Molecular weight and concentration dependences of the terminal relaxation time and viscosity of entangled polymer solutions

Abstract

A new model is presented for entangled polymer solutions which accounts for the observed molecular weight and concentration dependences of the zero-shear viscosity qo and the terminal relaxation time Td. Our development, based upon the coupling model of relaxation, quantitatively describes how relaxation of a primitive mode is modified by coupling through entanglements to its environment. The primitive mode is represented by a Rouse chain of Gaussian submolecules, each of root mean square length u equal to the entanglement distance and each characterized by an entanglement friction coefficient fo. By extending the analyses developed previously for polymer melts, the model predicts that qo 0: f *~l ( 1 -n )~y [~a ( 1 -v ) ] 2 / ( 1 -n ) where 4 is the polymer volume fraction. Here n is the coupling parameter describing the terminal relaxation and y, a , and u are given by GNo 0: @ y , Me 0: 4P, and u a 4-"m. Numerical examples are shown to agree with experiment; e.g., for n = 0.41, y = 2, a = 1, u = 0.6, qo a f*k@.4434. Comparison of the present results is also made to the reptation and scaling theory predictions.

Dynamics of solutions of triblock copolymers in a selective solvent: Effect of varying copolymer concentration

“…6,16 With increasing concentration, coupling effects similar to those that appear in glassy systems might become important. [35][36][37] Although the coupling model was originally developed for glassy dynamics, coupling in diffusing clusters in gelling sysems also has been described by the same phenomenological approach. The behavior of ␤ observed here is similar to that seen in semidilute solutions of associating random copolymers which approach gelation upon increasing copolymer concentration.…”

Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers

“…indicates that the value of n F should be approximately constant at a value near 0.41 for all entangled linear polymers [9,16,17] based on the usual approximately 3.4 power law exponent observed for the molecular weight (M) dependence of viscosity [18][19][20][21][22][23]. Even for the case of polyisobutylene where n a % n F and the effects of temperature on s a and s F are similar, thermorheological complexity is still noted in the softening zone due to the weaker temperature dependence of s R [24,25].…”

Dynamics of Laponite solutions: An interpretation within the coupling model scheme

“…The results of these investigations have been already discussed in our previous works [9][10][11]. The aim of this paper is to interpret these findings under the perspective of coupling model, devised by Ngai and co-workers [1,2,[20][21][22][23].Laponite RD is produced by Laporte Industries with a density of 2570 kg/m 3 . It is composed of rigid disc-shaped crystals with a well defined thickness of 1 nm and an average diameter of about 30 nm.…”

“…[11]. The results obtained from this fit analysis will be used in the following to test the basic predictions of the coupling model developed by Ngai and co-workers [1,2,22,23,30,31], deals the problem of how relaxation of a specific dynamic mode is modified by the coupling to complex surroundings. It was advanced to treat relaxation processes in complex correlated systems and Laponite can be considered complex because of the presence of a long range repulsive and a short range attractive interaction which causes an effective coupling between each particle of the dispersion affecting its dynamics.…”

“…Nevertheless if we roughly identify the parameters of the coupling model with the experimental values obtained from fit analysis through Eq. (3) as s 0 = s 1 , s * = s 2 and 1 À n = b, we can perform a preliminary test of the model by [1,2,22,23]. Starting from continuity condition expressed by Eq.…”