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In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems. [ABSTRACT FROM AUTHOR]

The flow-induced coil-stretch transition of high molecular weight polymers has generally been held to be of first order. But evidence of significant slowing down in the rate at which the polymers relax to equilibrium in the vicinity of the transition suggests that the thermodynamic character of the transition may be less clear-cut. The above slowing down effect is actually characteristic of a second-order transition, and it points to the existence of a broad spectrum of conformational states in the transition region, analogous to the existence of fluctuations of all length scales at a critical point. In this paper, using a path integral approach based on a free-draining finitely extensible chain model, we calculate various polymer properties as a function of elongational flow as a way of exploring different statistical mechanical details of the coil-stretch transition. These properties include the molecular weight dependence of the flow-extension curve of the polymer, the distribution of its steady-state end-to-end distances, and the characteristic relaxation time τR of these distances. Among other findings, our calculations indicate that the coil-stretch transition is discontinuous in the N → ∞ limit, that the effective free energy of the chain is unimodal at all values of the flow, becoming broad and flat in the immediate vicinity of the transition, and that the ratio of τR to the Rouse relaxation time increases abruptly at the transition before eventually reaching a plateau value at large flow strengths. These aspects of the coil-stretch transition place it among a larger class of unconventional nominally first-order single chain transitions that include the adsorption transition of surface-tethered polymers and the escape transition of compressed polymers. [ABSTRACT FROM AUTHOR]

Experimental observation of transition paths—short events when the system of interest crosses the free energy barrier separating reactants from products—provides an opportunity to probe the dynamics of barrier crossing. Yet limitations in the experimental time resolution usually result in observing trajectories that are smoothed out, recross the transition state fewer times, and exhibit apparent velocities that are much lower than the instantaneous ones. Here we show that it is possible to define (and measure) an effective transition-path velocity which preserves exact information about barrier crossing dynamics in the following sense: the exact transition rate can be written in a form resembling that given by transition-state theory, with the mean thermal velocity replaced by the transition-path velocity. In addition, the transition-path velocity (i) ensures the exact local value of the unidirectional reactive flux at equilibrium and (ii) leads to the exact mean transition-path time required for the system to cross the barrier region separating reactants from products. We discuss the coordinate dependence of the transition path velocity and derive analytical expressions for it in the case of diffusive dynamics. These results can be used to discriminate among models of barrier crossing dynamics in single-molecule force spectroscopy studies. [ABSTRACT FROM AUTHOR]

The theoretical description of the phase behavior of polymers dissolved in binary mixtures of water and other miscible solvents is greatly complicated by the self- and mutual-association of the solvent molecules. As a first step in treating these complex and widely encountered solutions, we have developed an extension of Flory-Huggins theory to describe mixtures of two self- and mutually-associating fluids comprised of small molecules. Analytic expressions are derived here for basic thermodynamic properties of these fluid mixtures, including the spinodal phase boundaries, the second osmotic virial coefficients, and the enthalpy and entropy of mixing these associating solvents. Mixtures of this kind are found to exhibit characteristic closed loop phase boundaries and entropy-enthalpy compensation for the free energy of mixing in the low temperature regime where the liquid components are miscible. As discussed byWidom et al. [Phys. Chem. Chem. Phys. 5, 3085 (2003)], these basic miscibility trends, quite distinct from those observed in non-associating solvents, are defining phenomenological characteristics of the "hydrophobic effect." We find that our theory of mixtures of associating fluids captures at least some of the thermodynamic features of real aqueous mixtures. [ABSTRACT FROM AUTHOR]

The phase behavior and the homogeneous nucleation of an equimolar mixture of octahedra and cuboctahedra are studied using thermodynamic integration, Gibbs-Duhem integration, and umbrella sampling simulations. The components of this mixture are modeled as polybead objects of equal edge lengths so that they can assemble into a space-filling compound with the CsCl crystal structure. Taking as reference the hard-core system where the compound crystal does not spontaneously nucleate, we quantified the effect of inter-species selective interactions on facilitating the disorder-to-order transition. Facet selective and facet non-selective inter-species attractions were considered, and while the former was expectedly more favorable toward the target tessellating structure, the latter was found to be similarly effective in nucleating the crystal compound. Ranges for the strength of attractions and degree of supersaturation were identified where the nucleation free-energy barrier was small enough to foretell a fast process but large enough to prevent spinodal fluctuations that can trap the system in dense metastable states lacking long-range order. At those favorable conditions, the tendency toward the local orientational order favored by packing entropy is amplified and found to play a key role seeding nuclei with the CsCl structure. [ABSTRACT FROM AUTHOR]

The phase behavior of a monodisperse melt of polymer molecules consisting of two rod-like segments joined at an angle a has been inspected within the Landau theory of phase transitions. The interactions between monomer units were assumed to be of the Maier-Saupe form. The Landau-de Gennes expansion of the free energy of the melt has been obtained up to the sixth order in powers of the nematic order parameter, the coefficients of this expansion have been calculated from the microscopic model of polymer molecule. The phase diagram contains the regions of stability of isotropic, prolate uniaxial, oblate uniaxial, and biaxial nematic phases. The isotropic-uniaxial nematic and uniaxial-biaxial nematic transitions are of the first and second order, respectively. We found two Landau points in the phase diagram at which continuous transition from biaxial nematic state to isotropic phase occurs. [ABSTRACT FROM AUTHOR]

Simulated tempering (ST) is a widely used enhancing sampling method for Molecular Dynamics simulations. As one expanded ensemble method, ST is a combination of canonical ensembles at different temperatures and the acceptance probability of cross-temperature transitions is determined by both the temperature difference and the weights of each temperature. One popular way to obtain the weights is to adopt the free energy of each canonical ensemble, which achieves uniform sampling among temperature space. However, this uniform distribution in temperature space may not be optimal since high temperatures do not always speed up the conformational transitions of interest, as anti-Arrhenius kinetics are prevalent in protein and RNA folding. Here, we propose a new method: Enhancing Pairwise State-transition Weights (EPSW), to obtain the optimal weights by minimizing the round-trip time for transitions among different metastable states at the temperature of interest in ST. The novelty of the EPSW algorithm lies in explicitly considering the kinetics of conformation transitions when optimizing the weights of different temperatures. We further demonstrate the power of EPSW in three different systems: a simple two-temperature model, a two-dimensional model for protein folding with anti-Arrhenius kinetics, and the alanine dipeptide. The results from these three systems showed that the new algorithm can substantially accelerate the transitions between conformational states of interest in the ST expanded ensemble and further facilitate the convergence of thermodynamics compared to the widely used free energy weights. We anticipate that this algorithm is particularly useful for studying functional conformational changes of biological systems where the initial and final states are often known from structural biology experiments. [ABSTRACT FROM AUTHOR]

A free energy functional for a crystal which contains both the symmetry-conserved and symmetrybroken parts of the direct pair correlation function has been used to investigate the fluid-solid transition in systems interacting via purely repulsive Weeks-Chandler-Anderson Lennard-Jones potential and the full Lennard-Jones potential. The results found for freezing parameters for the fluid-face centred cubic crystal transition are in very good agreement with simulation results. It is shown that although the contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is small compared to that of the symmetry conserving part, its role is crucial in stabilizing the crystalline structure and on values of the freezing parameters. [ABSTRACT FROM AUTHOR]

The solid-liquid interface (SLI) free energy was determined from molecular dynamics (MD) simulation for several body centered cubic (bcc) metals and B2 metallic compounds (space group: Pm3m; prototype: CsCl). In order to include a bcc metal with a low melting temperature in our study, a semi-empirical potential was developed for Na. Two additional synthetic "Na" potentials were also developed to explore the effect of liquid structure and latent heat on the SLI free energy. The obtained MD data were compared with the empirical Turnbull, Laird, and Ewing relations. All three relations are found to predict the general trend observed in the MD data for bcc metals obtained within the present study. However, only the Laird and Ewing relations are able to predict the trend obtained within the sequence of "Na" potentials. The Laird relation provides the best prediction for our MD data and other MD data for bcc metals taken from the literature. Overall, the Laird relation also agrees well with our B2 data but requires a proportionality constant that is substantially different from the bcc case. It also fails to explain a considerable difference between the SLI free energies of some B2 phases which have nearly the same melting temperature. In contrast, this difference is satisfactorily described by the Ewing relation. Moreover, the Ewing relation obtained from the bcc dataset also provides a reasonable description of the B2 data. [ABSTRACT FROM AUTHOR]

In continuation of our work in Gantapara et al., [Phys. Rev. Lett. 111, 015501 (2013)], we investigate here the thermodynamic phase behavior of a family of truncated hard cubes, for which the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. We used Monte Carlo simulations and free-energy calculations to establish the full phase diagram. This phase diagram exhibits a remarkable richness in crystal and mesophase structures, depending sensitively on the precise particle shape. In addition, we examined in detail the nature of the plastic crystal (rotator) phases that appear for intermediate densities and levels of truncation. Our results allow us to probe the relation between phase behavior and building-block shape and to further the understanding of rotator phases. Furthermore, the phase diagram presented here should prove instrumental for guiding future experimental studies on similarly shaped nanoparticles and the creation of new materials. [ABSTRACT FROM AUTHOR]

We have studied the equation of state (EOS) and the equilibrium behavior of a two-component mixture of equal-sized, nonadditive hard disks with an interspecies collision diameter that is larger than that of each component. For this purpose, we have calculated the fifth virial coefficient by evaluating numerically the irreducible cluster integrals by a Monte Carlo method. This information is used to calculate both the virial equation of state and an equation of state based on a resummation of the virial expansion. Then, the fluid-fluid phase coexistence boundaries are determined by integrating the EOS so as to obtain the free energy of the system. Canonical and Gibbs ensemble Monte Carlo simulations over a wide range of nonadditivity are also performed in order to provide a benchmark to the theoretical predictions. [ABSTRACT FROM AUTHOR]

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitable conditions, these MSMs can be used to calculate kinetic quantities (e.g., rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators. [ABSTRACT FROM AUTHOR]

We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the solution as a function of the radius of gyration and the average solvent number density within the gyration volume. The resulting system of coupled equations is solved varying the polymer-solvent repulsion strength at high solvent pressure in the bulk. We show that the coil-globule (globule-coil) transition occurs accompanied by a local solvent evaporation (condensation) within the gyration volume. [ABSTRACT FROM AUTHOR]

We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition-path theory we also provide a quantitative description of the unfolding pathways followed by the system. Our study shows a complex dynamical scenario. In particular, we see that the usual one-dimensional picture: free-energy vs end-to-end distance representation, gives a misleading description of the process. Unfolding can occur following different pathways and configurations which seem to play a central role in one-dimensional pictures are not the intermediate states of the unfolding dynamics. [ABSTRACT FROM AUTHOR]

The precise estimation of the location of phase transitions is an essential task in the study of many condensed matter systems. A recently developed technique denoted interface pinning (IP) [U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B. 88,094101 (2013); U. R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] can accurately estimate the location of fluid-solid transition using the NPzT ensemble for single-component systems by computing the free energy difference between a solid and a fluid. The IP method is extended here to be applicable to different ensembles for both single-component systems and binary mixtures. A more general scheme is also proposed for the extrapolation of properties targeting coexistence conditions. This framework is used to estimate the coexistence pressure for the isotropic-rotator phase transition for three single-component polyhedral systems and to estimate isotropic-crystal coexistence compositions for a binary mixture of hard cubes and spheres. In addition, by exploring various choices for the order parameter used to distinguish between the isotropic and ordered phases, it is found that volume provides a reasonable alternative to translational order parameters which can be either more expensive to calculate or unable to pin a two-phase interfacial state. [ABSTRACT FROM AUTHOR]

We used flat-histogram sampling Monte Carlo to study capillary phase transitions in deformable adsorbent materials. Specifically, we considered a pure adsorbate fluid below its bulk critical temperature within a slit pore of variable pore width. The instantaneous pore width is dictated by a number of factors, such as adsorbate loading, reservoir pressure, fluid-wall interaction, and bare adsorbent properties. In the slit pores studied here, the bare adsorbent free energy was assumed to be biparabolic, consisting of two preferential pore configurations, namely, the narrow pore and the large pore configurations. Four distinct phases could be found in the adsorption isotherms. We found a low-pressure phase transition, driven primarily by capillary condensation/evaporation and accompanied by adsorbent deformation in response. The deformation can be a relatively small contraction/expansion as seen in elastic materials, or a large-scale structural transformation of the adsorbent. We also found a high-pressure transition driven by excluded volume effects, which tends to expand the material and thus results in a large-scale structural transformation of the adsorbent. The adsorption isotherms and osmotic free energies can be rationalized by considering the relative free energy differences between the basins of the bare adsorbent free energy. [ABSTRACT FROM AUTHOR]