J. Chem. SOC., Faraday Trans. I, 1984, 80, 2619-2629 Ion Adsorption and Electron Transfer in Spinel-like Iron Oxide Colloids BY ELISABETH TRONC* Laboratoire de Chimie de la Matiere Condensee (LA 302), Ecole Nationale SupCrieure de Chimie de Paris, 11 rue Pierre et Marie Curie, 75231 Paris, France AND JEAN-PIERRE JOLIVET AND JEAN LEFEBVRE Laboratoire de Chimie des Polymeres Inorganiques, Universite Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris, France AND RENE MASSART Laboratoire de Physico-Chimie Inorganique (ERA 608), Universite Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris, France Received 25th July, 1983 The behaviour of aqueous spinel-like iron oxide colloids in the presence of metal ions, and especially Fe2+, has been studied protometrically and structurally. Fe2+ adsorption is shown to proceed reversibly with the release of two protons per adsorbed ion; subsequent implication of an Fe,O, outer shell is demonstrated. All the experimental features support electron transfer involving an octahedral site sub-lattice of the whole colloid.Phenomena occurring at the interface between metal oxides and aqueous electrolyte solutions are of interest in many areas such as corrosion and catalysis. Adsorption is generally treated using a surface complexation m ~ d e l l - ~ where protons or hydrolysed metal ions coordinate with surface oxygen species. In some cases, however, various processes may occur in the solid and the phenomena cannot be restricted to the interface. This is illustrated by the adsorption of protons or iron ions on iron oxides.Thus, in a-Fe203 adsorbed protons diffuse through the surface layer, suggesting a hydrated goethite-like interpha~e.~ Magnetite in a weakly acidic medium adsorbs protons but releases Fe2+ ions.6 Fe2+ adsorption on y-FeOOH may transform it to Fe304, probably via the formation of a surface intermediate.’ Paralleling the chemical insertion of lithium in Fe,04,8 diffusion of protons and Fe2+ ions through the spinel framework could also occur. Such phenomena are enhanced as the surface area of the solid increases, and in the colloid size range some remarkable features may result. We report here a study on the interactions in solution between spinel iron oxide colloids and metal ions, especially Fe2+, from both chemical and structural viewpoints.These colloidsg~ lo are the main constituents of aqueous magnetic sols and peptization of the solid results from the occurrence of surface electrical charges. Sol formation and charge evolutionll are understood classically in terms of acid-base reactions at amphoteric surface hydroxy group^.^^-^^ From their Fe2+ content, these materials stand between Fe,O, and y-Fe,O,. Magnetite has an inverse spinel structure and y-Fe20, differs from this in that it contains Fe3+ ions only and thus vacancies in the 26192620 ION ADSORPTION AND ELECTRON TRANSFER IN IRON OXIDE COLLOIDS octahedral metal sub-lattice. Stabilization of y-Fe,O, has been understoodl5-l7 in terms of protons occupying some or all of the vacancies up to the limiting composition HFe,O,; it has also been suggested that hydroxy groups take part in this stabilization.18 The structure of the (probably hydrogenated) colloids investigated, can be describedlO by an average pseudo-spinel unit cell with metal sub-lattices notably defective.EXPERIMENTAL TECHNIQUES AND ANALYTICAL METHODS The total Fe content of the sols was determined by atomic absorption spectrophotometry (Perkin-Elmer type 373) and the Fez+ content by potentiometric titration with K,Cr,O, after dissolution of the sample in concentrated HCI. Ultrafiltration of the sols was performed by using Millipore Hi-flux apparatus equipped with semipermeable membranes PSED with a retention limit of ca. 104-105 molecular weight. Protometric titrations and kinetic experiments were performed as follows : 20 cm3 of distilled water, 0.5 cm3 of the sol with an iron concentration of ca.1 rnol dmP3 and variable amounts (0.5-3 cm3) of FeC1, (0.1 mol dm-,) were introduced into a 50 cm3 cell. One glass electrode was connected to a potentiograph Metrohm E436 (forward titration) and another one to an automatic titrimeter Metrohm Combi-titreur 3D (back titration). The reference was a calomel electrode with a N(CH,),NC!, bridge. N, was continuously bubbled through the electrolyte solution to prevent oxidation. Forward titrations were performed by slowly adding N(CH,),OH (2 cm3 in ca. 15 min) and titration curves were recorded by the potentiograph; HCIO, was used for the back titrations. For the kinetic studies acid addition was adjusted automatically so as to keep the pH constant at 3.1.X-ray diffraction patterns were obtained in the transmission mode to check qualitatively the similarity between isolated colloids and those in the sol. Structural analysis was undertaken by powder X-ray diffraction methods as previously reported.1° Samples corresponded to colloids which were either ultrafiltered (sample H) or centrifuged (sample E), and kept under nitrogen in a dessicator at room temperature until the diffraction data were recorded. Integrated intensities were collected in air using a Philips PW 1050 diffractometer equipped with a graphite monochromator, using Co Ku radiation up to 26' = 120" at a 20 scanning rate of 0.25" min-l. The stability of the system was controlled by re-measuring the intensity of the two first lines at the end of each run.Data were corrected for background, Lorentz and polarization effects calculated at peak maximum positions. Scattering curves for neutral atomic species and the real component of the anomalous dispersion corrections were taken from ref. (19). No weighting coefficients were used and structural refinements were performed through a normal least-squares procedure. PREPARATION OF THE SOLS Tetramethylammonium hydroxide N(CH,),OH ( 10 % aqueous solution) was from Merck. All other reagents were RP Normapur Prolabo chemicals. The preparation of the sols was carried out by the procedure already d e s ~ r i b e d . ~ . ~ ~ An aqueous mixture of FeCI, (40 cm3, 1 rnol dm-,) and FeC1, (10 cm3, 2 mol dm-3, HC1 2 rnol dm-,) was added with vigorous stirring to a NH, solution (500 cm3, 0.7 mol drn-,) at room temperature. The black precipitate formed was separated from the supernatant and treated in one of two ways: (1) with concentrated N(CH,),OH ( 1 rnol dm-,), which led to peptization and anionic sol formation, excess hydroxide being removed by ultrafiltration and the sol being transferred to distilled water (pH ll), or (2) with concentrated HCIO, (3 mol dmW3), which gave a suspension, the flocculate being separated, resuspended in acid and centrifuged, after which it was easily peptized in distilled water, giving a cationic sol of The sols were made up of roughly spherical colloids of ca.100 A size. For cationic colloids the counterions were ClO,. The colloid average charge, defined as the molar ratio of protons titratable by a base to total iron, was ca.0.02-0.05. The overall composition of the sols corresponded to an Fe3+:Fe ratio of ca. 0.80-0.90. pH 2-3.E. TRONC, J-P. JOLIVET, J. LEFEBVRE AND R. MASSART 262 1 RESULTS PROTOMETRIC STUDY Unlike the anionic sol, which was stable in an air-free alkaline medium, the cationic sol underwent notable changes. As soon as the acidic flocculate was transferred to distilled water, it released Fe2+ ions. Similar behaviour has already been reported for magnetite in a weakly acidic medium.6 Fez+ migration into solution can be seen (fig. 1) by comparison of the N(CH,),OH titration curves of the sol before ultra- 10 PH .8 6 4 2 1 2 3 N( CH3)4 OH/cm3 Fig. 1. Protometric titration by N(CH,),OH (0.11 mol dm-3) of: (a) non-ultrafiltered cationic sol (20 cm3, [Fe] = 0.1 mol dm-3); (b) ultrafiltered cationic sol (20 cm3, [Fe] = 0.1 mol dmP3); (c) ultrafiltrate (20 cm3, [Fe] = 4.52 x lop3 mol dm-3).filtration [curve (a)], after ultrafiltration and transfer to water [curve (b)] and of the filtrate [curve (c)]. The latter is identical to the titration curve of ‘free’ Fe2+ ions (FeCl, solution) and yields an iron concentration in perfect agreement with the atomic absorption analysis of the filtrate. Cationic sol evolution resulted in the release of nearly all the Fez+ ions from the colloids. After ageing for a week at room temperature, the relative amount of Fe2+ in the colloids was lowered typically to ca. 0.02-0.05. All further experiments were performed on sols which were cleared of free Fez+ ions. Comparison of curves (a) and (c) of fig.1 shows that colloids alter the Fez+ neutralization process, preventing ferrous hydroxide precipitation. This is further illustrated in fig. 2, which shows titration curves for different Fe2+ concentrations. The2622 ION ADSORPTION AND ELECTRON TRANSFER IN IRON OXIDE COLLOIDS 1c e PH 6 4 2 Fig. 2. Protometric titration by N(CH,),OH of cationic colloid in the presence of Fez+ (FeCl,). [Fe2+],,/[Fe]initial = 0 (curve 1 ) ; 0.09(2); 0.19(3); 0.29(4); 0.31(5); 0.35(6); 0.36(7); 0.39(8); 0.48(9). ([Fe2+]/[Fe]),,,,,, = 0.04. Dotted line, titration of Fez+ without colloid. amount of FeC1, solution added to a fixed amount of colloid prior to titration will be called [Fe2+Iad. Two types of curve are apparent, one with a step at ca. pH 7 [type (a)], where flocculation occurs, and the other with a second step at pH 8.5-9 [type (b)].The latter corresponds to excess Fe2+ ions which no longer interact with the colloids and precipitate as Fe(OH),, it occurred only for values of [Fe2+Iad yielding a total concentration ratio [Fe2+] : [Fe] > ca. 0.33 ; i.e. cationic colloids can adsorb Fe2+ species up to a final concentration ratio [Fe2+]:[Fe3+] of ca. 1:2. Remarkably, this should characterize ideal magnetite, Fe,O,. Quantitative conservation of the Fe2+ and Fe3+ species involved was checked by dissolving the materials obtained at the end of the reaction (ca. pH 10) in 12 mol dm-3 HCl and titrating both iron ion species. Moreover, whatever the value of [Fe2+Iad, double this amount of base, [HO-I,,,, was needed up to the zero-charge point (near pH 10).This is shown in fig. 3, where the plot of [HO-I,,, against [Fe2+Iad is a straight line of slope 2. These results show that in the presence of the colloid, Fe2+ ions do not contribute to Fe(OH), precipitation. Though the straight line in fig. 3 does not define the end of iron fixation on the colloid, it indicates the implication of two HO- (or H30+) ions per adsorbed Fe2+ ion. The results can be understood in terms of an exchange reaction between Fe2+ species in the solution and protons in the colloid, or the reverse, particularly for the spontaneous changes of cationic sols in a weakly acidic medium. The expression ‘exchange’ does not necessarily imply that the reaction occurs between protons in the colloid surface layer and free Fe2+ ions.More complex situations, involving the adsorption of hydroxylated metal species or the hydrolysis of adsorbedE. TRONC, J-P. JOLIVET, J. LEFEBVRE AND R. MASSART 2623 Fig. 3. Variation of the amount of base added up to the end of the reaction (point of zero charge in protometric curves) with the amount of Fe2+ initially added. 10 pH 8 0 1 2 3 [HO-1 or [H,O+]/[ Fen] Fig. 4. Cationic colloid titration in the presence of Fez+: (a) forward titration by N(CH,),OH; (b) back titration by HClO, (same reactant addition rate).2624 ION ADSORPTION AND ELECTRON TRANSFER IN IRON OXIDE COLLOIDS 0 -4 m E Q - ; E B 0.35 B --- - + 3 Y 0.3 I I -1-- 5 10 15 tlh Fig. 5. Desorption kinetics of Fe2+ at pH 3.1 (HClO, addition) after sol neutralization in the presence of FeCl, ([Fe2+],,/[FeIinitial = 0.32).should also be considered. The pH associated with iron uptake covers the range over which Fe2+ irons are in solution; nevertheless, adsorption may proceed from species hydrolysed at the interface.20 Our results do not enable us to decide between such models. For the sake of simplicity, the cationic colloid in its initial form and the colloid brought to the alkaline medium in the presence of Fe2+ ions will be called pro tonated and exchanged, respectively . Back titrations confirmed the exclusive release of ferrous ions and proved the reversibility of the adsorption. Forward and back titration curves obtained under similar conditions (especially the rate of addition of titrant), are given in fig. 4. Similar features are observed in spite of a noticeable shift.This hysteresis effect is related to an important variation in the desorption kinetics and concerns ca. 30% of the ad- sorbed Fe2+ ions. The kinetics were further studied by the automatic measurement of acid consumption as a function of time at pH 3.1. Two distinct stages are seen (fig. 5) corresponding to high and low rates for the consumption of acid. The first step, up to 0.36 [H,O+] added, includes the titration of excess base (introduced during the forward titration), the positive charge on the colloid under the experimental conditions (evaluated by blank experiment on similarly treated colloid, but without additional Fe2+ ions) and partial re-exchange (ca. 70%) of Fe2+ ions. The second stage corresponds to desorption of the remaining Fe2+ ions which was very slow.After 17 h at pH 3.1, ca. lO-15% of the Fe2+ ions had still to be desorbed. Complete consistency between iron desorption and proton consumption, in the ratio I : 2, was also checked by colloid ultrafiltration and forward titration of the Fe2+ in the filtrate. The ability to adsorb other ions was also investigated. Addition of Co2+ ions prior to titration led to identical features (fig. 6). Hydroxide precipitation, however, occurred more rapidly with a Co2+ uptake which was ca. 3 times less than that of Fe2+.E. TRONC, J-P. JOLIVET, J. LEFEBVRE AND R. MASSART 2625 [ HO-I / [ Fe Iinitial Fig. 6. Protometric titration by N(CH,),OH of cationic colloid in the presence of Co2+ (CoC1,). ([Fe2+]/[Fe])initial = 0.04; [Co2+Iad/[Felinitial = 0 (curve 1); 0.04(2); 0.06(3); 0.09(4); 0.13(5); 0.20(6) ; 0.26(7).Dotted line, titration of Co2+ without colloid. The plot of [HO-I,,, against [Co2+Iad is also a straight line of slope 2; hence the occurrence of 2H+/Co2+ exchange is similarly deduced. Only one step with a high proton consumption rate could be detected in the desorption kinetics. This proves that all the Co2+ ions desorb readily. With Ni2+ any exchange reaction was hardly detectable; hydroxide precipitation occurred from an [Ni2+Iad: [Fe] ratio of 1 or 2: 100. Fe3+ and A13+ ions had different behaviour, Fe(OH), and Al(OH), precipitation was observed in acidic medium followed, as the pH increased, by neutralization of the colloid. The adsorption capacity of magnetite for metal ions is known to be high20-22 but it cannot compare with the Fe2+ uptake involved here.The ratio [Fe2+]:[Fe3+] in exchanged colloids and the drastic decrease in the affinity in the order Fe2+ > Co2+ > Ni2+ > Fe3+ emphasize the specificity of Fe2+ adsorption. Because of the magnitude of the phenomenon, structural information was thought to be within the scope of an X-ray diffraction investigation. STRUCTURAL STUDY X-ray powder diffraction data were obtained from protonated and exchanged colloids. Protonated colloids (H) correspond to a concentration ratio [Fe2+],: [Fe], = 0.07: 1 and exchanged colloids (E) to an uptake [Fe2+Iad : [Fe], = 0.35: 1, giving [Fe2+] : [Fe3+] ratios equal to 0.075 : 1 and 0.45 : 1, respectively.2626 ION ADSORPTION AND ELECTRON TRANSFER IN IRON OXIDE COLLOIDS Table 1.Observed and calculated diffraction line intensities for protonated (H) and exchanged (E) samples sample H sample E hkl IUbS Icalc! Iohs Icalc 111 220 222 400 33 1 422 333 53 1 620 622 444 71 1 642 73 1 800 R 90 1278 6721 2 525 0 1070 4 709 10858 545 1997 70 1 0 647 3 159 1743 - 114 1195 6 741 2475 68 1139 4685 10865 616 1996 820 91 720 3217 1749 0.02 1 119 1588 7 594 2 847 0 1445 5517 11 474 796 2 474 827 0 929 3 857 1966 - 119 1500 7 632 2 780 59 1471 5483 11 484 817 2457 986 87 99 1 3 794 1960 0.018 Table 2. Structural parametersa sample H sample E site 32e x x x x 0.2523(7) 0.2530(8) 16d 1/2 1/2 1/2 ab 12.84(35) 13.69(39) 8a 1/8 1/8 1/8 6.65(10) 7.22(12) 48s x 1/8 1/8 (X = 3/8) 1.66(15) 0.88(16) thermal factor/A2 1.71(7) 1.45(7) distance/A 0-Fe( 1 6 4 0-Fe(8a) 0-Fe(48f) Fe(48f)-Fe( 166) Fe(48f)-Fe( 8a) 2.07(1) 2.06( 1) 1.84( 1) 1.85( 1) 1.82( 1) 1.82( 1) 1.81 1.81 2.09 2.09 a Standard deviations are given in brackets.a refers to site occupancy.E. TRONC, J-P. JOLIVET, J. LEFEBVRE AND R. MASSART 2627 On1 spinel-type lines were detected and no variation in the unit-cell parameter observed broadening was dominated by the size effect. Colloid mean sizes were evaluated from the full-width at half-maximum, assuming Gaussian profiles for size and instrumental broadenings, and were found to be 104 A (H) and 116 A (E). Recalling our previous study,1° defective spinel structure models (space group Fd3m), based on a perfect oxygen atom framework (equipoint position 32e), were used and refinements focused on the statistical population of the various metal sub-lattices.First, unconstrained 16d octahedral and 8a tetrahedral site occupancies (five par- ameters: scale factor, overall isotropic thermal factor, oxygen coordinate x and two site occupancies) led to values of the reliability index, R = XI I, - I, I /E I,, of 0.090 (H) and 0.040 (E). The population of tetrahedral 48fsites (x 1/8 1/8, x = 3/8) by iron atoms significantly improved the fits (6 parameters), lowering R to 0.021 (H) and 0.018 (E). No significant residual electron density could then be detected in either site still available (8b, 16c). Observed and calculated diffraction data are listed in table 1 and structural parameters are given in table 2.Complete consistency with the previous investigationlo is obtained. Because of the order enhancement effect associated with X-ray diffraction it seems reasonable to consider that these data refer only to the crystalline bulk, ignoring eventual out-of-site atoms in the outer shell. The overall average cell contents deduced are Fe21.2(6)032 (H) and Fe21.8(,1032 (E). Such a small variation rules out any homogeneous distribution of the extra ions in the bulk [which would give Fe28.6032 (E)]. Even with a concentration gradient assumption, structural and chemical data cannot agree unless extension of the ordered oxygen array is taken into account. We therefore suggest that iron diffusion into the core is not prominent but that a growth occurs. The most simple description of colloid E is a coherent X-ray scattering two-phase system: a core made up of colloid H surrounded by an ordered outer shell.Mass balance, based on X-ray and chemical data and referred to unit-cell oxygen content, leads to partitioning: (8.35 K ) was observed. The angular dependence of the line-width confirmed that the which assesses the new layer composition at the magnetite one. Following this, site occupancy evolution is attributed to the outer layer, the values deduced from table 2 [8a+2.1(1), 16d+4.0(5), 48f-0.4(2)] show that iron species selectively locate in 8a tetrahedral and 16d octahedral sites in the ratio 1 : 2. This supports the above assumption and suggests that the outer shell has both the Fe and 0 concentration of Fe30, and its structure. As before,lO interpretation of 48f site occupancy, interstitials in the bulk or a surface effect, remains open.Neglecting any composition dependence of the unit-cell dimensions, a volume ratio, outer layer to core, of 0.31 : 1 is obtained. For a core diameter of 104 A (H) this yields a 5 A thick outer shell. This compares well with the size evolution deduced from the line-widths (6 A) and indicates that there are ca. 2 or 3 more ordered oxygen layers. X-ray diffraction data do not allow any differentiation between Fe3+ and Fe2+ species, but in conjunction with chemical data their respective amounts per unit cell may be evaluated. Corresponding Fe2+ contents are given in table 3. Comparison with values in table 2 shows that in cell E, overall 16d octahedral site population is twice the Fe2+ content.This suggests that, as in the inverse spinel structure, all Fe2+ ions locate in 16d sites with an equal number of Fe3+ ions in the outer shell and in the core.2628 ION ADSORPTION AND ELECTRON TRANSFER IN IRON OXIDE COLLOIDS Table 3. Iron content analysis from (1) chemical data (2) structural data and (3) both sample H sample E unit-cell H unit-cell E (2) Fe21.2032 Fe21.8032 Feg (3) Feii (7-4) 5.6 6.8 Fe",' - DISCUSSION The above structural model is schematic. Besides distribution in colloid mor- phology and surface irregularities, induced ordering of iron atoms in the hydroxylated interphase is ignored and the Fe,O, shell is assumed to be built up from adsorbed species only. Uncertainty remains as to the origin of the oxygen supply, which is from interphase ordering or from the solution or both.However, the perfect consistency obtained above and the complete coherence in the interpretation of the protometric features are highly corroborative and enable us to propose the following process. Adsorption of hydrolysed Fe2+ species by the colloid causes its growth by the development of a magnetite outer shell. Electrons produced by partial oxidation of adsorbed Fe2+ ions are pumped into the colloid core, causing the reduction of Fe3+ ions in 16d sites, up to the final Fe2+-Fe3+ equipopulation of these sites. This equilibrium state, given the initial amount of Fe2+ ions presumably in 16d sites, determines the magnitude of the electron transfer and thereby the Fe2+ uptake capacity. These itinerant 3delectrons may show a fast hopping, related to the pairwise electron hopping which exists in magnetite, thus stabilizing Fe2+-Fe3+ pairs in the defective material (interstitial atoms at 48f sites acting as impurities might help this electron transfer) unless they progressively fill the conduction band of octahedron chains and become delocalized.Information about this electron transfer may be provided by a Mossbauer study, even though a quantitative interpretation will be complicated by the superparamagnetic behaviour of the Within an ionic description, charge imbalance in the bulk could be compensated via hydrogen-species migration at the unit-cell level, or by inwards diffusion of surface protons. The small uptake capacity for Co2+ ions and Ni2+ ions corroborates that Fe2+-Fe3+ electron transfer is the driving force.Both Co2+ and Ni2+ ions have a marked tendency to occupy octahedral sites and form inverse-spinel ferrites. The slight variation in ionic radii from Fe2+ to Ni2+ 24 could not account, by itself, via a diffusion process, for the fundamentally different behaviour observed. Their oxidizability, on the other hand, parallels their decrease in uptake behaviour. Partial oxidation of Co2+ ions is possible under our experimental conditions and we suggest that the observed phenomena are governed by a redox reaction of the Co2+/Fe3+ couple. The exclusive location of cobalt at octahedral sites and the limited electron supply are probably responsible for the lower uptake capacity. Further information is obviously needed but note that such charge transfer is implicated in slightly non-stoichiometric cobalt f e r r i t e ~ .~ ~ Back exchange features may be understood by reversing the process. Iron desorbsE. TRONC, J-P. JOLIVET, J. LEFEBVRE AND R. MASSART 2629 exclusively in the ferrous state, in agreement with other observations.26* 27 We think this may be due to a charge effect, weakening Coulomb interactions and thus facilitating approach of the proton. This may even be reinforced by a distance effect since preferential occupation of octahedral sites leads to longer metal-oxygen bonds (table 2). Thus it is logically deduced that the fast desorption stage, concerning approximately two-thirds of the iron uptake, corresponds to leaching of Fe2+ ions from the Fe,O, layer, preferentially from octahedral sites, reduction to the ferrous state being assured by core-to-surface electron back transfer at the rate of one electron per two iron ions.The second stage implies slower processes. It may be connected, judging by the relative magnitudes, with iron in tetrahedral sites stabilized by its less easy reduction. Deeper octahedra may also be involved, hence implicating sluggish diffusion through an iron-deficient interphase constituted mainly of tetrahedrally coordinated ferric ions (possibly at 48fpositions). Whatever the process, the remaining mobile electrons are pumped back. Preferential exchange from octahedral sites is also corroborated by the fast desorption of all Co2+ ions. CONCLUSIONS The protometric results reported here demonstrate a reversible Fe2+ adsorption reaction at the colloid/solution interface in aqueous magnetic cationic sols.Structural investigations indicate that the uptake of ferrous ions proceeds with an extension of the spinel framework and formation of a Fe,O, outer shell. A consistent interpretation of all the experimental features leads us to conclude that it is governed by electron transfer between Fe2+ and Fe3+ ions involving the whole colloid, which behaves as an electron reservoir. The findings emphasize the specific properties of iron oxide colloids with a defective spinel structure when compared either with bulk materials or with Fe,O, colloids and may shed light on interesting catalytic properties. R. 0. James, P. J. Stiglich and T. W. Healy, Faraday Discuss.Chem. Soc., 1975, 59, 142. J. A. Davis, R. 0. James and J. 0. Leckie, J. Colloid Interface Sci., 1978, 63, 480. J. A. Davis and J. 0. Leckie, J. 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