Influence of Temperature on Ion Adsorption by Hydrous Metal Oxides

Dec 7, 1990 - Chemical Modeling of Aqueous Systems II. Chapter 22, pp 282–292. DOI: 10.1021/bk-1990-0416.ch022. ACS Symposium Series , Vol. 416...
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Chapter 22

Influence of Temperature on Ion Adsorption by Hydrous Metal Oxides

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Michael L. Machesky Geosciences Department, Pennsylvania State University, 208 Deike Building, University Park, PA 16802

Adsorption processes are most often studied and modeled at room temperatures. A t other temperatures, however, several factors act to perturb adsorption phenomena. These include shifts in equilibria among solution species, changes in the zero point of charge (pHzpc) of the sorbent, and changes in the ratio of adsorbed to solution phase ions. Fortunately, the magnitude of these factors can be predicted with standard thermodynamic relationships if solution and adsorption enthalpy data are available. Comparative adsorption studies at several temperatures, and calorimetry can be used to obtain adsorption enthalpies. Relatively few studies have been performed but these do suggest several general trends apply. First, the pHzpc of hydrous metal oxides appear to decrease with increasing temperature and consequently, proton adsorption enthalpies are exothermic. Typical values at the pHzpc are -20 to -45 kJ/mole which corresponds to pHzpc changes of less than ±0.5 p H units for 25 ±20°C. Second, anion adsorption decreases with increasing temperature while metal cation adsorption increases and as a result, anion adsorption is exothermic and metal cation adsorption endothermic. Available data suggest adsorption enthalpies are often ±20 kJ/mole or greater. This implies 20°C temperature gradients, which are rather common in temperate climates, could more than double or halve the adsorbed to solution ratio of a particular ion. Thus, temperature should be considered an important variable when investigating or modeling adsorption processes.

Cation and anion adsorption by hydrous metal oxides influence several processes of environmental concern including contaminant transport, nutrient availability, and mineral dissolution rates (1,2). Various factors influence the amount of a particular ion adsorbed including solution p H , type of oxide and its surface area and crystallinity, time, ionic strength, properties and concentration of the adsorbing species, and competing species. These factors have received various degrees of scrutiny in previous studies. Temperature is another potentially important variable but has not to date received as much 0097-6156/90/0416-0282$06.00/0 ο 1990 American Chemical Society

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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22.

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Influence of Temperature on Ion Adsorption

attention. Most laboratory studies have been conducted at room temperatures (20 to 30°C) and few investigations have obtained data at other temperatures for comparison. Extrapolating these room temperature data to actual environmental situations is difficult for a number of reasons and one of these may be the temperature differences involved. For example, average surface and shallow ground water temperatures are less than 25°C in polar and temperate climates and, seasonal fluctuations occur. In addition, thermoclines divide surface and deeper waters in many lakes and the oceans. Conversely, temperatures in deep sedimentary basins and hydrothermal systems are greater than 25°C and the importance of adsorption processes in these environments is largely unknown. Finally, the utility of metal oxides (e.g., alumina) as chromatographic supports or to help decontaminate waste process streams may be enhanced by manipulating temperature. The purpose of this paper is to outline a general framework with which the importance of temperature to ion adsorption processes can be evaluated. This will be accomplished by examining ion adsorption enthalpy data from several calorimetric and variable temperature studies. Hopefully, this information will stimulate further discussion and study concerning the temperature dependence of the adsorption process and result in more accurate predictions when modeling adsorption processes in natural systems is of concern. IMPORTANT FACTORS Several factors require consideration to assess the importance of temperature to adsorption processes. First, equilibria between solution forms of an adsorbing ion are temperature dependent. Second, the zero point of charge (pHzpc) will change with temperature and this alters the p H range of positive and negative surface charge. Third, adsorbed to solution phase ratios of cations and anions will vary with temperature. A fourth factor concerns adsorption kinetics but this is beyond the scope of this discussion which deals only with trends which can be defined on the basis of thermodynamic (i.e., adsorption equilibrium) relationships. Temperature Effects on Solution Equilibria Changes in solution species distributions with temperature must be considered because amounts adsorbed depend on the predominant form of a species present. For example, adsorption of a divalent anion onto a positively charged oxide surface would be favored over the monovalent form of the same species according to electrostatic effects. The simplest thermodynamic expression available for estimating changes in solution species distributions is the integrated form of the van't Hoff equation with the reaction enthalpy ( Δ Η ) taken to be independent of temperature, Γ

\og(K /K ) 2

{

= (AH/2.303R)

.(1.1) T

where

l

T

m

2

is the reaction equilibrium constant at temperature, T

2

(Kelvin);

K j is the reaction equilibrium constant at temperature, T j ; R is the gas constant. Thus, i f the reaction enthalpy can be determined and the reaction equilibrium constant is known at one temperature, the equilibrium constant at a second temperature can be calculated. If the reaction enthalpy is temperature dependent (invariably the case over a large enough temperature range), more complicated expressions involving heat capacity terms must be used Q ) .

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

284

CHEMICAL MODELING OF AQUEOUS SYSTEMS II

Fortunately, equation (1) is adequate for most solution reactions near room temperature, and several computer equilibrium models make these corrections i f the required enthalpy values are available. Unfortunately, enthalpy data for many important solution species (e.g., metal ion species and ion pairs) have not been determined. In a few instances the temperature dependence of a reaction is very well known. A particularily relevant example for aquatic chemistry is log K for water which is given by, w

log K

=

w

-4470.99 + 6.0875 - 0.01706T Τ

(2)

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where Τ is the temperature in Kelvin Q ) . Temperature Effects on the P H Z P C of Oxides This effect refers to how the affinity of the potential determining ions for hydrous oxide surfaces ( H , O H " ) change with temperature. Shifts in the pHzpc with temperature will change the magnitude of the surface charge at a particular p H and hence the electrostatic influence on ion adsorption processes will vary. Two methods have been used to evaluate this dependence; potentiometric acid-base titrations performed at various temperatures and isoperibol solution calorimetry adapted to suspension titrations. Procedural details for both these methods are available elsewhere (4,5). A simple modification of the various temperature technique termed a ' Δ Τ titration' has also been developed (6). Briefly, a hydrous metal oxide suspension is equilibrated at the pHzpc, the temperature is changed slightly, and the new p H equated to the pHzpc at that temperature. Good agreement was found for rutile and hematite between pHzpc values determined with ' Δ Τ titrations' and complete acid-base titrations at several temperatures (6). With isoperibol solution calorimetry, proton adsorption and desorption enthalpies are obtained and these can be used to predict how the pHzpc varies with temperature. The Ί p K ' model is especially useful for this purpose. +

a

4

This model has been gaining increasing popularity relative to the 2 p K ' model for describing the surface charging characteristics of hydrous metal oxide surfaces (7,&)· The basic charging equation for this model is, a

[SO"

1 / 2

+

+ 1

2

] + [H ] = [ S O H / ]

(3)

where SOH represents a surface hydroxyl group which has a formal charge of ±1/2 because of crystallographic considerations (7). Since at the pHzpc, - 1

2

+ 1

2

[SO / ] = [SOH / ]

(4)

it follows that, log K

H

= pHzpc

(5)

where K J J is the equilibrium constant for equation (3). Assuming the validity of the Ί p K ' model, proton adsorption enthalpies at the pHzpc can be used to predict the temperature variation of KJ_J (and therefore the pHzpc) with the van't Hoff relation (6), a

K

H

-

Δ Η . /2.303 R T

2

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

(6)

22.

MACHESKY where

AH j a (

285

Influence of Temperature on Ion Adsorption

$

is the proton adsorption enthalpy at the pHzpc which is

assumed to be independent of temperature. Conversely, i f the pHzpc variation with temperature is known (the dlog K / d T term), the proton adsorption enthalpy can be calculated. Table I lists the pHzpc values determined at various temperatures for several hydrous metal oxides along with proton adsorption enthalpy values calculated using equation (6). Except for one instance, pHzpc values decrease with increasing temperature and therefore calculated proton adsorption enthalpies are exothermic. The first η-Α^Ο^ entry is clearly anomalous in sign and magnitude and can not be considered representative of hydrous metal oxides in general. Table II lists proton adsorption enthalpies determined using calorimetry and there is reasonable agreement between Tables I and II for similar oxides. Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch022

H

Proton (TAS j ) ac

s

adsorption

free

energy

(AG j )

are also included in Table II.

a c

s

and

entropy

values

Free energy values are obtained

at the pHzpc using the standard thermodynamic relation, A G = -2.303 R T log K

(7)

H

assuming the validity of the ' l p K model and, adsorption entropies are determined by difference. Enthalpy and entropy both contribute to the favorable proton adsorption free energy values with enthalpy being relatively more important. Reaction enthalpies reflect bond formation energetics while net solvation changes are large contributors to reaction entropies in aqueous solutions Q7). Thus, the energetics of the bond formation process appears to be more important than net solvation changes in the interfacial region for proton adsorption. Also, proton adsorption free energies and enthalpies for ferric and Al-oxides are similar and larger than those for rutile. This is consistent with the larger formal charge of the T i cation (+4) which would tend to form weaker bonds with protons (6). However, other factors must also influence the strength of the proton-surface bond since some metal oxides with lower cation formal charges (e.g., NiO) have relatively small proton adsorption enthalpies. Proton adsorption enthalpy data at the pHzpc and equation (6) permit estimation of expected changes in pHzpc with temperature. Ferric and Al-oxides, for example, are characterized by a proton adsorption enthalpy in the pHzpc region of about -40 kJ/mole. Thus, we can predict that the pHzpc will decrease about 0.024 p H units per degree temperature increase or, a pHzpc of 8.0 at 25°C would be 8.5 at 5°C and 7.5 at 45°C. It has also been suggested that an 'upper bound' for proton adsorption enthalpies is the enthalpy of water formation which is -55.83 kJ/mole at 25°C (£). Most of the enthalpy values in Tables I and II are less than this value but a much larger data base is needed to confirm this hypothesis. For example, no enthalpy data are available for S1O2 although zeta potential values at p H 4 become more negative as temperature increases which suggests the pHzpc is also decreasing (J_8). The change in pHzpc with temperature although predictable for many hydrous metal oxides is rather slight given the variability in the measured pHzpc for a particular oxide. For example, pHzpc values for goethite range from 7.0 to 9.0 Q9). Thus, changes in pHzpc over earth surface temperature ranges are expected to only slightly influence cation and anion adsorption. A t higher temperatures, however, changes in the pHzpc will become relatively more important. a

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

CHEMICAL MODELING OF AQUEOUS SYSTEMS II

286

Table I. Changes in pHzpc with temperature obtained from the literature and corresponding proton adsorption enthalpy values calculated using equation (6)

Oxide

TempCC)

a-Fe 0 Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch022

2

3

7-Al 0

3

-Al 0

3

2

2

7

2

Co 0 3

4

NiO

s

(

k

J

/

m

o

l

e

)

S o u r c e

(6)

5 20 50

5.80 5.60 5.10

-26.7 (5 to 50°C) -17.6 (20 to 50°C)

(fi)

25 75

6.00 5.50

-19.9 (25 to 75°C)

(2)

25 90

6.55 5.40

-36.6 (25 to 90°C)

(1Û)

30 50 80

6.80 6.45 6.00

-32.8 (30 to 50°C) -32.8 (30 to 80°C)

(11)

10 50

4.45 8.95

+ 197 (10 to 50°C)

(12)

30 90

9.06 8.36

-24.6 (30 to 90°C)

(10)

25

8.00

-44 (25°C)

25 80

10.35 9.62

-26.7 (25 to 80°C)

(14)

25 80

9.85 9.06

-28.9 (25 to 80°C)

(14)

4

7-Al 0

d

-45.1 (5 to 60°C) -62.4 (5 to 20°C) -37.4 (20 to 60°C)

3°4

3

a

9.50 8.60 7.80

2

Fe 0

^H

5 20 60

3

Ti0 (rutile)

F e

pHzpc

1

(12)

Determined from the change in surface potential with temperature and the 2 p K ' model. The listed enthalpy is the average of 4

a

those for the individual surface hydrolysis constants (-54 and -34.8 kJ/mole).

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

22.

MACHESKY

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Influence of Temperature on Ion Adsorption

Table II. Proton adsorption enthalpies determined using calorimetry and calculated adsorption free energies and entropies at the pHzpc and 25°C

Oxide

Source

pHzpc

* ads

Ti0 (rutile) Ti0 (rutile) a-Fe 0

6.0 5.5 8.7

-22 -22 -38

-34 -31 -50

+ 12 +9 + 12

(5) (6) (6)

a-FeOOH 7-Al 0 a-Al 0

8.1 8.5 8.8

-39 -42 -44

-46 -49 -50

+7 +7 +6

(5) (il) (16)

G

* ads

H

T A S

ads

kJ/mole 2

2

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2

3

2

3

2

3

1

Estimated from heat of immersion data.

Temperature Effects on Cation and Anion Adsorption The specific adsorption of anions and cations are also influenced by temperature changes and adsorption studies at various temperatures and isoperibol solution calorimetry have been used to investigate this influence. However, relatively few of these studies have been conducted. Residual solution concentrations at two temperatures can be used with a form of the Clausius-Clayperon equation to calculate ion adsorption enthalpies (20). AH

a d s

= [2.303R log ( C / C j ) ] / ( 1.1) τ

(8)

2

2

T

]

where A H is the isosteric heat of ion adsorption (assumed to remain constant over the temperature range considered) at a given surface coverage; R is the gas constant; C is the equilibrium solution concentration of the ion at temperature, T and the given surface coverage; and C j is the equilibrium concentration of the ion at temperature T j and the given surface coverage. Complete adsorption isotherm data (low to high surface coverage) at several temperatures is most useful since this also provides information about the variation in adsorption enthalpy with surface coverage (20). If residual solution concentrations increase with increasing temperature (adsorption decreases) calculated adsorption enthalpies will be exothermic and residual solution concentrations will decrease with increasing temperature (adsorption increases) for endothermic adsorption enthalpies. Conversely, ion adsorption enthalpies determined using calorimetry can be used to predict the expected ratio of residual solution concentrations at two temperatures. Strictly speaking, comparison of isosteric and calorimetric enthalpies requires use of the relation, a d s

2

2

AH

isosteric

where

=

AH

differential

^^differential

r e

^

e r s

+

R

T

t 0

( 9 )

adsorption

enthalpy

measurements

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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determined incrementially from low to high surface coverage. In actual practice, however, adsorption enthalpies determined using calorimetry are probably intermediate between true differential and isosteric enthalpies (2J_). In any case, the R T factor (+2.48 kJ/mole at 25°C) makes only a slight contribution to the measured differential enthalpies. For ion adsorption studies, much more significant corrections are associated with proton uptake and release during anion and cation adsorption, respectively (6.22). Representative anion isosteric adsorption enthalpies at several surface coverages for goethite are compiled in Table III.

Table HI. Isosteric adsorption enthalpies for representative anions and several fractional surface coverages (Θ) of goethite

Anion

PH

7

5

3

HSe0 " 3

ads

(kJ/mole)

0.1 0.5 0.8

-24 -19 +3

4

0.1 0.5 0.8

-28 -17 -9

4

0.1 0.5 0.8

-27 -7 -7

4

0.1 0.5 0.8

-10 -7 0

6.7

0.074 0.15 0.22

-82 -29 -22

4

C H 0 -

AH

4

H P0 " 2

θ

Method

Calorimetry

Source

(22)

Ν

»

Η

Two Temperatures

(2Û)

In all instances adsorption enthalpies are exothermic at surface coverages < 80% of maximum for each anion. Adsorption enthalpies are more exothermic at low coverages with values as large as -82 kJ/mole for selenite at surface coverages < 10% of maximum. These data indicate the goethite surface is energetically heterogeneous with a relatively small fraction of the available surface sites (< 10%) being of highest energy. Also, phosphate, salicylate and selenite have similar adsorption enthalpies at low (10 to 20%) surface coverages which suggests bonding mechanisms are similar. This has been confirmed with in-situ spectroscopic techniques which indicate these anions adsorb in an inner-sphere bidentate or chelate type fashion (23,24)· Fluoride, however, must bind in a monodentate fashion and consequently, lower adsorption

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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Influence of Temperature on Ion Adsorption

289

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enthalpies result. It can also be suggested that outer-sphere complex formation would result in relatively low adsorption enthalpies (< -10 kJ/mole at low surface coverages). Fewer data, particularily calorimetric, are available for evaluating the influence of temperature on metal cation adsorption. The enthalpy of Cd(II) adsorption onto rutile was determined using isoperibol solution calorimetry and a value of +10 kJ/mole was found (6). A recent variable temperature study (25) allows enthalpies for Cd(II), Zn(II), and Ni(II) adsorption onto hematite (synthesized in the presence of 0.86% Si) to be calculated using equation (8). These data are summarized in Table IV.

Table IV. Residual solution concentrations at 5, 20, 25 and 35°C and average isosteric adsorption enthalpies calculated using equation (8) for cadmium, zinc and nickel onto hematite at pH=6 and a total metal concentration of ΙΟμΜ. Concentration data from (21)

Metal ion

5°C

20°C

25°C

35°C

AH

ads

(kJ/mole)

solution concentration (uM) Cd(II) Zn(II) Ni(II)

6.9 4.1 8.1

5.7 2.0 5.9

5.0 1.1 3.8

3.9 0.5 2.2

+ 13 +49 +30

The calculated enthalpies vary depending on which solution concentration data are used but they are always endothermic since residual solution concentrations decrease with increasing temperature. Calculated and measured adsorption enthalpies for Cd(II) agree very well even though two different oxides and techniques were used. Furthermore, since adsorption enthalpies are endothermic, the adsorption free energy is dominated primarily by a positive entropy contribution. Partial desolvation of the metal cation upon adsorption is most likely a primary contributing factor to this entropy increase (6). The paucity of available data does not permit an assessment how metal cation adsorption enthalpies and entropies vary as surface coverage increases. If previous calorimetric cation exchange studies prove to be analogous, however, enthalpies would become more endothermic and entropies more positive since an increasing fraction of hydration waters would be shed as surface coverage increases (2è). Table V illustrates the expected influence of temperature on ion adsorption processes for the range of exothermic adsorption enthalpies listed in Table III.

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

290

CHEMICAL MODELING OF AQUEOUS SYSTEMS II Table V . Calculated solution concentration ratios for the range of exothermic adsorption enthalpies listed in Table III. C25/C5 and C25/C45 refer to the ratios between 25 and 5°C and 25 and 45°C, respectively AH

ads

(kJ/mole)

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-80 -40 -20 -10 -5

C

25

/ C

10.2 3.2 1.8 1.3 1.2

5

c

2

5

/c

4

5

0.13 0.36 0.59 0.77 0.87

Residual solution concentrations are greater at 25 compared to 5°C and less at 25 compared to 45°C and both ratios approach unity as the enthalpy becomes less exothermic. Thus, at a given total concentration, a temperature decrease from 25 to 5°C is expected to result in increased adsorption while a temperature increase to 45°C should result in anion desorption. For cation adsorption, the expected concentration ratios are the inverse of those listed since cation adsorption enthalpies are endothermic. The predicted temperature influence is indeed significant since for an adsorption enthalpy of ±20 kJ/mole (less than that found for many species in Tables III and I V ) , a temperature ±20°C removed from 25°C would nearly double or halve residual solution concentrations. Thus, adsorption experiments should be conducted at the temperature of interest. In addition, temperature gradients or fluctuations of ±20°C are fairly common in natural systems. Thermoclines separate warm surface water from colder deeper waters in oceans and many lakes and it is conceivable that the scavenging of trace species by settling inorganic particulate matter is perturbed by this temperature gradient. In this case enthalpy data suggest cations would be released and anions scavenged more efficiently as particulates settle through the thermocline although p H decreases could augment or even dominate the temperature effect. As another example, seasonal temperature fluctuations in vadose zones or shallow ground waters could perturb adsorption processes affecting contaminant transport. CONCLUSIONS The influence of temperature on ion adsorption processes can be predicted using adsorption enthalpy data and standard thermodynamic relationships. Comparative studies at several temperatures and calorimetry can be used to obtain adsorption enthalpies and those data that are available suggest certain generalizations may apply. First, the pHzpc of hydrous metal oxides decreases as temperature increases and vice-versa. With one exception all data in Tables I and II follow this trend. Furthermore, the magnitude of the calculated (from variable temperature studies) and measured (using isoperibol solution calorimetry) proton adsorption enthalpies generally fall between -20 and -45 kJ/mole and there is reasonable agreement among different studies for the same solid. Still, more data is needed to confirm these trends. In any

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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291

event, the magnitude of the resulting pHzpc change is rather slight and so this influence on the specific adsorption of ions is not great provided the pHzpc and the 'adsorption edge' of a particular ion do not coincide. Second, specific adsorption of anions appears to increase and metal cation adsorption to decrease with decreasing temperature and vice-versa. This generalization is advanced on the basis of a very limited data set which suggests metal cation adsorption is endothermic and anion adsorption exothermic although it is far from certain that all adsorbed cations and anions will follow this trend. The reasons underlying this trend are still unclear but are probably strongly dependent on the net solvation changes of the adsorbing ion and displaced surface groups. In addition, the shift in pHzpc and anion or cation adsorption compliment each other. That is, as temperature decreases the pHzpc increases which enlarges the domain of positive surface charge and should enhance anion adsorption. Conversely, a temperature increase would decrease the pHzpc thereby promoting cation adsorption which is observed to increase as temperature increases. LITERATURE CITED 1.

2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Kinniburgh, D.G.; Jackson, M.L. In "Adsorption of Inorganics at Solid-Liquid Interfaces"; Anderson, M.A., and Rubin, A.J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; Chapter 3. Sigg, L.; Stumm, W. Colloids and Surfaces. 1981, 2, 101-117. Stumm, W.; Morgan, J.J. "Aquatic Chemistry"; Wiley-Interscience: New York, 1981, 2nd ed.; p. 68-72. Huang, C.P.; In "Adsorption of Inorganics at Solid-Liquid Interfaces"; Anderson, M.A., Rubin, A.J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; Chapter 5. Machesky, M.L.; Anderson, M.A. Langmuir. 1986, 2, 582-587. Fokkink, L.G.J. Ph.D. Dissertation, Agricultural Univ., Wageningen, The Netherlands, 1987. Van Riemsdijk, W.H.; De Wit, J.C.M.; Koopal, L.K.; Bolt, G.H. J. Colloid Interface Sci. 1987, 116, 511-522. Westall, J.C. In "Aquatic Surface Chemistry"; Stumm, W., Ed.; Wiley-Interscience: New York, 1987; Chapter 1. Berube, Y.G.; DeBruyn, P.L. J. Colloid Interface Sci. 1968, 27, 305-318. Tewari, P.H.; McLean, A.W. J. Colloid Interface Sci. 1972, 40, 267-272. Blesa, M.A.; Figliolia, N.M.; Maroto, A.J.G.; Regazzoni, A.E. J. Colloid Interface Sci. 1984, 101, 410-418. Akratopulu, K . Ch.; Vordonis,L.; Lycourghiotis, A. J. Chem. Soc., Faraday Trans. I. 1986, 82, 3697-3708. Vlekkert, H.V.D.; Bousse, L.; Rooij, N.D. J. Colloid Interface Sci. 1988, 122, 336-345. Tewari, P.H.; Campbell, A.B. J. Colloid Interface Sci. 1976, 55, 531-539. Machesky, M.L.; Jacobs, P.Α., Colloids and Surfaces, in press. Griffiths, D.A.; Fuerstenau, D.W. J. Colloid Interface Sci. 1981, 80, 271-283. Nancollas, G.H. "Interactions in Electrolyte Solutions"; Elsevier: Amsterdam, 1966; Chapter 5. Alekhin, Yu.V.; Sidorova, M.P.; Ivanova, L.I.; Lakshtanov, L.Z. Koll. Zhur. USSR (Engl. Trans.). 1984, 46, 1195-1198. Zeltner, W.A.; Anderson, M.A. Langmuir. 1988, 4, 469-474. Balistrieri, L.S.; Chao, T.T. Soil Sci. Soc. Am. J. 1987, 51, 1145-1151.

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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21. Hayward, D.O.; Trapnell, B.M.W. "Chemisorption"; Buttersworths: Washington, D.C., 1964, Chapter 6. 22. Machesky, M.L.; Bischoff, B.L.; Anderson, M.A., Environ. Sci. Technol. 1989, 23, 580-587. 23. Zeltner, W.A.; Yost, E.C.; Machesky, M.L.; Tejedor-Tejedor, M.I.; Anderson, M.A. In "Geochemical Processes at Mineral Surfaces"; Davis, J.A.; Hayes, K.F., Eds.; American Chemical Society Symposium Series No. 323: Washington, D.C., 1986, p. 142-161. 24. Hayes, K.F.; Roe, A.L.; Brown, G.E., Jr.; Hodgson, K.O.; Leckie, J.O.; Parks, G.A. Science. 1987, 238, 783-786. 25. Bruemmer, G.W.; Gerth, J.; Tiller, K . G . J. Soil Sci. 1988, 39, 37-52. 26. Clearfield, Α.; Tuhtar, D.A. J. Phys. Chem. 1976, 80, 1302-1305. RECEIVED August 31, 1989

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