Excluded volume contribution to the osmotic second virial coefficient for proteins

AIChE Journal ◽  
1995 ◽  
Vol 41 (4) ◽  
pp. 1010-1014 ◽  
Author(s):  
Brian L. Neal ◽  
Abraham M. Lenhoff
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Excluded Volume

HEATS OF DILUTION OF POLYISOBUTYLENE SOLUTIONS

1962 ◽  
Vol 40 (4) ◽  
pp. 734-738 ◽  
Author(s):  
M. Senez ◽  
H. Daoust
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Volume Effect ◽  
Excluded Volume ◽  
Dilution Technique ◽  
Molecular Weights ◽  
Calvet Microcalorimeter ◽  
Heats Of Dilution ◽  
Excluded Volume Effect ◽  
Benzene Toluene

The measurements of heats of dilution of polyisobutylene solutions in benzene, toluene, and chlorobenzene have been carried out with a Tian–Calvet microcalorimeter at 25 °C. The dilution technique previously described has been improved and the extrapolated enthalpy parameter κ1* for each system has been corrected for the excluded volume effect using the Krigbaum–Carpenter–Kaneko–Roig formulation for the second virial coefficient A2. No detectable variation in κ1* was found for high molecular weights (≥ 43,000); but a definite increase in κ1* was found for very low molecular weights.

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

Scattering of anyons with hard-disk repulsion and the second virial coefficient

1991 ◽  
Vol 44 (19) ◽  
pp. 10731-10735 ◽  
Author(s):  
Akira Suzuki ◽  
M. K. Srivastava ◽  
R. K. Bhaduri ◽  
J. Law
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Hard Disk

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

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