Test of Full and Partial Tube Dilation Pictures in Entangled Blends of Linear Polyisoprenes

The molecular picture of dynamic tube dilation (DTD) was tested for viscoelastic and dielectric data for two series of entangled binary blends of linear cis-polyisoprenes (PI) having 10-3 M 2 = 308 and 10-3 M 1 = 94.0 or 21.4. The volume fraction υ2 of the high-M chains was varied from 0.005 to 0.5. The Struglinski−Graessley parameter r SG (= M 2 M e 2 M 1 -3), specifying the constraint release (CR) contribution to the relaxation of high-M chains at small υ2, was quite different for the two series of blends (r SG = 0.0093 and 0.79). For large υ2 (= 0.5), the full-DTD picture treating the relaxed portions of the chains as a simple solvent held satisfactorily in the entire range of time t irrespective of the r SG value. However, on a decrease of υ2, this picture began to fail at intermediate t and further at long t (in the terminal regime of the high-M chains), and the failure was more significant for the blend with small r SG. This failure occurred when the number βCR(t) of the entanglement segments equilibrated through the Rouse−CR dynamics was smaller than the equilibration number assumed in the full-DTD picture, βf - DTD(t) = {φ‘(t)}- d with φ‘(t) and d (= 1.3) being the dielectrically determined tube survival fraction and the dilation exponent, respectively. A test was made also for the partial-DTD picture incorporating the maximum number of the segments that can be CR-equilibrated under the given φ‘(t) value. The behavior of the blends of various υ2, including the low-υ2 limit, was considerably well described by the partial-DTD picture, although nonnegligible differences still remained between this picture and experiments. Thus, the partial-DTD picture (including the full-DTD picture as an extreme case) was quite tempting, and a brief discussion was made for a possible improvement of existing molecular models on the basis of this molecular picture.