Second Virial Coefficient of Oligo- and Poly(α-methylstyrene)s. Effects of Chain Stiffness, Chain Ends, and Three-Segment Interactions

2003 ◽  
Vol 36 (14) ◽  
pp. 5311-5320 ◽  
Author(s):  
Wataru Tokuhara ◽  
Masashi Osa ◽  
Takenao Yoshizaki ◽  
Hiromi Yamakawa
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Chain Stiffness

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.

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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