Thermal-Diffusion Driven Concentration Fluctuations in a Polymer Solution

Abstract

Concentration fluctuations in polymer solutions that are in thermal equilibrium are well understood. The intensity of the polymer concentration fluctuations is proportional to the osmotic compressibility and the fluctuations decay exponentially with a decay rate determined by the mass-diffusion coefficient D. Probing these fluctuations with dynamic light scattering provides a convenient way for measuring this diffusion coefficient D [ 1]. It turns out that the nature of the concentration fluctuations is qualitatively different when polymer solutions are brought into stationary nonequilibrium states. Fuller et al. [2] have discussed the enhancement of the concentration fluctuations in polymer solutions subjected to external hydrodynamic and electric fields. In this paper we consider the enhancement of the concentration fluctuations when a polymer solution is subjected to a stationary temperature gradient in the absence of any (convective) flow, that is, while the polymer solution remains in a macroscopically quiescent state. Experimentally this situation can be realized by arranging for a horizontal layer of the polymer solution heated from above. As originally predicted by Kirkpatrick et al. [3] and confirmed by subsequent light-scattering experiments [4,5], a temperature gradient in a liquid induces enhanced temperature and viscous fluctuations that become very long ranged as reviewed by Dorfman et al. [6]. The effect of a temperature gradient on the concentration fluctuations in liquid mixtures was originally considered theoretically by Law and Nieuwoudt [7] and has been investigated by Segre et al. [8], Li et al. [9] and subsequently by Vailati and Giglio [10]. Here we consider the effect of a temperature gradient on the concentration fluctuations in polymer solutions. The advantage of polymer solutions is that the concentration fluctuations provide the dominant contribution to the Rayleigh component of the scattered light and can be readily measured experimentally.