electrostatics and metal oxide wettability

Published: June 28, 2011

r 2011 American Chemical Society 14914 dx.doi.org/10.1021/jp203714a | J. Phys. Chem. C 2011, 115, 14914–14921

ARTICLE

pubs.acs.org/JPCC

Electrostatics and Metal Oxide WettabilityGary Hanly, Daniel Fornasiero, John Ralston,* and Rossen Sedev

Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Mawson Lakes, Adelaide, SA 5095

’ INTRODUCTION

Wetting is strongly influenced by electrostatics, irrespective ofwhether an external voltage is applied across a solid�liquidinterface, as in the case of electrowetting,1,2 or the spontaneousformation of an electrical double layer, due to the adsorption ofpotential determining ions, which causes a decrease in contactangle.3,4 Moller was the first to investigate how electricalpolarization of a metal/solution interface influenced its contactangle.5 Contact angle�potential capillary curves were obtainedfor a range of noble metals, with a maximum occurring at thesame potential for all metals examined. Frumkin et al.6 confirmedthe parabolic dependence of contact angle on potential, butfound that the maxima occurred at different potentials fordifferent metals.7

For the mercury�electrolyte system, there are a number ofstudies existing where the influence of electrostatics has beencritically examined.8,9 In these systems, the celebrated Lippmannequation illustrates the dependence of the interfacial tension ofthe mercury�solution interfaces on potential and charge:10

� ∂γHg-sol∂E

!T, μS

¼ σo

where E is the applied potential, σ0 is the charge per unit area atthe mercury�solution interface, T is the absolute temperature,and μs is the chemical potential of the supporting electrolyte.When the Young�Dupre equation is invoked, the dependence ofcontact angle on E and σ0 is obvious.

8,9

For solid�liquid interfaces, the role of the electrical doublelayer in influencing wettability has received scant attention. Thedependence of the solid�liquid interfacial tension for solidFe2O3 in contact with an aqueous solution has been examined,with the interfacial tension reaching a maximum at the point of

zero charge.11 Hough and Ottewill3 and Laskowski andKitchener12 showed that the contact angle, θ, of silver iodideand methylated silica, measured through the aqueous phase,reached a maximum at the point of zero charge of the solid andwas strongly dependent on the concentration of potentialdetermining ions. Gribanova et al. conducted similar experi-ments on a variety of quartz and glass surfaces, observing asimilar trend.13 Fokkink and Ralston4 used a simple electricaldouble layer model to describe the pAg dependence of θ whileChatelier et al.14 extended this treatment to plasma-depositedfilms. Vittoz et al.15 adopted an approach similar to that ofFokkink and Ralston when examining the wettability of silicaand alumina.

In the various studies reported to date, the key element that islacking is the ability to examine a specific solid�liquid interfacewhere the number of hydrophobic and hydrophilic (charged anduncharged) groups is precisely controlled. pH and ionic strengthmay then be varied in a wide range around the point of zerocharge, enabling the influence of the electrical double layer to beexplored and related to the surface population of particulargroups. TiO2 is an excellent candidate for this investigation, witha surface chemistry that is well-defined,16,17 a negligible solubilityover a wide pH range, an easily accessible point of zero charge,and where surface modification is feasible using a silane that ischemically bound to the solid surface.18 In this study, we havestudied the θ (pH, ionic strength) dependence for hydropho-bized TiO2 and developed a quantitative model linking thepopulation of different surface groups to the wettability. Theoutcomes have wide ramifications for both static and dynamiccontact angle behavior.

Received: April 20, 2011Revised: June 7, 2011

ABSTRACT: The wettability of a titania surface, whose surface was partiallycovered with a strongly based octadecyltrihydrosilane, was studied above andbelow the isoelectric point (or pHiep). The advancing water contact angle is at amaximum at the pHiep, decreasing symmetrically on either side in a Lippmann-like manner. The change in wettability, for a given pH, became morepronounced with increasing salt concentration. Using a non-Nernstian modelof the electrical double layer, the experimental dependence of contact angle onboth pH and salt concentration was satisfactorily predicted.

14915 dx.doi.org/10.1021/jp203714a |J. Phys. Chem. C 2011, 115, 14914–14921

The Journal of Physical Chemistry C ARTICLE

’FREE ENERGY OF FORMATION OF AN ELECTRICALDOUBLE LAYER AND ITS IMPACT UPON WETTABILITY

a. General Approach. The approach here is based on thechange in electrochemical potential, μ̅ , when a potential deter-mining ion is transferred from the bulk solution to an initiallyuncharged surface. If dΓmoles per unit area are transferred, thenthe change in free energy, dF can be obtained. Recall that μ̅consists of both chemical and electrochemical parts. The processoccurs of course at constant temperature, volume, surface area,and overall composition.We proceed by calculating the work required to form the

electrical double layer from a system which is in an unchargedstate initially. [The information contained in the numerousreferences cited in this paper is widely dispersed, frequently usesdifferent symbols and generally covers only one or two of thetheory aspects. We have developed one coherent set of equationsand arguments here to help both current and future readers.] Thechange in surface force energy per unit area, dFdl, when dΓmolesper unit area are transferred from the bulk solution to the surfaceis given by (following Verwey andOverbeek,19 Grahame,20 Chanand Mitchell,21 Hunter,22 Trauble et al.23 and Payens,24 with themore recent insights of Biesheuvel)25

dFdl ¼ ðμ̅ s � μ̅ BÞ dΓ ð1Þwhere μ̅ s and μ̅B are, respectively, the electrochemical potentialof the potential-determining ions at the surface (s) and in thebulk solution (B).Furthermore,

μ̅ s ¼ μs þ Zeψo ð2Þwhereψo is the surface electrostatic potential andZe is the chargeof the potential determining ion, with Z as the ion valency and eas the electronic charge.Thus the specific surface free energy ΔFdl is

ΔFdl ¼Z σo

oψoðσÞ dσ þ

Z Γo

oðμs � μ̅ BÞ dΓ ð3Þ

where the surface charge density σo is given by

σo ¼ ZeΓo ¼ qΓo ð4Þand Γo is the equilibrium surface concentration of potentialdetermining ions.The first integral on the right-hand side (rhs) of eq 3 is the

electrical work done in creating the electrical double layer, whilethe second integral is called the chemical component of the freeenergy.Assuming that

μs ¼ μsðΓÞ ð5Þi.e., the chemical component of μ̅ s depends only on the quantityof ions adsorbed and not on the surface potential ψo, this meansthat all electrostatic contributions to μ̅ s in eq 2 are described byqψo while μs contains nonelectrostatic contributions, such asdispersion interactions, ion�solvent interactions, and the like, asnoted elsewhere.25,26 ΔFdl now becomes

ΔFdl ¼Z σo

oψoðσÞ dσ þ

Z Γo

oðμsðΓÞ � μ̅ BÞ dΓ ð6Þ

To evaluate the first integral, the functional form of ψo (σ) isrequired.For a simple Gouy�Chapmanmodel22 applied to a flat interface,

ψDo ðσÞ ¼ ψoðσÞ ¼ 2kT

esinh�1 eσ

2kεεokT

� �ð7Þ

where ψoD(σ) is a particular potential�charge relationship that

reflects the ion distribution in the diffuse electrical double layer, k isthe Boltzmann constant, T is the absolute temperature, ε is thedielectric constant of water, εo is the permittivity of free space, andkis the Debye reciprocal length.In the case of the second integral, the bulk electrochemical

potential of the adsorbing ions, μ̅B is taken to be constant.The amount of adsorbed charge is

σ ¼ qΓ ð8Þthus we can define a function ψo

s (σ) by

qψsoðσÞ ¼ � ½μsðΓÞ � μ̅ B� ð9aÞ

¼ � ½μsðσ=qÞ � μ̅ B� ð9bÞIf the amount of adsorbed charge is σ, then the surface

potential is ψos (σ) and at equilibrium

ψDo ðσoÞ ¼ ψs

oðσoÞ ð10Þthus

2kTe

sinh�1 εσo

2kεεokT

� �¼ � 1

qμs

σo

e

� �� μ̅ B

� �ð11Þ

for a planar electrical double layer.Using eqs 8 and 9, eq 6 now appears as

ΔFdl ¼Z σo

ofψD

o ðσÞ �ψsoðσÞg dσ ð12Þ

b. Nernstian Surfaces, Constant Potential. Recalling theapproach of Verwey and Overbeek,19 μs(Γ), the chemicalcomponent of the surface electrochemical potential, is assumedto be independent of Γ, the moles per unit area of potential-determining ions adsorbed. This means in eq 9 thatψo

s =ψo, theconstant potential case.Thus eq 12 becomes

ΔFdl ¼Z σo

oψoðσÞ dσ � σoψo ð13Þ

where, as noted by Verwey and Overbeek19 and Hunter,22

�σoψo is the chemical free energy decrease per unit area ofsurface, Δμchem, whereas the term

Roσoψo(σ) dσ represents the

electrical work and is equivalent to charging a capacitor.Thus

ΔFdl ¼ ΔFelecdl þ ΔFchemdl ð14Þfor constant potential. Note that ΔFdl

chem is independent of thestate of charge of the surface, which is true only at low chargedensity (see below for the more general case). By partialintegration, eq 13 becomes

ΔFdl ¼ -Z ψo

oσ dψ ð15Þ



We observe that the free energy is always negative, as expected.If the potential is low, where the Debye�Huckel approxima-

tion holds, then, using σo = εkψo

ΔFdl ¼ � 12εεokψ2

o ¼ � 12σoψo ð16Þ

For large potentials, σo increases with exp(Zeψo/2kT) and thusΔFdl falls between the limits of �1/2σoψo and �σoψo.In eq 15, inserting σo = (2kTεεok/e) sinh(Zeψo/2kT) yields

ΔFdl ¼ � 4k2T2εεokZe2

coshZeψo

2kT

� �� 1

� �ð17Þ

as the free energy of formation of a single, isolated diffuseelectrical double layer for the case of constant potential orNernstian surfaces, where the chemical component of μ̅ i isconstant and independent of Γ.c. Non-Nernstian Surfaces. This treatment stems from the

work of Chan andMitchell,21 with the original platform providedby Verwey and Overbeek19 and Payens,24 particularly. Chan andMitchell21 demonstrated how to remove the restriction of lowcharge density surfaces.We consider a monoacidic surface with the following reaction:

�MOH S �MO� þ Hþ ð18Þwhich has a dissociation constant Ka2.The surface charge densityσo = e(ΓH+�ΓS), whereΓH+ is the

amount of H+ adsorbed per unit area, and ΓS (= Ns) is the totalnumber of ionizable groups per unit area. From eq 9a we can seethat eψo

s = μ̅B � μs(ΓH+).Recalling eq 6, i.e.

ΔFdl ¼Z σo

oψoðσÞ dσ þ

Z Γs

ΓHþðμs � μ̅ BÞ dΓHþ ð19Þ

where H+ refers to the potential-determining ions.Clearly, in eq 19,

ΔFdl ¼ ΔF elecdl þ ΔF chem

dl

Now

ΔFelecdl ¼Z σo

oψo dσ ¼ σoψo �

Z ψo

oσo dψ

and, using eq 7,

ΔFelecdl ¼ σoψo � εεok2kTe

� �2cosh

eψo

2kT

� �� 1

� �ð20Þ

For Δdlchem, Chan and Mitchell21 and Chatelier et al.14 show

that

ΔFchemdl ¼ 1e

Z σo

oΔμ dσ ð21Þ

where, for any reaction, Δμ = Σμproducts � Σμreactants.The chemical potentials of products and reactants in reaction

18 are then expressed as a function of their respective concentra-tion, such as, for example,

μðMO�Þ ¼ μoðMO�Þ þ kT ln½MO�� ð22Þwhere μ�(MO�) is the standard chemical potential of MO�.

The change in chemical potential for reaction18 is then

Δμ ¼ Δμo þ kTðln½Hþ� þ ln½MO�� ln½MOH�Þ ð23Þwith

Δμo ¼ μoðMO�Þ þ μoðHþÞ � μoðMOHÞ¼ � kT ln Ka2

Concentrations can be related to surface charge, σ, through theexpression

σ ¼ R 3 e 3Ns

and

R ¼ ½MO��½MOH�T

where Ns is the number of surface sites, MOH and MO�, and[MOH]T = [MOH] + [MO�].As R is always a positive quantity, we use the absolute value of

σ. Then eq 23 becomes

Δμ ¼ kT ln½Hþ�Ka2

� lnðeNs � σÞ þ ln σ

( )ð24Þ

Incorparation of eq 24 into eq 21 gives

ΔFchemdl ¼ kTe

Z σo

oln½Hþ�Ka2

þ lnðeNs � σÞ þ ln σg dσ

(

ð25ÞAfter integration and rearrangement, eq 25 becomes14,21,27

ΔFchemdl ¼ kT 3Ns R ln½Hþ�Ka2

þ ð1� RÞ lnð1� RÞ þ R ln R

( )

ð26ÞAt equilibrium, Δμ = 0, and eq 24 becomes

lnσo

eNs � σo

� �þ ln

½Hþ�Ka2

¼ 0 ð27Þ

The surface potential, Ψo can be expressed as a function ofsurface potential using the Boltzmann equation, [H+] =[H+]b 3 exp(�eΨo/kT), and eq 27 ([H

+]b is the proton concen-tration in the bulk solution).

ψo ¼ � kTe

lnKa2

½Hþ�beNs

σo� 1

� �" #ð28Þ

Combining eqs 7 and 28 gives

2 sinh�1 eσo

2kTεεok

� �þ ln

Ka2

½Hþ�beNs

σo� 1

� �" #¼ 0 ð29Þ

which can be solved to giveσo for given values ofNs,Ka2, and [H+]b.

A similar approach can be used for reaction at a monobasicsurface with a dissociation constant Ka1:

�MOH þ Hþ S �MOH2þ ð30Þ

with

Δμ ¼ Δμo þ kTðln½MOH2þ� � ln½MOH� � ln½Hþ�Þ



and

Δμ ¼ kT lnσ

eNs � σ

� �þ ln

Ka1

½Hþ��

ð31Þ

ΔF chemdl ¼ kT 3Ns R ln R þ ð1� RÞ lnð1� RÞ þ R ln

Ka1

½Hþ��

ð32ÞAt equilibrium, Δμ = 0, and eq 31 becomes

lnσo

eNs � σo

� �þ ln

Ka1

½Hþ� ¼ 0 ð33Þ

The surface potential, Ψo, can be expressed as a function ofsurface potential using the Boltzmann equation for the protonconcentration and eq 33.

ψo ¼ kTeln

½Hþ�bKa1

eNs

σo� 1

� �" #ð34Þ

Combining eq 7 and 34 gives

2 sinh�1 eσo

2kTεεok

� �� ln

½Hþ�bKa1

eNs

σo� 1

� �" #¼ 0 ð35Þ

which can be solved to give σo for given values of Ns, Ka1, and[H+].From these values of σo, eq 7, 20, and 26 or 32 were then used

to calculate the surface potential and the electrical and chemicalcomponents of the free energy of formation of the double layer,respectively.d. Applicability to Contact Angle Changes on Charged

Surfaces. As shown by Fokkink and Ralston,4 in the presence ofsurface charge, the specific free energy of the solid�liquidinterface is

γSL ¼ γ�SL þ ΔFdl ð36Þwhere ΔFdl represents the free energy of formation of theionizable surface relative to the point of zero charge (pzc) foran ionizable surface with acidic or basic groups, where H+ is thepotential determining ion. Using the Young�Dupre equation,

cos θðpHÞ ¼ cos θðpzcÞ �ΔFdlγLV

ð37Þ

where ΔFdl = ΔFdlelec + ΔFdl

chem as noted above and elsewhere.3,7

ΔFdlelec andΔFdl

chem are calculated through eqs 20 and 26 or 32, asoutlined above.

’MATERIALS AND METHODS

Siliconwafers coveredwith a thin layer of TiO2were produced bysputtering titanium in an argon/oxygen environment for 41 minusing a radio-frequency (RF) magnetron source operating at 2 kW.Prior to sputtering, siliconwaferswere dipped in hydrofluoric acid toremove any native oxide layer. X-ray photoelectron spectroscopy(XPS) detected only the presence of Ti and O in a 1:2 ratio(detection limit 0.1 atomic %). This indicated that the surface layerwas pure titanium dioxide. X-ray diffraction showed that thedeposited titanium dioxide was amorphous.17 Imaging by AFMshowed a root-mean-square (rms) roughness of 0.3 nmwith a peak-to-valley height of 1.5 nm over 1 μm.28 The isoelectric point (iep),determined by streaming potential measurements, falls at 4.4( 0.1,

as we have described elsewhere, along with other characteristics.17,29

The TiO2-coated wafers were cut to a 10 mm� 10 mm size with adiamond tip pen, cleaned in ethanol, submerged in a 10% w/wKOH solution for 1 min, then rinsed with copious amounts of high-purity water and finally dried under a stream of high purity nitrogenand plasma cleaned with a Harris Plasma Cleaner. A test performedon a set of wafers showed that water completely wets the surface.

The high-purity water used in this study had a specific con-ductivity of less than 0.4 μS/cm, a surface tension of 72.8mN/m at20 �C, and a bubble residence time of less than 1 s. Octadecyl-trihydrosilane (OTHS, CH3(CH2)17SiH3) was obtained fromSigma-Aldrich (97.5% purity) and was used as supplied. ARcyclohexane (Chem-Supply) was dried with molecular sieves(Sigma-Aldrich) for a minimum of 24 h before use. All salts, acids,and bases (HNO3 andKOH)were of analytical grade or better, andsolutions were prepared daily.

All glassware was cleaned in a warm solution of 30% potassiumhydroxide for an hour, then washed thoroughly with high-puritywater and placed in an oven at 110 �C for 2 h. Measurementswere conducted in a Class 100 clean room at an ambienthumidity of 45% and temperature of 22 �C.Surface Modification Using OTHS. Titania surfaces were

hydrophobized using OTHS, using a method adapted fromFadeev and McCarthy.18

A stock solution of OTHS was prepared and diluted tothe required concentration with cyclohexane. Freshly cleanedTiO2 wafers were immersed in an OTHS solution for 15 h(preliminary experiments showed that equilibrium was achievedwithin this period), washed several times with cyclohexane in anultrasonic bath, followed by ethanol and then high-purity water.The TiO2 wafers were stored under high-purity water before useto minimize any adventitious contamination.Contact Angle Determinations. The contact angle was

measured using the captive bubble technique. The sample wassubmerged in an aqueous solution of predetermined ionic strengththat had been purged with high purity nitrogen gas for at least anhour. The cell was placed on an adjustable x�y�z stage, and acharge-coupled device (CCD) camera (Jai CVM10BX) was usedto take tagged image file format (TIFF) images of the bubbleplaced on the silanated titania surface, using a frame-grabbingsoftware package. Analysis was performed with an in-house soft-ware program. This instrumental arrangement minimized con-tamination of the sample and allowed easy manipulation of boththe pH and the ionic strength. A clean stainless steel needle wasused to produce a bubble of approximately 2 mm in diameter onthe surface, and the advancing and receding contact angles,measured through the aqueous phase, were recorded. All measure-ments were performed at least in quadruplicate. The standarddeviation in contact angle for all measurements was less than 3�.The pH of the electrolyte solution was adjusted to specified valuesby addition of small amounts of acid or base.Streaming Potential Measurements. Streaming potential

measurements were performed using an apparatus based on thedesign of Scales et al.29 Electrolyte solution (10�4 and 10�3 Manalytical grade KCl with a pH adjusted with analytical gradeKOH or HCl) was circulated through the cell under constanthydrostatic pressure, P, and the streaming potential, E, wasmeasured. The zeta potential, ζ, was calculated using theSmoluchowski equation:

ζ ¼ ηλ

εε0

ΔEΔP



where λ is the conductivity of the capillary, ε0 is the permittivityof free space, η is the viscosity of the liquid, and ε is its dielectricconstant.Two identical, clean (see above) plates were always used. All

procedures have been described in detail elsewhere.30,31

’RESULTS AND DISCUSSION

a. Contact Angles for Titania Surfaces.The maximumwateradvancing and receding contact angles obtained were 118� ( 2�and 101� ( 1�, respectively, representing the contact angles of atitania wafer at maximum OTHS surface coverage. These resultscompare favorably with the respective values of 117� and 100�reported by Fadeev and McCarthy18 at maximum surface cover-age of OTHS on titania, but are slightly higher than the advancingcontact angle reported for a surface fully covered with methyl-terminated groups, ∼110�.32 The water advancing and recedingcontact angles decrease with decreasing OTHS concentration to43� and 20�, respectively, at the smallest OTHS concentrationcurrently used in these experiments. In the absence of OTHS, thetitania advancing and receding contact angles were zero, i.e., thesurface completely wets. The surface coverage of OTHS wasdetermined using atomic force microscopy.28,31,33

The stability of the OTHS layer on titania surfaces of inter-mediate surface coverage was investigated as a function of pH.31

A change in pH could remove the OTHS layer and thereforeaffect the resulting contact angle.34

For titania surfaces with a partial coverage of OTHS (e.g., θa of82�), there was no detectable change in wettability for pH valuesbetween 2 and 12 for immersion times up to 24 h. Thereafter thecontact angle decreased by up to 11� over the next 1000 h. Ex situXPS surface analysis and in situ tapping-mode atomic forcemicroscopy investigations showed that there was no change ineither surface composition or topography over a 24 h period.Water contact angles for titania surfaces as a function of OTHS

surface coverage and pH are shown in Figure 1, and as a functionof KNO3 concentration and pH at a fixed surface coverage ofOTHS in Figure 2. At surface coverages less than 100%, both pHand salt concentration influence the wettability.In Figure 2, there is a maximum in the contact angle versus pH

curve at pH values between 4.0 and 4.3. The contact angle

changes were rapid (reaching equilibrium as quickly as the pHcould be altered) and reversible (shown by repeated cycling ofthe pH). The decrease in contact angle with change in pH ismorepronounced at the higher salt concentration. Moreover, thecontact angle appears to remain constant at pH values largerthan 8 and 9 at 10�1 M and 10�3 M KNO3, respectively.b. Calculation of Contact Angles: Nernstian Surfaces at

Constant Potential. Equations 17 and 37 were used to obtainΨo (the only unknown value) from the experimental contactangles in Figure 2 and θ(pzc) = 61.9� at 10�3 and 10�1MKNO3,using an iterative numerical method at each pH value. The valueof θ(pzc) equal to 61.9� was assumed to be independent ofKNO3 concentration and was estimated by taking an average ofthe highest contact angle values at pH around 3.9�4.6.Values of the surface potential, Ψo, as a function of pH are

shown in Figure 3. The surface potential is zero at pH valuesbetween 3.9 and 4.6 where the curves for 10�1 M and 10�3 MKNO3 concentrations intercept (in agreement with the measured

Figure 1. Advancing contact angle of water on a titania surface as afunction of pH at 10�3 MKNO3 and OTHS surface coverage; from top:100%, 87%, 68%, 54%. The lines are shown to guide the eye.

Figure 2. Advancing contact angle of water on a titania surface partiallycovered with OTHS (54% surface coverage) as a function of pH andKNO3 concentration. The lines are shown to guide the eye.

Figure 3. Surface potential as a function of pH and KNO3 concentra-tion obtained from eq 17 and 37 with θ(pzc) = 61.9� (T = 22 �C, γLV =0.0725 J m�2; 2kT/e = 50.89 mV; k = 3.3� 109 [KNO3]

0.5 m�1; z = 1for H+). The lines are shown to guide the eye.



iep of 4.5). The magnitudes of surface potential increase sharplyas the pH is move away from this interception point, but remainmore or less constant at pH values larger than 6 or less than 3.Figure 4 shows the values of surface charge, σo, calculated

using eq 38 and the values of Ψo in Figure 3.

σo ¼ 2kTεεoke

sinheψo

2kT

� �ð38Þ

As expected, the surface charge increases in magnitude withincreasing salt concentration, while the opposite is true for thesurface potential (Figure 3). These values are compared with theexperimental surface charge data of TiO2 particles of Yates andHealy16 following the scaling of pHpzc approach of Fokkink et al.

35

The calculated surface charge values are more than 4 times largerthan the experimental data. We do not expect a change in theelectrical properties of TiO2 particles for OTHS coverage of lessthan 60% for θ less than 46� (see Figure 5), as predictedelsewhere.36We also note that the surface charges remain constantfor pHg 8, which is not expected for surface charge�pH curves,

which normally increase exponentially as the pHmoves away fromthe point of zero charge.36,37

c. Calculation of Contact Angles: Non-Nernstian Surfacesat Constant Potential.Equations 20, 26 or 32, and 37 were usedto calculate the contact angle as a function of pH using anonlinear least-squares routine to fit the experimental contactangle versus pH data with Ka1 and Ka2 as fitting parameters.The calculated contact angles are compared with the experi-

mental data for 10�1 M and 10�3 M KNO3 in Figures 6 and 7,respectively, and various values ofKa1 andKa2. A site densityNs =8� 1018 sites/m238 obtained for rutile was used. It was found thatthe calculated contact angle was relatively insensitive to variationsin site density; therefore, a Ns value of 3 � 1018 sites/m2, whichtakes account of the loss of (100�54)% ionizable groups becauseof their reaction with OTHS (54% surface coverage by OTHS forthe data in Figures 6 and 7) was used in the final calculations.For the 10�1 M KNO3 data in Figure 6, the fit of the

experimental contact angles is good up to pH 7 for Ka1 and Ka2

values of 1.5 � 10�4 and 10�5 M�1, respectively. At pH values

Figure 4. (circles) Surface charge as a function of pH at KNO3

concentrations of (filled symbols) 0.001 M and (empty symbols) 0.1M calculated from surface potential values in Figure 3 and eq 38.(triangles) Experimental surface charges of Yates et al.16 for TiO2

particles. The surface charges versus pH curves of Yates et al. wereshifted to lower pH values so that their point of zero charge (pH 5.6)coincides with that in the present study (pH 4.4). The lines are shown toguide the eye.

Figure 5. Relationship between the experimental zeta potential andcontact angle of water on OTHS�titania particles at pH 10 (10�3 MKNO3). The line is shown to guide the eye.

Figure 6. (symbols) Experimental and (lines) calculated contact angleof water on titania wafer partially covered with OTHS (54%) in 10�1 MKNO3 as a function of pH and values of Ka1 and Ka2 (see text forexplanation).

Figure 7. (symbols) Experimental and (lines) calculated contact angleof water on titania wafer partially covered with OTHS (54%) in 10�3 MKNO3 as a function of pH and values of Ka1 and Ka2 (Ns = 3 � 10�18

sites/m2; see text for explanation).



higher than 8, the experimental contact angles remain constantwhile the calculated ones decrease. A similar trend is observed at10�3 M KNO3 in Figure 7 with Ka1 value of 2 � 10�5 M�1 andKa2 values between 10

�5 and 10�3 M�1, although the fit is ratherpoor. The contact angle data at pH values larger than 8 cannot beexplained by this model. At pH 8, the surface charge is approxi-mately �0.4 C/m2 at 10�1 M KNO3 (see Figure 10), whichcorresponds to anR value (proportion of charged surface sites) of0.7 (see Figure 8).Figures 9 and 10 show surface potential and surface charge

versus pH curves, respectively, calculated with Ka1 = 1.5 � 10�4

andKa2 = 10�5M�1 for 10�1MKNO3, andKa1 = 2� 10�5M�1

and Ka2 = 10�4 for 10�3 M KNO3. The magnitude of surfacepotential and surface charge, and trend with pH or electrolyteconcentration are the same as those in Figures 3 and 4 calculatedwith the Nernstian approximation.The Ka1 and Ka2 values obtained in this study compare

favorably to the values ofKa1 = 10�5.2 andKa2 = 10

�6.6 calculated

by Westall and Hohl39 for the experimental data of Yates et al.16

for rutile particles.The calculated electrical and chemical components of the free

energy of formation of the double layer are shown in Figure 11 asa function of pH and KNO3 concentration. They both increase inmagnitude as the pH moves away from the point of zero charge.ΔFelec is positive while ΔFchem is negative. ΔFchem is larger thanΔFelec. ΔFelec is relatively independent of salt concentration,while ΔFchem is slightly larger at 10�1 M KNO3.

’SUMMARY

This study is a combined experimental and theoreticalapproach aimed at explaining how electrostatics influence thewettability of metal oxides.

The wettability of a titania surface, whose surface was partiallycovered with a strongly based OTHS, was studied above and

Figure 8. Calculated fraction of positively and negatively charged sites,R+ andR� respectively, at the titania surface (Ka1 = 1.5� 10�4 andKa2 =10�5 for 10�1 M KNO3; Ka1 = 2 � 10�5 and Ka2 = 10�4 for 10�3 MKNO3; Ns = 3 � 10�18 sites/m2).

Figure 9. Calculated surface potential as a function of pH and KNO3

concentrations (Ka1 = 1.5� 10�4 and Ka2 = 10�5 for 10�1 MKNO3;Ka1 =

2 � 10�5 and Ka2 = 10�4 for 10�3 M KNO3; Ns = 3� 10�18 sites/m2).

Figure 10. Calculated surface charge as a function of pH and KNO3

concentrations (Ka1 = 1.5 � 10�4 and Ka2 = 10�5 for 10�1 M KNO3;Ka1 = 2 � 10�5 and Ka2 = 10�4 for 10�3 M KNO3; Ns = 3 � 10�18

sites/m2).

Figure 11. Calculated electrical and chemical components of the freeenergy of formation of the ionizable surface as a function of pH andKNO3 concentrations (Ka1 = 1.5 � 10�4 and Ka2 = 10�5 for 10�1 MKNO3; Ka1 = 2 � 10�5 and Ka2 = 10�4 for 10�3 M KNO3; Ns = 3 �10�18 sites/m2).



below the isoelectric point (or pHiep). The advancing watercontact angle is a maximum at the pHiep, decreasing symmetri-cally on either side in a Lippmann-like manner. The change inwettability, for a given pH, became more pronounced withincreasing salt concentration. Using a non-Nernstian model ofthe electrical double layer, the experimental dependence ofcontact angle on both pH and salt concentration was satisfacto-rily predicted.

The outcomes of this investigation are important in manyfields.We have shown that it is possible to alter the wettability of acoated metal oxide surface by simply changing the pH and/or saltconcentration. This has wide ramifications for mineral flotation,pigment dispersion and formulation, as well as microfluidics.

’ACKNOWLEDGMENT

Financial support from the Australian Research Council Spe-cial Research Centre Scheme is gratefully acknowledged. Fruitfuldiscussions with Maarten Biesheuvel are warmly acknowledged.

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