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
MONTMORILLONITE
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 ionexchange, 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.
THE PROPERTIES
OF MONTMORILLONITE
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~twn
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 chargeneutralizing 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.
THE SIMULATION
OF CHEMICAL SPECIATION
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,j9 is the number of moles of the uncomplexed species cj in the reaction to form one
mole of complex pi, and ni 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,
J
awt~ I~ffil
(3)
(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,
i=1
(6)
378
P. Fletcher and G. Sposito
where Tk is the total quantity of any primary component in the system. The variable mpi can be
eliminated from (6) using (4) to give:
I
Tk = mck + ~ v(i,k) ~
i=1
J
I - I m~"~"
(7)
jffil
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).
CLAY/ELECTROLYTE INTERACTIONS
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 rnn 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)
Ko Ko(fI,/g~).
(11)
therefore,
--
Chemical modelling of montmorillonite/electrolyte reactions
379
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.
max
(m~r~)(mxrA zA
K1
(t4)
and
Ks =
mBX
(mB~,B)(mx~,x)z"
(15)
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 ionexchange data in conjunction with some formal convention as follows.
The mole fraction terms in equation (1O) can be evaluated from the molalities of the surface
complexes, i.e.
xa = mAd(mAx + mBx)
(16)
xB = max/(mAx + mBx)
(17)
and
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.
Ko=
--
\~,]
For the case of heterovalent exchange on a solid of fixed cation-exchange capacity, where
(ZA ~ 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
380
P. Fletcher and G. Sposito
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 Ka 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
K AiYX =
(21)
(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 selfconsistency 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 + vxR+.
(23)
This reaction has an experimentally measurable equilibrium constant KQ of the form:
(XAYxfArx)(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 +
mAjx +
j=l
maz x ,
p=l
(26)
/
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~)(mxYx)(mcff o)
and
K.=
mNax
(30)
respectively.
The measurable quantity is the equilibrium constant for the reaction:
Ca 2+ + C1- + NaX ~- CaCIX + Na +,
(31)
i.e.
K, ---
(32)
(mcar c ) ( m c y 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.
THERMODYNAMIC
DATA FOR MONTMORILLONITE
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
382
P. Fletcher and G. Sposito
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 ~ MgX2 + 2Na +
Sr2+ + 2NaX ~,-~-SrX2 + 2Na +
Cu 2+ + 2 N a X ~ CuXz + 2Na +
Zn z+ + 2 N a X ~ 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 +
Mgz+ + CI+ + M g X ~ MgCIX+ Na +
Sr2+ + 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 N a 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 N H 4 > K > H > N a ~ Li. Average values for the ionexchange constants for these reactions are presented in Table 1. Where inconsistencies arise
in the published literature, data represent m e a n value taken from a range of sources (Gast,
1969, 1971; Gilbert & Laudelout, 1965; Gast et al., 1969; Martin & Laudelout, 1963).
Equilibrium 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 montmorillonite 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~ T h e n the value of the
complementary reaction for the group with the proton is chosen as the one which on
speciation of a 1% suspension o f montmorillonite gives the same percentage drop in retained
N a 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 N a or Li. D a t a are presented in Table 2.
Chemical modelling o f montmorillonite/electrolyte reactions
383
TABLE 2. Complex-ion formation reactions with clay
edges and conditional equilibrium constants.
Reaction
Equilibrium constant
Na + + E - ~ NaE
H:O + E- ~ HE + OHNH[ + E- ~ NH4E
K + + E- ~ KE
Li§ + E- ~ LiE
Ca 2+ + 2E- ~,~CaE2
Mg 2+ + 2 E ~,~ MgE2
Sr2§ + 2 E ~ SeE2
Ba 2+ + 2 E ~ BaE2
Cu 2§ + 2E- ~ CuE2
Zn 2+ + 2E- ~ ZnE2
Cd 2+ + 2E- ~ CdE2
Co2+ + 2E- ~ CoE2
Ni 2+ + 2E- ~,~ NiE2
101~
1.02
2.90 x 101~
1-80 x 10~~
0-95 x 101~
1.58 x 1024
1.58 x 102a
1.58 x 102a
1.58 x 102a
1.46 x 1024
1.46 x 102a
1.46 x 1024
1-46 x 102a
3-98 x 1023
E- represents one mole of montmorillonite edge charge.
Conditional equilibrium constants are defined in accordance with equation (14).
These reactions are true chemical reactions and not hypothetical in the same sense as those
for ion-exchange. However the method of estimation gives relative preferences for the clay
edge rather than true affinities.
Reactions with divalent cations
Binary ion-exchange isotherms for N a / C a , N a / M g , C a / M g and N a / C u have been
determined in perchorate background ionic m e d i a (Sposito et al., 1983a). This precludes
anion adsorption although these reactions must include contributions from clay edges. A n
interesting feature is that the C a / M g 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 d a t a on the extremities which commonly have the greatest error. The
value is typical for m a n y divalent exchange reactions with N a on montmorillonite and is
adopted as a convenient approximation for all unidivalent reactions in Table 1 including
transition metal exchange determined by Maes et al. (1976).
Estimates of equilibrium constants for reactions between Ca, Mg or Cu and the clay edges
can be extracted from these isotherms by a method of successive approximation. This
involves performing a computer simulation of the exact experiments conducted by Sposito et
al. (1983b) using the ion-exchange constants and the cation/edge constants estimated
previously. The appropriate value of the divalent ion/edge constant is the one which best fits
the isotherms. Ca edge constants were determined from the C a / M g 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 complexation constants (equations (21) and (24))
for Ca and Mg. These are again determined by successive computer simulation of the exact
384
P. Fletcher and G. Sposito
TAm.E 3. Complex-ion formation reactions, equilibrium constants and
compositional dependencies.
Reaction
Na + + X- ~ NaX
H20 + X - ~ H X + OHNH~ + X- ~ NH4X
K++X-~KX
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
Values of K~ x/~Ri and
compositional dependency
1010
1"26 x 10-4 x QO
2"90 x 101~ x QO
1.80 x 101~ x QO
0.95 • 10t~ • 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 u s i n g p r e v i o u s l y d e t e r m i n e d c o n s t a n t s . T h e v a l u e o f t h e u n k n o w n is t h e o n e
w h i c h b e s 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 e x c h a n g e .
S i m i l a r m e t h o d s o f s u c c e s s i v e a p p r o x i m a t i o n w e r e u s e d to e x t r a c t t h e r m o d y n a m i c d a t a for
all r e a c t i o n s o f first-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 i n g 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 v a l u e s d e t e r m i n e d b y M a e s et al. (1976). V a l u e s o f Ka x / ~
for
h y p o t h e t i c a l s u r f a c e r e a c t i o n s for t h e i t h ion, a l o n g 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.
COMPUTER
SIMULATIONS
A range of observations resulting from montmoriUonite/electrolyte interactions are
s i m u l a t e d u s i n g d a t a i n T a b l e s 2 a n d 3. A c t i v i t y coefficient c o r r e c t i o n s w e r e m a d e to t r u e
s o l u t i o n c o m p o n e n t s a s s u m i n g i d e a l b e h a v i o u r for t h e clay p h a s e .
Exchange between monovalent cations
Fig. 1 s h o w s 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 c h l o r i d e b a c k g r o u n d s a t t h r e e
d i f f e r e n t t o t a l c h l o r i d e 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 s o s h o w n are i s o t h e r m s for t h i s
Chemical modelling of montmorillonite/electrolyte reactions
385
1.0
&
0
HI
O
A
+
x
0.0
TN
TN
TN
TN
TN'
TN
0.1
0.05
0.025
0.1
0.I
0.1
pH 7
pH 7
pH 7
pH 6
pH5
pH 4
A~
~}
,4-
f
0,6
I
P
0.4
0.2
O
0.0
0.0
I
I
I
I
0.2
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
O TN0.1
O TN 0 . 0 5
O TN 0 . 0 2 5
TN0.1
+ TN0.1
• TN0.1
1.2
pH7
pH 7
pH 7
pH0
pH5
pH4
1.1
x..
1.o
L~
+
+
+
+
+
+
+
+
+
+-14-
0.9
x
x
x
x
x
x
x
x
x
xxX
0.8
0.7
0.0
#
0.2
I
0.4
I
0.8
I
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).
P. Fletcher and G. Sposito
386
1.0
'"'
I
0 I0 moi/t
2
0.05 mol/l
0.8 3 0.025rnol/1
0.6
L)
I
['~ 0.4
0.2
1
3
0.0
0.0
0,2
0.4
0,6
1.0
0.8
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 d e
Perehlorate Predicted
2 Chloride Predicted
EH
I
O.a
]J
~ / n
0.6
t
~
0.4
o.~
O
~
rn
o.o
0.0
0.2
0.4
0.6
0.8
1.0
E-Ca(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 N a / C a 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 Perchlorate
[] Chloride
D
1 Perchlorate Predicted
2 Chloride Predicted
0.B
o.~,~
i~ mb
0.4
0.2
~
0.0
0,0
[
0.2
]
0.4
I
0.6
08
1.0
E-~g(~
exchange in chloride and percholate solutions. E q u i v a l e n t fraction
magnesium in the clay (E-Mg(c)) vs. equivalent fraction of magnesium in solution (E-Mg(s)).
FIG. 5. M a g n e s i u m / s o d i u m
of
1.5
0 Ca
[] M g
-- Ca
--Mg
14
- Chloride
- Chloride
Predicted
Predicted
1.3
o
1.2
.~ 1.1
1.0
o
o
0.9
O.B
0.7
I
0.0
0.2
I
I
0.4
06
I
0.8
10
E-M(c)
chloride adsorption on C E C for C a / N a a n d M g / N a e x c h a n g e .
equivalent fraction of divalent ions on the clay (E-M(c)).
FIG. 6. Influence o f
C E C vs.
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
388
P. Fletcher and G. Sposito
1.0
0
Ca/Me Data
/
o.B
0.6
s
I
r-~ 0.4
0.2
0.0
0.0
I
I
I
I
0.2
0.4
0,6
0.8
1.0
Z-Me(c)
FIO. 7. Calcium/magnesiumexchange isotherm in perchloratesolution. Equivalentfraction 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
~
0.0
" t
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
O pH 6.0
12 p H 5 . 5
3.5
O pH 5.0
pH 4.5
3.0
DO
2.5
0
0
O
z.o
1.5
A
O
O
oA
~oo
o
o
o
aA~
A
A
A
O
A
O
A
A
1.0
0.5
0.0
I
0.2
I
0.4
I
0.8
I
0.8
1.0
E-Zn(c)
FIG. 9. The effect of nitrate adsorption and edge effects on apparent selectivity for Zn/Na
exchange. Kv 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 Kv 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.
390
P. Fletcher and G. Sposito
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
0-4 + 0-1
0-4 + 0-1
0.3 + 0"1
0"4 + 0"2
0"3 + 0.1
0"38 __+0"07
0"3 __+0.2
0.3 + 0.1
0"29 + 0"06
0.4 + 0.2
0.36
0-37
0-36
0"36
0"36
0"37
0'36
0.36
0-38
0"36
0"38
0-00 + 0.00
0.07 + 0-003
0.143 + 0.003
0"203 +_0"01
0"270 + 0.01
0"304 + 0"08
0"410 + 0"02
0-45 + 0-01
0"53 __ 0.02
0"56 __0"02
0-61 + 0"02
0.00
0-067
0.123
0.192
0.250
0"32
0.44
0.45
0"48
0"57
0"62
0.73 + 0.01
0.43 + 0.02
0.46 + 0-02
0.40 + 0.02
0.34 __ 0-01
0.33 __0.009
0-273 + 0.005
0-200 + 0.001
0.14 + 0.01
0-06 __ 0.05
0.00 + 0.00
0.64
0.56
0.52
0.44
0.39
0.32
0.23
0-19
0.14
0.064
0.00
0.2 + 0-06
0-14 + 0.09
0-1 + 0.03
0.1 _+0.07
0"20 + 0"06
0"15 + 0.08
0.16 + 0.07
0-17 + 0-08
0.15 + 0.09
0.23 + 0.08
0-1 + 0.09
0.23
0.23
0-23
0.23
0"23
0"23
0.22
0.23
0-23
0-22
0.23
0.00 + 0.00
0.071 + 0-005
0.145 + 0.005
0.250 + 0-02
0"370 + 0-01
0"45 + 0-01
0.55 +__0-01
0-59 + 0-04
0.64 + 0.02
0"63 _ 0.03
0.93 + 0.03
0-00
0.078
0.152
0.26
0"34
0'39
0.47
0.53
0.61
0-64
0-78
0.85 + 0.06
0.79 + 0.06
0.76 + 0-07
0.62 + 0-04
0-52 + 0-02
0.42 + 0-01
0.29 +_0.02
0.25 + 0.02
0.14 + 0.02
0.076 _ 0.006
0.00 _ 0.00
0-78
0-69
0.62
0.523
0.47
0.49
0.31
0.24
0.16
0.085
0.00
Concentrations in mol kg -1 dry clay.
m = measured.
p = predicted.
CONCLUSIONS
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 e d 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
u s i n g t h e c o n c e p t o f h y p o t h e t i c a l s u r f a c e 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 o n - a s s o c i a t i o n m o d e l s s u c h as G E O C H E M ( S p o s i t o & M a t t i g o d , 1980),
c a n b e u s e d to s i m u l a t e m u l t i p l e r e a c t i v i t y i n c l u d i n g s i m u l t a n e o u s i o n - e x c h a n g e , c o m p l e x ion formation and anion adsorption. Available literature data on the reactivity of
montmorillonite have been reviewed and a preliminary thermodynamic dataset compiled.
T h e s e d a t a w e r e u s e d to s i m u l a t e t h e e s s e n t i a l f e a t u r e s o f t h e r e a c t i v i t y o f W y o m i n g
b e n t o n i t e i n d i l u t e electrolytes to s h o w 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 n o n - i d e a l b e h a v i o u r c a n a r i s e 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 h e clay s u r f a c e s
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 r e a s s u m e d to b e ideal, w i t h a c t i v i t y
c o r r e c t i o n s m a d e to t r u e s o l u t i o n 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 t h e t e c h n i q u e s are flexible 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 a c t i v i t y
coefficients if r e q u i r e d . I m p r o v e d d a t a will b e o b t a i n e d if f u t u r e e x p e r i m e n t s a r e d e s i g n e d to
e x a m i n e specific effects w h i l e m i n i m i z i n g o r r e m o v i n g t h e 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
reactions.
Chemical modelling o f montmorillonite/electrolyte reactions
391
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