Semiempirical Equation Of State Research Articles

Vapour - Liquid Equilibrium Properties for Two- and Three-dimensional Lennard-Jones Fluids from Equations of State

Vapour–liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour–liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state.

Non-ideality of the system NH3–H2–N2. Comparison of equation of state and simulation predictions with experimental data

In this study, experimental PVT data of pure NH3, H2, N2 and He are used to extract parameters for a three-parameter semi-empirical equation of state (EOS) for a pure substance and interaction parameters for the exponential-6 (exp-6) potential. For ammonia, the experimental pressure and liquid density at 323 K in the liquid–vapour coexistence region and the experimental density at the same temperature and 9500 bar are taken as inputs in the fitting procedure. For the other species, supercritical data at pressures up to 10000 bar are selected. It is found that the EOS is not able to simultaneously fit both the liquid–vapour coexistence data and the high pressure region of ammonia. In contrast, the use of Monte Carlo simulations with an optimised set of exp-6 parameters leads to good agreement both at low and high pressure. The quality of the fits to H2 and N2 data using the EOS is significantly worse than that using the optimised exp-6 potential because the EOS requires physically unreasonable parameters for a good fit. Despite the higher deviations of the EOS results, their corresponding predicted equilibrium constants for the synthesis of ammonia from H2 and N2 in the industrial range agree just as well with the experimental data. Furthermore, the predicted critical point is slightly closer to the experimental value (a deviation of 10% in the critical temperature). Simulations with the exp-6 potential are performed for the system H2–He–NH3–N2 at pressures and temperatures occurring in the deep atmosphere of Jupiter. Comparison between previous ideal calculations and the simulation predictions indicates that the expected concentration of N2 at 2300 K is overestimated by about a factor of three when ideality is assumed.

New semi-empirical equation of state for nuclear materials

Abstract A simple semi-empirical equation of state with a single unknown constant is presented for predicting the behaviour of nuclear materials at high temperatures and densities.

Experimental vapor-liquid equilibria in the systems R 22-R 23, R 22-Co 2, Cs 2-R 22, R 23-Co 2, Cs 2-R 23 and their correlation by equations of state

Roth H., Peters-Gerth P. and Lucas K., 1992. Experimental vapor-liquid equilibria in the systems R 22-R 23, R 22-CO 2, CS 2-R 22, R 23-CO 2, CS 2-R 23 and their correlation by equations of state. Fluid Phase Equilibria, 73: 147-166. Vapor-liquid equilibria in systems with polar molecules tend to show a rather complex phase behavior. In order to investigate the phase boundaries in mixtures of dipolar and quadrupolar components five binary systems of the components R 22, R 23, CO 2 and CS 2 have been selected. Experimental VLE data for the systems R 22-R 23, R 22-CO 2, CS 2-R 22, R 23-CO 2 and CS 2-R 23 are reported in this paper at temperatures between 254 and 473 K and pressures up to 25 MPa. The data were correlated with one empirical and one semi-empirical equation of state.

Pressure dependent study of semiconductors using semiempirical equations of state

Abstract Variation of bulk modulus of Si, Ge and GaAs with pressure is studied using four semiempirical equations of state, two of which being proposed very recently. Hence an expression for bulk modulus for arbitrary pressure for the semiconductors similar to Cohen's formula for zero pressure is arrived at. The applicability of these equations of state for the high pressure phases of Si and Ge is tested using the recent experimental and theoretical pressure-volume data of these phases.

Influence of the molecular shape on the volumetric properties of mixtures. The excess volumes of hexafluorobenzene or fluorobenzene +an octane isomer

The excess volumes of C6F6 and C6H5F+an octane isomer (n-octane, cyclooctane, 2,2,4-trimethylpentane) have been measured at 25°C. The equimolar values increase from 2,2,4-trimethylpentane to n-octane to cyclooctane. The present results cannot be explained in terms of the scheme developed by Patterson for other alkane mixtures. Comparing the present results with others in the literature, the effect of the dipolar moment of the aromatic compound seems to be more complex than in previous studies of polar+non-polar components. The results have been analyzed in terms of two generalized van der Waals models, and a semiempirical equation of state. The results range from poor to fair.

Volumetric properties of mixtures of simple molecular fluids

The excess volumes, VE, of several binary mixtures of simple molecular fluids have been measured as a function of composition and temperature. The results cannot be explained qualitatively using perturbation theories based on mixtures of spherical molecules and multipoles. The interplay of different kinds of anisotropy in the intermolecular potential seems to display complicated behaviour. A generalized van der Waals equation, a model based on a lattice with holes and a semiempirical equation of state have been used for fitting the experimental results satisfactorily. However, none of the models manages to predict other excess functions even for these relatively simple fluids.

Convergence property of the mean potential density expansion for repulsive hard body fluids

The normalized density power expansion of the mean potential at contact distance is calculated for seventeen hard repulsive body fluids. It is shown that first coefficients of the virial series strongly decrease with increasing order. Thus only a very few virial coefficients of the mean potential at contact distance are necessary to calculate the compressibility factor within a few percent through the pressure equation for stable fluid densities. A semiempirical equation of state is proposed for hard repulsive body fluids using two shape factors which are simple analytical functions of the second virial coefficient of the compressibility factor and a mean length to breadth ratio.

Fluid Phase Equilibria of Binary Mixtures of SF6 with Octane, Nonane, Hendecane, and Decahydronaphthalene,cis at Temperatures between 280 K and 440 K and at Pressures up to 140 MPa in Comparison to Mixtures of Hydrocarbons with CO2, CF4, and CHF3

AbstractBinary mixtures of SF6 + octane, + nonane, + hendecane, and + decahydronaphthalene,cis were investigated up to 140 MPa. Measurements were performed according to the synthetic method using an optical high pressure cell. ‐ Going from SF6 + octane to SF6 + nonane the critical p(T)‐curves show a continuous transition between the type of liquid‐liquid (ll) phase equilibrium with upper critical solution temperatures (UCST) and the gas‐gas (gg) equilibrium of the 2nd kind. For the SF6 + n‐alkane systems there is a systematical shift of the high‐pressure branches of the critical curves of about 20 K to higher temperatures per CH2‐unit. The experimental results are discussed in comparison to computer calculations with two semiempirical equations of state. Solvent properties of SF6 are compared to those of CO2, CF4, and CHF3.

Vapour-liquid equilibrium at low pressures from the back equation of state

The BACK semiempirical equation of state was employed to determine the excess thermodynamic functions of five binary mixtures composed of benzene with cyclohexane, n-pentane, n-hexane, n-heptane, and n-octane at 298.15 K. Two sets of mixing rules are discussed and values of the excess thermodynamic functions of equimolar solutions, calculated on their basis, are compared with experimental data. The calculated and experimental equilibrium data are compared in the x-y diagrams.

A new semiempirical equation of state for fluids—I: Derivation

A semiempirical equation of state has been developed for non-polar and weakly polar fluid substances from the square well model of the inter-molecular

An accurate equation of state of a hard convex body fluid mixture

A method enabling to calculate the contact-point values of the pair correlation function of convex body fluids from a semi-empirical equation of state is presented and the accurate Nezbeda equation of the pure hard convex body fluid is extended to mixtures. Comparison of results for one- and two-component systems with Monte Carlo simulation data shows excellent agreement.

High pressure molecular dynamics of the partially miscible fluid mixture neon/krypton

The Ne/Kr fluid mixture, whose constituents have very different sizes and potentials, was studied by molecular dynamics calculations over the whole concentration range and a large temperature interval of 150–250 K, and at a pressure of about 2000 bar. Particular attention was given to the phase separation at high pressures found experimentally by Trappeniers et al. Our calculations were performed with Lennard-Jones (12–6) potentials. The calculated pressures agree well with experimental data fitted through a semi-empirical equation of state. The self-diffusion coefficients show a strong concentration dependence and exhibit no anomalities in the critical region, as it is confirmed by experiments on other systems. We observed an appreciable shift of the peaks of the radial pair-distribution functions (RDF) which cannot be explained by simply scaling the RDF of the pure substances. In the critical region the shifts of the second peak indicate a structural rearrangement in the mixture. The computation of the number of neighbours up to the first and the second coordination shell showed an accumulation of equal particles and an increase of the correlation length of the system near the critical point. The correlation length could roughly be estimated at 60 Å. This is in agreement with experiments on other binary mixtures. Furthermore, the critical concentration was found to be identical with the molar fraction where both the component molecules have equal numbers of next neighbouring particles of their own kind. It is assumed that this holds generally for partially miscible binary mixtures. We conclude that our simulation reproduces the critical region in accordance with the measurements of Trappeniers. This is confirmed by our additional calculation of the Gibbs free energy, which actually exhibits the shape necessary for a phase separation in a binary mixture.

Isentropic air flows at high stagnation pressures

Calculations of the gasdynamic parameters of air using different equations of state for a real gas in one-dimensional formulation were carried out in [1-3]. The results from these papers are of a limited nature, as the equation of state of a real gas, which occurs in the system of starting equations, is valid for a quite narrow range of total pressures and temperatures. In [4, 5], a semiempirical equation of state is proposed, which was used in [6, 7] for investigating the isentropic expansion of air and nitrogen. A method is proposed in this paper for calculating the parameters of air during its isen tropic expansion from high stagnation pressures, using the semiempirical equation of state proposed in [8]. Flow calculations are carried out for air at stagnation pressures p = 10-900 bars and stagnation temperatures T = 220-450~ over the range of Mach numbers M = 0 to 6. Over the stated wide range of stagnation parameters, where the effect of van der Waals forces is large, the calculations indicate a significant change of the dimensionless gasdynamic parameters of air as a function of the absolute values of the stagnation pressure and temperature. The experimental data confirm the accuracy of the results of the calculations.

Statistical thermodynamics of the liquid state, the liquid-glass transition and the glassy state of polymers

The principal question considered is the relationship between the liquid and the glassy state of amorphous polymers. It is discussed here in terms of the equation of state. A successful molecular theory can be formulated which contains as a structural quantity the hole fraction of the quasi-lattice. In terms of characteristic pressure, volume and temperature parameters it yields the equation of state of the liquid polymer and predicts the pressure coefficient of the glass temperature for a given polymer. A bridge between the statistical and the thermodynamic theory of frozen ordering parameters is established by treating the vacancy fraction 1 —y as such a parameter. For several polymers it has been shown thaty does not remain constant below the glass temperature but varies with temperature and pressure. By assuming thus that the only difference between the two states resides in the functional dependence ofy on the variables of state (determined in the liquid by the minimization of the configurational free energy), a semiempirical equation of state can be obtained which is valid between the glass temperature and theβ-relaxation region. These results indicate that a mechanism based on the picture of thermal vibrations cannot describe the configurational properties of the glass, except at extremely low temperatures. Here a successful theoretical equation of state and a low temperature theorem of corresponding states can be formulated, based on this concept. The approach discussed is general and should be extended to systems of low molecular weight as well.

Melting and evaporation of metals in an unloading wave

The thermodynamic states resulting in melting and evaporation in an isentropic expansion wave during dissociation are computed for sixteen metals. Semiempirical equations of state of the condensed phase and tabulated data on the melting and evaporation entropies are used.

A semiempirical equation of state for dense helium

Using eight isotherms in the range 83–323°K at pressures less than 700 bar a semiempirical equation of state for dense helium is constructed, permitting extrapolation into the high-pressure region.

Statistical Mechanics of Dense Ionized Matter. I. Equilibrium Properties of the Classical One-Component Plasma

The equilibrium properties of a classical one-component plasma, in a uniform background of opposite charge, are computed for systems of various sizes by the Monte Carlo method of Metropolis et al. Following the work of Brush, Sahlin, and Teller, the periodicity of the system is accounted for by replacing the long-range Coulomb potential by an effective Ewald sum. Thermodynamic properties are computed over the whole density range of the fluid phase of the system, and their $N$ dependence is carefully investigated. A semiempirical equation of state is proposed from which all thermodynamic properties can be easily derived. Quantum corrections to these properties are calculated to first order in the Wigner expansion. Radial distribution functions, direct-correlation functions, and structure factors at various densities are tabulated. It is shown that at all densities, the direct-correlation function tends rapidly towards its Debye-H\uckel form, in contrast to the radial distribution function. The behavior of the structure factor at small wave vectors is also shown to be in good agreement with the Debye-H\uckel predictions at all densities.

Equations of state for copper, silver, gold, aluminum, nickel, and lead

Semiempirical equations of state are obtained for copper, silver, gold, lead, nickel, and aluminum, which permit a study of the mechanical properties of the crystalline lattices of these metals when subjected to a complex system of stresses over the entire elastic deformation region, and lead to an evaluation of the mechanical destruction parameters of these lattices. As an example, the case of omnidirectional tension is examined.

Relationship between thermoelasticity and reinforcement in elastomers: Silica filled silicone elastomers

Increases in modulus, tensile strength, and swelling caused by reinforcing silicone rubber with silica filler were correlated with the thermoelastic parameter, fe/f. A new semiempirical equation of state, containing a generalized front factor, was derived to explain the experimental results. While the retractive force in pure gum elastomers is largely entropic in origin, reinforcement in silicone rubber-silica systems appears to arise by greatly augmenting the deformational free energy change stored in energetic modes.