Macromolecules, Vol.51, No.16, 6476-6496, 2018
Viscoelastic and Dielectric Relaxation of Reptating Type-A Chains Affected by Reversible Head-to-Head Association and Dissociation
For entangled linear polymer having type A dipoles and undergoing head-to-head association and dissociation reaction, viscoelastic and dielectric behavior is theoretically analyzed on the basis of the reptation dynamics combined with the reaction kinetics. Specifically, for the dissociated unimer and associated dimer (indexed with j = 1 and 2, respectively), the normalized complex modulus g(j)*(omega) and the normalized complex dielectric permittivity (epsilon) over tilde (j)*(omega) are analytically calculated via eigenfunction expansion of the orientational anisotropy and orientational memory defined in terms of the bond vectors u of entanglement segments. The reaction activates mutual conformational transfer between the unimer and dimer. Multiple coupling occurs for the anisotropy decay modes of the unimer and dimer due to this transfer, and the viscoelastic g(1)* and g(2)* of the unimer and dimer, respectively, exhibit considerably retarded and accelerated relaxation compared to the pure reptation case. In contrast, the memory decay modes of the unimer and dimer are only pairwisely coupled, so that the reaction-induced acceleration and retardation for the dielectric (epsilon) over tilde (1)* and (epsilon) over tilde (2)* are much weaker than those seen for the viscoelastic g(1)* and g(2)*. The orientational anisotropy is the tensorial, second-moment average of u associated with no cancellation in the conformational transfer, whereas the orientational memory is the vectorial, first-moment average accompanied by partial cancellation, which results in the difference between g(j)* and (epsilon) over tilde (j)*. This difference between g(j)* and (epsilon) over tilde (j)* is noted also for the associating/dissociating Rouse chains. Nevertheless, the reaction-induced retardation of the viscoelastic relaxation is stronger for the reptating unimer than for the Rouse unimer, whereas the reaction-induced acceleration is similar, in magnitude, for the reptating dimer and Rouse dimer. These features of g(j)* of the unimer and dimer are discussed in relation to the motional coherence along the chain backbone being present and absent in the reptation and Rouse dynamics.