Polymer system, multichain

Simulating the Dynamic and Equilibrium Properties of a Multichain Polymer System... 

As has already been emphasized in Fig. 1.1, there is the further problem of connecting the mesoscopic scale, where one considers length scales from the size of effective monomers to the scale of the whole coils, to still much larger scales, to describe structures formed by multichain heterophase systems. Examples of such problems are polymer blends, where droplets of the minority phase exist on the background of the majority matrix, etc. The treatment of... 

Micka et al. [169] were the first who simulated a multichain HPE system. They studied regular copolymers with alternating neutral and charged monomers (with a charge fraction of / = 1/3) in a poor solvent in the presence of monovalent counterions. The paper by Micka et al. [169] nicely demonstrated that the necklace microstructures exhibit a variety of conformational transitions as a function of polymer concentration. The end-to-end distance was found to be a nonmonotonic function of concentration and showed a strong minimum in the semidilute regime. 

Dynamic Monte Carlo simulations were first used by Verdier and Stockmayer (5) for lattice polymers. An alternative dynamical Monte Carlo method has been developed by Ceperley, Kalos and Lebowitz (6) and applied to the study of single, three dimensional polymers. In addition to the dynamic Monte Carlo studies, molecular dynamics methods have been used. Ryckaert and Bellemans (7) and Weber (8) have studied liquid n-butane. Solvent effects have been probed by Bishop, Kalos and Frisch (9), Rapaport (10), and Rebertus, Berne and Chandler (11). Multichain systems have been simulated by Curro (12), De Vos and Bellemans (13), Wall et al (14), Okamoto (15), Kranbu ehl and Schardt (16), and Mandel (17). Curro s study was the only one without a lattice but no dynamic properties were calculated because the standard Metropolis method was employed. De Vos and Belleman, Okamoto, and Kranbuehl and Schardt studies included dynamics by using the technique of Verdier and Stockmayer. Wall et al and Mandel introduced a novel mechanism for speeding relaxation to equilibrium but no dynamical properties were studied. These investigations indicated that the chain contracted and the chain dynamic processes slowed down in the presence of other polymers. 

Coombes and Katchalski [29] have considered a slightly more complex version of this mechanism in which a second propagation coefficient operates above a critical degree of polymerization. Katchalski et al. [30] calculated the molecular weight distribution obtained in a system following scheme (12) but also including a bimolecular termination step. Various authors have analysed more complex systems in which the initiator is a polymeric species. Thus Gold [31] has shown that initiation by a poly a-amino acid with a Poisson distribution leads to a polymeric product with an over-all Poisson distribution, and Katchalski et al. [32] demonstrated that in multichain polymers synthesized from polyfunctional initiators Poisson distributions also arise. 

Very large model systems, which are often necessary to track the morphological characteristics responsible for the peculiar properties of polymers, also present a great challenge in polymer simulations. Detailed atomistic multichain polymer models used today seldom contain more than a few thousands of atoms, although domain decomposition strategies on parallel machines offer the possibihty of going up to millions of atoms. 

At the microscopic level, polymer melts are modeled as multichain systems, see Refs [2, 12, 13, 51]. For example, all-atom or united-atom force fields, accounting explicitly for bond angle bending and torsion angle contributions (in addition to bond stretching and intermolecular interactions) [52, 53], are available. Different united-atom force fields are reviewed and compared, for example, in Refs [51, 54, 55]. From such detailed atomistic molecular dynamics (M D) simulations, the linear viscoelastic... 

For long flexible polymer chains it has been customary for a Imig time [1, 2] to reduce the theoretical description to the basic aspects such as chain connectivity and to excluded volume interactions between monomers, features that are already present when a macromolecule is described by a self-avoiding walk (SAW) on a lattice [3]. The first MC algorithms for SAW on cubic lattices were proposed in 1955 [164], and the further development of algorithms for the simulation of this simple model has continued to be an active area of research [77, 96, 165 169]. Dynamic MC algorithms for multichain systems on the lattice have also been extended to the simulation of symmetric binary blends [15, 16] comprehensive reviews of this work can be found in the literature [6, 81, 82]. It mms out, however, that for the simulation both of polymer blends [6, 9, 21, 82, 170, 171] and of solutions of semiflexible polymers [121 123], the bond fluctuation model [76, 79, 80] has a number of advantages, and hence we shall focus attention only on this lattice model. 

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