Theoretical study of two problems in polymer physics.

(1) Static Structure Factor and Shape of Reptating Telehelic Ionomers in Electric Fields: We calculate the static structure factor of reptating block copolymers which have a neutral middle block and charged ends. In the presence of an electric field, these telehelic ionomers reptate randomly in their "tubes" but the latter tend to orient along the field axis. If the two ends have different charges, competition between many length scales occurs. The resulting scattering function shows unusual features that are normally characteristic of highly polydisperse mixtures. (results published in Macromolecules, volume 26, number 8, pages 1905-1913). (2) Reptation, Entropic Trapping, Percolation and Rouse Dynamics of Polymer Chains in "Random" Environments: We report the simulation study of the dynamics of linear polymer chains in two-dimensional periodic arrays of obstacles where a fraction 1-c of obstacles are removed. We find Rouse dynamics when c is small, reptation dynamics when c = 1, as well as two other regimes between these two limits. Surprisingly, the diffusion coefficient actually decreases when we start removing obstacles. A study of the sites visited by the polymer molecules indicates that the latter are then entropically trapped in large but isolated voids. When about 60% of the obstacles are removed, the large voids form a percolation path and diffusion is easier when further obstacles are removed. Our results thus predict that the diffusion coefficient can vary in a non-monotonic way with concentration