On the phase behavior of hard aspherical particles

We use numerical simulations to understand how random deviations from the ideal spherical shape affect the ability of hard particles to form fcc crystalline structures. Using a system of hard spheres as a reference, we determine the fluid-solid coexistence pressures of both shape-polydisperse and monodisperse systems of aspherical hard particles. We find that when particles are sufficiently isotropic, the coexistence pressure can be predicted from a linear relation involving the product of two simple geometric parameters characterizing the asphericity of the particles. Finally, our results allow us to gain direct insight into the crystallizability limits of these systems by rationalizing empirical data obtained for analogous monodisperse systems.     

On Padé approximants to virial series

Padé approximants have long been used to predict virial series coefficients and to provide equations of state for low and high density materials. However, some justified criticism has appeared about this procedure. Although we agree to impose several restrictions on the use of Padé approximants, we indicate that the Padé approximant is still an excellent way to predict the first unknown virial series coefficients. As an example, we report a calculation of the B11=128.6 and B12=155 virial coefficients of the three dimensional hard sphere model that are in excellent agreement with the two most recent estimates. We also consider that the commonly used method to choose among Padé approximants is not completely reliable for this specific application and suggest an alternative new method.     

High-accuracy assessment of finiteness effects for hard disks

In a recent investigation the comparison between theoretical and computer-experimental results for the finiteness effects in hard disk systems has not been entirely conclusive. Thus, we present new Monte Carlo data of high accuracy. We also discuss some aspects of experimental design as well as refined methods of error analysis. The quantity considered is the compressibility factor Z, depending on the shape of the periodic box (for given density and particle number). The reported discrepancies in V dependence are stringently substantiated, and a semi-empirical correction of the theoretical approach is proposed. The new data also revealed an unexpected discrepancy in N dependence. For this second kind of finiteness effects, we replace the usual calculation via the virial coefficients by a computer-experimental estimate.     

Virial series for fluids of hard hyperspheres in odd dimensions

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].     

Excess virial coefficients with application in data analysis

This paper presents the general expression for excess virial coefficients of binary mixtures in the form of Bartlett's law. Imposing this expression in data reduction to determine mixture virial coefficients provides thermodynamically consistent evaluations of cross virial coefficients. Standard data reduction procedures do not provide values of the mixture and cross virial coefficients that are both consistent and accurate. We illustrate this new technique by analyzing Burnett data and direct density measurements. In addition, we present the general expression for cross virial coefficients under model solution behavior.     

Higher-order virial coefficients of water models

We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water are observed to greatly exceed the magnitude of corresponding coefficients for the simple Lennard-Jones model. We examine the coefficients in the context of the equation of state and the Joule-Thomson coefficient. Comparisons of these properties are made both to established molecular simulation data for each respective model and to real water. For all models, the virial series up to B5 describes the equation of state along the saturated vapor line better than the series that includes B6. At supercritical temperatures, however, the sixth-order series often describes pressure-volume-temperature behavior better than the fifth-order series. For example, the sixth-order virial equation of state for SPC/E water predicts the 673 K isotherm within 8% of published molecular simulation values up to a density of 9 mol/L (roughly half the critical density of SPC/E water).     

Coupled Influence of Colloidal and Hydrodynamic Interactions on the RSA Dynamic Blocking Function for Particle Deposition onto Packed Spherical Collectors

The influence of electrostatic double-layer and hydrodynamic interactions on random sequential adsorption (RSA) of colloidal particles onto packed spherical collectors was investigated using inverse analysis of colloid breakthrough data obtained from well-controlled particle deposition experiments. Deposition experiments were carried out using monodisperse aqueous suspensions of positively charged latex colloids and packed columns of negatively charged uniform glass beads for different combinations of ionic strength, particle size, and approach velocity. From the experimental particle breakthrough data, the initial particle deposition rates and the virial coefficients of the dynamic blocking function based on RSA mechanics were determined. The magnitudes of the virial coefficients were observed to increase from the hard sphere values with increasing flow rates and decreasing ionic strengths of the background electrolyte. Particle size also plays a significant role in governing the deposition dynamics. The deviation from the hard sphere RSA behavior becomes more prominent for larger particles. Copyright 2000 Academic Press.     

A simplified hard-sphere equation of state meeting the high and low density limits

A simplified hard-sphere equation of state has been developed, which meets the correct limit for close-packed conditions. It is shown that the proposed equation of state for hard spheres can represent accurately the computer simulation compressibility factor data and virial coefficients over a wide density range. The comparison of the results of the calculations using this equation, the Carnahan-Starling equation, and the two equations proposed by Iglesias-Silva and Hall, shows that the equation proposed here represents the compressibility factor data and the virial coefficients with better accuracy.     

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.     

Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular-dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.     

A multisolute osmotic virial equation for solutions of interest in biology

The osmotic virial equation was used to predict osmolalities of solutions of interest in biology. The second osmotic virial coefficients, Bi, account for the interactions between identical solute molecules. For multisolute solutions, the second osmotic virial cross coefficient, Bij, describes the interaction between two different solutes. We propose to use as a mixing rule for the cross coefficient the arithmetic average of the second osmotic virial coefficients of the pure species, so that only binary solution measurements are required for multisolute solution predictions. Single-solute data were fit to obtain the osmotic virial coefficients of the pure species. Using those coefficients with the proposed mixing rule, predictions were made of ternary solution osmolality, without any fitting parameters. This method is shown to make reasonably accurate predictions for three very different ternary aqueous solutions: (i) glycerol + dimethyl sulfoxide + water, (ii) hemoglobin + an ideal, dilute solute + water, and (iii) bovine serum albumin + ovalbumin + water.     

Generalised virial equation of state for natural gas systems

In this work we present a generalised virial equation of state for natural gas systems under custody transfer conditions. The model is based on corresponding states expressions for the second and third virial coefficients with argon as the reference fluid. These functional forms involve 12 adjustable coefficients. For the extension to mixtures we propose a one-fluid mixture model with binary interaction parameters in the combining rules for the mixture critical temperature and density. We obtained overall average absolute deviations (AAD) of 0.04 and 0.08% in pure-fluid compression factors and speeds of sound; AADs of 0.07 and 0.19% in compression factors and speeds of sound, respectively, of binary mixtures and AADs of 0.047, and 0.13% in natural gas compression factors and speeds of sound, respectively. These results compare favourably with equivalent calculations with other generalised virial coefficient models.     

Estimation of third virial coefficients at low reduced temperatures

We use the Clausius–Clapeyron equation to calculate third virial coefficients at low reduced temperatures. This procedure gives an alternative to predict third virial coefficients in a region where the third virial coefficient is difficult to measure. We compare the results of this method with published third virial coefficient data. Calculated third virial coefficients have average percentage deviations within 5% of the experimental values at reduced temperatures between 0.8 and 1.0.     

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.     

The equation of state of hard hyperspheres in nine dimensions for low to moderate densities

The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or singularities on or near the negative density axis, in qualitative agreement with the recently solved Percus-Yevick equation of state in nine dimensions.     

Hydrophobic interactions and osmotic second virial coefficients for methanol in water

A recent theory of the hydrophobic effect together with a simple model for an alcohol molecule is used to calculate the osmotic (McMillan-Mayer) second virial coefficientB ₂ for methanol dissolved in water. We use this calculation to study the validity of common arguments that try to draw microscopic structural information from experimental virial coefficient data. In disagreement with many workers, we find that the hydrophobic interaction between hard spheres in water is attractive and that its strength diminishes as temperature is raised. Models that have come to the opposite conclusions have neglected complications inherent to real solutes such as the role of the hydroxy groups in affecting the correlations between the apolar portions of neighboring alcohols. The calculations reported here indicate that this neglect is a poor approximation for methanol. Our calculations also show that osmotic virial coefficients are sensitive to subtle details in the potentials of mean force. Therefore, slowly varying (e.g., dispersion) interactions may also contribute significantly to the values of these coefficients without significantly changing the solvent structure near the solute molecules.     

Equation of state for hard-spheres and excess function calculations of binary liquid mixtures

Using our previously proposed matrix method, an equation of state for hard spheres is presented, which can reproduce the exact values of the first-eight virial coefficients. This equation meets both the low density and the close-packed limits and can predicts the first order fluid–solid phase transition of hard spheres. The results obtained show that the new equation of state can correlate the simulation data of compressibility factor up to high densities better than other equations of state.The new equation of state is extended to mixtures of hard spheres and excess functions of various binary liquid mixtures are calculated using the perturbation theory of Leonard–Henderson–Barker. The results are compared with existing theoretical and experimental data and with those calculated by other hard-sphere equations of state.It is seen that the results obtained by the new equation of state is quite satisfactory compared to other equations of state for the hard spheres and mixture of hard spheres.     

Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients

We present methods for computing contributions to the virial coefficients uniquely associated with molecular flexibility, and we demonstrate their use with application to the third, fourth, and fifth virial coefficients of united-atom models of linear alkanes and methanol belonging to the suite of transferrable potentials for phase equilibria (TraPPE-UA). We find that these uniquely flexible contributions are more difficult to compute than the remainder of the coefficient, especially for the conditions at which they appear to be most important. The significance of these contributions relative to the full virial coefficient grows with the number of sites (the size of the molecule), the number of molecules, and, to a certain extent, the temperature. The nature of the site-site interactions is of great importance: the significance of the uniquely flexible contribution at third and fourth order is orders of magnitude larger for TraPPE-UA methanol, which has Coulombic interactions, than for TraPPE-UA propane, which does not, even though both models have three sites per molecule and comparable bending potentials. While the uniquely flexible contribution of TraPPE-UA propane has a negligible impact on its third-order virial-equation-of-state estimate of the critical point, the uniquely flexible contribution of TraPPE-UA methanol increases this estimate of its critical pressure by about 5%.     

Corrections to scaling and crossover from good- to theta-solvent regimes of interacting polymers

We exploit known properties of universal ratios, involving the radius of gyration R(g), the second and third virial coefficients B(2) and B(3), and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to theta-solvent regimes of polymers of finite length L. The scaling limit and finite-L corrections to scaling are investigated in the good-solvent case and close to the theta temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio A(2)=B(2)/R(g) (3) over the whole temperature range, from the theta point to the good-solvent regime. The convergence with L (L< or =8000) is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the theta point, due to logarithmic corrections. A quantitative estimate of the universal ratio A(3)=B(3)/R(g) (6) as a function of temperature shows that the third virial coefficient remains positive throughout, and goes through a pronounced minimum at the theta temperature, which goes to zero as 1/ln L in the scaling limit.     

"Depth-profiling" and quantitative characterization of the size, composition, shape, density, and morphology of fine particles with SPLAT, a single-particle mass spectrometer

A significant fraction of atmospheric particles are composed of inorganic substances that are mixed or coated with organic compounds. The properties and behavior of these particles depend on the internal composition and arrangement of the specific constituents in each particle. It is important to know which constituent is on the surface and whether it covers the particle surface partially or entirely. We demonstrate here an instrument consisting of an ultrasensitive single-particle mass spectrometer coupled with a differential mobility analyzer to quantitatively measure in real time individual particle composition, size, density, and shape and to determine which substance is on the surface and whether it entirely covers the particle. For this study, we use NaCl particles completely coated with liquid dioctyl phthalate to generate spherical particles, and NaCl particles partially coated with pyrene, a solid poly aromatic hydrocarbon, to produce aspherical particles with pyrene nodules and an exposed NaCl core. We show that the behavior of the mass spectral intensities as a function of laser fluence yields information that can be used to determine the morphological distribution of individual particle constituents.