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The relaxation modulus, G(t,y), was measured for solutions of star-branched polystyrene with 4 arms in chlorinated biphenyl at magnitudes of shear, y, ranging from 0.3 to 7. Molecular weights were 7.63 X 106, 1.24 X 106, and 2.65 X 106, and the concentration ranged from 0.076 to 0.25 g cm"3. When the number of entanglements on the chain connecting two chain ends, MA/Me, was less than 4, the relaxation modulus at small strains, G(t), agreed with that of a linear polymer having the same value of M^/Me. The maximum relaxation time increased in proportion to (MA/Me)4•5. A function h(t,y) = G(t,y)/G(t) leveled off at a certain time, rk, independent of y. The characteristic time, rk, for the branched polymer was approximately equal to that of the linear polymer having the same MA/Me. The time-independent value of h(t,y) at long times, h(y), was slightly lower than that for the linear polymers and was in very good agreement with the prediction of the tube model theory. These features are in accord with the concept that the chain branching may hamper the reptational motion but may not affect the equilibration process of the chain contour length assigned as the origin of nonlinear viscoelasticity in the tube model theory.

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ABSTRACT:The birefringence, !'J.n, and the shear stress, u, were measured after an instantaneous shear deformation for a 10.5% solution of triblock copolymer, poly(methyl methacrylate)-block-polystyrene-block-poly(methyl methacrylate), in polychlorinated biphenyl. Hereafter M stands for methyl methacrylate and S for styrene. The mole fraction of S of the copolymer was 0.4. Measurements were performed at various magnitudes of shear, y, ranging from 0.4 to 3 and !'J.n was measured with a light led perpendicularly to the shear plane. Under assumptions that the !'J.n and u are sums of independent contributions from M and S blocks and that the stress-optical law holds good for the contribution from each block, the stresses, uM and u8, attributable to theM and S blocks, respectively, were separately evaluated. The result at short times was consistent with the assumption that the chain is uniformly deformed on instantaneous deformation of the material. The ratio u8lu increased with time. For small y, the result was consistent with the tube model theory if the ratio· u8lu was regarded as the fraction of stress attributable to the central portion of chain. At large deformations, the increase with time of the ratio was much less than expected from the theory.KEY WORDS Birefringence I Stress Relaxation I Nonlinear Viscoelasticity I Block Copolymer I Poly(methyl methacrylate-styrene-methyl methacrylate) I Entanglement I Tube Model I