US EPA

8710881 

Journal Article 

Friction Coefficient of Polymer Molecules in Dilute Solution near the Ɵ Point. 2. Concentration Dependence of the Friction Coefficient 

Mulderije, JJH 

1980 

1 

Macromolecules
ISSN: 0024-9297
EISSN: 1520-5835 

13 

6 

1526-1536 

English 

10.1021/ma60078a031 

Pyun and Fixman's equivalent-sphere theory (1964) about the concentration dependence of the friction coefficient of random-coil polymers in dilute solution is reconsidered at three points. Correction of the calculation of the coefficient for the linear concentration dependence of the friction coefficient for hard spheres yields a value 7.01 rather than 7.16. Secondly, a simple procedure for obtaining an approximate value for the friction coefficient of the body representing two spheres in partial overlap (dumbbell) is described. Thus the ellipsoid of ill-defined size can be removed and an unambiguous theoretical value can be established for the concentration dependence of the friction coefficient of interpenetrable spheres. When the calculation is made along lines analogous to those which Pyun and Fixman followed for calculating the velocity of two separate spheres in hydrodynamic interaction, the new value for a system in the state is about 20% larger than reliable experimental values found for polystyrene in cyclohexane. When, alternatively, the approximation is applied to more recent exact numerical data for the velocity of two interacting spheres, agreement is reached with the experimental value within the error margin. The rapid increase of the concentration dependence of the friction coefficient with temperature through the point is a sensitive measure of the temperature dependence of the excluded volume of the polymer molecules. This was reason to reconsider also the thermodynamic aspect of the P-F theory and to replace the uniform segment distribution of the friction equivalent sphere by the modified Flory-Krigbaum potential for calculating the distribution function for a second sphere in the vicinity of a first one. The temperature dependence of the osmotic second virial coefficient and the Flory parameter, evaluated from sedimentation experiments, thus become 11% higher and agree within the error margin with the values calculated by applying a theory by Yamakawa, which uses the same potential function but a quite different model for the hydrodynamic interaction. Equations are applied to data for polystyrene in cyclohexane. A dependence on the molecular weight is found for (dA2/dT)Ɵ and ή. 1980, American Chemical Society. All rights reserved.