Effect of Molecular Weight on Viscoelastic Properties of Polymers as Predicted by a Molecular Theory

Abstract

Calculations have been made covering the predictions of a model re presenting the vi s­ coelastic behavior of rubberlike polymers for molecular weights greater than 1\11., M. being the lower limit of t he range in which the viscosity is proportional to 1\113.4. A pronounced diff erence in the character of G" is predicted for polymers with molecu lar we ights between five and ten times 1 11. as compared with those whose molecular weights are outside this range. In a recent publication [1]1 we presented the steady state and transient behavior predicted by a model designed to repl'~sent the mechani~al behav:ior, in shear, of rubberhke polymers. ThIs model IS very similar to the molecular theor:v of Rouse [2], except that it includes directly the effect of entanglements found in long polymer chains. Our model assumes an entropy-type elasticity as the origin of t he relaxing force observed in it stress­ relaxation experiment. It involves a resistance coefficient per unit segment of a polymer chain which is evalu ated from the steady state viscous be­ havior, and the molecular weight of the polymer, expressed as the ratio of molecular weight to critical molecular weight, Me, defined as the lower limit of the range in which the viscosity is proportional to M 3. 4. For the particular example we presented in reference 1 this ratio was 60, and at the time we prepared this previous paper we did not have system­ atic calculations showing the predictions of the model for a range of molecular wei ghts. I'Ve made an effort (sec. 3, p . 176 of reference (1)) to relate the extrema of G" and J" to the molecular weight through the use of various approximate relationships, since the full expressions can only be treated numeril cally. We have now carried out further numerical calculations covering a range of molecular weights, and find that our previous approximate relations were completely inadequate to represent t he posi­ tions of these extrema as functions of molecular weight. In addition, we have found certain quite unexpected qualitative features of the predicted curves when the molecular weight is varied between one and ten times the critical molecular weight. I Since these quabtative features ma~T present the possibility of a rather critical test of the validity of this model, we pres en t the results here in some I detail. The results of our previous paper may be rep­ rf'sentf'd in terms of normalized functions. the