Modeling Effects of pH and Counterions on Surfactant Adsorption at

2844

Ind. Eng. Chem. Res. 1996, 35, 2844-2855

Modeling Effects of pH and Counterions on Surfactant Adsorption at the Oxide/Water Interface Nicholas P. Hankins, John H. O’Haver, and Jeffrey H. Harwell* School of Chemical Engineering and Materials Science and The Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019-0628

A model is presented that describes the effect of pH on the adsorption of an isomerically pure anionic surfactant species at a mineral oxide/water interface. A site-binding model, to account for effects of pH, surface heterogeneities, and counterions, is incorporated into a patchwise, phaseseparation modeling approach, making it possible to predict both the surface charge and the counterion association beneath an adsorbed surfactant aggregate. Parameters for the site binding model on R-alumina are obtained from experimental surface charge measurements. The formation of both local monolayers (hemimicelles) and bilayers (admicelles) is allowed, although the isotherms studied in this paper are fit by parameter values that predict admicelle formation only. The model is able to predict experimental measurements of the adsorption of an isomerically pure, anionic surfactant species on R-alumina as a function of pH. It reproduces several previously unexplained experimental observations; in particular, it offers an explanation for the observation of significant adsorption of anionic surfactant above the point of zero charge (pzc) of a mineral oxide surface. Introduction The adsorption of surfactants on minerals is important in areas such as enhanced oil recovery, surfactantenhanced soil remediation, formation of organic thin films, ore flotation, wetting, adhesion, detergency, and dispersion stability. In surfactant flooding and soil remediation, the loss of anionic sulfonate by adsorption is detrimental to the economics of the processes. The use however of a high pH preflush or high pH micellar slug may reduce considerably the adsorption of anionic surfactant.17 Conversely, lowering the pH gives rise to a higher anionic surfactant adsorption, which is advantageous in inducing film formation. No serious attempt to create a pH-dependent predictive model has appeared in the literature however. Two schools of thought exist concerning the modeling of physical adsorption of surfactants on mineral oxide surfaces from aqueous solutions. The first school includes the work of Ottewill,25 Fuerstenau and Somasundaran,31,32 Koopal,5-9 and Wilson and co-workers.19,35 The adsorbing surface is generally treated as being homogeneous. These workers essentially consider that at a certain critical concentration, hydrocarbon chains begin to associate at the surface. In the earlier models, single-layered, two-dimensional aggregates (hemimicelles) are formed, which contain small numbers of molecules. In these models, the adsorption is described by the Stern-Langmuir equation,25,11 the Stern-Grahame equation,31,32 modifications of these,5,6 or the FowlerGuggenheim equation.19,35 In later models, Wilson19 and Bo¨hmer and Koopal7-9 have allowed for the formation of bilayered structures at high surfactant concentrations. Wa¨ngnerud and Jo¨nsson34 have calculated that bilayered structures will form instantaneously at a critical concentration without prior monolayer formation, provided the surface charge density is high enough. The second school is typified by the work of Schechter,30 Scamehorn,29 Harwell and co-workers,15,37 and Cases and co-workers.10 Their models consider the oxide surface to consist of a distribution of patches of * To whom correspondence should be addressed. Phone: 405-325-5814. Fax: 405-325-5813. E-mail: [email protected].

S0888-5885(95)00637-3 CCC: $12.00

different adsorption energies,29,10 or surface charge densities.30,15,37 Adsorption proceeds on local patches of the surface either sparsely or as a result of spontaneous thermodynamic phase transitions resulting in a local monolayer (hemimicelle), a local bilayer (admicelle), or an intermediate structure. Both groups agree that the primary forces involved in the formation of ionic surfactant aggregates are analogous to those in micelles, being the Coulombic interactions between surfactant hydrophilic moieties and the mineral surface and the surfactant tail-tail interactions (hydrophobic effect).33 All these models attempt to explain the fine structure of the adsorption isotherm, Figure 1.31,29 All workers agree that the increase in the slope of the adsorption isotherm in region II results from the association of hydrocarbon chains at the surface. Somasundaran and Fuerstenau have interpreted the II/III transition in terms of superequivalent adsorption on a like-charged surface;31 Bo¨hmer and Koopal8 interpret it in terms of a change in the favored primary aggregate form from head-on monolayer to bilayer and do not believe it necessarily coincides with the mineral isoelectric point. The second school has interpreted this transition in terms of infilling of less favorable adsorption sites that have a wider distribution of energies.15,29,30 Plateau adsorption in region IV is attributed to the formation of a constant chemical potential sink by micelles of a monoisomeric surfactant at concentrations above the cmc.29 Bo¨hmer and Koopal7-9 have applied the self-consistent field lattice theory for adsorption and/or association (SCFA) to the study of ionic surfactants adsorbing on constant and variable charge surfaces. The structure of the adsorbed layer, and in particular the hydrophobic chain configuration, is calculated (rather than assumed); this enables them to calculate equilibrium volume fraction profiles of all the species (surfactant head and tail groups, solvent molecules, and salt ions). For variable charge surfaces at constant potential (taken as equivalent to constant pH), they demonstrate that adsorption of anionic surfactants causes a positive shift in surface charge, and at low adsorption and low salt concentration, the charge is modified on a 1:1 basis by © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 2845

Figure 2. Structure of 4-C11-parayxlene sulfonate.

Figure 1. Schematic presentation of a typical surfactant adsorption isotherm.

surfactant ions. This assumption is shown to be violated at high salt concentrations because of counterion association. The SCFA theory is able to predict four isotherm regions for a homogeneous surface, although the model requires a phase condensation to occur throughout the entire layer, delaying region II and yielding an “Sshape” isotherm. The authors believe that surface heterogeneity is unnecessary in explaining the isotherm structure, but instead consider that in region II local aggregates grow in size. Wa¨ngnerund and Jo¨nsson34 have extended an earlier model for micelle formation in which electrostatic effects are treated using the Poisson-Boltzmann equation. In addition, they consider the hydrophobic effect and the influence of dispersion forces, solvation, and steric effects, allowing them to calculate free energies of interaction between the bilayer and the homogeneous surface. Above the critical aggregate concentration, the bilayer thickness and the adsorption density increase. The charge density of the solid surface is held constant, so that charge adjustment is unfortunately neglected. In Cases and Villieras,10 the adsorbent surface is considered to be heterogeneous, and the isotherm is related to the infilling of surface domains. The adsorption process is characterized by the strength of the surface/surfactant normal bond and by undersaturation. The isotherms develop step-like discontinuities, adsorption occurring on progressively less energetic homogeneous domains. For strong adsorbent affinity, the steps represent the two-dimensional condensation of single layers. After infilling of the entire surface, a delayed large step occurs corresponding to complete bilayer formation. However, as Bo¨hmer and Koopal point out, this is unlikely to be observed on variable charge surfaces due to continuous charge adjustment. If the adsorbent affinity is weak, then the first domains are covered with monolayers, which become bilayers, and subsequent domains undergo bilayer transitions. In this case, admicelles can form directly without prior monolayer formation. The fullest experimental study of the effect of pH on the adsorption of an isomerically pure anionic surfactant at the mineral oxide/water interface appears to be that of Fuerstenau and Wakamatsu,13 for sodium dodecyl sulfate adsorbed on R-alumina. Adsorption above the pzc is negligible and interpreted as an absence of chemisorption. The dependence of adsorption on con-

centration and pH is modeled in terms of the SternGrahame electrical double layer. This approach, however, is strictly valid only at low surface coverage.14 Furthermore, the presence of co-ions and counterions on the surface is neglected. This model is unable to predict the physical adsorption of surfactant at a pH significantly above the pzc, although this has been observed on R- and γ-alumina.3,24,38 The model of Harwell et al. on the other hand considers that the stabilization of surface aggregates is promoted by high counterion binding,5,15,37 which is able to stabilize the aggregates on the surface at a high pH. The purpose of the present paper is to extend their work by specifically including other effects that they consider to be of significance:5 complexation of counterions with the mineral-oxide surface, enhancement of the concentration of hydrogen ions near the surface by the electrical field of the aggregate, and electrostatic binding of counterions in the top layer of bilayered structures. A significant test of the usefulness of the model will be its ability to predict adsorption on (initially) like-charged surfaces by a purely physical mechanism. Experimental Methods Materials. Sodium chloride (Gold Label reagent quality) was obtained from Aldrich. Baker HPLC grade water was millipore filtered. Samples of 0.1 N sodium hydroxide, 0.1 N hydrochloric acid, and pH buffer solutions were obtained from Fisher Scientific. An isomerically pure anionic surfactant 4-C11-paraxylene sulfonate (pxs, with the molecular structure given in Figure 2) was synthesized by ARCO Chemical Company using proprietary techniques. Assay and HPLC analysis revealed no detectable levels of any other isomer or impurity. The NaCl and the pxs were stored in a vacuum desiccator until used. Nonporous R-alumina was obtained from Union Carbide Corporation with a specific surface area of 14 m2/gm. Borosilicate glassware was obtained from Kimax. Methods. The adsorption of pxs on R-alumina from 0.03 M NaCl solution was measured at 43 °C. Solutions of pxs, of known gravimetric concentration (at “natural pH” ≈ 7.6), were added to R-alumina in screw-capped tubes. A given tube was sealed with pvc tape and rotated slowly in an oven for 24 h; the supernatant was then removed after centrifugation at 43 °C. The final pxs concentration was determined by HPLC, using a UV absorbance detector with a 60:40 mixture of 0.01 M tertbutylammonium chloride and acetonitrile as the mobile phase. Adsorption was determined as the total abstraction of pxs from the supernatant per unit mass of adsorbent. The potentiometric titration of R-alumina was carried out using techniques described fully elsewhere.39 The temperature was maintained at 43 °C using a water jacket, and the environment of the titration cell was purged with nitrogen to avoid CO2 absorption. Mixing

2846 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996

Figure 3. Schematic representation of a mineral oxide/aqueous solution interface with possible locations for charged species.

was achieved by nitrogen sparging; pH was determined using a Ross-Orion KCl glass electrode. An Orion pH meter was linked to a chart recorder to monitor and verify the approach to equilibrium. A single electrolyte concentration of 0.03 M NaCl was used; added amounts of acid and base had negligible effects on the electrolyte concentration. The effect of pH on the plateau adsorption of pxs (i.e., adsorption just above the cmc) was measured by first adjusting the pH of pxs solutions substantially above the cmc, and then determining the total pxs abstraction upon equilibration with R-alumina. The initial pH was adjusted by adding small amounts of acid or alkali and was chosen to give a wide spread of final pH. The final pH of the supernatant was measured by glass electrode. Theoretical Section Model Assumptions and Premises. (1) At critical concentrations, surfactant aggregates are formed. These may be single or double layered; packing density within adsorbed layers is constant. Surfactant aggregate formation is governed by Coulombic and hydrophobic interactions. (2) The adsorbent surface is heterogeneous; adsorption proceeds by the progressive infilling of surface domains by aggregates, the domains being characterized by particular ionization constants. The pzc remains constant from domain to domain. Identical domain “types” may or may not be contiguous. (3) Those domains not covered by aggregates adsorb individual surfactant molecules by surface complexation and tail/surface interaction. (4) Development of surface charge and counterion association beneath an adsorbed surfactant aggregate is described by the site-binding model. (5) Within aggregates, sulfonate ions do not take part in surface complexation reactions themselves. (6) All co-ions are displaced from the inner Helmholtz plane at the onset of aggregate formation. (7) Counterions in the top layer are bound by electrostatic forces. (8) The electrostatic potential experienced by any species is equivalent to the macropotential. Charge is uniformly smeared out within the top and bottom charge layers of the aggregates. The thickness of a charge layer is equal to the sum of the diameters of the sulfonate

group and a hydrated counterion. Electrostatic “edge effects” may be neglected. (9) The time-averaged electrostatic potential within a charged region may be approximated by the potential in the center of that region. The electrostatic potential of a surfactant ion in an admicelle may be characterized by an average value for the top and bottom layers. (10) The width of the hydrocarbon core of the aggregate is twice that of the hydrocarbon chain. (11) Above the cmc, the chemical potential of surfactant species is constant. Complexation Double Layer Model for r-Alumina. For colloids and solids in aqueous systems, and particularly for mineral oxide/water systems, a comprehensive “site-binding” model has developed to describe surface charge, electrokinetic potential, and electrolyte adsorption at the solid-liquid interface.12,16,18 Following Davis et al.,12 the development of an electrical double layer model requires (1) the reactions responsible for developing surface charge and (2) the potential and charge relationships at the interface. The surface of aluminum oxide is known to consist of chemically adsorbed water molecules, which can be protonated or deprotonated; they behave as amphoteric functional groups, with H+ and OH- as the potential determining ions (pdi).39,12 The amphoteric sites possess characteristic equilibrium constants Ka1 and Ka2; thus

AlOH2+ S AlOH + Ho+

AlOH S AlO- + Ho+

Ka1 )

Ka2 )

[AlOH][H+]e-yo [AlOH2+]

[AlO-][H+]e-yo [AlOH]

(1) (2)

[AlOH2+], [AlOH], and [AlO-] are concentrations of surface groups in differing states of protonation (see Figure 3), in units of mol/m2; their centers are all assumed to lie in a plane. In eqs 1 and 2, the concentration of protons at the surface is related to the bulk concentration by a Boltzmann-type expression, yo ) eψo/kT where ψo is the electrical potential at the surface, and [H+] and [Ho+] are concentrations (in mol/ dm3). To account for specific adsorption of electrolyte ions, the charged sites interact with the ions. Thus, for the


1:1 electrolyte NaCl

NS ) [AlOH] + [AlOH2+] + [AlOH2+-Cl-] + [AlO-] + [AlO--Na+] (9)

(KintNa)

AlO- + Na+β T AlO--Na+

(KintCl) (3)

AlOH2+ + Cl-β T AlOH2+-Cl-

These reactions are represented more instructively as complex ionization or ion exchange reactions:

AlOH + Na+β T AlO--Na+ + Ho+ *K

[AlO- - Na+][H+]e(yβ-yo)

int

Na

[AlOH][Na+]

AlOH2+-Cl- T AlOH + Ho+ + Cl-β *KintCl *KintNa ) Kinta2KintNa;

[AlOH][H+][Cl-]e(yβ-yo) [AlOH2+ - Cl-]

*KintCl ) Kintal/KintCl (4)

with yβ ) eψβ/kT and yo ) eψo/kT. Again, the surface concentrations of ions are related to bulk concentrations by a Boltzmann expression, and the centers of the ions are assumed to lie in a plane. The subscript “o” refers to values at the center of the layer of oxygen atoms that make up the oxide surface. The subscript “β” refers to values at the Stern plane (the plane of specifically adsorbed counterions). The subscript “d” refers to values at or beyond the plane representing the beginning of the diffuse layer. If σo and σβ are the charge densities at the two different planes and σd is the charge density within the diffuse layer, in Coulombs/m2, then the condition of electroneutrality requires that

σo + σβ + σd ) 0

(5)

The charge in the surface plane, σo, represents the net contribution from all charged sites, whether complexed or not. Thus

σo ) F([AlOH2+] + [AlOH2+-Cl-] - [AlO-] [AlO -Na ]) (6) -

(7)

From Gouy-Chapman diffuse layer theory, the diffuse layer charge at 43 °C is

σd ) -0.1209C1/2 sinh yd/2

σo ) C1(ψo - ψβ)

(10)

σd ) C2(ψd - ψβ)

(11)

where C1 and C2 are the two inner layer capacitances. The model thus contains six adjustable parameters: the four intrinsic ionization constants and the capacitances. They may be obtained by fitting data from various experiments, including surface potentiometric titration, electrophoretic mobility, and ion adsorption, as described below. In order to calculate the surface acidity constants, a least squares fit to the data in Figure 4 was obtained using the full system of equations described (eqs 1-11), where the four intrinsic constants were viewed as adjustable parameters. Following Yates et al.,36 the inner layer capacitances C1 and C2 were assumed to be 1.4 F/m2 and 0.2 F/m2, respectively. The final fit to the data is shown in Figure 5. Agreement is good over most of the pH range, but a departure from the prediction of the model is seen at extremes of the pH. This may be because of a number of reasons, such as steric restrictions on the electrolyte ions, lack of availability of all surface sites for binding electrolyte ions,12 not accounting for real activities, and discreteness (locally variable distribution) of charge. If it is assumed that the hydrated sodium and unhydrated chloride ions are similar in size and probably approach a similar distance to the oxide surface so that the same values of C1 and C2 can be used for each titration branch, then the resulting intrinsic constants are

p*Kinta1 ) 5.32

+

where F is Faraday’s constant. The complex AlOH2+Cl-, for example, makes a contribution to σo because the AlOH2+ atoms are assumed to be located in the plane of the surface, while the Cl- ion is assumed to be located in the Stern plane. Note also that a surface titration gives a direct measure of protons consumed by surface reactions, i.e., of surface charge. The charge in the Stern plane arises from specifically adsorbed counterions (in the form of surface complexes) and is given by

σβ ) F([AlO--Na+] - [AlOH2+-Cl-])

The surface site density used here is 8 sites/nm2, estimated from the density of oxygen atoms in the (1010) crystallographic plane of R-alumina. Constant capacitances are assumed to exist between the planes to which the charge is assigned. The charge/ potential relationships are as follows:

(8)

where C is the electrolyte concentration in mol/L, and yd the reduced diffuse layer potential, eψd/kT. The concentration of surface species is limited to the total sites available, NS:

p*Kinta2 ) 10.79 p*KintNa ) 7.98 p*KintCl ) 7.80

(12)

which are consistent with a point of zero charge (pzc) apparent from Figure 4 at pH ) 7.95 and with symmetric specific adsorption. These values agree in magnitude with those of Huang (cited in ref 39) for γ-alumina. Although the pzc is somewhat low compared to most reports for R-alumina, it is known that the pzc is a function of prior surface treatment. The surface complexation constants *KintNa and *KintCl agree in magnitude with values obtained using the approximate method of Davis et al.12 Statistical Thermodynamics of Patchwise Adsorption Following Harwell et al.,15,37 it is assumed that surfactant aggregation, producing either a monolayered structure (hemimicelle) or a bilayered structure (admi-


or

Kinta1i × Kinta2i ) constant

(13)

From eq 4, *KintNai varies as Kinta2i and *KintCli as Kinta1i. The intrinsic constants for the patch i are then defined by

Kinta1i ) Kinta1/ri Kinta2i ) Kinta2ri KintNai ) KintNari KintCli ) KintCl/ri Figure 4. Potential determining ion (pdi) abstraction on R-alumina from potentiometric titration.

where the values of Kinta1 etc. are given by eq 12. The set of constants {Kinta1i, Kinta2i, *KintNai, *KintCli} will be referred to below by the vector K(ri), a function of ri. A cumulative distribution function, F(Ki), is the fraction of the surface on which the set of intrinsic constants for the patches corresponds to a value of r exceeding ri. For these patches, calculations show that the csc will have been exceeded. Then F(K(ri + dr)) F(K(ri)) is the fraction of the surface with K lying between K(ri) and K(ri + dr). Alternatively, F(Ki) is the fraction of the surface upon which aggregates have formed, when an aggregate has just formed on a patch characterized by intrinsic constants Ki. This distribution function is an intrinsic property of the adsorbent material. If an admicelle will always form spontaneously before a hemimicelle, then

ΓS- ) ΓbilayerF(KA) + HFS-[1 - F(KA)] Figure 5. Site binding model for R-alumina.

celle), occurs on a given patch of a heterogeneous surface at a critical solution concentration (csc) of surfactant. The critical concentration is specific for that patch and will depend on the values of the patch intrinsic ionization constants, which determine the surface charge density and counterion binding beneath the aggregate. The constants vary from patch to patch as described below. The model assumes that the total adsorption is built up from adsorption on individual patches of the surface. All patches for which the critical solution concentration (csc) has been exceeded will be covered with aggregates at a given set of conditions. All other patches have surfactant molecules adsorbing sparsely and independently of one another. It will be assumed that, for the sparsely adsorbed surfactant at high total electrolyte concentration and constant pH, Henry’s law is obeyed. This assumption has been confirmed experimentally by Nunn24 and is discussed below. In order for the model to predict a different csc for different patches, a patch-distribution parameter must be introduced. Since the individual patches are characterized in essence by the site-binding model, a scaling factor, ri, is introduced, where ri is a variable specifying the values of the intrinsic ionization constants for the current patch i. If it is assumed that for each patch the pzc is constant, then int

pK

a1i

int

+ pK

a2i

)0

(14)

(15)

where ΓS- is the total surfactant adsorption density, Γbilayer is the bilayer adsorption density, A is the patch on which an admicelle has just formed, FS is the surfactant monomer concentration, and H is the effective Henry’s law constant for patches not covered by admicelles. The upper limit on FS is the cmc under the assumptions of the plateau adsorption model.15,29 If, on the other hand, a hemimicelle forms first and acquires a second layer at higher solution concentrations37,10 then

Γ S- )

ΓbilayerF(KH) ΓbilayerF(KA) + + HFS-(1 - F(KH)) 2 2 (16)

where F(KH) > F(KA), and the subscripts H and A refer to hemimicelle and admicelle, respectively. Thus, given a cumulative distribution function F(Ki) and the surfactant concentration for a given set of the intrinsic ionization constants at which an aggregate will form, it is possible to predict a complete adsorption isotherm at a given temperature, electrolyte concentration, and pH. The chemical potential of a solute molecule i in a mixture of j components is4

µi ) W(i|{Fj}) + kT ln(FiΛi3qi-1)

(17)

where Fj is the concentration of molecules of type j, Wi is the work of putting a molecule of type i at a fixed position in the bulk, qi is the internal partition function


(assumed independent of the local environment), and Λi ) (h/2πmikT)1/2 is the translational partition function. Similarly, for an amphiphilic molecule in a layered two-dimensional system, treated as a separate phase

µi ) W(i|{Γj}) + kT ln(4π2ΓiΛi2qi-1)

(18)

where Γi is the adsorption density and Wi is the work of placing a molecule in its most favorable orientation. The 4π2 accounts for the loss of orientational degrees of freedom of the molecule upon adsorption. At equilibrium

(Wi - Wi) + ln((4π2Γiqi)/(ΛiFiqi)) ) 0

(19)

For adsorption of an isomerically pure surfactant, Fi is the csc of surfactant monomer for the patch on which the aggregate has just formed. To a first approximation, the work term is given by

(Wi - Wi) ) Eel - mω

(20)

where Eel is the electrical work and mω is the free energy change on removing the hydrocarbon moiety from aqueous solution to the aggregate, m being the number of methyl groups and ω being the free energy change per methyl group. For counterions in the top layer:

(Wi - Wi) ) Eel

(21)

For spherically symmetrical counterions, there is no loss of orientational degrees of freedom on adsorption so the term 4π2 does not arise. For qi = qi, from eqs 19-21, the csc is

4π2ΓS-e(yS + mω/kT) Λ S-

FS- )

(22)

and the counterion adsorption density on the top layer is

ΓT,Na ) F0ΛNa+e(-yT,Na)

(23)

Here ΓS- is the surfactant monolayer adsorption density (mol/m2), F0 is the electrolyte concentration (mol/ m3), yS- is the reduced electrical potential of a surfactant ion in the top and bottom layers, and yT,Na is the reduced electrical potential of a counterion in the top layer. Boltzmann expressions are used once again to relate bulk concentrations to surface concentrations. In eq 23, the term ΛNa+ accounts for losses of translational degrees of freedom and rationalizes the units of surface concentration to mol/m2. Note that the electrical potentials of the surfactant ion in the bottom and top layers of an admicelle are different; however, the average value may be used in eq 22 to correctly account for the assumed constant adsorption density in the bottom and top layers. Derivation of Electrostatic Field within Admicelle An analysis of the electrostatic field within the aggregates is required to complete the adsorption model. The procedure used here will assume that the electrical potential experienced by all charged species within the

Table 1. Molecular Parameters Used in Model parameter

value

2l b w/δ1 C B T ΛNa ΛS mpxs Fo o ΓS mω/kT Γbilayer cmc

2.8 nm 1.25 nm 1.4 F/m2 2.2o 6o 6o 1.0 × 10-02 nm 5.151 × 10-03 nm 363/(NA× 1000) kg/molecule 1.8069 × 10-02 molecules/nm3 8.842 × 10-12 F/m 1.87 molecules nm2 -32.66 87 µmol/g ) 3.74 molecules/nm2 1.2 × 10-2 wt % ) 331 µmol/dm3

aggregate may be approximated by the macropotential as experienced by an infinitesimal test charge and ignoring discreteness of charge effects. The work of Harwell et al.15 showed that, for smeared charge models, corrections for the discreteness and finite size of ions, and for nearest neighbor Coulombic interactions under conditions of high counterion binding, were small and could be neglected. It is estimated below from adsorption measurements that the packing density of a 4-C11 pxs molecule in a monolayer is 1.87 molecules/nm2, corresponding to a distance between surfactant centers of 0.786 nm if surfactant ions are assumed to lie in a close packed planar hexagonal array. Furthermore, evidence suggests that counterions adsorb in their hydrated or almost hydrated state.22 Allowing the hydrated radius of a sodium ion to be the sum of ionic radius and water molecule diameter, the distance of closest approach of counterions is 0.74 nm, with the true value probably somewhat smaller. Considerable uncertainty exists about the size of hydrated counterions.28 Thus, the counterions will not hinder the planar surfactant packing, and the thickness of a charged layer is thus assumed to be the sum of the radii of the sulfonate group and hydrated counterion (=1.3 nm). Following Bockris,34 the dielectric constant of hydrated counterions is approximated as 6. All relevant molecular parameters for the model are given in Table 1. Improved estimates of these parameters might be obtained by using them to fit the model to electrokinetic data different surfactant adsorption levels and different pH values. It was not felt that such an effort would significantly improve the physical validity of the model, however, because of the uncertainties related to the surface heterogeneity and the location of the shear plane. In effect, the effort would have removed no more uncertainties than introduced. The model for the electrical field presented here follows the approach of Harwell et al.15 and assumes that the charge of surfactant head groups and counterions may be smeared uniformly throughout the region containing them (Figures 6 and 7). It is assumed that the total width of the hydrocarbon core is equal to twice the width of the surfactant hydrocarbon chain.37,27 It is assumed the aggregate is large enough that potential varies in a direction perpendicular to the surface only, i.e., the fringing effect of the electric field at the edges is negligible. This assumption may introduce significant errors at smaller aggregation numbers. Integration of the equations shown in Figure 6 for an admicelle with smeared charge may be carried out, applying the following boundary conditions:


In a similar way, the equations for the hemimicelle with smeared charge (Figure 7) may be solved to yield similar expressions:15,16,36

ψ0 ) ψd + σo(1/C + β/B + δ1/W) + σB(β/2B + 1/C) (31) ψB ) ψd + σo(1/C + β/2B) + σB(1/C + 3β/8B)

(32)

Assembly of Model Equations

Figure 6. Structure of an admicelle.

Figure 7. Structure of a hemimicelle.

continuity of the potential across the dielectric interfaces ψ1 ) ψ2

(24)

Gauss law at the interface in the absence of surface charge 1 dψ1/dz ) 2 dψ2/dz

(25)

Gauss law in the presence of surface charge 1 dψ1/dz - 2 dψ2/dz ) σo

(26)

The subscripts 1 and 2 refer to the two media, and σo is the surface charge density. This yields expressions for the electrical potential throughout the admicelle. If it is then assumed that the time-averaged electrical potential within a charged region may be approximated by the electrical potential in the center of that region, the following results:

ψT ) ψd + σo(β/2T) + σB(β/2T) + σT(3β/8T)

(27)

ψB ) ψd + σo(2l/C + β/2B + β/T) + σB(2l/C + 3β/8B + β/T) + σT(β/2T) (28) ψ0 ) ψd + σo(2l/C + β/B + δ1/W + β/T) + σB(β/2B + 2l/C + β/T) + σT(β/2T) (29) expressions,15,37,40

In these ψ0 is the potential in the plane of potential determining ions, and ψB and ψT are the potentials in the bottom and top layers, respectively. The remaining terms are defined in Figure 6. Again, the diffuse layer potential is given by eq 8. Also, the condition of electroneutrality implies the following:

σo + σB + σT + σd ) 0

(30)

The final set of equations to describe the complete model can now be assembled, with the geometrical configuration of an admicelle as given in Figure 8. In order to describe the surface charge on the mineral oxide and the associated counterions beneath an aggregate, the site-binding model is used. It will be assumed that all chloride ions are displaced by the surfactant aggregate from the inner Helmholtz plane at the onset of aggregate formation.24 Calculations in which their presence was included in the model showed their presence to be negligible. It will also be assumed that the counterions beneath an aggregate are those present as a result of surface complexation only. Electrostatically bound counterions may be excluded because of steric limitations, while specifically bound, complexed ions exchange part of their hydration sheaths with the oxide surface, allowing them to enter beneath the sulfonate layer. There is some experimental evidence for this,5 although this assumption does not affect the general conclusions of this work. The site-binding model is modified here to take into account the presence of surfactant aggregates. In the work of Schechter,30 the sulfonate ions within aggregates take part in the complexation reactions, but in this work it was assumed that sulfonate ions are sufficiently shielded and removed from the surface upon aggregate formation not to do so. This is equivalent to assuming that only the electrostatic and hydrophobic terms contribute to the adsorption potential of the surfactant ion. Considering the formation of an admicelle, the sitebinding component of the model requires equations 1, 2, 4, 6, 8, 9, and 30 (with all terms containing Cl negligible and yβ replaced by yB ) eψB/kT). Also

σB ) F([AlO--Na+] - ΓS-)

(33)

for the bottom layer charge, eq 29 for the surface potential, and eq 28 for the bottom layer potential. Similarly, the charge on the top layer is given by

σT ) F(ΓT,Na - ΓS-)

(34)

The reduced electrical potential of a surfactant ion in either layer is approximated by the average reduced electrical potential in the top and bottom layers and is given by

yS- ) -e(ψT + ψB)/2kT

(35)

where we require eq 27 for the top layer potential. The electrical potential of a top layer counterion is given by

yT,Na ) yT

(36)

The counterion adsorption on the top layer is then given by eq 23, and the csc (or critical admicelle concentration, cac) is given by eq 22. Given the intrinsic


Figure 8. One possible molecular configuration of an admicelle.

ionization constants for a particular patch and the ambient conditions (electrolyte concentration, pH, and temperature), it is necessary to solve 16 equations (1, 2, 4, 6, 8, 9, 22, 23, 27-30, 33-36) in 16 unknowns ([AlOH], [AlOH2+], [AlO-], [AlO--Na+], ΓT,Na, yo, yB, yT, yT,Na, yS-, yd, σo, σB, σT, σd, and FS), which can be achieved using Newton’s method. The solution to the equations contains a great deal of information, including the patch cac. It is now possible to generate a complete adsorption isotherm at the ambient conditions in conjunction with eq 15, which involves solving the above set of equations for every patch, i.e., for every Ki. All patches with a lower cac will already be covered, so that the total adsorption calculated from eq 15 corresponds to a surfactant concentration equal to the current cac. Determination of Cumulative Distribution Function. The distribution function for the surface is obtained by applying the above procedure to the experimental isotherm given in Figure 9. A set of values for Ki is chosen, a cac is calculated, an adsorption level is interpolated from Figure 9, and eq 15 is applied to calculate F(KA). Following Yeskie and Harwell (37), it is assumed that the surface charge is high enough in this case so that only admicelles form. The distribution function must tie in with the sitebinding model fit to the titration data in such a way that the intrinsic ionization constants obtained for the fit correspond to the area-weighted average of the patch intrinsic ionization constants. The mean value of r calculated from the distribution function must therefore equal 1.0. Determination of Adsorption in Region I (Henry’s Law Region). In region I, it is assumed that individual monomer head groups complex with the surface in much the same way that chloride ions do. However, the complexation of surfactant is enhanced

Figure 9. Adsorption of pxs on R-alumina.

by the hydrophobic interaction of the hydrocarbon tail with the surface. This follows the approach of Schechter.13 Thus, in addition to the standard set of equations for the site-binding model, the following describes the adsorption of surfactant (compare with eq 4):

KS )

[AlOH][H+o][S-β] [AlOH2+ - S-]

(37)

where [S-β] ) FS-e(yβ)e(ωH/kT), and ωH accounts for the tail interaction. The variable FS- is the surfactant monomer concentration and has units of mol/dm3. The


Figure 10. Plateau adsorption of pxs on alumina vs pH.

values of KS- and ωH may be obtained by curve fitting region I in Figure 9, for which the Henry’s law constant is 7.6 × 10-3 L/g. Equations 6, 7, and 9 include the term [AlOH2+-S-]. Strictly speaking, to be consistent with the treatment of heterogeneity, the Henry’s law constant should vary from patch to patch, whereas the above approach is an average for all patches. If the Henry’s law constant were varied for each patch, then the region I-type contribution to the isotherm would decrease in regions II and III as the patches with the highest Henry’s law constants became covered with admicelles. This complexity is not justified, however, since the Henry’s law adsorption makes a negligible contribution to the total adsorption above the region I/II transition. Results and Discussion Figure 9 presents the adsorption isotherm of pxs on R-alumina. These data clearly exhibit the four classic regions,31,29 as shown in Figure 1. Region I exhibits Henry’s law. Region II is steep and gives confirmation of aggregate formation on patches similar in charge density. Region III is rather less steep and corresponds to infilling of less energetic patches with a much wider charge density distribution. Region IV is relatively flat, with an increase in adsorption of 2-3 µmol/g (i.e., =3%) observed over a 5-fold increase in concentration. Figure 10 presents the plateau adsorption of pxs vs pH. At low pH, the adsorption is relatively constant, although a slight increase is observed as the pH decreases (see also Figure 14). According to Scamehorn et al.,29 the constant adsorption corresponds to bilayer completion on the surface with a corresponding adsorption density =87 µmol/g, or 3.74 molecules/nm2. This corresponds to a monolayer adsorption density of 1.87 molecules/nm2. As the pH increases, the adsorption starts to decrease at pH 8.5 (above the pzc), passes through an observable kink at pH 9.7, and then decreases fairly rapidly. By extrapolation, the adsorption reaches zero in the vicinity of pH 11. The “blind spot” in the data divides those solutions that were initially adjusted to low and high pH, respectively. In fact, calculations based on the data in Figure 4 revealed that the final pH has adjusted to a value considerably higher than that expected in the absence of sulfonate. This is in agreement with the findings of Bo¨hmer and Koopal,8

Figure 11. Site-binding prediction of region 1 adsorption.

Balzer and Lange,3 Bitting and Harwell,5 Lopata,37 and Partyka et al.,26 concerning the effect of surfactant adsorption on equilibrium pH. Figure 11 presents the results of the site-binding model of region I adsorption at various values of pH and 0.03 M NaCl solution. The free energy change arising from the specific tail interaction with the surface, ωH/ kT, was assigned a value of 4.0; the complexation constant, KS-, was chosen to be equal to that of the chloride ion. Different values could have been chosen from the literature, but the results would broadly be of the same quality. The model predicts a practically linear dependence of adsorption on concentration, becoming yet more linear at higher pH values. The Henry’s law coefficients decrease with increasing pH as one might expect. At low electrolyte concentrations, a decreasing slope is predicted in the isotherms with increasing surfactant concentration, indicating deviation from Henry’s law in accordance with the findings of Nunn (24). It is understood that the value of the model is somewhat limited due to an inadequate treatment of surface heterogeneity.1,2 Varying the site density of the system was tried but did not give sufficient sensitivity for a good numerical fit. However, this work was not done to address the weaknesses of surface heterogeneity models but to examine the interaction of surfactants, potential determining ions, and counterions/co-ions at the oxide/water interface, which we believe it has accomplished. The adsorption isotherm in Figure 9 was used in conjunction with the adsorption model, and eq 15, to generate a cumulative distribution function for the alumina surface (Figure 12). In the work of Harwell et al.,15 it was assumed that counterion binding to the bottom layer was constant and that, as adsorption increased along an isotherm, infilling of surface patches proceeded with progressively decreasing final surface charge density. On the other hand, in the present work it was found that the final surface charge density of the patches increases as adsorption proceeds while the net charge density in the bottom layer (surface charge plus charge on surfactant and sodium ions) decreases; thus the net “charging” of the alumina surface by the aggregate is to be seen as an important variable in promoting aggregate formation.


Figure 14. Model prediction of plateau adsorption of pxs on R-alumina vs pH.

Figure 12. Cumulative distribution function for surface of R-alumina.

Figure 13. Effect of pH on pxs adsorption.

It was found that admicelles always formed preferentially over hemimicelles for the range of conditions studied. The plateau adsorption isotherm could not be fit by sets of model parameters that showed hemimicelles forming before admicelles. This result may arise because of a fortuitous choice of molecular parameters; Yeskie and Harwell37 have shown that admicelles are predicted to form first almost always for large values of T and small values of β (as used here) due to electrostatic factors. According to Cases,10 however, this situation can arise only when the normal adsorbentadsorbate bond is relatively weak. Wa¨ngnerud and Jo¨nsson34 calculate instantaneous bilayer formation provided the surface charge density is high enough. If the aggregate induces the formation of such surface charge, then hemimicelles may not form before admicelles. In Figure 13, the predictions of the model are presented for complete adsorption isotherms as the pH is varied. These isotherms are all derived in conjunction with the cumulative distribution function, Figure 12.

Comparing these predictions with the data of Fuerstenau and Wakamatsu,13 it may be noted that the model predicts the various regions to remain linear on a log-log plot over a wide range of pH. Furthermore, the steepness of regions II and III decreases with decreasing pH, a trend observed in refs 8 and 13 with the exception of the data for the lowest pH (3.2). The adsorption level at the region I/II transition is also seen to decrease with increasing pH until a pH of 10 is reached, at which point the adsorption level increases. This trend arises as a result of a competition between decreasing Henry’s law coefficients and increasing monomer concentrations at which an aggregate will form on the first patch. The data of Fuerstenau and Wakamatsu were all measured below the pzc. In the present model, the adsorption level at the region II/III transition increases only slightly with decreasing pH, while the data in ref 13 show a more pronounced trend. Two reasons may be given for this. Firstly, the sensitivity to pH of the adsorption level at the region II/III transition depends, in this model, on the contribution of region I-type adsorption to the total adsorption level. The patchwise model allows region I-type adsorption to be occurring on all patches of the surface not covered with aggregates, even in regions II and III. The stronger the region I adsorption and the smaller the adsorption at the region II/III transition, the more sensitive the transition is to pH. Secondly, the insensitivity of the adsorption predicted by the model at the region II/III transition may arise as a result of the assumption that the top layer adsorption density in the admicelle equals that in the lower layer, when, as discussed above, this assumption is not strictly necessary. Calculations for the formation of an admicelle on a given patch revealed that while the upper layer electrical potential remained constant over all pH values, the lower layer electrical potential varied somewhat, increasing from 1.5 to 2 times the magnitude of the upper layer electrical potential in going from low pH to high pH. This would tend to favor the second layer adsorption at low pH and to increase the adsorption density at the region II/III transition. In region IV, the model assumes the adsorption to be constant. Variations in adsorption above the cmc can be accounted for by variations in chemical potential of the monomer, which is easily done using a mass-action model of micelle formation. In Figure 14, the predictions of Figure 13 for the plateau adsorption isotherm are plotted against pH and


Figure 15. Surface charge on R-alumina: influence of aggregate formation.

Figure 16. Counterion binding to pxs admicelle vs pH.

compared with the data in Figure 10. One of the adjustable parameters in the model is the hydrophobic interaction energy, ω. Its value is largely chosen by requiring the isotherm to exhibit a decline in plateau adsorption above pH 8.8. This corresponds to the requirement that the monomer concentration needed to form an aggregate on the final surface patch (r ) 0.068) is equal to the cmc at pH 8.8. As can be seen from the plot, the prediction gives at least a qualitative agreement with the data. Furthermore, the model has been able to predict the adsorption of sulfonate at a pH substantially above the pzc, while invoking a purely physical and reversible mechanism for the adsorption. This is to be viewed as the most significant result of the model. The fact that the fit was made using two adjustable parameters is also encouraging. The final value of ω was 1.1 kcal/mol of CH2 groups, which is physically realistic.29,15 Finally, Figures 15 and 16 show the variation in surface charge, σo, and counterion bindings (the ratio of counterions to sulfonate ions) on the mean patch (r ) 1.0) with pH. The tie with between the F(r) curve and an average value for r of 1 is limited. This could be improved by repeated iteration between choosing the actual values of Ka1 and Ka2 obtained from the titration fit (the “average” values) and requiring the resulting distribution function F(r) to yield an average value for r of 1, i.e., F(1) ) 0.5 (assuming only admicelle formation), which preserves the measured pzc value. More titration measurements are clearly needed to improve

these measurements. From these figures, the mechanism of adsorption of sulfonate onto R-alumina above the pzc becomes clear. The presence of a layer of negative sulfonate ions enhances the surface concentration of H+ ions; this shifts the site-binding equilibrium (eq 1) toward an increased concentration of Al(OH)2+ and thereby induces a positive charge beneath surface domains covered with aggregates. As the pH increases, charge resulting from this mechanism decreases, but more counterions are attracted to the lower layer so that counterion binding compensates for decreased surface charge in stabilizing the aggregate. As pH continues to increase, the counterions become increasingly unable to stabilize aggregate formation on the poorly charged surface. Finally, the counterion binding reaches its maximum limit, and the aggregates subsequently collapse. Clearly, such variables as the site density, the counterion type and bulk concentration, and the hydrophobic interaction all affect this process in such a way that physical adsorption may or may not be observed above the pzc, depending upon the details of the system. The counterion binding on the top layer of the admicelle is largely unaffected by these processes and remains roughly constant (=0.93) for variations in pH, counterion concentration, and surfactant concentration. All these binding values agree qualitatively with Bitting and Harwell.5 It is also clear from the calculations that each charge layer adjusts itself so as to approximate charge neutrality on a local scale. For example, the bottom layer counterions and sulfonate ions almost cancel the surface charge for all values of pH. Figure 15 offers an explanation for the shifts in equilibrium pH observed in adsorbing surfactant systems. At a pH above 7.6, the formation of surface aggregates results in a net abstraction of hydrogen ions and thus positive charge to the surface; for moderate values of pH few hydrogen ions are available in solution, so these ions must be removed and redistributed from other unadsorbed domains of the surface. In order to maintain equilibrium between unadsorbed surface and solution, the pH of the supernatant increases.3,26 As surface coverage increases, the shift in pH will increase.5,23 Conversely, at low pH, a decreasing trend in pH is expected as surface coverage increases.5 Conclusions The patchwise, phase-separation model of surfactant adsorption on oxides has been extended to include adjustable counterion binding to admicelles and to model the effect of pH. The model has incorporated the site-binding model to describe both the development of surface charge and the complexation of bottom layer counterions with the oxide surface; it emulates, at least qualitatively, many of the trends that have been observed experimentally. It has also explained some phenomena that otherwise have no explanation in earlier physical adsorption models. In particular, adsorption at a pH above the pzc of a mineral oxide has been explained on the basis of a purely physical mechanism. Additionally, the various effects of surfactant adsorption on equilibrium pH in a surfactant/alumina aqueous dispersion have also been explained. An important weakness of this model, and one which still remains from the original model of Harwell et al.,15 is the absence of an independent expression for the cumulative surface distribution function. Another important weakness is the use of the site-binding model


under conditions in which the electric fields are much stronger than normally present in simple electrolyte systems. Nevertheless, it is hoped that the model will find use in obtaining quantitative estimates and in explaining at least some of the counter-intuitive phenomena occurring in the physical adsorption of amphiphilic species. Its weaknesses serve only to open lines of further inquiry. Acknowledgment Many thanks are extended to the Link Foundation Energy Fellowship Program for a Doctoral Award to N.P.H. Additional support for this work has been provided by the Shell Oil Company, the Mobil Oil Company, and the Department of Energy through Grant AC19-85BC10845. Special thanks are also extended to ARCO Oil & Gas Company for permission to publish experimental research performed by N.P.H. in their Plano Production Research Center. J.H.H. is the Conoco/ DuPont Professor of Chemical Engineering at the University of Oklahoma. Literature Cited (1) Bakaev, V. A. Towards the Molecular Theory of Physical Adsorption on Heterogeneous Surfaces. Surf. Sci. 1988, 196, 571. (2) Bakaev, V. A. Molecular Theory of Physical Adsorption on Heterogeneous Surfaces: Temperature Dependence of Henry Constant. Surf. Sci. 1989, 215, 521. (3) Balzer, D.; Lange, H. KonKurrenz adsorption von alkylbenzolsulfonate und Polyanionen aus wa¨ssrigen Lo¨s ungen an γ-Aluminiumoxide. Colloid Polym. Sci. 1979, 257, 292. (4) Ben Naim, A. Water and Aqueous Solutions; Plenum: New York, 1974. (5) Bitting, D.; Harwell, J. H. Effects of Counterions on Surfactant Surface Aggregates at the Alumina/Aqueous Solution Interface. Langmuir 1987, 3, 500. (6) Bockris, J. O.’M.; Reddy, A. K. N. Modern Electrochemistry; Plenum/Rosetta: New York, 1977; Vol. 1. (7) Bo¨hmer, M. R.; Koopal, L. K. Adsorption of Ionic Surfactants on Constant Charge Surfaces. Analysis Based on a Self-Consistent Field Lattice Model. Langmuir 1992, 8, 1594. (8) Bo¨hmer, M. R.; Koopal, L. K. Adsorption of Ionic Surfactants on Variable-Charge Surfaces. 1. Charge Effects and Structure of the Adsorbed Layer. Langmuir 1992, 8, 2649. (9) Bo¨hmer, M. R.; Koopal, L. K. Adsorption of Ionic Surfactants on Variable-Charge Surfaces. 2. Molecular Architecture and Structure of the Adsorbed Layer. Langmuir 1992, 8, 2660. (10) Cases, J. M.; Villieras, F. Model of Nonionic Surfactant Adsorption-Abstraction on Heterogeneous Surfaces. Langmuir 1992, 8, 1251. (11) Chander, S.; Fuerstenau, D. W.; Stigter, D. W. On Hemimicelle Formation at Oxide/Water Interfaces. In Adsorption from Solution; Ottewill, R. H., Rochester, C. H., Smith, A. L., Eds.; Academic: London, 1983; p 197. (12) Davis, J. A.; James, R. O.; Leckie, J. O. Surface Ionization and Complexation at the Oxide/Water Interface. I. Computation of Electrical Double Layer Properties in Simple Electrolytes. J. Colloid Interface Sci. 1973, 43, 409. (13) Fuerstenau, D. W.; Wakamatsu, T. Effect of pH on the Adsorption of Sodium Dodecane-Sulphonate at the Alumina/Water Interface. Faraday Discuss. Chem. Soc. 1975, 59, 157. (14) Grahame, D. C. The Electrical Double Layer and the Theory of Electrocapillarity. Chem. Rev. 1947, 41, 441. (15) Harwell, J. H.; Hoskins, J. C.; Schechter, R. S.; Wade, W. H. A Pseudophase Separation Model for Surfactant Adsorption. Langmuir 1985, 1, 251. (16) Hingston, F. J.; Posner, A. M.; Quirk, J. P. Anion Adsorption by Goethite and Gibbsite. J. Soil Sci. 1972, 23, 177. (17) Holm, L. W.; Robertson, S. Improved Micellar/Polymer Flooding With High-pH Chemicals. J. Pet. Technol. 1981, 161. (18) James, R. O.; Parks, G. A. Characterization of Aqueous Colloids by Their Electrical Double-Layer and Intrinsic Surface Chemical Properties. In Surface and Colloid Science; Matijevic, E., Ed.; Plenum Press: New York, 1982; Vol. 12.

(19) Kiefer, J. E.; Wilson, D. Characterization of Aqueous Colloids by their Electrical Double-Layer and Intrinsic Surface Chemical Properties. Sep. Sci. Technol. 1980, 15, 57. (20) Koopal, L. K.; Ralston, J. Chain Length Effects in the Adsorption of Surfactants at Aqueous Interfaces: Comparison of Existing Adsorption Models with a New Model. J. Colloid Interface Sci. 1986, 112, 363. (21) Koopal, L. K.; Keltjens, L. Adsorption of Ionic Surfactants on Charged Solids. Adsorption Models. Colloids Surf. 1986, 17, 371. (22) Lindman, B.; Wennerstro¨m, H. Micelles: Amphiphile Aggregation onto Alumina from Some Solubilized Systems. Top. Curr. Chem. 1980, 87, 1. (23) Lopata, J. J. Study of the Adsorption of Binary Anionic Surfactant Mixtures. M.S. Thesis, The University of Oklahoma, 1988. (24) Nunn, C. C. Equilibrium Adsorption onto Alumina from Some Solubilized Systems. Ph.D. Dissertation, The University of Texas at Austin, 1981. (25) Ottewill, R. H.; Rastogi, M. C. The Stability of Hydrophobic Sols in the Presence of Surface-Active Agents. Trans. Faraday Soc. 1960, 56, 880. (26) Partyka, S.; Rudzinski, W.; Brun, B.; Clint, J. H. Calorimetric Studies on Adsorption of Anionic Surfactants onto Alumina. Langmuir 1989, 5, 297. (27) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W. Effects of Pentanol Adsorption on the Forces between Bilayers of a Cationic Surfactant. J. Phys. Chem. 1986, 90, 5841. (28) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1959. (29) Scamehorn, J. F.; Schechter, R. S.; Wade, W. H. Adsorption of Surfactants on Mineral Oxide Surfaces from Aqueous Solutions. J. Colloid Interface Sci. 1982, 85, 463. (30) Schechter, R. S. Modeling and Optimizing Surfactant Structure to Improve Oil Recovery by Chemical Flooding at the University of Texas; DOE/BC/10841-5; U.S. Government Printing Office: Washington, DC, July 1987. (31) Somasundaran, P.; Fuerstenau, D. W. Mechanisms of Alkyl Sulfonate Adsorption at the Alumina-Water Interface. J. Phys. Chem. 1966, 70, 190. (32) Somasundaran, P.; Healy, T. W.; Fuerstenau, D. W. Surfactant Adsorption at the Solid-Liquid InterfacesDependence of Mechanism on Chain Length. J. Phys. Chem. 1964, 68, 3562. (33) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, 1980. (34) Wa¨ngnerud, P.; Jo¨nsson, B. Adsorption of Ionic Amphiphiles as Bilayers on Charged Surfaces. Langmuir 1994, 10, 3268. (35) Wilson, D. J.; Moffat, K. R. Electrical Aspects of Adsorptive Colloid Flotation. IX. Effects of Surfactant Overdosing. Sep. Sci. Technol. 1979, 14, 319. (36) Yates, D. E.; Levine, S.; Healy, T. W. Site-Binding Model of the Electrical Double Layer at the Oxide/Water Interface. J. Chem. Soc. Faraday Trans. 1 1974, 70, 1807. (37) Yeskie, M. A.; Harwell, J. H. On the Structure of Aggregates of Adsorbed Surfactants: The Surface Changes Density at the Hemimicelle/Admicelle Transition. J. Phys. Chem. 1988, 92, 2346. (38) Yoon, R. H.; Salman, T. Chemisorption of Sodium Lauryl Sulphate on Gamma Alumina. In Colloid and Interface Science; Kerker, M., Ed.; Academic Press: London, 1976; Vol. III, p 233. (39) Yopps, J. A.; Fuerstenau, D. W. The Zero Point of Charge on Alpha-Alumina. J. Colloid Sci. 1964, 19, 61. (40) There are some typographic errors in the equations as presented in Harwell et al. (15) and Yeskie and Harwell (37).

Received for review October 19, 1995 Revised manuscript received June 13, 1996 Accepted June 14, 1996X IE9506375

Abstract published in Advance ACS Abstracts, August 15, 1996. X

Modeling Effects of pH and Counterions on Surfactant Adsorption at

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