Phase transitions in polymer solutions and in quantum percolation
Abstract
In this thesis we have studied phase transitions in a polymer solution and also in a two dimensional (2D) disordered system. In our study on the polymer system we present a model in an attempt to understand the observed crossover of a stiff polymer chain with side groups in a solution from its Gaussian (or ordinary random walk) behavior to a self avoiding walk (SAW) behavior. While our analysis based on usual persistent self avoiding walk (PSAW) and renormalization groupn this work does show a sudden onset of the excluded volume effect, much lik show a gradual increase in excluded volume effect, the relaxational method that we have developed ie that observed in the experiment [Murakami et al., Macromolecules 13, 345 (1980)]. We also have studied the transport properties of a 2D disordered system known as quantum percolation using stationary state and dynamical methods. Both methods involve the calculation of the transmission coefficient of a particle that enters through a lead at one side of the cluster and exits through another lead on the other side of the 2D cluster. Using the stationary state method we have shown that the transmission of a quantum particle crucially depends on the local phases of wave function. The states are observed to have high transmission if the local phases of the neighboring sites differ by 0 or ∼ 2π, where as those with a phase difference of ∼ π give low transmission. We have investigated the localization property of the 2D disordered system using both the stationary state and dynamical methods. Our study based on finite size scaling shows that, for a given energy, all states are exponentially localized for a sufficiently large disorder. As the disorder is decreased below a critical value (which depends on the energy of the particle), the particle state makes a transition to a power-law localized regime. A further decrease in disorder, to typically less than 15% (but dependent on energy), appears to result in a second phase transition from the power-law localization regime to an extended state regime.
Degree
Ph.D.
Advisors
Nakanishi, Purdue University.
Subject Area
Condensation
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.