Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Mixing rules for van-der-Waals type equation of state based on thermodynamic perturbation theory

A concept based on the thermodynamic perturbation theory for a `simple fluid' has been applied to the attractive term of a van-der-Waals type equation of state (EOS) to derive a simple mixing rule for the a parameter. The new mixing rule is a small correction to the original one-fluid approximation to account for the influence of particles of j-type on the correlation function of ii-type in a mixture consisting of particles of i and j types. The importance of the correction has been shown by comparison of the calculated results for binary mixtures of Lennard–Jones fluids with the data obtained by numerical method (Monte-Carlo simulation). The new mixing rules can be considered as a flexible generalization of the conventional mixing rules and can be reduced to the original v-d-W mixing rules by defaulting the extra binary parameters to zero. In this way the binary parameters already available in the literature for many systems can be used without any additional regression work. Extension of the new mixing rules to a multicomponent system do not suffer from `Michelsen–Kistenmacher syndrome' and provide the correct limit for the composition dependence of second virial coefficients. Their applicability has been illustrated by various examples of vapor–liquid and liquid–liquid equilibria using a modified Patel–Teja EOS. The new mixing rules can be applied to any EOS of van-der-Waals type, i.e., EOS containing two terms which reflect the contributions of repulsive and attractive intermolecular forces.     

Application of group contribution SAFT equation of state (GC-SAFT) to model phase behaviour of light and heavy esters

The group contribution SAFT approach developed for pure compounds in an earlier work [S. Tamouza, J.-P. Passarello, J.-C. de Hemptinne, P. Tobaly, Fluid Phase Eq. 222–223 (2004) 67] is here extended for the treatment of ester series. Parameters for groups CH₂ and CH₃ previously determined were reused for the alkyl chains while new parameters were determined for COO and HCOO groups. The polarity of these molecules was taken into account by the addition to the equation of state (EOS) of a dipole–dipole interaction term due to Gubbins and Twu [K.E. Gubbins, C.H. Twu, Chem. Eng. Sci. 33 (1978) 863]. This term requires an additional parameter, the dipole moment which was correlated to the COO chemical group position in the ester chain.Three different versions of SAFT were used here to test the validity of the method: the original SAFT [W.G. Chapman, G. Jackson, K.E. Gubbins, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709], VR-SAFT [A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168] and PC-SAFT [J. Gross, G. Sadowski, Fluid Phase Eq. 168 (2000) 183; J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244]. In all three cases, similar and encouraging results are obtained. Reasonable predictions are found on heavy esters that were not included in the regression database.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

Estimation of 2nd-order derivative thermodynamic properties using the crossover lattice equation of state

We apply the crossover lattice equation of state (xLF EOS) [M.S. Shin, Y. Lee, H. Kim, J. Chem. Thermodyn. 40 (2007) 174–179] to the calculations of thermodynamic 2nd-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, Joule–Thompson coefficient, and sound speed). This equation of state is used to calculate the same properties of pure systems (carbon dioxide, normal alkanes from methane to propane). We show that, over a wide range of states, the equation of state yields properties with better accuracy than the lattice equation of state (LF EOS), and near the critical region, represents singular behavior well.     

Heat inertia and temperature gradient in the treatment of DTA peaks

Historical development of methods and theoretical basis of differential thermal analysis (DTA) are outlined. DTA is a procedure in which the heat transfer toward the sample plays an important function and the associated process in the sample is manifested by deviation of temperature difference from its background. This difference ΔT is not directly proportional to the rate of the process (dα/dt) but includes also the effect of heat inertia proportional to the slope dΔT/dt as it was derived and incorporated into DTA equation by Vold (Anal Chem 21:683–688, 1949), Borchardt and Daniels (J Am Chem Soc 79:41–46, 1957), and suggested to be corrected in the authors’ previous papers (1976). However, the correction with respect to heat inertia has so far been omitted (particularly after the boom of non-isothermal kinetics started by paper of Kissinger (Anal Chem 29:1702–1706, 1957)). DTA experiments with rectangular pulses realized by micro-heater inside the sample show that the correction of DTA signal employing calculated heat inertia term of the DTA equation is reliable but not yet fully sufficient. It was a reason to derive a more complete DTA equation including a term expressing the changes in the temperature field inside the sample during process. Possibilities for improving of DTA (and DSC) data processing are discussed. Itemized 150 references with titles.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

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.     

A new coordination number model by using the local composition theory

A new coordination number model for square-well (SW) fluid is proposed in this work. It is based on the local composition theory and starts from the point that total site numbers around one molecule can vary with reduced density and reduced temperature. The total site numbers are correlated with reduced density and reduced temperature by using local composition theory and Monte Carlo (MC) simulation results. This new model agrees well with the MC simulation results for the pure SW fluids at the low-density limit and in the high-density region. In addition, it can predict the transition to the face-centered cubic (fcc) fluid property which is shown in Young and Alder’s [J. Chem. Phys. 73 (1980) 2430] phase diagram. An equation of state (EOS) is derived from this new coordination number model and gives satisfactory compressibility factors for SW fluids.     

Simple modification of the temperature dependence of the Sanchez–Lacombe equation of state

In this work, the interaction energy term of the Sanchez–Lacombe equation of state (SL EOS) was modified to take into account the temperature dependence of hydrogen bonding and ionic interactions. A simple function was used in the form of the Langmuir equation that reduces to the original SL EOS at high temperature. Comparisons are shown between the ?*-modified SL EOS and the original SL EOS. The ?*-modified SL EOS could represent volumetric data for the group of non-polar fluids, polar fluids and ionic liquids to within an absolute average deviation (AAD) of 0.85%, 0.51%, and 0.054%, respectively whereas, the original Sanchez–Lacombe EOS gave AAD values of 0.99%, 1.2%, and 0.21%, respectively. The ?*-modified SL EOS provides remarkably better PVT representation and can be readily applied to mixtures.     

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.     

High pressure vapor–liquid equilibrium data for the systems carbon dioxide/2-methyl-1-propanol and carbon dioxide/3-methyl-1-butanol at 288.2, 303.2 and 313.2 K

In this work, we report vapor–liquid equilibrium data for the systems carbon dioxide (CO₂)/iso-butanol and CO₂/iso-pentanol at 288.2, 303.2 and 313.2 K, and for pressures up to the critical point. The interaction parameters for the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) equations of state (EOS) that best fit the experimental results are also given.     

A novel equation of state for the prediction of thermodynamic properties of fluids

This work proposes a new equation of state (EOS) based on molecular theory for the prediction of thermodynamic properties of real fluids. The new EOS uses a novel repulsive term, which gives the correct hard sphere close packed limit and yields accurate values for hard sphere and hard chain virial coefficients. The pressure obtained from this repulsive term is corrected by a combination of van der Waals and Dieterici potentials. No empirical temperature functionality of the parameters has been introduced at this stage. The novel EOS predicts the experimental volumetric data of different compounds and their mixtures better than the successful EOS of Peng and Robinson. The prediction of vapor pressures is only slightly less accurate than the results obtained with the Peng-Robinson equation that is designed for these purposes. The theoretically based parameters of the new EOS make its predictions more reliable than those obtained from purely empirical forms.     

Electrochemical nucleation with diffusion-limited growth. Properties and analysis of transients

A general equation for the potentiostatic transient for the case of electrochemical nucleation with diffusion-controlled growth has been published recently [L. Heerman, A. Tarallo, J. Electroanal. Chem. 470 (1999) 70]. This equation essentially is a correction to the model of Scharifker and Mostany [J. Electroanal. Chem. 177 (1984) 13] but leads to quite different predictions. This paper discusses the differences between these two models with special emphasis on the analysis of experimental transients. Numerical data are presented which allow the determination of the nucleation parameters (nucleation rate constant A and site density N₀). Finally, it is shown that plots of I/I_max versus t/t_max, which are widely used in the literature for the graphical representation of experimental results, are not very sensitive and can easily lead to misinterpretation of experimental results.     

Phase equilibria in systems containing o-cresol,p-cresol,carbon dioxide,and ethanol at 323.15–473.15 K and 10–35 MPa

Phase equilibria in binary and ternary systems containing o-cresol, p-cresol, carbon dioxide, and ethanol have been investigated experimentally at temperatures between 323.15 K and 473.15 K and pressures ranging from 10 MPa to 35 MPa. The experimental results provide a systematic basis of phase equilibrium data, yielding the effect of temperature on the influence of the position of the methyl groups of cresols that are in phase equilibria with carbon dioxide. Based on the different solubilities of the cresol isomers in carbon dioxide, the separation of o-cresol and p-cresol was investigated. The dependence of the separation factor between both cresol isomers on concentration, temperature, and pressure is obtained from experiments in the ternary system, o-cresol+p-cresol+carbon dioxide. The influence of ethanol added to each of the binary systems, cresol isomer+carbon dioxide, in order to enhance the solubility of the cresols in the carbon dioxide-rich phase is also shown. The experimental data have been correlated using seven different equations of state, whereof four explicitly account for intermolecular association: Statistical Association Fluid Theory (SAFT) by Chapman, Gubbins, Huang and Radosz, the SAFT modification by Pfohl and Brunner for near-critical fluids, a modified cubic-plus-association equation of state (CPA EOS) according to the ideas by Tassios et al., and one of the EOS by Anderko. The mixing rule proposed by Mathias, Klotz, and Prausnitz, with two binary interaction parameters per binary system influencing intermolecular attractive forces, is used for all EOS as a basis for an objective comparison of the EOS.     

Equation of state for Lennard–Jones flexible ring fluids

We present a new equation of state for Lennard–Jones (LJ) flexible ring fluids. We perform Monte-Carlo simulations for freely-jointed Lennard–Jones chain fluids (3-, 6- and 8-mer) in the canonical ensemble and obtain the intramolecular end-to-end pair correlation function data under extensive density and temperature conditions. We correlate these as a function of the density, the temperature and the number of segments in a chain. We apply this function to thermodynamic perturbation theory (TPT) and obtain a new equation of state for Lennard–Jones flexible ring fluids. We also compare existing simulation data [J. Chem. Phys. 104 (1996) 1729] with the results obtained using the newly derived equation of state.     

纯流体在临界区内外的表面张力研究

An equation of state(EOS)applicable for both the uniform and non-uniform fluids was established by using thedensity-gradient expansion,in which the influence parameter к[p(r),T] was obtained by the use of direct correlationfunction.The density functional theory(DFT)provides a framework under which both the phase equilibria and in-terfacial properties can be investigated within a single set of molecular parameters.The phase equilibria inside thecritical region can be improved by the renormalization group theory(RGT).However,the correction of interracialproperties by DFT and RGT is computationally difficult.In the present work,the density gradient theory(DGT)inwhich к[p(r),T] is treated as a constant is used to combine with the RGT for interfacial properties inside the criticalregion.     

On the density scaling of pVT data and transport properties for molecular and ionic liquids

In this work, a general equation of state (EOS) recently derived by Grzybowski et al. [Phys. Rev. E 83, 041505 (2011)] is applied to 51 molecular and ionic liquids in order to perform density scaling of pVT data employing the scaling exponent γ(EOS). It is found that the scaling is excellent in most cases examined. γ(EOS) values range from 6.1 for ammonia to 13.3 for the ionic liquid [C(4)C(1)im][BF(4)]. These γ(EOS) values are compared with results recently reported by us [E. R. López, A. S. Pensado, M. J. P. Comu?as, A. A. H. Pádua, J. Fernández, and K. R. Harris, J. Chem. Phys. 134, 144507 (2011)] for the scaling exponent γ obtained for several different transport properties, namely, the viscosity, self-diffusion coefficient, and electrical conductivity. For the majority of the compounds examined, γ(EOS) > γ, but for hexane, heptane, octane, cyclopentane, cyclohexane, CCl(4), dimethyl carbonate, m-xylene, and decalin, γ(EOS) < γ. In addition, we find that the γ(EOS) values are very much higher than those of γ for alcohols, pentaerythritol esters, and ionic liquids. For viscosities and the self-diffusion coefficient-temperature ratio, we have tested the relation linking EOS and dynamic scaling parameters, proposed by Paluch et al. [J. Phys. Chem. Lett. 1, 987-992 (2010)] and Grzybowski et al. [J. Chem. Phys. 133, 161101 (2010); Phys. Rev. E 82, 013501 (2010)], that is, γ = (γ(EOS)/φ) + γ(G), where φ is the stretching parameter of the modified Avramov relation for the density scaling of a transport property, and γ(G) is the Gru?neisen constant. This relationship is based on data for structural relaxation times near the glass transition temperature for seven molecular liquids, including glass formers, and a single ionic liquid. For all the compounds examined in our much larger database the ratio (γ(EOS)/φ) is actually higher than γ, with the only exceptions of propylene carbonate and 1-methylnaphthalene. Therefore, it seems the relation proposed by Paluch et al. applies only in certain cases, and is really not generally applicable to liquid transport properties such as viscosities, self-diffusion coefficients or electrical conductivities when examined over broad ranges of temperature and pressure.