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We use molecular dynamics simulations over microsecond time scales to study the micellization behavior of recently proposed continuum-space, coarse grained surfactant models. In particular, we focus on the MARTINI model by Marrink et al. [J. Phys. Chem. B 111, 7812 (2007)] and a model by Shinoda et al. [Soft Matter 4, 2454 (2008)]. We obtain the critical micelle concentration (cmc) and equilibrium aggregate size distributions at low surfactant loadings. We present evidence justifying modest extrapolations for determining the cmc at low temperatures, where significant sampling difficulties remain. The replica exchange method provides only modest improvements of sampling efficiency for these systems. We find that the two coarse grained models significantly underpredict experimental cmc near room temperature for zwitterionic surfactants, but are closer to measured values for nonionic ones. The aggregation numbers for both zwitterionic and nonionic surfactants are near those observed experimentally, but the temperature dependence of the cmc is incorrect in both cases, because of the use of an unstructured solvent. Possible refinements to the models to bring them into quantitative agreement with experiment are discussed. [ABSTRACT FROM AUTHOR]

Recent experimental results demonstrated that polymer grafted nanoparticles in solvents display self-assembly behavior similar to the microphase separation of block copolymers and other amphiphiles. We present a mean-field theory and complementary computer simulations to shed light on the parametric underpinnings of the experimental observations. Our theory suggests that such self-assembled structures occur most readily when the nanoparticle size is comparable to the radius of gyration of the polymer brush chains. Much smaller particle sizes are predicted to yield uniform particle dispersions, while larger particles are expected to agglomerate due to phase separation from the solvent. Selected aspects of our theoretical predictions are corroborated by computer simulations. [ABSTRACT FROM AUTHOR]

A lattice model for diblock surfactants that incorporates orientational bonding has been developed for studying self-assembly in dilute solutions. Using grand canonical Monte Carlo simulations with histogram reweighting and mixed field finite size scaling, we examine the effect of amphiphile architecture on phase transitions and distinguish between first order transitions that create a disordered liquid phase and higher order transitions that indicate the formation of finite sized aggregates. As the solution temperature increases, we find that the critical micelle concentration for the orientational bonding model surfactants reaches a minimum value at a temperature that can be controlled by varying the number of bonding orientations between the solvophobic surfactant monomers and the implicit solvent. This trend is qualitatively similar to experimental data for ionic and nonionic surfactants in aqueous solutions. A comparable dependence on temperature is observed in the limit of amphiphile solubility for phase separating systems. None of the model surfactants considered here undergo both a first and a higher order transition over the range of densities and temperatures examined. [ABSTRACT FROM AUTHOR]

We perform histogram-reweighting Monte Carlo simulations of the ST2 model of water in the grand-canonical ensemble in order to investigate its low-temperature fluid-phase behavior. Using Ewald summation treatment of long-range electrostatic interactions, we locate the critical point of the liquid-liquid transition at T=237±4 K, ρ=0.99±0.02 g/cc, P=167±24 MPa. Contrary to previous reports in the literature [Brovchenko et al., J. Chem. Phys. 118, 9473 (2003); Brovchenko et al., J. Chem. Phys. 123, 044515 (2005)], according to which there are three liquid-liquid transitions in ST2 with simple truncation of electrostatic interactions, and two in ST2 with reaction field treatment of long-range Coulombic forces, we find only one liquid-liquid transition. Our work points to the sensitivity of results to the proper treatment of electrostatic interactions, and to the introduction of artificial constraints that limit the magnitude of density fluctuations. [ABSTRACT FROM AUTHOR]

Grand canonical Monte Carlo simulations on a cubic lattice are used to examine aggregation and phase separation of model amphiphiles with bulky head groups. The amphiphiles studied consist of a rigid, roughly spherical nanoparticle attached to one or more flexible chains. Overlapping distributions of energy and density are combined via histogram reweighting to obtain the free energy and osmotic pressure as a function of temperature and concentration. Finite size effects are used to distinguish between first order transitions to a disordered liquid or lamellar phase and continuous transitions to micelles. The transition type depends on the relative size of the solvophobic and neutral portions of the amphiphiles; none of the systems studied here exhibit both types of transition. The critical micellar concentration increases with temperature over the range of conditions examined. Solvophobic nanoparticles with neutral chains phase separate when the attached chain is short and form micelles for longer attached chains. For structures with neutral nanoparticles and solvophobic chains, amphiphile geometry plays a key role in determining whether the micelles that form are spheres or flat bilayers. Nanoparticles with many chains tend to form flat bilayers, while those with only one or two chains form nearly spherical aggregates. Particles with long chains undergo macroscopic phase separation instead of micellization, and the temperature range over which the first order transition occurs depends on the total volume occupied by the solvophobic segments. [ABSTRACT FROM AUTHOR]

The solution phase behavior of short, strictly alternating multiblock copolymers of type (AnBn)m was studied using lattice Monte Carlo simulations. The polymer molecules were modeled as flexible chains in a monomeric solvent selective for block type A. The degree of block polymerization n and the number of diblock units per chain m were treated as variables. We show that within the regime of parameters accessible to our study, the thermodynamic phase transition type is dependent on the ratio of m/n. The simulations show microscopic phase separation into roughly spherical aggregates for m/n ratios less than a critical value and first-order macroscopic precipitation otherwise. In general, increasing m at fixed n, or n at fixed m, promotes the tendency toward macroscopic phase precipitation. The enthalpic driving force of phase change is found to universally scale with chain length for all multiblock systems considered and is independent of the existence of a true phase transition. For aggregate forming systems at low amphiphile concentrations, multiblock chains are shown to self-assemble into intramolecular, multichain clusters. Predictions for microstructural dimensions, including critical micelle concentration, equilibrium size, shape, aggregation parameters, and density distributions, are provided. At increasing amphiphile density, interaggregate bridging is shown to result in the formation of networked structures, leading to an eventual solution-gel transition. The gel is swollen and consists of highly interconnected aggregates of approximately spherical morphology. Qualitative agreement is found between experimentally observed physical property changes and phase transitions predicted by simulations. Thus, a potential application of the simulations is the design of multiblock copolymer systems which can be optimized with regard to solution phase behavior and ultimately physical and mechanical properties. [ABSTRACT FROM AUTHOR]

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied. [ABSTRACT FROM AUTHOR]

Implicit water potentials are developed for the study of thermodynamic and structural properties of solutions of NaCl, LiCl, and KCl. The interaction potential between cations and anions is parametrized from the ionic crystal potential. Two short-range corrections were added to the system to account for the water solvent. The first is due to dielectric saturation which reduces the dielectric permittivity in the vicinity of an ion. The second is a repulsive Gaussian potential which represents the first hydration shell around the ions. Grand canonical Monte Carlo simulations were performed to calculate the mean ionic activity coefficients. Molecular dynamics simulations were performed to calculate the radial distribution functions of 1.0 molal solutions at 298 K which were used to compare the structure of the explicit and implicit water simulations. The implementation of dielectric saturation and a repulsive hydration potential results in an excellent description of the mean activity coefficient and is able to capture structural features of contact ion pairs and solvent separated ions. [ABSTRACT FROM AUTHOR]

We calculate the global phase diagram using classical statistical mechanics for an isotropic pair potential that has been previously [Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005)] shown to produce the low-coordinated two-dimensional honeycomb crystal as the ground-state structure. Low-coordinated crystals are of practical interest because they have desirable photonic band-gap properties. The phase diagram is obtained from Helmholtz free energies calculated using thermodynamic integration and Monte Carlo simulations. Our results show that the honeycomb crystal remains stable in the global phase diagram even after temperature effects are taken fully into account. Other stable phases in the phase diagram are high and low density triangular phases and a fluid phase. We find no evidence of gas-liquid or liquid-liquid phase coexistence. [ABSTRACT FROM AUTHOR]

The critical behavior of electrolyte mixtures was studied using grand canonical Monte Carlo simulations. Mixtures consist of large multivalent macroions and small monovalent co- and counterions. The system can be viewed as a binary mixture of macroions (with their counterions) and salt (co- and counterion pair). The primitive model description was used, in which the ions are point charges with a hard core and the solvent is treated as a uniform dielectric continuum. The grand canonical simulations are based on insertions and removals of neutral molecules: macroion with its counterions or coions and a counterion. We propose a distance biasing method that enables direct grand canonical simulations up to charge asymmetry of 10:1. We calculated the critical loci that connect the salt-free state, which consists of only macroions and counterions, with the pure salt state using mixed-field finite-size scaling with no pressure mixing. The critical parameters are determined for macroion to counterion charge asymmetries of 2:1, 3:1, and 10:1. Our results suggest that binary electrolyte mixtures are type-I mixtures, where the two components mix continuously. [ABSTRACT FROM AUTHOR]

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms), and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the Monte Carlo simulation, and on (computational) time scale separation between these and the remaining “slaved,” fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This “equation-free” framework, bypassing the derivation of explicit, closed equations for the observables (e.g., equations of state), may provide a computational bridge between direct atomistic/stochastic simulation and the analysis of its macroscopic, system-level consequences.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We discuss a coarse-grained approach to the computation of rare events in the context of grand canonical Monte Carlo (GCMC) simulations of self-assembly of surfactant molecules into micelles. The basic assumption is that the computational system dynamics can be decomposed into two parts—fast (noise) and slow (reaction coordinates) dynamics, so that the system can be described by an effective, coarse-grained Fokker–Planck (FP) equation. While such an assumption may be valid in many circumstances, an explicit form of FP equation is not always available. In our computations we bypass the analytic derivation of such an effective FP equation. The effective free energy gradient and the state-dependent magnitude of the random noise, which are necessary to formulate the effective Fokker–Planck equation, are obtained from ensembles of short bursts of microscopic simulations with judiciously chosen initial conditions. The reaction coordinate in our micelle formation problem is taken to be the size of a cluster of surfactant molecules. We test the validity of the effective FP description in this system and reconstruct a coarse-grained free energy surface in good agreement with full-scale GCMC simulations. We also show that, for very small clusters, the cluster size ceases to be a good reaction coordinate for a one-dimensional effective description. We discuss possible ways to improve the current model and to take higher-dimensional coarse-grained dynamics into account.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities—that is, the probabilities associated with move proposal only—we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang–Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The phase behavior of charge- and size-asymmetric primitive model electrolytes has been investigated using reservoir grand canonical Monte Carlo simulations. The simulations rely on the insertion and removal of neutral ion clusters from a reservoir of possible configurations. We first validated our approach by investigating the effect of R[sub c], the maximum allowable distance between the central cation and its associated anions, on the critical parameters of 2:1 and 3:1 electrolytes. We have shown that the effect of R[sub c] is weak and does not change the qualitative dependence of the critical parameters on size and charge asymmetry. The critical temperature for 2:1 and 3:1 electrolytes shows a maximum at R[sub c]≈3, while the critical volume fraction decreases more or less monotonically, consistent with previous results for 1:1 electrolytes by Romero-Enrique et al. [Phys. Rev. E 66, 041204 (2002)]. We have used the reservoir method to obtain the critical parameters for 5:1 and 10:1 electrolytes. The critical temperature decreases with increasing charge asymmetry and shows a maximum as a function of δ, the size asymmetry parameter. The critical volume fraction however, defined as the volume occupied by ions divided by the total volume of the simulation box, increases with increasing charge asymmetry and exhibits a minimum as a function of δ. This trend is contrary to what is generally predicted by theories, although more recent approaches based on the Debye–Hückel theory reproduce this observed trend. Our results deviate somewhat from the predictions of Linse [Philos. Trans. R. Soc. London, Ser. A 359, 853 (2001)] for the scaling of the critical temperature for a system of macroions with point counterions. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effects of the ratio of particle diameter to lattice spacing, ζ, on critical parameters for both polar and nonpolar fluids have been examined in detail. Nonpolar systems studied have short range Buckingham exponential-6 interactions, while polar systems have long range Coulombic forces treated with Ewald summation. Monte Carlo simulations in the grand canonical ensemble combined with histogram reweighting and mixed field finite size scaling have been used. Both critical temperature and critical density decrease on increasing ζ. The critical temperature scales as 1/ζ[sup α] where the exponent was obtained as ± = (6±2) for the nonpolar and α=(2±0.5) for the polar fluids. The large difference in a values between nonpolar and polar fluids results from a much weaker effect of discretization on the critical parameters of nonpolar fluids. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations in the grand canonical ensemble have been performed to obtain the phase behavior of the lattice restricted primitive model with additional short-range attractive interactions. Multihistogram reweighting techniques were used to obtain the phase diagrams as a function of the parameter ε[sup *], measuring the relative strength of the short-range (SR) to the Coulombic interactions. The results reveal a great variety of behaviors as ε[sup *] is varied. Specifically, for weak or vanishing SR interactions only order-disorder phase transitions and a tricritical point are found, while for strong SR interactions the high-density ordered phase becomes incommensurate with the lattice structure and only a gas-liquid coexistence and a critical point are observed. However, for a certain range of ε[sup *] between these two limits both the critical and the tricritical points can become stable. [ABSTRACT FROM AUTHOR]

We present a computer-assisted study of "coarse" stability/bifurcation calculations for kinetic Monte Carlo simulators using the so-called coarse timestepper approach presented in A. G. Makeev, D. Maroudas, and I. G. Kevrekidis, J. Chem. Phys. 116, 10083 (2002). Our illustrative example is a model of a heterogeneous catalytic surface reaction with repulsive adsorbate-adsorbate interactions and fast diffusion. Through numerical continuation and stability analysis, we construct one- and two-parameter coarse bifurcation diagrams. We also discuss several computational issues that arise in the process, the most important of which is the "lifting" of coarse, macroscopic initial conditions (moments of adsorbate distributions) to fine, microscopic initial conditions (distributions conditioned on these moments). [ABSTRACT FROM AUTHOR]

The critical parameters for the restricted primitive model of electrolyte solutions were determined from extensive grand canonical Monte Carlo simulations combined with mixed-field finite-size scaling. The fine-lattice discretization method was used for the calculations, with Ewald summation of the long-range coulombic forces. Ising criticality and no pressure mixing were assumed in the finite-size scaling analysis. The critical parameters were obtained as a function of boundary conditions at infinite distance (ε[sub ∞]), system size L, and lattice discretization parameter ζ. They were found to be sensitive to L for vacuum boundary conditions (ε[sub ∞]=1), but much less so for “tin-foil” boundary conditions (ε[sub ∞]=∞). The critical temperature and density decrease with increasing ζ. These calculations are compared to previous estimates of the critical parameters for this model. Extrapolation of our results to the thermodynamic limit in continuous space (L→∞ and ζ→∞) yields T[sub c][sup *]=0.0489±0.0003, ρ[sub c][sup *]=0.076±0.003. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We modify Larson's lattice model [J. Chem. Phys. 83, 2411 (1985)] and use it to study self-assembly of surfactants in a supercritical solvent by large-scale Monte Carlo simulations. Carbon dioxide and perfluoroalkylpoly(ethylene oxide) serve as prototypes for the solvent and surfactant, respectively. Larson-model type parameters for carbon dioxide and perfluoroalkylpoly(ethylene oxide) are obtained using experimental values of critical parameters and solubility along with a modified Berthelot combining rule. We perform canonical Monte Carlo simulations at a supercritical temperature, varying the number of surfactant head and tail segments, the solvent density and the surfactant concentration. Various properties such as the critical micelle concentration, the aggregate size distribution, and the size and shape of the micelles are evaluated and pseudophase diagrams are constructed. We further investigate the ability of the surfactant solutions to dissolve more solute than solutions without surfactants by calculating the partition coefficient. Water serves as a prototype for the solute and Larson-model type parameters for water are obtained in the same way as for carbon dioxide and perfluoroalkylpoly(ethylene oxide). [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations were performed to examine the structure and dynamics of sodium dodecyl sulfate (SDS) and dodecane ([C.sub.12]) molecular aggregates at varying surface coverages on the basal plane of graphite. The results showed that graphite-hydrocarbon chain interactions favor specific molecular orientations at the single-molecule level via alignment of the tail along the crystallographic directions.

Reports that intermolecular potential models for benzene and cyclohexane have been developed, parameterized to the vapor-liquid coexistence properties. United-atom description of the molecules used in the models for benzene and cyclohexane; Reservoir grand canonical Monte Carlo simulations; Free energy of insertion.

Investigates the coexistence curves of square-well fluids with variable interaction width and of the restricted primitive model for ionic solutions. Methodologies used in simulation; Histogram reweighting and multicanonical sampling; Finite-size scaling.

Investigates the critical point of the pure fluid and Lennard-Jones mixture. Application of Monte Carlo simulations; Details on the critical parameters of the Lennard-Jones potential; Results of the pure Lennard-Jones fluid-mixture simulation.

In this work, we report results for the phase diagram of the two-dimensional Coulomb system. We use a recently proposed simulation method, thermodynamic scaling Monte Carlo, to determine the Kosterlitz–Thouless insulator/conductor transition line and the first-order vapor–liquid coexistence curve. The Kosterlitz–Thouless line terminates at the first-order coexistence curve close to the gas–liquid critical point. Our estimate of the vapor–liquid critical point is, T*≊0.056, ρ*≊0.21, in only modest agreement with previous theoretical estimates and semiquantitative numerical results. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Vapor–liquid phase equilibria for lattice homopolymer systems are simulated in the Gibbs ensemble for chains of length n=1, 8, 16, 32, 64, and 128 using a newly proposed methodology for volume change moves [Mackie et al., Europhys. Lett. 27, 549 (1994)]. This is the first time that extensions of the Gibbs ensemble methodology for direct calculation of phase coexistence are presented for lattice models. The simulation results show, in agreement with experiment, that the chain length dependence of the critical temperature of polymer-hole systems follows the Schultz–Flory form. The critical densities obey an n-0.32 scaling relationship over this limited range in chain lengths, an exponent somewhat less than is found from experimental data. We show that both the Flory model and the Guggenheim theory do not agree with the simulation results, although the Guggenheim model permits better agreement in all cases. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]