Linear Viscoelasticity in Entangling Polymer Systems

摘要

Molecular models for polymers, such as the Rouse model, yield steady state shear complianceJeand terminal relaxation timetgr;maxof the formsJe, prop;Mthinsp;sol;thinsp;cRTandtgr;maxprop;eegr;Mthinsp;sol;thinsp;cRT, in whichcis the polymer concentration,Mis the molecular weight, andeegr;is the zero shear viscosity. Recent experiments have shown that in entangling systems these forms change, becomingJeprop;thinsp;sol;thinsp;c2RTandtgr;maxprop;eegr;thinsp;sol;thinsp;c2RT. It is proposed here that the changes are a consequence of the highly uncorrelated nature of entanglement drag interactions, as opposed to the smoothly varying interactions inherent in the Rouse analysis. A new model is proposed to account for this difference. The resulting predictions are consistent with the experimental forms ofGprime;lpar;ohgr;rpar;, GPrime;lpar;ohgr;rpar;, andGlpar;trpar;as well as those ofthgr;maxandJe. The molecular weight between entanglement points,Me, was estimated from several different viscoelastic properties of undiluted polystyrene. With the exception of that fromJe, similar values ofMewere obtained in all cases. Calculations ofJefor mixtures of two molecular weightsMAandMBwere made with and without the assumption of an uniformly effective drage coefficient. The former predicted an unrealistically weak dependence on polydispersity; the latter agreed with experimental results for cases in whichMBthinsp;sol;thinsp;MAwas in the range of 2, but overestimated the effects of polydispersity when the difference in molecular weights was greater.