Confinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.     

Relationships between self-diffusivity, packing fraction, and excess entropy in simple bulk and confined fluids

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. Here, we explore the connections between self-diffusivity, density, and excess entropy for two of the most widely used model "simple" liquids, the equilibrium Lennard-Jones and square-well fluids, in both bulk and confined environments. We find that the self-diffusivity data of the Lennard-Jones fluid can be approximately collapsed onto a single curve (i) versus effective packing fraction and (ii) in appropriately reduced form versus excess entropy, as suggested by two well-known scaling laws. Similar data collapse does not occur for the square-well fluid, a fact that can be understood on the basis of the nontrivial effects that temperature has on its static structure. Nonetheless, we show that the implications of confinement for the self-diffusivity of both of these model fluids, over a broad range of equilibrium conditions, can be predicted on the basis of knowledge of the bulk fluid behavior and either the effective packing fraction or the excess entropy of the confined fluid. Excess entropy is perhaps the most preferable route due to its superior predictive ability and because it is a standard, unambiguous thermodynamic quantity that can be readily predicted via classical density functional theories of inhomogeneous fluids.     

Using gamma distributions to predict self-diffusivities and density of states of fluids confined in carbon nanotubes

The density of states of rare gas atoms confined in carbon nanotubes is analyzed using a recently proposed model based on gamma distributions [Krishnan and Ayappa, J. Chem. Phys., 124 144503 (2006)]. The inputs into the model are the 2nd and 4th frequency moments that are obtained from molecular dynamics simulations. The predicted density of states, velocity autocorrelation functions and self-diffusivities are compared with those obtained from molecular dynamics simulations, for different nanotube loadings and temperatures. All results are reported for argon confined in a (16,16) carbon nanotube. The model predictions are extremely accurate at intermediate reduced densities of rhosigma(3) = 0.3, 0.4, where the majority of the self-diffusivity predictions lie within 10% of the simulation results. Since the frequency moments can be also obtained from Monte Carlo simulations, the study suggests an alternate route to the system dynamics of strongly confined fluids.     

Sorption of nitrogen-containing aromatic compounds on ultradispersed diamonds

Adsorption of a number of aniline and pyridine derivatives from water-acetonitrile solution on ultradispersed diamonds was investigated using dynamic sorption method. It was shown that the nature of functional substitutes and their position in molecules of nitrogen-containing compounds of pyridine and aniline have a pronounced effect on adsorption on the surface of ultradispersed diamonds. The dependence of chromatographic sorbate retention on the content of mobile phase could be described by a curve with a minimum. Such nonlinear relationship was explained by the change in the ratio of contribution of specific and non-specific interaction to the sorbate retention that was observed on varying the volume content of an organic component in mobile phase. The influence of temperature on sorption of pyridine and aniline derivatives on ultradisperesed diamonds was investigated. The changes in enthalpy and entropy factors of competitive sorption of sorbates were determined.     

Helix formation inside a nanotube: possible influence of backbone-water hydrogen bonding by the confining surface through modulation of water activity

Recent molecular dynamics simulations of Sorin and Pande [J. Am. Chem. Soc. 128, 6316 (2006)] in explicit solvent found that helix formation of an alanine peptide is disfavored inside a nanotube relative to that in bulk solution. Here, we present a theory to quantitatively rationalize their simulation results. The basic idea is that the nonpolar inner surface of the nanotube creates a depletion layer and raises the activity of the confined water. The raised water activity, in turn, stabilizes the coil state through hydrogen bonding with the backbone amides and carbonyls. We account for the influence of water activity on helix formation within the Lifson-Roig theory. With physically reasonable parameters, the dependence of the helical content on the diameter of the nanotube obtained in the simulations is well reproduced.     

A free-energy landscape picture and Landau theory for the dynamics of disordered materials

Landau's theory of phase transitions [Nature (London) 138, 840 (1936); Statistical Physics (Pergamon, London, 1959)] is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the potential-energy minima have negligible influence on the dynamics. The dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the curvature of the internal-energy maximum. The temperature dependence of the fluctuations yields Vogel-Tamman-Fulcher-type [Phys. Z. 22, 645 (1921); J. Am. Ceram. Soc. 8, 339 (1925); Z. Anorg. Allg. Chem. 156, 245 (1926)] relaxation rates and approximate time-temperature superposition, consistent with the Williams-Landell-Ferry [J. Am. Chem. Soc. 77, 3701 (1955)] procedure for analyzing the dynamics of complex fluids, while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.     

The free energy of the metastable supersaturated vapor via restricted ensemble simulations. II. Effects of constraints and comparison with molecular dynamics simulations

Extensive restricted canonical ensemble Monte Carlo simulations [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)] were performed. Pressure, excess chemical potential, and excess free energy with respect to ideal gas data were obtained at different densities of the supersaturated Lennard-Jones (LJ) vapor at reduced temperatures from 0.7 to 1.0. Among different constraints imposed on the system studied, the one with the local minimum of the excess free energy was taken to be the approximated equilibrium state of the metastable LJ vapor. Also, a comparison of our results with molecular dynamic simulations [A. Linhart et al., J. Chem. Phys. 122, 144506 (2005)] was made.     

Hard-sphere perturbation theory for a model of liquid Ga

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.     

Investigation of excess adsorption, solvation force, and plate-fluid interfacial tension for Lennard-Jones fluid confined in slit pores

The excess Helmholtz free energy functional is formulated in terms of a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)] for a short ranged repulsion and a first-order mean-spherical approximation theory [Y. P. Tang, J. Chem. Phys. 118, 4140 (2003)] for a long ranged attraction. Within the framework of the density functional theory, the density profile, excess adsorption, solvation force, and plate-fluid interfacial tension of a Lennard-Jones fluid confined in slit pores are predicted, and the results agree well with the simulation data. The phase equilibria inside the slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal, and the plate-fluid interfacial tensions at equilibrium states are predicted consequently.     

Comparing landscape calculations with calorimetric data on ortho-terphenyl, and the question of the configurational fraction of the excess entropy

Mossa et al. [Phys. Rev. E 65, 041205 (2002)] have calculated the total and configurational entropies of supercooled ortho-terphenyl liquid using the potential-energy landscape formalism and a simplified model of the intermolecular potential. I show here that the agreement of their calculated configurational entropy with the experimental data depends on what is assumed about the configurational fraction of the excess entropy and its temperature dependence. In particular, if the configurational fraction is taken as 0.70 and independent of temperature the agreement is excellent; if a marked temperature dependence of that fraction inferred from calorimetric data is assumed the agreement is only fair at best. This marked temperature dependence of the configurational fraction also implies some implausible behavior of contributions to the excess entropy at the Kauzmann temperature, but no obvious reason for disregarding it presents itself.     

石墨烯/纳米管复合结构吸附分离CO2/CH4混合物的分子模拟

采用巨正则蒙特卡洛(GCMC)及分子动力学(MD)方法探讨了石墨烯/碳纳米管三维骨架结构(GNHS)对等摩尔CO₂/CH₄二元混合物的吸附分离性能. 模拟结果表明CO₂比CH₄更易吸附于GNHS中, GNHS与(6, 6)SWCNT (单壁碳纳米管)相比具有更高的分离性能. 随着温度升高, CO₂的吸附量快速降低, 而CH₄的吸附量则呈现出先升高后降低的趋势. 最后采用分子动力学方法计算了CO₂与CH₄的自扩散系数及停留时间等动力学相关参数, 发现CO₂在GNHS内扩散的阻力更大. 而各组分在吸附剂外部吸附层内的扩散过程对混合物的分离也存在一定影响.     

Excess entropy scaling of transport properties in network-forming ionic melts (SiO(2) and BeF(2))

The regime of validity of Rosenfeld excess entropy scaling of diffusivity and viscosity is examined for two tetrahedral, network-forming ionic melts (BeF(2) and SiO(2)) using molecular dynamics simulations. With decrease in temperature, onset of local caging behavior in the diffusional dynamics is shown to be accompanied by a significant increase in the effect of three-body and higher-order particle correlations on the excess entropy, diffusivity, ionic conductivity, and entropy-transport relationships. The signature of caging effects on the Rosenfeld entropy scaling of transport properties is a distinctly steeper dependence of the logarithm of the diffusivity on the excess entropy in ionic melts. This is shown to be true also for a binary Lennard-Jones glassformer, based on available results in the literature. Our results suggest that the onset of a landscape-influenced regime in the dynamics is correlated with this characteristic departure from Rosenfeld scaling. The breakdown of the Nernst-Einstein relation in the ionic melts can also be correlated with the emerging cooperative dynamics.     

Evidence in support of levitation effect as the reason for size dependence of ionic conductivity in water: a molecular dynamics simulation

We report extensive molecular dynamics simulations of (i) model ions in water at high concentrations as a function of the size and charge of the ion as well as (ii) realistic simulation of Cl- and Br- ions at low concentrations in water at room temperature. We also analyze existing experimental data in light of the results obtained here. The halide ion simulations have been carried out using the interaction potentials of Koneshan et al. (J. Phys. Chem. B 1998, 102, 4193). We compute structural and dynamical properties of ions in water and explore their variation with size and charge of the ion. We find that ions of certain intermediate sizes exhibit a maximum in self-diffusivity in agreement with previous experimental measurements and computer simulations. We analyze molecular dynamics trajectories in light of the previous understanding of the levitation effect (LE) and the recent suggestion that ionic conductivity has its origin in LE (J. Phys. Chem. B 2005, 109, 8120). We report the distribution of void and neck radii that exist amidst water. Our analysis suggests that the ion with maximum self-diffusivity is characterized by a lower activation energy and a single-exponential decay of F(s)(k,t). The behavior of these and other related quantities of the ion with maximum self-diffusivity are characteristic of the anomalous regime of the LE. The simulation results of Br- and Cl- ions in water also yield results in agreement with the predictions of LE. A plot of experimental conductivity data in the literature for alkali ions in water by Kay and Evans (J. Phys. Chem. 1966, 70, 2325) also yields a lower activation energy for the ion with maximum conductivity in excellent agreement with the LE. To the best of our knowledge, none of the existing theories predict a lower activation energy for the ion with maximum conductivity.     

Modeling velocity autocorrelation functions for confined fluids using gamma distributions

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.     

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [Nature (London) 381, 137 (1996)], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity.     

Second virial coefficients of adsorption isotherms of organic molecules on porous polymers

The dependence of the specific retention volumes of sorbates on their concentration in the gas phase is investigated. It is shown that the slope tangent of the dependence is related to the second coefficient of the virial expansion of adsorption isotherm. It is established that the free energy of sorbate-sorbate interactions on the surface of porous polymer sorbents is constant for all investigated molecules. An equation for calculating retention volumes at different sorbate concentrations is proposed.     

Mesoscopic analysis of conformational and entropic contributions to nonspecific adsorption of HP copolymer chains using dynamic Monte Carlo simulations

Dynamic Monte Carlo simulations of short linear HP-type copolymers exhibiting proteinlike characteristics are used to investigate both chain dynamics and changes in chain conformational entropy and their contributions to the energetics of adsorption onto a solid-liquid interface. The dMC results show that the conformations and energies of adsorbed chains are highly degenerate. The ensemble-averaged energy of the adsorbed state is dependent on temperature, chain sequence, native-state stability, and sorbent surface geometry and hydrophobicity. Mesoscopic thermodynamic analyses reveal that, although increased chain conformational entropy contributes to the driving force for adsorption in certain cases, many conditions exist where the change in conformational entropy is either negligible or unfavorable due to constraints imposed by the need to form a large and specific number of favorable intra- and intermolecular contacts and by the impenetrable nature of the sorbent surface. Step-number-averaged energy trajectories, based on sampling of a large number of energy trajectories and thus conformational states at each step number, suggest that the search for a global energy minimum is gradual, so that adsorption is first reversible but becomes apparently irreversible with longer exposure to the sorbent. These results appear to be connected to the conformational adaptability of the chain both on the surface and in solution, and an adsorption model taking chain conformational dynamics into account is proposed.     

Ionic melts with waterlike anomalies: thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.