A new model to describe the sorption of surfactants on solids in non-aqueous media

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1 Journal of Colloid and Interface Science 292 (2005) A new model to describe the sorption of surfactants on solids in non-aqueous media P. Somasundaran a,, S. Krishnakumar b, Somil C. Mehta a a NSF Industry and University Cooperative Research Center for Advanced Studies in Novel Surfactants, Columbia University, New York, NY 10027, USA b Unilever Global Skin Technology Center, Trumbull, CT 06611, USA Received 31 March 2005; accepted 6 June 2005 Available online 14 July 2005 Abstract A new phenomenological model is developed to describe the sorption of surfactants on solids in non-aqueous media. This is based on the use of interaction parameters (δ) among solid, solute and solvent to assess the degree of the various interactions and computing an effective interaction parameter for the entire system represented by δ eff = abs { A δ solid δ solvent +B δ solute δ solvent C δ solid δ solute }. The effective interaction parameter determines the extent of adsorption that can occur in a given system. Interaction parameters typically account for dispersive interactions between the different components. This new model is used to describe the sorption behavior of a number of surfactant/solvent/solid systems Elsevier Inc. All rights reserved. Keywords: Effective interaction parameter; Solubility product; Hydrophobic interaction; Sorption model 1. Introduction Colloidal behavior of non-aqueous dispersion is often controlled by the adsorption of surfactants and polymers. While much research has been done on the effect of various surface active agents on dispersing of particles in organic media, there is currently no quantitative description of the adsorption process based on the fundamental properties of the system components. Some of the past models in the literature, while addressing the thermodynamic aspects of adsorption [1], fail to give adsorption model with predictive capabilities. Moreover, most of these models are system specific and require prior knowledge of several complex parameters to be of any practical use. Also, much of the attempt to describe solution behavior in non-aqueous media in terms of the dielectric constants has not been generally success- * Corresponding author. Fax: address: ps24@columbia.edu (P. Somasundaran). ful. In this work a model is described for the adsorption of surfactants on different solids in various solvents based on a fundamental property, solubility parameter, of the system components. This model has been successfully used to describe adsorption behavior of a variety of surfactants on dispersions of alumina, silica and graphite in a broad range of non-aqueous solvents. 2. Phenomenological description of adsorption Adsorption can be described as preferential partitioning of the solute molecules at the solid liquid interface and is determined by several factors including interfacial potential, covalent bonding of the adsorbate with the surface species, hydrophobic interaction in the bulk and at the interface, desolvation of surface species and adsorbate, and solute solubility in the bulk media [2,3]. On a broader scale one can consider these effects to essentially result from three /$ see front matter 2005 Elsevier Inc. All rights reserved. doi: /j.jcis

2 374 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) main interactions, namely the solute solvent (takes into account solubility and other bulk interaction/association of the solute), solvent solid (takes into account solvent displacement/competitive effects from the solid surface) and solute solid (takes into account hydrophobic, covalent, electrostatic or hydrogen bonding of solute with solid). Attempts to develop a predictive model for surfactant adsorption should first address the issue of quantitatively describing these interactions. The primary step is therefore to identify suitable parameters characteristic of the fundamental solute/solid/solvent properties that can be used to quantitatively predict the extent of their mutual interactions. One of the fundamental properties used to describe solvent interactions is Hildebrand s solubility parameter. 3. Theory of solubility parameter [4] Hildebrand [5] in his treatise on the thermodynamics of mixing of solutions states that H M = V M [ ( E1 /V 1 ) 1/2 ( E 2 /V 2 ) 1/2] 2 φ1 φ 2, where H M = overall heat of mixing of components 1 and 2 (cal), V M = total volume of mixing (cm 3 ), E = energy of vaporization of component 1 or 2 (cal), V = molar volume of component 1 or 2 (cm 3 ), and φ = volume fraction of component 1 or 2 in the mixture. The expression E/V is the energy of vaporization per molar volume; it is called internal pressure or the cohesive energy density and is a measure of the amount of energy to be put into 1 cm 3 of the liquid to overcome all the intermolecular forces that hold the molecules together. Rearranging the above equation, H M /V M φ 1 φ 2 = [ ( E 1 /V 1 ) 1/2 ( E 2 /V 2 ) 1/2] 2. It can be seen from this expression that the heat of mixing per cubic centimeter at a given concentration is equal to the square of the difference between the square roots of the cohesive energy densities of the components. The square root of the cohesive energy density is thus an important characteristic that determines solubility/miscibility and is called solubility parameter, δ. In terms of the solubility parameter, one can argue that (δ 1 δ 2 ) 2 must be relatively small for small heat of mixing, implying good miscibility. If (δ 1 δ 2 ) 2 = 0, then a solution is assured. If the δ values of two substances are nearly equal, the substances will be mutually miscible with each other. This also suggests that the two components will interact strongly with each other than among themselves; δ 1 δ 2 is thus a measure of mutual compatibility. The derivation of the solubility parameter involves no assumption regarding the polarity, solvation or association effects. The solubility parameter is a fundamental property of the solvent or polymer, like density, refractive index or molecular weight and can easily be calculated from readily (1) (2) available information on its structure formula, density and boiling point. Also the solubility parameter benefits from the fact that it does changes very little by variation in temperature. It is essentially governed by the enthalpic effects of mixing. In the case of polymer solvation, the entropy term decides the sign of the free energy of dissolution and has been widely used in the past to predict polymer solubility in a variety of media. For mixed solvents, the solubility parameters are approximately additive in proportion to the mole fraction provided the molecular volumes of the components are similar. Thus, if one were using a single solvent with δ more than that of the polymer, addition of a suitable amount of a second solvent with δ less than that of the polymer will improve the solvency because the mean δ value now will be closer to that of the polymer. Theoretically one should be able to mix two non-solvents (one with a higher δ and the other with a lower δ) in approximate proportion and form a good solvent for the polymer. Such phenomenon has been reported and is the basis for the fact that solvents with similar solubility parameters have similar solvent power, regardless of their chemical structure. A comparable theory that predicts polymer solubility is the Flory Huggins theory [6]. This approach defines a polymer solvent interaction constant χ 1, which characterizes the interaction between solvent and polymer segments. The difference in the energy of a solvent molecule immersed in a pure polymer as compared with one in a pure solvent is given by kt χ 1, where k is Boltzmann s constant and T is the absolute temperature. A good solvent for a polymer will havealowvalueofχ 1, i.e., there is little difference in the energy of a solvent molecule whether it is surrounded by polymer or solvent molecules. The quantity χ 1 is regarded as an empirical constant comprising entropy and enthalpy terms that have been found to be different from theoretical predictions. Also χ 1 is strictly not a constant and varies with the polymer concentration. A serious problem with the use of χ 1 pertinent to the current discussion is that it cannot be predicted or calculated and must be experimentally determined for each polymer solvent pair by involved measurements of properties such as osmotic pressure or polymer swelling. Determination of solubility parameters Solubility parameters can either be calculated in a number of ways from known physical constants or estimated experimentally by direct measurements [7]: (a) For solvents and other substances for which the heat of vaporization is accurately known, the solubility parameters can be calculated from first principles using the equation δ = [ ( H RT )/V ] 1/2. (b) The solubility parameter can be determined from the coefficient of thermal expansion α and compressibility β (4)

3 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) with the equation δ = (αt /β) 1/2. (c) It can be estimated from critical pressure of a substance through the empirical equation δ = 1.25P 1/2 c. (d) It can also be estimated from surface tension using the relationship δ = 4.1(γ /V 1/3 ) (e) A more practical method of calculation is by using the structural formula of the substance. This has particular relevance to the estimation of δ for surfactants and complex polymers since the molar attraction constants have been estimated for a wide variety of grouping and they are additive over the formula of the compound [8]. These molar attraction constants, G, are related to the solubility parameter as δ = d G/M, where G is the sum for all the atoms and groupings in the molecule, d is the density and M is the molecular weight. (f) Experimental determination of solubility parameter includes measurements of solubility in liquids of known δ values, or from swelling values of polymers in different liquids and from refractive index measurements. 4. Concept of interaction or cohesion parameter In the strictest sense, the solubility parameter as defined by Hildebrand is a liquid state property and applicable only to non-polar systems. To globally describe these parameters for solids as well, the term cohesion parameter as calculated from enthalpies of vaporization or sublimation of solids is used. Specifically, Hansen s modification differentiates both polar and hydrogen bonding interactions among the molecules from the dispersion interactions and can be applied for polar substances as well [9,10]. In the expanded cohesion parameter formulation, the energy of vaporization, E, can be divided into interaction energies for dispersion, induction, dipole orientation and hydrogen bonding, Vδ 2 = (E ii) d + (E ii ) in + (E ii ) o + (E ii ) hb, (9) where V is the molar volume. A simplification of the above equation leads to the threecomponent Hansen interaction parameter δ 2 t = δ 2 d + δ2 p + δ2 h, (5) (6) (7) (8) (10) where the values δ d is the same as the original Hildebrand solubility parameter, δ p and δ h, are contributions from the polar and hydrogen bonding interactions, and δ t is the total interaction parameter. Clearly, this parameter is more justifiable for molecules that are polar and hydrogen bonding type. Based on the work by F. Fowkes, C. Van Oss and M. Chaudhury, it is well known that acid base components are more important than polar and hydrogen bonding components [11]. This is mainly because in condensed phases, especially in aqueous media, the polar interactions are governed by hydrogen-donor and hydrogen-acceptor (or Brønsted acids and Brønsted bases). Moreover, it was shown that these electron-donor and electron-acceptor interactions are asymmetric in nature. Hence it is preferable to extend the concept of polar and hydrogen bonding in terms of electron-donor and electron-acceptor or Lewis acid base interactions [12]. Beerbower, Martin and Wu developed a four-component approach incorporating factors such as dispersion, orientation, acid and base components. Further, Beerbower and Hill also developed the concept of cohesive energy ratio (CER) which is used to characterize the influence of components of an emulsion. CER is defined as the ratio of cohesive energy of lipophile of oil to the cohesive energy of hydrophile of water. The structure of individual components decides their cohesive energy and hence CER and hence the stability of emulsion [13]. The above components of the interaction parameter can be theoretically estimated and in some cases experimentally determined. It is clear from the above discussion that these interaction/cohesion parameters can be useful in predicting interactions among various molecules. Since it has been successfully used to predict polymer solubility, it may be assumed that it will work as well with surfactant solvent systems for predicting compatibility of the surfactant with the solvent provided the interaction parameter involved can be estimated. The interaction parameters for surfactants have been estimated in some cases by considering them as liquids and using the approaches described previously. Alternately they can be theoretically calculated from their structural formula using the group theory approach described earlier. Similarly, if one can measure/calculate interaction parameter for a solid, then it should be possible to predict the compatibility/interaction of it with a given surfactant solvent system. For solid surfaces the interaction parameter can be estimated using a procedure similar to that used for polymers wherein the polymer is characterized by the centroid of the region in interaction parameter space where the polymer is soluble [14]. Only those solvents that dissolve the solute/polymer are considered in this case. For solid surfaces, rather than the solubility, the stability/dispersibility over a period of time is taken as a measure of the interaction. Determination of interaction parameters (a) Solvents. The total interaction parameters as well as the component values for the various solvents used in the study were obtained from literature [15,16] and are given in Table 1.

4 376 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) Table 1 Cohesion parameter values for various solvents used for the determination of cohesion parameters of the solids Solvents δ d δ p δ h δ t (MPa) 1/2 Cyclohexane Chloroform Carbon tetrachloride Tetrahydrofuran sec-butanol Propanol Acetone Diethyl ether Ethanol Methanol Dimethylsulfoxide Dimethylformamide ,4-Dioxane Water Table 2 Cohesion parameters estimated for various surfactants used in the study Surfactants δ(cal/cm 3 ) 1/2 Aerosol-OT 18.3 Dimethyl dodecyl amine 8.3 Sodium decyl sulfate 16 Sodium dodecyl sulfate 15 Sodium tetradecyl sulfate 14 Nonylphenol ethoxylate Nonylphenol ethoxylate Stearic acid 15 Doxyl stearic acid 17 Table 3 Cohesion parameters estimated for various solids used in the study Solids δ(cal/cm 3 ) 1/2 Alumina 16.9 Silica 15.3 Graphite 9.4 (b) Surfactants. The interaction parameter value for the surfactants was estimated from its structural formula using molar attraction constant values in the literature [12].In this case it was not possible to estimate the values of the three components separately. The values calculated for different surfactants are shown in Table 2. (c) Solids. For the solids an approach used earlier by Shareef et al. [17] to determine pigment solvent interactions was used. The algorithm also known as the SVS (spherical volume of suspension) algorithm involves determination of dispersibility of the solid in a number of solvents of known interaction parameters. A threedimensional weighted average of the interaction parameters of the solvents in which the solid disperses well is used to calculate the interaction parameter components of the solid. The values calculated for different solids are shown in Table 3. Experimental procedure 1 g of the solid was suspended in 15 g of the solvent in a graduated test tube, dispersed by tumbling for 3 h, then allowed to settle and the sediment volumes measured after 15 h. A low sediment volume is indicative of good dispersion in the medium under consideration. Solvents in which the sediment column was less than 3 cm 3 were considered as good dispersing media for the given solid. The δ d, δ p and δ p values of these solvents were then plotted on a 3D plot and the center of the sphere of minimum radius enclosing all these points was determined using a computer program [18]. The interaction parameter corresponding to the center of the sphere is assigned to the solid surface and is used in the ensuing calculations of mutual interactions. Let N points having coordinates δ d, δ p and δ h be represented on the X, Y and Z axis, respectively. The distance D ij between any two points P(x i,y i,z i ) and Q(x j,y j,z j ) is given by the equation D ij = [ (x i x j ) 2 + (y i y j ) 2 + (z i z j ) 2] 1/2. (11) There are a total of N(N 1)/2 possible distances between any two points constituting the cluster of N points representing the solvents. The pair of points having the maximum separation distance will essentially constitute the diameter of the interaction sphere and the radius of this sphere is denoted by C R = D ij (max)/2. The coordinates of the center of the sphere are then given by C x = x i + x j /2, C y = y i + y j /2, C z = z i + z j /2. The interaction parameter of the solid is then calculated as δ solid = [ Cx 2 + C2 y + ] 1/2. C2 z The computer program used for calculating δ solid is reported elsewhere [18]. 5. Describing adsorption using interaction parameters The first step for the development of the model is to define a relationship for estimating the extent of mutual interaction among the solute, solvent and the solid. The expanded interaction cohesion parameter concept has been used earlier to describe adsorption phenomenon for chromatography application [16]. Mcguire and Suffet [19] developed the net adsorption energy concept for describing the adsorption of trace organics from water onto activated carbon. Similarly we develop a generalized model for surfactant adsorption by first considering the simple algebraic difference between the interaction parameters as being proportional to the strength

5 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) of their mutual interactions. The larger the absolute value of δ i δ j, the weaker is the interaction between the two species. The complex interactions taking place during the adsorption are divided into three relatively simple binary interactions: (a) Solid solvent, characterized by δ solid δ solvent. Stronger the interaction between the solid and the solvent, more is the solvent interference with adsorption of the solute. Hence a low value of this difference is detrimental to adsorption. Alternatively, for good adsorption this difference should be large. (b) Solute solvent, characterized by δ solute δ solvent. Stronger the interaction between the solute and the solvent, lesser is the tendency of the solute to adsorb. As in the above case, large value of this difference is essential for significant adsorption. (c) Solid solute, characterized by δ solid δ solute. Stronger the interaction between these two species, more is the adsorption. Thus a small value of this difference is helpful for enhancing adsorption. Thus, Net adsorption = f ( δ solid δ solvent, δ solute δ solvent, δ solid δ solute ). (12) These three binary interactions can be combined in a number of different ways. The simplest case is to take a linear combination of these terms as shown below, X = abs { A δ solid δ solvent +B δ solute δ solvent C δ solid δ solute }, (13) wherein A, B and C are coefficients used to account for other potential interactions. It can be seen from the earlier discussion that for good adsorption this sum should be large, i.e., larger the value of X, the greater is the adsorption tendency. Conversely, one can argue that a low value of X will favor surfactant partitioning into the bulk solvent. The value X has been referred to as δ eff, the effective interaction parameter in the remainder of this discussion. OH adsorption bands (3800 cm 1 ) on the IR spectrum. For adsorption tests a 1-g mineral sample was added to 15 ml of surfactant solution in the desired solvent and conditioned for 12 h in a glovebox. Samples for the desorption experiment were prepared by first adsorbing the surfactant on the mineral from cyclohexane. Following this, the solids with the adsorbed surfactant were separated by centrifugation, vacuum dried for 12 h, and then conditioned with different solvents for 12 h, and the resultant supernatant was analyzed for the surfactant concentration. Analysis of the anionic and cationic surfactants was conducted by the two-phase titration technique described in the literature [12]. In all the cases δ eff is calculated using Eq. (13) and is plotted against the percentage desorption. The initial surface energy coverage before desorption in all the experiments was approximately 50%. Case 1. Aerosol-OT on alumina. Fig. 1 shows desorption of AOT as a function of δ eff (A = B = C = 1) for aerosol- OT/alumina system. There is a systematic decrease in the desorption amount (means there is higher adsorbed amount) with an increase in the value of δ eff. Case 2. Aerosol-OT on silica. Fig. 2 shows the variation of desorption for aerosol-ot/silica system, also showing a systematic decrease in desorption with increasing δ eff. The trend Fig. 1. Variation of desorbed amount as a function of δ eff for the AOT/ alumina system. 6. Correlation with experimental data A series of surfactant adsorption/desorption data published previously [20,21] was used to test the validity of this approach. In the above reference we report a series of experiments where surfactant pre-adsorbed solids were immersed in various solvents and the degree of desorption was estimated in the different solvents. Samples for adsorption studies were prepared by desiccating the mineral at 200 C for 6 h followed by cooling it for 2 h at 25 C in a vacuum desiccator. Dehydroxylation of alumina was done by heating it at 900 C for 72 h and confirmed by the disappearance of the Fig. 2. Variation of desorbed amount as a function of δ eff for the AOT/silica system.

6 378 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) observed in this plot is very similar to the one for aerosol- OT/alumina case. In both the above cases, electrostatic forces that may affect adsorption at least in the polar solvents are not considered. The electrostatic forces can be brought into this formulations by modifying the δ solute δ solvent term. If the solid and the surface have the same sign, i.e., repulsion between them, the interaction term is scaled up by a factor <1 (C <1), and if they are oppositely charged, it is scaled up by a factor >1 (C>1). The exact values of these factors may be related to the magnitude of the zeta potential under the adsorption conditions. Thus, in the case of silica the data point corresponding to desorption from water can be modified (because both silica and AOT are negatively charged here) and made to fit into Eq. (13). Case 3. Aerosol-OT on graphite. Fig. 3a showstheplot of desorbed amount as a function of δ eff for AOT/graphite case. Although showing a similar trend as in the previous two cases, the curve is quite different. For this system, hydrophobic interactions among the various species become an important factor for adsorption due to the hydrophobic nature of the solid substrate, graphite. Hydrophobic interactions can be of two types: (a) between the solid and the solute and (b) among the adsorbed solute molecules, i.e., the lateral interactions similar to those leading to colloid formation. The following guidelines can be used to modify Eq. (12) to incorporate these effects. Hydrophobic forces will drive the surfactant to the interface and potentially cause them to aggregate at the solid liquid interface depending on the nature of the solvent. Moreover, presence of micelles in solution may help the surfactants to desorb form solid surface and solubility in the micelle. If the solvent and the surfactant are compatible, i.e., δ solute δ solvent is small, the hydrophobic forces will be overshadowed by other forces and the surfactant will tend to stay dispersed in the solvent. However, if the solid is hydrophobic or in certain parts of the adsorption isotherm where lateral interactions are possible in the adsorbed layer, the term δ solute δ solvent needs to be modified to make the hydrophobic effect dominant and this term is scaled up by a factor >1 (B>1). Fig. 3b shows the results when A = 1, B = 1.4, C = 1 for aerosol-ot on graphite and this as in the earlier cases shows a systematic decrease in the desorbed amount with δ eff. Case 4. Sodium alkylsulfates on alumina. Fig. 4 shows the plots for sodium decyl, dodecyl and tetradecyl sulfates using Eq. (13) with A = B = C = 1. All these plots show a similar trend as before with desorption amount decreasing with increasing value of δ eff. From the results shown here for a variety of solute solvent solid systems it is clear that δ eff as given by Eq. (13) is an effective parameter for prediction of adsorption behavior in polar and non-polar liquids. Thus an equation of the form δ eff = abs { A δ solid δ solvent +B δ solute δ solvent C δ solid δ solute } (14) (a) is proposed for predicting adsorption/desorption of surfactants in various systems where A, B and C are systemspecific constants. The following guidelines are suggested from a correlation of the present experimental data with this model. (b) Fig. 3. Variation of desorbed amount as a function of δ eff for the AOT/ graphite system for A = B = C = 1 (a) and A = B = 1, C = 1.4 (b). Fig. 4. Variation of desorbed amount as a function of δ eff for the alkylsulfates/alumina system similar trend as before with desorption amount decreasing with increasing value of δ eff.

7 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) Conclusion A new theory has been described for adsorption of surfactants in media of varying polarity. Using interaction parameters to quantify solid solute solvent interactions we have developed a model for describing adsorption of surfactants in different solvents. An effective interaction parameter for the system calculated from fundamental properties of regarding the solid, solvent and surfactant is proposed: (a) δ eff = abs { A δ solid δ solvent +B δ solute δ solvent C δ solid δ solute }. The model was successfully applied to correlate the observed adsorption/desorption behavior of a number of surfactants. For adsorption of ionic surfactants on oxides it was found that adsorption is favorable if δ eff > 10. Similar correlations were found for adsorption on hydrophobic surfaces as well as for the adsorption of linear alkyl sulfates. This model can be used to predict sorption behavior of surfactants on different solids in non-polar and polar media from their fundamental properties. Acknowledgments (b) Fig. 5. Variation of desorbed amount as a function of δ eff (calculated using Eq. (15) (a) and Eq. (16) (b)) for the AOT/alumina system. B>1 for systems where hydrophobic interactions are expected to be significant for adsorption. For example, adsorption on a hydrophobic substrate or when phenomenon such as hemimicellization occurs. C<1 for systems where the surface and solute are similarly charged. C>1 for systems where the surface and solute are oppositely charged. Other forms of equations that were tested are given below: δ eff = { δ solid δ solvent 2 + δ solute δ solvent 2 δ solid δ solute 2} 1/2, δ eff = { δ 2 solid δsolvent 2 1/2 + δ 2 solute δsolvent 2 δ solid 2 δ2 1/2 } solute. 1/2 (15) (16) Figs. 5a and 5b show the plots for AOT on alumina using the above two equations. The plots show the same general trend as that in Fig. 1 and suggest that alternate combinations of these terms may also be used to predict overall adsorption tendency. Support of the National Science Foundation (NSF) and Department of Energy (DOE) are acknowledged. References [1] G.W. Woodbury Jr., L.A. Noll, Colloids Surf. 33 (3 4) (1988) [2] D.W. Fuerstenau, T.W. Healy, P. Somasundaran, Trans. Am. Inst. Mining Metallurg. Pet. Eng. 229 (1964) [3] P. Somasundaran, T.W. Healy, D.W. Fuerstenau, J. Phys. Chem. 68 (12) (1964) [4] H. Burrel, Interchem. Rev. (Spring 1955) [5] J. Hildebrand, R. Scott, The Solubility of Nonelectrolytes, third ed., Reinhold, New York, [6] P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, [7] R.J. Scott, M. Maggot, J. Polym. Sci. 4 (1949) 555. [8] P.A. Small, J. Appl. Chem. 3 (1953) 71. [9] C.M. Hansen, Doctoral dissertation, Copenhagen, [10] C.M. Hansen, J. Paint Technol. 39 (1967) 104, 505. [11] I. Yildirim, Doctoral dissertation, Virginia Polytechnic Institute & State University, [12] A.F. Barton, Handbook of Solubility Parameters and Other Cohesion Parameters, CRC Press, 1991, p [13] S. Gasic, B. Jovanovic, S. Jovanovic, J. Serb. Chem. Soc. 67 (1) (2002) [14] K.V.S.N. Raju, M. Yaseen, Langmuir 8 (1992) [15] Y. Du, Y. Xue, H.L. Frisch, in: Physical Properties of Polymers Handbook Mark Encyclopedia, 1996, pp [16] B.L. Karger, L.R. Snyder, C. Eon, J. Chromatogr. 125 (1976) [17] K.M. Shareef, M. Yaseen, M. Mahmood Ali, P.J. Reddy, J. Coat. Technol. 58 (1986)

8 380 P. Somasundaran et al. / Journal of Colloid and Interface Science 292 (2005) [18] S. Krishnakumar, Doctoral dissertation, Columbia University, [19] M.J. Mcguire, I.H. Suffet, J. Am. Waterworks Assoc. 70 (1978) 621. [20] S. Krishnakumar, P. Somasundaran, Langmuir 10 (8) (1994) [21] S. Krishnakumar, P. Somasundaran, J. Colloid Interface Sci. 162 (2) (1994)