Self-diffusion coefficient equation for polyatomic fluid

An equation for the self-diffusion coefficient in a polyatomic fluid is presented as a sum of three friction coefficient terms: the temperature-dependent hard-sphere contribution, the chain contribution and the soft contribution. This equation has been developed by using the molecular dynamics simulation data for the HS chain fluid and the expression for the Lennard–Jones (LJ) fluid proposed by Ruckenstein and Liu. The real nonspherical compounds are modeled as chains of tangent LJ segments. The segment diameter σ_LJ, segment–segment interaction energy ε_LJ and chain length N (the number of segments) are obtained from the experimental diffusion data. The equation reproduces the experimental self-diffusion coefficients with an average absolute deviation (AAD) of 3.72% for 22 polyatomic compounds (1081 data points) over wide ranges of temperature and pressure. The results have been compared with that of the rough LJ (RLJ) equation. To minimize the number of the fitting parameters, the energy parameter ε_LJ is estimated using a correlation obtained from viscosity data. The equation with two parameters gives an AAD of 4.72%.     

Second virial coefficients of Lennard–Jones chains

The second virial coefficients B₂ of Lennard–Jones chain fluids were calculated through Monte Carlo integration as a function of chain length m (up to 48 segments) and temperature. We found that at a fixed temperature the second virial coefficient decreases with chain length. At low temperatures, the virial coefficient changes sign from positive to negative as m increases. The simulation data also provide an estimate for the theta temperature T_Θ at which the attractive and repulsive interactions cancel each other for dilute solutions. It is found that the theta temperature T_Θ for Lennard–Jones chains with m>32 is 4.65 independent of chain length m. A comparison of simulated values of B₂ with those evaluated from two different perturbation theories for chain fluid shows that these approximate theories underestimate the second virial coefficients of Lennard–Jones chains.     

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.     

Viscosity Prediction for Oxygen,Nitrogen and Their Mixtures at Zero and Moderately Dense Regimes via Semi‐Empirically Based Assessment

The viscosity coefficients for the gaseous states of N₂ and O₂ and their mixtures are determined at zero and moderately density regimes. The Lennard‐Jones 12–6 (LJ 12–6) potential energy function is used as the initial model potential required y the technique. The interaction potential energies from the inversion procedure reproduce the viscosity commensurate to the best measurements. The initial density dependence of gaseous viscosity coefficient according to the Rainwater‐Friend theory, which was given by Najafi et al., has been considered for pure N₂ and pure O₂.     

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.     

由L-J流体的FMSA状态方程计算流体的PVT性质

运用Tang等提出的Lennard-Jones (L-J)流体两参数的一阶平均球形近似(FMSA)状态方程, 计算了流体的汽液共存相图和饱和蒸汽压曲线, 以及非饱和区的PVT性质, 并与文献数据进行比较. L-J参数由Tr＜0.95的汽液相共存数据回归得到. 计算结果表明, 对于分子较接近球形的流体, 除临界点附近外, 该方程可以在较大的温度和压力范围内计算真实流体的PVT性质, 结果满意. 对于球形分子, 该方程的精确度随分子尺寸的变大基本保持稳定. 该方程不适用于强极性物质. 在高密度区, 该方程的计算结果明显优于P-R方程. 对于分子偏离球形较远的流体, 该方程的适用性变差, 此时要考虑分子形状的影响, 可采用三参数的FMSA状态方程进行计算.     

受限于纳米狭缝中的四缔合Lennard-Lones流体的相平衡和界面张力研究

分别用改进的基础测量理论和平均球近似理论表达短程作用和长程作用对四缔合Lennard-Jones流体的过剩自由能的贡献. 在密度函泛理论的框架下, 研究了平均密度等温线, 密度分布, 未缔合分子在平衡汽相和液相中的分布, 相平衡以及平衡时的界面张力等热力学性质. 分析了缔合能量, 流体-固体作用和孔宽对受限于纳米狭缝中的四缔合Lennard-Jones流体相行为的影响.     

Molecular dynamics study on homonuclear and heteronuclear chains of Lennard–Jones segments

We report molecular dynamics (MD) simulation data for three simulated fluids: a homopolymer with 16 tangent Lennard–Jones (LJ) segments at the reduced temperature of 1.25, an equimolar binary homopolymer fluid with eight tangent LJ segments at 15 state points, and three corresponding copolymers with equimolar segment fraction and varying segment distribution at 15 state points. We find that the compressibility factors and energies do not change as the segment distribution varies in the copolymer example. The simulation data are compared with thermodynamic perturbation theory (TPT1) calculations. The TPT1 compressibility factors compare favorably with the MD data at high reduced temperatures but differ significantly at lower temperatures.     

Molecular dynamics simulation study of friction and diffusion of a tracer in a Lennard–Jones solvent

The friction and diffusion coefficients of a tracer in a Lennard–Jones (LJ) solvent are evaluated by equilibrium molecular dynamics simulations in a microcanonical ensemble. The solvent molecules interact through a repulsive LJ force each other and the tracer of diameter σ₂ interacts with the solvent molecules through the same repulsive LJ force with a different LJ parameter σ. Positive deviation of the diffusion coefficient D of the tracer from a Stokes–Einstein behavior is observed and the plot of 1/D versus σ₂ shows a linear behavior. It is also observed that the friction coefficient ζ of the tracer varies linearly with σ₂ in accord with the prediction of the Stokes formula but shows a smaller slope than the Stokes prediction. When the values of ratios of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation D = k _B T/ζ, from which the tracer is considered as a Brownian particle.     

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO₂) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6 MPa and two different temperatures (303.2 and 323.2 K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO₂ solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO₂ in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.     

Critical shift of a confined fluid in a nanopore

In a van der Waals model for a non-wetting confined fluid in a nanopore a shift in the critical temperature, with respect to the bulk value, is predicted. The agreement with experiment is good, giving that the characterization of fluids is done only by the Lennard–Jones potential parameters. The theory gives also a similar shift in the critical pressure.     

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.     

The self-diffusion coefficient in stable and metastable states of the Lennard-Jones fluid

Molecular-dynamics simulations have been employed to calculate the self-diffusion coefficient of a Lennard-Jones fluid for 198 sets of state parameters in the range of temperatures 0.35 ≤ k_BT/? ≤ 2.0 and densities 0.005 ≤ ρσ³ ≤ 1.2. Calculations have been made in stable and metastable states to the boundary of spontaneous nucleation in a model containing 2048 interacting particles. Results of computations, performed in the parameter range of stable states, are compared with the results of previous papers. Equations have been formulated, which describe the dependences of the self-diffusion coefficient on temperature and density and on temperature and pressure in the whole range of parameters including both the stable and metastable (supersaturated vapor, superheated and supercooled liquid) states of fluid.     

Prediction of Solubility Parameters Based on the Explicit Expression of Statistical Thermodynamics

A robust and efficient procedure is presented for calculating the solubility parameter. An analytical equation for internal pressure is proposed. Through a simple relation reported by Verdier and Andersen (fluid phase equilibrium 231: 125–137, 2005), one can easily find the solubility parameter via our analytical equation for the internal pressure. Also, the radial distribution function (RDF) of a Lennard–Jones LJ (12, 6) fluid, proposed by Xu and Hu (fluid phase equilibrium 30: 221–228, 1986), has been employed to calculate the internal pressure of normal alkanes from methane to decane. Their solubility parameters were evaluated according to the calculated values of the internal pressure. A comparison between the experimental and the estimated values demonstrated a very good agreement between them.     

Accurate CO2 Joule–Thomson inversion curve by molecular simulations

We present simulation of the Joule–Thomson inversion curve (JTIC) for carbon dioxide using two different approaches based on Monte Carlo (MC) simulations in the isothermal–isobaric ensemble. We model carbon dioxide using a two-center Lennard–Jones (LJ) plus point quadrupole moment (2CLJQ) potential. We show that a precision of four significant figures in ensemble averages of thermodynamic quantities of interest is needed to obtain accurately the JTIC. The agreement between the experimental data, Wagner equation of state (EOS) and our simulations results indicates that the 2CLJQ potential represents an excellent balance between simplicity and accuracy in modeling of carbon dioxide. Additionally, we calculate the JTIC using the BACKONE EOS (that uses the same intermolecular potential as in our simulations) and show that the BACKONE EOS performs very well in predicting the JTIC for carbon dioxide.     

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     

Application of thermodynamic perturbation theory to multicentre Lennard—Jones molecules. Results for CF4, CCl4, neo-C5H12 and SF6 as tetrahedral and octahedral models

Model fluids consisting of regular tetrahedral four- and five-centre and regular octahedral six- and seven-centre Lennard—Jones molecules are considered. The vapour—liquid equilibrium is determined by using perturbation theory on the liquid and virial expansion up to second virial coefficient on the gas side. Comparison is made with experimental data of CF₄, CCl₄, neo-C₅H₁₂ and SF₆.     

Modelling the VLE properties using van der Waals-type equation of state

The vapour–liquid equilibrium (VLE) properties of polar and non-polar fluids have been modelled by the use of two modified van der Waals (vdW)-type equations of state (EOSs). In this article, a revised method is applied to the above-mentioned EOSs to improve the representation of VLE properties of different class of fluids. In this respect, the repulsion parameter b is considered to be temperature dependent and also a temperature-dependent revision factor α(T) is introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration to reproduce the vapour pressure (P^s) of pure liquids. The present method is also extended to represent the VLE properties of binary mixtures containing noble gases, refrigerants and hydrocarbons. This method outperforms the original vdW-type EOSs in predicting the VLE and pressure-volume-temperature (PVT) properties of 22 pure substances and 7 binary mixtures.     

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.