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.     

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.     

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.     

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.     

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.     

Molecular dynamics investigations on Lennard–Jones systems near the gas–liquid critical point

NVT simulations on Lennard–Jones (L–J) systems near the gas–liquid critical point were performed by a direct approach. As a result, the two necessary conditions for simulating the systems in accordance with the thermodynamic limit were proposed: (i) L/ξ≳20 (L: the box-length, ξ: the correlation length), (ii) the total time of evolution, t_E>500 L–J units, for ξ≈3.5. The proposed conditions are probably very close to the sufficient ones. The influence of finite-size effects on pressure and density of small systems was qualitatively predicted. The prediction was confirmed by the simulations but only for L markedly lower than the length of typical critical wave, 2πξ. For L markedly higher, the evolutions were dominated by an effect called here the instability effect. The effect became negligible just when the condition for L/ξ was fulfilled. The ξ₀′ constant for L–J fluid was estimated from direct measurements of ξ to be 0.27±0.02 (L–J units). The thermodynamic parameters of the critical point, obtained from extrapolation, were in agreement with the results of other authors. The β_C exponent was estimated from minimization for a high range of temperatures to be 0.346. A comparison of the efficiency of NVT and NpT methods was also performed and no distinct differences were noted.     

Phase equilibria study of Lennard–Jones mixtures by an analytical equation of state

The recently developed equation of state (EOS) for Lennard–Jones mixtures [Y. Tang, B.C.-Y. Lu, Fluid Phase Equilibria 146 (1998) 73.] is further investigated in this work for describing phase equilibria of these mixtures. The investigation covers vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE) and vapor–vapor equilibria (VVE) over a wide range of temperatures, pressures and molecular characteristic parameters. Results from the van der Waals one-fluid (VDW1) theory are included for comparison. The newly proposed theory performs very well for VLE and LLE and the performance is better than the VDW1 theory; but both theories yield only qualitative results for VVE. It is also found that one system should exhibit VLLE, which was not noticed in previous investigations. Results from two other perturbation theories are also compared in some cases.     

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.     

Exact solution of the Schrödinger equation with a Lennard–Jones potential

The Schrödinger equation with a Lennard–Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given.     

Relationship Between Heat Capacity and Thermal Expansion Derived from the Lennard–Jones Potential

The relationship between heat capacity (C _p) and linear thermal expansion (α) derived from the Lennard–Jones potential is C _p=Aα(U ₀–E), where U ₀ is the heat of sublimation at T=0, E is the enthalpy and A is the coefficient. The values of A for different solidified inert gases coincide with one another within the limits of experimental error (±2%). The relationship is shown to be valid for various substances: solidified rare gases, diamond, halite and copper. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new equation for the correlation of surface tension–composition data of solvent–solvent and solvent–fused salt mixtures

An attempt has been made to propose accurate equations for correlating the surface tension of binary liquid mixtures. The method is applicable to the systems comprising of components with widely different molecular sizes. Two adjustable parameters, δ_p and δ_m obtained from the least squares analyses of the surface tension–composition data are reported for a number of systems. Temperature dependence of δ_p and δ_m is demonstrated for a few systems. The framework of operational equations has later been applied to cover multi-component systems comprising of fused salts with a single liquid component in full mole fraction range. Excellent fits of the surface tension for binary, ternary and multi-component ionic systems in aqueous or non-aqueous media have been obtained from the proposed method. The surface tension–composition data of 59 different types of systems with about 400 data points can be correlated by the equation with an average percent deviation of about 0.61. In contrast to previous equations from literature to calculate surface tension data, the proposed correlation is noted to be more accurate in different situations.     

Thermal diffusion in Lennard–Jones fluids in the frame of the law of the corresponding states

This work is related to the definition of a reduced thermal diffusion coefficient thanks to numerical microscale molecular dynamics simulations. This cross transport process, also called Soret effect, couples mass flux and thermal gradient and is still largely misunderstood. For this study, we have applied a boundary driven non-equilibrium molecular dynamics algorithm on Lennard–Jones spheres mixtures. Simulations have been performed at a constant reduced supercritical state, using a van der Waals’ one fluid approximation in order to fulfil the law of the corresponding states. In binary mixtures, we have studied the molecular parameters and the molar fraction influences on thermal diffusion separately and then combined. It is shown that, on pressure and on thermal conductivity, the corresponding states law is fulfilled for a wide range of molecular parameters ratios. In this frame, we have then constructed simple correlations which relate thermal diffusion factor to the mixture parameters. Combining the relations obtained, a reduced thermal diffusion factor taking into account all the various contributions has been defined. Finally, it is shown that this relation enables us to estimate thermal diffusion in various binary and ternary mixtures of Lennard–Jones spheres representing alkanes with a maximum deviation of 15%.     

Study on the microstructure and liquid–solid correlation of Al–Mg alloys

Based on the available structural models and theories of electrical resistivity (ER) of liquid alloys, the structure and the liquid–solid correlation of Al _(100-x) Mg_x (x = 0, 10, 20, 30, 40, 50) alloys have been qualitatively studied by measuring the ER during the heating/cooling process using the direct-current (DC) four-probe method, as well as by characterizing the solidification morphology and testing the hardness. The result shows that the ER of Al–Mg alloys increases with the increasing temperature and the Mg content; thermal state and history have an effect on the solidification structure and properties: the ER of Al–Mg alloys exhibits a lag phenomenon of structure change during the heating/cooling process. A higher heating/cooling rate contributes to the more obvious relaxation effect of ER and the more uniform structure. Furthermore, higher pouring temperature (PT) leads the melts and solidification structure to be more homogeneous, which increases the hardness.     

A new organic–inorganic hybrid based on Mn–salen and decavanadate

An organic–inorganic hybrid based on Mn-salen and decavanadate, [NH₄]₂[Mn(salen)(H₂O)₂]₄[V₁₀O₂₈]?·?6H₂O (1) (salen?=?N,N′-ethylene-bis(salicylideneiminate)), has been synthesized by the strategy of secondary building units in mixed methanol–water solution and was structurally characterized by single-crystal X-ray diffraction, elemental analyses, IR, and UV-Vis. The [Mn(salen)(H₂O)₂]⁺ cations and water molecules are located in the interspaces among the polyoxoanions [V₁₀O₂₈]^6? forming a POM-based supramolecule. Compound 1 is the first example of metal-Schiff-base polyoxovanadates. The photocatalytic analysis, cyclic voltammetry, and electrocatalytic analysis of 1 have been investigated.     

A new P-heterocyclic type of phosphonium–iodonium ylides based on dibenzophosphole

A novel mixed phosphonium–iodonium ylide was synthesized by alkylation of 5-phenyl-5H-dibenzophosphole with phenacyl bromide followed by deprotonation and oxidation of the resulting phosphonium ylide with (diacetoxyiodo)- benzene. The influence of the cyclic nature of the phosphonium moiety on the dynamic E/Z isomerism in the mixed ylide is discussed.     

Patterns of solid–fluid phase equilibria: new possibilities?

Thermodynamic phase space patterns of solid–liquid–vapor (slg) behavior in binary systems are reviewed. The van der Waals equation of state is used in combination with a common mathematical artifice for the solid–phase fugacity function to map out the slg loci for a model binary homologous series of solvent+solute mixtures as a function of the solute characterization. The computational results suggest the possible existence of a richer thermodynamic phase space topography than previously envisioned.     

Study on the structure–activity of dihydromyricetin and its new production

Myricetin (MY) was firstly synthesized from dihydromyricetin (DMY), and its antioxidant activity was analyzed. FTIR, NMR, and TG measurements confirmed that the DMY turned to MY. Scanning electron microscope observation showed that the 2,3-single bond offered great flexibility on the stage of crystallization to form imperfect crystalline regions; hence, DMY tends to form larger columnar crystals than MY. It has been found that the antioxidative efficiency of DMY was superior to MY, based on the measurement of radical scavenging activity by DPPH and the oxidation induction time of PP-antioxidant samples. The 2,3-double bond in MY structure, known as one of the characteristic determinants, was not an important requirement for antioxidant capacity or even negative correlation observed. Such a deduction was further supported by UV–Vis absorption spectra change when the pH was raised to pH 9. It was concluded that the ortho-trihydroxyl group in the B ring provides an antioxidant defense, and the 2,3-single band of C ring provides the structural stability.     

Analytical evaluation of zero-pressure Joule–Thomson coefficient using second virial coefficient and its application

In this paper, we present an analytical procedure to evaluate the zero-pressure Joule–Thomson coefficient using the second virial coefficient over the Lennard-Jones (12-6) potential. The analytical expressions are derived for the first and second derivatives of the second virial coefficient. The proposed formulae guarantee the accurate and fast calculation of the Joule–Thomson coefficient. As an example of application, the analytical expression obtained is used to calculate results for the molecules He, Xe, \(N_2 \), \(H_2 \), \(O_2 \), \({\textit{CO}}\), \(C_2 H_4 \), \(C_3 H_8 \) and \(C_5 H_{12} \). The results obtained by the present analytical expression are found to be in good agreement with the data in the literature. The calculation of results will help to estimate the Joule–Thomson coefficient with sufficient reliability and to determine the interaction potentials.     

A new organic–inorganic hybrid polyoxoniobate based on Lindqvist-type anion and nickel complex

A new organic–inorganic hybrid polyoxoniobate (H₂en)₂[Ni(en)₃][H₂Nb₆O₁₉] · 5.5H₂O (1) (en = ethylenediamine) has been synthesized by the diffusion method and structurally characterized by elemental analyses, infrared spectrum, ultraviolet (UV) spectroscopy, X-ray photoelectron spectroscopy (XPS), X-ray powder diffraction, thermogravimetric (TG) analysis, and single-crystal X-ray diffraction. Crystal structure analysis reveals that 1 exhibits a 3-D supramolecular architecture constructed from Lindqvist-type [H₂Nb₆O₁₉]^6? polyoxoanions and [Ni(en)₃]²⁺ via hydrogen-bonding interactions. The XPS measurement indicates that the oxidation state of Ni is +2. TG curve of 1 exhibits two steps of weight loss. In situ UV spectra display that 1 can exist in large pH range in aqueous solution.