This paper attempts to improve several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the Gibbs formalism for conventional statistical mechanics. This then permits the replacement of ‘phantom chains’, i.e. long polymer molecules with the fictitious property that they experience no forces except at cross link points and are transparent to one another, by realistic molecules which do experience forces and which can become entangled. The crosslinked points are no longer assumed to deform affinely with the gross behaviour of the solid. Under the simplest conditions forms like the classical are recovered but with a different coefficient, and the term representing the degrees of freedom lost by crosslinking, over which the classical theories are in dispute, is found to lie between the previous values in a formula which can reproduce the classical results by making different assumptions. The entanglements give rise to more complicated forms than the classical sum of squares of strain ratios, which under certain circumstances can reproduce the Mooney-Rivlin term which when added empirically to the free energy usually improves the fit with experiment. The general expression is complicated, but is nevertheless an explicit function of the density of crosslinks, the density of the rubber and the interchain forces.

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The control of exposure to welding fume is necessary to meet health and safety obligations. The work reported here examines the fundamentals of welding-fume formation. A physical chemistry model of the metal vapour mechanism for fume formation has been developed for non short-circuiting transfer gas metal arc welding (GMAW). The model includes the important contribution made by direct condensation of metal vapour onto the weldpool and workpiece, in removing a substantial fraction of the fume. The model shows that droplet size and wire feed speed control the fine fume formation rate. The understanding developed so far, indicates that the smaller the detached droplet size, the lower the total fume formation rate. The physics behind this is explained. The model gives an insight into how process modification might be used to control fume at source. Control at source is believed to be the most cost-effective and energy-efficient technique for dealing with welding fume. It is anticipated that the understanding gained from this project will be applied to determine the practical limits for the control of welding fume at its source.

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