Clausius-Mossotti-Type relation for planar monolayers
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Clausius–Mossotti-Type Relation for Planar Monolayers M. I. Ryazanov and A. A. Tishchenko Moscow Engineering Physics Institute (State University), Moscow, 115409 Russia e-mail: [email protected] Received March 24, 2006
Abstract—The dielectric properties of a quasi-two-dimensional molecular monolayer are analyzed. The dielectric function of the monolayer is expressed in terms of molecular polarizability and monolayer characteristics. The expression is analogous to the well-known Clausius–Mossotti equation for three-dimensional systems. The response of the monolayer to an external field is calculated. The case of a planar array of nanoparticles is also considered. The solution is obtained in the framework of a local-field theory. PACS numbers: 03.50.De, 78.67.-n DOI: 10.1134/S1063776106100049
1. INTRODUCTION The properties of molecular monolayers on condensed-matter surfaces were examined in numerous studies [1–9]. A molecular monolayer on solid surface affects both spectrum of electromagnetic surface waves [10] and reflection of light from the surface [11, 12]. These findings must be taken into account in studies of solid surfaces by near-field optical and ellipsometric methods. The effect of an adsorbed molecular monolayer on surface properties is particularly strong when the external field frequency is nearly resonant with some characteristic frequencies of the monolayer or the dielectric function of the substrate is unity at the field frequency. In these cases, the substrate has a negligible effect on the monolayer, and an isolated monolayer can be considered in the first approximation. A phenomenological model of a two-dimensional layer at the interface between two media was proposed in [13]. In [14], a relationship was found between the local field (called the near field by the authors [15, 16]) and the external plane-wave field incident on the monolayer, but no relationship was found between the monolayer polarization and the macroscopic field. It is interesting to find expressions for the dielectric characteristics of an isolated molecular monolayer as functions of the polarizability and configuration of molecules analogous to the well-known Clausius–Mossotti relations for three-dimensional systems. In this paper, we perform microscopic calculations to derive electromagnetic relations for a monolayer and obtain equations relating the macroscopic and local fields to the external field in the long-wavelength limit.
2. MICROSCOPIC AND LOCAL FIELDS IN MATTER It is well known that the average field acting on a molecule (generally called local field) differs from the macroscopic field obtained by averaging the solution to the microscopic Maxwell equations over the quantum states of atomic electrons and the thermal motion of nuclei. The microscopic field Emic in a monolayer is different from the incident field E0 generated by an external source in vacuum. Relations between the external field E0, the macroscopic field E, and the local field Eloc that lead to the Clausius–Mossotti formula for
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