Single-chain Monte Carlo simulations

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. 

The results from the 6-3IG basis set are close to what is observed experimentally. Calculations like these are valuable for molecular mechanics simulations because they provide high quality input data for polymer fragments. In addition, rotational isomeric state and atomistic Monte Carlo simulations of single isolated chains benefit greatly from accurate data derived from quantum mechanical calculations. 

Monte Carlo simulations may be used to study the behavior and characteristics of single chains. Detailed chemical structure is typically not included in a polymer MC simulation. Nonetheless, one finds MC simulations to be valuable aids to the understanding of universal characteristic behavior of polymers. The work by Wall et al. is among the first to exemplify the application of the... 

A complication arising from the extension of the theory to flexible macromolecules is that in general, the intermolecular and intramolecular radial distribution functions depend on each other.In modeling the bulk of a one-phase polymer melt, however, the situation resolves itself because the excluded volume effect is insignificant under these conditions the polymer chains assume unperturbed dimensions (see also the section on Monte Carlo simulations by Corradini, as described originally in Ref. 99). One may therefore calculate the structure of the unperturbed single chain and employ the result as input to the PRISM theory to calculate the intermolecular correlation functions in the melt. 

A number of possible moves are available for moving the surfactant chains (the options for the movement of single beads or very short chains are clearly limited). Binder [17] may be consulted for a detailed discussion of the various possible moves (and for a discussion of how such moves can be made to satisfy microscopic reversibility conditions—and ergodicity conditions in the case of dynamic Monte Carlo simulations), especially for long-chain molecules such as polymer chains. Here we consider only a few of the many options. 

Table 4.2 Equilibrated conformations from Monte Carlo simulations of complexes composed of a semi-flexible polyelectroly te and a single colloidal particle as a function of the solution ionic strength I and polyelectrolyte intrinsic rigidity k ng- By increasing the chain stiffness, solenoid conformations are progressively achieved at the particle surface, whereas an increase in ionic strength leads to the desorption of the polyelectrolyte.

Fig. 4.9 Dynamic Monte Carlo simulation results of single-chain collapse transition, (a) The curves of mean square radius of gyration /(N—l) vs. B/kT for varying chain lengths N as labeled. (0.032, 0.26) is the theta point, (b) Radial distributions of local-average concentrations < q > of chain units in 512-mer at various temperatures (Hu 1998) (Reprinted with permission)...

Having established the ability of the NPT Monte Carlo simulation to capture PVT behavior, we now turn to the prediction of melt structure and single chain... 

An alternative approach is to generate d>(k) through a single chain, Monte Carlo simulation by evaluating the average... 

Monte Carlo simulations with lattice models of chain dynamics have been concerned with segmental and with whole molecule relaxation. In each case the autocorrelation functions depend upon details of the lattice model. A cubic-lattice model, with random stifle bead motions has been used to study the relaxation of seven characteristics of instantaneous aspherical shape. Three decay functions are observed for iarge molecules with and without excluded volume considerations. The large difference in relaxation times and in their chain length dependence obtained here, and in earlier studies on including the excluded volume effect, is attributed to restrictions associated with the single bead mechanism, a view justified by simulations which obtained more flexible chains by... 

Data suggest that most SCNPs resemble an intrinsically disordered globular coil, but simulations of the folding process for a single polymer chain have shown that there is potential for these materials to mimic the control of many natural processes. Yoshinaga and coworkers, as well as Danilov et performed Monte Carlo simulations that provided great... 

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