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.     

Vibrational and thermodynamic properties of β-HMX: a first-principles investigation

Thermodynamic properties of β-HMX crystal are investigated using the quasi-harmonic approximation and density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), and GGA + empirical van der Waals (vdW) correction. It is found that GGA well describes the thermal expansion coefficient and heat capacity but fails to produce correct bulk modulus and equilibrium volume. The vdW correction improves the bulk modulus and volume, but worsens the thermal expansion coefficient and heat capacity. In contrast, LDA describes all thermodynamic properties with reasonable accuracy, and overall is a good exchange-correlation functional for β-HMX molecular crystal. The results also demonstrate significant contributions of phonons to the equation of state. The static calculation of equilibrium volume for β-HMX differs from the room-temperature value incorporating lattice vibrations by over 5%. Therefore, for molecular crystals, it is essential to include phonon contributions when calculated equation of state is compared with experimental data at ambient condition.     

Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo

The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along Γ-N in the TA branches soften to imaginary frequencies, indicating structural instability. For face-centred cubic Mo, the phonon calculations predicted the stability by promoting the frequencies from imaginary to real. Within quasi-harmonic approximation, we predicted the thermal equation of state and some other properties including the thermal expansion coefficient α, product αK(T), heat capacity C(V), entropy S, Grüneisen parameter γ and Debye temperature Θ(D). The melting curves of Mo were also obtained successfully.     

Thermodynamics of 4’-bromomethyl-2-cyanobiphenyl in different solvents

The melting properties and the heat capacity of the solid state and the melt state 4’-bromomethyl-2-cyanobiphenyl (OTBNBr) were determined. The enthalpy, entropy and Gibbs free energy of fusion were also calculated. The solubility of OTBNBr in eight organic solvents was experimentally measured at temperatures from (283.15 to 323.15) K by using a static method. The reasons for the differences of the solubility of OTBNBr in various solvents are discussed by using the intermolecular interaction. Furthermore, the experimental solubility values were well correlated by the modified Apelblat equation, the λh equation, the Wilson model and the van’t Hoff equation. Finally, the temperature dependence of the activity coefficient and the van’t Hoff enthalpy in the tested solutions was investigated and is discussed.     

Thermodynamic properties of the Mie n-6 fluid: a comparison between statistical associating fluid theory of variable range approach and molecular dynamics results

Molecular dynamics (MD) simulations of direct and derivative thermodynamic properties of the Mie n-6 fluid (n=8, 10, and 12) have been performed for liquid to supercritical states. Using the results, an in depth test of the monomer-monomer interaction estimation of a recently derived statistical associating fluid theory of variable range (SAFT-VR) equation of state [Lafitte et al., J. Chem. Phys., 124, 024509 (2006)] has been carried out based on the Mie n-6 potential. For pure fluids, using an appropriate scaling, MD simulations show that density and isometric heat capacity are nearly independent of n, whereas sound velocity and thermal pressure coefficient tend to increase with n. In addition, the results show that predictions provided by the equation of state are consistent with those coming from MD and catch correctly the trends of each property with n except for the heat capacity. The comparison is next extended to binary mixtures with components differing only in the value of the n parameter and which demonstrate the reliability of the scheme (MX1b) used by Lafitte et al. to deal with this parameter in the SAFT-VR equation of state. In addition, a new empirical one-fluid approximation of the n parameter is proposed thanks to MD simulations, which very favorably compare with the one-fluid model on n previously proposed in the literature. The consistency of this approximation is addressed by making use of it in combination with the SAFT-VR Mie equation of state. It is shown that using such an approach, which is easier to handle than the MX1b one, yields slightly improved results compared to those of the MX1b.     

A new two-parameter cubic equation of state for predicting phase behavior of pure compounds and mixtures

In this work, a new two-parameter cubic equation of state is presented based on perturbation theory for predicting phase behavior of pure compounds and of hydrocarbons and non-hydrocarbons. The parameters of the new cubic equation of state are obtained as functions of reduced temperature and acentric factor. The average deviations of the predicted vapor pressure, liquid density and vapor volume for 40 pure compounds are 1.116, 5.696 and 3.083%, respectively. Also the enthalpy and entropy of vaporization are calculated by using the new equation of state. The average deviations of the predicted enthalpy and entropy of vaporization are 2.393 and 2.358%, respectively. The capability of the proposed equation of state for predicting some other thermodynamic properties such as compressibility, second virial coefficient, sound velocity in gases and heat capacity of gases are given, too. The comparisons between the experimental data and the results of the new equation of state show the accuracy of the proposed equation with respect to commonly used equations of state, i.e. PR and SRK. The zeno line has been calculated using the new equation of state and the obtained result compared with quantities in the literatures. Bubble pressure and mole fraction of vapor for 16 binary mixtures are calculated. Averages deviations for bubble pressure and mole fraction of vapor are 9.380 and 2.735%, respectively.     

Thermodynamic properties of DCl in D2O solution from 5 to 50°C

The themodynamic properties of solutions of deuterium chloride (DCl) in deuterium oxide (D₂O) have been determined from emf measurements of the electrochemical cell without transference from 5 to 50°C, and from 0.002 to 1.0 mol-kg^–1. The standard potential of the silver/silver chloride electrode relative to the platinum/deuterium electrode has been determined. An equation for the Gibbs energy as a function of temperature has been derived from which the enthalpy, entropy, and heat capacity have been computed. Equations for the activity coefficient and the osmotic coefficient of DCl in D₂O have been developed. The excess Gibbs energy of the solution and the excess partial molar free energy as a function of temperature have been calculated, from which the other excess thermodynamic properties have been computed. The values for the heat capacity and the apparent molar heat capacity have been compared with calorimetric data in the literature. The relative partial molar enthalpy has been calculated. The solvent isotope effect on the excess thermodynamic functions is discussed.     

Effect of kinetic and thermal parameters on the process of cure of epoxy resin in a cylindrical mould

Various parameters were found to be important in the cure of epoxy resin, those concerned with the kinetics of the heat evolved from the reaction (such as the order, rate constant and activation energy) and those related to the thermal properties of the resin, such as thermal diffusivity and heat capacity. An important parameter in this case was also studied, viz. the coefficient of the heat transfer through the heated fluid-mould interface, controlled by convection. After modelling successfully the process with a numerical method with finite differences, each of the parameters was tested in turn, by considering the temperature and state of cure-history at the middle of the resin cured in a cylindrical mould. Some parameters were found to be significant in the cure, such as the cure enthalpy and heat capacity, the activation energy and the coefficient of heat transferred by convection. This new knowledge allowed further insight into the process of cure for thermosets.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

First‐principles calculations on thermodynamic properties of BaTiO3 rhombohedral phase

The calculations based on the linear combination of atomic orbitals have been performed for the low‐temperature phase of BaTiO₃ crystal. Structural and electronic properties, as well as phonon frequencies were obtained using hybrid PBE0 exchange–correlation functional. The calculated frequencies and total energies at different volumes have been used to determine the equation of state and thermal contribution to the Helmholtz free energy within the quasiharmonic approximation. For the first time, the bulk modulus, volume thermal expansion coefficient, heat capacity, and Grüneisen parameters in BaTiO₃ rhombohedral phase have been estimated at zero pressure and temperatures form 0 to 200 K, based on the results of first‐principles calculations. Empirical equation has been proposed to reproduce the temperature dependence of the calculated quantities. The agreement between the theoretical and experimental thermodynamic properties was found to be satisfactory. © 2012 Wiley Periodicals, Inc.     

On-line Calibration and Determination of the Heat of Reaction for Laboratory Scale Heat Transfer Calorimeters

A simple method for the on-line calibration, in which both the heat transfer coefficient and the heat capacity of the reactor contents are determined, is described for laboratory scale heat transfer calorimeters. The calorimeter is operated in the isoperibolic mode for the calibration and a constant power is supplied to a resistor placed inside the reactor. The reactor heat balance differential equation is used to produce a set of linear simultaneous equations with each data acquisition cycle giving one equation. The heat transfer coefficient and the heat capacity are obtained from this set of equations by linear least squares. The application of the calibration procedure is illustrated by experiments in which the heat of reaction is determined on-line fora simulated reaction with first order kinetics and for the hydrolysis of acetic anhydride. This revised version was published online in July 2006 with corrections to the Cover Date.     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Elastic Tensor and Thermodynamic Property of Magnesium Silicate Perovskite from First-principles Calculations

The thermodynamic and elastic properties of magnesium silicate (MgSiO₃) perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consis-tent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and tem-peratures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO₃ perovskite is determined in the wide pressure range. The geo-logically important quantities: Young's modulus, Poisson's ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.     

多溴代芴热力学性质的理论预测研究

为了预测环境污染物多溴代芴的热力学性质,计算了60种多溴代芴的分子连接性指数、电性距离矢量指数、电性拓扑状态指数以及分子形状指数.采用多元线性回归的方法建立了多溴代芴化合物的标准生成焓(Δ_fH~0)、标准熵(S~0)、标准生成吉布斯自由能(Δ_fG~0)及等容热容等热力学性质的QSPR相关性模型,方程的相关系数值均在0.99以上.与相关文献的相关系数R和标准误差S进行比较,该模型具有良好的预测能力和稳定性.     

Prediction of thermodynamic derivative properties of pure fluids through the Soft-SAFT equation of state

We present in this work the application of the soft-SAFT equation of state (EoS) to the calculation of some main derivative properties, including heat capacities, reduced bulk modulus, Joule-Thomson coefficient, and speed of sound. Calculations have been performed analytically through the derivation of a primary thermodynamic potential function. The application to the n-alkanes, n-alkenes, and 1-alkanols families has been done in a semipredictive manner, with the molecular parameters of the equation obtained from previous fitting to vapor-liquid equilibrium data of the same compounds. The equation is able to capture the typical extrema isothermal derivative properties exhibit with respect to density, providing quantitative agreement with experimental (or correlation) data in some cases. Results in the vicinity of the critical point are improved by adding a crossover treatment to take into account the long-range fluctuations present in this region. By taking advantage of the molecular nature of the equation, we have been able to separate and quantify the different contributions (reference fluid, chain, and association) to the total derivative properties. The association plays a predominant role in energetic properties, such as the heat capacities, while there is a competition between association and chain length as the chain length of the compound increases for volumetric properties, such as the isothermal compressibility. These results act in favor of the molecular-based equations, like soft-SAFT, as predictive tools for several applications.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

Molecular dynamics simulation of liquid sulfur dioxide

A previously proposed model for molecular dynamics (MD) simulation of liquid sulfur dioxide, SO(2), has been reviewed. Thermodynamic, structural, and dynamical properties were calculated for a large range of thermodynamic states. Predicted (P,V,T) of simulated system agrees with an elaborated equation of state recently proposed for liquid SO(2). Calculated heat capacity, expansion coefficient, and isothermal compressibility are also in good agreement with experimental data. Calculated equilibrium structure agrees with X-ray and neutron scattering measurements on liquid SO(2). The model also predicts the same (SO(2))(2) dimer structure as previously determined by ab initio calculations. Detailed analysis of equilibrium structure of liquid SO(2) is provided, indicating that, despite the rather large dipole moment of the SO(2) molecule, the structure is mainly determined by the Lennard-Jones interactions. Both single-particle and collective dynamics are investigated. Temperature dependency of dynamical properties is given. The MD results are compared with previous findings obtained from the analysis of inelastic neutron scattering spectra of liquid SO(2), including wave-vector dependent structural relaxation, tau(k), and viscosity, eta(k).     

A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state

Using methods and approaches developed by the authors, a new low-parametric state equation for describing the thermal properties of normal substances is obtained that allows us to describe the thermal properties of gases, liquids, and fluids over a range of densities from the ideal gas state to the triple point, except for a critical region, with a high degree of accuracy close to that of an experiment. The caloric properties and speed of sound are calculated for argon, nitrogen, and carbon dioxide without using any caloric data except for the enthalpy of an ideal gas. It is established that the calculated values of enthalpy, heat capacity, the speed of speed of sound, etc., are in good agreement with the experimental (reliably tabulated) data.     

复合固体功能材料热导率测定的Monte Carlo模拟

本文首先把固体功能材料格点化,在无源、稳态情况下得到格点化了的热传导方程。利用格点模型,用Monte Carlo方法模拟了复合固体功能材料在无源、稳态下的温度场,以此来求其热导率。模拟的结果表明,在掺入的良导热体的体积分数固定的情况下,随着掺入物热导率的增加,复合材料的热导率呈对数规律增长;在掺入物的热导率固定不变的情况下,随着掺入物在复合材料中所占比例的增加,复合材料的热导率呈指数规律增长。这些模拟结果与实验结果符合得较好。     

Thermodynamic calculation of supercritical-fluid equilibria: New mixing rules for equations of state

Simple cubic equations of state with conventional mixing rules have played an important role in the calculation of phase equilibria and other thermodynamic properties of non-polar fluid mixtures. In the application of supercritical fluids to separation processes, volumetric as well as phase equilibrium properties are very important for rational process design.

Heyen (1980) proposed a cubic equation of state which shows better accuracy in the calculation of volumetric properties, compared to the Peng-Robinson equation of state. In order to apply his equation to polar mixtures, Heyen recently proposed a density-independent mixing rule, but this does not obey the universally-observed quadratic mixing rule of the second virial coefficient in the low-density limit.

This paper proposes a new density-dependent mixing rule for the Heyen equation of state. The Heyen equation of state with our new mixing rule appears to calculate the phase equilibria and the volumetric properties of CO₂-containing non-polar as well as polar mixtures with good accuracy.