Bemstein-Kearsley-Zapas

The simple fluid theory has not yet yielded general relations for ij" and Xk- A constitutive equation of Bernstein, Kearsley, and Zapas does give parallel relations for rj and x as discussed by Booij (/2a, p. 63). The rigid dumbbell results above are not consistent with the Bemstein-Kearsley-Zapas formulae. 

B.Bemstein, E.A.Kearsley, L.J.Zapas, A study of stress relaxation with finite strain,7VTons Soc. Rheol. 2 (1963), 391-410. 

For the multibranched polymers, an additional mechanism not considered for the linear/star-branched polymers needs to be introduced. For the simplest multibranched polymer, the pom-pom polymer schematically illustrated in Figure 16, McLdsh and Larson combined the equilibrium mechanisms (arm retraction/trunk reptation in the dynamically dilated tube) and the nonequilibrium mechanisms (arm/trunk stretch, CCR, and the arm withdrawal) to formulate a constitutive equation. The arm withdrawal mechanism, leading to partial contraction of the trunk up to a point of tension balance with the arms, is the mechanism not considered for the linear/ star-branched chains. The resulting constitutive equation for the pom-pom chains cannot be cast in a Bemstein-Zapas-Kearsley (BKZ)-type convolution form. This pom-pom con-stimtive equation reproduces the hierarchical relaxation (from... 

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