The title is "A Monte Carlo Study on the Effects of Excluded Volume Interactions on the Scattering from Block Copolymer Micelles and Branched Polymers", and was supervised by Prof. dr. scient. Jan Skov Pedersen (Department of Chemistry, University of Aarhus) and Prof. dr. Scient. Ole G. Mouritsen (MEMPHYS-Center for Biomembrane Physics Physics Department, University of Southern Denmark).
Scattering techniques are ideal for investigating the structure of matter. However, it is non-trivial to relate the measurements to structural properties of samplein general. The object of interest in my project was diblock-copolymer micelles. The micelles were modelled as a dense core surrounded by a diffuse corona of the solvated blocks, the chains interacted through hard sphere excluded volume interactions, and chains were furthermore excluded from the core region (as shown on the renderings below).
The method of my Ph.D. project was to perform Monte Carlo (MC) simulations of a diblock-copolymer micelle, in order to obtain the configurationally averaged scattering for the model. The purpose was to use the simulated scattering to formulate and validate a model for the scattering, a model that inturn can then be used to analyse real experimental data.
At a zero-level approximation one can neglect the fact that the corona consists of chains, and assume it is a just radial density profile decaying away from the micellar core. This level of approximation provides core-shell models, and you can get a estimate of the width of the profile using such a model. However, as all chain information has been averaged out so no information is provided about single chain properties. However, my simulation results show that adding a effective single chain scattering expression in the form of a RPA approximation to the core-shell model. This is in effect the scattering one would get from a semi-dilute solution with a radial concentration profile.
The new model provides a very accurate representation of the micellar scattering within the statistical errors for reduced surface coverages less than one, and a very good fits are obtained for all the simulated surface coverages (e.g. surface coverages less than 5). This result is obtained and validated for micelles (with a spherical core). However, the instantanious density distribution of any tethered chain structure can be regarded as an average density distribution, and an instantanious density fluctuation distribution. Thus the scattering can be regarded as arrising from the Fourier transform of these two distributions. And a fluctuation-dissipation theorem relates the zero-mode Fourier component of the density fluctuation distribution to the osmotic compressibility of the system.
Hence, the new model provides radius of gyration, corona osmotic compressibility/corona apparent second osmotic virial coefficient, as well as information about the shape of the radial profile. The model should furthermore be easily generalizable to any tethered chain structure, where chains are not stretched too much, and concentration is locally in the dilute/semi-dilute regime such that an RPA approximation is valid.