PRISM theory atomistic

The outline of the paper is as follows. In Sect. 2 we describe the basic RISM and PRISM formalisms, and the fundamental approximations invoked that render the polymer problem tractable. The predicticms of PRISM theory for the structure of polymer melts are described in Sect. 3 for a variety of single chain models, including a comparison of atomistic calculations for polyethylene melt with diffraction experiments. The general problem of calculating thermodynamic properties, and particularly the equation-of-state, within the PRISM formalism is described in Sect. 4. A detailed application to polyethylene fluids is summarized and compared with experiment. The develojanent of a density functional theory to treat polymer crystallization is briefly discussed in Sect. 5, and numerical predictions for polyethylene and polytetrafluoroethylene are summarized. 

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]. 

In this section we examine athermal binary mixtures using PRISM theory. Tests of both the structural and thermodynamic predictions of PRISM theory with the PY closure against large-scale computer simulations are discussed in Section IV.A. Atomistic level PRISM calculations are presented in Section IV.B, and the possibility of nonlocal entropy-driven phase separation is discussed in Section IV.C at the SFC model level. Section IV.D presents analytic predictions based on the idealized Gaussian thread model. The limitations of overly coarse-grained chain models for treating athermal polymer blends are briefly discussed. 

Summarizing, the major conclusion of this section is that PRISM theory provides an excellent description of the structure and (constant volume) free energy of mixing of high-density athermal polymer blends composed of the short and modest chain length molecules presently accessible to computer simulation. This has motivated the application of the theory to experimentally relevant situations such as long chain N lO -lO ) and chemically realistic atomistic models. 

Finally, Honeycutt" has applied blend PRISM theory at an atomistic RIS model level to study the effect of tacticity (stereochemical differences) on the phase behavior of a commercially important binary polymer mixture. Tacticity is found to result in significant changes of the computed spinodal boundaries, which serves to again emphasize the importance of monomer structure and local packing on the free energy of mixing. 

It is possible to empirically modify PRISM theory for polyethylene [59] by making the direct correlation longer range by simply adding a power law tail to C(r) beyond some hard core diameter. The power law exponent can then be adjusted to force the theory to yield the correct compressibility. This procedure led [59] to almost quantitative agreement of the theoretical g r) with MD for polyethylene. Unfortunately, this modification to PRISM theory is not useful for atomistic polymer models involving more than a single site since constraints, in addition to the compressibility, are needed to fix the exponents of the various direct correlation functions. 

The infortnation provided in this chapter can be divided into four parts 1. introduction, 2. thermodynamic theories of polymer blends, 3. characteristic thermodynamic parameters for polymer blends, and 4. experimental methods. The introduction presents the basic principles of the classical equilibrium thermodynamics, describes behavior of the single-component materials, and then focuses on the two-component systems solutions and polymer blends. The main focus of the second part is on the theories (and experimental parameters related to them) for the thermodynamic behavior of polymer blends. Several theoretical approaches are presented, starting with the classical Flory-Huggins lattice theory and, those evolving from it, solubility parameter and analog calorimetry approaches. Also, equation of state (EoS) types of theories were summarized. Finally, descriptions based on the atomistic considerations, in particular the polymer reference interaction site model (PRISM), were briefly outlined. 

The broad message of all the atomistic PRISM studies of the linear hydrocarbons is that the theory is capable of an essentially quantitive, ab initio description of melt structure for the structurally simplest case of... 

The Influence of several physical features on the predictions of the PRISM/HTA theory of blends and the simplified SFC and Berthelot models of polymer structure and interactions need to be investigated. These include (i) the effect of atomistic-level structure features such as explicit chain branching, (ii) mixing volume changes and composition-dependent blend packing fraction, (iii) nonideal conformational perturbations, and (iv) possible T-dependent modifications of local packing (beyond HTA). 

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