Search Results - (Author, Cooperation:X. C. Zeng)

2012-08-21

American Association for the Advancement of Science (AAAS)

0036-8075

1095-9203

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1089-7690

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We have employed density functional theory to study gas–liquid nucleation in binary fluids. Effects of surface enrichment and curvature are naturally included in this novel statistical mechanical approach, allowing the classical capillarity approximation to be tested. In this paper we apply the theory to mixtures of Lennard-Jones fluids (modeled on argon and krypton). For these nearly ideal mixtures, the magnitude of nonclassical effects tend to be small, but systematic deviations do appear, with the ratio of the classical to nonclassical rate showing a maximum at intermediate compositions.

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1089-7690

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Our recently proposed effective liquid free energy model (ELFEM) density functional theory is extended to nonuniform binary systems. The theory is based on mapping the excess free energy of a nonuniform binary system onto that of an effective binary liquid. In the uniform density limit, the theory is required to reproduce the known properties of the liquid. The present theory is applied to the freezing of a binary hard sphere liquid into a substitutionally disordered fcc solid. Comparisons with previous density functional investigations and recent computer simulations are made.

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We propose a relation among the crystal–melt surface tension τsl, the compressibility KT, and the thickness wsl of the crystal–melt interface for simple liquids, based on the density-functional approach of Moore and Raveche.1 Combining this with a similar relation in note I by Mon and Stroud, we obtain a formula connecting the surface tension ratio τsl/τlv, and ratio of surface width wsl/wlv. A new empirical law of freezing is conjectured.

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1089-7690

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A study is conducted on the square−gradient theories of polymer blend interfaces.Polymer blend exhibits a phase transition at a critical value of the interaction parameter. (AIP)

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We have applied a nonclassical density functional theory of nucleation to the gas–liquid and liquid–gas transitions of a Lennard-Jones fluid. For the liquid-to-gas transition (cavitation) deviations from classical theory are extremely large: 15 orders of magnitude in rates. For the gas-to-liquid transition (condensation) the deviations are smaller in magnitude but still systematic. Our nonclassical theory agrees with classical theory in its prediction of the dependence of nucleation rates on supersaturation, but it differs in its prediction of temperature dependence. Good agreement is found between our theory and experiments on condensation nucleation of nonane.

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1089-7690

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A new formulation of the weighted density approximation, the so-called modified weighted density approximation (MWDA), has been developed recently by Denton and Ashcroft [Phys. Rev. A39, 4701 (1989)]. In the present article, the MWDA theory is examined by applying it to the freezing of simple liquids in low dimensions such as one-dimensional hard rods and two-dimensional hard disks, and also applying it to three-dimensional adhesive hard spheres and classical one-component plasma systems. Comparisons with previous density functional investigations and computer simulations are also presented.

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1089-7674

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Physics

The temporal evolution of the plasma sheath in a small cylindrical bore with an auxiliary electrode is calculated for zero-rise-time voltage pulses. The ion density, flux, dose, ion energy distribu-tion, and electric field are determined by solving Poisson's equation and the equations of ion motion and continuity using finite difference methods. Our results indicate that the implantation time is about halved and slightly more than 50% of the ions possess impact energy higher than the maximum achieved when an auxiliary electrode is absent. The resulting ion flux, ion current, as well as ion energy distribution, are also determined. © 1997 American Institute of Physics.

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1089-7550

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Physics

A model utilizing cold, unmagnetized, and collisionless fluid ions as well as Boltzmann electrons is used to comprehensively investigate the sheath expansion into a translationally invariant large bore in the presence of an auxiliary electrode during plasma immersion ion implantation (PIII) of a cylindrical bore sample. The governing equation of ion continuity, ion motion, and Poisson's equation are solved by using a numerical finite difference method for different cylindrical bore radii, auxiliary electrode radii, and voltage rise times. The ion density and ion impact energy at the cylindrical inner surface, as well as the ion energy distribution, maximum ion impact energy, and average ion impact energy for the various cases are obtained. Our results show a dramatic improvement in the impact energy when an auxiliary electrode is used and the recommended normalized auxiliary electrode radius is in the range of 0.1–0.3. © 1998 American Institute of Physics.

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A nonclassical theory of nucleation, based on the density-functional (DF) approach, is developed for the gas–liquid transitions of two-dimensional (2D) Lennard-Jones (LJ) fluids. The methods of Weeks–Chandler–Andersen perturbation theory are used to approximate the LJ potential with a temperature-dependent hard-disk diameter plus an attractive tail. The resulting free energy functional is then used to calculate the free energy barrier to nucleation. We find that the curvature of the 2D nucleus is not important to the rate of nucleation (in contrast to the 3D counterpart). The effect of curvature is readily inferred from the ratio of nucleation rate from classical Becker–Döring theory to that from DF theory. Our calculation suggests that classical nucleation theory actually works reasonably well for 2D LJ fluids in predicting the temperature-dependence of the nucleation rate (whereas for 3D LJ fluids it fails badly). © 1996 American Institute of Physics.

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1077-3118

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Physics

The temporal evolution of the plasma sheath in a small cylindrical bore in the presence of an auxiliary electrode is determined for different electrode radii. The ion density, velocity, flux, dose, ion energy distribution, and average impact energy are calculated by solving Poisson's Equation and the equations of ion motion and continuity using finite difference methods. The particle-in-cell method is also used to confirm the validity of the data. Our results indicate that more ions will attain high impact energy when the auxiliary electrode radius is increased, but the dose will decrease. Our results suggest that the normalized auxiliary electrode radius should range from 0.10 to 0.30 in order to maximize the dose and produce a larger number of ions with higher impact energy. © 1997 American Institute of Physics.

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We have investigated droplet nucleation and bubble cavitation in the quantum fluid helium-3 based on a nonlocal density-functional approach. A marked effect of droplet (or bubble) curvature on the rate of droplet nucleation or cavitation has been found. Without considering this curvature effect (as in the classical theory of nucleation) the droplet nucleation rate for helium-3 could be underestimated (i.e., near 1 K) or overestimated (i.e., near 2.5 K) by orders of magnitude, respectively; for bubble cavitation, the rate could be underestimated by more than twenty orders of magnitude (near 1 K). © 1996 American Institute of Physics.

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In the framework of modified mean-field density-functional theory, effects of a uniform electric field on the interfacial properties of a model dipolar fluid [Teixeira and Telo da Gama, J. Phys.: Condens. Matter 3, 111 (1991)] are studied. Both density and orientational order-parameter profiles of the planar vapor-liquid interface are obtained as a function of the field strength. For the dipolar fluids with reduced dipole moment μ0*≤1, we find that the field (under the condition μ0*E*/T*(very-much-less-than)1) can shift the surface tension by few percent. We also find that the electric field actually reduces the thermodynamical surface tension but enhances the mechanical surface tension at the equimolar dividing surface. To detect these field effects on the surface tension we estimate the field strength which can be as high as 108 V/m. © 2001 American Institute of Physics.

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The effects of a physisorbed film on the force of static friction in a model contact (monatomic adsorbate confined between plane-parallel walls) were investigated by Monte Carlo simulation. At fixed coverage the friction curve (shear yield stress vs normal stress) exhibits a marked nonlinearity, which results from a competition between adsorbate–wall interactions that predominate at low loads and wall–wall interactions that set in beyond a threshold load, which increases with coverage. Previous proximal-probe and computer experiments, carried out at high coverages, see only the initial (low-load) linear portion of the friction curve. © 2000 American Institute of Physics.

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The formation free energy of clusters in a supersaturated vapor is obtained by a constrained Monte Carlo technique. A key feature of this approach is to set an upper limit to the size of cluster. This maximum cluster size serves essentially as an extra thermodynamic variable that constrains the system. As a result, clusters larger than the critical cluster of nucleation in the supersaturated vapor can no longer grow beyond the limiting size. Like changing the overall density of the system, changing the maximum cluster size also results in a different supersaturation and thereby a different formation free energy. However, at the same supersaturation and temperature it is found that the formation free energy has a unique value, independent of the upper limit of cluster size. The predicted size of critical cluster of nucleation is found to be consistent with the nucleation theorem as well as previous results using different simulation approaches. © 1999 American Institute of Physics.

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Monte Carlo simulation method is used to calculate the Helmholtz free energies of liquid cluster with boundary fixed in laboratory frame and a fluctuating center-of-mass (CM) and with a fixed boundary centered on a fixed CM. The former type of cluster is called drop conventionally and the latter type is the so-called Lee–Barker–Abraham (LBA) cluster. The free energy difference between the drop and the LBA cluster characterizes the free energy contribution due to the CM fluctuation. The simulation result is close to the theoretical estimate of Reiss, Katz, and Cohen than that of Abraham and co-workers. © 1998 American Institute of Physics.

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In the framework of density functional theory (DFT), a patching model for the density profile of the liquid–vapor interface is developed. The patching is based on analytical expressions of the asymptote of the density profiles. Derived from the model the surface tension of planar liquid–vapor interface as well as the Tolman length can be computed from analytic expressions. Two prototype systems are considered; the Yukawa and the Lennard-Jones. As a result, the temperature dependence of the surface tension as well as the Tolman length are obtained. The results are compared with numerical DFT calculations. © 1999 American Institute of Physics.

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Hydrophobic and hydrophilic interactions are two major intermolecular forces between hydrophobic nonpolar and hydrophilic polar sites of macromolecules or materials surfaces in solvents. To further understand these two interactions at the microscopic level, an idealized polyatomic model is devised, which includes hydrophobic, hydrophilic, and partially hydrophilic polyatomic planar square molecular sheets. The hydrophobic molecular sheet is composed of the Lennard-Jones particles while the hydrophilic molecular sheet consists of positive and negative charge sites. In the framework of the extended reference interaction site model integral equation theory the solvent-induced interactions (or the potential of mean forces) between two parallel molecular sheets in water and in the hypothetical nonpolar water are investigated in a systematic fashion. Such a highly idealized model allows us to isolate and to explore the important effects of molecular size, relative intermolecular position (e.g., in- or out-of-registry configuration), and hydrophilic site distribution on the hydrophobic and hydrophilic interactions in both water and the hypothetical nonpolar water. Significant insight into these effects at the molecular level is obtained. For the hydrophobic planar molecules in water we find solvent separated hydrophobic interaction becomes less favored as sheet size increases. Moreover, the contact hydrophobic interaction between two molecular sheets in the out-of-registry configuration is always most favorable. For the latter case we find it is the van der Waals attraction, rather than the hydrophobic attraction, that dominates the total interaction. We also find that in both water and the hypothetical nonpolar water the solvent-induced interaction between two hydrophobic sheets behaves similarly. One possible explanation is that the hydrophobic hydration originating from the hydrogen bonding network in water plays an insignificant role in the solvent-induced interaction, at least in the infinitely dilute aqueous solution. For hydrophilic planar molecular sheets in water, we find water-induced hydrophilic interaction is much more substantial compared with the hydrophobic one. In many cases, the hydrophilic interaction is found directly against the intermolecular force between two parallel molecular sheets in vacuum. Finally, for the partially hydrophilic planar molecules in water, a newly discovered feature is that a disperse hydrophilic site distribution gives rise to stronger solvent-induced interaction compared with the clustered hydrophilic site distribution. © 1997 American Institute of Physics.

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A small-system grand canonical ensemble Monte Carlo method is developed to evaluate cluster size distribution and barrier to the nucleation in a supersaturated Lennard-Jones vapor. The theoretical foundation is a physical cluster theory in which the Stillinger cluster is used as a prototypical physical cluster. Using method of Mayer's cluster expansion, the cluster–vapor interaction is effectively taken into account. From a separate canonical ensemble Monte Carlo simulation using a test particle method, the averaged volume of the cluster is obtained and is also incorporated in the small-system ensemble simulation. By this implementation our simulation is computationally more efficient compared to that based on the n/v Stillinger cluster theory in that instead of searching the saddle point on a two-dimensional free energy surface (a function of cluster size n and volume v) one needs only to find the peak on a free energy curve (a function of n only). A comparison with the height of barrier obtained from a large-system ensemble Monte Carlo simulation [K. Oh and X. C. Zeng, J. Chem. Phys. 110, 4471 (1999)] shows that omission of the vapor–cluster attraction can cause an overestimation of the height by several kBT. © 2000 American Institute of Physics.

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Nucleation free-energy barrier height and size of the critical nucleus are expanded in powers of the chemical potential difference between the supersaturated vapor (or expanded liquid) in the metastable state and the saturated vapor-liquid system in the stable equilibrium state at the same temperature. The coefficients in the expansions are expressed in terms of the thermodynamic properties at the stable equilibrium state. Comparisons with the results obtained from the density-functional calculation for nucleation of the Lennard–Jones fluid show that systematic improvement in predicting properties of the critical nucleus, either liquid droplet or vapor cavity, is achieved by adding the higher order terms in the expansions. The scaling relations proposed by McGraw and Laaksonen are found to be good approximations to the general expansion; in particular, the barrier height displacement appearing in these scaling relations is naturally given as the second order coefficient in the expansion of the barrier height. © 1999 American Institute of Physics.

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