describe the bulk properties of matter. Intermediate between the microscopic and macroscopic descriptions lies the mesoscopic world characterized by lengths long on a microscopic scale but short on a macroscopic one. Each level generates its own conceptual, theoretical, and computational challenges, but perhaps the most significant challenge lies in providing a bridge between the different levels. Thus, a goal of the complete molecular modeling of materials involves use of molecular theories to compute the property information necessary to describe the processing or performance behavior of the new bulk materials.
Because many theories of polymers in concentrated solutions and bulk rely on single-chain concepts developed and tested in dilute solutions, the understanding of dilute polymer solutions has repercussions throughout polymer science. Hence, dilute solutions of flexible polymers have received much attention in the past 50 years, and as a result many aspects of the average conformation of an isolated polymer molecule are now well understood. Nevertheless, many problems remain, especially for solutions of stiff polymers and their hydrodynamic properties. As the solution concentration increases, these theoretical problems become even more complex, and these properties are less well understood.
Flexible polymer molecules in the undiluted amorphous state generally assume unperturbed random-coil configurations. This fundamental conclusion is derived from both theoretical and experimental studies on very flexible and non-polar polymers. However, many technologically important polymers normally contain considerable numbers of polar atoms or groups and exhibit considerably reduced chain flexibility. Because sufficient chain stiffness and/or orientation-dependent polar interatomic interactions produce anisotropic ordered phases, the embryonic structure of such order is present in amorphous polymers, which are not very flexible or which contain polar groups, as indicated by recent computer simulations. Simulations and theoretical studies are needed, therefore, of the local correlations among such molecules in the amorphous state to guide and interpret suitable experimental studies. An amorphous polymer is a glass below its glass transition temperature, Tg. Such glasses are never in thermodynamic equilibrium, and consequently their properties depend on their thermal and mechanical histories. Although significant efforts have been made recently in both theoretical and simulation studies of the glass transition, and new computational advances have opened the way to simulation of the properties of the glassy state, much more effort is needed to explain the underlying cause of the glass transition,