Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.

STUDY ON THE CONCENTRATION EFFECTS IN GPC IV A NEW METHOD FOR DETERMINATION OF SECOND VIRIAL COEFFICIENTS FROM THE CONCENTRATION EFFECTS

In this paper a new relation between the second virial coefficients A_2, (?)_w and (dV_(es)/dC)_c→0=K_s was derived from proposed model theory of concentration effects in GPC for mono-and poly-dispersed polymers. Based on this relation a new method for determination of second vifial coefficients from the combination of (dV_(es)/dC)_c→0=K_3, (?)_w and K_H measurements was proposed.The values of A_2 for mono-and poly-dispersed polystyrenes with molecular weight range from 10~4 to 10~6 in good and theta solvents were determined by proposed method. Results show that their values of A_2 are in agreement with those obtained by light scattering.

The scaling behavior of the second virial coefficient of linear and ring polymer

The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer(θ_L) is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U(r) between two ring polymers as well as the second virial coefficient A_2 of ring polymers at θ_L, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A_2 of ring polymers at θ_L: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.

Based on the Second Virial Coefficient(A2)to Study Effect of the Synergistic Action of Solvent and External Electric Field on the Solution Behavior and Film's Condensed State Structure

The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based on the second virial coefficient(A2),effect of the synergistic action of solvents and external electric field on both solution behavior and the film’s condensed state structure for the semi-rigid conjugated polymer,poly[2-methoxy-5-(2’-ethylhexoxy)-1,4-phenylvinylene](MEH-PPV)was investigated by dynamic/static light scattering,photoluminescence spectroscopy and transmission electron microscopy,etc.It was found that although the MEH-PPV solutions with different solvents(toluene,chlorobenzene,chloroform and tetrahydrofuran)all could generate a response to the external electric field,the degree of response varied significantly with the change of solvent nature.Furthermore,ordered degree of the film from the solutions was also obviously different.The essential reason for this responsive difference was firstly revealed in the research,which actually depended on the degree of interaction between the solute and solvent,and this degree of interaction could be quantitatively described by the second virial coefficient(A2).The bigger the A2,the stronger the interaction between solvent and solute in the solution,and the stronger the response to the external electric field.Further,under the induction of external electric field,chains aggregations with different sizes were formed accompanied by large-scale chains ordered structure in the solution.This ordered structure not only can effectively transfer to film prepared by the precursor solution but also is beneficial to enhance the carrier mobility and device efficiency of the photoelectronic film.

Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical(except the second virial coefficient, where the sign is different)when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1(J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose(Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose(Fermi) gas.

The Potential Function for Double Square-Well Model and Its Application to Calculation of the Second Virial Coefficient

In the present paper,the mechanism of molecular aggregation and the character of potential function for square-well model have been investigated with the principle of molecular thermodynamics,leading to the potential function for double square-well(DSW) model,In addition,the equation of second virial coefficient for DSW model is derived from the statistical mechanics method.The above equation obtained has been verified by tests and the test results are excellent.It is concluded that this equation can well represent the behaviour of fluid molecules.

Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids

Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.

Analysis and Comparison of the Alpha Functions of SRK Equation of State

Alpha functions of Soave-Redlich-Kwong （SRK） equation of state proposed by Soave, Twu, and Luo were different in mathematic tendency. They were compared in modeling methane-alkanes equilibria with van der Waals mixing rule and Modified Huron-Vidal （MHV1） mixing rule, respectively. Results showed that Luo＇s alpha function was a little more accurate than Soave＇s, and Twu＇s alpha function lacked accuracy in modeling methane-alkanes equilibrium. SRK equation of state was expanded as virial form, and then the equivalent terms were contrasted with terms of virial equation of state. Results showed that Soave＇s and Luo＇s alpha functions matched the tendency of virial coefficient better than Twu＇s, and Luo＇s alpha function matched better than Soave＇s in wide temperature range, which sustained the conclusions of phase equilibria calculation. Luo＇s alpha function keeps decreasing when Tr〉 1 and becomes negative at sufficient high temperature, thus the conventional cubic equation of state expressed pressure as the sum of repulsion pressure PR （〉0）, and attraction pressure PA （〈0） could be improved to be the sum of hard-sphere repulsion pressure PH （〉0） and intermolecular force pressure P1 （P1〈0 at low temperature and p1〉0 at sufficient high temperature）.

Pressure-volume-temperature and excess molar volume prediction of amorphous and crystallizable polymer blends by equation of state

In this work the statistical mechanical equation of state was developed for volumetric properties of crystalline and amorphous polymer blends.The Ihm-Song-Mason equations of state(ISMEOS) based on temperature and density at melting point(T_m and ρ_m) as scaling constants were developed for crystalline polymers such as poly(propylene glycol) + poly(ethylene glycol)-200(PPG + PEG-200),poly(ethylene glycol) methyl ether-300(PEGME-350) + PEG-200 and PEGME-350 + PEG-600.Furthermore,for amorphous polymer blends containing poly(2,6-dimethyl-1,4-phenylene oxide)(PPO) + polystyrene(PS) and PS + poly(vinylmethylether)(PVME),the density and surface tension at glass transition(ρ_g and γ_g) were used for estimation of second Virial coefficient.The calculation of second Virial coefficients(B_2),effective van der Waals co-volume(b) and correction factor(α) was required for judgment about applicability of this model.The obtained results by ISMEOS for crystalline and amorphous polymer blends were in good agreement with the experimental data with absolute average deviations of 0.84%and 1.04%,respectively.

Study of CH_(4)and CO_(2)competitive adsorption on shale in Yibin,Sichuan Province of China

Shale gas is an unconventional gas source with substantial development potential.In this study,Longmaxi Formation shale from the Silurian system in Yibin,Sichuan Province was collected for characterizing total organic carbon(TOC),clay mineral content,and other reservoir properties.The pore structure of shale was analyzed by field-emission scanning electron microscopy and low-temperature N_(2) adsorption–desorption method.Isothermal adsorption experiments for CH_(4)and CO_(2)mixtures in shale samples were performed.The second Virial coefficient was used to calculate for the compressibility factor of the gas mixture.The influencing factors of gas adsorption capacity of shale were analyzed.Finally,the CH_(4)and CO_(2)adsorption capacities and selection of shale samples were investigated.Under low pressure,the total gas mixture capacity of shale samples was positively correlated with pressure.When the pressure increased to a certain extent,the growth trend of gas mixture adsorption capacity of shale samples decreased.The mixed gas adsorption volume is high at 50℃ for all the proportion.Given the same temperature and pressure,the CO_(2)adsorption of shale samples is higher than the CH_(4)adsorption.In competitive adsorption,shale prefers to adsorb CO_(2).Therefore,CO_(2)is easier to be adsorbed by shale and this causes CH_(4)to be released from the adsorption site.

Speed of Sound and Ideal-Gas Heat Capacity at Constant Pressure for HFC-125

The gaseous speed of sound, the ideal gas heat capacity at constant pressure, and the second Virial coefficient were determined for pentafluoroethane (HFC 125). A total of 49 data points of speed of sound for gaseous HFC 125 were measured for temperatures from 273 to 313 K and pressures from 32 to 479 kPa with a cylindrical, variable path acoustic interferometer. The ideal gas heat capacity at constant pressure and the second acoustic Virial coefficient were determined over the temperature range from the speed of sound measurements and were correlated as functions of temperature. An analytical expression for the second Virial coefficient derived using the square well intermolecular potential model was compared with the data.