Journal of Membrane Science 203 (2002) 257273
Assessing short-range membranecolloid interactionsusing surface energetics
Jonathan A. Brant, Amy E. ChildressDepartment of Civil Engineering, University of Nevada at Reno, Mail Stop 258, Reno, NV 89557-0152, USA
Received 7 August 2001; received in revised form 14 December 2001; accepted 4 January 2002
AbstractThe contribution of acidbase (AB) (polar) interactions to the total interaction energy between membranes and colloids
was investigated. The surface energetics of several membranes and colloids were evaluated using the Lifshitzvan der Waalsacid-base approach. This provides the van der Waals (LW) and polar interaction energies between various surfaces frommeasurements of contact angles of different probe liquids on these surfaces. In addition, the surface potentials of the mem-branes and colloids were determined using electrokinetic measurements, yielding the electrostatic (EL) interaction betweenthese surfaces. The three interaction energy components (LW, EL, and AB) were combined according to the extendedDerjaguinLandauVerweyOverbeek (extended DLVO or XDLVO) approach to evaluate membranecolloid interactionenergies. Predictions of interaction energy based on the XDLVO approach were compared to the corresponding predictionsfrom the classical DLVO theory. For all the membranecolloid combinations studied, the DLVO potentials were quite sim-ilar. However, inclusion of AB interactions resulted in a substantially different (qualitative and quantitative) prediction ofshort-range (separation distances
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ac colloid radiusA Hamaker constante electronic charge (1.6 1019 C)G interaction energy per unit area
between two infinite planar surfacesh surface to surface separation
distance between flat plate and sphereJ permeate fluxJ0 initial permeate fluxk Boltzmanns constant
(1.38 1023 J/K)ni number concentration of ion
i in bulk solutionT temperatureU total interaction energy between
membrane and particley separation distance between two
infinite planar surfacesy0 minimum separation
distance (0.158 nm)zi valence of ion i
Greek lettersr0 permittivity of the suspending liquid surface tension inverse Debye screening length decay length of AB interactions
in water contact angle zeta potential
SuperscriptsAB acidbaseDLVO DerjaguinLandauVerweyOverbeekEL electrostaticLW Lifshitzvan der WaalsTOT totalXDLVO extended DLVO+ electron acceptor electron donor
Subscriptsc colloidl liquidm membranes solid
circumstances, the discrepancy between the theoreti-cal DLVO predictions and experimental observationsis typically accounted for using additional mecha-nisms and hypotheses. For example, these discrepan-cies have sometimes been attributed to chemical andmorphological heterogeneity of the membrane sur-faces [10,2125], while in other instances, they havebeen attributed to additional types of interactions be-tween the membranes and foulants . It is quitepossible that the presence of morphological and chem-ical heterogeneities can result in surfaces with verydifferent energy distributions than smooth or chem-ically homogeneous surfaces [10,2125], and hence,can result in substantially different fouling behaviorcompared to theoretical DLVO predictions. Equallylikely, however, is the presence of additional interac-tions between a membrane and a foulant, particularlyat very small separations, leading to aberrant foul-ing propensities. For many uncharged materials, thepresence of additional interactions induced by the po-larity of the solvent has been observed , andthis has led to a school of thought that proposes anextended DLVO (XDLVO) type approach to accountfor the total interactions in such systems [3,27,2933].
The additional interaction in the XDLVO modelis often attributed to a short-ranged acidbase (AB)(electron donor/electron acceptor) interaction (possi-bly stemming from hydrogen bonding) between twosurfaces immersed in a polar solvent (e.g. water)[3,27,30,3235]. This interaction may be attractive(hydrophobic attraction) or repulsive (hydrophilic re-pulsion). The presence of these interactions is stronglysupported by the measurement of surface tensionsof various substances. For example, in the case ofwater, the major contribution (51 mJ/m2) to the totalsurface tension (72.8 mJ/m2) stems from these polarinteractions, while the van der Waals contribution(21.8 mJ/m2) is much lower. Interfacial tension mea-surements for many polymeric surfaces immersed inwater have also revealed a substantial AB contribution[4,20,31,36]. The fouling of polymeric membranes, istherefore, likely to be influenced by AB interactionsand the contribution of polar interactions to colloidalmembrane fouling should be examined.
Comparisons between the DLVO theory and theXDLVO approach have been made in previous inves-tigations concerning deposition and aggregation inaqueous systems (e.g. [31,33,37]). Meinders et al. 
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investigated deposition efficiencies and reversibilityof bacterial adhesion on various substratum surfacesand compared those results to DLVO and XDLVOpredictions. It was concluded that bacterial adhesionto the surfaces studied was more accurately explainedby the XDLVO approach. Ohki and Ohshima analyzed the interaction and aggregation of lipid vesi-cles using the DLVO and XDLVO models and foundthat the XDLVO approach was more accurate in de-scribing interactions occurring at a separation distance
260 J.A. Brant, A.E. Childress / Journal of Membrane Science 203 (2002) 257273
It has been suggested by van Oss  that energybalances performed for aqueous systems must alsoaccount for the AB interaction energy in addition tothe LW and EL interaction energies. Inclusion of theAB interaction term results in the extended DLVO ap-proach, which may be written as
UXDLVOmlc = ULWmlc + UELmlc + UABmlc (2)where UXDLVO is the total interaction energy betweenthe membrane and colloid immersed in water and UABis the AB interaction term.
2.2. Lifshitzvan der Waals acidbase approach
Application of the XDLVO approach requires thatthe surface energy parameters of the membrane andcolloid be determined experimentally. Surface energydata can be calculated for membranes and colloidsusing contact angle data and the acid-base approach[27,31]. The acid-base approach has been widely usedas a method for determining surface tension compo-nents of a solid and interfacial free energies per unitarea between two phases (e.g. [3,53,54]).
van Oss et al.  represented the total surface ten-sion of a pure substance as the sum of an LW and anAB component, yielding
TOT = LW + AB (3)where TOT is the total surface tension and LWand AB are the LW and AB components of surfacetension, respectively. The non-polar LW componentrepresents a single electrodynamic property of a givenmaterial, while the polar AB component comprisestwo non-additive electron acceptor and electron donorparameters [27,53]. The polar AB component of amaterials surface energy is given by [3,36,53,56]AB = 2
where + is the electron acceptor parameter and is the electron donor parameter.
The surface tension components/parameters of asolid surface ( LWs , +s , s ) can be determined byperforming contact angle measurements using threeprobe liquids with known surface tension parameters( LWl , +l , l ) and employing the extended Youngequation . The extended Young equation relatesthe contact angle of a liquid on a solid surface to the
surface tension parameters of both the solid and theliquid and is given by [4,36,56]
(1+ cos ) TOTl= 2
+s l +
where is the contact angle. The subscripts s and lcorrespond to the solid surface and the liquid, respec-tively. The extended Young equation is best describedas an equilibrium force balance. The left-hand sideof the equation represents the free energy of cohe-sion per unit area of the liquid (l) and the right-handside represents the free energy of adhesion per unitarea between the liquid (l) and the solid (s) [27,57].According to van Oss , two of the probe liquidsshould be polar and one of the probe liquids shouldbe apolar. The apolar liquid is used to calculatethe non-polar component of surface tension ( LWs )[27,58]. Furthermore, high energy (polar and apolar)liquids are recommended to produce larger, moreeasily measured contact angles .
2.3. Free energy of adhesion
Surface tensions for membranes and colloids cal-culated using the acid-base approach can be used toevaluate the free energies of adhesion per unit area,GLWy0 and G
ABy0 , between these surfaces. Expres-
sions for the LW and AB adhesion energies per unitarea are, respectively given by 
GLWy0 = 2(
GABy0 = 2+l
+m c +m +c
The free energy of adhesion per unit area signifies theinteraction energy per unit area between two planarsurfaces (bearing the properties of the membrane andthe colloid) that are brought into contact. Because it
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is known that the LW interaction between two ma-terials diverges when the surfaces physically toucheach other, contact is assumed to occur at a hypothet-ical minimum equilibrium cut-off distance . Theminimum equilibrium cut-off distance, y0, is usuallyassigned a value of 0.158 nm (0.009 nm) and maybe regarded as the distance betw