A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000?K and at pressures ranging from vapour pressure up to 40,000?bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.     

Application of hard convex body and hard sphere equations of state to the critical properties of binary mixtures

The critical properties of hydrocarbon mixtures, perfluorocarbon + hydrocarbon, perfluoromethylcyclohexane + siloxane, acetone + hydrocarbon and polydimethyl siloxane mixtures have been calculated from an equation of state for hard convex bodies and from Guggenheim's equation of state for hard spheres. In general, the results of both equations agree well with experimental data.It appears, however, that taking shape factors into account (by using the hard convex body equation) does not lead to a significant improvement in the agreement between theory and experiment for the critical properties.     

A new non-cubic equation of state

A new non-cubic equation of state is presented in this work. This expression is obtained from the original Redlich—Kwong equation of state by assuming that the attraction parameter depends not only on temperature, but also on density. Vapour—liquid equilibria in the coexistence region and PVT properties for the liquid, gas and supercritical fluid phases are accurately calculated with four parameters per isotherm. The generalization of this equation by a corresponding states correlation enables it to be applied over wide ranges of temperature, pressure and hydrocarbon molecular weight.     

Modification of Simha–Somcynsky equation of state for small and large molecules

The Simha–Somcynsky equation of state (SS EOS) represents the PVT behavior of polymers quite satisfactorily, but cannot be applied to gases at low pressures. This work proposes a modification of the free volume contribution of the SS EOS to allow representation of gaseous state of low molecular-weight substances by introducing the perturbed hard-chain theory of Beret and Prausnitz into the EOS. In addition to this modification, two universal constants are introduced to the free volume term for better representation of properties of low molecular-weight substances. Characteristic parameters in the modified SS EOS were determined for 44 low molecular-weight substances and 64 polymers. The absolute average deviations (AADs) for critical temperature, critical pressure and vapor pressures were 0.86, 2.38 and 2.01%, respectively, while AAD for critical density and saturated liquid density at normal boiling point were somewhat larger, being 20.46 and 5.30%, respectively. The high performance of the original SS EOS for polymer PVT behavior was maintained in the modified EOS with grand AAD of 0.050% for densities.     

Thermodynamic properties for liquid mercury using GMA equation of state

The important known regularities and thermodynamic properties of liquid mercury have been studied based on the average potential energy. Recognised regularities, the linearity of Zeno contour, bulk modulus and secant bulk modulus as functions of temperature, isochors of pressure versus temperature and near linearity of the inverse isobaric expansion coefficient have been investigated, all evaluated using the Goharshadi–Morsali–Abbaspour equation of state. The validity of the equation of state in predicting thermophysical properties is confirmed by a statistical parameter, absolute average deviation, with a maximum value of 0.41, showing excellent agreement with the experiment at temperatures between 293.15 and 323.15?K from low to high pressures.     

Generalized boublick equation: an accurate expression for the equation of state of hard fused spheres

Abstract

A simple expression to calculate the shape factor of hard bodies is proposed. Introducing this factor in the Boublik equation of state, very good results are obtained for hard dumbells and more complicated systems of linear homonuclear hard fused spheres. Agreement with available Monte Carlo results are also satisfactory enough for heteronuclear molecules. Furthermore, the new expression is reduced to the classical shape factor for hard convex bodies and provides a common basis to manage to concave and convex hard bodies.     

Densities and Apparent Molar Volumes of Aqueous H<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>BO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript> Solutions at Temperatures from 296 to 573 K and at Pressures up to 48 MPa

Densities of four aqueous H₃BO₃ solutions (0.062, 0.155, 0.315, and 0.529 mol-kg^–1) have been measured in the liquid phase with a constant volume piezometer immersed in a precisely controlled liquid thermostat. Measurements were made at temperatures between 296 and 573 K and pressures from 0.82 to 48 MPa. The total uncertainties of the density, pressure, temperature, and molality measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.0005 mol-kg^–1, respectively. The accuracy of the method was confirmed by PVT measurements on pure water for two isobars (30 and 39 MPa) at temperatures from 313 to 573 K. The experimental and calculated (IAPWS formulation) densities for pure water show excellent agreement which is within their experimental uncertainties (average absolute deviation, AAD=0.012%;). Apparent and partial molar volumes were derived using the measured densities for solutions and pure water, and these results were extrapolated to zero concentration to yield the partial molar volumes of the electrolyte (H₃BO₃) at infinite dilution. The temperature, pressure, and concentration dependencies of the apparent and partial molar volumes were studied. Small pressure and concentration effects on the apparent molar volumes were found at temperatures up to 500 K. The parameters of a polynomial type of equation of state for the specific volume V_sol(P, T, m) as a function of pressure, temperature, and molality were obtained with a least-squares method using the experimental data. The root-mean-square deviation between measured and calculated values from this polynomial equation of state is ±0.2 kg-m^–3 for density. Measured values of the solution densities and the apparent and partial molar volumes are compared with data reported in the literature.     

Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase

Costas, M. and Sanctuary, B.C., 1984. Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase. Fluid Phase Equilibria, 18: 47–60.Equation of state parameters for a theory of pure r-mers (Costas and Sanctuary, 1981) are presented for sixty common substances. The equation of state is tested for its ability to reproduce and predict thermodynamic data in the liquid phase. The theory has only two adjustable parameters: ν^*, the close-packed volume of the r-mer, and ?^* = z?/2, where ? is the nonbonded mer-mer attractive interaction energy and z is the lattice coordination number, set to be a constant equal to 12. The number of r-mers per molecule, r, is also fixed for a given liquid to be equal to the number of atoms in the molecule other than hydrogen. The fitting proceduce is fast and simple. The adjustment only involves the use of widely available density data. Comparisons between experimental and calculated first- and second-order thermodynamic properties are shown for several substances. A comparison with the equation of state due to Jain and Simha (1981) for PVT data for n-dodecane is presented. The theory qualifies as a useful tool, especially in engineering applications, for estimating thermodynamic properties in the liquid phase.     

PVT properties of an alternative biofuel: dimethyl ether

Dimethyl ether is an important chemical material and it has many engineering applications. It is a clean and economical alternative fuel and an ozone-friendly refrigerant. In this work, its PVT properties have been object of study. In particular, the experimental work was performed both in the two-phase region and in the superheated vapor region phase by means of the isochoric method. The isochoric measurements were carried out at temperatures from 219 K to 363 K and at pressures from 22 kPa up to 1,740 kPa. A total of 159 points, both in the two phase (71 points) and in the superheated vapor region (88 points) were obtained. The present experimental PVT data contribute to the deeper knowledge of the behaviour of the fluid both in the superheated vapour and in the saturation pressure region and to the development of a new equation of state.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Alkyl Monolayer Passivated Metal–Semiconductor Diodes: 2: Comparison with Native Silicon Oxide

To understand the electrical properties at passivated metal–semiconductor interfaces, two types of mercury–insulator–silicon (n‐type) junctions, Hg|C₁₀H₂₁? Si and Hg|SiO₂? Si, were fabricated and their current–voltage and capacitance–voltage characteristics compared. Both of them exhibited near‐ideal rectifying characteristics with an excellent saturation current at reverse bias, which is in contrast to the previously reported ohmic behavior of an unmodified mercury–silicon junction. The experimental results also indicated that the n‐decyl monolayer passivated junction possesses a higher effective barrier height, a lower ideality factor (that is, closer to unity), and better reproducibility than that of native silicon oxide. In addition, the dopant density and build‐in potential, extracted from capacitance–voltage measurements of these passivated mercury–silicon junctions, revealed that alkyl monolayer derivatization does not alter the intrinsic properties of the silicon substrate. The calculated surface state density at the alkyl monolayer|silicon interface is lower than that of the silicon oxide|silicon interface. The present study increases the possibility of using advanced organic materials as ultrathin insulator layers for miniaturized, silicon‐based microelectronic devices.     

Pressure–volume–temperature of molten and glassy polymers

The pressure–volume–temperature (PVT) dependencies of several amorphous polymers (PS, PC, PPE, and PPE/PS 1:1 blend) in the glassy and molten state were studied. The Simha–Somcynsky (S–S) lattice‐hole equation of state (EOS) was used. Fitting the PVT data in the molten state to the EOS yielded the free volume quantity, h = h(T, P), and the characteristic reducing parameters, P*, V*, and T*. The data within the glassy region were interpreted assuming that the latter parameters are valid in the molten and vitreous state, than calculating h = h(T, P) from the experimental values of V = V(T, P). Next, the frozen free volume fraction in the glass was computed as FF = FF(P). The FF values of polystyrene (PS) resins at ambient pressure showed little scattering (FF_P=1 = 0.691 ± 0.008), while their P‐dependencies varied, reflecting the thermodynamic history of the glass formation as well as the PVT measurements protocol. The pressure gradient of T_g was compared with the Ehrenfest relation for the second‐order transition; here also agreement depended on the method of vitrification. The experimental values of FF at ambient pressure decreased with increasing values of the characteristic temperature reducing parameter, T*. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 270–285, 2007.     

PVT properties of linear and dendritic polymers

The aim of this article is to examine the limits of applicability of the Simha‐Somcynsky (S‐S) equation of state (EOS) by comparing the pressure‐volume‐temperature (PVT) data and the derivatives (compressibility, κ, and thermal expansion coefficient, α) of anionic linear polystyrene (PS) with poly(benzyl ether) dendrimers (PBED). Fitting the PVT of PBED data to the S‐S EOS was similarly satisfactory as that of PS and the computed Lennard‐Jones (L‐J) interaction parameters showed similar errors of ca. 1%. Next, the experimental derivatives, α and κ of PS and PBED were compared with these functions computed from the S‐S EOS—good agreement was obtained for α at ambient pressure, P, indicating validity of the S‐S theory at least up to the first derivative. While the predicted κ = κ(P) dependence for PS and a linear PBED homologue was correct, for dendrimers the compressibility was higher at low pressure and it was lower at high P than theory predicts. Also the extracted values of the L‐J repulsion volume, v*, between a segment pair was smaller than expected. The specific architecture of dendrimer molecules is responsible for this behavior, since their 3D configuration is significantly different from the S‐S model with uniform segmental density and oxygen bonds in the main and side chains add flexibility. © 2009 NRC Canada. J Polym Sci Part B: Polym Phys 48: 322–332, 2010     

Equations of state for polyamide‐6 and its nanocomposites. 1. Fundamentals and the matrix

The pressure‐volume‐temperature (PVT) surface of polyamide‐6 (PA‐6) was determined in the range of temperature T = 300–600 K and pressure P = 0.1–190 MPa. The data were analyzed separately for the molten and the noncrystalline phase using the Simha‐Somcynsky (S‐S) equation of state (eos) based on the cell‐hole theory. At T_g(P) ≤ T ≤ T_m(P), the “solid” state comprises liquid phase with crystals dispersed in it. The PVT behavior of the latter phase was described using Midha‐Nanda‐Simha‐Jain (MNSJ) eos based on the cell theory. The data fitting to these two theories yielded two sets of the Lennard‐Jones interaction parameters: ε*(S‐S) = 34.0 ± 0.3 and ε*(MNSJ) = 22.8 ± 0.3 kJ/mol, whereas v*(S‐S) = 32.00 ± 0.1 and v*(MNSJ) = 27.9 ± 0.2 mL/mol. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At constant P, κ followed the same dependence on both sides of the melting zone near T_m. By contrast, α = α(T) dependencies were dramatically different for the solid and molten phase; at T < T_m, α linearly increased with increasing T, then within the melting zone, its value step‐wise decreased, to slowly increase at higher temperatures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 299–313, 2009     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

Structure of polymer fluids in colloidal dispersions

We have calculated some structural properties of a fluid of hard sphere polymer chains about a variable sized central hard sphere with the Monte Carlo method in the canonical ensemble. We have additionally calculated these structural properties with an integral equation based on density functional theory. The integral equation theory gives good agreement with the simulations at all but the highest densities.     

An equation of state for melts of linear homopolymers

We analyze the capability of the continuous Gaussian chain model to describe melts of linear homopolymer chains. We derive the equation of state of a system of n interacting chains by including long chain correlations by means of the one loop diagrams. These correlations which give rise to two combinations of the molecular parameters are found to be necessary for the proper quantification of pressure-volume-temperature (PVT) behaviour of the melts. The adjustment of the value of the prefactor of the small density term which is in accord with the liquid character of polymeric melts lead to a complete agreement between the experimental results and the outcomes of the theory. The proper dependence on the molecular weight is also predicted and isotherms of narrow distribution polystyrenes of three different molecular weights are used for the evaluation of the molecular parameters.     

PVT properties of imidazolium-, phosphonium-, pyridinium- and pyrrolidinium-based ionic liquids using critical point constants

Song and Mason equation of state (EOS) with a simple modification has been extended to modelling PVT properties of ionic liquids (ILs). The considered ILs are [C₁mim][MeSO4], [C₁mim][CH₃OC₂H₅SO₄], [C₁mim][(CH₃)₂PO₄], [C₂mim][MeSO4], [C₂mim][BF₄], [C₂mim][SCN], [C₂eim][NTf₂], [C₄mim][C(CN)₃], [C₄mim][CF₃SO₃], [C₄mim][SCN], [C₅mim][NTf₂], [C₈mim][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Cl], [(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Ac], [C₃mpyr][NTf₂], [C₄mpyr][NTf₂] and [Py][C₂H₅OC₂H₄SO₄]. Three temperature-dependent parameters in the proposed EOS have been scaled as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just critical temperature and critical density is sufficient to predict the PVT properties of these ILs. The overall average absolute deviation of calculated densities from literature values for 1347 data points of 18 ILs was found to be 0.58%. The predicted density of ILs from proposed EOS has been compared with those obtained by other literature work. Moreover, we indicate that the Zeno line regularity can well be predicted by proposed model for ILs.     

Transport Properties from the Equation of State by Means of Enskog Theory for d-Dimensional Hard Spheres

Abstract

In this work we have used Enskog theory to evaluate transport properties in d-dimensional hard spheres. In order to carry out this study we have made use of the relation between the compressibility factor Z and the ratio X_E/X ₀, where X_E is the Enskog value for a transport property and X ₀ is that corresponding to a dilute gas. From the available numerical data for Z in simulation experiences, we have calculated the aforementioned ratio for the diffusion coefficient D, the shear viscosity coefficient η, the bulk viscosity coefficient η and the thermal conductivity coefficient λ. This calculation has been extended to hard disks (d = 2), hard spheres (d = 3) and hard hyperspheres (d = 4,5) in the maximum allowable range of densities. We have also tested the suitability of some algebraic equations of state proposed for such bodies by comparing their respective values for X_E/X ₀. Finally, we have obtained numerical values for the ratio D/D_E in the cases d = 4,5. The behavior is similar to that of hard spheres.