Polymer statistics under confinement and multiple scattering theory for polymer dynamics and elasticity
In this dissertation we report new theoretical results—both analytical and numerical—concerning a variety of polymeric systems.
Applying path-integral and differentiable manifolds techniques, we have obtained original results concerning the statistics of a Gaussian polymer embedded on a sphere, a cylinder, a cone and a torus. Generally, we found that the curvature of the surfaces induces a geometrical localization area. Next we employ field theoretical (instanton calculus) and differential equations techniques (Darboux method) to obtain approximate and exact new results regarding the average size and the Green function of a Gaussian, one-dimensional polymer chain subjected to a multi-stable potential (the tunnel effect in polymer physics).
Extending the multiple scattering formalism, we have investigated the steady-state dynamics of suspensions of spheres and Gaussian polymer chains without excluded volume interactions. We have calculated the self-diffusion and friction coefficients for probe objects (sphere and polymer chain) and the shear viscosity of the suspensions. At certain values of the concentration of the ambient medium, motion of probe objects freezes. Deviation from the Stokes-Einstein behavior is observed and interpreted.
Next, we have calculated the diffusion coefficient and the change in the viscosity of a dilute solution of freely translating and rotating diblock, Gaussian copolymers. Regimes that lead to increasing the efficiency of separation processes have been identified.
The parallel between Navier-Stokes and Lamé equations was exploited to extend the effective medium formalism to the computation of the effective shear and Young moduli and the Poisson ratio of a composite material containing rigid, monodispersed, penetrable spheres. Our approach deals efficiently with the high concentration regime of inclusions.
0759: Fluid dynamics
0794: Materials science