Surface Tension of Charge-Stabilized ColloidalSuspensions at the Water-Air InterfaceLichun Dong and Duane Johnson*Department of Chemical Engineering, University of Alabama,Tuscaloosa, Alabama 35487-0203Received June 25, 2003. In Final Form: September 22, 2003Inthispaper,weshowthatthesurfacetensionofcharge-stabilizedtitaniasuspensionsstronglydependson the particle concentration. The surface tension first decreases significantly with an increase in theweightpercentandthenincreaseswithafurtherincreaseintheweightpercent.Thermodynamicargumentsare used to explain the initial decrease in the surface tension for lower particle concentrations. For higherconcentrations, it is hypothesized that the capillary forces acting between the immersed particles at theinterface cause the increase in the surface tension.IntroductionSuspensions or dispersions of particles in a liquidmediumareubiquitous. Controlofthe structureandflowpropertiesisvitaltotheprocessingandpropertiesofsuchsuspensions. For example, during the coating of disper-sions,thesurfacetensionisoftenanimportantparameterthat determines the film properties. Over the past fewyears,therehasbeenanincreasinginterestinthebehaviorofsolidparticlesatliquid surfaces in theabsenceofothersurface-active materials such as surfactants or polymermolecules.When the surface tension of a viscous fluid is notuniform,spatialgradientsofthesurfacetensionwillcreatea surface shear that can only be balanced by shear flowin the adjacent surface layers. The general phenomenonis known as Marangoni flow, and the surface tensiongradient driving the flow can be caused by temperaturegradients (thermocapillary flows), surface concentrationgradients (solutocapillary flow),1and electric charges(electrocapillaryflows).2-4Recently,CassonandJohnsonhaveshownthatsimplecolloidal particlescanalsocreatecapillaryflows.5Theydemonstratedthecapillaryflowfora variety of particles: 5 and 50 µm polyamide particlesand 5 µm silver-coated silica particles. In their paper,theyhypothesizedthattheaggregatesofcolloidalparticlesat the interface create a localized decrease in the surfacetension. These aggregates therefore generate surfacetension gradients that cause significant capillary flows.Therehavebeenseveralinvestigationsoftheadsorptionof particles at the water-air or water-oil interface.6-8Results show that the particles are strongly attached tothefluid(R)-fluid(β)interface,whethertheparticlesarehydrophobicorhydrophilic.Considerasphericalparticle(s) of radius r that is initially in phase β and issubsequentlyadsorbedtotheRβ interface(Figure 1).TheinterfacessR,sβ,andRβ have interfacialtensionsγsR,γsβ,and γRβ, respectively. Ignoring the line tension acting atthe three-phase contact line (Rβs), adsorption of theparticles at the interface results in an area sβ being lostbut being replaced by an equal area of the sR interface.More importantly, however, an area of the Rβ interface(normally of high tension) isalso lost due to the presenceoftheparticles,andthisareadependsonthecontactangle,θ.Assumingtheparticleissmallenoughsothattheeffectof gravity is negligible, the energy E required to removethe particle from the interface to the R phase or β phaseis given bywhere θ is the contact angle based on the β phase.9Paunov et al. investigated the adsorption ofindividualparticles on a liquid-fluid interface and developed athermodynamic approach to the adsorption of sphericalcharged colloidal particles on the water-air interface.10They ignored the entropic contribution of the change onthe free energy and derived the adsorption equation forthe case when the air-water interface is not charged.Their results show that the total free energy favors theadsorptionofthe particlestotheair-waterinterfaceandthe formation of the double layer at the particle surfacecan make the particles more hydrophobic (a larger truecontact angle θ). On the other hand, collective effects ofchargeaccumulationorchargedisplacementcanregulateor suppress the adsorption.When particles are placed at an interface, they aretypically classified into two categories: flotation or im-(1) Nepomnyashchy, A. A.; Velarde, M. G.; Colinet, P. InterfacialPhenomenaandConvection;Brezis,H.,Douglas,R.G.,Jeffrey,A.,Eds.;Chapman & Hall/CRC: New York, 2001.(2) Saville, D. A. Annu. Rev. Fluid Mech. 1997, 29, 27.(3) Casson, K.; Johnson, D. Phys. Fluids 2002, 14 (8), 2935.(4) Johnson,D.ElectrocapillaryFlows;Narayanan,R.,Ed.;Springer-VerlagLecture Notes inPhysics;Springer-Verlag: New York, 2003(inpress).(5) Casson, K.; Johnson, D. J. Colloid Interface Sci. 2001, 242, 279.(6) Horvolgyi, Z.; Mate, M.; Daniel, A.; Szalma, J. Colloids Surf., A1999, 156, 501.(7) Schwartz, H.; Harel, Y.; Efrima, S. Langmuir 2001, 17, 3884.(8) Ghezzi, F.; Earnshaw,J. C.;Finnis, M.;McCluney, M. J. ColloidInterface Sci. 2001, 238, 433.(9) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21.(10) Paunov, V. N.; Binks, B. P.; Ashby, N. P. Langmuir 2002, 18,6946.Figure 1. Schematic diagram before (a) and after (b) theadsorption of a spherical particle to the interface. After theadsorption of the particle at the interface, an area of the sβinterfaceisreplacedbyanequalareaofthesR interface.Atthesame time, an area of the Rβ interface is also lost.E ) πr2γRβ(1 - cos θ)2(1)10205Langmuir 2003, 19, 10205-1020910.1021/la035128j CCC: $25.00 © 2003 American Chemical SocietyPublished on Web 10/31/2003mersion, where the particles are freely floating at theinterface or partially immersed (confined) into a liquidlayer,respectively(Figure2).Forbothconditions,lateralcapillary forces are created by the deformation of theinterface. For flotation forces, the particles are attractedby the hydrostatic pressure created by the interfacedeformation. This force is proportional to the radius tothe sixth power and is therefore negligible for particlesless than 10 µm.11However, for the immersed particles,theparticleattractionisrelatedtothewettingpropertiesof the particle surface. The immersion force depends onthe square of the particle radius and is significant forparticles as small as a few nanometers.12The interactionenergybetweenthesetwoimmersedparticlesisestimatedby eq 2.whereγRβisthesurfacetension,Q) rsin(θ)isthecapillarycharge of the particle, r is the radius of the contact line,θ is the meniscus slope angle at the contact line, q ) ∆Fg/γRβ, ∆F is the density difference between the two fluids,g is gravity, and K0is the modified Bessel’s function ofzero order. The
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