No description available.

After a brief introduction to the problem of directed polymers in a random medium, several aspects of the problem are addressed in more detail. It is possible to show that, in high enough dimension and above a certain temperature, a phase exists in which the free energy is given by the annealed free energy, with probability one. The proof of this statement is extended to obtain upper and lower bounds on the temperature transition between this phase and a low temperature phase and hence prove the existence of the phase transition. The mean field solution is reviewed and a method of obtaining high dimension expansions around it is presented. The method uses the idea of 'n-tree approximations' as a systematic way of including the correlations present in finite dimensions. Using this approach 1/d expansions are obtained for the free energy, transition temperature, transverse fluctuations and overlaps. The results are consistent with the existence of a finite upper critical dimension above which the behaviour is of a mean field nature. Directed polymers are then considered on disordered hierarchical lattices. On these lattices the problem reduces to the study of the stable laws that occur when one combines random variables in a nonlinear way. Recursion relations for various properties of the system are obtained which are studied using numerical and analytical techniques. It is possible to obtain a perturbative expansion for the free energy, overlaps and non-integer moments of the partition function. Finally, a generalisation of the standard directed polymer problem is considered, in which one allows the walks to contribute positive and negative weights to the partition sum. The solution of the mean field limit of this problem is obtained indirectly, by using the relationship between the mean field directed polymer problem, the random energy model (REM) and the generalised random energy model (GREM). Numerical simultions are presented which give good confirmation of the analytical predictions. It is observed that in solving this generalised polymer problem one has also obtained a formula for the largest Lyapounov exponent of a product of large, sparse random matrices.

A short review is given of the theoretical and technological importance of molten salts. The structure of several molten salts has been studied using. Neutron diffraction and the equipment used to carry out neutron diffraction experiment at a high temperature is described. Total structure factors have been obtained for the molten forms of KC1, CaCl2 and TiCl4, and the limited structure information revealed by the Fourier transform of these data is discussed in terms of earlier work on these and similar systems. More detailed information may be obtained by using the technique of isotopic substitution in order to obtain partial structure factors. The difficulties in extracting partial structure factors for such experiment mean that a direct method is unlikely to be possible and the algorithm which was developed to enable a solution to be found is described. Partial structure factors have been obtained for molten NaCl at 875°C and 1075°C, and also for molten BaCl2 at 1025°C. The relationship between the present work and earlier theoretical studies is discussed.

No description available.

The aim of this research was to investigate intercomponent motion by employing systems where the motion, although difficult to observe directly, has an observable effect on a measurable property in the systems of study. The initial target of this research was to synthesise a [2]polyrotaxane. On cleaving a removable stopper the macrocycle would be free to translate along the backbone of the polymer chain before being irreversibly lost to the system in solution. The initial research presents the attempts to functionalise a rotaxane auxiliary with a polymer chain, firstly by Atom Transfer Radical Polymerisation (ATRP) of a rotaxane initiator, and then by attaching a poly(ethylene glycol) monomethyl ether chain to a rotaxane auxiliary. The design and application of a new rotaxane template motif is also presented. An alternative approach to the study of intercomponent motion is then presented. A series of symmetrical molecular shuttles, defined as a [2]rotaxane comprised of two identical stations that are separated by an alkyl chain, was synthesised. The macrocycle in such systems is known to ‘shuttle’ between the two stations, spending roughly half the time on each station, and this rate can be observed and measured. By reducing the length of the alkyl chain between the two stations, a faster rate of shuttling between the stations was observed. The series incorporated shuttles with different length alkyl (C2, C4, C6, C8, C10, C12) spacers, different stations and different macrocycles. Shuttling or site exchange rates were measured by ¹H Nuclear Magnetic Resonance using Spin Polarisation Transfer by Selective Inversion Recovery (SPT-SIR) technique. We attempt to use the experimental results to validate a theoretical model for the intercomponent motion. Finally a study of a unique tristable molecular shuttle is presented. This unique system displays some of the unanticipated behaviour that highlights our incomplete understanding of interlocked systems.

A large program of ab initio studies of conjugated molecules has been completed. A major point of interest was the molecular geometry in a number of planar and nonplanar cases. The method was first applied to small molecules of known geometry, and then to large systems including cyclo-octatetraene, the larger annulenes, and various 7- and 9-membered ring heterocycles.

No description available.

Using Raman lineshape analysis and dielectric relaxation techniques, the reorientation dynamics of single molecules in partially disordered phases is studied. Reorientation correlation functions for a prototypical isotropic liquid <i>CS</i>₂ are presented over a broad temperature range. Calculated values of the integrated correlation time, rms intermolecular torque and collision frequency suggest the onset of substancial local structuring in the liquid phase on cooling to below 220<i>K</i>. An <i>ab initio</i> DFT computer simulation shows that the intermolecular torque arises from a strong dipole moment interaction created by the bending mode vibration of <i>CS</i>₂ and by a weaker dipole moment interaction which oscillates on a much faster time-scale due to the anti-symmetric stretch vibrational mode. A solvation dynamics study of <i>CS</i>₂ in cyclohexane provides the first observation of the free-volume effect occurring at the isotropic-plastic crystal phase transition. Reorientation correlation functions are presented for various members of the nCB [4-n-Alkyl-4'-Cyanobiphenyl] homologous series in the isotropic phase. Two distinct relaxation processes are observed; A very fast intra-molecular relaxation mechanism assigned to the flexibility of the anisotropic molecules, and a slow exponentially-decaying rotational-translational relaxation process with a complex temperature dependence. The results of dielectric relaxation studies under high pressure of two liquid crystals (6PCH [4-trans-4-n-Hexyl-Cyclohexyl-Benzonitrile] and 8CB) are presented. The extraction of reorientational activation parameters in the isotropic, nematic and smectic A phase allows the formulation of a reorientational model. Steric effects determine the predominant relaxation process. Increasing the molecular alignment, reduces the steric interaction and facilitates molecular reorientation about the short-molecular axes, though molecular flexibility and dipole-dipole interactions also play a role. The order parameter in the nematic phase is seen to be strongly dependent on the rigidity of the constituent molecules.

The aim of this work was to develop an experimental tool to perform flow-sheeting tasks throughout the course of chemical process design. Such design proceeds in a hierarchical manner increasing the amount of detail in the description of the plant, and, correspondingly, in the mathematical models used to describe the plant. The models range from the simplest overall mass balance to rigorous unit models, and the calculations required in the course of a design may include the modelling of the complete plant or any of its constituent parts at any level of detail between these two extremes. Object oriented programming has been used to represent the hierarchy of units required throughout a hierarchical design. A flexible modelling tool requires that models compatible with both the designer's intention and the context of the design are created. Sets of equations are defined in a generic form independent of process units with their selection as part of a model being dependent on the function and context of the unit being modelled. The expansion of the generic equation descriptions is achieved with reference to the structure of the unit, e.g. number of inlets and outlets, while the context of an equation determines the form of the equation to be applied, e.g. ideal or non-ideal behaviour. Equations are, therefore, represented as relations between a process item and its structural and contextual properties. An increase in modelling flexibility is obtained by allowing the designer to interact with generated models. Different sets of equations can be selected within constraints imposed by the system. At a lower level, terms in individual equations can be modified for particular applications. In chemical process design, many different analyses are performed. To demonstrate the application of different tools to a central model, the modelling system has been incorporated within a process synthesis framework. The application of the system to simple design case studies is described.

Molecular Dynamics simulations have been carried out on systems of increasing complexity and biological relevance, in particular aqueous solutions of ions and peptides, in order to establish the local association patterns of solute and solvent molecules, as well as the structure formed by the solvent around the solvated ions/molecules. To account for quantum effects not readily observed in classical MD, ab initio Car-Parrinello simulations have been carried out. To establish a connection with experimental findings and thus underpin simulation results, techniques were developed to compute and refine structure factors from simulations to compare with experimental scattering data. Based on these findings, water models’ qualities as a solvent have been evaluated, resulting in a firm disinclination to the TIP3P model. Further tools to quantify local structure have been developed and implemented, including the development of an order parameter to gauge the four-fold co-ordination of water in pure and mixed form as a function of a parameter of interest, here temperature, and special density calculations to visualise the local neighbourhood of molecules. A key objective was to elucidate previously disputed areas in the fundamental findings surrounding the systems in question. This has been achieved in the case of aqueous solution of L-proline with regards to the formation of macromolecular association and the formation of intermediate structure, as well as the question of close ion contact and local ion solvation structure and co-ordination of aqueous NaCl. Beyond that, new insight into the mechanism of exchange of members of the first solvation shell of Na, as well as into the molecular mechanism based on the hydrogen bonding pattern of inter-proline and proline-water association as a facilitator to the cryoprotectant nature of proline was gained. Finally, the nature of the helix formed by the gp41 polypeptide in water was expounded.