Efficient molecular simulation of chemical potentials

Thermodynamics of liquid and fluid mixtures from the kinetic Monte Carlo viewpoint

In this study a binary mixture is modelled in a uniform simulation cell at various temperatures using an extended version of the grand canonical kinetic Monte Carlo (GC-kMC) method. The main goal of this study is to consider the thermodynamic properties of binary liquids, gases, and gas-liquid mixtures from a more general point of view than that applied to the particular case of vapour-liquid equilibrium when the pressure and partial chemical potentials in coexisting phases are the same. Particular attention is paid to thermodynamic functions such as chemical potentials, Gibbs free energy and entropy. For the pair potential of unlike molecules a more universal scheme is proposed in comparison with the Lorentz-Berthelot combining rule. The approach is tested on an Ar-Kr mixture in a wide range of temperatures. In all cases, the obtained values of chemical potentials, pressure and internal energy for the entire set of component densities and temperature fully satisfy the Gibbs-Duhem equation with a high degree of accuracy. For the case of vapour-liquid equilibrium, the developed approach made it possible to reproduce the experimental pressure-composition diagrams with the highest accuracy ever achieved in the literature. Despite the fact that the Ar-Kr mixture, according to Raoult's law, is close to an ideal system, it was found that the partial pressures in the liquid phase or in a dense supercritical gas mixture are non-linear functions of the composition, and the partial pressure of the heavier component (Kr) can even be negative.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Atomistic Modeling of Hydrogen and Oxygen Solubility in Semicrystalline PA-6 and HDPE Materials

Hydrogen is a clean and sustainable energy carrier which plays a major role in the transition of the global energy market to a less fossil fuel dependent future. Polymer-based materials are crucial in the production, storage, transportation, and energy extraction of hydrogen. More insights in the hydrogen-polymers interactions are required to guide material design and product development, especially for hydrogen solubility in polymers, which is crucial in many applications. The current study aims at rationalizing the determining factors of hydrogen solubility in two relevant polymers: polyamide-6 (PA-6) and high density polyethylene (HDPE). Based on atomistic molecular dynamics simulations and experimental data, we have reached several conclusions related to hydrogen and oxygen solubility in these two polymers. The crystal phases of PA-6 and HDPE are impenetrable to hydrogen and oxygen at elevated pressures, despite the small molecular size of hydrogen and oxygen. The practical implication for gas barrier applications is that polymer crystals act as impermeable obstacles and gas migration takes place primarily in the amorphous phase. Experimental hydrogen and oxygen solubilities in PA-6 and HDPE at elevated pressures can be predicted in a semiquantitative manner by molecular simulations. The discrepancies between experimental and predicted values could be attributed to neglect of the effect of crystal regions on the amorphous polymer domains. Although hydrogen is smaller than oxygen, it has been experimentally observed that hydrogen has a lower solubility in PA-6 and HDPE than oxygen. This observation has been confirmed by molecular simulations and attributed to the more favorable energetic interactions of oxygen with PA-6 and PE than of hydrogen. These interactions dominate the solubility behavior over the distribution of the accessible volume in the polymers.

Molecular Characterization of Membrane Gas Separation under Very High Temperatures and Pressure: Single- and Mixed-Gas CO2/CH4 and CO2/N2 Permselectivities in Hybrid Networks

This work illustrates the potential of using atomistic molecular dynamics (MD) and grand-canonical Monte Carlo (GCMC) simulations prior to experiments in order to pre-screen candidate membrane structures for gas separation, under harsh conditions of temperature and pressure. It compares at 300 °C and 400 °C the CO₂/CH₄ and CO₂/N₂ sieving properties of a series of hybrid networks based on inorganic silsesquioxanes hyper-cross-linked with small organic PMDA or 6FDA imides. The inorganic precursors are the octa(aminopropyl)silsesquioxane (POSS), which degrades above 300 °C, and the octa(aminophenyl)silsesquioxane (OAPS), which has three possible meta, para or ortho isomers and is expected to resist well above 400 °C. As such, the polyPOSS-imide networks were tested at 300 °C only, while the polyOAPS-imide networks were tested at both 300 °C and 400 °C. The feed gas pressure was set to 60 bar in all the simulations. The morphologies and densities of the pure model networks at 300 °C and 400 °C are strongly dependent on their precursors, with the amount of significant free volume ranging from ~2% to ~20%. Since measurements at high temperatures and pressures are difficult to carry out in a laboratory, six isomer-specific polyOAPS-imides and two polyPOSS-imides were simulated in order to assess their N₂, CH₄ and CO₂ permselectivities under such harsh conditions. The models were first analyzed under single-gas conditions, but to be closer to the real processes, the networks that maintained CO₂/CH₄ and CO₂/N₂ ideal permselectivities above 2 were also tested with binary-gas 90%/10% CH₄/CO₂ and N₂/CO₂ feeds. At very high temperatures, the single-gas solubility coefficients vary in the same order as their critical temperatures, but the differences between the penetrants are attenuated and the plasticizing effect of CO₂ is strongly reduced. The single-gas diffusion coefficients correlate well with the amount of available free volume in the matrices. Some OAPS-based networks exhibit a nanoporous behavior, while the others are less permeable and show higher ideal permselectivities. Four of the networks were further tested under mixed-gas conditions. The solubility coefficient improved for CO₂, while the diffusion selectivity remained similar for the CO₂/CH₄ pair and disappeared for the CO₂/N₂ pair. The real separation factor is, thus, mostly governed by the solubility. Two polyOAPS-imide networks, i.e., the polyorthoOAPS-PMDA and the polymetaOAPS-6FDA, seem to be able to maintain their CO₂/CH₄ and CO₂/N₂ sieving abilities above 2 at 400 °C. These are outstanding performances for polymer-based membranes, and consequently, it is important to be able to produce isomer-specific polyOAPS-imides for use as gas separation membranes under harsh conditions.

Molecular dynamics simulation for membrane separation and porous materials: A current state of art review

Computational frameworks have been under specific attention within the last two decades. Molecular Dynamics (MD) simulations, identical to the other computational approaches, try to address the unknown question, lighten the dark areas of unanswered questions, to achieve probable explanations and solutions. Owing to their complex microporous structure on one side and the intricate biochemical nature of various materials used in the structure, separative membrane materials possess peculiar degrees of complications. More notably, as nanocomposite materials are often integrated into separative membranes, thin-film nanocomposites and porous separative nanocomposite materials could possess an additional level of complexity with regard to the nanoscale interactions brought to the structure. This critical review intends to cover the recent methods used to assess membranes and membrane materials. Incorporation of MD in membrane technology-related fields such as desalination, fuel cell-based energy production, blood purification through hemodialysis, etc., were briefly covered. Accordingly, this review could be used to understand the current extent of MD applications for separative membranes. The review could also be used as a guideline to use the proper MD implementation within the related fields.

Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation

Several new biased sampling methods were summarized for solution chemical potential calculation methods in the field of emulsion microencapsulation. The principles, features, and calculation efficiencies of various biased Widom insertion sampling methods were introduced, including volume detection bias, simulation ensemble bias, and particle insertion bias. The proper matches between various types of solution in emulsion and biased Widom methods were suggested, following detailed analyses on the biased insertion techniques. The volume detection bias methods effectively improved the accuracy of the data and the calculation efficiency by inserting detection particles and were suggested to be used for the calculation of solvent chemical potential for the homogeneous aqueous phase of the emulsion. The chemical potential of water, argon, and fluorobenzene (a typical solvent of the oil phase in double emulsion) was calculated by a new, optimized volume detection bias proposed by this work. The recently developed Well-Tempered(WT)-Metadynamics method skillfully constructed low-density regions for particle insertion and dynamically adjusted the system configuration according to the potential energy around the detection point, and hence, could be used for the oil-polymer mixtures of microencapsulation emulsion. For the macromolecule solutes in the oil or aqueous phase of the emulsion, the particle insertion bias could be applied to greatly increase the success rate of Widom insertions. Readers were expected to choose appropriate biased Widom methods to carry out their calculations on chemical potential, fugacity, and solubility of solutions based on the system molecular properties, inspired by this paper.

Gibbs-ensemble Monte Carlo simulation of H_{2}-He mixtures

We explore the performance of the Gibbs-ensemble Monte Carlo simulation technique by calculating the miscibility gap of H_{2}-He mixtures with analytical exponential-six potentials. We calculate several demixing curves for pressures up to 500 kbar and for temperatures up to 1800K and predict a H_{2}-He miscibility diagram for the solar He abundance for temperatures up to 1500K and determine the demixing region. Our results are in good agreement with ab initio simulations in the nondissociated region of the phase diagram. However, the particle number necessary to converge the Gibbs-ensemble Monte Carlo method is yet too large to offer a feasible combination with ab initio electronic structure calculation techniques, which would be necessary at conditions where dissociation or ionization occurs.

Entropy in Molecular Fluids: Interplay between Interaction Complexity and Criticality

Using flat-histogram simulations, we calculate the entropy of molecular fluids along the vapor-liquid phase boundary. Our simulation approach is based on the evaluation of the canonical and grand-canonical partition functions, which, in turn, provide access to entropy through the statistical mechanics formalism. The results allow us to determine the critical entropy of molecular fluids and to uncover that the transition occurs symmetrically from an entropic standpoint. This can best be seen through the patterns exhibited by the thermodynamic variables temperature and pressure when plotted against the entropy of the coexisting phases. This behavior is found to hold for apolar, quadrupolar, and dipolar fluids. Finally, we identify functional forms that characterize the relation between thermodynamic variables and entropy along the coexistence curve up to the critical point.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Simulating Water Exchange to Buried Binding Sites

Traditional molecular dynamics (MD) simulations of proteins, which relies on integration of Newton's equations of motion, cannot efficiently equilibrate water occupancy for buried cavities in proteins. This leads to slow convergence of thermodynamic averages for such systems. We have addressed this challenge by efficiently integrating standard Metropolis Monte Carlo (MC) translational water moves with MD in the AMBER simulation package. The translational moves allow water to easily enter or exit buried sites in a thermodynamically correct way during a simulation. To maximize efficiency, the algorithm avoids moves that only interchange waters within the bulk around the protein instead focusing on moves that can transfer water between bulk and the protein interior. In addition, a steric grid allows avoidance of moves that would lead to obvious steric clashes, and a fast grid-based energy evaluation is used to reduce the number of expensive full energy calculations. The potential energy distribution produced using MC/MD was found to be statistically indistinguishable from that of control simulations using only MD, and the algorithm effectively equilibrated water across steric barriers and into binding pockets that are not accessible with pure MD. The MC/MD method introduced here should be of increasing utility for applications spanning protein folding, the elucidation of protein mechanisms, and free energy calculations for computer-aided drug design. It is available in version 18 release of the widely disseminated AMBER simulation package.

Molecular Simulation of Gas Solubility in Nitrile Butadiene Rubber

Molecular simulation is used to compute the solubility of small gases in nitrile butadiene rubber (NBR) with a Widom particle-insertion technique biased by local free volume. The convergence of the method is examined as a function of the number of snapshots upon which the insertions are performed and the number of insertions per snapshot and is compared to the convergence of the unbiased Widom insertion technique. The effect of varying the definition of local free volume is also investigated. The acrylonitrile content of the polymer is altered to examine its influence on the solubility of helium, CO₂, and H₂O, and the solubilities of polar gases are found to be enhanced relative to those of nonpolar gases, in qualitative agreement with experiment. To probe this phenomenon further, the solubilities are decomposed into contributions from the neighborhoods of different atoms, using a Voronoi cell construction, and a strong bias is found for CO₂ and H₂O in particular to be situated near nitrogen sites in the elastomer. Temperature is shown to suppress the solubility of CO₂ and H₂O but to increase that of helium. Increasing pressure is found to suppress the solubility of all gases but at different rates, according to a balance between their molecular sizes and electrostatic interactions with the polymer. These results are relevant to the use of NBR seals at elevated temperatures and pressures, such as in oil and gas wells.

Chemical potential of a test hard sphere of variable size in a hard-sphere fluid

The Labík and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is applied using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, P₀(η,σ₀), of tracer hard-sphere (HS) particles of different diameters, σ₀, in a host HS fluid of diameter σ and packing fraction, η, up to 0.5. It is shown analytically that the only polynomial representation of -ln⁡P₀(η,σ₀) consistent with the limits σ₀→0 and σ₀→∞ has necessarily a cubic form, c₀(η)+c₁(η)σ₀/σ+c₂(η)(σ₀/σ)²+c₃(η)(σ₀/σ)³. Our MD data for -ln⁡P₀(η,σ₀) are fitted to such a cubic polynomial and the functions c₀(η) and c₁(η) are found to be statistically indistinguishable from their exact solution forms. Similarly, c₂(η) and c₃(η) agree very well with the Boublík-Mansoori-Carnahan-Starling-Leland and Boublík-Carnahan-Starling-Kolafa formulas. The cubic polynomial is extrapolated (high density) or interpolated (low density) to obtain the chemical potential of the host fluid, or σ₀→σ, as βμ^ex=c₀+c₁+c₂+c₃. Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident.

Order and correlation contributions to the entropy of hydrophobic solvation

The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by identifying the structural feature responsible for the entropy change, and point to a possible explanation for the observed dependence on length scale. Our key results are that the hydrophobic effect, i.e. the signature, temperature-dependent, solvation entropy of nonpolar molecules in water, is largely due to a dispersion force arising from correlations between rotating permanent dipole moments, that the strength of this force depends on the Kirkwood g-factor, and that the strength of this force may be obtained exactly without simulation.

Field induced gradient simulations: a high throughput method for computing chemical potentials in multicomponent systems

We present a simulation method for direct computation of chemical potentials in multicomponent systems. The method involves application of a field to generate spatial gradients in the species number densities at equilibrium, from which the chemical potential of each species is theoretically estimated. A single simulation yields results over a range of thermodynamic states, as in high throughput experiments, and the method remains computationally efficient even at high number densities since it does not involve particle insertion at high densities. We illustrate the method by Monte Carlo simulations of binary hard sphere mixtures of particles with different sizes in a gravitational field. The results of the gradient Monte Carlo method are found to be in good agreement with chemical potentials computed using the classical Widom particle insertion method for spatially uniform systems.

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.

Predicting water sorption and volume swelling in dense polymer systems via computer simulation

Atomistic model structures of amorphous polyamide 6 (PA-6) and of an adhesive system consisting of the diglycidyl ether of bisphenol A (DGEBA) as epoxy resin and isophorone diamine (IPD) as a curing agent are generated. For the adhesive, we use a new approach for the generation of the cross-linked polymer networks. It takes into account the chemical reaction kinetics of the curing reaction and, therefore, results in more realistic network structures. On the basis of the corresponding model structures, the equilibrium water content and the swelling ratio of amorphous PA-6 and of the DGEBA+IPD networks are calculated via computer simulation for different thermodynamic conditions. A hybrid method is used combining the molecular dynamics technique with an accelerated test particle insertion method. The results are in reasonable agreement with experiments and, in the case of the PA-6 system, with results obtained via other computer simulation methods.

Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.

Why gases dissolve in liquids

The thermodynamics and statistical mechanics of solubility are fairly well understood. It is still very difficult, however, to make quantitative predictions of solubility for real systems from first principles. The purposes of this article are to present the results of solubility experiments in some prototype solute-solvent systems, to show how far they may be understood from molecular first principles, and to discuss some of the things that are still missing. The main systems used as examples have the inert gas xenon as solute and some simple organic liquids as solvents.

How Does Solute-Polarization Affect the Hydrophobic Hydration of Methane?

We simulate the solubility and solvation free energy of methane dissolved in water at infinite dilution. Molecular dynamics simulations of TIP4P-Ew model water are carried out at ambient pressure conditions over a large temperature interval, ranging from 250 K to 370 K. Solvation free energies are determined using the Widom particle insertion method. The fitted temperature dependent data is used to calculate solvation enthalpies, entropies, as well as the heat capacity of solvation. In particular we study the effect of polarizability of methane on those thermodynamic parameters. Solute polarization leads to a lowering of the solvation free energy at 298 K to 8.3 kJ mol−1, almost exactly matching the experimental value. A close inspection of the enthalpic and entropic contributions, however, reveals that this coincidence is a consequence of a compensation of enthalpic and entropic contributions, each of them deviating even larger from their respective experimental values. Surprisingly, the solute polarizability is apparently affecting the solvation entropy more strongly than the solvation enthalpy, leading to an about 5 J K−1 mol−1 smaller (less negative) solvation entropy compared to the non-polarizable model. The solute-water radial distribution functions of the polarizable particle reveals significant modifications, favoring small distances, as well as structural changes, very similar to those caused by a temperature increase. This is suggesting that the reduced negative solvation entropy of a polarizable methane particle is related to a more disordered, "high-temperature"-like hydration shell.

Computing Activity Coefficients of Binary Lennard-Jones Mixtures by Gibbs-Duhem Integration

We determine activity coefficients of both components of different binary Lennard-Jones mixtures obtained at T * = 2.0 and ρ * = 0.6 by using two different strategies: (i) direct evaluation of the excess chemical potentials of both components applying the potential distribution theorem, and (ii) using the Gibbs-Duhem integration based on the activity coefficients of the counter-component, which was calculated directly from the potential distribution theorem approach. Both methods lead numerically to similar results and therefore offer a route to determine activity coefficients of mixtures with large complex molecules by alternatively calculating chemical potentials of potentially simpler counter-constituents.

Water harvesting using a conducting polymer: a study by molecular dynamics simulation

The results of extensive molecular simulations of adsorption and diffusion of water vapor in polyaniline, made conducting by doping it with HCl or HBr over a broad range of temperatures, are reported. The atomistic model of the polymers was generated using energy minimization, equilibrium molecular dynamics simulations, and two different force fields. The computed sorption isotherms are in excellent agreement with the experimental data. The computed activation energies for the diffusion of water molecules in the polymers also compare well with what has been reported in the literature. The results demonstrate the potential of conducting polyaniline for water harvesting from air.

Atomistic simulation of nanoporous layered double hydroxide materials and their properties. II. Adsorption and diffusion

Nanoporous layered double hydroxide (LDH) materials have wide applications, ranging from being good adsorbents for gases (particularly CO(2)) and liquid ions to membranes and catalysts. They also have applications in medicine, environmental remediation, and electrochemistry. Their general chemical composition is [M(1-x)(II)M(x)(III)(OH(-))(2)](x+)[X(nm)(m-)nH(2)O], where M represents a metallic cation (of valence II or III), and X(nm)(m-) is an m-valence inorganic, or heteropolyacid, or organic anion. We study diffusion and adsorption of CO(2) in a particular LDH with M(II)=Mg, M(III)=Al, and x approximately = 0.71, using an atomistic model developed based on energy minimization and molecular dynamics simulations, together with a modified form of the consistent-valence force field. The adsorption isotherms and self-diffusivity of CO(2) in the material are computed over a range of temperature, using molecular simulations. The computed diffusivities are within one order of magnitude of the measured ones at lower temperatures, while agreeing well with the data at high temperatures. The measured and computed adsorption isotherms agree at low loadings, but differ by about 25% at high loadings. Possible reasons for the differences between the computed properties and the experimental data are discussed, and a model for improving the accuracy of the computed properties is suggested. Also studied are the material's hydration and swelling properties. As water molecules are added to the pore space, the LDH material swells to some extent, with the hydration energy exhibiting interesting variations with the number of the water molecules added. The implications of the results are discussed.

Simulations and density functional calculations of surface forces in the presence of semiflexible polymers

We simulate interactions between adsorbing and nonadsorbing surfaces immersed in solutions containing monodisperse semiflexible chains. Apart from the nature of the surfaces, we investigate responses to changes of the intrinsic chain stiffness, the degree of polymerization, and the bulk concentration. Our simulations display a sufficient accuracy and precision to reveal free-energy barriers that are small on a typical scale of surface force simulations, but still of the same order as the expected van der Waals interactions. Two different approaches have been tested: grand canonical simulations, improved by configurational-biased techniques, and a perturbation method utilizing the isotension ensemble. We find the former to be preferable when the surfaces are nonadsorbing, whereas the isotension approach is superior for calculations of interactions between adsorbing surfaces, especially if the polymers are stiff. We also compare our simulation results with predictions from several versions of polymer density functional theory. We find that a crucial aspect of these theories, in quantitative terms, is that they recognize that end monomers exclude more volume to the surrounding than inner ones do. Those theories provide satisfactorily accurate predictions, particularly when the surfaces are nonadsorbing.

Synergistic approach to improve "alchemical" free energy calculation in rugged energy surface

The authors present an integrated approach to "alchemical" free energy simulation, which permits efficient calculation of the free energy difference on rugged energy surface. The method is designed to obtain efficient canonical sampling for rapid free energy convergence. The proposal is motivated by the insight that both the exchange efficiency in the presently designed dual-topology alchemical Hamiltonian replica exchange method (HREM), and the confidence of the free energy determination using the overlap histogramming method, depend on the same criterion, viz., the overlaps of the energy difference histograms between all pairs of neighboring states. Hence, integrating these two techniques can produce a joint solution to the problems of the free energy convergence and conformational sampling in the free energy simulations, in which lambda parameter plays two roles to simultaneously facilitate the conformational sampling and improve the phase space overlap for the free energy determination. Specifically, in contrast with other alchemical HREM based free energy simulation methods, the dual-topology approach can ensure robust conformational sampling. Due to these features (a synergistic solution to the free energy convergence and canonical sampling, and the improvement of the sampling efficiency with the dual-topology treatment), the present approach, as demonstrated in the model studies of the authors, is highly efficient in obtaining accurate free energy differences, especially for the systems with rough energy landscapes.

Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: a general algorithm and its extension for free energy calculation on rugged energy surface

An approach is developed in the replica exchange framework to enhance conformational sampling for the quantum mechanical (QM) potential based molecular dynamics simulations. Importantly, with our enhanced sampling treatment, a decent convergence for electronic structure self-consistent-field calculation is robustly guaranteed, which is made possible in our replica exchange design by avoiding direct structure exchanges between the QM-related replicas and the activated (scaled by low scaling parameters or treated with high "effective temperatures") molecular mechanical (MM) replicas. Although the present approach represents one of the early efforts in the enhanced sampling developments specifically for quantum mechanical potentials, the QM-based simulations treated with the present technique can possess the similar sampling efficiency to the MM based simulations treated with the Hamiltonian replica exchange method (HREM). In the present paper, by combining this sampling method with one of our recent developments (the dual-topology alchemical HREM approach), we also introduce a method for the sampling enhanced QM-based free energy calculations.

Effect of curvature and chirality for hydrogen storage in single-walled carbon nanotubes: A Combined ab initio and Monte Carlo investigation

Combined ab initio and grand canonical Monte Carlo simulations have been performed to investigate the dependence of hydrogen storage in single-walled carbon nanotubes (SWCNTs) on both tube curvature and chirality. The ab initio calculations at the density functional level of theory can provide useful information about the nature of hydrogen adsorption in SWCNT selected sites and the binding under different curvatures and chiralities of the tube walls. Further to this, the grand canonical Monte Carlo atomistic simulation technique can model large-scale nanotube systems with different curvature and chiralities and reproduce their storage capacity by calculating the weight percentage of the adsorbed material (gravimetric density) under thermodynamic conditions of interest. The author's results have shown that with both computational techniques, the nanotube's curvature plays an important role in the storage process while the chirality of the tube plays none.