The Surface-Induced Ordering of Triblock Copolymer Micelles at the Solid−Liquid Interface. 2. Modeling

Previously, we have shown from neutron reflectometry that the surface-induced ordering of triblock copolymer micelles in aqueous solution at the hydrophilic surface of quartz can be modeled as solid spheres with and without tethered Gaussian chains at a structureless hard wall. In this article, we present a detailed account of the necessary steps for obtaining the density profile of the ordering of micelles at a hard wall from specular reflectivity data. A numerical expression for the density of hard spheres at a hard wall, which is equivalent to the center distribution of the hard spheres, is obtained from Monte Carlo simulations valid in the hard-sphere volume fraction range from 0.05 to 0.4789. By convoluting the center distribution of the hard spheres with the projected scattering length density of the solid sphere with or without tethered chains, a five parameter expression is obtained from which we can fit the neutron reflectivity profiles. The presented model is generally applicable to other systems interacting through a hard-sphere potential close to a nonattractive planar surface.