Temperature Dependent Hard Sphere Diameter Research Articles

Structural Properties of In<sub>1-</sub><i><sub>x</sub></i>Sn<i><sub>x</sub></i> at Different Concentrations and Temperatures

The partial structure factors for liquid alloy In1-xSnx have been computed at varying concentration and temperatures using pseudopotential theory. The structure factor S(q) and pair correlation function g (r) have been determined using the hard-sphere approximation. The temperature dependent hard-sphere diameter σ (T) is estimated using Vσ=Vminr+12kBT criterion from the computed pair potential. The modified empty-core local pseudopotential, which represents the orthogonalisation effect due to s-core states, is used for electron–ion interaction with proper screening function. The only potential parameter, the core radius, is determined at different temperatures from the knowledge of structure factor. Intrinsic temperature effects have been studied through dimensionless damping term (see formula in paper) in the pair potential. The effect of temperature and concentration on structure factors is discussed to shed light on bonding in technologically important alloy. This used pseudopotential proved successful in explaining the structural properties of non-crystalline alloys at higher temperatures.

Temperature Dependent Structural Properties of Liquid Ga

We present the calculation of structural properties for liquid Ga at different temperatures using pseudopotential theory. The temperature dependence of structure factor has been determined using the hard-sphere Percus-Yevick approximation which is characterized by single parameter hard sphere diameter or equivalently packing fraction. The temperature dependent hard-sphere diameter σ (T) is estimated using criterion from the calculated effective pair potential. The modified empty-core pseudopotential due to Hasegawa et al. (J. Non-Cryst. Solids. 117/118 (1990) 300), which is valid for all electrons and contains the repulsive delta function to achieve the necessary s-pseudisation is used for electron–ion interaction. The temperature effects have been studied via dimensionless damping term and potential parameter in the pair potential. Finally, the predicted results for structure factor, pair correlation function and coordination numbers have been compared with recent available data, and a good agreement has been achieved.

Rowlinson’s Concept of an Effective Hard Sphere Diameter

Attention is drawn to John Rowlinson's idea that the repulsive portion of the intermolecular interaction may be replaced by a temperature-dependent hard sphere diameter. It is this approximation that made the development of perturbation theory possible for realistic fluids whose intermolecular interactions have a steep, but finite, repulsion at short separations.

Entropy convergence in hydrophobic hydration: a scaled particle theory analysis

The occurrence of entropy convergence in hydrophobic hydration is verified from available experimental thermodynamic data for both noble gases and hydrocarbons. The entropy convergence phenomenon can be reproduced by means of the scaled particle theory, provided that a temperature-dependent hard sphere diameter is used for water molecules. The calculated work of cavity creation shows a non-monotonic temperature dependence with a flat maximum slightly above 100 °C, irrespective of the cavity size. The corresponding cavity entropy changes converge approximately 100 °C, in qualitative agreement with the experimental finding.

Predicting diffusivities in dense fluid mixtures

In this work the Enskog solution of the Boltzmann equation, as corrected by Speedy, together with the Weeks-Chandler-Andersen (WCA) perturbation theory of liquids is employed in correlating and predicting self-diffusivities of dense fluids. Afterwards this theory is used to estimate mutual diffusion coefficients of solutes at infinite dilution in sub and supercritical solvents. We have also investigated the behavior of Fick diffusion coefficients in the proximity of a binary vapor-liquid critical point since this subject is of great interest for extraction purposes. The approach presented here, which makes use of a density and temperature dependent hard-sphere diameter, is shown to be excellent for predicting diffusivities in dense pure fluids and fluid mixtures. The calculations involved highly nonideal mixtures as well as systems with high molecular asymmetry. The predicted diffusivities are in good agreement with the experimental data for the pure and binary systems. The methodology proposed here makes only use of pure component information and density of mixtures. The simple algebraic relations are proposed without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent mixtures.

Transport coefficients of the Lennard-Jones fluid: Analysis of molecular dynamics data

Chapman-Enskog, CE, theory for the transport coefficients of the hard sphere fluid has been empirically extended to liquid densities using hard sphere molecular dynamics computer simulation data. The CE relationships have been applied to the transport coefficients of the Lennard-Jones, LJ, fluid, by attaching a temperature dependent hard sphere diameter to the LJ molecule. New expressions for the activation energies and volumes are given which are in terms of the properties of the underlying hard sphere fluid and LJ thermodynamics. The model successfully reproduces the LJ shear viscosity, η, and self-diffusion coefficient, D, obtained by simulation over a wide density and temperature range. The thermal conductivity and bulk viscosity are appreciably overestimated over most of the phase diagram by this model. Deviations are attributed to the influence of the attractive part of the LJ potential.

Self-diffusion in compressed supercritical water

The self-diffusion coefficients D of compressed supercritical water have been measured as a function of pressure in the temperature range 400 to 700 °C using the NMR spin–echo technique. The experimental diffusion data were compared to theoretical predictions based on a dilute polar gas model using a Stockmayer potential for the evaluation of collision integrals and a temperature dependent hard sphere diameter. The empirical expression ρDαTn, where n = 0.76, fits the experimental data to within±10% over the entire density and temperature region studied. The value of the exponent n = 0.76 agrees favorably with the n values found for diffusion of other gases. The product ρD is density independent under isothermal conditions which indicates that two-body collisions dominate the diffusion behavior. This finding is in agreement with our earlier results for proton relaxation in compressed supercritical water which were analyzed using a binary collision approximation and a collision modulated spin–rotation interaction described by a single correlation function which is an exponential function of time. The hydrodynanic Stokes–Einstein equation appears to hold at densities above ρc. As expected, the diffusion data cannot be described in terms of a hard sphere model but an empirical fit to lnρD = (A/T)+B, where A and B are constants, represents the experimental data well over the range of temperatures and densities studied.

Thermodynamic properties of a hard sphere fluid with temperature dependent effective hard sphere diameter

The residual thermodynamic quantities for a rigid sphere fluid with temperature dependent hard sphere diameter have been calculated with an analytical equation of state (Carnahan-Starling). The incorporation of the coefficient of thermal expansion of the effective hard sphere diameter, l=(dσ/dT)σ−1, results in the appearance of internal energy U* and heat capacity CV*. These and other quantities are reported for a wide range of fluid density. By using parameters pertaining to liquid argon, CV* was calculated for the corresponding hard sphere fluid over a large temperature interval (Tt<T<0.9Tc) and then compared to experimental data of argon. The agreement is regarded as being satisfactory.

A simple theory of liquid—solid phase transitions

A simple phenomenological theory of liquid—solid phase transitions, based on the use of perturbation theory about a hard-sphere fluid, is examined. A temperature dependent hard-sphere diameter is determined which permits the prediction of solid and liquid densities and melting pressures. Calculations presented here for the Lennard-Jones 12-6 fluid show good agreement with the computer simulation results. Provided pair potentials are available, the theory may also be used for other fluids, including liquid metals.

Pressure and temperature dependence of the self-diffusion of carbon tetrachloride

A modified diaphragm cell method has been used to measure the self-diffusion coefficient of carbon tetrachloride at 283, 298, 313 and 328 K over the pressure ranges 1–769, 1–1216, 1–1469 and 1–1475 bar, respectively. These results are compared with less extensive data from other methods and used with data reported elsewhere for benzene and cyclohexane to test some current theories of transport. In a test of the Stokes–Einstein relation best agreement between theory and experiment was obtained for the pseudo-spherical molecules of carbon tetrachloride for which constancy of (Dη/T) is maintained over the full range of temperature and pressure. A comparison of the present results with literature values calculated from molecular dynamics of hard spheres shows that the density dependence is not the same and the two cannot be reconciled by a temperature dependent hard sphere diameter. Internal pressures calculated from the data are not dependent on a model of the liquid and are in reasonable agreement with directly determined values.