On the molecular weight dependence of the thermodynamic and of the hydrodynamic pair interaction between chain molecules. IV. Second virial coefficients revisited

1987 ◽  
Vol 87 (10) ◽  
pp. 6156-6165 ◽  
Author(s):  
F. Gundert ◽  
B. A. Wolf
Keyword(s):  
Molecular Weight ◽  
Virial Coefficients ◽  
Pair Interaction ◽  
Chain Molecules ◽  
Second Virial Coefficients ◽  
Molecular Weight Dependence

Second virial coefficients for chain molecules

1994 ◽  
Vol 33 (1) ◽  
pp. 146-150 ◽  
Author(s):  
Costas P. Bokis ◽  
Marc D. Donohue ◽  
Carol K. Hall
Keyword(s):  
Virial Coefficients ◽  
Chain Molecules ◽  
Second Virial Coefficients

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 Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
Author(s):  
Anatol Malijevský ◽  
Tomáš Hujo
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Low Density ◽  
Second Virial Coefficients ◽  
The Third ◽  
Temperature Dependences ◽  
Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

Sign in / Sign up

Export Citation Format

Share Document