Effective Hard-sphere Diameter Research Articles

Molecular dynamics simulations of athermal polymer blends: Finite system size considerations

Molecular dynamics simulations of binary, athermal blends of chains consisting of 50 tangent sites were carried out over a range of compositions at liquidlike packing fractions. The sites interact with repulsive Lennard-Jones potentials and have effective hard sphere diameters of approximately 1.0 and 1.2 for the two site types. The intrachain and interchain correlation functions were found and, except for the single component systems, the interchain correlations were seen to be strongly dependent on system size. Trivial, long range correlations due to the finite system size can be approximated from simple physical arguments, and the coarse, interchain, radial distribution functions can be ‘‘corrected’’ for these effects. The resulting correlation functions are seen to behave at large separation as would be expected of interchain radial distribution functions in an infinite sized system, permitting meaningful comparisons with the predictions of liquid state theory.

Kinetics of reduction of hexakis(acetamide)- and hexakis(dimethylacetamide)-iron(III) by tris(3,4,5,6,7,8-hexamethyl-1,10-phenanthroline)iron(II) in acetonitrile

The kinetics of outer-sphere electron transfer between [Fe(hmphen)3]2+(hmphen = 3,4,5,6,7,8-hexamethyl-1,10-phenanthroline) and substitutionally labile Fe3+ introduced as [FeL6]3+[L = dma (dimethylacetamide) or aa (acetamide)] in acetonitrile has been studied at 25 °C with the salts added as the perchlorates. Both reactions can be described by one mechanism implying that the acidic hydrogens of aa do not appreciably complicate the issue. To accommodate the variations in the redox rate constants, three rapid solvation pre-equilibria [FeL6]3+⇌[FeL3]3++ 3L (co-ordinated MeCN is omitted) have to be invoked where, for driving-force reasons, only [FeL4]3+ and [FeL3]3+ are redox-active. Further, the acceleration with salt is well described by ion pairing and ion tripling of the trivalent ions with perchlorate, treated in terms of the reduction in Coulombic repulsion in forming the precursor complexes. For the solvate speciation, the overall reaction rates are controlled by both the reactivities of the reacting species and their availabilities. In the context of previous work, the differences between the two reactions are as follows: the redox rate constants of the aa species are larger than those of the corresponding dma species, which is primarily a driving-force effect with dma being the stronger Lewis base; on the other hand, the availabilities of the reacting species are higher in the case of dma, contrary to expectation. On the balance of the experimental evidence available, it does appear that the stabilities of the [FeL6]3+ solvate species are not a function of the donor strength of L but rather of its size tentatively expressed by the effective molecular hard-sphere diameter.

Density-mediated transport and the glass transition: high pressure viscosity measurements in the diamond anvil cell

Three methods have been recently demonstrated for obtaining accurate high pressure viscosity data which combine to give a viscosity range of ten decades. Dynamic light scattering is useful in the range 10 −1–10 2 cP, the rolling-ball diamond-cell viscometer covers the range 10 −1–10 7 cP and the centrifugal-force diamond-cell viscometer operates in the 10 5–10 9 cP range. The overall accuracy of these devices is 10% or better. Within this accuracy, it is found that the simple free-volume model describes the high-pressure data over wide compression ranges. Several features of these fits are noteworthy. First, extrapolation of the fitted function to 10 15 cP yields a calculated pressure, P ∗ , which correlates well with the glass transition pressure obtained experimentally by other techniques. Second, the effective molecule diameter obtained from the free-volume fits is considerably different from that obtained from thermal data, but the diameter is comparable to the effective hard-sphere diameter obtained from a modified Carnahan-Starling—van der Waals equation of state model. Third, it is found that a scaling behavior, analogous to that of fragility for thermal data, is obtained when the viscosity data are plotted versus the volume normalized to that calculated at P ∗ .

Approximate theories of the Raman non-coincidence effect: a critical evaluation in the case of liquid acetone

Approximate theories of the Raman non-coincidence effect are examined on the basis of the results of Monte Carlo simulations. Special emphasis is laid upon the treatments of liquid structures incorporated in those theories. The concept of “screening of two-body electrostatic interactions”, which is involved in one theory of the Raman non-coincidence effect, is shown to be inadequate in view of the calculated pair distribution functions. However, the mean spherical approximation, on which another theory of the Raman non-coincidence effect is based, properly describes the local order in the liquid giving rise to that effect, although ambiguities in estimating the effective hard sphere diameter cannot be avoided.

Approximate theories of the Raman non-coincidence effect: a critical evaluation in the case of liquid acetone

Approximate theories of the Raman non-coincidence effect are examined on the basis of the results of Monte Carlo simulations. Special emphasis is laid upon the treatments of liquid structures incorporated in those theories. The concept of “screening of two-body electrostatic interactions”, which is involved in one theory of the Raman non-coincidence effect, is shown to be inadequate in view of the calculated pair distribution functions. However, the mean spherical approximation, on which another theory of the Raman non-coincidence effect is based, properly describes the local order in the liquid giving rise to that effect, although ambiguities in estimating the effective hard sphere diameter cannot be avoided.

A Method for the Prediction of the Transport Properties of Dense Fluids: Application to Liquid n-Alkanes

A new method is presented for the prediction of the transport properties (viscosity, thermal conductivity, and diffusion coefficient) of liquids. The method is based on the rough hard sphere theory of Chandler and incorporates the recent molecular dynamics results for Lennard-Jones fluids reported by Heyes. The Lennard-Jones parameters and the effective hard sphere diameter required in the calculations were determined from a knowledge only of the density-temperature behavior of the fluid at atmospheric pressure using the Ross variational perturbation method. Analytical expressions are presented for the transport properties of the n-alkanes, and comparisons are shown between calculations and experiment. The results generally agree with published results within experimental error

Effective Atomic Diameter Changes on Mixing Liquid Metals

Abstract A simple model based on the variational Gibbs-Bogotiubov method is used to investigate the manner in which the effective hard sphere diameters change on mixing liquid metals. It implies that in general the diameter of the ions with lower pure liquid valence electron density contracts while the other expands, provided the bare pseudopotentials are unaffected by alloying.

Solubility of 13 non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran at 273.15 to 303.15 K and 101.33 kPa partial pressure of gas

Gibanel, F., López, M.C., Royo, F.M., Pardo, J. and Urieta, J.S., 1993. Solubility of 13 non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran at 273.15 to 303.15 K and 101.33 kPa partial pressure of gas. Fluid Phase Equilibria, 87: 285-294. Solubility measurements of several non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran in the temperature range 273.15–303.15 K and at 101.33 kPa partial pressure of gas are reported. Standard changes in thermodynamic functions for the solution process (Gibbs energies, enthalpies and entropies) at 298.15 K are evaluated from experimental solubilities and their variation with temperature. Lennard-Jones 6,12 pair potential parameters and the temperature dependence on effective hard-sphere diameter for 2-methyltetrahydrofuran are estimated using the scaled particle theory applied to gas-liquid solubility. Experimental solubilities as mole fractions are compared with calculated values using this theory.

Transport properties in dense fluids and their binary mixtures

Abstract A critical appraisal of the ability of the effective diameter hard-sphere theory (EDHST) for predicting thermal conductivities, and shear and bulk viscosities of fluids interacting through the Lennard-Jones potential is presented. This method relies on the use of the kinetic theory of hard-spheres and the state-dependent effective diameters given by the equilibrium liquid state theory. Predictions using this method are compared with molecular dynamics data given by several authors. In the dense regime this procedure, using a variational scheme to obtain the effective hard-sphere diameters makes predictions with an average global deviation of 37% for the shear viscosity, 32% for the bulk viscosity, and 10% for the thermal conductivity. However, in certain regions of the phase diagram the predictions are better. All other schemes give worse results than the variational scheme, except in the case of the shear viscosity in certain regions of the phase diagram (for this case we include the low density regions), where the Verlet and Weis scheme gives better results. For mixtures, we calculated the transport properties of mixtures using the equivalent one-fluid approximation, and comparisons with molecular dynamics calculations previously reported were performed. Our results are quite satisfactory. In addition, we made comparisons with actual fluids and extended our procedure to fluids of nonspherical molecules.

Crystalline-to-glass transition in charge polydisperse colloids

The crystalline-to-glass transition in dilute charge polydisperse colloidal suspensions is investigated using Monte Carlo simulations assuming pairwise additivity of the interaction. The time averaging of coordinates is used to reduce the broadening of the pair correlation function due to random thermal motion. The suspension is found to remain crystalline at low polydispersities and becomes disordered at large charge polydispersities (CPDs). The behaviour of particle diffusion in the suspension is used to characterize the disordered state as glass. The dependence of structural parameters such as Smax, gmin/gmax and particle diffusion suggests that the transition occurs at 26% CPD. The polydispersity of effective hard-sphere diameters is obtained and compared with that of a size polydisperse system.

Calculation of effective hard sphere diameters from perturbation theory

Abstract Effective hard sphere diameters are calculated for methane, ethane, propane, n-butane, isobutane, ethene, propene, nitrogen and carbon dioxide by a CWA-perturbation theory based on the Lennard-Jones 12-6 potential. Temperature and density dependence of the diameters are investigated. As expected the density dependence is weak and the temperature dependence is somewhat stronger. The temperature dependence of the reduced diameter is nearly independent of substance.

Effective hard-sphere diameters and equations of state

A simple way to derive and express accurate effective diameters for simple fluids is given. Effective hard-sphere diameters are essential to write explicit equations of state. The procedure relies on a density expansion of the effective diameters and is illustrated for systems with purely repulsive forces. Equations for the free energy and pressure of a system with an inverse-12 potential are obtained. The pressure equation has a relative RMS deviation of 0·15% with respect to Monte Carlo data over the entire fluid range.

Prediction of transport properties for Lennard-Jones fluids and their binary mixtures using the effective-diameter hard-sphere kinetic theory

We present a critical appraisal of the ability of effective diameter hard sphere theory to predict thermal conductivities and shear and bulk viscosities of fluids interacting through the Lennard-Jones potential. This method relies on the use of the kinetic theory of hard spheres and on state dependent effective diameters given by the equilibrium liquid state theory. Predictions using this method are compared with molecular dynamics data given by several authors for pure fluids in many states (65 states for the thermal conductivity, 105 for the shear viscosity, and 45 for the bulk viscosity). In the dense regime, this procedure makes predictions with an average global deviation of 37% for the shear viscosity, 32% for the bulk viscosity, and 10% for the thermal conductivity when a variational scheme is used to give the effective hard sphere diameters. In specific regions of the phase diagram, however, the predictions are much better. All other schemes give worse results, although shear viscosity in certain ...

Transport properties of dense fluids via spherical models of the interaction potential

The method for evaluation of the dense fluid viscosity and thermal conductivity (translational part) from intermolecular interaction information is derived on the basis of the local similarity principle. The non-equilibrium criteria of mapping a real-system interaction function U r( R) to the reference Van der Waals potential U b( R, A) are formulated first. Then the density dependence for the kinetic effective hard-sphere diameter is studied. The test of the proposed approach has been carried out for a number of spherical potential models (Ne-Ne, Ar-Ar, Kr-Kr, Xe-Xe, CO 2-CO 2, N 2-N 2, O 2-O 2) in the range of the reduced densities 0.4< nΣ 3<1 and temperatures 0.9< kT/ϵ<20. A comparison of the evaluated values of the viscosity η and thermal conductivity λ with the empirical data has shown the reliability of the suggested approach in application to spherical and weakly anisotropic molecular systems: the mean discrepancies δη and δλ are usually in the range of 3–5%.

Application of rough hard sphere theory to diffusion in supercritical fluidst

The limiting mutual diffusion coefficients of benzene and carbon tetrachloride were measured in subcritical and supercritical carbon dioxide at 298 and 309 K in the pressure range 8.96 – 26.0 MPa using the Taylor dispersion technique. The rough hard sphere theory was used for interpretation of the data obtained in this study as well as the data in the literature for limiting and self-diffusion coefficients. The theory represents the data successfully for pure fluids with a density-independent coupling parameter. The effective hard sphere diameters extracted from the data match closely with the diameters calculated by other methods. The same functional dependence of the self-diffusion coefficients on molar volume was also observed for limiting mutual diffusion coefficients determined in this work and for naphthalene data in the literature. Hence, a correlation based on the rough hard sphere theory was developed for prediction of diffusivities in sub- and supercritical carbon dioxide. The correlation reproduces the data with an average absolute deviation of 7.68%.

The thermal conductivity of dense fluids using revised Enskog theory

A predictive method designed to obtain the thermal conductivities of one-component dense fluids is described. This method is based on the revised Enskog theory. Here, an effective state-dependent hard-sphere diameter is used to obtain the hard-sphere diameter needed by the revised Enskog theory in order to deal with actual fluids. In addition, we introduce the contribution of the internal degrees of freedom through the Mason-Monchick procedure. Our predictions for noble gases and hydrocarbons, at high density, are compared with predictions coming from the conformal solution model, with empirical correlation schemes, and with experimental data. A very satisfactory agreement is found.

Densities of tetramethylsilane, tetraethylsilane, and tetraethoxysilane under high pressures

Accurate density data for tetramethylsilane, tetraethylsilane, and tetraethoxysilane in the temperature range from 283.15 to 333.15 K under pressure up to 100 MPa have been measured in order to test existing correlation methods. We have also measured the saturated liquid densities of tetramethylsilane, tetraethylsilane, and tetraethoxysilane in the temperature range from 283 to 343 K. The modified Rackett equation and the COSTAD correlation were used to correlate the saturated liquid density data. The Tait equation and a modified van der Waals equation of state were used to correlate the liquid density data under pressure. It was found that the average absolute deviations of the experimental values from those calculated with the Tait equation and the modified van der Waals equation of state were less than 0.01 and 0.21%, respectively. The effective hard sphere diameters for these three silane compounds were determined from the modified van der Waals equation of state parameter. It was found that the effective hard-sphere diameter decreases with temperature.

Calculation of the Dielectric Constant of Water to 1000°C and Very High Pressures

AbstractMeasured data for the dielectric constant of water exist to 550°C and 5000 bar and to 400°C and 3000 bar (critical temperature: 374°C). The present calculations extend to 1000°C and a density of 1 g cm−3 (16000 bar). Results are given for densities between 0.1 and 1 g cm−3 and for temperatures to 1000°C. From 400 to 1000°C at densities of 0.1, 0.5 and 1.0 g cm−3 the dielectric constant varies from 2.04 to 1.50, from 10.45 to 4.69 and from 29.4 to 11.06 respectively. The calculation is based on a hard‐sphere with dipole moment molecular interaction model and an approximate equation of Patey et al. based on a linearized hypernetted chain procedure. The effective hard sphere diameter of 2.68 Å has been derived from fitting to existing PVT data to 1000°C by a suitable equation of state. The effective dipole moment of 2.33 D was obtained from fitting to existing experimental dielectric constant values to 550°C and high densities with the Patey equation. Analogous calculations of the dielectric constants of supercritical, dense HCl, NH3 and CH3F are presented.

Statistical-mechanical theory of a new analytical equation of state

We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks–Chandler–Andersen decomposition of the potential and the Carnahan–Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule–Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p–v–T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases. As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is incorrect. Limited testing on the polyatomic gases CH4, N2, and CO2 suggests that the results for spherical molecules (CH4) may be as good as for the noble gases, nearly as good for slightly nonspherical molecules (N2), but poor at high densities for nonspherical molecules (CO2). In all cases, however, the results are accurate up to the critical density. Except for the eight-parameter empirical Benedict–Webb–Rubin equation, this appears to be the most accurate analytical equation of state proposed to date.

Solubility of He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, O 2, CH 4, C 2H 4, C 2H 6, CF 4, SF 6 and CO 2 in cyclopentanone from 273.15 K to 303.15 K and gas partial pressure of 101.33 kPa

Solubility measurements of several non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, O 2, CH 4, C 2H 4, C 2H 6, CF 4, SF 6 and CO 2) in cyclopentanone at 273.15 K to 303.15 K and a gas partial pressure of 101.33 kPa are reported. Thermodynamic functions (standard changes in Gibbs energy, enthalpy and entropy) for the solution process at 298.15 K and gas partial pressure of 101.33 kPa are evaluated. Use is made of the scaled particle theory applied to gas solubility for determining Lennard-Jones (6,12) pair potential parameters and temperature dependence of effective hard-sphere diameter of the solvent. The values that this theory predicts for the solution thermodynamic functions are also calculated.