Freezing line of the Lennard-Jones fluid: a phase switch Monte Carlo study

We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.     

Monte Carlo simulation of crystal-fluid coexistence states in the hard-sphere system under gravity with stepwise control

Monte Carlo (MC) simulations were performed for hard spheres (with diameter sigma and mass m) placed between well-separated upper and lower hard walls. A periodic boundary condition was imposed in the horizontal direction. The system was exposed to the gravitational field with the acceleration due to gravity g. After preparing a melt as the initial state, g was increased stepwise up to mgsigma/k(B)T(identical with g(*))=1.5 or 2.0 with an increment Deltag(*) = 0.1; k(B)T is the temperature multiplied by Boltzmann's constant. We maintained g(*) at each value for 2.0 x 10(5) MC cycles. The transition of the system into a metastable state such as a polycrystalline state due to trapping phenomena was successfully avoided. A monotonic increase and subsequent saturation were observed for the development of the crystalline region formed at the bottom of the system. The development of this region accompanied a shrinkage of the defective (or less ordered) crystalline region that was formed between the bottom region and the fluid phase. As the development of the bottom region almost saturated, the defective region grew upward again.     

Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids

We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid. Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity. The radial distribution function and potential of mean force are calculated to high precision.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Configurational bias Monte Carlo simulation of phase segregation in block copolymer networks

Cross-linked block copolymers are used as adhesives in fiber-reinforced composite material manufactures for automotive applications. Good adhesion between the polymer matrix and fibers in the interphase region is required for the structural integrity of these materials. Experimental evidence indicates that superior adhesion is obtained when phase segregation occurs between the two matrix phase block copolymers. It is therefore desirable to predict the conditions under which phase segregation is expected to occur. Configurational bias Monte Carlo simulations of two-component, trifunctional block copolymer networks were carried out to investigate phase segregation in these materials. The effects of four principal parameters on phase segregation were examined: the weight fractions of the two components, the cross-link length, the connectivity of the network, and the ratio of the square-well interactions. The molecular simulation results confirmed trends observed in laboratory measurements.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.