Polymeric liquids, density functional theory

The hrst hve chapters (Part 1) present an overview of some methods that have been used in the recent hterature to calculate rate constants and the associated case studies. The main topics covered in this part include thermochemistry and kinetics, computational chemistry and kinetics, quantum instanton, kinetic calculations in liquid solutions, and new applications of density functional theory in kinetic calculations. The remaining hve chapters (Part II) are focused on apphcations even though methodologies are discussed. The topics in the second part include the kinetics of molecules relevant to combustion processes, intermolecular electron transfer reactivity of organic compounds, lignin model compounds, and coal model compounds in addition to free radical polymerization. 

More modem approaches borrow ideas from the liquid state theory of small molecule fluids to develop a theory for polymers. The most popular of these is the polymer reference interaction site model (PRISM) theory " which is based on the RISM theory of Chandler and Andersen. More recent studies include the Kirkwood hierarchy, the Bom-Green-Yvon hierarchy, and the perturbation density functional theory of Kierlik and Rosinbeig. The latter is based on the thermodynamic perturbation theory of Wertheim " where the polymeric system is composed of very sticky spheres that assemble to form chains. For polymer melts all these liquid state approaches are in quantitative agreement with simulations for the pair correlation functions in short chain fluids. With the exception of the PRISM theory, these liquid state theories are in their infancy, and have not been applied to realistic models of polymers. 

The close interrelations among mass, momentum, and energy transport can be explained in terms of a molecular theory of monatomic gases at low density. The continuity, motion, and energy equations can all be derived from the Boltzmann equation for the velocity distribution function, from which the molecular expressions for the flows and transport properties are produced. Similar derivations are also available for polyatomic gases, monatomic liquids, and polymeric liquids. For monatomic liquids, the expressions for the momentum and heat flows include contributions associated with forces between two molecules. For polymers, additional forces within the polymer chain should be taken into account. 

Over the p t several years we and our collaborators have pursued a continuous space liquid state approach to developing a computationally convenient microscopic theory of the equilibrium properties of polymeric systems. Integral equations method [5-7], now widely employed to understand structure, thermodynamics and phase transitions in atomic, colloidal, and small molecule fluids, have been generalized to treat macromolecular materials. The purpose of this paper is to provide the first comprehensive review of this work referred to collectively as Polymer Reference Interaction Site Model (PRISM) theory. A few new results on polymer alloys are also presented. Besides providing a unified description of the equilibrium properties of the polymer liquid phase, the integral equation approach can be combined with density functional and/or other methods to treat a variety of inhomogeneous fluid and solid problems. 

The combination of polymeric density functional methods and PRISM theory for the liquid correlations allow a wide range of closure and inhomogeneous material problems to be studied [109]. Present research involves using this approach to treat at an atomistic level the crystallization of the entire alkane series, and the structure of hydrocarbon fluids near surfaces and interfaces [109]. An alternative, purely integral equation approach to the latter problem is to employ the wall-PRISM theory of Yethiraj and Hall [37]. 

---