Calculation Of Second Virial Coefficient Research Articles

Calculation of Second Virial Coefficient of DNA

In this work, a new calculate method has been presented to calculate second virial coefficient with structure factor. The second virial coefficient for DNA have been defined using the calculated structure factor and the programmed fitting technique of Mathematica Software 7.0. The obtained results have been compared with theoretical data and shown in good agreement with literature.

Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform.

The second virial coefficient, B2, measures a protein solution's deviation from ideal behavior. It is widely used to predict or explain solubility, crystallization condition, aggregation propensity, and critical temperature for liquid-liquid phase separation. B2 is determined by the interaction energy between two protein molecules and, specifically, by the integration of the Mayer f-function in the relative configurational space (translation and rotation) of the two molecules. Simple theoretical models, such as one attributed to Derjaguin, Landau, Verwey, and Overbeek (DLVO), can fit the dependence of B2 on salt concentrations. However, model parameters derived often are physically unrealistic and hardly transferable from protein to protein. Previous B2 calculations incorporating atomistic details were done with limited sampling in the configurational space, due to enormous computational cost. Our FMAP method, based on fast Fourier transform, can considerably accelerate such calculations, and here we adapt it to calculate B2 values for proteins represented at the atomic level in implicit solvent. After tuning of a single parameter in the energy function, FMAPB2 predicts well the B2 values for lysozyme and other proteins over wide ranges of solvent conditions (salt concentration, pH, and temperature). The method is available as a web server at http://pipe.rcc.fsu.edu/fmapb2 .

Sutherland Potansiyeli Kullanılarak İkinci Virial Katsayısının Analitik Belirlenmesi ve Gerçek Gazlara Uygulamaları

A simple and efficient analytical formula for the calculation of second virial coefficient over Sutherland potential is derived. The compute conclusions of the second virial coefficient determined for Sutherland potential are compared with calculations of second virial coefficient using Lennard-Jones (12-6) potential and Exp-6 potential. The accuracy of the analytical formula is tested by application to molecules Kr, Xe,Ne and Ar . The results of the calculations for wide temperature range show excellent agreement with the data existing in the literature.

Drug Design Outlook by Calculation of Second Virial Coefficient as a Nano Study

Intermolecular potential energy surface for an interaction of drug with Na has been examined using HF level of theory with 6-31G* basis set. The name of drug is meso-tetrakis (p-sulphonatophenyl) porphyrin (here after abbreviated to TSPP) . The numbers of Na+ have a significant effect on the calculated potential energy curve (including position, depth, and width of the potential well). Counterpoise (CP) correction has been used to show the extent of the basis set superposition error (BSSE) on the potential energy curves obtained for TSPPNa. The second virial coefficients are calculated by these data.

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 (Tm and ρm) 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 (ρg and γg) were used for estimation of second Virial coefficient. The calculation of second Virial coefficients (B2), 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.

Accurate calculation of second virial coefficient of the Exp-6 potential and its application

In this study, a new approach to calculate the second virial coefficient of the Exp-6 potential is proposed. Over a wide temperature range, the calculated results of the second virial coefficient determined from Exp-6 potential are comparable with the calculations of second virial coefficient over Lennard-Jones (12-6) potential. As an example of application, the formulas obtained for second virial coefficient are calculated for molecules Kr,Xe,N2,Hg,CH4 and C2H6. The obtained results are in good agreement with the data available in the literature.

Ability of analytical and artificial approaches for prediction of the volumetric properties of some polymer blends

In this research the statistical–mechanical equation of state and artificial neural network approaches are developed for volumetric properties of polymer blends. The Ihm–Song–Mason (ISM) and Tao–Mason (TM) equations of state based on density and surface tension at melting point (ρm and γm), as scaling constants, were developed. The calculation of second virial coefficients (B2), effective van der Waals co-volume (b) and correction factor (α) are required for judgment about applicability of these models. Also another model such as an artificial neural network (ANN) based on back propagation training with 15 neurons was used. A collection of 5397 data points for five polymer blends in the temperature range of 298.15–605.05K and pressures to 200MPa was used. The obtained results by ISM, TM and ANN models had good agreement with the experimental data with absolute average deviations of 0.72%, 0.84% and 0.34%, respectively. Among the applied methods, higher efficiency and better accuracy was achieved using ANN.

Volumetric properties of polymer blends from Tao–Mason equation of state

The present study is an improvement of previous work (Yousefi and Karimi, Ionics 18:135–142, 17) concern to the assessment of the ability of the Tao–Mason equation of state to predict pressure–volume–temperature (PVT) of melting polymers. The present paper, focus on the modeling of volumetric properties of polymer blends based on melting temperature (Tm) and melting point density (ρm), as scaling constants. The calculation of second Virial coefficients (B2), effective van der Waals co-volume (b) and correction factor (α) are required for judgment about applicability of this model. The new correlations were used to predict the PVT behavior of polymer blends containing poly(propylene glycol) + poly(ethylene glycol) (PEG-200), poly(ethylene glycol) methyl ether(PEGME-350) + PEG-200, PEGME-350 + PEG-600, poly(2,6-dimethyl-1,4-phenylene oxide) + poly styrene(PS), and PS + poly(vinylmethylether) in different temperatures, pressures, and mole fractions. A collection of 5,397 data points has been examined for the aforementioned polymers in the temperature in the range of 298.15–605.05 K and pressures up to 200 MPa. The average absolute deviation between the calculated and experimental densities is of the order of 0.78 %.

Theoretical study of basis set effects on the nano intermolecular potential energy surface of alanine -methionine: Calculation of second-virial coefficients

The potential energy of Alanine-Methionine was studied on the basis of ab initio calculations performed by using the HF,DFT-B3LYP and MP2 methods with 6-31G and 6-31G* basis sets. The following trends with basis set can be deduced for the depth (De= -Eint (Re) = -Emin) of the potential well of the calculated intermolecular potential energy surfaces (IPSs). In ab initio calculations the basis set superposition error (BSSE) is important. This error can be eliminated to some extent by using the counterpoise correction method (CPC). In this work, to estimate the interaction energy in the system we use the Morse potential model, and we estimate adjustable parameters used in the Morse model and theoretically second virial coefficient for the system. To determine the second virial coefficients, is used to obtained the model’s parameters over the range of temperatures of interest. Key words: IPS, second virial coefficient, basis set superposition error, counterpoise correction method, MP2, HF and DFT-B3LYP method.

Towards universal potentials for (H2)2 and isotopic variants: Post-Born–Oppenheimer contributions

Adiabatic corrections are evaluated for the interaction of two hydrogen molecules (H(2))(2) and isotopic variants. Their contribution to the cluster formation amount up to 10% of the interaction energy. Added to the best ab initio Born-Oppenheimer isotropic potential, they correct especially its short range repulsive part. Calculations of second virial coefficients are improved in general, with an impressive agreement with experiments for gaseous D(2) in a large range of temperatures. The potentials are available in both analytical and numerical forms.

Calculation of absolute scattering phase shifts

Use of a simple semiclassical estimate of Bessel function phase for arbitrary argument avoids the modulo π errors which the conventional approach tends to introduce into the calculation of absolute quantal phase shifts for high partial waves. This has significant implications for the direct quantum mechanical calculation of second virial coefficients at high temperatures.

An extension of the group contribution method for estimating thermodynamic and transport properties part II. Polyatomic gases (F2, Cl2, CS2, H2S, NO and N2O)

Earlier work on the group contribution method applied to the Kihara potential is extended to polyatomic gases for the calculation of second virial coefficients, viscosities and diffusivities of dilute gases with a single set of gas group parameters. Functional group parameters are evaluated from the simultaneous regression of second virial coefficient and viscosity data of pure gases. Parameters for gas groups (F2, Cl2, CS2, H2S, NO, nd N2O) are found to provide good predictions of second virial cross coefficients, mixture viscosities and binary diffusion coefficients of gas-gas mixtures. Application of the model shows that second virial coefficient data can be represented with good results comparable to the values by means of the corresponding states model. The reliability of the present model in viscosity predictions is proved by comparison with the Lucas method. Predictions of binary diffusion coefficients are in excellent agreement with experimental data and compare well with values obtained by means of the Fuller method.

Determination of second virial coefficients by grand canonical Monte Carlo simulations

In this communication, we investigate the use of grand canonical Monte Carlo simulations to estimate the second virial coefficient. Histogram reweighting calculations were performed to collect two-dimensional histogram for the number of particles and the energy to evaluate the density and pressure at low density. The histogram collected is reweighted for a series of chemical potentials to accumulate pressure, density, and temperature data along the isotherm to obtain the second virial coefficient. While exact calculation of second virial coefficients for arbitrary systems (e.g. mixtures and polyatomic molecules) involves multidimensional integrals, grand canonical simulations can, in principle, provide equation of state information from simulations at appropriately low densities. Our results indicate that the methodology yields reasonable estimates of the second virial coefficient. Agreement to analytical and experimental values is within a few percent for a variety of model and real fluids. There are however practical accuracy issues associated with this method. We discuss why this approach fails to find more precise values of the second virial coefficient even when long runs are used.

Atomic-potential parameters for H 2 and D 2: quantum corrections in the calculation of second-virial coefficients

First-order quantum corrections were introduced into the computation of the second-virial coefficients of H 2 and D 2. The quantum effects, for the studied two light molecules, are considerable even at the room temperature and become prominent at low temperatures. Atomic potentials, incorporating the quadrupole interactions, were employed in the calculations. Optimum atomic-potential parameters ε H, σ H, ε D and σ D were obtained from the nonlinear least-squares fit of the experimental second-virial coefficients. The fitted virial coefficients cover the temperature ranges of 173–423 and 153– 423 K for H 2 and D 2, respectively.

Monte carlo calculations of second virial coefficients of chain molecules

AbstractMonte Carlo calculations have been performed for different types of chain molecules whose units interact through Lennard‐Jones potentials. From the averaged Mayer function, we have evaluated the intermolecular two‐body cluster integral, obtaining results for second virial coefficients. We have investigated the following points: a) the site modelization of alkanes by comparison of our results with gas phase data of different linear and branched alkanes and their mixtures. b) the prediction of interpenetration factors for flexible linear and star polymer chains in a good solvent (or excluded volume conditions). c) the determination of the theta point for a model of flexible polymer chains and the comparison of data for finite chains with theoretical predictions.

Determination of the potential parameters of a site model from calculations of second virial coefficients of linear and branched alkanes

Determination of the potential parameters of a site model from calculations of second virial coefficients of linear and branched alkanes

Determination of the potential parameters of a site model from calculations of second virial coefficients of linear and branched alkanes

A previously established method to assign Lennard-Jones parameters for the methyl and methylene site groups in n-alkanes is now generalized to the case of branched alkanes. The method is based on Monte Carlo calculations of the binary cluster integral of the chain molecules, and their comparison with experimental data of second virial coefficients in the gas phase. We have arrived at a single set of values for the parameters epsilon and sigma of the different sites, CH3, CH2, CH and C, that reproduces adequately the virial coefficient data of linear and branched molecules, and also of their mixtures. This way we have also clarified the validity of the different alternative sets proposed in our earlier study for n-alkanes.

Tricritical behavior of an off-lattice flexible polymer model: Monte Carlo calculation of second virial coefficients

Simulation data of second virial coefficients have been obtained for an off-lattice model of linear polymer chains by means of Monte Carlo method with different values of the variable that describes intramolecular attractions between units. The data have allowed us to study the theta, or tricritical, region where binary interactions cancel out. These Monte Carlo results are quantitatively compared with numerical predictions from the tricritical renormalization group theory. With this purpose, we have employed the same values for the three-body and the cutoff theoretical parameters that were previously used to reproduce the mean size data.

A group contribution model for thermodynamic and transport properties of dilute gases

A group contribution method is proposed for the estimation of second virial coefficients and dilute gas transport properties. In earlier work, the group contribution concept was applied to the Kihara potential function for teh calculation of second virial coefficients. In this study, the Chapman-Enskog theory is used to extend the method to viscosity and diffusivity for dilute gases. Applications are made to normal and branched alkanes, alkenes, nitrogen, and carbon dioxide, as well as to a variety of mixtures of these compounds. Group parameters beyond those presented earlier are provided. Parameters evaluated from second virial coefficient and viscosity data for pure hydrocarbons are found to predict accurate second virial cross coefficients, mixture viscosities and binary diffusivities for hydrocarbon mixtures. Group parameters evaluated from second virial cross coefficient data for mixtures of nitrogen or carbon dioxide with an alkane are found to provide good predictions of mixture viscosities and binary diffusivities for these systems.

Calculation of second virial coefficients and gaseous viscosities of the refrigerants HFC-32 (CH2 F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2)

The second virial coefficients of refrigerants HFC-32 (CH2F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2) have been correlated on the bisis of site site model potential and have been compared with experimental results. The molecular interactions consisted of repulsion dispersion and electrostatic parts. From the site site potentials adjusted to the experimental second virial coefficients, spherically averaged potentials have been determined and a subsequent calculation of gaseous viscosity has been carried out. Agreement between measured and calculated values of second virial coellicients and gaseous viscosity is satisfactory. Calculated values of second virial coefficients and gaseous viscosity beyond available experimental data, therefore. can be assumed as a reliable extrapolation to lower and higher temperatures.