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III. Diffusion of Adsorbed Ions in Soil Clays and Clay-Type Minerals

III. Diffusion of Adsorbed Ions in Soil Clays and Clay-Type Minerals

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P. H. NYE



230



1 , Micas and Vermiculites



The self-diffusion coefficients of ions in mica and vermiculite minerals are

shown in Table I. In these experiments the ion exchanges with its own isotope,

and the interlayer spacing does not change during the exchange. Many experiments have also been made on the release of ions from micas and vermiculites.

Although these reactions are undoubtedly controlled in part by the rate of diffusion of the interlayer ions in exchange for different ions in the surrounding

solution, the c-axis spacing changes simultaneously, and the interpretation of the

measurements is uncertain.

Clearly, the main factor influencing the diffusion coefficient is the interlayer

spacing. For the unexpanded potassium illite studied by de Haan et al. (1965),

the value of D lod2'm2/seccorresponds to a penetration of only about 0.3 nm,

or the diameter of one ion in a year. Of the different cation forms of a dioctahedral vermiculite studied by Graf et al. (1968), the Rb and Cs forms are unexpanded, and their self-diffusion coefficients were too low to measure. The Ba

and Sr forms, with a c-axis spacing of 1.24-1.23 nm, corresponding to one molecular layer of water between the sheets, yielded values of D 10-'7-10-16m 2/seC.

The Ca and Mg forms with a c-axis spacing of 1.5-1.4 nm, correspondingto two

molecular layers of water, gave values of D

10-'5-10-'6 m2/sec. For other

vermiculites containing two water layers, greater mobilities have been reported.

Keay and Wild (1961) found D = ( 1.3-4.5) x lo-" mYsec for the self-diffusion

of Ba in six different minerals, and Lai and Mortland (1968) found D = 6.1 X

m2/secfor Na vermiculite. The difference in these results may be caused by

the structure of the octahedral layer. In the trioctahedral forms the 0 - H bond near

the center of the hexagonal network of tetrahedrally coordinated silicon atoms is

directed along the c-axis. In the dioctahedral forms the direction of the 0-H

group is altered; consequently, a cation in the interlayer will be less shielded by

the proton from the negative 0 atom, and will occupy a more stable position.

Rausell-Colom et al. (1965) have offered this explanation for the relative stability of dioctahedral micas to weathering.

The interlayer .water in expanded (1.4-1.5 nm) vermiculite has an ordered

structure (Walker, 1956; Barshad, 1949; Bradley and Serratosa, 1960) in which

it surrounds the interlayer ions between the aluminosilicate layers. It is therefore

to be expected that the activation energy for diffusion will be greater than that for

ions in solution, which is about 17 M/mole. Keay and Wild (1961) determined

activation energies of 46 kJ/mole for Na self-diffusion in Na vermiculite. When

Na replaced divalent (Mg, Ca, Sr, Ba) cations, the activation energy was 37

kJ/mole, but for the reverse reaction the activation energy was 56 kJ/mole. In

both forms the spacing corresponded with two molecular layers of water, and the

difference is the increase in enthalpy in the change from the Na to the divalent

form. Walker (1959) determined an activation energy of 50 M/mole for diffusion



-



-



-



TABLE I

Self-Diffusion Coefficients of Interlayer Ions in Mica and Vermiculite



System



Ion



Temperature



D



c-axis spacing

(nm)



(m Z/sec)



Activation

energy

(kJ/mole)



References



__________~



lllitic subsoil (< 2-pm

fraction)



K



Laboratory



Dioctahedral vermiculite

5-20 pm CEC 2.29



Rb

cs

Ba

Sr



25°C



mqk



Vermiculites 3.6-mm

diameter



Ba



CEC 1.1-1.6 mq/g



Na



Montana vermiculite

(< 2 pm)



Na



25°C



1.53



1.51



20°C



Very low

Very low

8.9 x 10-l*

1.8 x 10-1"



1.01

1.06

I .24

I .23



I .48

I .43



Ca

Mg



de Haan et a1

(1965)



10-27



1.5



(7.2



2



Graf er al.

( 1968)



<4 x lo-':'

2.9) x lo-''



(1.3-4.5) x lo-"



Not determined

6.1 x



10-13



Keay and Wild

(1961)



46

Lai and Mortland

(1968)



232



P. H. NYE



of Sr into Mg vermiculite, during which there was a slight expansion of the

lattice from 1.45 to 1 S O nm.

2 . Montinorillonites and Kaolins

In the studies with micas and vermiculites the movement of the ion in the plane

of the aluminosilicate layers into a surrounding solution has been measured. In

the work on clay pastes, which will now be described, the particles are, as a rule,

oriented randomly, and movement through the whole mass is studied. The pathway for the movement of the ions is thus tortuous, and the observed mohility

includes a “geometry” effect. Most of the work has been done on montmorillonite,

in which the number of water molecules between the aluminosilicate layers

is greater than in vermiculite, and the surface charge density is less.

A great variety of experimental conditions have been used. In some examples

the mobility of the ions has been determined from the electrical conductivity of

the homoionic pastes, prepared in a variety of ways; in others, from the selfdiffusion of the ions, determined by a variety of methods. The proportion of clay

to solution has ranged from a dilute suspension to a stiff paste, and solutions of

varying electrolyte concentration have been used. The resulting measurements

have been interpreted in a number of ways. Table I1 attempts to order them by

comparing the apparent mobilities of the ions in “salt-free” gels with their

mobilities in solution at infinite dilution. Although many gels that are claimed to

be salt-free are in fact hydrolyzed, in all instances the mobility cited can be

attributed to the overwhelming majority of cations that are satisfying negative

charges on clay lattices rather than on free anions in solution.

In spite of the inclusion of geometry effects, all the ions have greater mobility

in the montmonillonites and kaolins than in the vermiculites. The values are also

consistent in showing that the ion with the largest unhydrated radius suffers the

greatest reduction in mobility. This is particularly well shown by Cremers (1968)

for the alkali cations on both montmorillonite and kaolinite, and by Gast (1962)

for the alkali and alkaline earth cations on montmorillonite. Large cations are

more polarized in an electric field than small ones, and they interact more strongly

with the negatively charged 0 atoms that form the clay surfaces (Bolt et al., 1967).

(See Section III,B,2.) There is some indication that the divalent ions have lower

mobility than monovalent ions of comparable unhydrated size (cf. Na+, r = 0.095

nm, and Ca2+,r = 0.099 nm), although Hoekstra (1965)found that Na and Ca had

similar mobilities in frozen Na and Ca bentonite pastes, where in each case the

unfrozen water amounted to 56%.

The mobilities of the monovalent ions on kaolinite are similar to their

mobilites on montmorillonite, in spite of the fact that the ions on kaolinite are

adsorbed on external suifaces, whereas on montmorillonite they will be mainly in

interlayer positions.



TABLE I1

Mobility of Ions in Salt-Free Clay Gels Relative to Solution at 25°C

Ion

Method



Clay concentration



Li



Na



K



Rb



cs



Ca



Sr



Ba



References



Montmorillonires



Conduction

Diffusion

Diffusion

Diffusion

Diffusion

Conduction



0.1-10 g clayllO0 ml

soh

15-28%



0.27



4-6 g clay/100 g gel

4.9-10.6 g clay/

100 g gel

3 g clay/100 ml soh

60 g clay/100 g gel



56 g clay/100 g gel

70 g clayll00 g gel

3 1-35 g clay/ 100 ml

gel

Self-diffusion coefficients in water at

infinite dilution (m2/sec x 1 0 9



Diffusion

Conduction

Conduction



0.37

0.19



0.13



van Olphen (1957)



0.22



Lai and Mortland

( 1962)

Bloksma (1957)

Fletcher and Slabough

(1960)

Gast (1962)

Cremers ( 1968)



0.37

0.08



0.19



0.25

0.13



0.23

0.06



0.06

0.02

0.01

Kaolinites



0.28

0.18



0.08



0.03



0.08

0.08



1.35



0.04



Bloksma (1957)

Cremers (1968)

Gast (1966)



0.05



0.14



1.04



0.09



1.98



2.07



2.11



0.78



0.78



0.84



P. H.NYE



234



TABLE IIl

Diffusion Coeffscients of Ions Diffusing into Water-Saturated Clay Films in Ca Form"



Clay



gHzO/goven-dry clay



Kaolinite

Montmorillonite

Mite

Vermiculite

Diffusion coefficient

in free solution

x log mZ/sec



49

44

39

30



CEC

(me/100 g)

6.5

70

20

80



Cu



Mn



Zn



0.22

0.02

0.09

0.01



0.25

0.05

0.12

0.02



1.09



1.04



0.32

0.06

0.12

0.04

0.73



Fez+



Fe3+



0.055



0.01



"From Ellis el a / . (1970a,b)



Ellis et al. (1970a,b) measured the diffusion of heavy metal ions into watersaturated films of Ca clay deposited on a slide. The clay particles were highly

oriented so that hindrance caused by tortuosity should be slight. Since they

measured the concentration profile of the penetrating ions by X-ray flourescence,

they were able to determine the diffusion coefficient at varying proportions of the

metal ion in the exchange complex. At low proportions nearly all the ion is in the

exchangeableform and little is in the solution, so that the correspondingdiffusion

coefficient is a measure of the mobility of the ion in the adsorbed state. Table I11

shows the values obtained.

The order of mobility was kaolinite > illite > montmorillonite > vermiculite.

In kaolinite all ions will be on external surfaces. In illite and montmorillonite

most exchangeable ions are in interlayer positions. However, when the heavy

metal ion is diffusing into the clay, it may diffuse preferentially on external

surfaces, and this may explain its greater mobility in illite than in

montmorillonite, which has a wider interlayer spacing. In vermiculite the c-axis

spacing is 1.5 nm, which accounts for the low mobility. The mobility of the

heavy metal ions is in the order Zn > Mn > Cu, which does not accord with

either their mobility in solution or their unhydrated radii.

The mobility of Fe3+ is about a fifth of that of Fez+, although it will be noted

that Fe3+has appreciable mobility. The mobility of the divalent heavy metal ions

is of the same order of magnitude as for the Ca, Sr, Ba series on kaolinite and

montmorillonite in Table 11.

The important feature of the activation energies for diffusion in clay gels

shown in Table IV is that they nearly all lie in the range 17-25 kJ/mole. In the

lower range this is close to the activation energy for diffusion in solution, and it is



235



DIFFUSION OF SOLUTES IN SOILS



considerably lower than the value of about 42 kJ/mole found for diffusion in the

structures having two water layers.

Davey and Low (1968) have shown that the activation energies reported for Na

bentonite may be up to 4.2 kJ/mole too high because of the formation of hydrous

aluminum oxide on the surface during preparation of the Na-saturated clay. Street

et al. (1968) and Miller and Brown (1969) also hold aluminum oxide responsible

for the variability in activation energies reported for Li, Na, and K bentonites.

These general findings have been illuminated by a number of detailed studies.

It would be expected that the mobility of ions in clays would be reduced by

geometry effects, by electrostatic attraction between the ions and the clay lattice,

and by changes in the structure of the water near the clay surfaces. These effects

will now be discussed.

B. FACTORS AFFECTING THE DIFFUSION COEFFICIENTS



1 . Geometry Effects

Cremers and Thomas (1966). Cremers and Laudelout (1965), and Thomas and

Cremers (1970) have measured the conductance of the sodium forms of

montmorillonite, illite, and kaolinite clays suspended in sodium chloride solutions. Both the proportions of clay and the concentration of electrolyte were

varied over a wide range. Figure 3 illustrates their results. They relate the



TABLE IV

Activation Energies for Self-Diffusion or Conduction in Salt-Free Clay Gels"

Ion

Method



Li



Na



K



Rb



Cs



Ca



Sr



References



Montmorillonite



Diffusion

Conduction

Conduction

Conduction

Conduction



18



16

25

18

19



24



17

20

18



36

45



Lai and Mortland ( 1962)



18

16



Cremers (1968)

Street et al. (1968)

Gast (1966)



16



Cremers (1968)

Gast (1966)



L o w (1958)



22



1 41 6



23



Kuolinite



Conduction

Conduction



18



17

16



21



Values given in kilojoules per mole.



25



236



P. H. NYE

150



/



-



/



/

/



I

E



u

P



Y



K, (mblholcm)



FIG.3. Electrical conductivity (mMho/cm) of Na montmorillonite gels, K,, versus conductivity

of equilibrium NaCl solutions, Kl, for various porosities. I is the isoconductivity. From top to

bottom: 0 = 1 (broken line); 0.96,0.91, 0.86, 0.80, 0.73, 0.64. After Cremers (1968).



specific conductance of the gel, KO,to the specific conductance of the solution in

the pores, K l , by the equation



+K,



K O = K&



(3)



K , is the excess specific conductance created by the mobility of the exchangeable

ions. At high electrolyte concentration K , will be small in comparison with K 1 .

The “formation factor,” 8, is then a measure of the extent to which the solid

particles reduce the specific conductance of the gel in relation to the solution by

reducing the cross section for the passage of the ions, and by increasing the

tortuosity and viscosity of their pathway.

They found that the experimental values obtained for 8 in dilute gels (porosity

of 1.O-0.65 for montmorillonites and 1.O-0.5for kaolinites) are well described

by a theoretical equation due to Fricke (1924):



8 = 1 + (1 + 0.21n)(i



-



eye



( n > 10)



(4)



Here 8 is the volume fraction of the liquid, and n is the ratio of the diameter of

the particles to their thickness. A plot of 8 - 1 against (1 -8)/8 is a straight line

passing through the origin, and the slope gives the value of n (see Fig. 4). These

values of n, in the range 10-60, for six different clays, agreed very well with

independent determinations by electron microscopy or viscosity. In concentrated



DIFFUSION OF SOLUTES IN SOILS



237



gels Cremers (1968) found that fF: is better described by a theoretical equation due

to Bruggeman and developed by Meredith and Tobias (1962):

Q = (I/e)(l + 0.21n)

(n > 10)

(5)

The high values of Q measured for clays with high axial ratios are quite inconsistent with a cubic model of a concentrated clay gel, which has sometimes been

used to deduce geometry effects.

Turning now to the excess conductivity created by the exchangeable ions, we

see in Fig. 3 that there is an “isoconductivity” value (I) at which the specific

conductivity of the gel is the same as that of the solution-for all concentrations

of clay. Dakshinamurti (1960, 1965) had previously noticed this property in a

number of clay systems. Cremers (1968) shows that, because there is such an

isoconductivity point, the exchangeable ions may be assigned a constant “surface conductance,” and that this is governed by the same formation factor as the



I



I



1



1



I



7-



F-1



FIG. 4. Formation factors versus porosity according to the Fricke equation. W-B (Wyoming

bentonite), C-B (Camp Berteau montmorillonite), K-2 (Zettlitz kaolinite), K-B (Boulvit kaolinite). n

is the axial ratio. After Cremers (1968).



238



P. H.NYE



ions in solution. Thus, as far as the geometry effect is concerned, the exchangeable ions behave in Fq. (3) as though they were distributed uniformly over the

adjacent pore solution-by no means an obvious result. With this knowledge of

the geometry effect for the exchangeable ions, Cremers is able to conclude that

the conductivity of the gels is “consistent with” 0.5-0.6 of the exchangeable Na

in each clay having the same mobility as in solution and the remainder being

immobile.

For other cations the experimental data are less complete, but Cremers concludes tentatively that on montmorillonite the following fractions are freely

mobile: K 0.3, Cs 0.15, Ca 0.15; and on kaolinite: K 0.15, Cs 0.05.



2 . Electrostatic and Viscosity Efsects

It is difficult to distinguish experimentally between a proportion of exchangeable ions having the same mobility as in free solution with the rest having none,

and a more continuous distribution of mobilities over all the exchangeable ions.

That the activation energy for diffusion of Na in clays approximates that in water

is some indication that the observed mobility derives from freely mobile ions.

The somewhat higher activation energies for K, Rb, and Cs ions (see Table IV)

suggest that some ions with modified hydration are contributing to the observed

mobility. This problem has been analyzed further by Shainberg and Kemper

(1966a) and by van Schaik et al. (1966), who have developed the ideas of Low

(1962, 1968). He calculated the variation in electrostatic potential of an ion as it

moved parallel to the surface of a clay lattice from one position of stability to the

next. He estimated that there would be a negligible potential barrier to surmount

if the ion were more than 1.0 nm above the plane of negative charge on the

lattice. Shainberg and Kemper (1966a) calculated that if the negative charge is in

the octahedral layer (as in montmorillonite) an unhydrated ion adjacent to the

surface will require 4.8 kJ/mole more activation energy than an ion separated

from the surface by one molecular thickness of water (about 0.25 nm). This

effect alone would lead to a sixfold difference in the mobility of the ion. If, in

addition, the first molecular layer of water is more viscous than subsequent

ones-and there is much evidence for this (Low, 1961; Grim, 1968)-it is

reasonable to assume that the mobility of the unhydrated ions can be neglected.

The next step is to consider how much the mobility of the hydrated ions is

restricted by reduction in the fluidity of water near the surfaces. By measuring

the diffusion of DOH in oriented flakes of bentonite containing varying amounts

of water, Kemper er al. (1964) found that in Na bentonite the relative mobility of

water in layers one, two, and three molecular thicknesses from each bentonite

surface was 0.3, 0.6, and 0.65; in Ca bentonite the corresponding values were

0.05, 0.5, and 0.7.



DIFFUSION OF SOLUTES IN SOILS



239



Against this background, van Schaik et al. (1966) have measured the selfdiffusion of Na and Ca in oriented, expanded flakes of Wyoming bentonite.

Because the ions were diffusing in the plane of the flakes, the tortuosity factorthe factor by which the mobility is multiplied to allow for an increased path

length-was high, 0.55, as estimated from diffusion of DOH in similar flakes.

They were able to calculate a weighted average fluidity of the water surrounding

the hydrated ions, the weighting factors being provided by the relative concentrations of ions in each molecular layer calculated from the theory of the diffuse

double layer. The reasonable assumption was made that the relative diffusion

coefficient of DOH is a measure of the relative fluidity of water. From the

measured diffusion coefficients they concluded that 0.60-0.87 of the Na ions

and 0.15-0.47 of the Ca ions are, on a time average, hydrated.

By measurement of conductivity of Li, Na, and K bentonite pastes, Shainberg

and Kemper (1966a) have similarly estimated that the hydrated fractions are Li

0.64, Na 0.57, and K 0.39. This work was, however, done with centrifuged

pastes, pushed from a glass tube into the conductance cell; and it has been

assumed that the tortuosity factor can be taken as 0.67. If the flakes were not well

oriented, this value seems likely to be too high. A lower value would have the

effect of increasing the fractions hydrated.

Although these estimates of the fraction of hydrated ions are subject to numerous uncertainties-for example, the average fluidity depends on the accuracy of

the calculation of the distribution of ions in the diffuse double layer; and the

assumption that unhydrated ions are virtually immobile is very sensitive to the

value chosen for the dielectric constant near the surface of the lattice-they

illustrate well the difficulties that arise in arriving at an exact model of ion

movement through clays. They also agree reasonably well with the independent

calculations of Shainberg and Kemper (1966b), based on considerations of electrostatic energy, that the fractions of ions hydrated in homoionic bentonites are Li

0.82, Na 0.64, K 0.51. These calculations also are admittedly uncertain, since

they neglect terms involving the energy of water-to-water links.

Further insight into the fluidity of interlayer water is provided by neutronscattering spectroscopy, which has been applied to clays by White, Hunter, and

co-workers (Olejnick and White, 1972). Figure 5 shows a plot of log,oDH,o

against the reciprocal of the thickness of the interlayer water in Li and Na

montmorillonite and Li and Na vermiculite. The experimental values agree well

with the theoretical expression represented by the straight line in Fig. 5:

D = Dbulkexp(-26VIdRT)

where 6 = surface energy of included water plus ions;

V = molar volume of water;

d = interlayer thickness of water.

Here 26Vld is the reduction in free energy of water confined between two



P. H.NYE



240



-



b



x



05 -



0



%

E



\

N



Y



0



N



I



n



b



0.1 :



\

0.02

0



I



'



1



8



I



'



0.05



'



1



'



'



01



'



n



'



1



0.15



n



'



'



0.2



'



1



'



1 '



' ' '



0.25

(Water layer thickness)-',d-' &I)



I



03



*



"



I



a



035



'



1



'



0



FIG. 5 . Variation of the diffusion coefficient of water in montmorillonite and vermiculite with

reciprocal of the interlayer spacing. After Olejnick and White (1972).



parallel plates. The reduction is equal to an increase in the activation energy of

diffusion because the water molecules jump from a lower energy level.

These measurements of water mobility are lower than those obtained from

diffusion of DOH by a factor of about 4. If correct, they indicate that the fraction

of ions hydrated is underestimated by van Schaik et al. (1966).

3 . Effect of Dehydrating Clays



The work on montmorillonite described in the previous section has been done

with clay suspensions or pastes with expanded lattices. Work has also been done

on drier montmorillonites in which only one or two molecular layers of water lie

between the sheets; in this respect it links with the studies of diffusion in vermiculites.

Mott (1967) has measured the self-diffusion coefficients of Na and Sr in

homoionic bentonite at varying degrees of hydration. Figure 6 shows his results.

He used oriented flakes in which diffusion in the plane of the flakes was very little

reduced by geometry; in fact it proceeded 300 times as fast as it did across the

plane of the flakes in specimens with two water layers between the sheets (279

mg of H20per gram of dry clay). The mobility of Na over the range 350-200 mg

of H20per gram of clay (three to two water layers) was also measured by

electrical conductivity, with satisfactory agreement between the two methods. In

drier clay the conductivity method proved unreliable because of difficulty in



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III. Diffusion of Adsorbed Ions in Soil Clays and Clay-Type Minerals

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