Effect of annealing cold-drawn polystyrene and polymethylmethacrylate below Tg

Annealing of both cold-drawn atactic polystyrene and cold-drawn poly-methylmethacrylate at temperatures ranging from 50°C to their respective T_g's and for times ranging from 1 to 6 days gradually but completely eliminates the orientation arcing from the wide-angle X-ray diffraction pattern but induces only ～25% recovery of the cold-drawn deformation (as calculated from dimensional shrinkage). Analogous studies show that the birefringence of cold-drawn polystyrene is reduced by 57% during the annealing treatment. The results are evidence for segmental molecular motion below T_g and suggest that the molecular alignment responsible for the wide-angle X-ray diffraction arcing is not necessarily the same molecular orientation required for dimensional recovery. We have tentatively interpreted these results in terms of our recently proposed structural model consisting of both ordered domains and connecting disordered regions in the amorphous polymeric solid state. Annealing below T_g can produce chain backbone motion within the disordered regions and cause disorientation of the aligned ordered domains brought about by the initial cold-draw process.     

Two-dimensional Quantum Random Walk

We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129–161, 2002).     

Anionic polymerization with expansion in volume

New bicyclic and tricyclic compounds have been synthesized by the Lewis acid-catalyzed condensation of epoxides with cyclic acid anhydrides or cyclic bislactones. These materials take part in the anionic addition polymerization of amine-functional polyamides with diepoxides, and modify the shrinkage that is characteristic of the reaction. It is possible to control the extent of shrinkage by choosing an appropriate comonomer and by adjusting the concentration of this material in the reaction mixture.