Molecular models, polymeric systems, Monte

Experimental study of infinitely-dilute polymers Is difficult and few direct measurements have been reported for configurational properties of isolated polymers in solution. Molecular simulation offers an alternate powerful method for studying the properties of model polymeric systems, including infinitely-dilute polymers in solution. Computer simulations have been performed in several cases for examining the conformational behavior of isolated, uncharged polymers [28-30] and, on a more limited basis, for studying isolated, fu/Zy-zon/zec/polyelectrolytes [31, 32]. Hooper et al [14, 15] recently performed Monte-Carlo computer simulations for a lattice model of an isolated, partially-ionized polyelectrolyte. Here, we present some of the primary results from references 14 and 15, and discuss how these results can improve our understanding of phase behavior in aqueous/polymer systems. 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Science is in incessant evolution it grows with more precise theories and better instrumentation. The thermodynamic theories of polymers and polymeric systems move toward atomistic considerations for isomeric species modeled mathematically by molecular dynamics or Monte Carlo methods. At the same time good mean-field theories remain valid and useful—they must be remembered not only for the historical evolution of human knowledge, but also for the very practical reason of applicability, usefulness, and as tools for the understanding of material behavior. 

Monte Carlo methods have seen important advances over the last decade. These advances have permitted calculations that just a few years ago were beyond the possibilities of molecular simulations. For conciseness, the discussion presented in this article is limited to the methodological aspects of the simulation of continuum space polymeric systems. Given the nature of this encyclopedia, cited articles have been chosen for their pedagogical and scientific value, rather than for the assignment of priorities. Little reference is made to the numerous applications that have been reported in the past. It is also important to point out that much of the literature on Monte Carlo studies of polymers has been concerned with lattice models, and that several reviews of such woric have appeared in the past. While techniques employed for either on- or off-lattice systems are, to some extent, transferable, a few recent reviews have specifically addressed some of the intricacies that arise when simulating polymers in a continuum " reference to these sources for specific topics will be made whenever appropriate. 

With the development of molecular closures, PRISM theory has shown the ability to predict a x parameter with composition and degree of polymerization dependence that is consistent with simulation results [114]. Smdies of symmetric block copolymer liquids show qualitative agreement with Monte Carlo simulation, but both the R-MMSA and R-MPY closures fail to predict a point of spinodal decomposition for finite degrees of polymerization [73, 74], These results are for the somewhat unrealistic system of a symmetric blend model where each species has the same chain length and site diameter and the interactions between monomers of the same type are purely repulsive while the cross term has an attractive tail. 

---