Jayant K. Singh

Appropriate methods to combine forward and reverse free-energy perturbation averages

We consider the accuracy of several methods for combining forward and reverse free-energy perturbation averages for two systems (labeled 0 and 1). The practice of direct averaging of these measurements is argued as not reliable. Instead, methods are considered of the form β(A1−A0)=−ln[〈w(u)exp(−βu/2)〉0/〈w(u)exp(+βu/2)〉1], where A is the free energy, β=1/kT is the reciprocal temperature, u=U1−U0 is the difference in configurational energy, w(u) is a weighting function, and the angle brackets indicate an ensemble average performed on the system indicated by the subscript. Choices are considered in which w(u)=1 and 1/cosh[(u−C)/2]; the latter being Bennett’s method where C is a parameter that can be selected arbitrarily, and may be used to optimize the precision of the calculation. We examine the methods in several applications: calculation of the pressure of a square-well fluid by perturbing the volume, the chemical potential of a high-density Lennard-Jones system, and the chemical potential of a model for ...

Surface tension and vapor–liquid phase coexistence of the square-well fluid

Vapor–liquid interfacial tension of square-well ~SW! fluids is calculated using three different methods viz., molecular dynamics ~MD! with collision-based virial evaluation, Monte Carlo with virial computed by volume perturbation, and Binder’s density-distribution method in conjunction with grand-canonical transition-matrix Monte Carlo ~GC-TMMC!. Three values of the SW attractive well range parameter were studied: l51.5, 1.75, and 2.0, respectively. The results from MD and GC-TMMC methods are in very good mutual agreement, while the volume-perturbation method yields data of unacceptable quality. The results are compared with predictions from the statistical associating fluid theory ~SAFT!, and SAFT is shown to give a good estimate for the systems studied. Liquid and vapor coexistence densities and saturation pressure are determined from analysis of GC-TMMC data and the results are found to agree very well with the established literature data.

Molecular simulation of shale gas adsorption and diffusion in inorganic nanopores

We studied the structural and dynamical properties of methane and ethane in montmorillonite (MMT) slit pore of sizes 10, 20 and 30 Å using grand canonical Monte Carlo and classical molecular dynamics (MD) simulations. The isotherm, at 298.15 K, is generated for pressures up to 60 bar. The molecules preferentially adsorb at the surface as indicated by the density profile. In case of methane, we observe only a single layer, at the pore wall, whose density increases with increasing pressure. However, ethane also displays a second layer, though of low density in case of pore widths 20 and 30 Å. In-plane self-diffusion coefficient, D‖, of methane and ethane is of the order of 10− 6 m2/s. At low pressure, D‖ increases significantly with the pore size. However, D‖ decreases rapidly with increasing pressure. Furthermore, the effect of pore size on D‖ diminishes at high pressure. Ideal adsorbed solution theory is used to understand the adsorption behaviour of the binary mixture of methane (80%) and ethane (20%) at 298.15 K. Furthermore, we calculate the selectivity of the gases at various pressures of the mixture, and found high selectivity for ethane in MMT pores. However, selectivity of ethane decreases with increase in pressure or pore size.

Surface tension and vapor-liquid phase coexistence of confined square-well fluid.

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.

Wetting transition of nanodroplets of water on textured surfaces: a molecular dynamics study

The crossover behaviour of water droplets state from the Wenzel state to the Cassie state with varying pillar height and surface fraction is examined critically using molecular dynamics. We report the effect of the system size on the wetting behaviour of water droplets by examining the contact angle for both regimes. We observe that when the droplet size is comparable to the pillar dimension, the contact angle of droplets fluctuates with increasing droplet size because of the contact line pinning, which is more pronounced in the Wenzel regime. We further demonstrate the phantom-wall method to evaluate free energy of intermediate wetting states.

Molecular Simulation Study of Vapor-Liquid Critical Properties of a Simple Fluid in Attractive Slit Pores: Crossover from 3D to 2D

We present the effect of surface attraction on the vapor-liquid equilibria of square well (SW) fluids in slit pores of varying slit width from quasi 3D to 2D regime using molecular simulation methodologies. Four to five distinct linear regimes are found for shift in the critical temperature with inverse slit width, which is more prominent at higher surface fluid interaction strength. On the other hand, shift in the critical density and the critical pressure does not show any specific trend. Nevertheless, critical density and pressure show the sign of approaching toward the 3D bulk value with increase in the slit pore width, H, beyond 40 molecular diameters. The crossover from 3D to 2D behavior for attractive pores is observed around 14-16 molecular diameters, which is significantly different from the crossover behavior in the hydrophobic slit pore. Critical properties for H <or= 2 molecular diameters are indifferent to the surface characteristics. Corresponding state plot displays fluctuating positive deviation of spreading pressure for large pores and negative deviation for small pores from the bulk saturation value. Such behavior is more accentuated at stronger surface-fluid interaction strength. We also present vapor-liquid surface tensions of the SW fluid for different attractive planar slit-pores of variable slit-widths. Vapor-liquid surface tension or interfacial width values are insensitive to the surface-fluid interaction strength for slit width, H <or= 2 molecular diameters. At a given slit width and temperature, vapor-liquid interfacial width is found to decrease with increasing wall-fluid interaction for H > 2. However, interfacial properties approaches to the bulk value with increasing slit width. On the other hand, surface tension at a reduced temperature displays a nonmonotonic behavior with the change in H, which is in good agreement with the nature of the corresponding scaled interfacial width.

Removal of Heavy Metal Ions Using a Functionalized Single-Walled Carbon Nanotube: A Molecular Dynamics Study.

The adsorption behaviors of heavy metal ions Cd(2+), Cu(2+), Pb(2+), and Hg(2+), in aqueous media using functionalized single-walled carbon nanotube (SWCNT) with functional groups -COO(-), -OH, and -CONH2 are studied using molecular dynamics (MD) simulations. The results show that adsorption capacity is improved significantly using surface modification of SWCNT with carboxyl, hydroxyl, and amide functional groups. In addition, the adsorption capacity is found to increase with increasing metal-ion concentration. It is observed that the CNT-COO(-) surface effectively adsorbs over 150-230% more metal ions than the bare CNT surface. On the contrary, -OH and -CONH2 are relatively weak functional groups where excess metal-ion adsorption compared to the bare CNT is in the range 10-47%. The structural properties, self-diffusion coefficients, and adsorption isotherms of the metal ions are computed and analyzed in detail. Moreover, the potential of mean force (PMF) is computed to understand the free energy of metal ions, in the presence of functional groups, which is remarkly higher in absolute terms, leading to significant affinity for adsorption compared to the case for the bare CNT. In general, the following order of adsorption of the metal ions on functionalized CNT is observed: Pb(2+) > Cu(2+) > Cd(2+) > Hg(2+).

Coarse-grain molecular dynamics simulations of nanoparticle-polymer melt: Dispersion vs. agglomeration

In this work, we study the influence of polymer chain length (m), based on Lennard-Jones potential, and nanoparticle (NP)-polymer interaction strength (ɛnp) on aggregation and dispersion of soft repulsive spherically structured NPs in polymer melt using coarse-grain molecular dynamics simulations. A phase diagram is proposed where transitions between different structures in the NP-polymer system are shown to depend on m and ɛnp. At a very weak interaction strength ɛnp = 0.1, a transition from dispersed state to collapsed state of NPs is found with increasing m, due to the polymers excluded volume effect. NPs are well dispersed at intermediate interaction strengths (0.5 ⩽ ɛnp ⩽ 2.0), independent of m. A transition from dispersion to agglomeration of NPs, at a moderately high NP-polymer interaction strength ɛnp = 5.0, for m = 1-30, is identified by a significant decrease in the second virial coefficient, excess entropy, and potential energy, and a sharp increase in the Kirkwood-Buff integral. We also find that NPs undergo the following transitions with increasing m at ɛnp ⩾ 5.0: string-like → branch-like → sphere-like → dispersed state.

Vapor-liquid critical and interfacial properties of square-well fluids in slit pores

Vapor-liquid phase equilibria of square-well (SW) fluids of variable interaction range: lambdasigma=1.25, 1.75, 2.0, and 3.0 in hard slit pores are studied by means of grand-canonical transition-matrix Monte Carlo (GC-TMMC) simulation. Critical density under confinement shows an oscillatory behavior as slit width, H, reduced from 12sigma to 1sigma. Two linear regimes are found for the shift in the critical temperature with the inverse in the slit width. The first regime is seen for H>2.0sigma with linear increase in the slope of shift in the critical temperature against inverse slit width with increasing interaction range. Subsequent decrease in H has little consequence on the critical temperature and it remains almost constant. Vapor-liquid surface tensions of SW fluids of variable well extent in a planar slit pore of variable slit width are also reported. GC-TMMC results are compared with that from slab based canonical Monte Carlo and molecular dynamics techniques and found to be in good agreement. Although, vapor-liquid surface tension under confinement is found to be lower than the bulk surface tension, the behavior of surface tension as a function of temperature is invariant with the variable pore size. Interfacial width, xi, calculated using a hyperbolic function increases with decreasing slit width at a given temperature, which is contrary to what is being observed recently for cylindrical pores. Inverse scaled interfacial width (xi/H), however, linearly increases with increase in the scaled temperature (T(c,bulk)-T)/T(c,bulk).

On the characterization of crystallization and ice adhesion on smooth and rough surfaces using molecular dynamics

Coarse-grained molecular dynamics is utilized to quantify the behavior of a supercooled water drop on smooth and rough surfaces. Crystallization on rough surface is characterized based on wetting states. Freezing temperature and work of adhesion of water droplet are linearly associated with roughness parameters corresponding to the Cassie-Baxter and Wenzel states. The behavior is insensitive to different surface-fluid affinity. We show in general, for Wenzel states, work of adhesion is higher than that of Cassie-Baxter state for surfaces that have identical freezing temperatures.