the chemical modelling of clay/electrolyte...

Clay Minerals (1989) 24, 375-391

THE C H E M I C A L M O D E L L I N G OF C L A Y / E L E C T R O L Y T E I N T E R A C T I O N S FOR

M O N T M O R I L L O N I T E

P. F L E T C H E R AND G. S P O S I T O *

Schlumberger Cambridge Research, PO Box 153, Cambridge CB3 0HG, UK, and *Department of Plant and Soil Biology, The University of California, Berkeley, Ca 94720, USA

(Received 9 May 1988; revised 18 January 1989)

A B S T R A C T : A study of the ion-exchange properties of montmorillonite has been performed in order to facilitate computer predictions of the chemical properties of natural fluids and mineral assemblies. Clay/electrolyte interactions can be described using a technique based on the concept of hypothetical surface complex formation. This technique, which is compatible with ion-association models such as GEOCHEM, can be used to simulate simultaneous ion- exchange, hydrolysis of clay edges and anion adsorption on clay surfaces. Effects such as variable cation-exchange capacity and compositionally dependent exchange constants, normally indicating non-ideal behaviour, can be simulated using different combinations of ideal reactions involving charged surfaces and complexing groups representing clay edges. The modelling procedures are flexible and thermodynamically self-consistent. The techniques were appliexl to data on the ion-exchange characteristics of Wyoming bentonite to yield thermodynamic data for the reactivity of this clay with alkali metals, alkaline earths and a range of firsbrow transition metals at 25~

It is common in the application of the classical thermodynamic treatment of ion-exchange (Argersinger, 1950; Gaines & Thomas, 1953; Hogfeld, 1953) to assume that reactivity is dominated by a process of stoichiometric replacement of ions on the surfaces of a material of fixed charge. However, with clays this reaction may be accompanied by simultaneous anion uptake and hydrolysis, with the consequence that the effects of these additional reactions are embodied in the values of solid-phase activity coefficients. This feature may be undesirable, and it is the aim of this paper to offer a simple description of clay/electrolyte interactions which formally acknowledges the existence of multiple reactions.

The approach developed here is compatible with existing multi-component equilibrium models (Nordstrom et aL, 1979) based on the principle of ion association. In essence, the methods herein involve transforming classical ion-exchange constants into sets of formation constants which can be used in the above speciation models. A preliminary attempt has been made to apply these techniques to the properties of Wyoming bentonite.

T H E P R O P E R T I E S O F M O N T M O R I L L O N I T E

It is appropriate to first review the behaviour of montmorillonite with a view to defining a set of properties which form the basis of a numerical description of surface reactivity.

�9 1989 The Mineralogical Society

376 P. Fletcher and G. Sposito

Ideal ion-exchange behaviour

The stoichiometric replacement of ions on a surface of fixed charge can be described by the ion-exchange reaction (equation 8). Ideal ion-exchange is consistent with the compositional independence of the conditional equilibrium constant (equation 10). Sposito & Mattigod (1979) used data by Maes et al. (1976) to show this to be the case for a range of first-row transition metals exchanging with Na on Chambers montmorillonite. Measurements by Sposito et al. (1981) on Cu/Na exchange on Wyoming bentonite yielded an equilibrium constant of 1.32 + 0.08, which is consistent with ideality. Similar measurements for Ca/Na, Mg/Na and Ca/Mg supported ideality with slightly less certainty (Sposito et al., 1983a,b,c). Gast (1969) has shown that binary reactions between Na, K and Rb on Wyoming bentonite give conditional equilibrium constants which vary by less than 15% over the entire isotherm; only reactions involving Cs, and possibly Rb, show significant signs of non-ideal behaviour. Near ideal behaviour is also exhibited by binary reactions between Na, Li and NH4 on Camp Berteau montmorillonite (Gast, 1969; Gast et al., 1969). Ideality on montmorillonite is supported generally by a range of data reviewed by Bolt (1982), although this review shows that other clay minerals are unlikely to conform to ideal behaviour.

Anon a ~ o ~ t w n

There is much evidence to suggest that an increase in the occupancy of clay surfaces by divalent ions is accompanied by an increase in the total adsorbed metal charge and an apparent increase in the selectivity for the divalent ion. Data reviewed by Sposito et al. (1983a) support the argument that anions form complexes with divalent cations on the surfaces of clays to become part of the surface excess, resulting in an increase in the total quantity of charge-neutralizing cations. It appears that in dilute electrolyte solutions monovalent cations do not encourage this type of adsorption (Gast, 1969). Additionally, Sposito et al. (1983a,b) could not detect anion adsorption in perchlorate background ionic media, suggesting that larger monovalent cations are not easily accommodated on or near clay surfaces.

Acid/base behaviour

Clay surfaces have similar affinities for both Na and the proton (Gilbert & Laudelout, 1965). Consequently, protons should not displace significant quantities of charge- neutralizing cations at pH > 4. However, acid/base titration characteristics determined by Marshall & Krinbill (l 942) and Marshall & Bergman (1942a; 1942b) and the pH-dependence of the cation-exchange capacity (CEC) (Maes et al., 1976) show selective removal of Na in the pH range 4-6. These data are consistent with a negatively charged group, comprising ~ 15% of the total clay charge, which can be neutralized by cations including the proton. This functional group probably results from hydrolysis of AIOH and SiOH groups on clay edges. The simplest description considers the group to be a negative species with cation-complexing properties. Reactions of this species take the form:

N zn§ + ZnE- ~- NEz~ (1)

where E- is the edge species and N zn" is any cation of charge Kn+. This simple treatment assumes that activity coefficients for the edge species conform to the Debye-Hiickel limit,

Chemical modelling of montmorillonite/electrolyte reactions 377

which may not be the case, and neglects the specific adsorption of anions to the edge sites at low pH (Bolt, 1978). These problems may be resolved in later refinements of the treatment.

T H E S I M U L A T I O N OF C H E M I C A L S P E C I A T I O N

The general aspects of chemical speciation models which can be modified to include the description of ion exchange are as follows.

Chemical equilibria

For a system containing J primary components (elements or stable ligands such as SOl-) and I complexes, a general reaction equation can be written for the formation of the ith complex:

J

v<i,j~cj + niH20 ~ Pi (2) j = l

where v~i,j 9 is the number of moles of the uncomplexed species cj in the reaction to form one mole of complex pi, and n i is the number of moles of water in the reaction. Both n and v are positive if the species are consumed and negative if produced in the reaction.

The thermodynamic equilibrium constant for this reaction is:

mp, Tp, = (3)

t~ J aw I~ffil (mcj Tcj) v~')

where m~j and mpi are the molal concentrations of the uncomplexed species and the complex

respectively, ? is the respective single-ion activity coefficient and awis the activity of water. This can be formulated as a mass action quotient expressed in terms of concentrations

only, i.e. mp,

~ - (4) = I m ~ ~

Then, J

~ aw ~ ~cj h',,. (5) j = l

Mass action quotients can be calculated from equilibrium constants in dilute electrolytes using an equation for the ionic strength dependence of single ion activity coefficients by Davis (1962).

Mass balance

Equation (4) can be combined with statement of mass balance to calculate speciation. The general mass balance equation for the kth primary component gives the summation of all species which contain the component and is:

I

Tk = mck + ~ Vo, k)mpi, (6) i = 1


where T k is the total quantity of any primary component in the system. The variable mpi can be eliminated from (6) using (4) to give:

I J

Tk = mck + ~ v(i,k) ~ I - I m~ "~" (7) i =1 jff i l

This mass balance equation applies to all components except protons or hydroxides whose concentrations are described by an equation similar to (7) (Morel & Morgan, 1972).

Thus, equation (7) constitutes J equations with J uncomplexed species as the basis set. These equations can be solved using a linear multidimensional Newton-Raphson method. The solution of these equations gives the electrolyte composition including pH. However, the mass balance equations include mass action quotients which have a composition dependence through the activity coefficients; therefore the following sequence is followed.

(1) Estimation of ionic strength, activity coefficients and the subsequent calculation of mass action quotients using equation (5). (2) Solution of equation (7) to yield values of mcl to m~j. (3) Calculation of mp~ with equation (4) using predicted values m,~ to m~j leading to an improved estimate of ionic strength. Items (1) to (3) are repeated until a constant value of ionic strength is achieved.

This framework can be used to describe ion-exchange components as if they were complexed species using a procedure suggested by Shaviv & Mattigod (1985).

C L A Y / E L E C T R O L Y T E I N T E R A C T I O N S

Ion-exchange

The reaction equation describing stoichiometric replacement of ions on the surface of a solid fixed charge is:

Z~A(s) + ZABXz. ~ ZAB~s) + Z,,aXzA, (8)

where Z A and ZB are the valence charges on ions A and B, X is the solid exchanger and (s) denotes ions in the solution phase.

The thermodynamic equilibrium constant for this reaction is:

(XAfa)Z'(mBTs) z"

K a = (xnfB)Z,(rnAT~)z, (9)

where x a and x n are the mole fractions of ions on the exchanger phase, fA and fn are the respective activity coefficients, mAand rn n are the molalities of ions in the aqueous phase and

TA and Tn the single-ion activity coefficients respectively. A conditional equilibrium constant can be defined as:

x~a'(rnnyn) z" Kv = ~,(mAr~)z , (10)

therefore,

Ko -- Ko(fI,/g~). (11)


The equations to here are consistent with the classical thermodynamic treatment which yields the solid-phase activity coefficients using the Gibbs-Duhem equation (Argersinger et al., 1950). Our approach is to describe ion-exchange by implementing a convention based on the concept of surface complex formation. This is a quasi-thermodynamic approach designed to predict the macroscopic transfer of ions between phases; it is not a description of molecular configurations at clay surfaces.

Defining a reactive component X- as a hypothetical aqueous species representing one mole of charged surface with unit valency allows hypothetical complex reactions for this species to be written: i.e.

a~ . + ZAX~ ~ ,~ AXzA (12)

and

Such equations are identical with those describing the formation of aqueous complexes from hydrated aqueous ions and have similarly defined equilibrium constants: i.e.

and

K 1 max (t4)

(m~r~)(mxrA zA

mBX Ks = (15)

(mB~, B)(m x~, x) z"

Here, max and mBx are the molalities of the surface complexes (ion-exchange components). These reactions are hypothetical, therefore the single-ion activity coefficients for the complexes are defined as unity. Equilibrium constants such as these can be used in any conventional speciation model. However, since the reactions are hypothetical the value of mx is not directly measurable from the constants and must be evaluated using measured ion- exchange data in conjunction with some formal convention as follows.

The mole fraction terms in equation (1 O) can be evaluated from the molalities of the surface complexes, i.e.

xa = mAd(mAx + mBx) (16)

and

xB = max/(mAx + mBx) (17)

Eliminating mole fractions from equation (11) and combining with equations (14) and (15) gives the relationship between an equilibrium constant for ion-exchange and the two conditional formation constants for the hypothetical surface reactions, i.e.

K o = - - \ ~ , ]

For the case of heterovalent exchange on a solid of fixed cation-exchange capacity, where (Z A ~ ZB) and (max + mBx) is dependent on the level of exchange, the ratio of (/~d//~r must be dependent on both the level of exchange and the total quantity of exchanger in the system. This treatment differs from that of Shaviv & Mattigod (1985) who did not consider the


composition correction. The constants given by them will be compositionally dependent and cannot be used in any general application.

Both K~ and K2 are in principle unknown. However, if one constant is known (K2 for example) then the value of K~ required to maintain consistency with K a at any given level of exchange (i.e. a known value of mAx + mBx) is given by:

K, = [K,,I~2~ \ f~A" "~ (mAx +mnx)(z'-z~)] (19)

In this way reaction (13) may be used as a reference reaction, having a constant value of K2, to evaluate the internally consistent value of KI. This can be used with/(2 to simulate the process of ion-exchange in models such as GEOCHEM (Sposito & Mattigod, 1980). The only modification to such a model is the inclusion of the facility to continually modify K1 for successive improvements in the predicted value of mAx + mBx in accordance with equation (19). This is similar to the activity coefficient correction to the mass action quotient (equation 4) and may be performed simultaneously. The choice of reference reaction and constant is arbitrary but it is essential to use a constant which is large enough to ensure that the predicted value of X- is small enough to make a negligible contribution to mass balance. In order to generalize this approach for multi-component exchange the term max + max in the mole fraction equations and equation (19) should be replaced with the sum of the molalities of all surface complexes including those containing adsorbed anions.

Anion adsorption

A reaction equation for the formation of one mole of surface complex from a cation Ai z~+, an anion yz,- and the hypothetical surface species X- is as follows.

vA, Ai z~ + vrY z'- + vxX- ~- AvAiYvrXvx (20)

where the vs represent the number of moles of reactant and are chosen so that the resulting surface complex is neutral. The conditional equilibrium constant is:

mAiXY (21) K AiYX = (mAy A).ai(m rY r). r (mxY x).x "

As with the ease of simple ion-exchange, this constant must be evaluated using a measured ion-exchange constant and a complementary reference reaction. An important algebraic simplification can be obtained if the reference ion is monovalent. For the purpose of self- consistency the reference reaction should be the same as for the simultaneous ion-exchange reactions, i.e.

R + + X - ~- RX. (22)

A complementary exchange reaction which includes the anion yz, can be constructed, i.e.

VA:i + vxRX + Vr Yz'- ~- Ai, AiYvrX~x + vx R+. (23)

This reaction has an experimentally measurable equilibrium constant KQ of the form:

( X A Yxf A rx)(m ,T ~ "x

K, = (mAYA)VA~(x~fp~)OX(mx~x),r. (24)

Chemical modelling o f montmorillonite/electrolyte reactions 381

The equilibrium constant for equation (23) can evaluated from:

Q is the sum of the molalities of all surface complexes evaluated from:

Q = mRx + mAj x + maz x , (26) j=l p=l /

where J is the number of exchanging ions, P is the number of surface complexes containing anions and mAzx is the molality of any surface complex containing anions; this includes the specified anion yz,-.

An example would be the uptake of chloride accompanying the ion-exchange of Ca on montmorillonite. The hypothetical surface complex reaction is:

Ca 2+ + X- + C1- ~ CaCIX, (27)

with the reference reaction being the reaction between Na and the hypothetical anion X-, i.e.

Na + + X- ~ NaX, (28)

The equilibrium constants for these reactions are:

mcacIX KI = (29)

( mc~r c~)(m xY x)(mcff o) and

mNax K.=

respectively. The measurable quantity is the equilibrium constant for the reaction:

Ca 2+ + C1- + NaX ~- CaCIX + Na +, i.e.

(30)

(31)

K, --- (32) (mcar c ) ( mcy o)( xN~xf ~ax) "

Therefore, in accordance with equation (25):

The equilibrium constant K1, evaluated this way, can be used along with any number of additional surface complex reactions to describe simultaneous ion-exchange and anion adsorption. Reactions of this stoichiometry are particularly simple since the compositional correction reduces to unity.

T H E R M O D Y N A M I C D A T A F O R M O N T M O R I L L O N I T E

In view of the multiple reactivity of most clay/electrolyte interactions it is difficult to extract precise equilibrium constants for any one reaction in isolation. Consequently, elementary


TABLE 1. Ion-exchange reactions and equilibrium constants.

Reaction Value of constant Ka

NH~ + NaXos- NH4X+ Na + H + + N a X ~ H X + Na + K + + N a X ~ K X + N a + Li + + N a X ~ LiX+ Na +

Ca 2+ + 2NaX ~ CaX2 + 2Na § Mg 2+ + 2 N a X ~ MgX 2 + 2Na +

Sr 2+ + 2NaX ~,-~- SrX2 + 2Na + Cu 2+ + 2 N a X ~ CuXz + 2Na + Zn z+ + 2NaX~ ZnX 2 + 2Na + Cd z§ + 2 N a X ~ CdXz + 2Na + Co z+ + 2 N a X ~ COXz + 2Na + Ni 2+ + 2NaX,-~ NiX2 + 2Na +

Ca 2+ + C1 + + N a X ~ CaCIX + Na + Mg z+ + CI + + M g X ~ MgCIX+ Na +

Sr 2+ + CI + + N a X ~ SrC1X + Na + Ba 2+ + CI + + NaX~.~ BaCIX+ Na + Cu 2+ + CI + + N a X ~ CuC1X+ Na +

Zn 2+ + NO$ + N a X ~ ZnNO3X+ Na + Cd 2+ + NO~ + NaX~- CdNO3X+ Na +

Co 2+ + C1 + + N a X ~ C o a X + Na + Ni 2+ + CI + + NaX ~,-~ NiC1X + Na +

2-90 1.26 1.80 0.95 1-48 1.48 1.48 1.35 1.48 1.48 1.48 1.79 193 181 190 190 249 498 172 185 10.3

methods of successive approximation were used, in conjunction with some simplifying

approximations, to generate a preliminary database for montmorillonite.

First, a convention is adopted that the reference hypothetical surface reaction involves one

mole of Na ions reacting with one mole of exchanger surface and has an equilibrium constant KR of 101~ (equations 31 and 33).

Reactions with monovalent cations

Ion-exchange measurements by Gast (1969) and data compiled by Bolt (1982) suggest that

the affinity for clay surfaces is NH4 > K > H > Na ~ Li. Average values for the ion-

exchange constants for these reactions are presented in Table 1. Where inconsistencies arise

in the published literature, data represent mean value taken from a range of sources (Gast,

1969, 1971; Gilbert & Laudelout, 1965; Gast et al., 1969; Martin & Laudelout, 1963).

Equil ibrium constants for reactions between these ions and the clay edges can be estimated

using data by Maes et al. (1976) on the pH-dependence of C E C for Chambers

montmorillonite. First it is assumed that the edge contribution to montmoril lonite charge is

15% of the total charge of 1 mmol g-~. The convention is adopted that the reaction between

N a and the clay edge has an equilibrium constant of 101~ Then the value of the

complementary reaction for the group with the proton is chosen as the one which on

speciation of a 1% suspension of montmoril lonite gives the same percentage drop in retained

Na as that predicted by Maes et al. (1976). Constants for K and Li are estimated assuming

that the same relative preference applies to the clay edges as to the surfaces, i.e. K is slightly

preferred to Na or Li. Data are presented in Table 2.

Chemical modelling o f montmorillonite/electrolyte reactions

TABLE 2. Complex-ion formation reactions with clay edges and conditional equilibrium constants.

Reaction Equilibrium constant

Na + + E - ~ NaE 101~ H:O + E- ~ HE + OH- 1.02 NH[ + E- ~ NH4E 2.90 x 101~

K + + E- ~ KE 1-80 x 10 ~~ Li § + E- ~ LiE 0-95 x 101~

Ca 2+ + 2E- ~,~ CaE2 1.58 x 1024 Mg 2+ + 2 E ~,~ MgE2 1.58 x 102a

Sr 2§ + 2 E ~ SeE2 1.58 x 102a Ba 2+ + 2 E ~ BaE2 1.58 x 102a Cu 2§ + 2E- ~ CuE2 1.46 x 1024 Zn 2+ + 2E- ~ ZnE2 1.46 x 102a Cd 2+ + 2E- ~ CdE2 1.46 x 1024 Co 2+ + 2E- ~ CoE2 1-46 x 102a Ni 2+ + 2E- ~,~ NiE2 3-98 x 1023

E- represents one mole of montmorillonite edge charge. Conditional equilibrium constants are defined in accordance with equation (14).

383

These reactions are true chemical reactions and not hypothetical in the same sense as those for ion-exchange. However the method of est imation gives relative preferences for the clay edge rather than true affinities.

Reactions with divalent cations

Binary ion-exchange isotherms for Na/Ca , Na/Mg, Ca /Mg and Na /Cu have been determined in perchorate background ionic media (Sposito et al., 1983a). This precludes anion adsorption although these reactions must include contributions from clay edges. A n interesting feature is that the Ca /Mg isotherm is congruent with the non-preference isotherm. Also, the binary reactions involving N a have a single value for Kv of 1.48 + 0.3. This is calculated neglecting da ta on the extremities which commonly have the greatest error. The value is typical for many divalent exchange reactions with N a on montmori l loni te and is adopted as a convenient approximat ion for all unidivalent reactions in Table 1 including transit ion metal exchange determined by Maes et al. (1976).

Est imates of equil ibr ium constants for reactions between Ca, Mg or Cu and the clay edges can be extracted from these isotherms by a method of successive approximat ion. This involves performing a computer simulation of the exact experiments conducted by Sposito et al. (1983b) using the ion-exchange constants and the cat ion/edge constants est imated previously. The appropr ia te value of the divalent ion/edge constant is the one which best fits the isotherms. Ca edge constants were determined from the Ca/Mg isotherm rather than the C a / N a isotherm in view of the greater uncertainty in the latter.

Separate experiments by Sposito et al. (1983b) for binary ion-exchange in the presence of chloride can be used to evaluate the chloride complexat ion constants (equations (21) and (24)) for Ca and Mg. These are again determined by successive computer simulation of the exact


TAm.E 3. Complex-ion formation reactions, equilibrium constants and compositional dependencies.

Values of K~ x/~R i and Reaction compositional dependency

Na + + X- ~ NaX H20 + X - ~ H X + OH- NH~ + X- ~ NH4X

K + + X - ~ K X Li + + X- ~ LiX

Ca 2+ + 2X- ~- CaX2 Mg 2+ + 2X- ~- MgX2

Sr 2+ + 2X- .~ SrX2 Ba 2+ + 2X- ~ BaX2 Cu 2+ + 2X- ~ CuX 2 Zn 2+ 4- 2X- ~ ZnX2 Cd 2+ + 2X- ~ CdX2 Co 2+ + 2X- ~ CoX2 Ni 2+ + 2X- ~ NiX2

Ca 2+ + X- + C1- ~- CaXC1 Mg 2+ + X- 4- C1- ~ MgXC1

Sr 2+ + X- + C1- ~ SrXCI Ba 2+ + X- + CI- ~ CaBaCI Cu 2+ + X- + CI- ~ CuXCI

Zn 2+ + X- + NO~ ~ ZnXNO 3 Cd 2+ + X- 4- NO5 ~- CdXNO 3

Co 2+ 4- X- 4- C1- ~ CoXCI Ni 2+ 4- X- 4- CI- ~- NiXCI

1010

1"26 x 10 -4 x QO 2"90 x 101~ x QO 1.80 x 101~ x QO 0.95 • 10 t~ • QO 1"48 • 1020 • Q-1 1-48 • 1020 • Q-1 1.48 • 1020 • Q-I 1.48 • 1020 • Q-1 1.35 x 1020 • Q-t 1.48 • 1020 • Q-1 1.48 • 102~ • Q-1 1.48 • 1020 • Q-1 1-79 • 1020 • Q-1 1.93 x 1012 + Q-O 1-81 x 1012 x Q-O 1-90 x 1012 • Q-O 1"90 x 1012 x Q-O 2"49 x 1012 x Q-O 4.98 x 1012 x Q-O 1.72 x 1012 x Q-O 1"85 • 1012 • Q-O 1"03 • 1011 • Q-O

x - represents one mole of montmorillonite surface charge. Equilibrium constants are defined in accordance with equations (14) and (21). The term Q is the compositional correction defined by equation (26).

e x p e r i m e n t s us ing p rev ious ly d e t e r m i n e d cons t an t s . T h e va lue o f t he u n k n o w n is t he one

w h i c h bes t fits t h e v a r i a t i o n in C E C w i t h level o f exchange .

S imi l a r m e t h o d s o f success ive a p p r o x i m a t i o n were used to ex t r ac t t h e r m o d y n a m i c d a t a for

all r e ac t i ons o f f i rs t - row t r a n s i t i o n m e t a l s o n N a - m o n t m o r i U o n i t e u s ing i o n - e x c h a n g e

i s o t h e r m s a n d C E C values d e t e r m i n e d by M a e s et al. (1976). Va lues o f Ka x / ~ for

h y p o t h e t i c a l sur face r e a c t i o n s for the i th ion, a long w i t h t h e i r c o m p o s i t i o n a l d e p e n d e n c i e s ,

are g i v e n in T a b l e 3.

C O M P U T E R S I M U L A T I O N S

A r a n g e o f o b s e r v a t i o n s r e su l t i ng f r o m m o n t m o r i U o n i t e / e l e c t r o l y t e i n t e r a c t i o n s a re

s i m u l a t e d us ing d a t a in T a b l e s 2 a n d 3. A c t i v i t y coeff icient co r r ec t i ons were m a d e to t rue

so lu t ion c o m p o n e n t s a s s u m i n g idea l b e h a v i o u r for t he clay phase .

Exchange between monovalent cations

Fig. 1 shows s i m u l a t e d i s o t h e r m s for N a / K e x c h a n g e in ch lo r ide b a c k g r o u n d s a t t h r e e

d i f fe ren t to ta l ch lo r ide c o n c e n t r a t i o n s a t a fixed p H o f 7. A l so s h o w n are i s o t h e r m s for th i s


1.0

0.0

0,6

I

0.4

0.2

& 0 TN 0.1 p H 7 HI TN 0 . 0 5 p H 7 O TN 0 . 0 2 5 p H 7 A TN 0.1 p H 6 A~ + TN' 0.I pH5 ~}

x TN 0.1 pH 4 , 4 -

f

O

I

0.2

P

0.0 I I I

0.0 0.4 0.6 0.8 1.0

E - K ( c )

Fro. 1. Sodium/potassium exchange isotherm. Equivalent fraction of potassium in the clay (E-K(c)) vs. equivalent fraction of potassium in solution (E-K(s)).

1.3

1.2

1.1

x . .

1.o

L~

0.9

0.8

O T N 0 . 1 p H 7 O TN 0 . 0 5 p H 7 O TN 0 . 0 2 5 p H 7

T N 0 . 1 p H 0

+ T N 0 . 1 p H 5 • T N 0 . 1 p H 4

+ + + + + + + + + +-14-

x x x x x x x x x xxX

0.7 # I I I

0.0 0.2 0.4 0.8 0.8 1.0

E-K(c)

FIo. 2. Effect of pH on cation-exchange capacities for sodium/potassium exchange. CEC vs. equivalent fraction of potassium in the clay (E-K(c)).

reaction at total chloride concentration of 0-1 mol dm -3 over the pH range 6-4. All isotherms are congruent and consistent with a pH-independent selectivity, although apparent CECs, which exclude contributions from the proton, show a continual reduction with decreasing pH (Fig. 2). These features are consistent with data by Gast (1969, 1971) and Maes et al. (1976).


1.0 '"'

I 0 I 0 m o i / t

2 0 . 0 5 m o l / l 3 0.025 r n o l / 1 0.8

0.6

L) I

['~ 0.4

0.2 1 3

0.0 0.0 0,2 0.4 0,6 0.8 1.0

Z-Ca(~)

FIo. 3. Calcium/sodium exchange isotherms in different perchlorate backgrounds. Equivalent fraction of calcium in the clay (E-Ca(c)) vs. equivalent fraction of calcium in solution (E-Ca(s)).

1.D , , , , ,

O Perehlorate rq C h l o r i de E H

I Perehlorate Predicted ] J

O.a 2 Chloride Predicted ~ / n

0.6

t

~ 0.4

o.~ O ~ rn

o.o 0.0 0.2 0.4 0.6 0.8 1.0

E - C a ( c )

FIG. 4. Calcium/sodium exchange in chloride and perchlorate solutions. Equivalent fraction of calcium in the clay (E-ca(c)) vs. equivalent fraction of calcium in solution (E-Ca(s)).

Exchange involving divalent cations

Fig. 3 shows simulated isotherms for Na /Ca exchange at three different total concentrations of the non-complexing anion perchlorate. The isotherms are incongruent with an apparent increase in selectivity at lower perchlorate concentrations. The isotherms are consistent with ideal behaviour and constant apparent CEC and the concentration effect is a

Chemical modelling, of montmorillonite/electrolyte reactions 387

1.0

0.B

0 Perchlorate [] Chloride

1 Perchlorate Predicted 2 Chloride Predicted

D

o.~,~ i ~ m b 0.4

0.2 ~ [ ] I

0.0 0,0 0.2 0.4 0.6 08 1.0

E-~g(~

FIG. 5. M a g n e s i u m / s o d i u m exchange in chloride and percholate solutions. Equ iva l en t fraction of magnesium in the clay (E-Mg(c)) vs. equivalent fraction of magnesium in solution (E-Mg(s)).

1.5

14

1.3

1.2

.~ 1.1

1.0

0.9

O.B

0.7 0.0

0 Ca - Chloride

[] Mg - Chloride

-- Ca Predicted

--Mg Predicted

o

o o

I I I I

0.2 0.4 06 0.8 10 E-M(c)

FIG. 6. Inf luence o f chloride adsorption on C E C for C a / N a and M g / N a exchange . C E C vs.

equivalent fraction of divalent ions on the clay (E-M(c)).

natural consequence of heterovalent exchange (Barrer & Klinowski, 1974) which must be predicted if the numerical techniques are thermodynamically self-consistent

The effect of anion adsorption is emphasized in Figs 4 and 5 which show Na/Ca and Na/Mg isotherms respectively at a total chloride concentration of 0.052 mol dm -3. Comparisons with the equivalent perchlorate isotherm show the increased selectivity


1.0

0 Ca/Me Data /

o.B

0.6

s I

r-~ 0 .4

0 .2

0 . 0 I I I I

0.0 0.2 0.4 0,6 0.8 1.0 Z-Me(c)

FIO. 7. Calcium/magnesium exchange isotherm in perchlorate solution. Equivalent fraction of calcium in the clay (E-Ca(c)) vs. equivalent fraction of calcium in solution (E-Ca(s)).

1.5

0 Cu/Na Data Cu/Na Predicted

1.0

O O

0 0

I

0.5

0 . 0 ~ " t

0 .0 0.2 0 .4 0 .6 0 .8 1.0

~:-Cu(c)

Fzo. 8. Copper/sodium exchange isotherm in perchlorate solution. Equivalent fraction of copper in the clay (E-Cu(c)) vs. equivalent fraction of copper in solution (E-Cu(s)).

observed for the divalent cation ion in the presence of chloride. These are simulations of the experiments performed by Sposito et al. (1983b), the data from which are included for comparison. Fig. 6 shows the increase in apparent CEC with increasing Na replacement to be over 20% at high divalent ion coverage. Generally experimental data in Figs 4 to 6 are predicted adequately; this is also true for Ca/Mg and Na/Cu isotherms measured by Sposito

Chemical modelling o f montmorillonite/electrolyte reactions 389

4.0

3.5

3.0

2.5

z .o

1.5

1.0

O p H 6 . 0

12 p H 5 . 5

O p H 5 . 0

p H 4 . 5

D O

0 0

O A

O O

O A O A

~ o o o o o oA A a A ~ A A A

0.5 I I I I

0.0 0.2 0.4 0.8 0.8 1.0

E - Z n ( c )

FIG. 9. The effect of nitrate adsorption and edge effects on apparent selectivity for Zn/Na exchange. K v vs. equivalent fraction of zinc on the clay (E-Zn(c)).

et al. (1981, 1983a) shown in Figs 7 and 8. Ion-exchange isotherms and CECs for transition metal exchange with Na determined by Maes et al. (1976) can be equally well predicted.

It is possible to define an apparent Kv which is evaluated by including all cations of one type (regardless of actual surface speciation) into the mole fractions calculations. This apparent K v contains effects due multiple reactivity and is the constant determined most commonly. The effect of changing pH on the apparent Ko for Zn/Na exchange is emphasized in Fig. 9. These simulations (of an isotherm constructed from a 1 ~ suspension of clay at total nitrate concentration of 0-025 mol dm -3) show the dependence of the apparent Ko on the level of Na replacement at four different pHs. At the highest pH the compositional dependence of Kv shows a minimum resulting from the combined effect of complex formation at clay edges, which progressively lowers selectivity in this case, and an increase in Ko due to nitrate adsorption. As pH decreases, the clay edges become saturated with protons and the edge effect becomes less pronounced while the effect due to nitrate adsorption remains constant. These prediction are in general agreement with data by Maes et al. (1976).

Ternary ion exchange

Sposito et al. (1983c) constructed experiments on the ternary ion exchange between Ca, Mg and Na on a Wyoming bentonite in a 0.5 mol dm -3 percholarate background. Experiments involved constructing Ca/Mg isotherms using a 2.5~o suspension of Na-montmorillonite in the presence of an additional concentration of Na. Isotherms were constructed at two different Na concentrations. Table 4 shows the simulation of the compositions of the clay phase after equilibration compared with measured compositions. In most cases predictions fall within the limits of experimental uncertainty given by Sposito et al. (1983c) although there is some tendency to underestimate the quantity of Mg adsorbed by a few percent at high Mg coverage.


TABLE 4. Predictions of the ionic compositions of montmorillonite under conditions of ternary exchange equilibria with calcium, magnesium and sodium.

Na m Nap Ca m CaP Mg m MgP

0.3 _4- 0.08 0.36 0-00 + 0.00 0.00 0.73 + 0.01 0.64 0-4 + 0-1 0-37 0.07 + 0-003 0-067 0.43 + 0.02 0.56 0-4 + 0-1 0-36 0.143 + 0.003 0.123 0.46 + 0-02 0.52 0.3 + 0"1 0"36 0"203 +_ 0"01 0.192 0.40 + 0.02 0.44 0"4 + 0"2 0"36 0"270 + 0.01 0.250 0.34 __ 0-01 0.39 0"3 + 0.1 0"37 0"304 + 0"08 0"32 0.33 __ 0.009 0.32

0"38 __+ 0"07 0'36 0"410 + 0"02 0.44 0-273 + 0.005 0.23 0"3 __+ 0.2 0.36 0-45 + 0-01 0.45 0-200 + 0.001 0-19 0.3 + 0.1 0-38 0"53 __ 0.02 0"48 0.14 + 0.01 0.14

0"29 + 0"06 0"36 0"56 __ 0"02 0"57 0-06 __ 0.05 0.064 0.4 + 0.2 0"38 0-61 + 0"02 0"62 0.00 + 0.00 0.00

0.2 + 0-06 0.23 0.00 + 0.00 0-00 0.85 + 0.06 0-78 0-14 + 0.09 0.23 0.071 + 0-005 0.078 0.79 + 0.06 0-69

0-1 + 0.03 0-23 0.145 + 0.005 0.152 0.76 + 0-07 0.62 0.1 _+ 0.07 0.23 0.250 + 0-02 0.26 0.62 + 0-04 0.523

0"20 + 0"06 0"23 0"370 + 0-01 0"34 0-52 + 0-02 0.47 0"15 + 0.08 0"23 0"45 + 0-01 0'39 0.42 + 0-01 0.49 0.16 + 0.07 0.22 0.55 +__ 0-01 0.47 0.29 +_ 0.02 0.31 0-17 + 0-08 0.23 0-59 + 0-04 0.53 0.25 + 0.02 0.24 0.15 + 0.09 0-23 0.64 + 0.02 0.61 0.14 + 0.02 0.16 0.23 + 0.08 0-22 0"63 _ 0.03 0-64 0.076 _ 0.006 0.085

0-1 + 0.09 0.23 0.93 + 0.03 0-78 0.00 _ 0.00 0.00

Concentrations in mol m = measured. p = predicted.

kg -1 dry clay.

C O N C L U S I O N S

A t e c h n i q u e to m o d e l i o n - e x c h a n g e a n d r e l a t ed p h e n o m e n a o n clays h a s b e e n d e v e l o p e d

us ing the c o n c e p t o f h y p o t h e t i c a l sur face c o m p l e x f o r m a t i o n . T h i s m e t h o d , w h i c h is

c o m p a t i b l e w i t h i on - a s s oc i a t i on mode l s such as G E O C H E M (Sposi to & M a t t i g o d , 1980),

c a n be used to s imu la t e mu l t i p l e r eac t iv i ty i n c l u d i n g s i m u l t a n e o u s i on -exchange , complex -

ion f o r m a t i o n a n d a n i o n ads o r p t i on . A v a i l a b l e l i t e r a tu re d a t a o n the r eac t i v i t y o f

m o n t m o r i l l o n i t e h a v e b e e n r e v i e w e d a n d a p r e l i m i n a r y t h e r m o d y n a m i c d a t a s e t compi l ed .

T h e s e d a t a were used to s imu la t e the essen t i a l f ea tu re s o f the r eac t i v i t y o f W y o m i n g

b e n t o n i t e in d i lu te e lec t ro ly tes to show t h a t effects s u c h as v a r i a b l e c a t i o n - e x c h a n g e c a p a c i t y

a n d non - idea l b e h a v i o u r c a n ar i se f r o m c o m b i n a t i o n s o f ideal r e a c t i o n s o f t he c lay sur faces

a n d edges. F o r t h i s p a r t i c u l a r clay all r e a c t i o n s a re a s s u m e d to b e ideal , w i t h ac t iv i ty

co r r ec t i ons m a d e to t rue so lu t ion species only. T h i s is c o n s i s t e n t w i t h e x p e r i m e n t a l e v i d e n c e

a l t h o u g h the t e c h n i q u e s are f lexible e n o u g h to a c c o m m o d a t e e x c h a n g e r - p h a s e ac t iv i ty

coeff ic ients i f r equ i red . I m p r o v e d d a t a will be o b t a i n e d i f fu tu re e x p e r i m e n t s a re d e s i g n e d to

e x a m i n e specif ic effects whi le m i n i m i z i n g or r e m o v i n g t he c o n t r i b u t i o n s f r o m a d d i t i o n a l

r eac t ions .

Chemical modell ing o f montmoril loni te/electrolyte reactions 391

R E F E R E N C E S

ARGERSINGER W.J., DAVIDSON A.W. & BONNER O.D. (1950) Thermodynamics and ion exchange phenomena. Trans. Kansas Acad. Sci. 53, 404.

BAggER R.M. & KLINOWSKI J. (1974) Ion exchange selectivity and electrolyte concentration. J.C.S. Faraday I. 70, 2080.

BOLT G.H. (1978) Chapter 5 in: Soil Chemistry A. Basic Elements. (G. Bolt and M. G. M. Bruggenwert, editors). Elsevier.

DAvis C.W. (1962) Ion Association. Butterworths, London. G M ~ s G.L. & THOMAS H.C. (1953) Adsorption studies on clay minerals: II. A formulation of the

thermodynamics of exchange adsorption. J. Chem. Phys. 21, 714. G~T R.G. (1969) Standard free energies of exchange for alkali metal cations on Wyoming bentonite. Soil Sci.

Soc. Am. Proc. 33, 37. G~T R.G. (1971) Alkali metal cation exchange on Chambers montmorillonite. Soil Sci. Soc. Am. Proc. 36, 14. GAST R.G., VAN BLADEL R. & DESCHPANDE K.B. (1969) Standard heats and entropies of exchange for alkali

metals on Wyoming bentonite. Soil Sci. Soc. Am. Proc. 33, 661. GILBERT M. & LAUDELOUT H. (1965) Exchange properties of hydrogen ions in clays. Soil Sci. 100, 157. HOGFELD E. (1953) On ion exchange equilibria. II Activities of components in ion exchangers. Arkiv Kemi 5,

147. MAES A., PEIGNEUR P. & CREMERS A. (1976) Thermodynamics of transition metal ion exchange in

montmorillonite. Proc. Int. Clay Conf. 1975, 319. MARSHALL C.E. & BERGMAN W.E. (1942a) The electrochemical properties of mineral membranes. II.

Measurement of potassium-ion activities in colloidal clays. J. Phys. Chem. 24, 52. MARSHALL C.E. & BER(;MAN W.E. (1942b) The electrochemical properties of mineral membranes. III and IV.

III The estimation of ammonium ion activities. J. Phys. Chem. 46, 325. MARSHALL C.E. & KRIrCBILL C.A. (1942) The clays as colloidal electrolytes. J. Phys. Chem. 46, 1077. MARTIN H. & LAUDELOUT H. (1963) Thermodynamique de l'exchange des cations alcalins dans les argiles. J.

Chim. Phys. 60, 1086. MOREL F. & MORGAN J. (1972) A numerical method for computing equilibria in aqueous chemical systems.

Env. Sci. Technol. 6, 58. NORDSTROM D.K., PLUMMER L.N., WlGLEY T.M.L., WOLERY T.J., BALL J.W., JENNIE E.A., BASSETT R.L.,

CRERAR D.A., FLORENCE T.M., FRITZ B., HOFFMAN M., HOLDREN G.R., LAFON G.M., MATrlGOD S.V., McDUFF R.E., MOREL F., REDDY M.M., SPOSITO G. & THRAILKILL J. (1979) A comparison of computerised chemical models for equilibrium calculations in aqueous solutions, Am. Chem. Soc. Symp. Ser. 93, 857.

SHavIV A. & MATTIGOO, S.V. (1985) Cation exchange equilibria in soils expressed as cation-ligand complex formation. Soil Sci. Soc. Am. J. 49, 569.

SposiTo G., HOLTZCLAW K.M., CHARLET L., JOUANY C. & PAGE A.L. (1983a) Cation selectivity in sodium- calcium and sodium-magnesium exchange on Wyoming bentonite at 298K. Soil Sci. Soc. Am. J. 47, 917.

SPOSlTO G., HOLTZCLAW K.M., CHARLET L., JOUANY C. & PAGE A.L. (1983b) Sodium-calcium and sodium- magnesium exchange on Wyoming bentonite in perchlorate and chloride background ionic media. Soil Sci. Soc. Am. J. 47, 51.

SPOSITO G., HOLTZCLAW K.M., JOHNSTON C.T. & LEVESQUE X. (1981) Thermodynamics of sodium-copper exchange on Wyoming bentonite at 298K. Soil Sci. Soc. Am. J. 45, 1079.

SPOSITO G., JOUANY C., HOLTZCLAW K.M. & LEVESQUE X. (1983c) Calcium-magnesium exchange in the presence of adsorbed sodium. Soil Sci. Soc. Am. J. 47, 1081.

SPOSITO G. & MATTIGOD S.V. (1980) G EOCHEM: A computer program for the calculation o f chemical equilibria in soil solutions and other natural water systems. Kerney Foundation of Soil Sci., University of California, Riverside.

SPosiTo G. & MATrlGOD S.V. (1979) Ideal behaviour in Na-trace metal cation exchange on Camp Bertaux montmorillonite. Clays Clay Miner. 27, 125.

the chemical modelling of clay/electrolyte...

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