Monte Carlo simulations of vapor–liquid–liquid equilibrium of some ternary petrochemical mixtures

The aim of this study was to determine the capability and accuracy of Monte Carlo simulations to predict ternary vapor–liquid–liquid equilibrium (VLLE) for some industrial systems. Hence, Gibbs ensemble Monte Carlo simulations in the isobaric–isothermal (NpT) and isochoric–isothermal (NVT) ensembles were performed to determine vapor–liquid–liquid equilibrium state points for three ternary petrochemical mixtures: methane/n-heptane/water (1), n-butane/1-butene/water (2) and n-hexane/ethanol/water (3). Since mixture (1) exhibits a high degree of mutual insolubility amongst its components, and hence has a large three-phase composition region, simulations in the NpT ensemble were successful in yielding three distinct and stable phases at equilibrium. The results were in very good agreement with experimental data at 120 kPa, but minor deviations were observed at 2000 kPa. Obtaining three phases for mixture (2) with the NpT ensemble is very difficult since it has an extremely narrow three-phase region at equilibrium, and hence the NVT ensemble was used to simulate this mixture. The simulated results were, once again, in excellent agreement with experimental data. We succeeded in obtaining three-phase equilibrium in the NpT ensemble only after knowing, a priori, the correct three-phase pressure (corresponding to the force fields that were implemented) from NVT simulations. The success of the NVT simulation, compared to NpT, is due to the fact that the total volume can spontaneously partition itself favorably amongst the three boxes and only one intensive variable (T) is fixed, whereas the pressure and the temperature are fixed in an NpT simulation. NpT simulations yielded three distinct phases for mixture (3), but quantitative agreement with experimental data was obtained at very low ethanol concentrations only.     

Birefringence of polyethylene melt in transient elongational flow at constant strain rate

Simultaneous birefringence and elongational viscosity measurements were carried out on molten commercial grade, low-density polyethylenes during simple elongational flow at constant strain rate and constant temperature. The birefringence increased with time during constant strain rate elongation. The increase in birefringence was a linear function of elongational stress throughout whole elongation, but the elongational viscosity increased in two stages. The increase in elongational viscosity can be divided into linear viscoelastic and nonlnear viscoelastic regions. The linear region appeared at small strain and the nonlinear region appeared at strain greater than 0.7. The elongational viscosity in the nonlinear region increased much more rapidly than that in the linear region. The Gaussian approximation, which is commonly used in molecular models, could be used for the transient elongational flow. A constant stress-optical coefficient C = 1.3 × 10^?10 cm²/dyn was obtained for all the elongational experiments, independent of strain rate (0.002-0.2s^?1). The stress-optical coefficients were weakly dependent on temperature, as predicted by the theory of rubber elasticity.     

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.     

Prediction of Vapor–Liquid Equilibria for Pb–Pd and Pb–Pt Alloys Using Ab Initio Methods in Vacuum Distillation

The vapor–liquid equilibrium (VLE) phase diagrams of Pb–Pd and Pb–Pt alloy systems in vacuum distillation were obtained based only on pure-component properties and the structures of the atoms. The interaction energies between pairs of atoms were calculated from ab initio methods and were used as the input energy parameters for the Wilson equation. The calculated activity data of the components, using energy parameters which were obtained by ab initio methods, are in good agreement with the experimental data. It is revealed that a cluster size of eight atoms, optimized using the NVT ensemble at 300 K, a time step of 1 femtosecond, and the simulation time 10 ps gives a good representation of the liquid phase systems. This approach can be used to obtain accurate VLE predictions for alloy systems in vacuum distillation. The VLE phase diagram has a significant advantage in guiding experiment and industrial production in vacuum metallurgy.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Interfacial tension of blends containing thermotropic liquid crystalline polymers

A method is proposed to determine the interfacial tension of immiscible blends containing a liquid crystalline polymer (LCP) and a flexible-molecule polymer, under flow conditions. The method is based on Taylor's theorem for immiscible fluids, i.e., that a suspended drop of liquid A in liquid matrix B is deformed in shear or elongational flow in proportion to the ratio of interfacial to viscous stresses. Taylor's theorem, as originally derived, applies to low concentrations, Newtonian fluids and small deformations. Thus, the theorem was modified to account for “Power Law” fluids in elongational flow and large deformations, more applicable to the system under investigation. The elongational viscosities of the LCP and the flexible polymer (polycarbonate) as a function of elongational rate were determined using converging type flow. The two polymers exhibited a Power-Law behavior in elongational flow and, hence, the experimental constitutive equations of state were used to quantify the viscous stresses. The interfacial stresses were modified for large deformations by taking into consideration the deformed shape and hence increased surface area of the elongated LCP particle. Using the modified expression, the interfacial tension of LCP and PC was determined to be in the range of 5–6.6 dyne/cm.     

Phase equilibria in carbon dioxide expanded solvents: Experiments and molecular simulations

We present complementary molecular simulations and experimental results of phase equilibria for carbon dioxide expanded acetonitrile, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. The volume expansion measurements were done using a high-pressure Jerguson view cell. Molecular simulations were performed using the Gibbs ensemble Monte Carlo method. Calculations in the canonical ensemble (NVT) were performed to determine the coexistence curve of the pure solvent systems. Binary mixtures were simulated in the isobaric-isothermal distribution (NPT). Predictions of vapor-liquid equilibria of the pure components agree well with experimental data. The simulations accurately reproduced experimental data on saturated liquid and vapor densities for carbon dioxide, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. In all carbon dioxide expanded liquids (CXL's) studied, the molecular simulation results for the volume expansion of these binary mixtures were found to be as good as, and in many cases superior to, predictions based on the Peng-Robinson equation of state, demonstrating the utility of molecular simulation in the prediction of CXL phase equilibria.     

Computer simulation of chiral liquid crystal phases VIII. Blue phases of the chiral Gay-Berne fluid

The phase diagram of chiral calamitic liquid crystals was studied in the temperature-chirality parameter plane by means of computer simulation. Bulk systems composed of N = 2048 uniaxial chiral calamitic Gay-Berne molecules, i.e. with interactions described by the Gay-Berne potential and an additive term for the energy of the chiral interaction, were investigated using Monte Carlo (MC) simulations in the canonical ensemble (NVT). A rich polymorphism of chiral liquid crystal phases was observed along an isotherm with increasing chirality parameter describing the strength of the chiral interaction. In addition to the cholesteric phase (N*), for the first time a blue phase I (BP I) could be proven by computer simulation of a many-particle system based on model intermolecular interactions. Additionally, at high values of the chirality parameter, a phase with randomly oriented squirming double twist tubes was found as characteristic for the so-called spaghetti model for blue phase III (BP III). The structures of all phases were characterized by order parameters, a set of scalar and pseudoscalar orientational correlation functions, and especially by visual representations of selected configurations.     

Computer simulation of chiral liquid crystal phases VIII. Blue phases of the chiral Gay-Berne fluid

The phase diagram of chiral calamitic liquid crystals was studied in the temperature-chirality parameter plane by means of computer simulation. Bulk systems composed of N = 2048 uniaxial chiral calamitic Gay-Berne molecules, i.e. with interactions described by the Gay-Berne potential and an additive term for the energy of the chiral interaction, were investigated using Monte Carlo (MC) simulations in the canonical ensemble (NVT). A rich polymorphism of chiral liquid crystal phases was observed along an isotherm with increasing chirality parameter describing the strength of the chiral interaction. In addition to the cholesteric phase (N*), for the first time a blue phase I (BP I) could be proven by computer simulation of a many-particle system based on model intermolecular interactions. Additionally, at high values of the chirality parameter, a phase with randomly oriented squirming double twist tubes was found as characteristic for the so-called spaghetti model for blue phase III (BP III). The structures of all phases were characterized by order parameters, a set of scalar and pseudoscalar orientational correlation functions, and especially by visual representations of selected configurations.     

HMX/TATB复合材料弹性性能的MD模拟

用分子动力学(MD)方法COMPASS力场, 分别在正则系综(NVT)和等温等压系综(NPT)下, 模拟计算了著名常用高能炸药HMX(环四甲撑四硝胺)与著名钝感炸药TATB (1,3,5-三氨基-2,4,6三硝基苯)所构成的混合体系在室温时的弹性性能和结合能. 结果表明, 在NVT和NPT两种系综下模拟所得结果呈平行一致的趋势; 与纯HMX相比, HMX/TATB复合材料的拉伸模量、体模量和剪切模量均有所下降; 在NVT系综下, 还完成了HMX/TATB混合体系的不同温度的MD模拟. 发现当温度在245～345 K范围时, 体系的刚性和弹性变化很小; 但当温度达到395 K时, 材料的刚性减弱, 柔性增强.     

Phenomenological analysis of elongational flow birefringence in semidilute solutions of hydroxypropylcellulose

The relaxation time of a polymer chain in an elongational flow field was investigated for hydroxypropylcellulose (HPC) semidilute solution systems by two methods: phenomenological analysis of elongational flow-induced birefringence, and dynamic light scattering (DLS) and rheological measurements. To understand the relaxation time of an entangled semiflexible polymer solution in an elongational flow field, scaling analysis of the elongational flow-induced birefringence curve was performed. The results of both temperature and concentration scaling analyses showed that birefringence curves at different temperatures and at several HPC concentrations were described well by a universal birefringence–strain rate curve. This scaling behavior was compared with the "fuzzy cylinder" model. The critical strain rate corresponded to the correlation time of the slow relaxation mode determined by DLS measurement and the relaxation spectrum obtained by dynamic viscoelasticity measurement. The elongational flow-induced birefringence observed in an HPC semidilute solution was concluded to be attributed to the orientation of the HPC segment in the entangled molecular system, because the dominant relaxation mode is found to be the concentration fluctuation of an entangled molecular cluster in a quiescent state.     

Molecular dynamics of polystyrene solutions in microwave fields

Equilibrium and nonequilibrium molecular dynamics simulation techniques were used to assess the influence of an applied microwave field on the dynamics of methylamine-methanol and methylamine-dimethylformamide (DMF) solutions bound within atactic polystyrene over a range of polymer densities from 35 to 96 wt % polymer. Atomistically detailed systems were studied, ranging from 3000 to 10 644 particles, using previously established potential models. Structural and dynamical properties were determined in the canonical (NVT) ensemble at 298 K. The simulated DMF self-diffusion coefficients in polystyrene solutions were compared with the zero-field experimental results established with pulsed-gradient spin-echo NMR spectrometry. A simulated external microwave field, with a rms electric field intensity of 0.1 VA, was applied to these systems and the simulated dynamical results over field frequencies up to 10(4) GHz were compared with the zero-field values. Simulated evidence of athermal effects on the diffusive characteristics of these mixtures is reported.     

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.     

Molecular simulation of dendrimers and their mixtures under shear: comparison of isothermal-isobaric (NpT) and isothermal-isochoric (NVT) ensemble systems

Flow properties of dendrimers are studied with the aid of nonequilibrium molecular dynamics techniques. Simulations are performed in the NpT ensemble using the NpT-SLLOD algorithm [P. J. Davis and D. J. Evans, J. Chem. Phys. 100, 541 (1994)] and are compared to the results from simulations performed in the NVT ensemble reported earlier [J. T. Bosko, B. D. Todd, and R. J. Sadus, Chem. Phys. 121, 12050 (2004)]. Shear thickening observed at high strain rates vanishes in systems kept under constant pressure. Also the exponents in the power-law dependencies of the viscosity and the normal stress coefficients change. The variations are significant only at high strain rates and do not affect largely microscopic properties such as shape, alignment, or rotation of molecules. The NpT-SLLOD algorithm has been applied to study various systems including dendrimers in solution and their blends with linear chain molecules of the same molecular mass, and some results for these systems are presented.     

热力学抑制剂作用下甲烷水合物分解过程的分子动力学模拟

采用正则系综(NVT)分子动力学方法模拟研究277.0 K、11.45 mol·L-1的热力学抑制剂乙二醇(EG)溶液作用下甲烷水合物分解微观过程. 模拟显示甲烷水合物的分解从甲烷水合物固体表面开始, 逐渐向内部推移, 固态水合物在分解过程中逐渐缩小, 直至消失. 固态水合物的分解从晶格扭曲变形开始, 之后笼形框架结构破裂, 最后形成笼形结构碎片. 同时已经分解的甲烷水合物在外层形成水膜, 包裹里层正在分解的甲烷水合物, 增大里层甲烷水合物分解传质阻力.     

Free energy of solvation of simple ions: molecular-dynamics study of solvation of Cl- and Na+ in the ice/water interface

Molecular-dynamics simulations of Cl(-) and Na(+) ions are performed to calculate ionic solvation free energies in both bulk simple point-charge/extended water and ice 1 h at several different temperatures, and at the basal ice 1 h/water interface. For the interface we calculate the free energy of "transfer" of the ions across the ice/water interface. For the ions in bulk water in the NPT ensemble at 298 K and 1 atm, results are found to be in good agreement with experiments, and with other simulation results. Simulations performed in the NVT ensemble are shown to give equivalent solvation free energies, and this ensemble is used for the interfacial simulations. Solvation free energies of Cl(-) and Na(+) ions in ice at 150 K are found to be approximately 30 and approximately 20 kcal mol(-1), respectively, less favorable than for water at room temperature. Near the melting point of the model the solvation of the ions in water is the same (within statistical error) as that measured at room temperature, and in the ice is equivalent and approximately 10 kcal mol(-1) less favorable than the liquid. The free energy of transfer for each ion across ice/water interface is calculated and is in good agreement with the bulk observations for the Cl(-) ion. However, for the model of Na(+) the long-range electrostatic contribution to the free energy was more negative in the ice than the liquid, in contrast with the results observed in the bulk calculations.     

Rigid-body dynamics in the isothermal-isobaric ensemble: a test on the accuracy and computational efficiency

We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal-isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics [Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291] to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics [Martyna, G. J. et al., J Chem Phys 1994, 101, 4177]. A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.     

Extension-Enhanced Conductivity of Liquid Crystalline Polymer Nano-Composites

Our aim here is to predict elongational flow-induced enhancements in thermal or electrical conductivity of liquid crystal polymer (LCP) nano-composites. To do so, we combine two classical mathematical asymptotic analyses: slender longwave hydro-thermo-dynamics for fibers and exact analysis of pure elongation of LCPs in solvents for bulk phases without boundary effects; and homogenization theory for effective properties of low volume-fraction spheroidal inclusions. Two implications follow: elongational flow dominates fiber free surface and thermal effects on electrical and thermal conductivity enhancements; and, there appears to be no sacrifice in enhancements by producing much higher radius, bulk fibers.     

Elongational flow induced ordering in surfactant micelles and mesophases

We have used small angle neutron scattering, SANS, to investigate the elongational flow induced ordering in surfactant micelles and mesophases. Spatially resolved SANS measurements have been used to determine the distribution of orientational ordering over the flow velocity pattern in an elongational flow cell, and comparison with the effects of shear flow are made. Two different surfactant systems have been studied, the charged wormlike mixed micelles of hexaethylene monododecyl ether, C16E6/hexadecyl trimethylammonium bromide, C16TAB (3% C16E(6)/5 mol% C16TAB), and the Lalpha lamellar phase of C16E6 (50.6 wt% C16E6 at 55 degrees C), and a substantially different response is observed. The orientational distribution of the Lalpha lamellar phase of C16E6 reflects the flow velocity pattern distribution within the cell, whereas for the wormlike mixed micelles of C16E6/C16TAB this is not the case, and this is associated with the shear thinning behavior of that system.     

Langevin dynamics in constant pressure extended systems

The advantages of performing Langevin dynamics in extended systems are discussed. A simple Langevin dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting equations of motion generate the isobaric-isothermal ensemble. The Parrinello-Rahman ensemble is then discussed and we show that despite the presence of intrinsic probability gradients in this system, a Langevin dynamics approach samples the extended phase space in the correct fashion. The implementation of these methods in the ab initio plane wave density functional theory code CASTEP [M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clarke, and M. C. Payne, J. Phys.: Condens. Matter 14, 2717 (2003)] is demonstrated.