of De/Di is then 3.01 x 10-8 cmzsec-l/

0.55 x 10" cm2 sec-1 = 5.28.

V. ORIENTATION EFFECTS
Theoretical Considerations

Cationic diffusion in the clay minerals with very low
moisture content is suggested to be a movement along the
surface. Figure 9 shows diffusion pathways on the surface
of a platelet seen edgewise and oriented at an angle 9 with
respect to the diffusion flux in the y direction. As
shown in Fig. 9, ED is the width (w) of the particle, AB
the height (h), and o the angle between diagonal BC and
width BD. When only the geometry factor is considered, the

following mathematical manipulations are easily seen from

Fig. 9:
BC = (w2 + h2)1/2 (9)
y - BE - BC cos (a - o) (10)
y = (w2 + h2)1/2 cos (ew- ¢) (11)

Since the mean square displacement (APZ) of diffusion at
time t is (34)

AP2 = 2Dt (12)
When the diffusion time t zis constant, equation [12] may
be written as

D = kAP2 (13)
where k is a constant. If y in Fig. 9 is a displace-
ment of diffusion atha certain diffusion time t, as y2 = AP2

the following equation is obtained:

50

Figure,9.

 

51 ‘

 

Model used for analysis of diffusion
pathways on the surface of a platy
particle seen edgewise and oriented

at an angle a with respect to the
diffusion flux.

. 52

D = k(w2 + hz) cos2 (6 - 0) (14)
For a definite particle size, w and h are constant,
equation [14] may be shown as

D - k' cos2 (6 — ¢) (15)
where k' is another constant representing k(w2 + h”)
of equation [14] If plots of D versus cos2 (6 - ¢) are
made, a straight line should result.

Mathematically the following relation between the three
angles which any straight line makes with the coordinate
axes is known

cos2 d + cos2 B + cos2 y = 1 (16)
where o. B, and y are the angles which the given line makes
with the axes x, y, and 2 respectively. If the true dif—
fusion coefficients are the same in all the axes but the
apparent diffusion coefficients are dissimilar in the dif-
ferent directions due to geometry factors, then the equation
is

Dofiy = Do cos2 a + D5 cos2 B + Dy cos2 y (17)

where Do is the total resulting coefficient, and Do' D

63/ {5'
and Dy are the component diffusion coefficients along the
three corresponding axes. If the diffusion is in a plane
which is expressed with the ordinary cartesian coordinate
system, then in equation [17], y = 90°, o + B = 90°, say

B = 90° - o. and equation [17] may be written as

= 2 ' 2
DoB Do cos a + DB sin a (18)

This general equation can be applied to the condition

53
as shown in Fig. 9. Suppose Fe is the resulting diffusion

flux along BE with apparent diffusion coefficient D9,
the component fluxes Fw along BD (w) with Dw and Fh

along BA (h) with Dh’ respectively: and suppose Fw is

larger than Fh. It is seen that D is equivalent to

9
to D , and e to a, respectively: and thus

oB’ h B

equation [18] becomes

D DW tO Da, D

= 2 ' 2
D9 Dw cos 9 + Dh Sin 9. (19)
This equation also describes the relationship that exists

between the diffusion coefficients parallel and perpendicular

to the c—axis of the lattice of noncubic metal crystals (72).
Effect of Orientation on Diffusion

Figure 10 shows the apparent diffusion coefficients of
Na ions into K-vermiculite pellets at 20° 1 0.05°C under
81.0% relative humidity at various angles of 6. It shows-
that the apparent diffusion coefficients vary non-linearly
with cos” 9. If the vermiculite flakes are perfectly
oriented as shown in Fig. 2, the angle 9 in Figs. 2 and 9
should be the same. According to equation [15] the appar-
ent diffusion coefficients vary linearly with cos” (6 - ¢).
D and 6 in equation [15] were experimentally found, and
¢ could be found by trial-and-error method to fulfill
equation [15]. For 2 - 5n K-vermiculite used in this study
the ¢ was found to be 10°, and that of < 2u was 6°, the
resulting straight lines as shown in Fig. 10. The angle ¢

can be used to calculate the axial ratio (width:height) of

Figure 10.

54

Relationship of cos” 9 and cos” (6 - 0) with
the diffusion coefficient of Na ion in K-
vermiculite oriented at various angles of 6
with respect to the diffusion flux and equi-
librated at 81.0% relative humidity (20°c).

The moisture contents of 2-5u and < 2n part-
icles of K-vermiculite were 3.9 and 3.6% by
weight respectively (105°C).

D X IO7 cmz sec"

 

0 0 I2 0'4 O;6 0&8 I10
. ’/’O
’z’6 O

 

PARTICLE SIZE:

 

 

 

 

 

2-5p
0.8 110
053 I'O
,,o
2.0“ ’,—o"o/
e
©0§:”6/
’/O’O Q‘s O
,0- ,,o"o Mod) _ PARTICLE SIZE:
' / 005 ‘ ’ (21”
//’ I
Q: L 1 1 J
0 02 04 05 08 IO
cosz(o 0)

56
the platelet from which the "true" diffusion coefficient
can be evaluated. This will be discussed later in this
study.

If the angle 9 in Figs. 2 and 9 is the same as mentioned
in the above section, from equation [19] the values of Dw
and Dh can be calculated from D6 and 6 which are experi-
mentally measurable. Meanwhile, when 9 of Fig. 2 is oriented
at either 0° or 90° experimentally, these two observed
diffusion coefficients are assumed equivalent to Dw and Dh
of equation [19]. Table 1 shows both observed values of Dh
and Dw at 90° and 0° respectively and calculated re-
sults at various intermediate values of 6. It is apparent
that the calculated values are very close to the observed

values for both Dw and Dh' with both 2-5u and < 2n part-

icles of K-vermiculite.
Orientation Effects in Heterogeneous System

Both equations [15] and [19] are derived on the basis
that there is external surface diffusion only, thus this
system should be homogeneous. The K-vermiculite has the
homogeneous property as shown in Fig. 4. From Fig. 10
and Table 1 it is apparent that this homogeneous system fol-
lows equations [15] and [19]. It is of interest to see the
application of these two equations to a heterogeneous dif-
fusion system. As indicated in Fig. 4, the Na-vermiculite
has shown heterogeneous behavior. The effect of orientation

on the diffusion of Na ion in clay size Na-vermiculite was

57

Table 1. Observed diffusion coefficients of Na ion in K-
vermiculite oriented at angle 6 = 90° (D ) and 0°
(D ) with respect to the diffusion flux 8nd calcu-
laEed results at various intermediate values of 9.

 

 

9 De x 107 Dh x 107 Dw x 107
(cm” sec-1) (cm” sec-1) (cm” sec-1)
Particle size: 2-5u
0 1.22*
90 0.31*
22.0 1 11* 0.53** 1.20**
47.5 0.84* 0.37** 1.23**
57.0 0.73* 0.35** 1.42**
Particle size: < 2n
0 2.21*
90 0.45*
22.5 1.97* 0.69** 2.19**
48.5 1.35* 0.43** 2.52**
57.0 1.05* 0.56** 2.21**

 

*Experimentally observed values.

**
Calculated values from simultaneous equations based
on equation {19].

58
measured the same way as that of K-vermiculite. Figure 11
shows the results which the apparent self-diffusion coef-
ficients of Na ion in vermiculite versus cos” 6 is plotted.
When Fig. 11 is compared with Fig. 10, the differences are

/

apparent. In Fig. 10 with K-vermiculite, theeD versus

cos” 6 has a convex curvature, so thet a D versus cos”(6 - ¢)
resulting in a straight line as described in equation [15]
can be found. With Na-vermiculite as shown in Fig. 11 it

is a concave curve from which the angle ¢ cannot be ob-
tained as in K-vermiculite. It appears that the equation

[15] cannot be directly applied to the heterogeneous Na—

vermiculite system as in the case of homogeneous K-vermicu-

lite.
Equation [19] was also used.to calculate Dh and Dw from
different values of D6 to compare the observed Dh and Dw

in Na-vermiculite as in K—vermiculite. The results are
shown in Table 2. When Table 2 is compared with Table 1,
it is seen that for the Na-vermiculite system, the calcu-
lated results at various angles of 9 are not in as good
agreement with the observed data at 0° and 90° as in the

K-vermiculite systems.
Evaluation of True Diffusion Coefficient

Cationic diffusion in clay minerals at very low moisture
contents is mainly controlled by the nature of the dif—
fusing cation, electrochemical interactions of this cation

with the clay mineral, and the tortuosity factor. The first

'o
I

I

D X I08 cm2 sec-l
O

 

Or—

Figure 11.

59 I

O/

l l l

0.2 0.4 0.6 0.8 I.0
cos2 0

U

I I

Relationship of cos2 6 i with the diffusion

_coefficient of Na ion in Na-vermiculite

oriented at various angles of‘e with respect
to the diffusion flux and equilibrated at
81.0% relative humidity (20°C).

60

Table 2. Observed diffusion coefficients of Na ion in Na-
vermiculite oriented at angle 6 - 90° (D ) and
0° (D ) with respect to the diffusion flax and
calchated results at various intermediate values

 

 

of 9.
D x 108 D x 108 D x 108
9 9 h 1 w
(cm” sec-1) (cm” sec- ) (cm” sec-1)
O 1.18*
90 0.18*
22.0 0.86* 0.26** 0.79**
47.5 0.50* 0.19** 0.97**
60.0 0.39* 0.09** 0.99**

 

*-
Experimentally observed values.

*9?
Calculated values from simultaneous equations based
on equation [19].

61
two effects may be considered as the factors affecting the
"true" diffusion coefficient in a particular clay mineral
system. Most experimentally observed diffusion coefficients
are apparent values which include the tortuosity effects.
For unconsolidated systems some mathematical equations have
been worked out to solve the tortuosity problems (12,40,50).
Cremers and Thomas (16) applied a "formation factor" equa-
tion in the study of self-diffusion of Na ion in a suspen-
sion of montmorillonite, and Cremers and Laudelout (17) used
the same equation in measuring surface mobilities of several
cations in montmorillonite gels. In consolidated systems
cationic movement occurs through tortuous paths and channels
which can hardly be classified and described mathematically.
Because of the complexity of these geometry factors, only
some empirical correlations are available (49).

If a homogeneous diffusion system such as the diffusion
of Na ion in K-vermiculite has only one "true" diffusion
coefficient, the various apparent coefficients observed at
different orientation angles (De, Dw' and Dh) as shown in
the previous results must mainly be due to tortuosity ef-
fects. The orientation effects could be then applied in
evaluating the "true" diffusion coefficient in a particular
system. Based on this assumption, the evaluation is pro-
posed in the following section.

Great difficulties exist in the direct measurement of
the "true" diffusion coefficient (Dt) of cations on a clay

mineral surface. If the formation factor (F) is known, the

62
true coefficient can be calculated from the experimentally

observed value (DO) as D = F Do' Although the formation

t
factor is not available for consolidated media, such as clay
pellets in this study, some other value relating to a forma-
tion factor may be worked out.

The formation factor is a function of effective area
and porosity (50). If in a given medium the porosity is
constant, the formation factor relates only to the effective
area. On the other hand, when the diffusion process is
treated macroscopically, the net flow of ions per second
over a plane of unit area at a certain point is the product
of the diffusion coefficient times the concentration gradi-
ent along the direction of flow resulting in the general
equation (80):

m- d_c
dt - -D dy (20)

.1.
A
where dN refers to a net flow of ions through area A at a
time interval dt, and dC/dy is the concentration gradient.
It shows that the diffusion coefficient is inversely pro-

portional to area, when other conditions are equal. There-

fore, it is easily seen that the following relationship holds:

Dtp - A0 2
D - K— ( 1)
0 e

where Dtp means the "true" diffusion coefficient in a medium
with effective area Ae at a given porosity condition, and
D0 is the observed apparent coefficient with observed total

diffusion area A0 at the same porosity condition. When the

63

angle 9 (Fig. 9) is at 0° only the area along the width

(w) of the particle, which is parallel to the diffusion
flux, contributes to the effective area. On the other hand,
the area along the height (h) which is perpendicular to

the flux makes no contribution. As the angle 6 changes to
90° the opposite is true, the area along the height of the
particle is effective, and not that along the width. There-
fore, the effective diffusion area of the same particle
changes with the variations of angle 6 (Fig. 9), and the

effective area may be calculated as follows:

6° Effective area
0 Ae = w x b
90 A = h X b

e

where w, h, and b are the width, height, and length of the
particle respectively. When 6 is either 0° or 90°, the ob-
served total diffusion area may include two portions: one
is the area parallel to the diffusion flux and another is
that perpendicular to the flux, and the conditions of ionic
movement in these two areas may not be the same. When the
angle 6 = 0°, the flux direction is parallel to the width
and when 6 = 90°, it is parallel to the height of the par-
ticle. In the above conditions the resulting direction of
the flux is uni-directional, although basically each ion in
the diffusion process moves randomly from one position to
another. When ions move in the area perpendicular to the
direction of diffusion flow, such as when they move in the

area along the height of the particle in case of 6 = 0° and

64
that of width in case of e = 90°, it is considered as two-
directional movement. In this situation, the average dif-
fusion area is half of the physical dimension. The above
develOpment relates to Barrer's (4) discussion of infinite
and semi-infinite systems. Therefore, the observed total

diffusion area may be calculated as follows:

6° Total diffusion area
0 A0 = (w + h/2) x b
90 A0 = (h + w/2) x b

Suppose R is an effective diffusion area factor which is
the ratio of effective area to the observed total diffusion
area (Ae:AO), then equation [21] is written as

Dtp = l/R x Do' (22)

The effective area factor R of the same particle also

changes with the variations of angle 9, it follows:

 

 

9° Effective.area factor"
Ae w x b w
0 R ' 52" (w'+ h72) x b ' w + h72 (23)
A g.
_._e _ h x b = h "
9° R ' A0 (h + w/2) x b h + w 2 (24)

The actual values of w and h of the particle may not

be easily determined: however, the ratio of w:h can be
obtained from this study. From equation [15] the angle ¢
of K-vermiculite used in this study was found to be 10°

for 2-5u, and 6° for < 2u particles. The width:height
ratios were then 5.7:1 and 9.5:1 respectively. These ratios

may not be exactly the physical dimension of the K-vermiculite

65
particles because they are calculated from data obtained
from the diffusion process, but may be considered as an
"effective diffusion dimension". This may be the reason
that these ratios do not agree well with the results re-
ported by Raman and Mortland (69), in which the ratios were
calculated from surface area data obtained from the B.E.T.
equation. The width:height ratios obtained in this study
may be applied better in evaluation of the effective area
factor. When the experimentally obtained w:h ratio is ap-
plied to calculate the effective area factor as shown in
equations [23] and [24], the Dtp can be then calculated
from the experimentally observed diffusion coefficient (Do)
according to equation [22]. The calculated values of Dtp
and R, the experimentally obtained data of w:h and DO at
angle 9 = 0° and 90°, and also the apparent density of the
pellets of both 2-5u and < 2n particles of K-vermiculite,
are listed in Table 3. It shows that for both 2-5u and

< 2n particles the two calculated values of'D , from Do

tp
at e = 0° and 90°, agree rather well.

Formation factor relates both effective area and poro-
sity. Here only the effective area factor is evaluated.
Even though the pellets of two kinds of particle sizes,
2-5u and < 2n, of K-vermiculite were prepared the same way
by pressing in a die under 1,000 pounds per square inch
pressure, the apparent density of the pellet of 2-5u particles

was smaller than that of < 2n particles as shwon in Table 3.

The porosity of these two kinds of Specimens should then be

66

Table 3. Values of width:height ratio (w:h), effective
area factor (R), observed (D ), and "true"
diffusion coefficients (Dt )Oof Specimens ori-
ented at angle 9 - 0° and p90° with reSpect to
the diffusion flux of Na ion in two different
particle sizes and apparent densities of K-
Vermiculite pellets.

 

 

7 7
6 w:h R Do x 191 DE? x E?

(cmgsec ) (c sec )

Particle size: 2-5u Apparent density: 1.79 g/cc
0 5.7:1 0.919 1.22 1.33
90 5.7:1 0.260 0.31 1.19

Particle size: < 2n Apparent density: 1.87 g/cc
0 9.5:1 0.950 2.21 2.33

90 9.5:1 0.174 0.45 2.58

 

67

different. The effects of porosity on diffusion include
the factors of size, shape, and unit number of pores. For
consolidated media, no matter which factors (Size, shape,
and unit number of pores) affect the diffusion, the overall
influence will be the distance between the particles, or

in other words, the compactness of the diffusion specimen.
When all other conditions are the same, the more compact
the specimen, the faster the diffusion rate. This observa-
tion was made by Graham—Bryce (32) and Phillips and Brown
(63,64) who also found that the cationic diffusion coef-
ficients increased with increasing bulk density. For ex-
ample, in a given soil, as the bulk density increased from
1.34 to 1.64 g/cc at 21°C, the Rb ion diffusion coefficient

8 to 8.1 x 10.8 cm sec.1 (32). In

increased from 1.8 x 10-
these two papers, they both attempted to explain the ef-
fect of bulk density on diffusion based on the basis of
"hopping distance" (which has the same physical meaning

as jump distance (72), that is used in the modern termin-
ology in diffusion) as reported by Lai and Mortland (37,
38). The increase of clay content and bulk density resulted

in a shorter average "jump distance" between particles, and

the overall? result is the increase of diffusion rate.

VI. CONCLUSIONS

1. This study shows that at least two cationic dif-
fusion pathways are possible in clay minerals at very low
moisture content. For 1:1 clay minerals which have ex-
ternal surface only, and collapsed or clogged 2:1 minerals
where the cation cannot move into the interlayer space,
there is only one pathway and may be considered as a homo-
geneous system. The expanded 2:1 clay minerals are hetero-
geneous diffusion systems in which cationic movement can
take place along external surfaces and through the inter—
layer regions of the minerals.

2. In these particular experiments the diffusion coef-
ficient of Na ion on the external surface of Na-vermiculite
was about 5 times larger than in the interlayer surface.
The much greater magnitude of Na diffusion in the homo-
geneous system (Na—K-vermiculite) compared with that of Na
into the heterogeneous system (Na-vermiculite) is easily
explained by the above results.

3. There are two basic assumptions on the application
of equations [15] and [19] to the cationic diffusion in
clay minerals: (i) the system should have an external sur-
face diffusion pathway only, and (ii) the diffusion Specimen
should be perfectly oriented. Because of the homogeneity
of the diffusion pathway of K—vermiculite, experimental re-
sults show that the diffusion of Na ion in these systems,
both 2-5u and < 2n particles, conformed with equations

[15] and [19]. 68

69

4. The preparation of the clay pellets resulted in a
high degree of orientation of the clay platelets. The ob-
served values of diffusion coefficients of Na ion in K-ver-
miculite showed considerable difference between specimens
oriented at 0° and 90° with respect to the direction of
diffusion flux. The calculated "true" coefficients in a
given size particle system agreed very closely. however,
regardless of direction of diffusion. This supports the
homogeneous nature of cationic diffusion in K-vermiculite.

5. The diffusion of Na ion in Na-vermiculite, a
heterogeneous diffusion system, did not Show conformity with
equations [15] and [19]. Based on this and other results
from this investigation, it suggests that cationic diffusion
studies in clay minerals must consider the nature of the
system and whether or not it has homogeneous or heterogeneous

properties.

 

10.

11.

12.

13.

L ITERATURE C ITED

Allen, G. F., Schurig, H., Slade, L., and Thomas, H.C.
1963. Development of a method for measuring ionic
self-diffusion. J. Phys. Chem. 67:1402-1407.

Barber, S. A. 1962. A diffusion and mass flow con-
cept of soil nutrient availability. Soil Sci. 93:39-49.

Barber, S. A., Walker, J. M., and Vasey, E. H. 1963.
Mechanism for the movement of plant nutrients from the
soil and fertilizer to the plant root. J. Agr. and
Food Chem. 11:204-207.

Barrer, R. M. 1941. Diffusion in and through Solids.
Cambridge Univ. Press, London.

Bear, F. E. 1964. Chemistry of the Soil. 2nd Ed.
Reinhold Publishing Corp., New York.

Bloksma, A. H. 1957. The diffusion of sodium and
iodide ions and of urea in clay pastes. J. Colloid
Sci. 12:40-52.

Bouldin, D. R. 1961. Mathematical description of dif-
fusion processes in the soil-plant system. Soil Sci.
Soc. Amer. Proc. 25:476—480.

Boyd, G. E., Adamson, A. W., and Myers, L. 8., Jr.
1947. The exchange adsorption of ions from aqueous
solutions by organic zeolites. II. Kinetics. J.
Amer. Chem. Soc. 69:2836-2848.

Boyd, G. E., and Soldano, B. A. 1953. Self diffusion
of cations in and through sulfonated polystyrene cation-
exchange polymers. Ibid. 75:6091—6099.

Bray, R. H. 1954. A nutrient mobility concept of soil—
plant relationships. Soil Sci. 78:9-22.

Brown, D. A., Fulton, B. W., and Phillips, R. E. 1964.
Ion diffusion: I. A quick-freeze method for the measure-
ment of ion diffusion in soil and clay systems. Soil
Sci. Soc. Amer. Proc. 28:628-632.

Carman, P. C. 1956. Flow of Gases through Porous Media.
Butterworths, London.

Chaussidon, J. 1965. Mobilities of cations in soils
and clays at very low moisture content. ;Q_Plant Nu-
trient Supply and Movement. Interl. Atomic Energy
Agency, Vienna. Tech. Rep. No. 48:36-42.

70

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

71

Cloos, P., and Mortland, M, M. 1964. ~Apparatus for
electrical conductivity measurements of clay plugs in
corrosive gases and at low temperatures. Soil Sci.
Soc. Amer. Proc. 28:719-720.

'Crank, J. 1956. The Mathematics of Diffusion. Oxford

Univ. Press, London.

Cremers, A., and Thomas, H. C. 1966. Self-diffusion
in suspensions. Sodium in montmorillonite at equi-
librium. J. Phys. Chem. 70:322973234.

Cremers, A. E., and Laudelout, H. 1966. Surface
mobilities of cations in clays. Soil Sci. Soc. Amer.
Proc. 30:570-576.

Dakshinamurti, C. 1965. Ionic migration in soils and
clays. ;p_ Plant Nutrient Supply and Movement. Interl.
Atomic Energy Agency, Vienna. Tech. Rep. No. 48:57-71.

Dawson, L. R., Sears, P. G., and Graves, R. H. 1955.
Solvents having high dielectric constants. II. Solu-
tions of alkali halides in N-methylacetamide from 30-
60°. J. Amer. Chem. Soc. 77:1986-1989.

de Boer, J. H. 1953. The Dynamical Character of Ad-
sorption. Oxford Univ. Press, London.

Dutt, G. R., and Low, P. F. 1962. Diffusion of
alkali chlorides in clay-water systems. Soil Sci.
93:233-240.

Evans, S. D., and Barber, S. A. 1964. The effect of
cation-exchange capacity, clay content, and fixation
on rubidium-86 diffusion in soil and kaolinite systems.
Soil Sci. Soc. Amer. Proc. 28:53-56.

Evans, S. D., and Barber, S. A. 1964. The effect of
rubidium-86 diffusion on the uptake of rubidium-86 by
corn. Ibid. 28:53-56.

Fayed, L. A. 1966. ~x-ray diffraction study of ori-
entation of the micaceous minerals in slate. Clay
Minerals 6:333-340.

Fisher, J. C. 1951. Calculation of diffusion pene-
tration curves for surface and grain boundary diffusion.
J. Appl. Phys. 22:74-77.

Fletcher, G. E., and Slabaugh, W. H. 1960. Self-
diffusion of calcium ions in Ca-montmorillonite gels.
J. Colloid Sci. 15: 485—488.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

72

Gast, R. G. 1962. An interpretation of self-diffusion
measurements of cations in clay—water systems. Ibid.
17:492-500.

Girifalco, L. A. 1964. Atomic Migration in Crystals.
Blaisdell Publishing Co., New York.

Graham-Bryce, I. J. 1963. Self-diffusion of ions in
soil. I. Cations. J. Soil Sci. 14:188-194.

Graham-Bryce, I. J. 1963. Self-diffusion of ions in
SO11. II. Anions. Ibid. 14:195-200.

Graham-Bryce, I. J. 1963. Effect of moisture content
and soil type on self diffusion of Rb-86 in soils.
J. Agric. Sci. 60:239-244.

Graham-Bryce, I. J. 1965. Diffusion of cations in
soils. 22. Plant Nutrient Supply and Movement. Interl.
Atomic Energy Agency, Vienna. Tech. Rep. No. 48:42-56.

Husted, R. F., and Low, P. F. 1954. Ion diffusion in
bentonite. Soil Sci. 77:343-353.

Jost,.W. 1960. Diffusion in Solids, Liquids, Gases.
Academic Press, New York.

Klute, A., and Letey, J. 1958. The dependence of
ionic diffusion on the moisture content of nonadsorb-
ing porous media. Soil Sci. Soc. Amer. Proc. 22:
213—215.

Lai,.T. M., Juang, T. C., and Chang, C. H. 1961. Dif-
fusion of Sr-90 and Cs-137 in soils. Proc. 4th Conf.
RadioisotOpes, Tokyo, Japan. 1127-1135.

Lai, T. M., and Mortland, M. M. 1961. Diffusion of
ions in bentonite and vermiculite. Soil Sci. Soc.
Amer. Proc. 25:353-357.

Lai, T. M., and.Mortland, M. M. 1962. Self-diffusion
of exchangeable cations in bentonite. Clays and Clay
Minerals, 9:229-357.

Lai,.T. M., Fang, I. J., and Shieh, T. S. 1964. Root
surface absorption zone as related to diffusion of im-
mobile ion in soil. Rep. Taiwan Sugar Exp. Sta. 35:
91-106.

Laudelout, H., and Cremers, A. E. 1965. Tortuosity
effects in clay gels. 13_ Plant Nutrient Supply and
Movement. Interl. Atomic Energy Agency, Vienna, Tech.
Rep. No. 48:90-92.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

73

Le Claire, A. D. 1963. The analysis of grain boundary
diffusion measurements. Brit. J. Appl. Phys. 14:
351-356.

Levine, H. S., and MacCallum, C. J. 1960. Grain
boundary and lattice diffusion in polycrystalline
bodies. J. Appl. Phys. 31:595-599.

Lewis, D. G., and Quirk, J. P. 1962. Diffusion of
phOSphates in soil. Trans. Joint Meeting Comm. IV &
V Interl. Soc. Soil Sci. 132-138.

Lewis, D. G., and Quirk, J. P. 1967. Phosphate dif-
fusion in soil and uptake by plants. I. Self-diffusion
of phOSphate in soils. Plant and Soil 26:99-118.

Lewis, D. G., and Quirk, J. P. 1967. PhOSphate dif-
fusion in soil and uptake by plants. II. Phosphate
uptake by wheat plants. Ibid. 26:119-128.

Longsworth, L. G. 1947. Experimental tests of an
interference method for the study of diffusion. J.
Amer. Chem. Soc. 69:2510-1516.

Low, P. F. 1961. Physical chemistry of clay-water
interaction. lp_ Advances in Agronomy 13:269—327.

Mahmound, K. A., and Kamel, R. 1958. Tracer diffusion
of cadmium 115 in pure cadmium. IE. Extermann, R. C.
(Ed.) 1958. RadioisotOpes in Scientific Research
1:271-278.

Meredith, R. E. and Tobias, C. W. 1962. Conduction
in heterogeneous systems. gp| Advances in Electro-
chem. and Electrochem. Eng. 2:15-47.

Millington, R. J., and Quirk, J. P. 1964. Formation
factor and permeability equations. Nature 202:143-145.

Mokady, R. S., and Low, P. F. 1966. ~Electrochemical
determination of diffusion coefficients in clay—water
systems. Soil Sci. Soc. Amer. Proc. 30:438-442.

Mokady, R. S., and Low, P. F. 1967. Simultaneous
movement of water and salt throu h Clays. I. General
experimental methods. (In press .

Mokady, R. S., and Low, P. F. 1967. Simultaneous
movement of water and salt through clays. II. Results
and discussion. (In press).

Mortland, M. M. 1961. Influence of some organic salts
on the absorption of potassium by vermiculite. Nature
192:481-482.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

74

Mortland, M. M. 1966. Urea complexes with montmoril-
lonite: An infrared absorption study. ’Clay Minerals
6:143-156.

Mortland, M. M., and Ellis, B. 1959. -Release of fixed
potassium as a diffusion controlled process. Soil Sci.
Soc. Amer. Proc. 23:363-364.

Nye, P. H. 1966. The measurement and mechanism of
ion diffusion in soil I. The relation between self—
diffusion and bulk-diffusion. J. Soil Sci. 17:16-23.

Olsen, S. R., Kemper, W. D., and Jackson, R. D. 1962.
PhOSphate diffusion to plant roots. Soil Sci. Soc.
Amer. Proc. 26:222-227.

Olsen, S. R., Kemper, W. D., and Van Schaik, J. C.
1965. Self-diffusion coefficients of phOSphorus in
soil measured by transient and steady-state methods.
Ibid. 29:154-158.

Olsen, S. R., and Watanabe, F. S. 1963. Diffusion of
phosphorus as related to soil textrue and plant uptake.
Ibid. 27:648-653.

Patil, A. S., King, K.-M., and Miller, M. H. 1963.
Self diffusion of rubidium as influenced by soil'
moisture tension. Canad. J. Soil Sci. 43:44-51.

Phillips, R. E., and Brown, D. A. 1964. Ion dif-
fusion II. Calculation and comparison of self- and
counter-diffusion coefficients. Soil Sci. Soc. Amer.
Proc. 28:758-763.

Phillips, R. E., and Brown, D. A. 1965. Ion diffusion
III. The effect of soil compaction on self diffusion
of Rb86 and Sr39. Ibid. 29:657-661.

Phillips, R. E., and Brown, D. A. 1966. Counter dif-

fusion of Rb86 and Sr89 in compacted soil. J. Soil
Sci. 17:200-211.

Place, G. A., and Barber, S. A. 1964. ~The effect of
soil moisture and rubidium concentration on diffusion
and uptake of rubidium-86. Soil Sc. Soc. Amer. Proc.
28:239-243.

Porter, L.~K., Kemper, W. D., Jackson, R. D., and

.Stewart, B. A. 1960. Chloride diffusion in soils as

influenced by moisture content. Ibid. 24:460-463.

Prokhorov, V. M. 1965. Relationship between the dif-
fusion rate of strontium 90 and soil moisture content.
Soviet Soil Sci. 1184-1186.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

75

Prokhorov, V. M., and Frid, A. S. 1966. Influence
of humus on the diffusion rate of strontium-90 in
quartz sand. Ibid. 303-305.

Raman, K. V., and Mortland, M. M. 1966. External
specific surface area of vermiculite. Amer. Min.
51:1787-1792.

Sawhney, B. L. 1966. Kinetics of cesium sorption by
clay minerals. Soil Sci. Soc. Amer. Proc. 30:565-569.

Schofield, R. K., and Graham-Bryce, I. J. 1960. Dif-
fusion of ions in soils. Nature 188:1048-1049.

Shewmon, P. G. 1963. Diffusion in Solids. McGraw-
Hill Book Coy New York.

Thomas, H. C. 1956. A new method for the measurement
of self-diffusion. Proc. Natl. Acad. Sci. 42:909-913.

Vaidyanathan, L. V., and Nye, P. H. 1966. The measure-
ment and mechanism of ion diffusion in soils II. An
exchange resin paper method for measurement of the
diffusive flux and diffusion coefficient of nutrient
ions in soils. J. Soil Sci. 17:175-183.

van Schaik, J. C., Kemper, W. D., and Olsen, S. R. 1966.
Contribution of adsorbed cations to diffusion in clay-
water systems. Soil Sci. Soc. Amer. Proc. 30:17-22.

Vasey, E. H., and Barber, S. A. 1963. Effect of
placement on the absorption of Rb86 and P32 from soil
by corn roots. Ibid. 27:193-197.

Wajda, E. S. 1954. Grain boundary self-diffusion in
zinc. Acta Met. 2:184—187.

Walker, G. F. 1959. Diffusion of exchangeable cations
in vermiculite. Nature 184:1392-1393.

Walker, J. M., and Barber, S. A. 1961. Ion uptake by
living plant roots. Sci. 133:881-882.

Wert, C. A., and Thomson, R. M. 1964. Physics of
Solids. McGraw-Hill Book Co., New York.

Whipple, R. T. P. 1954. Concentration contours in
grain boundary diffusion. Phil. Mag. 45:1225-1236.

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