Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state

We have discussed the capability of the soft-SAFT equation of state (EoS) to predict second order thermodynamic derivative properties of pure fluids in a recent paper [F. Llovell, L.F. Vega, J. Phys. Chem. B 110 (2006) 11427–11437]. The goal of this work is to extend these calculations to selected binary mixtures. The equation was applied in a semi-predictive manner: the pure component molecular parameters needed to apply soft-SAFT to experimental systems were obtained by fitting vapor–liquid equilibrium data and used, without further fitting, to calculate isochoric and isobaric heat capacities of selected alkane + n-alkane and n-alkane + 1-alkanol binary mixtures; isentropic compressibility coefficients and the speed of sound of selected n-alkane + 1-alkanol mixtures were calculated following the same procedure. We have used the crossover soft-SAFT equation which explicitly incorporates a renormalization group term in order to take into account the long range fluctuations appearing in the near critical region. Soft-SAFT was able to capture the qualitative behavior of the mixture properties studied, for a wide range of conditions, showing quantitative agreement with experimental data in some of the cases. As a further test to the equation, we have also calculated excess properties. The equation was able to capture the non-ideal behavior upon mixing experienced by these properties. This work shows the robustness of the molecular parameters and the equation to calculate properties not included in the fitting procedure, in a predictive manner.     

Global fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equation

We present here the extension of the crossover soft-statistical associating fluid theory (soft-SAFT) equation of state to mixtures, as well as some illustrative applications of the methodology to mixtures of particular scientific and technological interest. The procedure is based on White's work (White, J. A. Fluid Phase Equilib. 1992, 75, 53) from the renormalization group theory, as for the pure fluids, with the isomorphism assumption applied to the mixtures. The equation is applied to three groups of mixtures: selected mixtures of n-alkanes, the CO2/n-alkane homologous series, and the CO2/1-alkanol homologous series. The crossover equation is first applied to the pure components of the mixtures, CO2 and the 1-alkanol family, while an available correlation is used for the molecular parameters of the n-alkane series (Llovell et al. J. Chem. Phys 2004, 121, 10715). A set of transferable molecular parameters is provided for the 1-alkanols series; these are accurate for the whole range of thermodynamic conditions. The crossover soft-SAFT equation is able to accurately describe these compounds near to and far from the critical point. The theory is then used to represent the phase behavior and the critical phenomena of the selected mixtures. We use binary interaction parameters xi and eta for dissimilar mixtures. These parameters are fitted at some particular conditions (one subcritical temperature or binary critical data) and used to predict the behavior of the mixture at different conditions (other subcritical conditions and/or critical conditions). The equation is able to capture the continuous change in the critical behavior of the CO2/n-alkane and the CO2/1-alkanol homologous series as the chain length of the second compound increases. Excellent agreement with experimental data is obtained, even in the most nonideal cases. The new equation is proved to be a powerful tool to study the global phase behavior of complex systems, as well as other thermodynamic properties of very challenging mixtures.     

Thermodynamic properties and aggregate formation of surfactant-like molecules from theory and simulation

The goal of this work is twofold: to predict the phase equilibria behavior of simplified surfactant models and to predict the population of aggregates as a function of pressure. We compare Monte Carlo simulation results of these systems with predictions from a modified version of the statistical associating fluid theory (soft-SAFT). Surfactant-like molecules are modeled as Lennard-Jones chains of tangent segments with one or two association sites. We study the influence of the number and location of the association sites on the thermodynamic properties and fraction of nonbonded molecules in all cases. The influence of the chain length is also investigated for a particular location of the sites. Results are compared with NPT Monte Carlo simulations to test the accuracy of the theory, and to study the molecular configurations of the system. Soft-SAFT is able to quantitatively predict the MC PVT results, independently of the location of the association sites. The theory is also able to capture the qualitative trend of the population of aggregates with pressure. Quantitative agreement is only obtained for specific locations of the sites.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

The gas-liquid phase-transition singularities in the framework of the liquid-state integral equation formalism

The singularities of various liquid-state integral equations derived from the Ornstein-Zernike relation and its temperature derivatives, have been investigated in the liquid-vapor transition region. As a general feature, it has been found that the existence of a nonsolution curve on the vapor side of the phase diagram, on which both the direct and the total correlation functions become complex-with a finite isothermal compressibility-also corresponds to the locus of points where the constant-volume heat capacity diverges, in consonance with a divergence of the temperature derivative of the correlation functions. In contrast, on the liquid side of the phase diagram one finds that a true spinodal (a curve of diverging isothermal compressibilities) is reproduced by the Percus-Yevick and Martynov-Sarkisov integral equations, but now this curve corresponds to states with finite heat capacity. On the other hand, the hypernetted chain approximation exhibits a nonsolution curve with finite compressibilities and heat capacities in which, as temperature is lowered, the former tends to diverge.     

Heat capacities of butanol and pentanol in aqueous dodecyltrimethylammonium bromide solutions

Heat capacities of the ternary systems water-dodecyltrimethylammonium bromide (DTAB)-butanol and water-DTAB-pentanol were measured at 25°C. The standard partial molar heat capacities of pentanol in micellar solutions show a maximum at about 0.35 mol-kg^–1 DTAB that has been attributed to a micellar structural transition. This maximum tends to vanish by increasing the alcohol concentration and by decreasing the alcohol alkyl chain length; in the case of butanol it was not detected. The behavior of the standard partial molar heat capacities of alcohols in micellar solutions in the region above the cmc and below the structural transition was explained using a previously reported mass-action model for the alcohol distribution between the aqueous and the micellar phase and the pseudophase transition model for micellization. In the resulting equation the contributions due to the temperature effect on the shift of both the micellization equilibrium and the distribution are shown to be negligible so that only the distribution effect and the shift of the micellization equilibrium due to the added alcohol remain. The distribution constant and the partial molar heat capacities of alcohols in the aqueous and micellar phases have been derived by linear regression. The distribution constant for both alcohols agree well with those previously obtained using different techniques. Since the best fit below the structural transition correlates as well with the experimental points above the structural transition, it seems that no difference exists in the standard partial molar heat capacities of alcohols in the two shapes of the micelles. Also, from the present data and those for alkanols in sodium dodecylsulfate reported in the literature it seems that the standard heat capacity of alcohols in the micellar phase does not depend on both the alcohol alkyl chain length and the nature of the hydrophilic moiety of the head group of the micelles.     

Interfacial properties of Lennard-Jones chains by direct simulation and density gradient theory

We perform a series of molecular dynamics simulations of Lennard-Jones chains systems, up to tetramers, in order to investigate the influence of temperature and chain length on their phase separation and interfacial properties. Simulation results serve as a test to check the accuracy of a statistical associated fluid theory (soft-SAFT) coupled with the density gradient theory. We focus on surface tension and density profiles. The simulations allow us to discuss the success and limitations of the theory and how to estimate the only adjustable parameter, the influence parameter. This parameter is obtained by fitting the surface tension, and then used to obtain the density profiles in a predictive manner. A good agreement is found if the temperature dependence of this parameter is neglected.(c) 2004 American Institute of Physics.     

Thermodynamic properties in the molecular dynamics ensemble applied to the gaussian core model fluid

The thermodynamic properties of pressure, energy, isothermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound are considered in a classical molecular dynamics ensemble. These properties were obtained using the treatment of Lustig [J. Chem. Phys. 100, 3048 (1994)] and Meier and Kabelac [J. Chem. Phys. 124, 064104 (2006)], whereby thermodynamic state variables are expressible in terms of phase-space functions determined directly from molecular dynamics simulations. The complete thermodynamic information about an equilibrium system can be obtained from this general formalism. We apply this method to the gaussian core model fluid because the complex phase behavior of this simple model provides a severe test for this treatment. Waterlike and other anomalies are observed for some of the thermodynamic properties of the gaussian core model fluid.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

Estimation of second-order derivative thermodynamic properties using the crossover cubic equation of state

In this research, we apply the crossover cubic equation of state (XCubic EOS) [1] to the calculations of thermodynamic second-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, the Joule–Thomson coefficient, and speed of sound). This equation of state is used to calculate those 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 each property with a much better accuracy than the original PT equation of state and near the critical region, represents the singular behaviour well.     

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.     

Limiting Partial Molar Excess Heat Capacities and Volumes of Selected Organic Compounds in Water at 25°C

Well-known Picker flow microcalorimeters for the differential measurements of volumetric heat capacities have been employed in conjunction with vibrating tube densimeters to determine the molar heat capacity, volume, and the apparent properties in dilute aqueous solutions for 17 organic solutes of moderate hydrophobicity. The dependence on concentration of the apparent properties allowed the limiting partial molar quantities at infinite dilution to be extrapolated and the limiting partial molar excess quantities to be evaluated. Comparison with available literature data shows good agreement. The application of group contribution rules to the limiting partial properties has been tested using the original method and parameters proposed by Cabani et al. The predicted values of the partial molar volumes are in fair agreement with the present data except for some less common solutes. With partial molar heat capacities, the agreement is less satisfactory. To improve the performance of the method, missing parameters for some types of monofunctional and bifunctional molecules have been evaluated.     

Heat capacities,volumes and solubilities of pentanol in aqueous alkyltrimethylammonium bromides

Apparent molar heat capacities and volumes of pentanol, 0.05m in decyl-, tetradecyl- and hexadecyltrimethylammonium bromides micellar solutions, were measured at 25°C. They were assumed to approach the standard infinite dilution values and rationalized by means of previously reported equations following which the distribution constant between the aqueous and the micellar phase, heat capacity, and volume of pentanol in both phases are simultaneously derived. The present results show that the volume of the micellar core does not seem to have a significant effect on the apparent molar volume and heat capacity of pentanol in the micellar phase and on the free energy of transfer of pentanol from the aqueous to the micellar phase. We report an equation correlating the free energy of transfer of alcohols in alkyltrimethylammonium bromides as a function of the number of carbon atoms in the alcohol and surfactant alkyl chain. Also, the apparent molar heat capacities of pentanol in micellar solutions as a function of surfactant concentration show evidence of two maxima, which, by increasing the alkyl chain length of surfactant display an opposite dependence on concentration. The second maximum can be attributed to a sphere to rod transition. The second transition was also found in the case of butoxyethanol in hexadecyltrimethylammonium bromide. It is more difficult to explain the nature of the first maximum although an attempt is made.     

Chain length dependence of the thermodynamic properties of linear and cyclic alkanes and polymers

The specific heat capacity was measured with step-scan differential scanning calorimetry for linear alkanes from pentane (C(5)H(12)) to nonadecane (C(19)H(40)), for several cyclic alkanes, for linear and cyclic polyethylenes, and for a linear and a cyclic polystyrene. For the linear alkanes, the specific heat capacity in the equilibrium liquid state decreases as chain length increases; above a carbon number N of 10 (decane) the specific heat asymptotes to a constant value. For the cyclic alkanes, the heat capacity in the equilibrium liquid state is lower than that of the corresponding linear chains and increases with increasing chain length. At high enough molecular weights, the heat capacities of cyclic and linear molecules are expected to be equal, and this is found to be the case for the polyethylenes and polystyrenes studied. In addition, the thermal properties of the solid-liquid and the solid-solid transitions are examined for the linear and cyclic alkanes; solid-solid transitions are observed only in the odd-numbered alkanes. The thermal expansion coefficients and the specific volumes of the linear and cyclic alkanes are also calculated from literature data and compared with the trends in the specific heats.     

Thermodynamic and transport properties of (1-Butanol + 1,4-Butanediol) at temperatures from (298.15 to 318.15) K

Densities and kinematic viscosities have been measured for (1-butanol + 1,4-butanediol) over the temperature range from (298.15 to 318.15) K. The speeds of sound within the temperature range from (293.15 to 318.15) K have been measured as well. Using these results and literature values of isobaric heat capacities, the molar volumes, isentropic and isothermal compressibility coefficients, molar isentropic and isothermal compressibilities, isochoric heat capacities as well as internal pressures were calculated. Also the corresponding excess and deviation values (excess molar volumes, excess isentropic and isothermal compressibility coefficients, excess molar isentropic and isothermal compressibilities, different defined deviation speed of sound and dynamic viscosity deviations) were calculated. The excess values are negative over the whole concentration and temperature range. The excess and deviation values are expressed by Redlich–Kister polynomials and discussed in terms of the variations of the structure of the system caused by the participation of the two different alcohol molecules in the dynamic intermolecular association process through hydrogen bonding at various temperatures. The predictive abilities of Grunberg–Nissan and McAllister equations for viscosities of mixtures have also been examined.