Monte Carlo and mean field studies of polymers in solution

Pepin, Marc (1999) Monte Carlo and mean field studies of polymers in solution. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

This thesis presents a comprehensive study of the structure and physical properties of polymers in solution. The focus is on Monte Carlo (MC) simulations. The results are compared with mean field theoretical predictions and used to study the limitations of the mean field theories. -- Four distinct systems are investigated. The first one consists of A-b-? diblock copolymer crew-cut micelles in .4 solvent. The relatively long B block is incompatible with the solvent and forms the core of the micelles, and the relatively short A block forms a thin corona. Results from simulations for the size of the core as a function of the molecular weight of the B block are compared with simple mean field theories in the literature and extensions in this thesis. They support the argument that the weaker dependence observed in recent experiments is a non-equilibrium effect. -- When a small amount of ? homopolyrncr is added to the block copolymer solution, it can be solubilized within the micelle cores and swell the micelles, or separate into a macrophase with the copolymers at the homopolvmer-solvent interface and/or in micelles. Results from Monte Carlo simulations show a threshold volume fraction of homopolymer below which the homopolymer is solubilized within the micelle cores and above which macrophase separation occurs. These results are in qualitative agreement with previous experiments and a simple mean field theory. -- In the third system, one end of each polymer is end-tethered to a surface and the remaining section of the polymer stretches into good solvent forming an end-tethered layer. The fourth system includes free polymer in solution. The focus of this work is on system regimes which correspond to those studied in most experiments. In both systems, the results of the MC simulations agree well with those of the numerical self-consistent field (NSCF) calculations for surface concentrations above a threshold. A scaling analysis of the layer thickness shows that the systems arc not in the limit of high molecular weight and highly stretched chains. Furthermore, in systems with relatively high molecular weight free polymers, the degree of penetration of the free polymer into the end-tethered layer is greater than predicted by asymptotic SCF theories, although still less than observed in recent experiments.

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