The goal of this research is the development of a mathematical theory, models, and computational tools which underpin the design and of macromolecular materials and nano-composites. These materials are comprised of anisotropic molecules (nematic polymers), which undergo a spontaneous disorder-order transition above a critical concentration. Materials made from nematic polymers achieve their properties through the collective molecular alignment structure. Specific molecular elements yield diverse property enhancements, from strength (the Dupont product Kevlar and spider silk), to electrical conductivity (carbon tubes and conducting polymers), to barrier penetration properties (discotic clay platelets). The major technological challenge is to extend results with fibers to other geometries such as films and molds. However, in typical laminar processing flows, the molecular response is highly sensitive to flow type and strength, and to molecular properties such as shape and concentration. In addition to complex dynamics, during flow processing there is a spatial conflict between interior flow response and molecular anchoring conditions at solid boundaries. The result is that instead of a uniform molecular orientational distribution, as in fiber processing flows, film and mold flows always generate morphology on length scales between the molecules and the processing devices. These ubiquitous structures are not understood, either theoretically or experimentally, yet they dictate the effective properties of the end-use materials. The research supported by this award will help to understand the dynamics and structures that occur in typical laminar flows of nematic polymers.
Modern high-performance materials and nano-composites are primarily designed with simple elements, from rod-like to platelet molecules. Remarkable property enhancements have been achieved thus far in laboratory-scale experiments, with increased strength and durability, the ability to shield heat or gases, and to tune electromagnetic wave transmission. The technological challenge is to scale these experimental results to industrially viable processes and materials. The challenge to mathematics and computational science is to build a solid foundation of theory, modeling, and simulation tools from which to design and control the processes and final material properties. The theory of flowing molecules in confined spaces is still unable to predict and control the molecular structure created during flow processing. Yet micron-scale molecular structures always occur in processed films and molds of nano-composites. Furthermore, the bulk material performance properties as well as their failure and damage modes are dominated by the molecular structures generated in processing. The award will support a research program combining theory, modeling, simulations, and comparisons with laboratory data in the dynamics and structure properties of nematic polymer materials and nano-composites in processing flows. These results will be the basis for the next phase of the materials pipeline, where bulk material properties are deduced from the molecule properties.
