Entangled system molecular weight between entanglements

In thermorheological simple systems, the time-temperature correspondence principle holds. Chapter 8 gives examples of isotherms for compliance functions and relaxation moduli. The shift factors are expressed in terms of terminal viscoelastic parameters, and the temperature dependence of the shift factors is interpreted in terms of the free volume and the WLF equation. The chapter outlines methods for determining the molecular weight between entanglements, and analyzes the influence of diluents and plasticizers on the viscoelastic functions. 

The purpose of our study was a rheological evaluation of the effect of composition on the properties of ABS resins in the molten state. Steady-state viscosity was determined over a wide range of temperatures and shear rates. The shear modulus in the molten state was determined by measurement of the diameter of the extrudate. ABS resins in the molten state behaved as an amorphous homophase polymer. The effect of the elastomer phase on the viscoelastic properties which characterize the behavior of the continuous matrix, i.e. monomer friction coefficient and molecular weight between entanglements (Me), was calculated by the application of the molecular theories. The significance of these properties in heterophase systems is discussed. 

The studies of model SBS systems show that the T2L component (corresponding to the PB chain between PS blocks) increases proportionally to the number of mobile protons until the critical molecular weight for the formation of entanglement of the rubber segment (40000) is reached then the two T2s are observed for a linear PB 9S). Calculated and NMR determined mobile proton fractions are in a good agreement, except for the smallest (1-f) values. 

The critical value of molecular weight can be identified with the transition point between weakly and strongly entangled systems, the position of which was estimated in Sections 4.2.3 and 5.1.2 as... 

For entangled systems, the two first conditions are fulfilled in the framework of reptation theories a comprehensive expression of the monodisperse relaxation modulus G(M,t) is given by expression 3-24 and the double reptation model generalized to a continous molecular weight distribution provides the integral relation between the MWD function P(M) and the polydisperse experimental... 

The unique dependence of Qc on the width of the interface has also been found for interfaces between high molecular weight random copolymers and homopolymers [69,70]. It is apparent from Fig. 40b, however, that while regimes I and II are also observed, the critical width, where the transition from regime I to regime II occurs, varies for different PS-based systems even though the bulk entanglement structure is the same. 

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