Analytical models of polymer nucleation

In this thesis we investigate and develop analytic models for polymer nucleation and other barrier crossing problems. Our most broadly appealing method for certain multi dimensional barrier crossing problems is a one-dimensional projection which includes a novel technique to extract rate kinetics from simulations [M J Hamer et al., Soft Matter, 2012, 8, 11396-11408]. The scenarios we expect our method to be potentially useful are situations where barrier crossings are rare, and the dominant mechanism is through a series of unlikely incremental steps. The rate kinetics extraction technique is also reliant on the equilibrium energy barrier being relevant to non-equilibrium system, but is not appropriate when strong kinetic contributions dominate the process, and enable crossings over highly unfavourable energetic pathways. We explore and significantly enhance the Graham-Olmsted (GO) polymer nucleation simulation [R S Graham and P D Olmsted, Phys. Rev. Lett., 2009, 103, 115702], producing a combinatorial calculation to obtain exact energy landscapes from it’s basic stochastic rules of monomer attachment [M J Hamer et al., J. Non-Newton. Fluid., 2010, 165, 1294-1301]. We apply our rate kinetics extraction technique to the GO model and find that for most flow rates in purely long chain melts, nuclei tend to grow along similar paths over energy landscapes. The technique reveals a clear signature when this pattern is disobeyed, as in the case of blends of long and short chain polymer melts, some of which display highly anisotropic growth. In addition, we design several one-dimensional barrier crossing models with distinct characteristics, predicting the average and the distribution of crossing times with great accuracy. That finally enables us to completely describe the GO simulation’s nucleation rates with analytic theory, by presenting a model of polymer nucleation featuring crystal rotation, which vastly impacts nucleation rates when polymer melts are subject to flow