Light scattering with evanescent waves: Intermolecular interference and the structure factor for an ideal flexible chain at an interacting interface

We report the evaluation of the structure factor for polymer chains near an interface when illuminated with evanescent light. The evanescent light is generated when there is total internal reflection of light at an interface between two dielectric media. We begin with a general virial expansion for the scattering intensity in powers of the polymer surface concentration to define the nature of the extrapolation to the infinite dilution limit, and to thereby extract the structure factor in that limit. The scattering per unit surface area is a function of the chain surface concentration when the polymers are attached to the surface, and a function of the bulk polymer concentration when the chains are distributed throughout the solution. The single chain scattering function is evaluated for Gaussian chains interacting with an impenetrable interface and either terminally anchored to the surface or free to move throughout the solution. The structure factors are obtained for the independent in-plane and out-of-plane scattering geometries, which provide information, respectively, about the chain dimensions parallel and perpendicular to the interface. The dependence of the evanescent wave scattering on such parameters as the scattering angle and the polymer-surface interaction parameter is explained on the basis of the exponential decay of the evanescent wave intensity away from the interface.