A theoretical investigation of the relaxation of random linear polymers and of the elasticity of single polymer chains

Polymeric and biological disordered materials are characterized by unique dynamical features. Although the details of the physical dynamical mechanisms are different, the disorder seems to be a common cause for non-exponential relaxation in these materials. The numerous experimental results which reveal a rather universal form of relaxation, namely a KWW or stretched exponential type function ( e-t/tb , beta < 1) have not yet been adequately explained by a unified theory. Such a disordered polymeric system is studied in this thesis and its relaxation is analysed in the framework of the well known Rouse model. This model allows for exact solutions and different types of disorder are analysed here. Exact solution and a good control over the disorder provide us with a fundamental description of the transition towards KWW behaviour. Our results favor a theory of relaxation based on parallel relaxation modes.; The second part of the thesis focuses on the elasticity of a single polymer chain. The correct statistical mechanical ensemble associated with an experimental measurement probing single chain properties is an issue of great interest given the breakthroughs in the development of methods which can directly probe single chain mechanics. The complicated force-extension expressions obtained for a chain subjected to spatial constraints are available only as approximations, even for ideal models. The use of such relations in theoretical studies as well as in computer simulations is cumbersome and time consuming. A systematic method to construct simpler but still accurate expressions for the force function is given. As we demonstrate, these approximations can provide expressions with an arbitrary degree of accuracy and the proper mean statistical properties.