Critical Behavior of the Restricted Primitive Model

Impact of Charge Regulation on Self-Assembly of Zwitterionic Nanoparticles

Zwitterionic modification of colloids with weak acids and bases represents a promising strategy in creating functional materials with tunable properties and modeling the self-organization of charged proteins. However, accurate incorporation of the dynamic dissociation or association of ionization groups known as charge regulation (CR) is often intractable in theoretical and computational investigations since charge redistribution and configuration need to be evolved self-consistently. Using hybrid Monte Carlo and molecular dynamics simulations, we demonstrate that a dilute suspension of overall charge-neutral zwitterionic Janus nanoparticles shows a conformational transition from an open assembly of string or bundle to compact cluster along with the variation in pH. The behavior under CR is qualitatively different from the commonly employed constant charge condition where the transition is absent. The CR-induced clustering is due to the inhomogeneous and fluctuating charges localized near the equatorial boundary of the Janus particle. These features are enhanced particularly at low salt concentration and high electrostatic coupling strength. Our results indicate the critical role of charge regulation in the spatial self-organization of zwitterionic nanoparticles.

Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: phase diagram and clustering

We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.

Toward the description of electrostatic interactions between globular proteins: Potential of mean force in the primitive model

Monte Carlo simulations are used to calculate the exact potential of mean force between charged globular proteins in aqueous solution. The aim of the present paper is to study the influence of the ions of the added salt on the effective interaction between these nanoparticles. The charges of the model proteins, either identical or opposite, are either central or distributed on a discrete pattern. Contrarily to Poisson-Boltzmann predictions, attractive, and repulsive direct forces between proteins are not screened similarly. Moreover, it has been shown that the relative orientations of the charge patterns strongly influence salt-mediated interactions. More precisely, for short distances between the proteins, ions enhance the difference of the effective forces between (i) like-charged and oppositely charged proteins, (ii) attractive and repulsive relative orientations of the proteins, which may affect the selectivity of protein/protein recognition. Finally, such results observed with the simplest models are applied to a more elaborate one to demonstrate their generality.

Structure and thermodynamics of a two-dimensional Coulomb fluid in the strong association regime

The behavior of a two-dimensional neutral Coulomb fluid in the strong association regime (low density, high ionic charge) is explored by means of computer simulation and the hypernetted chain integral equation. The theory reproduces reasonably well the structure and thermodynamics of the system but presents a no-solution region at temperatures well above the computer simulation estimates of the metal-insulator transition. In contrast with hypernetted chain predictions for the three-dimensional Coulomb fluid, here the breakdown of the solution is not accompanied by divergences in any physical quantity.

Discretization dependence of criticality in model fluids: a hard-core electrolyte

Grand-canonical simulations at various levels, zeta=5-20, of fine-lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or restricted primitive model (RPM). With the aid of finite-size scaling analyses, it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of zeta (> or approximately 4), thus the continuum (zeta--> infinity ) RPM exhibits Ising-type (as against classical, self-avoiding walk, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the intrinsically erratic zeta dependence, yielding (T*(c),rho*(c)) approximately equal to (0.0493(3),0.075) for the zeta=infinity RPM.

Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model

The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for "fat" stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.

Surface tension of the restrictive primitive model for ionic liquids

Hybrid molecular dynamics and Monte Carlo simulations are performed to study the liquid-vapor interface of the restricted primitive model (RPM) of ionic fluids. We report for the first time simulation results of the surface tension associated to this interface. The RPM accurately predicts experimental surface tensions of ionic salts and good agreement with theoretical predictions that include the idea of ion association is found. The simulation results indicate that the structure of an ionic liquid-vapor interface is rather rough. This is reflected in the interfacial thickness, larger than that observed in simple fluids and water.

Monte carlo study of coulombic criticality in polyelectrolytes

The role of charges in determining the water solubility of polyelectrolytes, a question of considerable relevance to biology, is currently unresolved. We use computer simulations to study the purely Coulombic phase separation of flexible polyelectrolytes with monovalent counterions in an athermal solvent. In agreement with recent theories we find that the critical temperature for this transition increases with chain length, but that the critical density remains unchanged. We therefore stress that the phase behavior of polyelectrolytes is qualitatively different from uncharged polymers, where the critical density decreases towards zero for long chains.

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using loci in the temperature-density or (T,rho) plane of isothermal rho(2-k) vs pressure inflections, of Q identical with<m(2)>(2)/<m(4)> maxima, and of canonical and C(V) criticality, yield estimates of (T(c),rho(c)) to +/-(0.04,3)%. Extrapolated exponents and Q ratio are (gamma,nu,Q(c)) = [1.24(3), 0.63(3); 0.624(2)], which support Ising (n = 1) behavior with (1.23(9), 0.630(3); 0.623(6)), but exclude classical, XY (n = 2), self-avoiding walk (n = 0), and n = 1 criticality with potentials varphi(r)>Phi/r(4.9) when r-->infinity.

Critical behavior of ionic solids

Phase transitions of lattice models of ionic crystals are studied by computer simulation. The nature of order-disorder transitions on different crystal structures is established and compared with the behavior of related Ising models. It is found that for both, continuous and first order transitions the basic features seem to be similar to those of Ising systems.

Precise simulation of criticality in asymmetric fluids

Extensive grand canonical Monte Carlo simulations have been performed for the hard-core square-well fluid with interaction range b=1.5 sigma. The critical exponent for the correlation length has been estimated in an unbiased fashion as nu=0.63+/-0.03 via finite-size extrapolations of the extrema of properties measured along specially constructed, asymptotically critical loci that represent pseudosymmetry axes. The subsequent location of the critical point achieves a precision of five parts in 10(4) for Tc and about 0.3% for the critical density rhoc. The effective exponents gamma+(eff) and beta(eff) indicate Ising-type critical-point values to within 2% and 5.6%, respectively, convincingly distinguishing the universality class from the "nearby" XY and n=0 (self-avoiding walk) classes. Simulations of the heat capacity CV(T,rho) and d2psigma/dT2, where psigma is the vapor pressure below Tc, suggest a negative but small Yang-Yang anomaly, i.e., a specific-heat-like divergence in the corresponding chemical potential derivative (d2 musigma/dT2) that requires a revision of the standard asymptotic scaling description of asymmetric fluids.

Criticality and crossover in accessible regimes

The near-critical behavior of (d = 3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different "nearby" universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc.