Equation of state for compressed liquids from surface tension (original) (raw)
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Analytical equation of state for molecular fluids: Comparison with experimental data
Physical Review A, 1990
An analytical equation of state for real molecular Auids is presented, based on an extension of a previously presented perturbation theory for hard convex bodies [Song and Mason, preceding paper, Phys. Rev. A 42, xxxx (1990)]. It is a fifth-order polynomial in the density and seems to be valid over the range from the dilute gas to the metastable liquid, both below and above the critical temperature. The temperature-dependent parameters of the equation can be calculated if the intermolecular pair potential is known. However, knowledge of just the second virial coefficient plus some liquid densities is sufficient to predict reasonably accurate parameters and hence the whole pv-T surface. Three scaling constants characterize the equation: an interaction energy, an interaction distance, and a dimensionless nonsphericity or inner hard-core parameter. The equation is tested with experimental p-v-T data for eight selected systems: N2, CO~, C2H6, C3H8, CF4, SF6, NH3, and H20. Agreement is quite remarkable.
Thermodynamic regularities in compressed liquids: II. The reduced bulk modulus
Journal of Physics-condensed Matter - J PHYS-CONDENS MATTER, 2006
In a previous work, we analysed some regularities found in the behaviour of the thermal expansion coefficient, α p , in compressed liquids. We confirmed that a given liquid presents a characteristic pressure range in which the condition (∂α p /∂ T ) p = 0 is fulfilled within a narrow range of reduced densities. We also found that the density at which the condition (∂α p /∂ T ) p = 0 is satisfied, ρ α , decreases with temperature, a key feature not described before. Earlier studies by other authors suggested that similar regularities are expected for the reduced bulk modulus, B. We present here a detailed analysis of the temperature and density dependence of B from existing experimental results at high pressures. Several liquids have been analysed: argon, krypton, xenon, ethylene, tetrafluoromethane, trifluoromethane, carbon dioxide, carbon disulfide, n-butane, n-hexane, toluene, ethanol, 1-hexanol, m-cresol, and quinoline. We locate that the density ρ B that fulfils the condition (∂ B/∂ T ) ρ = 0 occurs at a particular region of the phase diagram, between 3.4 and 2.4 times the critical density of each liquid. Interestingly, the previously found density ρ α is close to ρ B , in a similar region of the reduced phase diagram. However, we note that ρ B typically decreases to a lesser extent with temperature than ρ α . In addition, we have found that ρ B (T ) behaves in a parallel fashion for the different liquids, showing larger values of ρ B as the complexity of the molecules increases. These findings provide a strong basis for developing general equation of state models to describe the behaviour of liquids in the high-pressure regime.
A compressed liquid density correlation
Fluid Phase Equilibria, 2000
A new correlation is developed for calculation of the compressed liquid density of pure compounds and Ž . mixtures. This correlation is used together with the Hankinson-Thomson COSTALD correlation of saturated liquid density and the Riedel equation for the calculation of vapor pressures. The range of application of this correlation is quite wide; from freezing point temperature to critical point temperature and from saturation pressure to 500 MPa. The average of error for the prediction of the compressed liquid volume of 31 compounds consisting of 3324 experimental data points is 0.77% with y0.24% bias from the experimental data. For mixtures, the average of error for the prediction of the compressed liquid volume of 13 mixtures consisting of 2101 experimental data points is 1% with y0.22% bias from the experimental data. The comparison with other correlations shows that the new correlation is somewhat better and quite reliable to very high pressures. q
Physical Chemistry Chemical Physics, 2011
We validate here the Two-Phase Thermodynamics (2PT) method for calculating the standard molar entropies and heat capacities of common liquids. In 2PT, the thermodynamics of the system is related to the total density of states (DoS), obtained from the Fourier Transform of the velocity autocorrelation function. For liquids this DoS is partitioned into a diffusional component modeled as diffusion of a hard sphere gas plus a solid component for which the DoS(u) -0 as u -0 as for a Debye solid. Thermodynamic observables are obtained by integrating the DoS with the appropriate weighting functions. In the 2PT method, two parameters are extracted from the DoS self-consistently to describe diffusional contributions: the fraction of diffusional modes, f, and DoS . This allows 2PT to be applied consistently and without re-parameterization to simulations of arbitrary liquids. We find that the absolute entropy of the liquid can be determined accurately from a single short MD trajectory (20 ps) after the system is equilibrated, making it orders of magnitude more efficient than commonly used perturbation and umbrella sampling methods. Here, we present the predicted standard molar entropies for fifteen common solvents evaluated from molecular dynamics simulations using the AMBER, GAFF, OPLS AA/L and Dreiding II forcefields. Overall, we find that all forcefields lead to good agreement with experimental and previous theoretical values for the entropy and very good agreement in the heat capacities. These results validate 2PT as a robust and efficient method for evaluating the thermodynamics of liquid phase systems. Indeed 2PT might provide a practical scheme to improve the intermolecular terms in forcefields by comparing directly to thermodynamic properties. a Calculated from mean squared deviation-equation A.II.2a, ESIw. b Calculated from Green-Kubo formalism-equation A.II.2b, ESIw. c Ref. 92-94. d Values for F3C, SPC/E and TIP4P-Ew below taken from ref. 39.
Journal of Molecular Liquids, 2011
Experimental densities of three groups of liquid organic substances (acids, esters, alcohols) have been correlated using Goharshadi-Morsali-Abbaspour (GMA) equation of state and then the values calculated from the equation of state have been compared with the experimental data. The paper reports new correlation for the density of 20 organic liquids (7 acids, 7 esters and 6 alcohols) at temperatures between 293.15 K and 393.15 K and pressures between 0.1 MPa and 35 MPa. A comparison with experimental data in the specified range of temperature from low to high pressures has been made. Some generalized correlations are also used for comparison with GMA equation of state and experimental data. The results show that the equation of state reproduces the experimental PρT data of liquid organic compounds with good accuracy. The excellent agreement with experimental data indicates that this equation of state can be used to calculate the density of liquid organic compounds with a high degree of certainty. The comparison with other correlations shows that the GMA equation of state is better to some extent and reliable in the given temperature and pressure range.
Surface tension for pure fluids by molecular thermodynamic model and PHTC equation of state
Physics and Chemistry of Liquids, 2019
In this study, the modified square well model is combined with perturbed-hard-trimer-chain (PHTC) EOS to correlate the surface tension of normal alkanes and refrigerant fluids. The performance of the proposed model has been evaluated by calculating the surface tension of 15 hydrocarbons range within 112-440 K and pressures up to 4.72 × 10 −6 MPa. From 251 data points examined the average relative deviation (ARD) of the correlated and calculated densities and surface tension from the experimental ones was found to be 1.63% and 2.46%. Besides, some surface thermodynamic functions such as the surface entropy (S S) and surface enthalpy (H S) of studied liquids were also computed via our method. The ARD (in %) were found to be equal to 3.94 and 2.44, respectively. Finally, our method has also been employed to estimate the critical temperature of 15 hydrocarbons with ARD (in %) equal to 7.92.
Density and Temperature Dependencies of Liquid Surface Tension
Iranian Journal of Chemistry Chemical Engineering International English Edition, 2011
In this paper the density and temperature dependencies of surface tension are investigated. Using the Lennard-Jones (12,6), as an effective pair interaction potential, a linear expression is derived for isotherms of γ /ρ 2 versus ρ 2 for some normal and ChloroFluoroCarbons (CFCs) fluids, where is surface tension and ρ = 1/v is molar density. The linearity behavior of the derived equation is well fitted onto the experimental data of surface tension for monatomic, diatomic, nonpolar, polar, hydrogen-bonded and chlorofluorocarbons. In addition, the temperature dependence of surface tension for 20 different fluids is examined, in which the contributions of both terms of the average effective pair potential to the γ are determined. For all liquids investigated in this work, surface tension increases with density except for water. The surface tension of water for isotherms within 280-300 K decreases with density, whereas increases within the range of 310-320 K.
The Journal of Chemical Physics, 2003
We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short ͑20 ps͒ molecular dynamics trajectory is used to obtain the vibrational density of states ͑DoS͒ which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase ͑highly fluidic͒, described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3N g , the total number of gas phase modes ͓3N g →0 for a solid and 3N g →3(NϪ1) for temperatures and pressures for which the system is a gas͔. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids ͑and gases and solids͒.