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The work described in this thesis comprises two distinct components. In the first part, Monte-Carlo computer simulation methods are employed within a finite-size scaling framework to investigate both universal and non-universal behaviour in two scalar models, the 1-d φ<SUP>4</SUP> model and the 2-d Lennard-Jones fluid. In both these models the properties of interest are obtained from studies of the large-length scale configurational patterns via measurements of the probability distribution function (PDF) of the coarse-grained (block) ordering variable. For the 1-d φ<SUP>4</SUP> model, simulations are employed to obtain the block PDF of the spin variable. This function is shown to map onto an analytically-derived expression for the 1-d Ising chain, thus exposing the model's essentially Ising-like character. It is further demonstrated that the corrections to the limiting form of the block PDF reflect system-specific features of the 1-d φ<SUP>4</SUP> model associated with its elementary excitations. In the 2-d Lennard-Jones fluid, the combined use of simulation and finite-size scaling is shown to provide a powerful method for accurately determining the location of the liquid-vapour coexistence curve and critical point. At the critical point, the limiting form of the coarse-grained density distribution is found to collapse onto a previously determined function characteristic of the 2-d Ising model, thereby confirming and clarifying fluid-magnet universality. Clear evidence is also presented for mixing of the temperature and chemical potential in the two relevant scaling fields-a phenomenon responsible for the failure of the law of rectilinear diameter. As an addendum, a discussion is given of the prospects for generalising to fluids, the cluster updating techniques recently developed to reduce critical slowing down in simulations of spin systems.

This Thesis describes the use of synthetic chemistry to investigate mechanisms for controlling molecular-level motion. Initially, the principles that all experimental designs for working molecular machines must follow are elucidated; tracing the development of ideas about molecular-level motion from their genesis, to the modern-day contributions of molecular biology and theoretical nonequilibrium statistical physics. In the rest of the Thesis, these theoretical considerations are applied and extended through the construction and operation of molecular machines based on interlocked molecules. Two simple rotaxane-based examples serve to demonstrate the novel concept of ‘compartmentalized’ molecular machines. Correlating chemical, physical and statistical descriptions of these simple devices with their behaviour, reveals the fundamental mechanistic elements that are involved in the operation of any compartmentalized Brownian machine and suggests how these can be combined to create different types of device. This leads to the construction of a [2]catenane that is the first example of a reversible synthetic rotary molecular motor and which operates via an energy ratchet mechanism. Next, a fundamentally different mechanism is investigated through the construction and analysis of a compartmentalized molecular machine that is the first to operate via an information ratchet mechanism. Finally, the classic stimuli-responsive molecular shuttle design serves as an ideal test bed for investigating a new structural series of rotaxane-based molecular machines that are controlled by redox processes and which show promise for operation at surfaces.

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