A Theoretical Treatment of Polymer Solutions and Polymer Blends

这项研究基金由材料研究和化学系资助，旨在提供对聚合物溶液和混合物的描述，这些溶液和混合物具有坚实的统计力学基础，但实验者可以了解当前的结果并设计未来的工作。这项研究涉及利用积分方程式技术对这些体系进行理论描述，目标是了解平衡性质，特别是那些与可混性有关的性质。用晶格模型来描述二元不可压缩混合物和可压缩纯流体已经取得了进展。将在两个方面进行新的研究：进一步发展晶格模型和将这种处理扩展到连续介质模型。格子模型可以解析地求解，可以与模拟结果进行核对，几乎所有的模拟结果都是在格子解上完成的。连续介质模型更接近现实，但解析解是不可能的。将进行%计算来描述液体聚合物及其混合物的性质。这些模型将基于液体的统计力学结果，并补充描述这些材料系统的其他模型。这些结果将对解释实验结果和设计新材料具有重要意义。

This research grant, funded by the Divisions of Materials Research and Chemistry, is aimed at providing a description of polymer solutions and blends which has a solid basis in statistical mechanics, yet is accessible to experimentalists for understanding current results and designing future work. The research involves developing a theoretical description of these systems using integral equation techniques where the goal is to understand equilibrium properties, especially those concerned with miscibility. Progress has already been made using a lattice model to describe a binary incompressible mixture and a compressible pure fluid. New research will be done in two areas: further development of the lattice model and extension of this treatment to a continuum model. The lattice model, which can be solved analytically, can be checked against simulation results, almost all of which are done on lattice solutions. The continuum model is closer to reality, but analytic solutions are not possible. %%% Calculations will be done to describe the properties of liquid polymers and their mixtures. The models will be based on statistical mechanics results for liquids and complement other models describing these material systems. The results will be important in interpreting experimental results and for designing new materials.