The Second Virial Coefficients of n-Alkanes and Their Mixtures from the Kihara Convex Core Intermolecular Pair Potential

1993 ◽  
Vol 58 (10) ◽  
pp. 2489-2504 ◽  
Author(s):  
Jan Pavlíček ◽  
Karel Aim ◽  
Tomáš Boublík
Keyword(s):  
Geometric Mean ◽  
Second Virial Coefficient ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Liquid Density ◽  
Second Virial Coefficients ◽  
Uncertainty Estimates ◽  
Pure Compounds ◽  
The Individual ◽  
Convex Core

The second virial coefficients for a series of C2 to C8 n-alkanes and the second virial cross coefficients for their binary mixtures were calculated as a function of temperature from the exact expressions derived for the Kihara rod-like molecules. The three parameters of Kihara pair potential, ε/k, σ and l for the individual compounds were either used as determined from vapour-liquid equilibrium and saturated liquid density data in a previous study or with ε/k adjusted to the second virial coefficient data. The results are accurate almost within experimental uncertainty estimates of the data. In the case of mixtures the second virial cross coefficients were calculated from a similar expression in which only the ε12/k parameter was adjusted whereas σ12 = (σ1 + σ2)/2 and l1 and l2 of pure compounds were employed. It appears that the correction factor to the geometric mean combining rule for ε12/k is always less than and close to unity. Comparison with the values obtained from the Tsonopoulos generalized correlation reveals fair agreement between the characteristic binary k12 parameters from the two methods.

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
Keyword(s):  
Methyl Acetate ◽  
Virial Coefficient ◽  
Methyl Formate ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Ethyl Formate ◽  
Carbonyl Oxygen ◽  
Second Virial Coefficients ◽  
Theoretical Significance ◽  
Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

MODELING THERMOPHYSICAL PROPERTIES OF NOBLE GAS INVOLVED MIXTURES

2011 ◽  
Vol 08 (01) ◽  
pp. 19-39 ◽  
Author(s):  
MOHAMMAD MEHDI PAPARI ◽  
JALIL MOGHADASI ◽  
SOUDABEH NIKMANESH ◽  
ELHAM HOSSEINI ◽  
ALI BOUSHEHRI
Keyword(s):  
Thermal Conductivity ◽  
Potential Energy ◽  
Thermophysical Properties ◽  
Noble Gas ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Model Potential ◽  
Intermolecular Potential ◽  
Inversion Method ◽  
Second Virial Coefficients

The present work involves in determining isotropic and effective pair potential energy of binary gas mixtures of Kr–Xe , Kr–C2H6 , Xe–C2H6 , Kr–C3H8 , and Xe–C3H8 from thermophysical properties consisting of viscosity and second virial coefficients through inversion method. Typically, the calculated intermolecular potential energy of Kr–Xe system has compared with HFD model potential reported in literature. A desirable harmony between our model potential and HFD model has been obtained. In order to assess the potential energies obtained, transport properties including viscosity, diffusion, thermal diffusion factor, and thermal conductivity of aforementioned mixtures were predicted using the calculated models potential. The deviation percentage of the calculated viscosity and thermal conductivity of above-mentioned mixtures from the literature values are, respectively, within ±2%, ±3%.

On the determination of intermolecular energies by inductive analysis

1942 ◽  
Vol 38 (2) ◽  
pp. 224-230
Author(s):  
William J. C. Orr
Keyword(s):  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Rare Gases ◽  
Second Virial Coefficients ◽  
Classical Expression ◽  
The Individual ◽  
Image Position ◽  
Range Of Values ◽  
Inductive Analysis

For a direct comparison of the individual attractive and repulsive terms of an intermolecular potential determined by the inductive analysis of themodynamic data with the same terms calculated by quantal methods it is desirable to carry out the analyses, in the first approximation, with an intermolecular potential of the form ø(R) = Pe−aR − A1/R6 − A2/R8. For mathematical convenience, in place of the above expression, two potential functions,andare considered, the first being taken to be adequate in the range of values of R between 0 and R0 (the minimum of the potential function) and the second, in the range from R0 to ∞. By dividing the problem in this way it is possible to find substitutions which permit the integration of the classical expression for the second virial coefficients (and other appropriate thermodynamic data) directly in terms of fairly simple series in | ψ0 |, R0, a and r. Finally it is pointed out that for such simple atoms or molecules as the rare gases, oxygen, nitrogen and methane r may be taken as 0·15 throughout, which considerably simplifies the application of the method to the experimental data.

scholarly journals Applications of the second virial coefficient: protein crystallization and solubility

2014 ◽  
Vol 70 (5) ◽  
pp. 543-554 ◽  
Author(s):  
William W. Wilson ◽  
Lawrence J. DeLucas
Keyword(s):  
Membrane Proteins ◽  
Protein Crystallization ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Protein Crystal ◽  
Second Virial Coefficients ◽  
History Of ◽  
Technological Improvements ◽  
Diagnostic Indicator

This article begins by highlighting some of the ground-based studies emanating from NASA's Microgravity Protein Crystal Growth (PCG) program. This is followed by a more detailed discussion of the history of and the progress made in one of the NASA-funded PCG investigations involving the use of measured second virial coefficients (Bvalues) as a diagnostic indicator of solution conditions conducive to protein crystallization. A second application of measuredBvalues involves the determination of solution conditions that improve or maximize the solubility of aqueous and membrane proteins. These two important applications have led to several technological improvements that simplify the experimental expertise required, enable the measurement of membrane proteins and improve the diagnostic capability and measurement throughput.

The second virial coefficients of mixed organic vapours

1952 ◽  
Vol 210 (1103) ◽  
pp. 557-564 ◽  
Keyword(s):  
Hydrogen Bonding ◽  
Binary Mixtures ◽  
Diethyl Ether ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Corresponding States ◽  
Linear Variation ◽  
Second Virial Coefficients

The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.

Solution Properties of Polybutadiene and trans-Polyisoprene Fractions

1963 ◽  
Vol 36 (2) ◽  
pp. 488-501
Author(s):  
W. Cooper ◽  
D. E. Eaves ◽  
G. Vaughan
Keyword(s):  
Molecular Weight ◽  
Light Scattering ◽  
Benzene Solution ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Γ Radiation ◽  
Branched Polymer ◽  
Butyl Lithium ◽  
Second Virial Coefficients ◽  
Molecular Weights

Abstract Linear polybutadienes, prepared with butyl lithium as catalyst, and polybutadienes branched by exposure to γ-radiation have been fractionated and the fractions examined by osmometry and light scattering. Turbidimetric second virial coefficients (A2τ) of mixed polymer fractions are virtually the same as those of the higher molecular weight components of the mixtures for most compositions. This is true both for mixtures of linear with linear and linear with branched polymer. The higher the molecular weight of the fraction, the greater the effect; the addition of 1 per cent microgel to a linear polymer reduced A2τ by a factor of three. The presence of microgel or high molecular weight branched polymer has been shown to be responsible for the very high molecular weights previously reported for polybutadienes from light scattering measurements. It is conveniently removed by shaking the solutions with calcium sulfate. Second virial coefficients obtained either by light scattering or osmometry are, within the limits of experimental error, uninfluenced by branching in the polymer. In general those factors which lead to increased branching also result in increased polydispersity, and it is the latter which results in the decrease in A2τ. The fall of the osmotic second virial coefficient (A2τ) with molecular weight is much smaller than would be calculated theoretically, and the fall in A2τ is greater than would be expected, notwithstanding the fact that for some of the fractions Mw/Mn<1.1. This indicates that A2τ is sensitive to the low molecular weight species present in the fractions, whereas the reverse must apply to A2τ. Natural or synthetic trans-polyisoprene showed analogous behavior to polybutadiene, although, owing to experimental difficulties, sharp branched fractions could not be obtained. The following viscosity-molecular weight relationships were obtained in benzene solution: [η]=1.45×10−4M0.76 for butyl lithium-catalyzed polybutadienes, and [η]=4.37×10−4M0.65 for natural and synthetic trans-polyisoprenes.

The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

Calculation of Thermodynamical, Transport and Structural Properties of Neon in Liquid and Supercritical Phases by Molecular Dynamics Simulations Using an Accurate ab initio Pair Potential

2003 ◽  
Vol 68 (3) ◽  
pp. 627-643 ◽  
Author(s):  
Muthusamy Venkatraj ◽  
Markus G. Müller ◽  
Hanspeter Huber ◽  
Robert J. Gdanitz
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Structural Properties ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Energy Curve ◽  
Second Virial Coefficients ◽  
Analytical Potential ◽  
Supercritical Phase ◽  
Dynamics Simulations

An analytical potential energy curve (NE3) is constructed from points obtained by accurate ab initio calculations. The quality of the pair potential is established by a comparison of calculated and experimental second virial coefficients as a function of temperature. Molecular dynamics equilibrium simulations are performed with the NE3 potential for pressures between 20 and 1000 MPa and temperatures between 100 and 600 K in the supercritical phase and for one point in the liquid phase of neon. The properties are compared with those obtained from experiment. It is found that the accurate pair potential has a large effect on pressure, energies and enthalpies and a significant influence on other thermodynamic properties but little influence on transport and structural properties. In the supercritical phase the deviation between the calculated quantum-corrected and experimental pressure values is always less than 2%.

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