Generalized Van Der Waals Equation Research Articles

A four-parameter generalized van der Waals equation of state: theoretical determination of thermodynamic stability boundary and vapor–liquid equilibrium of vanadium, niobium and tantalum

ABSTRACT A new four-parameter generalized van der Waals equation of state is proposed. The criteria for the applicability of the proposed equation of state in describing the thermodynamic properties of substances have been formulated. The generalized van der Waals equation of state is found to be applicable to vanadium, niobium and tantalum. To validate the generalized van der Waals equation of state, the spinodal, ideal tensile strength, thermodynamic limit of superheat and binodal of vanadium, niobium and tantalum have been determined. The obtained results agree with that of Filippov correlation and other equations of state. Using the obtained spinodal, the binodal of vanadium, niobium and tantalum has been determined.

The bubble effect on the thermal expansion coefficient of few-layer MoS2

The thermal expansion coefficient of van der Waals layered structures plays an important role in governing the thermal stability of high-performance electronic devices. Meanwhile, bubbles are frequently observed in the van der Waals layered structures due to the weak inter-layer interaction and the extremely small bending stiffness of the layered structure, but the effect of bubbles on the thermal expansion coefficient for layered structures remains unclear. We derive an analytic formula for the bubble effect on the length variation of the MoS2 layer. In the analytic derivation, the MoS2 layer is described by three mechanics models, including the elastic membrane theory, the nonlinear plate theory, and the linear plate theory. The gas inside the bubble is described by two types of state equations, including the ideal gas law and the generalized van der Waals equation. It is found that the nonlinear plate theory with the generalized van der Waals equation gives the most accurate description for the bubble effect, since MoS2 has a moderate bending stiffness. The analytic formula shows that the bubble can cause strong thermal contraction for few-layer MoS2 with increasing temperature. The analytic predictions are verified by comprehensive molecular dynamic simulations for few-layer MoS2 with different layer numbers and different gas molecule numbers. These results shall be valuable for understanding the thermal stability of functional devices based on the van der Waals layered structure.

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid- vapour critical—point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy, have been derived. In all the cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. This shows that the parameters of any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the thermodynamic properties of substances other than the liquid-vapour critical point. Moreover, an isothermal compressibility regularity is formulated on the basis of the gvdWEoS and it is found to satisfactorily trace the literature data for saturated liquid alkali metals.

Effects of porous media on the phase behaviour of polypeptide solutions

The generalized van der Waals equation for anisotropic fluids in porous media, proposed by the authors in previous works, is used to describe the effect of porous media on the phase behavior of polypeptide solutions. By introducing the temperature dependence for the depth of the potential well and the geometric parameters of the spherocylinder, the main features of phase behavior of the polypeptide poly (γ-benzyl-L-glutamate) (PBLG) in a solution of dimethylformamide, including the existence of two nematic phases, is reproduced. It is shown that the presence of a porous medium shifts the phase diagram to the region of lower densities and lower temperatures.

Isothermal compressibility of saturated refrigerants: Chlorodifluoromethane and 1,1,1,2-tetrafluoroethane

A new five-parameter generalized van der Waals equation of state is employed for calculating the isothermal compressibility of saturated refrigerants such as chlorodifluoromethane and 1,1,1,2-tetrafluoroethane in the liquid and vapor states over a temperature range from the boiling point to the critical point. This generalized van der Waals equation of state differs from the known van der Waals equation by the modified repulsive and attractive terms. The parameters of the equation of state are determined through the characteristic thermodynamic parameters of the refrigerants. The generalized van der Waals equation-of-state parameters are compared with the known van der Waals equation-of-state parameters.

Analytical treatment of the critical properties of a generalized van der Waals equation

Abstract The two-parameter van der Waals (vdW) equation of state is generalized, by adding another two parameters to the attractive term. General relations between thermodynamic functions of the generalized vdW equation and the hard sphere gas are derived. The cubic equation of the generalized vdW is solved and the critical points (P c , V c , T c ) are obtained for general k. The critical properties of the vdW real gas such as the isothermal compressibility K T , the isobaric expansion coefficient α and the isobaric heat capacity C P are calculated exactly. The temperature dependence of K T , α and C P is investigated close to the critical point on the critical isobar path P r = 1(P = P c ). Numerical calculations for K T and C P are presented above and below P r .

Generalized Van der Waals Equation for Liquid-Vapor Equilibria in a Stationary Gravitational Field

The behavior of liquids undergoing phase transition in the gravitational field is studied by considering the generalized Van der Waals equation. Considering the two simple models for liquid-vapor boundary of a pure classical fluid, the generalized Van der Waals equation shows how the three critical parameters (critical temperature, critical volume and critical pressure), suffice to describe the reduced state parameters (reduced temperature, reduced volume and reduced pressure), the concentration profile and the liquid-vapor boundary position, which can be used to observe transition phenomenon. This model shows how the form of the equation can influence the vertical phase separation induced by the stationary gravitational field, and on the gas condensation effects.

Generalized van der Waals equation of state for in-line use in hydrodynamic codes

Generalized van der Waals equation of state for in-line use in hydrodynamic codes

A mathematical recursive model for accurate description of the phase behavior in the near-critical region by Generalized van der Waals Equation

Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.

Equation of State for a Two-Dimensional Coulomb Gas

This work develops the cluster approach proposed by L.A. Bulavin and M.N. Malomuzh to the description of the phase diagram for a two-dimensional Coulomb gas. We restrict ourselves by the ensemble of the simplest clusters – dipole pairs. The effective interaction potential of dipole pair conserving a two particle configuration integral is constructed. In order to reflect more completely the long-range interaction in the system, the third virial coefficient is taken into account. The phase diagram of the Coulomb gas is analyzed on the basis of the generalized van der Waals equation of state, whose parameters are some functions of the temperature and the density. The position of the critical point is determined in different approximations. It is shown that this problem is essentially non perturbative.

Correlations of the Characteristic Thermodynamic Parameters of Alkali Metals

This work deals with a theoretically and technologically important thermodynamic study on the correlation of the Boyle temperature , the inversion temperature and the acentric factor of cesium, rubidium and potassium. This correlation is established through a generalized van der Waals equation of state. The obtained correlation fits the experimental data for the Boyle temperature , the inversion temperature and the acentric factor of cesium, rubidium and potassium. It has also been established that cesium, rubidium and potassium obey the single-parameter law of corresponding states. It is shown that the ratio of the inversion temperature and the Boyle temperature or the acentric factor can be used as the thermodynamic similarity parameter for cesium, rubidium and potassium.

A correlation of maximum attainable superheat and acentric factor of alkali metals

The maximum attainable reduced temperature of superheating at zero pressure and the acentric factor of cesium, rubidium and potassium are correlated through the generalized van der Waals equation of state. This three-parameter equation differs from the known van der Waals equation of state by the modified expression for molecular pressure. The obtained correlation fits the experimental data for the maximum attainable reduced temperature of superheating at zero pressure, with an accuracy of 2.756%, 2.408% and 2.638%, for cesium, rubidium and potassium, respectively. It has also been established that cesium, rubidium and potassium obey the single-parameter law of corresponding states with the maximum attainable reduced temperature of superheating at zero pressure or the acentric factor as the thermodynamic similarity parameter.

Phase behavior of mixtures of ionic liquids and organic solvents

A corresponding-states form of the generalized van der Waals equation, previously developed for mixtures of an ionic liquid and a supercritical solute, is here extended to mixtures including an ionic liquid and a solvent (water or organic). Group contributions to characteristic parameters are implemented, leading to an entirely predictive method for densities of mixed compressed ionic liquids. Quantitative agreement with experimental data is obtained over wide ranges of conditions. Previously, the method has been applied to solubilities of sparingly soluble gases in ionic liquids and in organic solvents. Here we show results for heavier and more-than-sparingly solutes such as carbon dioxide and propane in ionic liquids.

A New Model Approach for the Near-Critical Point Region: 1. Construction of the Generalized van der Waals Equation of State

To date, it has been considered that all classical equations of state (EOS) have failed to describe the properties of fluids near the critical region, where the density fluctuations have a significant influence on fluid properties. In this paper, we suggest a newly constructed equation for fluid states, the generalized van der Waals (GvdW) EOS with the highly simplified Dieterici's form P = [RT/(V - b)] - a(b/V)c by a new model potential construction describing intermolecular interactions. On the basis of the model potential construction, it is shown that the a, b, and c parameters have physical interpretations as an internal pressure, a void volume, and a dimensionless value that represents an inharmonic intermolecular cell potential, respectively. As an illustration of our model approach, we initially apply it to near the critical point (cp) region, where all classical EOS descriptions have been incorporated with experimental thermodynamic data, and we obtain a table of three parameters for 12 pure normal fluids, which precisely describes thermodynamic critical values. On the basis of the basic relations between pressure and volume at the critical point, we express the corresponding EOS in terms of the c parameter, and by this means, we also obtain a theoretical vapor-liquid equilibrium (VLE) line, which closely coincides with the experimental data for several pure normal fluids near the critical region. As a result, we show that thermodynamic properties near the critical region can be described analytically by only three parameters. In addition, to validate our EOS for the temperature-differential derivatives, we show that the calculated isochoric heat capacity (Cv) of saturated argon closely coincides with the experimental data. Moreover, the possibility of a precise description with respect to the entire fluid region is also argued, in terms of the physical cases from the triple point to the ideal gas region.

Correlations of attainable superheat of fluid alkali metals

The maximum attainable temperature of superheating, the Boyle temperature and the critical compressibility coefficient of cesium, rubidium and potassium are correlated through the generalized van der Waals equation of state. This three-parameter equation differs from the known van der Waals equation of state by the modified attractive term. For cesium, rubidium and potassium, the ratios of the maximum attainable temperature of superheating to the Boyle temperature are estimated. The results of estimation are in agreement with experimental data. It has been established that cesium, rubidium and potassium obey the single-parameter law of corresponding states with the ratio of the maximum attainable temperature of superheating to the Boyle temperature as the thermodynamic similarity parameter.

Critical parameters and equation of state for heavy liquid metals

Heavy liquid metals (HLM), such as mercury (Hg), lead (Pb), bismuth (Bi) and lead–bismuth eutectic (Pb–Bi), have been studying in several countries as potential materials for spallation neutron sources. However, experimental data on their thermal properties in the temperature range of interest are rare. In this case, an equation of state (EOS) developed on the basis of the fundamental thermodynamics and limited experimental data can play a very important role. Different approaches to construction of EOS are considered in the present work: the generalized van der Waals equation, the Redlich–Kwong equation and the concept of internal pressure of liquids. The results of calculation of the critical temperature, the critical pressure and the critical density of Hg, Pb, Bi and Pb–Bi obtained with these models and available experimental data on thermal properties of these HLM at lower temperatures and normal pressure are presented and discussed. An EOS is proposed which allows to estimate densities of liquid and vapour phases of HLM at high temperatures and pressures.

Superheating of Liquid Alkali Metals

The maximum attainable temperature of superheating and the critical temperature of cesium, rubidium, and potassium are correlated using the generalized van der Waals equation of state. This study shows that the maximum attainable temperatures of superheating for liquid cesium, rubidium, and potassium are 1722, 1802, and 2039 K, respectively. The results of the determination of the maximum attainable temperatures of superheating of liquid cesium, rubidium, and potassium are in agreement with experimental data. The given study establishes that liquid cesium, rubidium, and potassium can be superheated up to temperatures of about 200 K below their critical temperatures of 1924, 2017, and 2280 K, respectively. Moreover, cesium, rubidium, and potassium have been found to obey the single-parameter law of corresponding states, with the maximum attainable reduced temperature of superheating as the thermodynamic similarity parameter.

Correlations of Vapour-Liquid Critical Point Parameters of Alkali Metals

The critical temperature, critical compressibility factor and the inversion temperature of cesium, rubidium and potassium are correlated through the generalized van der Waals equation of state. This three-parameter equation differs from the known van der Waals equation of state by the modified attractive term. For cesium, rubidium and potassium, the reduced inversion temperature and its ratio to the critical compressibility factor were estimated. The results of estimation were in agreement with experimental data. It has been established that cesium, rubidium and potassium obeyed the single-parameter law of corresponding states with the reduced inversion temperature or its ratio to the critical compressibility factor as the thermodynamic similarity parameter.

Acentric Factor of Alkali Metals

The acentric factors of cesium, rubidium and potassium are determined on the basis of the generalized van der Waals equation of state. This generalized equation differs from the known van der Waals equation of state by the third parameter n in the expression for molecular pressure. The results of the determination of the acentric factors of cesium, rubidium and potassium are in good agreement with experimental data.

Phase explosion under ultrashort pulsed laser ablation: modeling with analysis of metastable state of melt

We present a model of femtosecond laser ablation for a metal target, including three sets of equations for different time scales and ablation conditions: a two-temperature model of laser radiation absorption by conduction electrons and electron–lattice relaxation; the thermal conductivity equation to describe the subsequent temperature evolution; the Euler equations supplemented with generalized van der Waals equation to describe vapor expansion. The solid–liquid interface is followed in the calculations. A metastable state of the molten layer has been shown to occur for regimes both below and above the ablation threshold that may not lead to phase explosion. For phase explosion to be put into effect, an external action has to be applied. For laser fluences below the ablation threshold, a probe laser pulse can play the role of the external action, whereas for high fluences the recoil pressure of the expanding vapor causes explosive boiling.