Coexistence curve of a polydisperse polymer solution near the critical point

1997 ◽  
Vol 55 (3) ◽  
pp. 3159-3163 ◽  
Author(s):  
Rio Kita ◽  
Toshiaki Dobashi ◽  
Takao Yamamoto ◽  
Mitsuo Nakata ◽  
Kenji Kamide
Keyword(s):  
Polymer Solution ◽  
Critical Point ◽  
Coexistence Curve ◽  
Polydisperse Polymer

Critical-point equations for polydisperse polymer solutions

1987 ◽  
Vol 414 (1846) ◽  
pp. 103-110 ◽  
Keyword(s):  
Finite Number ◽  
Polymer Solution ◽  
Critical Point ◽  
Mass Distribution ◽  
Simple Form ◽  
Critical State ◽  
Molar Mass ◽  
Necessary Conditions ◽  
Polydisperse Polymer ◽  
Gibbs Theory

Based on the generalized Flory-Huggins concept replacing Huggins’s χ -term by a function depending on a finite number of moments of the molar mass distribution, a simple form of the necessary conditions for the critical state of a polydisperse polymer solution is established in the framework of classical Gibbs theory. The derived critical-point equations permit a substantial diminution of the order of the corresponding determinants.

Truncation theorems for spinodals and critical points of mean-field models for polydisperse polymer solutions

1981 ◽  
Vol 375 (1762) ◽  
pp. 397-408 ◽  
Keyword(s):  
Molecular Weight ◽  
Critical Point ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Polymer Solutions ◽  
Mathematical Proof ◽  
Mean Field ◽  
Combinatorial Theory ◽  
Mean Field Models ◽  
Polydisperse Polymer

An exact truncation theorem is proved for the expansion, in terms of moments of the molecular weight distribution, of the Gibbs spinodal determinants of a wide class of generalized mean-field Flory-Huggins models for polydisperse polymer solutions. A similar truncation theorem for the critical-point determinants is derived on the assumption that an expansion in a finite number of moments exists. These truncations have been exploited elsewhere through the relative economy they confer on computations involved in the testing and refinement of such theoretical models by fitting them to experimental data. A much simplified general and explicit expression is found for the relevant spinodal determinants of the mean-field models. If the relevant free energy of mixing is assumed to depend on the moments M 0 , M 1 , . . . , M n of the molecular weight distribution, this expression shows the spinodal to be a function of M 0 , M 1 , . . , M 2 n +1 . The critical point is a function of M 0 , M 1 , . . . , M 3 n +2 . The truncations at M 2 n +1 and M 3 n +2 betoken a collapse to a small subspace of the formal Hilbert-space representation of the composition space of the solution. The mathematical proof follows the pathway of the classical routes to the rigorous theory of function spaces opened up by von Koch and Fredholm, and the spinodal expression bears the imprint of a classical solution of Stieltje’s moment problem. In addition, modern operational methods of combinatorial theory are relevant to future extensions of the present work. Theoreticians may, therefore, be interested to come to the aid of experimentalists struggling with the analysis of data of much practical import.

Coexistence curve of 2,6-lutidine + water, near its lower critical point

1980 ◽  
Vol 76 (1) ◽  
pp. 172-174 ◽  
Author(s):  
M.A. Handschy ◽  
R.C. Mockler ◽  
W.J. O'Sullivan
Keyword(s):  
Critical Point ◽  
Coexistence Curve

Coexistence curve for polystyrene–cyclohexane near the critical point

1975 ◽  
Vol 62 (11) ◽  
pp. 4278-4283 ◽  
Author(s):  
Mitsuo Nakata ◽  
Nobuhiro Kuwahara ◽  
Motozo Kaneko
Keyword(s):  
Critical Point ◽  
Coexistence Curve

Nmr Measurements of the Xenon Coexistence Curve Near the Critical Point

1969 ◽  
Vol 23 (25) ◽  
pp. 1424-1426 ◽  
Author(s):  
L. M. Stacey ◽  
B. Pass ◽  
H. Y. Carr
Keyword(s):  
Critical Point ◽  
Coexistence Curve
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