Dielectric Friction in Restricted Geometries
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DIELECTRIC FRICTION IN RESTRICTED GEOMETRIES
M. URBAKH AND J. KLAFTER
School of Chemistry, Tel-Aviv University, 69978, Ramat-Aviv, Tel-Aviv, Israel
ABSTRACT
The influence of a solid-liquid interface on the relaxation of a point dipole embedded in the liquid side is discussed. The dielectric friction of a dipole as a function of its distance from a boundary is calculated. The calculations are carried out assuming a nonlocal dielectric function of the liquid, characterized by a typical correlation length which may depend on temperature. The corrections to the relaxation of a dipole due to the presence of a boundary are shown to be small. Larger corrections can be introduced by postulating structural changes in the nature of the liquid near the boundary.
INTRODUCTION A large number of experimental and theoretical studies have been devoted to the understanding of the role of spatial restrictions in modifying the properties of embedded liquids and molecules. Both thermodynamical and dynamical questions have been addressed, i.e. changes in freezing and viscosity as well as chemical reactions and energy transfer properties [1-5]. Also translational and rotational diffusion of probe molecules have been shown to be influenced by the presence of boundaries [1]. It is by now well established that liquids in small confinements differ significantly from bulk liquids. The behavior of molecular systems under geometrical restrictions is of importance in a wide range of problems related to catalysis, microemulsions, polymer solutions, biological membranes and more. In this paper we concentrate on the question of the rotational relaxation of a dipole in a liquid close to a boundary. This problem has been investigated experimentally, among others, by Awschalom et al [2] using optical birefrigence and by Zinsli [3] and more recently by Drake et al [4] using optical depolarization. The common observation has been that in the vicinity of the boundary there is a pronounced change of molecular reorientation time. Awschalom et al. [2], who conducted temperature dependence studies near the liquid freezing point, have inferred from their studies the temperature and pore size dependence of a molecule's rotational time. A detailed microscopic picture for the observed phenomena is still missing. We will study the rotational relaxation of a point dipole within the continuum approach based on the dielectric friction [6] in a liquid which is characterized by a nonlocal dielectric function. The effect of an interface is introduced through the concept of additional boundary conditions [7] which leads to a generalization of the image charges picture [8]. The nonlocal nature of the liquid defines a length scale, A, which is a measure of spatial correlations in the liquid. For instance, in aqueous solutions the correlation length, A, is of the order of the extension of local hydrogen-bonded clusters. This correlation length enables one to introduce temperature into observable quantities at least phenomenologically and creates dipole-boundary dista
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