Conformational Properties of Polymers and Gels
Abstract
A wide range of connectivity problems in critical phenomena are studied by Monte Carlo and Series Expansion methods. In particular we focus on the conformational properties of linear and branched polymers, modelling these systems by selfavoiding walks and lattice animals respectively. We incorporate corrections to leading scaling behavior and thereby obtain very accurate estimates of the correlation length exponent of the above models in two and three dimensions. Specifically, we identify problems in series analysis experienced by previous researchers in the field and resolve several controversies concerning the values of the critical exponents. Furthermore, we introduce a new model for linear polymer growth that describes more appropriately than the selfavoiding walk model, the growth of a linear polymer chain. For this model, we construct a mean field theory of the Flory type and carry out extensive Monte Carlo and series enumeration studies confirming, roughly, the prediction of the Flory theory. Finally we show, subject to plausible assumptions, that such a model corresponds to the problem of a linear polymer at its theta point. Monte Carlo simulations indicate that data are indeed consistent with such a picture.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT.......125M
 Keywords:

 SERIES;
 MONTE CARLO;
 Physics: Condensed Matter