Plateau modulus semidilute solution

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

Tnteractions are not important. The dynamics on these intermediate scales (for r < t< Te) are described by the Rouse model with stress relaxation modulus similar to the Rouse result for unentangled solutions [Eq. (8.90) with the long time limit the Rouse time of an entanglement strand Tg]. At Te, the stress relaxation modulus has decayed to the plateau modulus Gg[kT per entanglement strand, Eq. [(9.37), see Fig. 9.9)]. The ratio of osmotic pressure and plateau modulus at any concentration in semidilute solution -in athermal solvents is proportional to the number of Kuhn monomers in ... 

Consider a solution of polystyrene with molar mass M= 0°g moP in cyclohexane at 35 °C (0-solvent with viscosity ris = 7.6 x 10 Pa s). Estimate the relaxation time, plateau modulus, viscosity, and diffusion coefficient as functions of concentration in semidilute solution. 

FIGURE 25 Dimensionless plateau modulus versus the ratio of the Kuhn step length, 1r, to the packing length, p. Experimental data for melts (+) and semidilute solutions (x) are included, along with various calculated values (squares, circles, and diamonds). (From Everaers, Sukumaran, Grest etal.[3m].)... 

The mean entanglement spacing Ng is experimentally derived from the plateau modulus which is related to Ng according to Eg. (38). Substituting Eg. (52) into this expression, we predict that the plateau modulus of semidilute solutions will scale with polymer density according to... 

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