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III. Adsorption on Variable-Charge Surfaces

III. Adsorption on Variable-Charge Surfaces

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REACTION OF ANIONS AND CATIONS



187



The similarity in behavior is illustrated by this method of specifying the

reactions. The reactions differ in that the product of the first reaction is

negatively charged, while that of the second is positively charged. In both

cases, the reactions can be categorized by the pK value, which is the pH at

which the concentration of the reactant and the product (for example, HA

and A-) are equal.

Substances that are strongly adsorbed usually have a pK value in the

middle range, say, between 3 and 11. This fact led to suggestions that

adsorption requires the presence of both the charged (e.g., A-) and uncharged species (e.g., HA). However this suggestion did not account for all

the observations, and the more mechanistic explanations to be described later

are now preferred (Hingston, 1981). The observation that neither strong

bases nor strong acids are adsorbed is also explained differently (Bowden et

al., 1980a). Cations derived from strong bases, for example, Na' and K', are

surrounded by a sheath of water molecules. There is little tendency for any of

these water molecules to lose a proton and thus little tendency to coordinate

with electrophilic centres on mineral surfaces. At the other extreme, anions

derived from strong acids, for example, C1- and NO;, have a weak affinity

for protons. It has been suggested that this means they also have a weak

affinity for the electrophilic metal ions (Bowden et al., 1980a).

The ion species present in solution may be more complex than the above

simple equations suggest. Several important anions derive from acids with

more than one proton. For example, phosphoric acid has three protons and

the three pK values are approximately 2,7, and 12. Thus H,PO; is a weak

acid with a pK value of about 7. As the pH is increased, the concentration of



PH



FIG.1. Adsorption of a range of metals on (a) hematite and (b) goethite when they were

added at a rate of 20 pmollg of adsorbate.The values for the pK, for dissociation of the metals to

give the monovalent MeOH' ions are Pb, 7.71; Cu, 8; Zn, 8.96;Co, 9.65;Ni, 9.86; and Mn, 10.59

(Baes and Mesmer, 1976). (From McKenzie, 1980.)



188



N. J. BARROW



H,PO, falls and that of HPO2- rises until, near pH 7, they are equal.

Further, the metal cations tend to form complexes with anions to give species

such as Me(H,O),Cl+. These species need to be taken into account when

considering the possible reactions.

Several comparisons have been made of the adsorption of hydrolyzable

metal ions on oxides. These comparisons are often plotted as in Fig. 1,

derived from McKenzie (1980),with each line representing a given ratio of

adsorbate to adsorbent. These data are characteristic of many published

results in that they show a rapid transition from little adsorption to almost

complete adsorption over a pH range of slightly more than one pH unit. They

are also characteristic in that they show a general trend for the pH at which

adsorption occurs to be correlated with the pK for dissociation of the metal

(Fig. 1). However, adsorption occurs at a pH that is several pH units lower

than the pK. This difference is partly a function of the experimental

conditions because adsorption occurs at a lower pH when the ratio of

adsorbate to adsorbent is higher (Benjamin and Leckie, 1981). Nevertheless,

adsorption occurs when the concentration of the monovalent ion species

(simply written MeOH') is low but increasing 10-fold for each increase of

one pH unit.

The results in Fig. 1 are also characteristic in that they show some

inconsistency between the adsorbents in the preference for metals. Thus, in

one case lead is adsorbed at a lower pH than copper, and in the other the

opposite is true. The differences between adsorbents become greater when the

comparison is between, on the one hand, iron oxides such as hematite and

goethite and, on the other hand, manganese oxides such as birnesite. The iron

oxides have a point of zero charge near pH 8, whereas birnesite has a point of

zero charge near pH 2. Birnesite is therefore negatively charged above pH 2.

McKenzie (1980) showed that birnesite adsorbs the positively charged

cations more effectively at low pH than do the iron oxides.

Fewer comparisons have been made of the adsorption of anions on oxides.

The outstanding example is the work of Hingston et al. (1972). The behavior

is clearly different from that of the metals. Two kinds of pattern can be

discerned (Fig. 2). For fluoride and silicate, increasing pH increased adsorption until a peak was reached near the pK of the acid. For fluoride, the species

present were H F and F-; for silicate, H,Si04 and H,SiO,. For selenite and

phosphate, increasing pH decreased adsorption but the decrease became

more marked above the pK,. The ions present in these cases were HSeO, ,

SeOi- and H,PO;, HPO:-, respectively.

Sets of graphs such as those in Figs. 1 and 2 can be prepared for a given

adsorbate but with varying levels of addition. From such graphs both

adsorption and final concentration can be interpolated at given values of pH.

Plots can then be prepared of adsorption against final concentration at given



189



REACTION OF ANIONS AND CATIONS



-



0,



>



5



200



I



P

e



w



9

.g

C



100



a



2



4



6



8



10



12



14



PH

FIG. 2. Adsorption of a range of anions on goethite (redrawn from Hingston et al. 1972).

Two samples of goethite were used and the level of addition of adsorbing ion differed between the

different ions.



values of pH. This interpolation procedure has frequently been used in place

of the technically more difficult method of keeping the pH constant. It has

been widely used in studies on anion adsorption, perhaps because analogous

adsorption-concentration curves are common in studies on soil.

When a hydrolyzable metal reacts with an oxide, there is a decrease in pH.

This is usually recorded as a release of protons. The effect could equally be

produced by coadsorption of O H - ions, but the conventional terminology

will be used here. Some representative values are tabulated by Schindler

(1981). The observed values usually lie between 1 and 2 mole of protons per

mole of metal adsorbed. These measurements are usually done in a nitrate or

perchlorate medium in order to avoid complexities due to ion pairs with

chloride, and hence the average charge on the ions in solution is close to 2.

The difference between the protons released and the average charge on the

ions in solution is the charge conveyed to the surface. Thus, we may describe

the same phenomenon by either specifying the protons released or the charge

conveyed to the surface. For hydrolyzable metals it is more common to

specify protons released; for anions it is more common to specify the charge

conveyed to the surface than to specify hydroxyls released. Whichever

method of specification is used it is common to specify one number as if it

were a characteristic of the adsorbate-adsorbent system. This is not so. For

example, Schindler (1981) noted that the value for protons released tends to

be higher at low pH; Hingston et al. (1972) showed that the charge conveyed

by selenite to goethite depends on the ionic strength of the medium; Bowden



190



N. J. BARROW



et al. (1980b) showed that the charge conveyed by phosphate to goethite is

high at low pH, passes through a minimum, and is high again at high pH; and

Bolan and Barrow (1984) showed that the charge conveyed during adsorption varies in a complex way with the amount of adsorption. From the

observations that reaction changes the charge, it also follows that the point of

zero charge of the oxides will be changed by reaction either with hydrolyzable

metals or with anions (for references, see Pyman et al., 1979).

The reaction between adsorbate and adsorbent may also be followed in a

third way. The electrophoretic mobility may be measured and, from this, the

electrostatic potential in the slip plane or the zeta potential calculated.

However the calculations of potentials from the observed mobility is difficult,

especially when the particles are not spherical and, indeed, van Olphen (1977)

recommended that results of such measurements be reported as mobilities

rather than be converted to potentials.



B. MODELSUSED TO DESCRIBE ADSORPTION ON

SURFACE



A VARIABLE-CHARGE



In this section the three models that have been used to describe adsorption

will be compared. The models are similar in that, in all three, the complex

distribution of ions near the surface is simplified and particular ions are

assigned to mean planes of adsorption. The models differ in the number of

No. of layers

Layer



s



1



4



3



S



s



a



B



d



Change in

potential

with

distance



Ions

adsorbed



etc.



FIG. 3. Diagram representing the interface between the solution and the surface on which

metal cations, or anions, may be adsorbed. In each case the bulk of the adsorbing material is to

the left and the solution to the right. The diagram indicates the mean planes to which individual

classes of ions are allocated and shows the change in the electrostatic potential )I with distance.



REACTION OF ANIONS AND CATIONS



191



planes that are specified and in the allocation of ions (Fig. 3). They also differ

in the way the surface reactions are specified.

1 . Single-Layer Model



In the simplest model, protons, hydroxide ions, and specifically adsorbed

ions such as phosphate are all assigned to one mean plane of adsorption. No

explicit account is taken of the background electrolyte and, in a given

electrolyte, a single value for the capacitance is used to characterize the

surface. This capacitance gives the proportionality between surface potential

and surface charge. It is apparently because the value of the capacitance is

independent of charge (Sigg and Stumm, 1980) that this model has been

called the constant capacitance model. However, this independence is also

incorporated in most other models. This terminology is also confusing on

another ground. If the identity or the concentration of the electrolyte is

changed, a different value of the capacitance is used (Westall and Hohl, 1980).

Hence, in this sense it is not constant. In this article, this model will be called

the single-layer model.

This model was introduced by Schindler and Stumm (for references, see

Westall and Hohl, 1980). It has been used to describe the adsorption of

anions on goethite by Sigg and Stumm (1980) and the adsorption of

phosphate on oxides by Goldberg and Sposito (1984). It is a characteristic

of this model that a surface site is treated like a chemical which can dissociate

to give the three species in eqn. (l), that is, SOH:, SOH', and SO-. Sites can

also react with species in solution to give products such as

SOH + H,PO,



<

SHPO,I

+ H20



+ Hf



(4)



This is one of the three equations used by Goldberg and Sposito (1984) in

their model of phosphate adsorption. The various surface products are

considered to be mutually exclusive and hence, given the concentration of the

reactants and appropriate reaction constants, the concentration of the

various products can be calculated. A complication, however, is that the

reaction takes place at a charged surface and is affected by the electrostatic

potential of the surface. Hence, in the case of Eq. (4), the intrinsic equilibrium

constant K is related to the reactants by



K exp(F$/RT)



=



[SHPO,][H+]

CSOHICH ,PO41



(5)



where $ is the surface electrostatic potential, F is the Faraday constant, R the

gas constant, and T the temperature. Goldberg and Sposito (1984) regard

the exponential term as a solid-phase activity coefficient that corrects for the



192



N. J. BARROW



charge of a surface species. The value of the electrostatic potential cannot be

measured. However, the potential can be treated as a component in computer

programs designed to calculate the species present as a result of chemical

equilibria and the system of equations can be solved.

The single-layer model was used to describe adsorption of fluoride, sulfate,

silicate, and phosphate on goethite by Sigg and Stumm (1980). For fluoride

the model described both adsorption and the charge on the surface. It is

perhaps not surprising that the small fluoride ion could be considered as

occupying the same adsorption plane as hydroxide ion. For sulfate, however,

the fit of the model was poor. This could be because, for sulfate, the

assumption of a common plane was inappropriate. For both silicate and

phosphate it is difficult to judge the model, because many of the results

seemed to involve removal of most of the ions from solution, that is,

adsorption was mostly determined by the initial concentration of adsorbate.

Although only a limited amount of data was presented by Goldberg and

Sposito (1984), the single-plane model was able to describe the effects of pH

and of phosphate concentration on phosphate adsorption fairly well.

Four criteria may be suggested by which this, or any other model, may be

judged. These are simplicity, comprehensiveness, precision, and correspondence with reality. The single-layer model is simple in concept. Provided it is

restricted to one concentration of a given electrolyte, few parameters are

needed to describe the charge components of the model. However, several

parameters are needed to model adsorption of ions. Sigg and Stumm (1980)

used five separate equations to describe reactions of phosphate with the

surface, and hence five parameters were needed to represent the reaction

constants of these equations. Goldberg and Sposito (1984) used three

equations and hence three parameters. Therefore, in this respect the model is

not especially simple. Further, the simplicity of the concepts may well be at

the cost of comprehensiveness. Is the model able to provide a consistent

description of the adsorption of a wide range of anions and cations and, at the

same time, describe the change in charge produced by that adsorption?

Current evidence suggests that it is not. In order to judge precision, the model

needs to be compared with a wide range of data to test how precisely it can

reproduce them. This has not been done. Correspondence with reality can

never be complete, because all models must simplify the real situation.

However, some aspects of the model can be compared with reality. For

phosphate adsorption on iron oxides, two of the hydroxyl groups of the

phosphate form links to the surface (Parfitt et al., 1976). The third hydroxyl

group would not normally dissociate until high pH, but for adsorbed

phosphate it appears to be half dissociated at about pH 6.7 (Nanzyo and

Watanabe, 1982). Thus there are two surface species, both with two links to

the surface. This does not correspond with the model of Goldberg and



REACTION OF ANIONS AND CATIONS



193



Sposito (1984), which required three surface species, each with a single link to

the surface.



2. Three-Layer Model

This model differsfrom the single-layer model in that ions near the surface

are allocated to three distinct planes. It was introduced by Yates et al. (1974),

Davis and Leckie (1978), and Davis et al. (1978). There is an innermost layer

containing adsorbed H + and OH- ions. These are responsible for the charge

gSand experience the potential $ s . This layer is separated from a second layer

that contains electrolyte ions (for example, N a + , Cl-) plus adsorbed ions (for

example, Cu2', H2P0,). These ions are responsible for the charge ap and

experience the potential $ p . A third layer contains the ions of the diffuse

layer.

The ions in the second layer are bound to surface groups, and equations for

the reactions that are thought to be involved are then written. For example,

for the electrolyte ions one might write

SO-



+ Na'



SOH;



+ C1-



SO-Na'



(6)



S0H;Cl-



(7)



and

+_



When the ions of adsorbates such as copper and phosphate are considered,

more than one species of ion may be present in solution, for example, Cu2+

and CuOH'; H 2 P 0 , and HPOi-. They may also react with two sites to

form binuclear bridging commands. Several equations might therefore be

written for each adsorbed. However, the equations used have been analogous

to the following:

SOH + Cu2+



SO-Cu2+ + H +



(8)



and



+ CU" + H,O - 1



+ 2H+



(9)

An intrinsic equilibrium constant is then defined for each reaction, and by

rearranging the equation the concentration of product may be obtained. For

example, from Eq. (8), we have

SOH



[SOCU'] = K



SO-CUOH'



[SOH] [Cu2 '1 exp( - 2F$,/R T )

CH '1 exp( - F$s/RT)



where K is the intrinsic equilibrium constant. The exponential terms in

Eq. (10) were introduced by assuming that the concentration of the reacting



194



N. J. BARROW



ions would be different at the surface from that in the bulk solution and that

this difference would be described by the Bolzmann distribution. This

approach has been criticized by Sposito (1983), who argued that it was both

unnecessary and undesirable to involve the Boltzmann distribution. Rather,

the exponential terms came from the effect of the electrical field on activity

coefficients.

As for the single-layer model, occupation of a site by one product is

considered to exclude others. Hence, given the concentrations of the reactants

and the reaction constants, the equilibrium concentrations can be calculated.

Again this involves adaptation of computer programs designed for calculating speciation in solution to permit estimation of the terms for electrostatic potential.

It is instructive to consider how this model attempts to match the charge

conveyed to the surface and how it describes the effects of pH on adsorption.

Reactions (8) and (9) convey, respectively, a charge of + 1 and a charge of

zero to the surface and consequently release, respectively, one and two

protons. Matching the observed release of protons therefore involves getting

the right mixture of reactions (8) and (9) by choosing the appropriate values

for the intrinsic equilibrium constants. In the three-layer model (and also in

the single-layer model), the effect of pH can be thought of as operating

through two mechanisms. One is via the mass-action effects of H + in Eqs. (8)

and (9) [and in Eq. (4)]. This affects the total amount of adsorption-clearly

the higher the pH, the more the reactions will go to the right and the higher

the adsorption will be. The mass-action effects also affect the balance between

Eqs. (8) and (9)-the lower the pH, the less Eq. (9) will be favored relative to

Eq. (8). [We may also view Eqn. (9) as a hydrolysis of CuZf to CuOH'

followed by adsorption of CuOH +. This hydrolysis reaction is favored by

high pH.1 The other mechanism by which pH operates is through the

exponential terms in Eq. (10) [and Eq. ( 5 ) ] . For example, in Eq. (10) a

negative value for the potential t,bp would give rise to a large value for the

exponential term and favor adsorption of the positively charged copper ions,

as would be expected. However, the potential t,bs would also be negative, and

so the effect would be partly offset by the effect of electrostatic potential on

the Ht ions.

The three-layer model was shown by Davis and Leckie (1978) to describe

the effects of pH on adsorption of the following cations: lead on aluminium

oxide, cadmium on titanium dioxide, and copper and silver on iron oxyhydroxide. The effect of concentration of adsorbate was not tested, nor was the

change in charge. Davis and Leckie (1980) used the model to describe

adsorption on iron hydroxide of one level of sulfate and four levels of selenate

and the effects of ionic strength on chromate adsorption. The match to the

chromate data was not good. James et al. (1980) used the model to describe



195



REACTION OF ANIONS AND CATIONS



the effect of pH on adsorption on titanium oxide of one level of cadmium, the

charge and zeta potentials in the absence of cadmium and the surface charge

in the presence of one level of cadmium.

The three-layer model is less simple and more comprehensive than the

single-layer model. It requires at least two parameters for any given adsorbate in order to specify equations that are analogous to Eqs. (8) and (9). In

addition, Davis and Leckie (1980) introduced a further parameter to permit

an adsorbed anion to cover more than one surface site. Its precision has not,

as yet, been adequately tested in a wide range of data. And, as the adsorption

equations are specified in a similar way to those of the single-layer model, it is

likely that the surface products do not correspond to those shown by direct

examination of the surface.

3. Four-Layer Model

a. Description of the Model. This model was developed by Bowden et al.

(1980b) from a simpler model described by Bowden et al. (1977) and in earlier

papers. It originates from the same “school” as earlier simple models

proposed by Hingston. These earlier models are still widely quoted (Mott,

1981; Schindler, 1981). However, the four-layer model is now regarded

(Hingston, 1981) as a more useful mechanistic explanation. It differs in two

main ways from the three-layer model. First, and obviously, an extra layer is

introduced and ions such as phosphate and copper are allocated to this layer.

Although we speak of a four-layer model, the position of the extra layer is not

fixed. It is envisaged that some adsorbed ions, for example, fluoride, would

reside, on the average, closer to the surface than, say, sulfate ions. Ions are

therefore postulated to differ not only in their affinity for the surface but in

their mean position when adsorbed. Hence, if widely differing ions were

present, we would have to specify further layers, for example, separate layers

for fluoride, phosphate, and sulfate.

The second difference from the other models is the way in which a surface

site is envisaged and, as a consequence, the way the adsorption equations are

derived. In this model a neutral site is considered to be

OH



/

\



Me



OH2



Hence the hydrolysis reaction is written as

/OH:

Me

\



OH 2



OH

,

I

Me’

\



OH,



+ H+



OH-







Me

‘OH



+2H+



(11)



196



N. J. BARROW



This difference has important consequences when considering the reaction

with ions. Suppose a neutral site were to react with a monovalent anion (A-),

displacing an hydroxyl group and thus causing no change in charge:

OH



A



+ A-



Me’



\



I Me’

+ OH‘OH,



OH2



(12)



One of the remaining protons could then dissociate to give a negative site.

Thus the charge conveyed to the surface could be somewhere between zero

and one, depending on the proportion of the reacting sites from which a

proton was lost. Furthermore, occupation of the sites is not mutually

exclusive. The fact that a site has reacted with the anion does not prevent it

from varying its charge by gaining or losing a proton. This is illustrated for

phosphate in the equations given by White (1980). A different approach

is therefore needed to specify the amount of adsorption produced. Consequently Bowden et al. (1977) did not write a set of reaction equations.

Rather, they argued that the electrochemical potential of an ion could be

defined by an expression that includes a term for the electrostatic potential it

experiences plus a term for its chemical activity. This equation can then be

arranged to relate activity to electrostatic potential. They then assumed that

the surface activity is equal to the ratio of the occupied sites to the vacant

sites. This gives rise to an equation that can be written as

A, =







N , ki ai exp( -zt+baFIR T )

1 kiaiexp(-z$,F/RT)



+



where A , is the adsorption of ion i, N , the maximum adsorption (in the same

units), ki a binding constant, and ai the activity in solution.

Equation (13) can be understood if it is compared to the familiar Langmuir

equation which, using similar terms, would be written as

A



=N,



kc/( 1 + kc)



(14)



Two major differences are obvious. First, the Langmuir equation, as

commonly used in soil science, does not specify individual ions. Thus for

phosphate at, say, pH 7, it implies that reaction is with all the phosphate in

solution, whereas reaction must be with phosphate ions. Second, Eq. (13)

contains the exponential terms. These may be thought of as acting as a

multiplier for the binding constant ki. Thus, for an anion, z is negative, and

hence the value of the exponential term will be small if $a is negative. This has

the same effect as decreasing the value of the binding constant. As a result, for

negative surfaces adsorption of anions is decreased, but not prevented.

Similarly, for a cation, z is positive and a negative value of $a will then



REACTION OF ANIONS AND CATIONS



197



increase the value of the product with the binding constant and so increase

adsorption. Thus, for this model, the electrostatic properties of the surface are

very important in determining the extent of the reaction. They are therefore

considered further.

b. Effects of Electrostatic Potential in the Four-Plane Model. In general,

high pH will produce a low value for the electrostatic potential t+ha and will

favor adsorption of cations and decrease adsorption of anions. This effect will

be influenced by the zero point of charge of the oxides-the lower the zero

point, the more likely that the oxide is negatively charged and, other things

being equal, the less likely it is to favor adsorption of anions and the more

likely to favour adsorption of cations. This effect was noted earlier (Section

II1,A) in that the manganese oxide (birnesite) with a point of zero charge at

about pH 2 was a more effective adsorber of cations than the iron oxides.

In this model there is a further way in which the electrostatic potential can

be altered-the position of the adsorbed layer relative to the s layer may be

changed. If the adsorbed layer is placed close to the s layer, the changes in

potential with pH in that layer are exaggerated. At low pH and therefore

b



0



i



1001



I

4



P



6



I

8



1



I

10



FIG.4. Adsorption of hypothetical anions on goethite. The goethite was assumed to have the

same properties as that used for adsorption of phosphate by Bowden et al. (1980b). It is assumed

that the ions differ in the position of the mean plane of adsorption and hence in the capacitance

between the mean planes of adsorption. The five different positions, relative to the planes s and /I,

are shown diagrammatically. (a) monovalent anion with pK, equal to 6; (b) divalent anion with

pK, well below 4 and pK, equal to 6. Values for the binding constant and for the concentrations

were chosen to give near-maximum adsorption for line 1. It was assumed that the divalent ion

would occupy twice the area of the monovalent and so have half the maximum adsorption.



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