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. 
J.A. Brant, A.E. Childress / Journal of Membrane Science 203 (2002) 257273 259
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
J.A. Brant, A.E. Childress / Journal of Membrane Science 203 (2002) 257273 261
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 between the outer elec-tron shells (van der Waals boundaries) of adjoiningnon-covalently interacting molecules [20,59].
2.4. Interaction energy between a sphericalcolloid and an infinite planar surface
As the separation distance between two surfacesincreases, the LW and AB interaction energy com-ponents diminish from their corresponding adhesionenergy (i.e. the interaction energy at contact given byEqs. (6) and (7)) following a unique decay pattern.The LW interaction energy per unit area decays withthe inverse square of the distance between two infiniteplanar surfaces :
GLW(plate plate) = A
where A is the Hamaker constant and y is the separa-tion distance between the two interacting planar sur-faces. The Hamaker constant can be calculated fromthe LW component of the free energy of adhesion byrearranging Eq. (8):A = 12y20 GLWy0 (9)
Estimates of free energy of adhesion obtained fromthe surface tension components provide informationabout interaction energy per unit area between two in-finite planar surfaces. To obtain the actual interactionenergy between the membrane (assumed to be an infi-nite planar surface) and the colloidal particle (assumedto be a sphere), a technique that converts the interac-tion energy per unit area to the total interaction energyfor a given geometry is required. Derjaguins tech-nique , was therefore, used to scale the interactionenergy per unit area between two infinite flat surfacesto the corresponding interaction energy between a flatsheet (membrane) and a sphere (colloid). Applyingthis technique to Eq. (8), the LW interaction energybetween an infinite flat plate and a spherical colloid is
ULW(platesphere) = Aac6h
where ac is the radius of the spherical colloid and his the surface to surface separation distance betweenthe flat plate (membrane) and the sphere (colloid).Combining Eqs. (9) and (10) gives the expression forthe LW interaction energy between a membrane anda colloid in an aqueous environment:
ULWmlc (h) = 2 LWy0y20ac
The expression for the AB interaction energy as afunction of separation distance is derived similarly.The AB interaction energy per unit area decays expo-nentially with separation distance between two infiniteplanar surfaces :
GAB(plateplate) = GABy0 exp[y0 y
where is the characteristic decay length of AB in-teractions in water, whose value is between 0.2 and1.0 nm . A commonly used value of for aqueoussystems is 0.6 nm [20,34]; this value was used in thecurrent investigation. Applying Derjaguins techniqueto Eq. (12), the decay behavior of AB interactionsbetween a membrane and a colloid in an aqueousenvironment is
UABmlc = 2ac GABy0 exp[y0 y
The EL interaction energy per unit area between twoinfinite planar surfaces decays with separation distanceaccording to 
2( 2m + 2c )
1 coth(y)+ 2mc( 2m + 2c )
where 0r is the dielectric permittivity of the sus-pending fluid, the inverse Debye screening length,and m and c are the surface potentials of the mem-brane and colloid, respectively. Once again, applyingDerjaguins technique to Eq. (14), the decay behaviorof the EL interaction energy between a membraneand a colloid in an aqueous environment is
UELmlc(h) = r0ac(
1+ eh1 eh
+( 2c + 2m) ln(1 e2h))
262 J.A. Brant, A.E. Childress / Journal of Membrane Science 203 (2002) 257273
In the current investigation, the surface potentialswere assumed to be the same as the measured zetapotentials of the surfaces involved. The zeta potentialsof the membranes were determined from streamingpotential measurements while the zeta potentials ofthe colloids were determined from electrophoreticmobility measurements. For both membranes andcolloids, zeta potential values at pH 5.6 were usedto determine the EL interaction energy term. The in-verse Debye screening length was determined usingthe following relationship :
where e is the electron charge, ni the number con-centration of ion i in the bulk solution, zi the valenceof ion I, k Boltzmanns constant, and T is absolutetemperature. For this investigation, a backgroundelectrolyte of 0.01 M NaCl was assumed.
3. Materials and methods
3.1. Representative membranes
The three RO membranes selected for this investi-gation were the FT-30, CD, and CE membranes. TheFT-30 membrane (Film Tec, Minneapolis, MN) is athin-film composite polyamide membrane. The CDand CE membranes (Osmonics Desal, Vista, CA) areheat-treated cellulose triacetate/diacetate blend mem-branes. All of the membranes were stored in ultrapurewater at 5 C.
3.2. Representative colloids
The three colloids selected for this investigationwere commercial silica colloids, aluminum oxide col-loids, and polystyrene microspheres. The commercialsilica colloids (MP-1040, Nissan Chemical AmericaCorporation, Houston, TX) were supplied dispersedin deionized water; the dispersion was stored at roomtemperature. According to the manufacturer, the silicacolloids have an average particle diameter of 100 nmand a density of 2.2 g/cm3. The aluminum oxidecolloids (Aluminum Oxide C, Degussa Corporation,Akron, OH) were supplied as a powder and stored at
room temperature. According to the manufacturer, thealumina colloids have an average particle diameterof 13 nm and a density of 3.2 g/cm3. The polystyrenemicrospheres (PSO2N, Bangs Laboratories, Inc.,Fishers, IN) were supplied dispersed in deionizedwater; the dispersion was store...