Comparison of Dielectric and Viscoelastic Relaxation Functions of cis-Polyisoprenes:  Test of Tube Dilation Molecular Picture

Abstract

Within the context of the generalized tube model, the tube representing the entanglement constraint is not necessarily fixed in space but moves with time. This tube motion results in constraint release (CR) as well as dynamic tube dilation (DTD) for the chain trapped in the tube. For monodisperse systems, the DTD molecular picture leads to the normalized relaxation modulus µ(t) ()G(t)/GN) being proportional to square of the surviving fraction of the dilated tube. In contrast, the normalized dielectric relaxation function Φ(t) of the chain having noninverted type-A dipoles is proportional to this fraction. Thus, the viscoelastic and dielectric relaxation functions satisfy a relationship µ(t) ) [Φ(t)] 2 if the tube dilates in time scales of the chain relaxation. The validity of this relationship was examined for linear cis-polyisoprene (PI) chains having those type-A dipoles. The relationship was approximately valid, and thus, the tube dilated for the PI chains with M/Me ) 10-30 in their bulk state, although these chains did not necessarily reptate in the dilated tube with their intrinsic curvilinear diffusion coefficient. On the other hand, the relationship reformulated for blends was not valid for dilute PI probe chains in entangling matrices of much shorter polybutadiene (PB) chains. The probe fully relaxed via the CR mechanism during the DTD process and did not obey this relationship. The lack of DTD was also confirmed for the same probe in a much longer, CR-free PB matrix.

Analytical Rheology of Polymer Melts: State of the Art

“…Advances have been more forthcoming for polydisperse mixtures of LPs for three reasons, (i) there is a plethora of well-characterized experimental data [60,[206][207][208][209][210][211][212], (ii) rheological models have been built, tested, refined, and calibrated extensively [213], and (iii) it is possible to use approximate "double reptation-" type models [135,214], in lieu of the full tube model [142], which makes the mathematical model and its numerical solution more expedient.…”

Tube theory of entangled polymer dynamics

“…In the single idealized case of a chain di using in a ®xed tube, the two functions G…t † and F d …t † are identical, since they both simply measure the fraction of original tube still occupied by chain ·…t † ( [31] and see below section 4.2.2). However, experiments on entangled linear, monodisperse polymers comparing both rheology and dielectric relaxation [180,181] have found that in melts, to a good approximation…”

Viscoelastic Relaxation of Linear Polyisoprenes: Examination of Constraint Release Mechanism

“…Therefore, a test of the CR feature is desired for polymers other than PS so that the CR model 2,3) can be refined on a rigid experimental basis. This test is desired in particular for cis-polyisoprenes (PI) for which molecular tests [15][16][17][18][19][20][21][22][23][24] of the entanglement dynamics have been recently made with the aid of the combination of the † To whom correspondence should be addressed.…”

“…8, we note that τ obs is longer than τ CR for these systems and the difference between τ obs and τ CR is enhanced time comparable with the reptation time thereby broadening the terminal mode distribution. 2,3) This broadening can be well described through the molecular picture of dynamic tube dilation, [17][18][19][20][21][22][23][24] a coarse-grained picture for the CR mechanism.…”