The preparation of carbon fibres: a study of the physics and chemistry of the preparation of carbon fibres from acrylic precursors

High strength, high modulus carbon fibres are becoming increasingly important as high performance engineering materials. This thesis describes how they may be prepared by heat treatment from filaments spun from polyacrylonitrile and its copolymers. The chemistry of the first stages of heat treatment is very important in controlling the mechanical properties of the carbonised product. A cyclisation reaction has been found to be responsible for the relatively high thermal stability of pyrolysed polyacrylonitrile, but without oxidation the fibres degrade and fuse. An initial oxidation stage is, therefore, essential to the preparation of fibre of high orientation. The cyclised product of pyrolysis is probably a poly 1,4 dihydropiridine and oxidation converts this to aromatic structures, and cyclised structures containing carbonyl and other oxygenated groups. Oxidation is found to assist the carbon fibre preparation process, by producing a product which condenses at an earlier stage of heat treatment, before fusion can occur. Carbon fibre strength and modulus are dependent upon producing a highly oriented crystal structure. While oxidation of the polymer stabilises the fibre so as to prevent disorientation, further large increases in orientation, with a commensurate improvement in strength and modulus, can be obtained by stretching at temperatures above 1,700 °C. This process is analogous to the way fibre orientation is increased by the stretching of the precursor. A lamellar graphite structure can be created in high temperature fibre, by carefully controlling the degree of oxidation. This type of graphite can produce very high values of Young's modulus. More often, however, graphite fibre has a fibrillar fine structure, which is explicable in terms of continuous graphite ribbons. A ribbon model is the most satisfactory representation of the structure of carbon fibre, as it explains the mechanism of the development of long range order and the variation of Young's modulus with crystalline preferred orientation.

Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.