Monte Carlo simulation solvent properties

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. 

One way to test and compare these various statistical approaches is by computer simulation. Molecular dynamics (MD) simulations are based on the classical equations of motion to be solved for a limited number of molecules. From such simulations information about equilibrium properties as well as the dynamics of the system are obtained. In order to test theories based on primitive models for the solvent, Monte Carlo simulations are more appropriate. In Monte... 

Suter and co-workers presented a novel class of Monte Carlo simulation methods aimed at dense polymer systems.i Properties like the chemical potential and solubilities in polymer systems may be calculated from simulations of this type. The authors presented results on the solubility of long alkanes in polyethylene and for various solutions of long alkanes in near-critical solvents. 

The best strategy to be followed in order to get accurate sets of A values has not been defined, so at present more or less complex statistical elaborations of some data are used. Among the numerical data that have been used we mention solvation and solvent transfer energies, intrinsic solute properties (electron isodensity surfaces, isopotential electronic surfaces, multipole expansions of local charge distribution), isoenergy surfaces for the interaction with selected probes (water, helium atoms), Monte Carlo simulations with solutes of various nature. All these sets of data deserve comments, that are here severely limited not to unduly extend this Section. 

A. Sariban and K. Binder (1988) Phase-Separation of polymer mixtures in the presence of solvent. Macromolecules 21, pp. 711-726 ibid. (1991) Spinodal decomposition of polymer mixtures - a Monte-Carlo simulation. 24, pp. 578-592 ibid. (1987) Critical properties of the Flory-Huggins lattice model of polymer mixtures. J. Chem. Phys. 86, pp. 5859-5873 ibid. (1988) Interaction effects on linear dimensions of polymer-chains in polymer mixtures. Makromol. Chem. 189, pp. 2357-2365... 

More recently, the influence on the Bi(ai bj) (n,7t ) excitation of 1 in water was studied starting from ab initio CASSCF (complete active space self consistent field) estimates of the gas-phase electronic excitation properties, followed by Monte Carlo simulations to elucidate the structures of the liquid around the ground and excited state solute. Finally, the solvent shift was evaluated based on gas-phase charge distributions and solvent structures. One linear H-bond to each N-atom of 1 is predicted for diluted solutions <2003CPL(368)377, 2004JCC813>, and three H-bonds to the ground state... 

These results show that simplified molecular dynamics simulations can qualitatively account for micellization quite well. However, the computation time necessary for even such simple models is too great to allow the model to be useful for the calculation of other micellar properties or phase behavior or for an in-depth study of solubilization. Stochastic dynamics simulations, in which the solvent effects are accounted for through a mean-field stochastic term in the equations of motion, can also be used to study surfactant self-assembly [22], but the most efficient approach to date is still the one based on lattice Monte Carlo simulations, which are discussed next. 

Finally, Mattice and coworkers have used lattice Monte Carlo simulations for various studies of micellization of block copolymers in a solvent, including micellization of triblock copolymers [43], steric stabilization of polymer colloids by diblock copolymers [44], and the dynamics of chain interchange between micelles [45]. Their studies of the self-assembly of diblock copolymers [46-48] are roughly equivalent to those of surfactant micellization, as a surfactant can in essence be considered a short-chain diblock copolymer and vice versa. In fact, Wijmans and Linse [49,50] have also studied nonionic surfactant micelles using the same model that Mattice and coworkers used for a diblock copolymer. Thus, it is interesting to compare whether the micellization properties and theories of long-chain diblock copolymers also hold true for surfactants. 

Molecular sciences look for explanations of macroscopic properties, e.g., solubility, from the microscopic properties of matter. Statistical mechanics is one of such disciplines, which hnks those two pictures through the probabilistic treatment of particle ensembles. The application of Kirkwood s continuum solvent approach to nondissociating fluids resulted in a variety of simulation techniques. Applications of such techniques to study phase equilibria have been reported widely in literature [1-10]. Although some simple hydrocarbons can nowadays be reasonably well described by molecular modeling (molecular dynamics and Monte Carlo simulations), water and especially water mixtures, still represent challenges for such simulations techniques despite 30 years of active parameterization of appropriate force-fields. This is due to the extremely strong and complicated electrostatic and hydrogen-bond interactions. 

Monte Carlo simulation techniques have been extensively used to study solvent effects on molecular properties and equilibrium points. Jorgensen has summarized theoretical work of condensed-phase effects on conformational equilibria [63]. 

Monte-Carlo calculations provide us with an alternative route to the local properties in the bulk of a liquid which are closer to first principles than the above model although the molgcgle needs to be somewhat simplified. We performed several computations on model liquids in order to evaluate the electric field which a molecule undergoes from the liquid and to compare it with the values predicted by the model. The main result of this comparison is that, due to the error bars of the Monte-Carlo calculation, and to the uncertainties on the dielectric constant of the medium, the model reproduces the electric field fairly well, especially when the charge distribution reduces to a single moment. In turn, noticeable deviations appear between the model and the Monte-Carlo simulation when the charge distribution of the solute is represented by more than one dominant moment (e.g. a dipole and a quadrupole) and when the solvent is represented by point dipoles at the centre of non polarizable molecules. This is easily understandable if one bears in mind that the model replaces this medium by a continuum. Nevertheless these discrepancies are expected to be less important in the case of a real medi] m, due to the molecular polarizabilities which are nonlocal properties. ... 

The scaled particle theory of fluids is a theory that offers an excellent conceptual framework with which to understand solvent effects. The theory was originally designed to give the thermodynamic properties of a fluid of hard spheres, but experimentally determined parameters can be introduced to treat real liquids. The treatment of simple liquids is better than the treatment of structured liquids such as water. The theory has been applied extensively to certain aspects of hydrophobic solvation and interactions. In some studies of hydrophobic solvation based on molecular dynamics or Monte Carlo simulations, scaled particle theory has provided useful guidelines for analysis of the results. ... 

The equilibrinm properties of a polymer are not affected by hydrodynamic interactions. Indeed, the resnlts for various equilibrium quantities - such as the radius of gyration - of MPC simulations are in excellent agreement with the results of molecular dynamics of Monte Carlo simulations without explicit solvent [73]. 

Furthermore, in comparison with experiments, it turns out that % is also a function of concentration. Most listed values of % are for the particular polymer in the given solvent at a stated temperature and at infinite dilution. Some values of x are listed in Table 2.3 for polymers in what are known as good solvents. A number of more rigorous expressions for and AG have been presented over the years [15]. The predictions of various theories have been compared with Monte Carlo simulations [16,17] that are able to compute thermodynamic properties with fewer assumptions than in the original models. 

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