POLYMER ENTANGLEMENTS

Entanglements in concentrated random-coil flexible polymers are considered in terms of a network of bridges. A bridge is a segment of a polymer chain which is long enough to form one loop on itself On the basis of a random-walk analysis, the onset of a bridge network is proposed to occur at the critical entanglement molecular weight M(c) = 30.89C(infinity)M0/alpha2j, where C(infinity), M0, and j are the characteristic ratio, monomer molecular weight, and number of backbone bonds per monomer, respectively. The factor alpha is determined by alpha = C/(bzj), where C, b, and z are the C-axis dimension of the unit cell, bond length, and number of monomers per C-axis length, respectively, and for many vinyl polymers alpha2j almost-equal-to 1. The theoretical M(c) expression, which contains no fitting parameters, was found to be in excellent agreement with experimental M(c) values. The dependence of M(c) on polymer concentration c, in the semidilute region was determined as M(c) is similar to c-5/4, using the Blob model proposed by de Gennes and Daoud. The plateau modulus, G(N)degrees, Was found to depend on concentration as G(N)degrees is similar to c9/4, which is in excellent agreement with experiment. The model predicts that the zero shear viscosity eta0 is affected by the entanglement connectivity and for reptating chains behaves as eta0 is similar to M3,4c3,5.