Modeling the binding of fulvic acid by goethite: The speciation of adsorbed FA molecules

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1 Pergamon PII S (02) Geochmca et Cosmochmca Acta, Vol. 67, No. 8, pp , 2003 Copyrght 2003 Elsever Scence Ltd Prnted n the USA. All rghts reserved /03 $ Modelng the bndng of fulvc acd by goethte: The specaton of adsorbed FA molecules JEROEN D. FILIUS, 1 JOHANNES C. L. MEEUSSEN, 2 DAVID G. LUMSDON, 2 TJISSE HIEMSTRA, 1 and WILLEM H. VAN RIEMSDIJK 1, * 1 Department of Envronmental Scences, Sub-department Sol Qualty, Wagenngen Unversty, P.O.B. 8005, 6700 EC Wagenngen, The Netherlands 2 Macaulay Land Use Research Insttute, Cragebuckler Aberdeen AB15 8QH, Scotland, UK (Receved June 1, 2001; accepted n revsed form May 6, 2002) Abstract Under natural condtons, the adsorpton of ons at the sold water nterface may be strongly nfluenced by the adsorpton of organc matter. In ths paper, we descrbe the adsorpton of fulvc acd (FA) by metal(hydr)oxde surfaces wth a heterogeneous surface complexaton model, the lgand and charge dstrbuton (LCD) model. The model s a self-consstent combnaton of the nondeal compettve adsorpton (NICA) equaton and the CD-MUSIC model. The LCD model can descrbe smultaneously the concentraton, ph, and salt dependency of the adsorpton wth a mnmum of only three adjustable parameters. Furthermore, the model predcts the coadsorpton of protons accurately for an extended range of condtons. Surface specaton calculatons show that almost all hydroxyl groups of the adsorbed FA molecules are nvolved n outer sphere complexaton reactons. The carboxylc groups of the adsorbed FA molecule form nner and outer sphere complexes. Furthermore, part of the carboxylate groups reman noncoordnated and deprotonated. Copyrght 2003 Elsever Scence Ltd 1. INTRODUCTION Natural organc matter (NOM) and metal(hydr)oxde surfaces can both be regarded as geo-collods. Consderable attenton has been and s stll gven to the understandng of the (surface) chemstry of these geo-collods per se. NOM and metal(hydr)oxdes are, for nstance, very mportant for the chemcal specaton and transport of nutrents and pollutants n the sol and sedment. In natural systems, both types of geo-collods are smultaneously present and they wll nteract. The mutual nteracton may nfluence ther role as reactve surfaces n the natural envronment. The nteracton between organc matter and oxde surfaces can sgnfcantly alter the characterstcs of both the organc matter and the oxde surface. Davs (1982) stated that a realstc representaton of the surfaces of natural partculate matter mght requre a heterogeneous multste model. To date, only a few attempts have been made to nclude NOM adsorpton n surface specaton calculatons (Vermeer et al., 1998; Karltun, 1998; Evanko and Dzombak, 1999; Flus et al., 2000). For such an mportant challenge, a fundamental understandng of the adsorpton behavor of NOM by oxde surfaces s requred to make progress. Well-defned small organc acds have often been used as model compounds to study the adsorpton of larger ll-defned natural organc acds. (Balstrer and Murray, 1986; Al and Dzombak, 1996; Flus et al., 1997, 2001; Boly et al., 2000). The descrpton of the adsorpton of these well-defned organc molecules has shown that three factors are essental: 1) the stochometry of the reacton, 2) the chemcal affnty of the organc molecules for the oxde surface, and 3) electrostatc nteractons between the charged organc molecules and the oxde surface. However, the descrpton of the adsorpton of large, ll-defned organc molecules (humc and fulvc acd; HA * Author to whom correspondence should be addressed (Wllem.VanRemsdjk@bodsch.benp.wau.nl) and FA) s more complex for several reasons: (1) HA and FA are mxtures of molecules wth dfferent sze, number of reactve groups, etc.; (2) FA and especally HA have many more reactve groups per molecule that can form bonds wth the oxde surface; (3) the organc molecules and the metal(hydr)oxde surface have both a varable charge; and (4) HA and FA have a relatvely large sze. In the studes of Karltun (1998), Evanko and Dzombak (1999), and Flus et al. (2000), the adsorpton of FA by goethte s descrbed assumng a dscrete number of surface speces. We refer to ths type of modelng as dscrete modelng. In these studes, as well as n the present approach, FA s treated as a mxture of the same molecules wth averaged propertes. Fgure 1 shows three dfferent schematc confguratons of a bound FA molecule. The reactve groups (carboxylate and hydroxylate) of the FA molecule can react wth mneral surface groups, may bnd protons, or reman deprotonated. The confguraton of the FA molecule bound by the oxde surface wll vary wdely wth ph, salt level, surface loadng, and other factors. In the dscrete modelng, the varyng confguraton s ntroduced by defnng dfferent surface speces. Flus et al. (2000) calculated that wth such an approach a FA molecule wth eght reactve groups can form potentally easly over a thousand dfferent surface speces. To reduce the number of adjustable parameters, the number of surface complexes used however has been mnmzed. Flus et al. (2000) only used four dfferent surface speces to descrbe the data. The lmted number of surface speces, s physcally and chemcally less realstc. For larger molecules, e.g., HA, the number of reactve groups s even larger than for FA and the number of possble surface speces s almost nfnte. Therefore, the dscrete modelng approach s n our opnon not sutable for modelng the bndng of molecules larger and more complex than FA molecules. Recently, we developed the lgand and charge dstrbuton (LCD) model (Flus et al., 2001) and descrbed the adsorpton

2 1464 J. D. Flus et al. 2. MODELING THE BINDING OF FA In ths study, the overall adsorpton of FA by goethte s represented by the followng overall reacton: a b FeOH 1/ 2 a b c H FA z K overall, 0, 1 1/ N Fe a FeOH 2 b FAH 2 a bc z c ah 2 O (1) Fg. 1. A schematc representaton of three possble confguratons of an adsorbed FA molecule. of multple carboxylc acds by goethte. Usng the CD (charge dstrbuted complexaton) model (Hemstra and Van Remsdjk, 1996) and the consstent nondeal compettve adsorpton (NICA) equaton (Koopal et al., 1994; Knnburgh et al., 1999), the LCD model calculates the dstrbuton of organc molecules over the mneral and the soluton phase and the specaton (or confguraton) of the adsorbed and dssolved molecules smultaneously and n a self-consstent way. Electrostatc effects on the specaton of the goethte and the adsorbed FA are taken nto account wth a unted electrostatc model. The am of ths study s to extend the model approach presented by Flus et al. (2001) to descrbe the adsorpton of FA by goethte for a wde range of condtons (ph, onc strength, and surface loadng). As FA contans both carboxylc and hydroxylc groups, the orgnal LCD model s extended takng the full specaton of the hydroxylate groups of the adsorbed FA molecules nto account. The model s calbrated for the adsorpton data of Strchen Fulvc Acd (SFA) by goethte. Furthermore, the model s tested predctng the coadsorpton of protons as a functon of the SFA adsorpton by goethte at constant ph for condtons where almost 100% of the SFA molecules are adsorbed. n whch FeOH represent the sngly and trply coordnated surface groups of goethte, a s the number of surface groups formng nner sphere complexes, b the number of surface groups that wll form outer sphere complexes wth carboxylate (RCOO ) and hydroxyl (RCOH) groups, and c the number of protons formng noncoordnated RCOOH and RCOH groups. z represents the charge of the fully deprotonated FA molecule. The macroscopc adsorpton reacton (Eqn. 1) s characterzed by the stochometry coeffcents a, b, andc, the overall affnty constant (K overall ), and the overall electrostatc nteractons ( 0, 1 ) between the oxde surface and the organc molecule. The calculaton of these parameters and the detals of ths equaton wll be dscussed later (see Table 1 and secton 2.2.2). It should be mentoned that both sngly and trply coordnated goethte surface groups are supposed to nteract wth the reactve groups of the FA molecule. However, n the text the reactons are only wrtten for sngly coordnated stes for reasons of smplcty. The adsorpton of FA by goethte s calculated wth the LCD model (Flus et al., 2001). Fgure 2 shows the basc structure of the LCD approach. The startng pont for the teratve modelng s the calculaton of the macroscopc dstrbuton of FA over the soluton (FA dss ) and the nterface (FA ads ). Ths dstrbuton s calculated wth the CD-MUSIC models (I n Fg. 2). The CD-MUSIC model s fed by parameters ganed from two submodels n whch the lgand dstrbuton at the surface s calculated (LD model) and the soluton specaton of FA molecules s found (ND model). These two models are n turn based on the results of the CD model. The three models form a self-consstent teratve calculaton scheme. A more detaled descrpton of the model wll be gven below. We wll start at the mcroscopc level before descrbng the FA adsorpton at the macroscopc level Interacton of the Organc Groups wth Protons and Surface Stes In Soluton Table 1 shows the adsorpton and protonaton reactons of the carboxylc and hydroxylc groups of dssolved and adsorbed FA molecules. Reactons 1 and 2 of the table represent the protonaton of the carboxylc and hydroxylc groups n soluton respectvely. Reactons 3 through 6 of Table 1 represent the adsorpton and protonaton of a soluton-orented carboxyl or hydroxyl group of the bound FA molecule. The soluton-orented group does not have a drect nteracton wth the goethte surface groups, but s bound by the surface due to the complex formaton of surface stes wth other functonal groups of the same adsorbed organc molecule. Ths structural feature s ndcated by # n the reactons.

3 Modelng the adsorpton of fulvc acd by goethte 1465 Table 1. Reacton equatons for the reactons possble to occur on the surface wth the correspondng affnty constants, change of charge ( z )n plane, and stochometry coeffcents. Reactons logk z 0 z d St. coeff. 1 RCOO H N RCOOH 0 logk H,1 2 RCO H N RCOH 0 logk H,2 3 # RCOO H N # RCOOH 0 logk H,1 0 0 c 1 4 # RCOO N # RCOO z 1 a 1 b 1 c 1 5 # RCO H N # RCOH 0 logk H,2 0 0 c 2 6 # RCO N # RCO z 2 a 2 b 2 c 2 7 FeOH 0.5- H RCOO N Fe OOCR] 0.5- logk n logk H a 8 FeOH 0.5- H RCOO N FeOH 2... OOCR] 0.5- logk out,1 logk H b 1,1 9 FeOH 0.5- H RCO N FeOH 2... OCR] 0.5- logk out,2 logk H b 2,1 10 FeOH 0.5- H RCO N FeOH... HOCR] 0.5- logk out, b 2,2 logk H,2 Note R represents the rest of the molecule. # ndcates the adsorbed FA molecule of whch the soluton-orentated reactve groups can be protonated (reactons 3 and 5) or reman deprotonated (reactons 4 and 6). Note that the charge of the bound RCOO and of the RCOOH 0 s located n the d-plane. In the modelng, outer sphere complexaton reactons are assumed for both sngly and trply coordnated groups. Here the reactons (reactons 8 10) are only wrtten for sngly coordnated groups. The charge dstrbuton and affnty constant are assumed to be the same for outer sphere complexaton wth sngly and trply coordnated groups. The stochometry coeffcents n the table are related to the stochometry coeffcents of Eqn. 1 by b b 1 b2; b2 b 2,1 b 2,2 ; c c 1 c 2 ;andz z 1 z At the Interface Carboxylc Groups Based on spectroscopc evdence (Parftt et al., 1977a, b; Gu et al., 1994; Kaser et al., 1997; Boly et al., 2000), we assume n ths study that the carboxylc groups of FA can form nner sphere complexes wth the sngly coordnated surface groups and outer sphere complexes wth sngly and trply coordnated surface groups. Inner sphere complexaton (reacton 7 of Table 1) s characterzed by the exchange of a surface water group of a sngly coordnated surface group for one oxygen atom of the carboxylate group. We assume that the charge of the carboxylate groups ( 1 valence unt; vu) s equally dstrbuted over both oxygens (.e., each oxygen 0.5 vu). In case of the exchange reacton, the charge of the ron n the sold ( 0.5 vu) s fully neutralzed by the charge of the carboxylate oxygen ( 0.5 vu). Inner sphere coordnaton therefore results n an uncharged bondng oxygen. The charge of the second carboxylate oxygen s located n the d-plane. In case of H bond formaton, the 1 vu of the organc group s located n the d-plane (reacton 8 of Table 1). The proton nvolved attrbutes 0.8 vu of ts charge to the surface plane. The remanng 0.2 vu s located n the d-plane together wth the 1 vu of the carboxylate group. In the rest of the text, H bondng s descrbed only for sngly coordnated surface groups. In the modelng, the H bondng wth trply coordnated groups s taken nto account n the same manner as the H bondng wth sngly coordnated groups, wth the same charge dstrbuton and affnty constant Hydroxylc Groups The hydroxylc groups, and other types of OH groups of FA wth a hgh proton affnty are supposed to protonate and deprotonate and to form outer sphere complexes wth sngly and trply coordnated surface groups. The outer sphere complexes are formed due to H bondng (reactons 9 and 10 n Table 1). In case of H bondng, both the protonated reactve surface group and the hydroxylc group of the FA can, n prncple, act as the proton donor. Fgure 3 shows both optons and ndcates the dfferent charge dstrbuton of both types of outer sphere complexes over the nterface. When the goethte surface ste s the proton donor, 0.8 vu of the charge of the proton s located n the surface plane. The remanng 0.2 vu s located n the d-plane together wth the 1 vu of the carboxylate or hydroxylate group (Fg. 3a; reacton 9 of Table 1). In case the reactve organc group s the proton donor, the 0.2 vu of the proton s located n the 0-plane. The remanng 0.8 vu s located n the d-plane together wth the 1 vu of the carboxylate or hydroxylate group (Fg. 3b; reacton 10 of Table 1). To determne whch group s the actual proton donor, the ntrnsc proton affnty of both groups as well as the electrostatc potental at the locaton of the reactve group should be taken nto account. The overall affnty for the formaton of the H bond n whch the surface ste s the donor s gven by a combnaton of the protonaton of the surface group (K H ), the formaton of the H bond (K out,2 ), and the electrostatc nteractons (e 0.8F 0/RT.e 0.8F 1/RT ). The overall affnty for the formaton of the H-bond n whch the hydroxylc group s the donor s a combnaton of the protonaton of the reactve FA group (K H,2 ), the formaton of the H bond (K out,2 ), and the electrostatc nteractons (e 0.2F 0/RT.e 0.2F 1/RT ). The surface ste wll therefore domnate as the H-bond donor n case K H.e 0.8F 0/RT.e 0.8F 1/RT K H,2.e 0.2F 0/RT.e 0.2 1/RT (reacton 9 of Table 1; Fg. 3a). The hydroxylc group wll domnate as the H-bond donor n case K H,2.e 0.2F 0/RT.e 0.2F 1/RT K H.e 0.8 0/RT.e 0.8F 1/RT (reacton10oftable 1; Fg. 3b). When the reactve surface group and the hydroxylate group have smlar proton affntes, the relatve presence of both types of H bond donors depends on the electrostatc potental n the 0- and d-plane. Note that n prncple the carboxylc groups can also form both types of H bonds. However, because logk H,1 logk H, the overall affnty for the formaton of the H bond n whch the carboxylate oxygen s the donor s much smaller than n case

4 1466 J. D. Flus et al. Fg. 2. Calculaton scheme for the new model approach. (I) CD-MUSIC model calculates the dstrbuton of the organc molecules over the sold and soluton phase. (II) The LD model calculates the mean adsorpton mode of the adsorbed organc molecules, whch determnes the nput parameters for the CD-MUSIC model. (III) Converts the dssolved amount of FA nto a reference speces FA z, whch s used as nput for the CD-MUSIC model. The affnty constant (logk overall ), charge dstrbuton ( z 0, z 1 ), stochometry coeffcents (a, b, andc) of the reacton, and the actvty of the FA n soluton (FA z ) are the nput parameters for the CD&MUSIC model. The values of logk overall, z 0, z d,anda, b, andc are also output of the specaton calculaton of the adsorbed FA molecule. the surface oxygen s the donor. Model calculatons show that the carboxylc FA group wll not act as the H bond donor for ph Calculaton of the FA Molecule Specaton: The Consstent NICA Model In general, organc materal contans functonal groups wth a wde range of affntes for protons, competng metal ons, and, n ths case, reactve oxde surface groups. The NICA model s a ste-bndng model that takes heterogenety and competton nto account explctly. For the calculaton of the specaton of the adsorbed FA and the FA n soluton (II and III n Fg. 2) the NICA model s used. The bmodal NICA equaton s gven by: Q,t Q max1 n,1 n H,1 Q max2 n,2 n H,2 K,1c,D n,1 K,1 c,d n,1 K,2c,D n,2 K,2 c,d n,2 n,1 p 1 K,1 c,d 1 n,1 p 1 K,1 c,d n,2 p 2 K,2 c,d 1 n,2 K,2 c,d p 2 (2) where Q,t s the total amount of component bound to the humc substance, Q max s the total ste densty (mol/kg), subscrpt 1 and 2 refer to the frst and second type of stes n the affnty dstrbuton, K s a medan affnty constant, and c,d s

5 Modelng the adsorpton of fulvc acd by goethte 1467 (1999) ntroduced an emprcal relaton between v D and the onc strength: logv D k. 1 logi) 1 (5) Although ths relaton shows a varaton n v D wth onc strength whch s much larger than can be expected based on structural models of fulvc acd (Langford et al., 1983; Avena et al., 1999; Lead et al., 2000), the Donnan model can mmc the salt effects on the chargng very well. For more detal refer to Knnburgh et al. (1999). Fg. 3. Schematc representaton of the formaton of an H-bond between a hydroxylc group of a FA molecule and a sngly coordnated reactve surface group of the goethte surface. (a) The reactve surface group acts as the H-bond donor; (b) the hydroxylc group acts as the H-bond donor. the concentraton of n the Donnan phase. The value of p (0 p 1) accounts for the ntrnsc chemcal heterogenety of the sorbent, whch s the same for all components. The parameter n accounts for the on-specfc heterogenety or nondealty of component that s not accounted for by ntrnsc heterogenety and/or the electrostatc model (n 1 nondeal, n 1 deal) Specaton of the Dssolved FA Molecules For the condtons n soluton as dscussed n ths paper, the NICA equaton reduces to a smple LF equaton because the proton s the only nteractng component: K H,1 H D m1 K Q H Q max1 1 K H,1 H D Q H,2 H D m2 m1 max2 (3) 1 K H,2 H D m2 n whch m (m n H p) s a heterogenety parameter that reflects the combned effect of the ntrnsc heterogenety (p) and the on-specfc heterogenety (n H ). A smple Donnan model can account for the nonspecfc bndng (Benedett et al., 1996; Knnburgh et al., 1999). The Donnan approach assumes that at each charge the overall electroneutralty s entrely preserved by the accumulaton or depleton of salt ons n the gel phase. q/v D z j c j e zjf D/RT 1 0 (4) where q s the charge of the fulvc acd n mol kg 1, v D s the specfc volume of the gel phase n L/kg, and c j s the concentraton of on j n the external soluton n mol/l. e z jf D /RT s the Boltzmann factor n whch subscrpt D ndcates the potental n the Donnan phase. For a gven charge densty and salt level, v D s the only unknown parameter to solve Eqn. 4 for D. Knnburgh et al Specaton of the Adsorbed FA Molecules So far, the NICA model has been used successfully to calculate the compettve bndng between protons and metal ons for HA and FA (Chrstensen et al., 1998; Pnhero et al., 1999; Knnburgh et al., 1999; Berbel et al., 2001). Instead of metal ons, now surface stes compete for the bndng stes of the FA. The NICA equaton s combned wth the basc Stern (BS) model, whch accounts for the electrostatcs near the surface (see CD-MUSIC model): Q,t Q max1 n,1 n H,1 Q max2 n,2 n H,2 K,1c X 0,X d, n,1 K,1 c X 0, X d, n,1 K,2c X 0,X d, n,1 K,2 c X 0, X d, n n,1 p 1 K,1 c X 0, X d, 1 n,1 p 1 K,1 c X 0, X d, n,2 p 2 K,2 c X 0, X d, 1 n,2 p 2 K,2 c X 0, X d, n whch X 0, and X d, ndcate the Boltzmann factors (e z 0F 0 /RT,e z df 1 /RT ) for complex type n the 0- and d-plane respectvely. Note that n ths equaton the concentraton of surface stes (c ) s expressed n mol/l The Dstrbuton of FA Over the Mneral Surface and Soluton In ths study we assume that the reacton at the macroscopc level (Eqn. 1) s the result of all nteractons at the mcroscopc level (Table 1). For the calculaton of the dstrbuton of FA molecules over the mneral surface and soluton (I n Fg. 2) wth the CD-MUSIC model (see Hemstra et al., 1989a, b and Hemstra and Van Remsdjk, 1996 for detals), the nput parameters (reference state of the dssolved FA molecule, stochometry coeffcents, overall affnty constant, and overall charge dstrbuton) are obtaned from the mcroscopc specaton calculaton of the FA molecules. Ths wll be descrbed n more detal n the next sectons The Reference State of the Dssolved FA In ths study we take the actvty of the fully deprotonated speces as the reference state of the FA molecules n soluton. (6)

6 1468 J. D. Flus et al. Table 2. Basc physcal chemcal parameters used for the descrpton of the chargng behavor of FA wth the NICA-Donnan model. The actvty of the fully deprotonated FA s not easy to derve from the NICA equaton. For smplcty we assume that the actvty of the fully deprotonated FA molecules s related to the total FA n soluton accordng to: FA z FA z *FA dss (7) n whch FA dss s the total concentraton of FA n soluton and FA z s the fracton of the deprotonated FA whch can be defned as the product of the deprotonated fractons of the carboxylc fd carb and hydroxylc fd hydr groups: fd fd FA z carb * phen (8) The ndvdual fractons can be found from applcaton of Eqn. fd H 3 knowng that carb carb 1 for the carboxylc groups, n whch H carb s the fracton of the carboxylc groups of the FA molecule that s protonated. Ths yelds: 1 fd carb (9) 1 K H,1 H D m1 fd for the carboxylc groups. phen can be calculated wth Eqn. 9 usng the constants of the second dstrbuton (logk H,2 and m 2 of Table 2). The actvty of the fully deprotonated FA molecules can now be calculated accordng to: 1 FA z 1 K H,1 H D * 1 m1 1 K H,2 H D *FA m2 dss Stochometry Coeffcents Qmax (mol/kg FA) logk H, m Carb. ( 1 ) Phen. ( 2 ) k 0.57 M m (g/mol) a 683 a Van Zomeren and Comans (2002). (10) In the LD model (III n Fg. 2), the mean specaton of the adsorbed FA molecule s calculated. In Eqn. 1, the stochometry coeffcent for nner sphere complexaton (see reacton 7 of Table 1) s gven by a. The stochometry coeffcent b n Eqn. 1 conssts of the summaton of the stochometry coeffcents of the dfferent types of outer sphere complexes as gven by reactons 9 and 10 of Table 1, e.g.: b b 1 b 2 b 1 b 1,1 b 1,2 (11a) (11b) b 2 b 2,1 b 2,2 (11c) n whch thefrst subscrpt refers to ether carboxylc groups (1) or hydroxylc groups (2). The second subscrpt dscerns the two types of outer sphere complexes for hydroxylc groups. b 2,1 refers to the stuaton where the proton s closest to the reactve ste of the goethte surface, whereas b 2,2 refers to the stuaton where the proton s closest to the hydroxylc group. Fnally, n Eqn. 1 c represents the stochometry coeffcent of the proton complexes formed: c c 1 c 2 (12) n whch the ndex refers to carboxylc (1) or hydroxylc groups (2). The mcroscopc stochometry coeffcents (a, b,j, c ;expressed n mol complex/mol FA) are related to the total amount of the dfferent types of surface complexes formed (Q s,t, Q os,j,t, Q H,t) for nner sphere, outer sphere, and proton complexes respectvely; e.g., the quantty of organc groups that forms a complex of type expressed n mol complex/kg FA) and calculated wth the NICA equaton (Eqn. 6) by: a M FA. Q s,t b, j M FA. Q os, j,t c M FA. Q H,t (13a) (13b) (13c) n whch M FA s the averaged molecular mass of the FA molecules (kg/mol). The subscrpts and j are the same as used for the stochometry coeffcents b and c n the correspondng reactons n Table 1. Van Zomeren and Comans (2002) determned the M FA for SFA to be kg/mol (see Table 2). Note that the stochometry coeffcents are not constants, but depend on the ph, onc strength, surface coverage, and so forth The Overall Reacton Constant The overall affnty s composed of the constants for the formaton of the dfferent complexes weghed by ther relatve contrbuton: logk overall a. logk n b 1. logk out,1 b 2. logk out,2 a b 1 b 2,1. logk H c 1. logk H1 b 2,2 c 2. logk H2 (14) The dfferent reacton stochometry coeffcents (a, b, c) are defned n the prevous secton and n Table 1. The frst three terms of the rght-hand sde of Eqn. 14 refer to the bonds formed between the FA groups and the surface, n whch logk n s the medan affnty constant for the formaton of nner sphere complexes and logk out,1 and logk out,2 are the medan affnty constants for the formaton of outer sphere complexes formed by carboxylc and hydroxylc groups respectvely. The last three terms refer to the protonaton reacton of the metal oxde surface groups (logk H ), the free carboxylate groups of adsorbed FA (logk H1 ), and the free hydroxylate groups of adsorbed FA (logk H2 ) respectvely. Note that we have assumed that the affnty constants of the dfferent outer sphere complexes are assumed to be the same for the reacton wth sngly and trply coordnated groups (logk out,2 for reactons 9 and 10 of Table 1).

7 Modelng the adsorpton of fulvc acd by goethte The Overall Charge Dstrbuton The charge dstrbuton can be calculated f we assume that the charge of the fully deprotonated adsorbed FA molecule s located n the d-plane except the charge of the FA groups that s located n the 0-plane due to the formaton of nner (a), outer sphere (b) complexes (see charge dstrbutons for reactons 7 to 10 n Table 1). The change n charge due to the protonaton of the noncoordnated groups s assumed to take place n the d-plane. The charge dstrbuton over the 0- and d-plane s therefore gven by: z 0,FA a 0.8b 1 b 2,1 0.2 b 2,2 z d,fa z a 0.8b 1 b 2,1 0.2 b 2,2 c 3.1. Goethte 3. MATERIALS AND METHODS (15a) (15b) The goethte s prepared accordng to the procedure descrbed n detal by Hemstra et al. (1989b). The BET-N 2 surface area of the sample was 94 m 2 g Fulvc Acd Extracton Sol fulvc acd was extracted from a sol sample usng methods based on those recommended by the Internatonal Humc Substances Socety (Aken et al., 1970; Swft, 1996). The sol materal used was from a Bs horzon of a peaty podzol (Strchen assocaton). The extracton s descrbed n detal by Flus et al. (2000) 3.3. Data Analyses The onc strength s calculated for each data pont explctly takng nto account both the background electrolyte ons and free H and OH. From the calculated onc strength (I), the actvty coeffcents (f) were determned usng an adapted Daves equaton: logf 0.51 * z 2 * I 1 I 0.2 * I (16) Blank correcton for each data pont was carred out by calculatng the amount of ttrant requred to ncrease the ph of an equvalent volume of background electrolyte soluton. Ths was subtracted from the volume of ttrant used for the sample Adsorpton Experments The FA adsorpton by goethte was measured n background electrolytes of 0.01 mol/l and 0.1 mol/l NaNO 3, usng a batch equlbraton procedure. The data are obtaned from Flus et al. (2000) Proton-Ion Ttratons at Constant ph Samples of 60 ml of a goethte suspenson were ttrated to ph 4, 5.5, or 7 and left overnght whle purgng wth most clean N 2. The samples have an electrolyte concentraton of 0.01 mol/l or 0.1 mol/l NaNO 3. The goethte soluton was ttrated wth a 5 g/l FA soluton havng the same ph and onc strength as the goethte soluton. Both goethte suspenson and FA soluton were kept under N 2 durng the entre experment. After each FA addton, the ph was corrected to the ntal ph wth acd or base. A reacton tme of at least 20 mn and a maxmum drft crteron of ph unt per mnute were used between each addton of FA to reach equlbrum. The total amount of added FA was suffcently small compared to the total surface area of the goethte to have more than 99% of the FA bound. The acd/base balance can be calculated from the amount of added acd and base because the ph was kept constant and vrtually no FA remans n soluton Model Calculatons The model calculatons were carred out wth the computer program ORCHESTRA (Objects Representng CHEmcal Specaton and TRAnsport; Meeussen et al., 2001) whch was developed specfcally to facltate the mplementaton of advanced adsorpton models. The most contrastng dfference wth any of the standard specaton algorthms s that n OR- CHESTRA the model type defntons are completely separated from the calculaton kernel, and even from the source code. Model types are defned n the form of objects n a separated database. Ths allows users to freely change or add new model defntons wthout changng the source code. The object-orented structure of the model type defntons makes t possble to desgn a small set of fundamental object classes that can be used as buldng blocks for specfc model mplementatons. Ths greatly smplfes the mplementaton of new chemcal models and the combnaton of exstng models as done n ths study. The ORCHESTRA model and the nput fle for the LCD model can be obtaned from 4. RESULTS AND DISCUSSION 4.1. Basc Chargng Behavor and FA Adsorpton The LCD model combnes the chargng characterstcs of the oxde surface and the adsorbed FA. The basc chargng behavor of the goethte surface and the FA molecules can be descrbed usng the ndvdual fundamental models (CD-MUSIC for the metal oxde and NICA for the natural organc acd). The basc chargng behavor of both components s determned n separate experments. The chargng behavor of goethte s very smlar to the reported chargng behavor of goethte by Venema et al. (1996) and Retra et al. (2000). Table 3 gves the parameters used to descrbe ths chargng behavor wth the CD-MUSIC model. Fgure 4 shows the chargng behavor of SFA n soluton for four dfferent electrolyte concentratons. The expermental setup s gven n detal by Flus et al. (2000). The lnes n Fg. 4 ndcate the model calculatons wth the NICA-Donnan model. The fttng strategy of the expermental data to the NICA-Donnan model s descrbed elsewhere (Knnburgh et al., 1999). The parameters used to descrbe the chargng behavor of SFA wth the NICA-Donnan model are gven n Table 2. Fgure 5 shows the adsorpton envelopes for three dfferent

8 1470 J. D. Flus et al. Table 3. Basc physcal chemcal parameters used for the descrpton of the chargng behavor of the goethte. FeOH 0.5- H 0.5 N FeOH 2 log K H Fe 3 O 0.5- H N FeOH 0.5 log K H A: 94 m 2 /g C: 0.9 F/m 2 N s (FeOH): 3.45 stes/nm 2 N s (Fe 3 O): 2.7 stes/nm 2 log K H PPZC: 9.2 log K Na 1 log K NO3 1 total amounts of FA at constant goethte concentratons as determned n a prevous study (Flus et al., 2000). The data show lttle salt dependency but the adsorpton s strongly ph dependent. Ths type of sorpton behavor s commonly found for FA and other fractons of NOM (Tppng, 1981; Becket and Le, 1990; Wang et al., 1997; Au et al., 1999). The lnes n Fg. 5 represent the model descrpton. Table 4 lsts the parameter values used to descrbe the adsorpton data Number of Adjustable Parameters In prncple, two parameters are adjustable for each type of defned reacton;.e., the medan ntrnsc affnty constant of the complex and the nondealty parameter n. In addton, the parameter p determnes the wdth of the ntrnsc affnty dstrbutons of carboxylc and hydroxylc groups. However, the number of adjustable parameters can be reduced by a number of assumptons. We assume a partal correlaton between the dstrbutons of the affnty constants of the dfferent complexes. Accordng to Rusch et al. (1997) the NICA model can be nterpreted to relate to a partal correlaton when the n-values for the dfferent reactons are equal and smaller than 1. Therefore we assume: n n H n n n out,. Mlne et al. (2001) determned the generc NICA-Donnan model parameters for 25 data sets. Ther results show a varaton n the value of the nondealty factor n. We have taken the value for the n H value of Mlne et al. (2001) for our n parameter. The ntrnsc chemcal heterogenety parameter p wll follow n ths approach from the n H value taken from the generc parameter set and the dstrbuton wdth (m n * p) found from the nterpretaton of the H-ttraton data (Fg. 4). Therefore, the medan affnty constants for each type of complex formed are the only adjustable parameters. In the applcaton of the LCD model, we assume further that the protonaton of the adsorbed organc lgands can be descrbed wth the same parameters as found for the descrpton of the basc chargng behavor of FA n soluton. Furthermore, the dfference n affnty for the two types of outer sphere complexaton reactons of the hydroxylc groups s assumed to be only due to the proton affnty of the hydroxyl group n case the hydroxyl group act as the proton donor (reactons 9 and 10 of Table 1). Therefore, n the model approach used here only three adjustable parameters reman,.e., logk n, logk out,1, and logk out,2. The parameters that are taken from the generc data set (Mlne et al., 2001) or ndependently obtaned from curve fttng of soluton ttraton data are gven n Table 4. The number of adjustable parameters s comparable to the number often needed to descrbe the adsorpton of much smpler anons, such as oxyanons (Bowden et al., 1980; Dzombak and Morel, 1990; Mannng and Goldberg, 1996; Geelhoed et al., 1998). Wth a mnmum of the three adjustable affnty constants we are able to descrbe the data presented n Fg. 5 takng nto account all reactons of Table Specaton of the Adsorbed FA Based on the descrpton of the data we can analyze the adsorpton behavor of FA. The adsorpton of FA by goethte s largely determned by the specaton of the adsorbed FA molecules. In Fg. 6, the specaton of the adsorbed FA molecules s gven for the hghest FA:goethte rato presented n Fg. 5c. In a large range of ph values (ph 4 to 12), Fg. 6 represents the specaton of the bound FA at the pseudoplateau of the adsorpton sotherms. Fgure 6a shows the fate of the carbox- Fg. 4. Basc chargng behavour of SFA n soluton at four salt levels.

9 Modelng the adsorpton of fulvc acd by goethte 1471 Table 4. Parameters for the NICA model used for the calculaton of the specaton of the adsorbed FA molecules. logk n 1 Ftted logk out, Ftted logk out,2 3.5 Ftted n Generc data set a n Generc data set a p m n H. p p m n H. p a Mlne et al., Fg. 5. The adsorpton envelopes of SFA by goethte n 0.01 mol/l (open symbols and dotted lnes) and 0.1 mol/l NaNO 3 (sold symbols and full lnes). The suspenson densty of goethte s 5 g/l and three dfferent total FA concentratons: (a) 75 mg/l; (b) 150 mg/l; (c) 300 mg/l. ylc groups of an adsorbed FA molecule. Under the condtons of apparent maxmal adsorpton, model calculatons show that the carboxylc groups react predomnantly va outer sphere complexes. At low ph, nner sphere complexes become more mportant owng to ther favorable charge dstrbuton. Wth ncreasng ph, the electrostatc nteractons wll ncreasngly favor outer over nner sphere complexaton. Over the entre ph range, part of the carboxylc groups s dssocated. Only a small fracton of the carboxylc groups becomes protonated at low ph. Ths behavor agrees wth the fndngs of Boly et al. (2000) who studed the bndng of three carboxylc acds. They nferred from spectroscopc data that outer sphere complexes are mportant at hgh ph, whereas nner sphere complex formaton becomes sgnfcant at low ph. For multple carboxylc acd (e.g., pyromelltc acd) Boly et al. found that the protonated reactve groups become notceable. Fgure 6b shows the fate of the hydroxylc groups. Almost all hydroxylc groups are nvolved n the complexaton reactons wth the goethte surface over a wde ph range. The dfferences n charge dstrbuton of the two hydroxylc outer sphere complexes cause a preferental formaton of the complex n whch the hydroxylc FA group acts as the H-bond donor at low ph. Wth ncreasng ph, the complex s replaced by the goethte surface group as the proton donor. At low ph, the specaton calculatons show that the hydroxylc groups that are not assocated wth the surface start to become notceable. Accordng to the calculatons, these groups are protonated. To date, no spectroscopc data are avalable to verfy the presented specaton calculatons for the hydroxylc groups presented n Fg. 6b. In the present model, the man parameters determnng the specaton are the medan affnty constant, the nondealty coeffcent, and the charge dstrbuton of the dfferent complexes. As was found by Flus et al. (2000, 2001), the medan affnty constants for the formaton of outer sphere complexes are much hgher than for the formaton of nner sphere complexes. Ths ndcates that the replacement of a water molecule n case of nner sphere complex formaton s not necessarly favorable. The hgher affnty constant for the formaton of outer sphere complexes nvolvng a hydroxylc group compared to carboxylc groups corresponds wth the larger undersaturaton of the hydroxylate oxygen ( 1 per O) compared to the carboxylate oxygens ( 0.5 per O) of the organc molecule Verfcaton of the LCD Model To verfy the LCD model, we predct the coadsorpton of protons n case 99% of the added FA s adsorbed. Recently, Retra et al. (1999) ponted out that proton-on ttratons at constant ph and a hgh sold/lqud rato provde addtonal nformaton under these condtons. The adsorbed amount of FA (x-axs) n such experments follows drectly from the added total amount. The number of protons that coadsorb/ desorb (y-axs) follows from the amount of acd (or base) added to mantan a constant ph. The coadsorpton of protons s measured as the extra amount of protons consumed upon the adsorpton of FA at constant ph. In ths study, we have measured the proton-fa adsorpton stochometry for three dfferent ph values and two electrolyte concentratons. Fgure 7 shows the results of the proton-on ttratons. The lnes n the fgure ndcate model predctons. Note that the model s calbrated on the FA adsorpton data of Fg. 5 where the goethte has a relatvely hgh FA loadng. The FA:goethte rato used n the proton-on ttratons s much lower than the ratos used n the adsorpton experments (ph 7: 18 to 180 g FA/m 2 and60to630 g FA/m 2 respectvely).

10 1472 J. D. Flus et al. Fg. 6. The specaton of adsorbed FA molecules on the goethte surface expressed n number of complexes per adsorbed FA molecule (FA ads) plotted as functon of ph at the hghest goethte:fa rato of Fg. 5. (a) The specaton of the adsorbed carboxylc groups; (b) the specaton of the adsorbed hydroxylc groups. Note that the number of complexes per adsorbed FA molecule s equvalent to the stochometry coeffcent of that partcular complex. The calculatons of the proton coadsorpton are therefore pure predctons for stuatons whch are extrapolatons compared to Fg. 5 and not nterpolatons. The effects of ph, onc strength, and surface loadng on the proton adsorpton are predcted qute accurately. 5. CONCLUSIONS The LCD model enables the smultaneous descrpton of the concentraton, ph, and salt dependency of FA adsorpton and the related charge phenomena: basc proton chargng, coadsorpton of protons upon FA adsorpton. The model exhbts dfferent levels of detal. At a mcroscopc scale, the types of complexes between protons and the reactve groups of FA and the surface are defned. The structures of the complexes are, f possble based on nformaton obtaned from spectroscopc studes. Protons n soluton and reactve surface groups compete for the same reactve groups of the FA molecule. The nteractons result n a specaton of the adsorbed FA molecule that depends on ph, onc strength, surface loadng, and so forth. Ths level of detal s comparable to the bndng of protons and heavy metals by humc materals. The specaton of the adsorbed FA molecules s calculated usng the NICA model. The specaton of the adsorbed FA molecule mplctly determnes the most mportant factors for NOM bndng by oxde surfaces, e.g., the overall bndng affnty, the charge dstrbuton near the surface, and the stochometry of an adsorbed FA molecule. The macroscopc dstrbuton of FA over the dssolved and adsorbed state s calculated usng the CD-MUSIC model. The couplng of the NICA equaton and the CD-MUSIC model s self-consstent. Ths means that the specaton of the bound FA determnes the overall affnty constant, the overall charge dstrbuton, and the stochometry of the adsorpton reacton and vce versa. For the calculaton of the specaton of the bound FA, as well as n the calculaton of the overall adsorpton of FA by goethte, the electrostatc nteractons are taken nto account usng the BS approach.

11 Modelng the adsorpton of fulvc acd by goethte 1473 Fg. 7. The coadsorpton of protons as functon of the adsorbed amount of FA at three ph values and two onc strengths. The open symbols and dotted lnes represent the data at 0.01 mol/l NaNO 3 and the sold symbols and sold lnes the data at 0.1 mol/l NaNO 3. The model lnes are pure predctons. Because of the complex nature of the nteractons between organc materals and oxde surfaces, spectroscopy studes gve at present lttle nformaton about the specaton of the adsorbed organc molecules. The spectroscopc data provde quanttatve nformaton about the types of complexes formed between the reactve groups of the surface and of the organc molecule. Ths nformaton corresponds to the mcroscopc level of detal of the present approach and constrans the types of complexes used n the model. The calculated surface specaton of the adsorbed FA molecule (Fg. 6) shows that almost all hydroxylc groups are nvolved n surface complexaton reactons. The noncoordnated groups of adsorbed FA molecules are predomnantly deprotonated carboxylate groups. The model calculatons show that the carboxylc groups are mportant for the FA bndng at low ph, whereas the hydroxylc groups are relatvely more mportant at hgh ph. Ths s n agreement wth studes determnng the sorpton of small, well-defned, weak organc carboxylc and hydroxylc acds. Inner sphere complexes become mportant at low ph; outer sphere complexes are mportant at hgh ph. Ths s n agreement wth the complex formaton nferred from spectroscopy studes of small organc acds. The advantage of the model approach presented here s that t can also be appled or extended for larger, complex molecules lke humc acds. For the adsorpton of molecules larger than humc acd (e.g., large polyelectrolytes), the conformatonal changes due to a varaton n the formaton of so-called loops and tals wth changes n ph and salt level are mportant. As entropc and hydrophobc contrbutons are taken nto account only mplctly n the LCD model, the model s less sutable for descrbng the adsorpton of the polyelectrolyte molecules wth very large molecular weght. In the near future, the LCD model wll be used to test how far the approach wll gve satsfactory results for complex systems n whch oxyanons and polyvalent catons wll be smultaneously present together wth the oxde and the FA. Acknowledgments We would lke to thank the revewers for ther constructve comments on ths paper. Assocate edtor: S. J. Trana REFERENCES Aken G. R., Thurman E. M., Malcolm R. L., and Walton H. F. (1970) Comparson of XAD macroporous resns for the concentraton of fulvc acd from aqueous soluton. Anal. Chm. Acta 51, Al M. A. and Dzombak D. A. (1996) Compettve sorpton of smple organc acds and sulfate on goethte. Envron. Sc. Technol. 26, Atknson et al., 1967; Evanko and Dzombak 1998; and Gu et al., 1995; Mlne Au K-K., Pensson A. C., Yang S., and O Mela C. R. (1999) Natural organc matter at oxde/water nterfaces: Complexaton and conformaton. Geochm. Cosmochm. Acta 63, Avena M. J., Vermeer A. W. P., and Koopal L. K. (1999) Volume and structure of humc acds studed by vscometry: ph and electrolyte concentraton effects. Collods Surfaces A 151, Balstrer L. S. and Murray J. W. (1986) The nfluence of the major ons of seawater on the adsorpton of smple organc acds by goethte. Geochm. Cosmochm. Acta 51, Beckett R. and Le N. P. (1990) The role of organc matter and onc composton n determnng the surface charge of suspended partcles n natural waters. Collods Surfaces 44, Benedett M. F., Van Remsdjk W. H., and Koopal L. K. (1996) Humc substances consdered as a heterogeneous Donnan gel phase. Envron. Sc. Technol. 30, Berbel F., Díaz-Cruz J. M., Arño C., Esteban M., Mas F., Garcés J. L., and Puy J. (2001) Voltammetrc analyss of heterogenety n metal on bndng by humcs. Envron. Sc. Technol. 35, Boly J. F., Persson P., and Sjoberg S. (2000) Benzenecarboxylate surface complexaton at the goethte (a-feooh)/water nterface: II. Lnkng IR spectroscopc observatons to mechanstc surface com-

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