solution interface of (hydr)oxides: A new approach

Multisite Proton Adsorption Modeling at the Solid/Solution Interface of (Hydr)oxides: A New Approach I. Model Description and Evaluation of Intrinsic Reaction Constants T. H I E M S T R A ,

W . H. V A N R I E M S D I J K , AND G. H. B O L T

Department of Soil Science and Plant Nutrition, WageningenAgricultural University, P.O. Box 8005, NL 6700, EC Wageningen, Netherlands Received July 18, 1988; accepted January 23, 1989 At the solid/solution interface of (hydr)oxides various types of surface groups exist, each reacting according to its own affinity constant (K) for protons. A model is presented that estimates the value of the log K of various types of surface groups (singly, doubly, and triply metal-coordinated O(H) and OH(H) surface groups) of (hydr)oxides. The intrinsic affinity constants (K) depend on many factors, e.g., the valence of the central cation (Me) of the (hydr)oxides, its electron configuration, and the MeH distance of the reacting surface group. Besides these also the number of surrounding ligands, the number of central cations coordinating with a ligand, and the type of reacting ligand (an oxo or hydroxo species) determine the proton affinity constant. Proton adsorption reactions can in principle be considered as a two-step proton adsorption reaction, forming OH and OH2 species at the surface. Analysis of the calculated affinity constants shows, however, that generally a surface group will react in a limited pH range (for instance pH 3-10) only according to a one-step protonation reaction (l-pKmodel). A general MUltiSlte Complexation model (MUSIC) is presented, which is based on crystallographic considerations. The new site bindingmodel (MUSIC) can unify the classical 2-pK model and the recently presented 1pK model, both being special cases of the model described here. The surface charge of a surface with more than one type of surface group can be described with one proton adsorption reaction and one discrete K for each type of surface group. © 1989AcademicPress,Inc. INTRODUCTION

o r d i n a t e d to the oxygen o r h y d r o x y l a n d the c o o r d i n a t i o n o f the m e t a l i o n (11 ). In this s t u d y various surface groups will be distinguished, based on the n u m b e r o f m e t a l ions w h i c h c o o r d i n a t e with surface O ( H ) or O H ( H ) ions. A specific surface ( o x y g e n ) g r o u p m a y be present as such o r associated with one or two protons. These f o r m s are here i n d i c a t e d as surface species. I n general, p r o t o n a d s o r p t i o n m o d e l s are based on t h e c o m b i n a t i o n o f a site b i n d i n g m o d e l a n d s o m e electrostatic m o d e l w h i c h relates the c o n c e n t r a t i o n o f the e q u i l i b r i u m sol u t i o n to the local c o n c e n t r a t i o n in a n electric field. This s t u d y will deal with the d e s c r i p t i o n o f the p r o t o n a d s o r p t i o n at the various surface g r o u p s o f the ( h y d r ) oxide surfaces, a n d with the d e t e r m i n a t i o n o f the p r o t o n affinity con-

A t the s o l i d / s o l u t i o n interface o f m e t a l ( h y d r ) oxides several types o f groups exist, as has b e e n f r e q u e n t l y o b s e r v e d in infrared studies ( 1 - 4 ) . T h e presence o f different types o f surface g r o u p s (singly, d o u b l y , a n d t r i p l y m e t a l - c o o r d i n a t e d ) at the surface has b e e n r e c o g n i z e d in the p a s t (5, 6 ) b u t has nevertheless b e e n i g n o r e d generally in site b i n d i n g models. S o m e t i m e s in these m o d e l s low site densities have b e e n used ( 7 - 1 0 ) for ( h y d r ) oxides, m u c h lower t h a n the surface site d e n s i t y o f close p a c k e d oxygens or hydroxyls, i n d i c a t i n g t h a t p a r t o f the surface g r o u p s have i m p l i c i t l y b e e n c o n s i d e r e d n o t to be reactive. O n e o f the m a i n reasons t h a t causes a difference in b e h a v i o r o f various surface oxygens o r h y d r o x y l s is the n u m b e r o f m e t a l i o n s co91

0021-9797/89 $3.00 Journal of ColloM and Interface Science, Vol. 133, No. l, November 1989

Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.

92

HIEMSTRA, VAN RIEMSDIJK, AND BOLT

MODEL DESCRIPTION stants for the proton adsorption reactions for these groups at the solid/solution interface. Surface Chemistry In the classical site binding models the tiIonic crystals can be seen as structures in tration behavior of surface groups is generally described assuming that only one type of sur- which interior ions are surrounded by neighface oxygen is reactive, adsorbing protons in bors of opposite signs. In stable ionic structures two consecutive steps, each having its own the principle of electroneutrality implies that discrete affinity constant (2-pK model). Re- the charge of a cation is compensated by the cently models have been proposed that com- charge of the surrounding anions and therefore bine a distribution (continuous or discrete ) of the neutralization of the positive charge can intrinsic proton affinity constants with an be considered as a distribution of its charge electrochemical double layer model ( 12-16). over the anions that coordinate to the cation. In this study we will consider discrete surface In turn, the charge of an anion in a crystal heterogeneity and relate it to the particular structure is in general compensated by parts surface structure of the crystal faces of min- of the electric fields of several cations and is therefore only partially neutralized by one erals. The description of the charging of the sur- cation. If the degree of neutralization of charge face by more than one type of surface group is expressed per bond, the neutralization of implies the use of a set of K values for the the anionic charge will be equal to the sum of proton adsorption reactions of the various the coordinated cationic charges reaching the groups involved. The development of proton anion. This concept was introduced by Pauling adsorption models involving more than one (20) and is often called the principle of local type of reactive surface group has lagged due neutralization of charge. The neutralization of to the absence of knowledge about the mag- charge over the surrounding bonds leads to nitude of the various K values of the different the definition of a formal bond valence (v) as proton adsorption reactions (16). In the pres- the charge (Z) of a cation divided by its coent study a general formulation for a ordination number (CN). Pauling (20, 21) MUltiSIte Complexation (MUSIC) model for referred to the bond valence v as the "strength metal (hydr)oxides will be developed. It will of the electrostatic bond." The use of this forbe shown that the affinity constants of the pro- mal charge will be illustrated for a simple crystonation reactions involving different types of tal structure like gibbsite. The A1(OH)3 (s) surface groups may be estimated rather ac- structure is characterized by aluminum ions curately, making use of a combination of in hexa-coordination with hydroxyls. The A1 knowledge gained from crystallographic and ions distribute their charge (3+) over six surrounding hydroxyls, neutralizing on the avphysical-chemical considerations. In the literature two types of site binding erage half a unit charge per AI-OH bond. It models for metal (hydr) oxides have been pre- implies a bond valence v of ½for an A1 ion in sented, the classical two-pK model and the a gibbsite crystal. Two A1 ions are needed to more recently presented one-pK model as in- neutralize the charge of the O H - ion in the troduced by Van Riemsdijk (17) and by Bolt structure. The overall chemical formula for and Van Riemsdijk (18). We will show that AI hydroxide can now be represented as the MUSIC model presented here can unify AI(OH)6/2 or more generally for simple (one both approaches because the one- and two- set of coordination numbers) metal (hydr)pKmodels from the literature are special cases oxides as of the more general model. In Part II (19) the MeOt(1-f).CN/n)OH(f. CN/n), [1] new model will be applied to several important metal (hydr) oxides. where n is the coordination number of the an. Journal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

MULT1SITE

ADSORPTION,

ion and f the fraction of anions in the structure, present as O H ions. The neutralization of charges of anions exposed on the surfaces of a crystal tends to be quite different from the interior situation due to a lower degree of metal coordination of the O / O H ions at the interface. It leads to the existence of broken bonds, causing a lower degree of neutralization. Part of the lacking neutralization of charge of the - O and - O H groups at the (hydr)oxide solid/solution interface is realized by the adsorption of protons leading to the formation o f - O H a n d / o r -OH2 surface groups. The number of protons adsorbed depends on the composition of the solution and for this reason interfaces develop the wellknown characteristics of variable charge. Besides the number of protons, the charge of a surface species is also depending on the number of coordinating cations and its formal attribution of charge. Similar singly coordinated (n = 1 ) species, M e - O H surface groups, may show quite different values for the local effective charge, visualized for instance as Si-OH 0, T i - O H 1/3-, A1-OH 1/2-, and M g - O H 2/3-. The fractional number can be considered as formal charges, attributed to the individual surface species for a proper bookkeeping of charges. The protonation of metal (hydr) oxide surface groups can be represented by the two reactions Men-O I"'v-2) + H~+ ~ Me.-OHCn'~-l); K,,l ~ .

.,-,.TT(n'v)

M e n - O H ~n'v-1) + H~+ ~ lwen-ura2

[21 ;

K~,2 [31 in which n is the number of metal cations coordinated with surface O ( H ) and v the bond valence reaching the oxygen or hydroxyl. The local proton concentration near the surface is given as [H+]. The K values for the proton adsorption reactions of the different types of surface groups are a priori unknown and almost impossible

I

93

to determine from experimental data unless in a certain pH range only one type of surface group is reactive according to only one surface reaction. For a very limited number of (hydr)oxides this is the case. From the observation that various surface groups of metal (hydr)oxides have different affinities for protons, the question arises which main factors are responsible for this difference in behavior. This will be evaluated in terms of differences in the Gibbs free energy levels of the groups involved. The intrinsic free energy o f the reactions [2] and [3] can be considered to be made up of a local electrostatic AGcoul and other contributions AG ~ (6, 22): o o AGintr = AG,~ + AGcoul.

[4]

In general two types of electrostatic interaction can be distinguished. In proton adsorption models generally one deals only with the electrostatic double layer interaction due to excess adsorption of protons in the surface layer. This contribution can be considered as the lateral part of electrostatic interaction and is calculated with an electrostatic model. Changes of AGi~tr are, however, due to electrostatic attraction and repulsion of protons by the local cations and anions of the surface group. This local electrostatic contribution is generally not expressed explicitly in classical site binding models (6, 22). Generally it has been included in the free energy term AG ~ and therefore in the intrinsic K value o f the proton association reactions. However, in our approach we make the local electrostatic contribution explicit in order to show the nature of the differences in the K values o f proton adsorption reactions, e.g., being due to different local electrostatic contributions. The local electrostatic energy which is gained or spent by the approach o f a H + to the anions and cations in the solid can in principle be calculated. In the calculation of the local electrostatic energy contribution the adsorption of protons cannot be treated without further ado as a proton adsorption at individJournal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

94

HIEMSTRA, VAN RIEMSDIJK, AND BOLT

ual groups isolated from the rest of the surface. It is more realistic to include at least those groups that are in the coordination sphere of the metal cation, which complicates a general formulation for hGc°oul. However, according to Yoon et al. (23), Pauling's concept of a bond valence v or "strength of the electrostatic b o n d " (Pauling (20, 21)) can be used as a simplification that accounts for the potential fields exerted by the surrounding ligands of the central metal ion. This bond valence v for the central metal ion cancels out the influence of the additional surrounding ligands in the coordination shelf of the metal ion. Due to the reduction of the valence ( Z ) of the central metal ion to a formal or effective valence v, one is able to treat the surface groups as individual surface groups isolated from the rest of the surface. The local AGo°oul due to the approach of a H ÷ to a surface site, as defined in reactions [2] and [3 ], m a y be calculated by assuming as a first approximation point charges for the ions, which are situated at certain distances in a certain geometry. The intrinsic free energy change due to O ( H ) - H and M e - H interaction is given as

]We2

Aai°tr = AG,~ + ZHZO(H) 47rElr Ne 2 + n. Z H v - -

4a-e2L

= -RTln

Kintr

in which n is the n u m b e r of metal ions coordinated with a surface group, ZH = 1 is the valence of the adsorbed proton and Zo(ri) is the valence of the surface oxygen or hydroxyl ( - 2 and - 1 , respectively), v is the effective bond valence, N i s the Avogadro constant, and e 1 and E2 are effective microscopic dielectric constants. The effective dielectric constant e2 should not be regarded as accessible to physical interpretation because of the simplicity of the present model in which a sum of electrostatic interactions is replaced by one term in which in fact an interaction parameter is implicitly introduced. The distance of charge separation (L) of the point charges is defined in Fig. 1. It follows from Eq. [ 5 ] that the log K value of the protonation reaction depends not only on the n u m b e r of cations which are coordinated to a surface species (n) but also on the coor-

Me

0

H

r I

ro

FIG. 1. The geometricmodel of the position of the central cation (Me), the oxygen(O), and the proton(s) (H) in hydroxo and oxo complexesin solution. The distances ri, ro, and ron refer respectivelyto the radius of the central cation, the equivalent oxygen radius, and the O-H distance. The Me-H distance is given by L. Journal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

[5]

MULTISITE

ADSORPTION,

dination number ( C N ) of these cations (v = Z / C N ) . This is in accordance with recent quantum-chemical studies ( 11 ). Equation [ 5 ] can be rewritten and simplified to the expression logK = A-B.n.~-,

V

[6]

L

where A -

ZHZ°(H)Ne2 2.3RT47rqr

AG~ 2.3RT

[7]

95

I

rounding ligands, neutralizing on an average Z~ C N unit charge per bond which is equivalent with v. The assumption that these ligands differ simply in the number of protons (one or two) suggests that an oxygen vacillates continuously between one or two H + ions. Treating these ligands as individual O H ( H ) species leads to the following formal description of the protonation reaction: M e - O H (v-l) + H + ~ Me-OHm;

o . [9] Km

In the same way the protonation of cation oxo complexes (for instance S i ( O H ) 3 0 - ) can be treated, leading to

and Z u Ne 2

B =

2.3 RT47rE2L "

[81

Equation [ 6 ] allows us to estimate by calculation the log K value of proton association reactions of various types of surface groups for various (hydr)oxides from v and L if the parameters A and B are known. In order to evaluate these constants for surface reactions and to show that the suggested model can be applied more generally, an analogy with relevant proton association reaction of solution monomers will be discussed first. Solution Chemistry

The protonation reactions of the solution monomers should correspond as close as possible to the situation of a (hydr)oxide at the point of zero charge, e.g., it implies that one should evaluate the proton adsorption reactions of overall neutral metal hydroxo and oxo monomers. Let us assume that Pauling's bond valence principle is also applicable to hydroxylated cation species in solution. Neutral cation hydroxide monomers in solution are generally coordinated with O H as well as OH2 ( C N >1 4). The neutral A I ( O H ) ° monomer, for instance, is believed to be hexa-coordinated in solution, e.g., surrounded by three O H and three OH2 ligands. According to the concept of a bond valence the positive charge of the central cation is distributed over the sur-

Me_O (v-2) + H + ~ Me_OH(V-i); K°I.

[10]

Note the use of the superscript (zero) for the log K values (Eqs. [9] and [10]) in order to distinguish these values for reactions of the solution monomers from the corresponding reactions at the interface (Eqs. [2] and [3], respectively}. According to the model description given above a relationship between the log K ° and v / L should exist for cation oxo and hydroxo complexes with a similar electronic structure. For this reason only the log K ° values of protonation reactions of those hydroxy monomers are used which have central cations with a similar electron configuration. All cations have been taken into account of which the relevant log K ° values are available (24). Two different sets of comparable cations were chosen (Table I): ( 1 ) cations which have an electron configuration identical to that of rare gases and (2) cations which in addition to these electrons also have a completely filled d-orbital. In addition to these Fe 3+ was chosen because of its relevance. Fortunately, as will be shown, Fe 3+ does not deviate from the cations with an electron configuration identical to that of rare gases. In order to correlate log K ° to v / L the distance of cationic charge separation L in solution complexes should be known. These Journal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

96

HIEMSTRA, V A N RIEMSDIJK, A N D BOLT

distances (Fig. 1 ) can be estimated based on ionic radii (Table I). Although the electron density of an ion extends in principle indefinitely in space, it is nevertheless possible to use an empirical set of ionic radii (for instance Pauling radii presented by Phillips and Williams (25)), such that the sum of the radii reproduces the interionic distances in ionic crystals with a reasonable accuracy. Assuming that these ionic radii also predict the ionic distance L between the central cation and the proton bound at the surrounding hydroxyls and water molecules with sufficient accuracy, we can calculate the repulsion between both cations if B is known. The oxygen-hydrogen

distance is set equal to the distance found in water (r = 0.96 × I 0 -10 m). The assumption that the charge of the central cation is distributed equally over the surrounding ligands implies the use of the coordination number (CN). The number of ligands depends on the ratio of the radii of the cation and anion (25). A tetrahedral coordination is assumed for central cations surrounded by hydroxyls, with a radius smaller than 0.50 × 10-1° m and a coordination number of 8 for central cation ions with a radius larger than 0.88 × 10 -~° m. The relevant log K ° values are taken from Baes and Mesmer (24).

TABLE I Log K~,, and log K~I,2 Values for the Proton Association Reaction of Negatively Charged Oxo Complexes and Neutral Cation Hydroxide Monomers Respectively and Z / C N / L as used in Fig. 2 a

Element

Atomic no.

Z

CN

ri

Z/CN/L

log K~,2

log g~l,i

A log /~DI,1.1

H Be A1 Sc Ti Fe Y Zr Nb Li Na K Si P S Mo Zn Ga Ag Cd In Ge As Te\(~

1 4 13 21 22 26 39 40 41 3 11 19 14 15 16 42 30 31 47 48 49 32 33 52

1 2 3 3 4 3 3 4 5 1 1 1 4 5 6 6 2 3 1 2 3 4 5 6

2 4 6 6 6 6 8 6 6 6 8 8 4 4 4 4 6 6 8 8 6 4 4 6

--0.44 0.31 0.50 0.81 0.68 0.64 0.93 0.80 0.70 0.60 0.95 1.33 0.41 0.34 0.29 0.62 0.74 0.62 1.26 0.97 0.81 0.53 0.47 0.56

0.331 0.207 0.192 0.173 0.241 0.183 0.125 0.231 0.299 0.062 0.042 0.037 0,398 0.511 0.625 0.553 0.118 0.184 0.038 0.082 0.173 0.381 0.486 0.376

-- 1.74 8.3 5.7 6.4 2.5 6.3 9.6 4.6 0.6 13.8 14.1 14.2

15.74

--0.91

9.86 2.14 - 1.98 3.65

-0.62 -0.64 -0.65 -0.58

9.31 2.24 7.68

-0.59 -0.61 -0.59

7.9 4.4 12.0 10.3 4.6

a Log K values are taken from Ref. (24). Distances are given in angstrSrns (10 -1° m). The sets of data are related to similar electron configurations of the cations (configuration of the rare gases and a configuration with complete dorbitals, resp.). The correction term A log KODL',1 for negatively charged oxo complexes is given in the last column.

Journal of Colloid and Interface Science, Vol. 133,No. 1, November1989

MULTISITE ADSORPTION, I The relationship found between log K ° values of the different proton association reactions of hydrolyzed cations and v/L is given in Fig. 2. The two pairs of parallel lines correspond to the different protonation reactions involved, e.g., the protonation of an - O H species (hydroxo) and of an - O species (oxo). In view of the simplicity of the model involved, it is remarkable to see such a good correlation for the set of log K°2 values (protonation of - O H species), the more so as a very wide range of valences ( Z = 1-5) and coordination numbers (CN = 4 - 8 ) is used (Table I). The log K°,, (protonation o f - O species)is less well correlated with v/L. This is probably due to the lesser ionic character of these species (like for instance H3 PO4 ). F r o m the mutual position of the lines one can conclude for both sets of cations that the log K ° for the protonation o f - O ligands and - O H ligands differs very strongly. The m e a n difference in log K ° values for the cations in-

97

volved equals 14 and one m a y wonder why this difference is so very large compared with the log K ° values found for the successive protonation steps of for instance polyprotic acids. The large difference in log K ° between two consecutive protonation steps at the same ligand is evidently related to the type of ligand present ( - O or - O H ) and partly due to the absence of a p r o t o n - p r o t o n repulsion in case of the protonation of ligands of oxo complexes in comparison with hydroxo complexes (Fig. 1 ). The formation of an - O H species is therefore m u c h more easily realized than the binding of a second proton at the ( - O H ) ligand. The ApK ° value of polyprotic acids is about 5 (26, 27), m u c h lower than the value reported above. The low value can be explained by realizing that the successive steps ofprotonation of polyprotic acids occur at different ligands of the acid. So the successive protonation reactions are in principle of one and the same type (e.g., for oxyacids, the protonation o f o x o

2O

solution monomers

|

"',,

hydroxo

0

oxo

~%'""" •

0.2

o'-.m

0,4

0.6

v/Lc,o-'°m~

FIG. 2. The log K° values for the protonation of hydroxo and oxo complexesversus the quotient of the bond valence (v) and the distance of Me-H charge separation (L). The solid symbols (I) indicate the log K~I,2values of the proton adsorption reaction of neutral hydroxo complexes,having a central cation with an electron configuration of rare gases. The corresponding open symbols (D) indicate the log K% for the protonation of corresponding negativelycharged oxo complexeswith a similar electron configuration. The log/Q~,2 and log K~,.Ifor the protonation of hydroxo and oxo complexesof cations with 10d electrons are indicated by diamonds (~). The log K° valuesfor the protonation of OH and H20 are indicated by triangles (A). Journal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

98

HIEMSTRA, V A N RIEMSDIJK, A N D BOLT

species). The difference in log K ° for the successive steps of protonation of a polyprotic acid is related to an overall increase of charge of the acid. The large difference in log K ° values for the protonation of oxo and hydroxo complexes can also be illustrated by considering the equilibria between H 2 0 and the species H 3 0 + and O H - according to +

0

- -

[111 If one assumes that one of the H + ions of O H and H 2 0 can be considered to be equivalent with the central cation in our approach, the O H - can be regarded as an oxo complex ( H O - ) and H20 as a hydroxo complex ( H - O H ) . The corresponding proton affinity constants for the protonation of the weak bases O H and H 2 0 can be defined respectively as

~'~

[H20I = [H+]

[12]

• [OH-]

and [H30+] K°'2 = [H+] • [H20] '

[13]

where [H20] is the molar concentration of water (55.5 moles/liter). The log K°,l and log /(~1,2 values of these reactions equal 15.7 and - 1 . 7 , respectively, which leads to a difference in log K ° for both reactions of about 17, even somewhat larger than the mean difference reported above. The log K ° values for the protonation of O H - and H 2 0 can be plotted in Fig. 2. One of the protons of O H - and H20 is considered as a central ion and its coordination number CNis assumed to be equal to the coordination number o f a proton in ice (CN = 2). Both log K ° values fit well. The constants A and B of Eq. [ 6 ] for the relation log I~,2-v/L have been determined by linear regression (A = 16.4 and B = 52.7 Journal of Colloid and Interface Science, Vol. 133,No. 1, November1989

× 10 -l° m) for the cations with an electronic configuration equal to that of rare gases (solid symbols). The other three lines in Fig. 2 are drawn parallel to the fitted line (A = 14. l, 16.4, 28.2, and 30.7, respectively, for the lines given in Fig. 2). It is now possible to estimate by calculation the log K ° values of other protonation reactions. The relationship given in Fig. 2 predicts for instance an extremely low value of log K~1,2(about - 4 ) for the protonation of Si(OH)4, which means that the protonation of these hydroxyls will not occur in solution, as is generally accepted. The log K ° value of present oxo complexes, in contrast to that of hydroxo complexes, comprises besides a local electrostatic contribution also an electrostatic double layer interaction. In site binding models for interfaces, however, such an interaction is calculated separately with an electrostatic double layer model. It implies that the double layer contribution in the log /~1,1 values should not be present in the log K~I,1 values which are used to calculate the intrinsic log K values for the corresponding surface reactions. The log K°,I can be corrected. Treating the oxo complexes (with valence Zi) as spheres with a radius L, the electrostatic work related to the discharging of the ion (2XGgL) equals (28) N Z 2e2

AGODL --

8~r~reoL

[14]

in which N is the Avogadro constant and Ethe dielectric constants. The calculated correction term expressed in log K units (using Er = 78) is given in Table I. The correction term is small and the mean difference in intrinsic log K values between oxo and hydroxo complexes now becomes 13.8. L O G K OF SURFACE REACTIONS

Minerals with well-defined simple surfaces with one reactive group allow us to determine unequivocally the proton affinity constant. Gibbsite for instance is a representative of this

MULTISITE ADSORPTION, I type of minerals and the K value for the protonation reaction of the A1-OH 1/2- group logKl,2 equals 10 + 0.5 (29). Comparison of this value with the corresponding K°,2 value of the protonation of the m o n o m e r in solution indicates that the proton affinity constant for protonation of surface groups is higher ( A log K ~ 4). This difference might be the result of a different arrangement of the - O H ( H ) species and solute molecules in a flat surface structure compared with spatial arrangement for the monomer. In order to predict the log K values of the proton association reaction of surface groups it is assumed that the main deviation from the log K°-v/L relation given above is due to a different A value in Eq. [6], caused by some change of AG~ of the surface group. This means an upward parallel shift of the log K °v/L curves of Fig. 2. The log K-v/L relationship for surface groups is fixed by considering the known experimental value of the protonation of the singly coordinated A1OH 1/2group as reference value and with the assumption that the difference between hydroxo and oxo reactions remains constant (A log K = 13.8). In order to calculate the log K values from the new constantsA (A = 18.4, 19.7, 32.2, and 34.5) the M e - H distance (L) for the surface groups of (hydr)oxides is needed. It can be found rather accurately from crystallographic data (23). Because of the minor difference in the distance L in oxides in comparison with the hydroxide, the log K value for the proton adsorption of the groups given in Table II refers within the range of uncertainties to both hydroxides and oxides of the metal cations. The distances L used in the calculation of the log K values of the protonation reactions of singly, doubly, and triply coordinated O / O H groups have been given in Table II. The log K values have been calculated for the protonation of several important surface groups of a limited number of (hydr)oxides, but it can easily be extended. As can be seen in Fig. 2 the log K ° values of several cations

99 TABLE II

The CalculatedProtonAssociationConstantsfor Several Important Surface Reactions at Various Important (Hydr)oxidesa Surface group

Formal charge

log K

L

AI-OH Alz-O A12-OH A13-O Fe-OH Fe2-O Fe2-OH Fe3-O Ti-OH Ti2-O Ti3-O Si-O Si-OH Si2-O

-½ -1 0 _ !2 - 1 -1 0 _ 21 -~l -~ 0 - 1 0 0

10.0 12.3 -1.5 2.2 10.7 13.7 -0.1 4.3 6.3 5.3 -7.5 11.9 -1.9 -16.9

2.59 2.43 2.43 2.49 2.73 2.58 2.58 2.66 2.67 2.51 2.59 2.32 2.32 2.05

The surfacegroupspresented referto the mostnegative group in the reaction. The distance of cationic chargeseparation L is given in angstrtims (10-mm). Hexa-coordination is assumed for the metal cation in the (hydr)oxides, except for silica.

deviate somewhat from the corresponding regression line. If one assumes that this deviation is due to individual differences in the AG~ values, this deviation should also be taken into account in the prediction of a corresponding log K value of a surface protonation reaction. The log K values given in Table II have been corrected for this deviation. The interesting aspect of our approach is that the affinity constants for the protonation of doubly and triply coordinated surface groups at the surface of metal (hydr)oxides can be calculated, whereas the log K ° value for the corresponding m o n o m e r is based on single coordination only. PROTON ADSORPTION MODELING In principle the protonation of each type of surface group can be described as a two-step association reaction with two association constants, leading to the presence of different surJournal of Colloid and Interface Science, Voh 133, No. I, November 1989

100

HIEMSTRA,

VAN RIEMSDIJK,

face species -O, - O H , and -OH2, belonging to one type of surface group. The treatment of the protonation as a two-step charging reaction corresponds with the classical treatment of the charging behavior of the surface (2-p K model). In the classical treatment only one type of surface group is considered to be responsible for the charging behavior of a metal (hydr)oxide. However, (hydr)oxides possess in general more than one type of surface group and different crystal faces. In our treatment we will consider more than one type of surface group to be reactive simultaneously. The surface groups are treated as individual groups with a two-step protonation which leads to expressions for equilibrium constants according to Eqs. [2] and [3]. Introduction of the Boltzmann accumulation factor [ e x p ( - F ~ P o / R T ) ] , relating the local proton concentration H + to its equilibrium concentration in solution and taking logarithms, leads to the expressions 0n,1

pH = log Kn,l -- log 1 -

G,I

AND BOLT

ao = ~ N s ( n ) F ' { n ' v ' O n , 2 + ( n . v - 1) n )'( On, 1 -]- ( n . v

[191 Equation [19] is valid for simple metal (hydr)oxides with surface groups having one set of coordination numbers (each n only one v). It can, however, easily be extended for other (hydr)oxides. To relate finally the surface charge o-0 and the surface potential ~P0an electrostatic model is required, for instance the basic Stern model (BS) comprising a Stern layer and a fiat diffuse double layer (9). On the basis of the BS theory the surface charge can be calculated from electrostatic reasoning with the formulas ( 18, 30) fro = C(ffo - ffd) 1

O"d = -I- ~

X -

- 2 ) . ( 1 - On,l - On,2)},

[20]

V8000¢r¢oRT

C o exp

RT

G,2

where ~Pdis in the Stern approximation of the potential of the Stern layer (which has a capacitance C) and C o is the molar equilibrium pH = log Kn, 2 - log ~ 2 _ F~Po/(2.3RT), concentration of cations and anions in solun,l [16] tion with valence Zk. The charge and the countercharge in the D D L are represented by where if0 is the electric potential at the surface. ~0 and as, respectively. The fraction of a surface group present as a In crystalline materials like SiO2, TiO2, specific surface species on a specific crystal face FeOOH, and AI(OH)3 various crystal faces (0) is defined in case of the protonation ac- may have been developed each with its own cording to reactions [ 2 ] and [ 3 ], respectively, type of surface structure with several types of as groups (5, 29). The behavior of such materials On,1 = M e n - O H ( n ' v - t ) / N s ( n ) [17] can be modeled using the MUSIC model presented here, assuming that the spatial sepaand ration of faces is such that each crystal face (n-l)) 0n,2 = Men-OH2 /Ns(m. [18] can develop its own surface potential without interference. The titration behavior of the The site density of the specified surface group overall colloid is in that case the weighted sum on a given face, Ns(n) , is defined as the sum of of the charges developed at the different crystal all species with the same value of n of this faces (13). In the extreme case of a complete face. The surface charge density for a crystal double layer overlap, one and the same surface potential may apply for all crystal faces (31 ). face is given by - Ft~o/(2.3RT)

[15]

Journal of Colloid and Interface Science, Vol. 133,No. 1, November 1989

MULTISITE

ADSORPTION,

DISCUSSION

Analysis of the log K values as calculated by the MUSIC model presented above indicates that particular surface species will not be present. It appears that nature generally allows only those surface species to be present in aqueous solutions which have a charge (absolute value) equal to or lower than one. Surface species like A10 3/2- or Ti2OH~/3+ for instance will not be found at the interface in aqueous solutions. These formation constants are therefore not given in Table II. The presented general model can be simplified to the classical 2-pK model if one assumes the presence of only one type of reactive surface group and if n • v equals 1, which is the case for singly coordinated SiOH ° groups or doubly coordinated A12OH ° and FezOH ° reaction sites. Only in these cases may the surface groups be present as - O - , - O H °, and -OHm. The reaction equations are in that case equivalent to the classical two-step protonation reactions S O - + 2H + ~ SOH ° + H + ~ SOH~ [22] with K1 and/£2, respectively. Equation [19] reduces to ~o = N s F { ( 0 2 )

-

(1 - 01 - 02)}

[23]

in which 02, 02, and ( 1 - 01 - 02) are the fractional surface coverages of the -OHm, - O H °, and - O species, respectively. As can be seen in Table II the log K values for the consecutive protonation of oxo and hydroxo groups differ very strongly (Ap K ~ 14). This is partly due to a very strong proton-proton repulsion at an -OH2 surface species, while this repulsion is absent in an - O H surface species. The ApK value that can be derived from the application of the classical 2-pK model in the literature is in the range of 2-6 (9, 32, 3 3). The discrepancy between these values and the value derived here is due to the fact that the classical 2-pK model has been applied to situations where the model is physically not very realistic. The parameters should be treated in

I

101

such a case as fitting values that allow a good description of the data, but they should not be interpreted as physically realistic constants. In general three different situations with respect to the position of the two consecutive log K values in the pH range of titration can be distinguished (Fig. 3). If one of the log K values is positioned in or near the pH range of titration, the titration behavior of this group is governed by only o n e protonation reaction, like for instance the proton association of SiOgroups (Fig. 3, A1 ). This means that the titration behavior can be described by one log K value and that the second association step can be neglected. Two log K values can, however, also be situated more or less symmetrically around, but outside, the pH range of titration, leading to the presence of surface groups that often can be neglected as important reaction sites for the adsorption of protons (Fig. 3, B). This occurs for doubly coordinated groups (A1EOH ° and Fe2OH °) at the surface A1 and Fe (hydr)oxides, respectively, as is shown in Part II (19). Beside these two cases both log K values can also be positioned far outside the relevant p H range of interest (Fig. 3, C). This is in fact equivalent to no protonation reaction at all, e.g., the group can be considered as inert, for instance triply coordinated Ti30 ° groups or doubly coordinated Si20 ° groups, the latter being present in many phyllosilicates. The correlation between surface proton association reactions and corresponding reactions in solution has been suggested in the past by Parks (34) and was recently used by Schindler and Stumm (6). However, this correlation is based on surface reactions formulated by the classical two-pK model which explicitly assumes the formation of o x o complexes ( S O - ) and they are compared with the proton association reactions of negatively charged h y d r o x o complexes in solution (6). This approach is difficult to understand in view of the above given analysis. It could be argued that the formulation of the reactions according to the two-pK model should be considered as Journal ofColloM andlnterface Science, Vol. 133,No. 1, November 1989

102

HIEMSTRA, VAN RIEMSDIJK, AND BOLT

,e,. w

¢,

B

• A1

¢,

¢ ¢

~"

A2

¢

log K

I

I 3

10

-e,,-

L

b pH

FIG. 3. The schematicinterposition of the log K valuesof consecutiveprotonation reactions of one surface group with respect to the pH range of titration (pH 3-10). Position A: one of the log K values of a certain surface group in or near the pH range of titration (for example, AI: SiO(H); A2: A10(H)); position B: both values are more or less symmetricalaround, but outside, the pH range of titration (for example, Fe20(H)); and position C: both log K values are far outside the pH range of titration like in the case of Si20 or Ti30 surface groups. formal. The following equivalent surface groups can be given in order to give the twop K model a more realistic base (35-37), at least if it is applied to iron and a l u m i n u m (hydr)oxides: /.OH

-1

OH2 o Me(

Me \ OH

OH Me ( OH2

+1

[24]

OH2 In doing that, one in fact assumes that the surface hydroxyls react in pairs and the site density is half of the values in the traditional formulation. For correlation of the log K with log K ° values in solution, one should assume that ligands around the central metal ion in solution also react in pairs. No evidence is available for this. The above given alternative formulation of the surface groups leading to a t w o - p K model (Eq. [24]) can only be derived for (hydr)oxides with n- v = 1. If one would like to jusJournal of Colloid and Interface Science, Vol. 133, No. 1, November 1989

tify the use of the classical t w o - p K model for (hydr)oxides like TiO2 or Mg(OH)2, one needs to assume that three equivalent surface sites behave as one entity because v equals and I, respectively. The surface site density should in such a case be one-third of the total n u m b e r of sites based on for instance crystallographic considerations. If the alternative formulation of the 2 - p K model (Eq. [24]) is used, the admission that groups should react in pairs or triplets implies that surface complexation reactions of metal ions with two surface sites (6) will correspond in reality with a reaction with four or more equivalent O H groups at the surface, which m a y be doubted in terms of physical reality. Recently Van Riemsdijk (17) and Bolt and Van Riemsdijk (18) introduced a o n e - p K protonation model in order to describe the titration behavior of singly coordinated surface groups of A1 and Fe (hydr)oxides. It has been used successfully by V a n Riemsdijk et al. (14) for the description of the titration curves of crystalline and amorphous Fe (hydr)oxides and by Hiemstra et al. (29) for the ~o-pH curves of AI(OH)3(s) (gibbsite). This pro-

MULTISITE ADSORPTION,

tonation model can be deduced from the general multisite complexation model presented here. Again it should be realized that the position of the log Kwith respect to the p H range (Table II) and the large difference in log K values of two consecutive protonation steps of a surface group imply that in general only one protonation step suffices to describe the titration behavior of that group in a normal pH range. The model formulation follows directly from Eqs. [ 16 ] to [ 19 ] for the two (hydr) oxides mentioned, when their titration behavior is determined by the singly coordinated hydroxyls (n = 1, v = 1 ). The general protonation reaction (Eq. [3 ]) can in this case be written w i t h n = l a n d v = ½as SOH

1 / 2 - -t-

H + ~ SOH~/2+;

KH

[25]

in which H + is the local proton near the surface. Once again it is noticed that the presented charges in Eq. [25] should be considered as formal, attributed to the individual surface groups for a proper bookkeeping of charges in the model description. The surface charge is found by rewriting Eq. [ 19 ], knowing that the fractional coverage of the surface with SO 3/2groups is negligible, e.g., ( 1 - 01,1 - 01,2) equals zero. The surface charge density is then given by ~ro = NsF(OH - ½),

[26]

where OHis the fractional surface coverage with SOH ~ groups. Very recently another one-step charging model has been presented (37), which is at a first glance very similar to the o n e - p K model presented by Van Riemsdijk (17) and Bolt and Van Riemsdijk (18). Its deduction starts by assuming a two-pK model which has a first proton association constant which is smaller than that of the second association reaction. This assumption is very strange in view of the values given in Table II, which suggest that the opposite is the case. A lower/£1 than K2 implies that neutral surface groups do not exist at the surface and only oppositely charged surface groups are present (37). The equilib-

103

I

rium between these two groups is characterized by only one log K according to S O - + 2H~+ ~ SOH~-;

/~2.

[27]

This formulation has been used earlier by Parks ( 34 ) and Yoon et aL ( 2 3 ) for their study of the PZC of minerals. Equation [27] leads to

V s-0= -

t281

The last expression is quite different from the formulation of a o n e - p K model as presented originally by Van Riemsdijk (17) and Bolt and Van Riemsdijk (18) and can not be reduced to that as suggested by Westall (37). It is well known that most surfaces of (hydr)oxides have a more complicated surface structure due to the presence of more than one type of surface group. As will be shown in Part II (19) the analysis of the proton adsorption behavior with the recognition of the existence of more than one reactive surface group will elucidate some unexpected and before incomprehensible behavior of hydr(oxides). The validity of the proton affinity constants and the applicability of the MUSIC model presented here for surfaces with two or more types of reactive groups will be discussed in Part II (19). CONCLUSIONS

- - T h e proton affinity constants of neutral solution monomers depend on the valence of the central cation (Me) and its electron configuration, the number of surrounding ligands (CAT), the type of ligand (hydroxo or oxo), and the M e - H distance. - - T h e logarithm of the proton affinity constants for the consecutive formation of oxo and hydroxo complexes differs by about 14 units, which implies that generally only one type of these complexes can be protonated in aqueous solution, leading to only one protonation reaction per group. Journal of Colloid and Interface Science, VoL 133, No. 1, November 1989

104

HIEMSTRA, VAN RIEMSDIJK, AND BOLT

actions at the Soil Colloid-Soil Solution Interface" - - T h e protonation of metal hydroxo and (M. H. Hayes and G. H. Bolt, Eds.). Genth (Beloxo monomers in solution can be considered gium) in press. as an analogue of the protonation reaction of 16. Bolt, G. H., and Van Riemsdijk, W. H., in "Aquatic surface groups. The assumption of a correlaSurface Chemistry" (W. Stumm, Ed.), Chap. 6. tion between the relevant corresponding reWiley, New York, 1987. action in solution and at surfaces implies that 17. Van Riemsdijk, W. H., Internal Report, Wageningen Agricultural University, Netherlands, 1979. proton affinity constants of surface groups can 18. Bolt, G. H., and Van Riemsdijk, W. H., in "Soil be predicted. Chemistry. B. Physio-chemical Models" (G. H. - - T h e MUltiSIte Complexation (MUSIC) Bolt, Ed.), 2nd ed., p. 459. Elsevier, Amsterdam, model presented here also allows the calcu1982. lation of proton affinity constants of proton- 19. Hiemstra, T., De Wit, J. C. M., and Van Riemsdijk, W. H., J. Colloid Interface Sci. 132 (1989). ation reactions of surface groups (doubly and 20. Pauling, L., J. Amer. Chem. Soc. 51, 1010 (1929). triply coordinated) which have no corre- 21. Pauling, L., in "The Nature of the Electrostatic Bond," sponding equivalent reactions in solution. 3rd ed., Chap. 13-6. Cornell Univ. Press, Ithaca, NY, 1967. - - T h e classical one- and two-p K site binding models are special cases of the general 22. Hingston, F. J., in "Adsorption of Inorganics at SolidLiquid Interfaces" (M. A. Anderson and A. J. MUSIC model presented here. REFERENCES

23.

1. Peri, J. B., 3. Phys. Chem. 69, 220 (1965). 2. Jones, P., and Hockey, J. A., Trans. Faraday Soc. 67, 2679 (1971). 3. Parfitt, L. R., Atkinson, R. J., and Smart, P. St. C., Soil Sci. Soc. Amer. Proc. 39, 837 (1975). 4. Lewis, D. G., and Farmer, V. C., Clay Minerals 21, 93 (1986). 5. Yates, D. E., Ph.D. thesis, University of Melbourne, Melbourne, 1975. 6. Schindler, P. W., and Stumm, W., in "Aquatic Surface Chemistry" (W. Stumm, Ed.), Chap. 4. Wiley, New York, 1987. 7. Huang, C. P., and Stumm, W., J. Colloid Interface Sci. 43, 409 (1973). 8. Hohl, H., and Stumm, W., J. Colloid Interface Sci. 55, 281 (1976). 9. Westall, J. C., and Hohl, H., Adv. Colloid Interface Sci. 12, 265 (1980). 10. Kummert, R., and Stumm, W., J. Colloid Interface Sci. 75, 373 (1980). 11. Kawakami, H., and Yoshida, S., J. Chem. Soc.i Faraday Trans. 2 81, 1117 (1985). 12. Van Riemsdijk, W. H., Bolt, G. H., Koopal, L. K., and Blaakmeer, J., J. Colloid Interface Sci. 109, 219 (1986). 13. Van Riemsdijk, W. H., De Wit, J. C. M., and Koopal, L. K., Neth. J. Agric. Sci. 35, 241 (1987). 14. Van Riemsdijk, W. H., De Wit, J. C. M., Koopal, L. K., and Bolt, G. H., J. Colloid Interface Sci. 116, 511 (1987). 15. Van Riemsdijk, W. H., and Bolt, G. H., in "Inter-

24.

Journalof Colloidand InterfaceScience, Vol.133,No. t, November1989

25.

26.

27. 28.

29. 30.

31. 32. 33. 34. 35. 36. 37.

Rubin, Eds.), Chap. 2. Ann Arbor Science Pub., Ann Arbor, MI, 1981. Yoon, R. H., Salman, T., and Donnay, G., J. Colloid Interface Sci. 70, 483 (1979). Baes, C. F., and Mesmer, R. E., The Hydrolysis of Cations. Wiley, New York, 1976. Phillips, C. S. G., and Williams, R. J. P., in "Inorganic Chemistry I," 2nd ed., Chap. 5. Oxford Univ. Press, London, 1966. Phillips, C. S. G., and Williams, R. J. P., in "Inorganic Chemistry II," 2nd ed., Chap. 14. Oxford Univ. Press, London, 1966. Pauling, L., in "College Chemistry," 3rd ed., Chap. 19. Freeman, San Francisco, 1964. Bockris, J. O'M., and Reddy, A. K. N., in "Modern Electro Chemistry 1," Chap. 2. Plenum, New York, 1976. Hiemstra, T., Van Riemsdijk, W. H., and M. G. M. Brnggenwert, Neth. J. Agric. Sci. 35, 281 (1987). Bolt, G. H., in "Soil Chemistry. B. Physio-chemical Models," (G. H. Bolt, Ed.), 2nd ed., Chap. 1. Elsevier, Amsterdam, 1982. Koopal, L. K., and Van Riemsdijk, W. H., J. Colloid Interface Sci. 128, 188 (1989). Davis, J. A., James, R. O., and Leckie, J. 0., 3. Colloid Interface Sci. 63, 480 (1978). Koopal, L. K., Van Riemsdijk, W. H., and Roffey, M. G., J. Colloid Interface Sci. 118, 117 ( 1987 ). Parks, G. A., Chem. Rev. 65, 177 (1965). Hingston, F. J., Posner, A. M., and Quirk, J. P., J. Soil Sci. 23, 177 (1972). Pulver, K., Scbindler, P. W., Westall, J. C., and Grauer, R., J. Colloid Interface Sci. 101, 554 (1984). Westall, J. C., in "Aquatic Surface Chemistry" (W. Stumm, Ed.), Chap. 1. Wiley, New York, 1987.