Ellipsometric study of critical adsorption at the surface of a polymer solution: Evidence for a slowly decaying interfacial profile

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Abstract
We have measured the coefficient of ellipticity ρ̄ of light reflected at the free liquid surface of solutions of polystyrene (M̄w=110 000) in cyclohexane near the upper critical solution point of the system. At the critical composition φc it is observed upon approaching the critical solution temperature Tc from above that the ellipticity exhibits a finite maximum (ρ̄max) about 0.4 K above Tc. This behavior can be explained semiquantitatively in terms of the increasing width of the interface, which is proportional to the correlation length ξ of composition fluctuations in the bulk liquid and diverges with ξ on approaching Tc. The calculation of ρ̄ starts from a dielectric profile function ε(z) which models the short-ranged number density profile of the surface and the superimposed slowly decaying composition profile from the surface into the bulk solution. The ellipticity is obtained by a numerical algorithm originally developed for calculating the reflection properties of stratified dielectric media. The temperature dependence of ρ̄ for samples of concentrations higher and lower than φc, above and below the phase separation temperature, is also discussed in the light of these calculations.