Viscoelastic and Dielectric Relaxation of Reptating Type-A Chains Affected by Reversible Head-to-Head Association and Dissociation

Abstract

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 *­(ω) and the normalized complex dielectric permittivity ε̃ j *­(ω) 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 ε̃1* and ε̃2* 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 ε̃ j *. This difference between g j * and ε̃ 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.

Contraction and Tumbling Dynamics of DNA in Shear Flows under Confinement Induced by Transverse Viscoelastic Forces

“…where the three analytical summations are down following Ref. 28 Setting a = 0, we obtain the limiting case first found by Bhattacharyya and Cherayil 29 where Eq. (19) simplifies to…”

Dielectric Relaxation of Type-A Rouse Chains Undergoing Reversible End-Adsorption and Desorption

“…We consider an equilibrium system of free and end-adsorbed Rouse chains, the latter being equivalent to a chain grafted to a fixed point in space, as illustrated in where τ ads and τ des indicate the corresponding adsorption and desorption time constants, respectively. These τ's are not of purely chemical nature but contributed from the local chain motion (triggered by the chemical reaction), as fully discussed in a previous study 10) . Despite this contribution, those τ's are independent of time t and can be utilized as the basic time constants in our analysis 10) .…”

“…These τ's are not of purely chemical nature but contributed from the local chain motion (triggered by the chemical reaction), as fully discussed in a previous study 10) . Despite this contribution, those τ's are independent of time t and can be utilized as the basic time constants in our analysis 10) .…”

“…being the dielectric relaxation intensity of the chain j (= f, g), is related to the Laplace transformation of the normalized di- 10,11) (6a)…”

“…Thus, with an attempt to find a clue for investigation of the effect of the dynamic exchange on the PNC relaxation, we have made a theoretical analysis for dielectric relaxation of model chains, linear chains having type-A dipoles and undergoing reversible end-adsorption and desorption. For chains in melts and solutions, combination of the Rouse or reptation dynamics and the association/dissociation reaction kinetics has been successfully formulated on the basis of the eigenfunction expansion [8][9][10][11] . We have extended this formulation to end-adsorbed and desorbed chains having so-called type-A dipoles parallel along the chain backbone to analytically obtain their dielectric relaxation function.…”