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We present a coarse grain representation for Gaussian chains in the presence of hard surfaces. Whereas a Gaussian chain in the bulk can be represented by a bead-spring model with a quadratic potential between adjacent beads, the presence of a surface reduces the number of allowed chain configurations and modifies the effective potential between the beads. We derive the corrected potentials for several surface geometries: a single wall, two parallel walls (slit), and a spherical or cylindrical object (nanoparticle). Those potentials can be used in any model that includes a Gaussian chain, regardless of the simulation method. As an illustration, we consider a coarse grain model of a polymeric melt and, using Monte Carlo simulations, we compute the density profiles for (i) a melt confined in a slit and (ii) a melt in the vicinity of a nanoparticle. The case of a polymeric solution confined within a slit is also addressed, and the proposed approach is shown to yield results in qualitative agreement with those obtained with field-theoretic simulations. [ABSTRACT FROM AUTHOR]

Long polyglutamine chains have been associated with a number of neurodegenerative diseases. These include Huntington’s disease, where expanded polyglutamine (PolyQ) sequences longer than 36 residues are correlated with the onset of symptoms. In this paper we study the folding pathway of a 54-residue PolyQ chain into a β-helical structure. Transition path sampling Monte Carlo simulations are used to generate unbiased reactive pathways between unfolded configurations and the folded β-helical structure of the polyglutamine chain. The folding process is examined in both explicit water and an implicit solvent. Both models reveal that the formation of a few critical contacts is necessary and sufficient for the molecule to fold. Once the primary contacts are formed, the fate of the protein is sealed and it is largely committed to fold. We find that, consistent with emerging hypotheses about PolyQ aggregation, a stable β-helical structure could serve as the nucleus for subsequent polymerization of amyloid fibrils. Our results indicate that PolyQ sequences shorter than 36 residues cannot form that nucleus, and it is also shown that specific mutations inferred from an analysis of the simulated folding pathway exacerbate its stability. [ABSTRACT FROM AUTHOR]

The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations. [ABSTRACT FROM AUTHOR]

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 [uppercase_phi_synonym](qN) 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. [ABSTRACT FROM AUTHOR]

In this paper a new algorithm is presented that improves the efficiency of Wang and Landau algorithm or density of states (DOS) Monte Carlo simulations by employing rejected states. The algorithm is shown to have a performance superior to that of the original Wang-Landau [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] algorithm and the more recent configurational temperature DOS algorithm. The performance of the method is illustrated in the context of results for the Lennard-Jones fluid. [ABSTRACT FROM AUTHOR]

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer. [ABSTRACT FROM AUTHOR]

The hydration of Na-saturated Wyoming-type montmorillonite is investigated by Monte Carlo simulations at constant stress in the NP[sub zz]T ensemble and at constant chemical potential in the μVT ensemble, at the sedimentary basin temperature of 353 K and pressure of 625 bar, equivalent to 2–4 km depth. The simulations use procedures established in Chávez-Páez et al. [J. Chem. Phys. 114, 1405 (2001)]. At these conditions, simulations predict a single stable form of 1,2-water layer Na–montmorillonite, containing 164.38 mg/g or 53.37 molecules/layer of adsorbed water and having a spacing of 12.72 Å. The corresponding density is 0.32 g/ml. Sodium ions are coordinated with six molecules of water separated 2.30–2.33 Å. Water molecules are closer to the central interlayer plane and the spacing is larger than that at 300 K and 1 bar. The interlayer configuration consists of two symmetrical layers of oriented water molecules 1.038 Å from the central plane, with the hydrogen atoms in two outermost layers, 3.826 Å apart, and the sodium ions on the central plane located between the water layers. The interlayer configuration can be considered to be a stable two-layer intermediate between the one- and two-layer hydrates. Our simulations do not predict formation of other hydrates of Na–montmorillonite at 353 K and 615 bar. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and dynamic field theory are used to study spherical particles suspended in a nematic liquid crystal. Within these two approaches, we investigate the binding of the defects to the particles, the adsorption of a particle at a solid surface, and two particles interacting with each other. Quantitative comparisons indicate good agreement between the two approaches. A Monte Carlo method based on the combination of canonical expanded ensemble simulations with a density-of-state formalism is used to determine the potential of mean force between one particle and a hard wall. On the other hand, the potential of mean force is evaluated using a dynamic field theory, where the time-dependent evolution of the second rank tensor includes two major aspects of liquid crystalline materials, namely the excluded volume and the long-range order elasticity. The results indicate an effective repulsive force that acts between the particle and the wall. Layer formation at the surface of the hard wall gives rise to local minima in the potential of mean force. The director profile for a particle at contact with a solid surface is characterized by a disclination line distorted and attracted towards the wall. The structure of the nematic for two particles at short distances is also investigated. Our results indicate a structure where the two particles are separated by a circular disclination line. The potential of mean force associated with this configuration indicates an effective attractive interaction between the two particles. [ABSTRACT FROM AUTHOR]

In this work a novel Monte Carlo method is developed to simulate the equilibrium thermodynamic properties of strongly associating fluids. The highly anisotropic nature of intermolecular interactions in these fluids makes conventional simulation techniques of little use. By introducing biased sampling techniques we are able to explore configuration space efficiently, thereby obtaining reliable estimates for the thermodynamic properties, including phase equilibria, of model systems. The results of our simulations are used to assess the accuracy and validity of various theories for associating fluids. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations have been used to predict the interlayer basal separations of sodium-saturated Wyoming clays at constant stress (NP[sub zz]T ensemble) and at constant chemical potential (μVT ensemble). These simulations use the Ewald summation technique to incorporate long-range Coulombic interactions in the calculation of the total potential energy and the pressure tensor. A comparison is made between the use of one, two, and three sheets of clay. It is shown that, for small separations, at least two separate clay sheets must be used to avoid system-size effects. The stable interlamellar separations are determined by combining results from isostress-isothermal and grand canonical simulations. It is shown that, consistent with experiments, at the temperature and pressure studied here, the cations in the interlayer are hydrated, except at the smallest basal separations. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We have performed Monte Carlo simulations of a three-dimensional quenched-annealed system on a cubic lattice with nearest-neighbor interactions. A small fraction of the lattices sites are blocked, thereby creating a quenched matrix. Histogram reweighting techniques are applied to investigate the critical behavior of the system. We have studied lattice sizes ranging from L=10 to L=18. For each size, we have evaluated the number of matrix replicas necessary to obtain statistically meaningful results. This number, determined by analyzing the convergence of the histograms, ranged from 50 for the smallest system sizes to 200 for the largest sizes. We have evaluated the critical temperature, the fourth cumulant of Binder et al. [K. K. Kaski, K. Binder, and J. D. Gunton, Phys. Rev. B 29, 3996 (1984)], and the critical exponents 1/ν and β/ν. The estimated critical temperature is only slightly lower than that of the three-dimensional Ising model. The simulated critical exponents, however, differ significantly from those for Ising-class three- and two-dimensional systems. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]