Statistical Mechanics of Supramolecular Self-Assembly in Soft Matter Systems

In this thesis, unusual phase transitions in liquid crystals formed from compounds with novel shapes and polymers are investigated using different techniques including, statistical modelling, Monte Carlo and molecular dynamics simulation. An unusual phase transition, between two columnar phases of the same hexagonal symmetry, has been discovered in a liquid crystal formed from taper-shaped Minidendrons. This unique transition requires a quantised drop in the number of molecules in the columnar cross-section on heating. A mean field theory is developed which models a single self-assembled column as a one-dimensional Ising spin chain. Dominant energetic terms are calculated and fed into the theory, accompanied by small mean field terms. Close quantitative agreement is found between theory and experiment, providing an elegant description of the first-order nature of the transition. Next, a nanometre-scale square tiling in X-shaped liquid crystal compounds has been achieved with zero in-plane expansion. A previously unseen order-disorder transition, between a two-colour segregated chessboard phase and a single-colour mixed phase, has been observed on heating. The transition is a close real-life example of the 3d Ising model. Monte Carlo simulation is performed, considering important interactions inside the nano-compartments. The results for different lattice sizes in simulation, when compared to experimental data, show how kinematic effects dominate within the liquid crystal. Then the newly observed crystallisation behaviour of isotactic polypropylene, at large undercoolings, has indicated an additional mesophase appears which overtakes the ordered-phase growth. Their competition results in a kinetic barrier, similar to that observed in folded n-alkanes, whereby the extended form is blocked by the attachment of folded chains. This process is called self-poisoning. Using a 1d solid-on-solid model the two-step process of mesophase attachment and subsequent meso-order conversion required to grow the ordered form is studied. Monte Carlo simulation is used to study the importance of neighbouring interactions and better fit the experimental data. Finally, it is well known that a two-dimensional crystal melts before a three-dimensional one. Adsorbed model polyethylene monolayers however are exceptional and are found recently to melt up to 80K above the bulk melting temperature. Atomic force microscopy studies have shown unusual pre-melting behaviour in graphite adsorbed ultra-long n-alkanes. The monolayers resist melting by gradually disordering from their ends inwards, to over half their extended length, before finally melting. Molecular dynamics simulations are performed, at different temperatures, by leveraging a new coarse-grained model of bulk polyethylene. The results show remarkable agreement with AFM images, providing new insights into polymer melting.