Describing the Relaxation Spectrum of Entangled Homopolymer Blends with the Dynamic Random-Phase Approximation

Abstract

Detailed calculations of the intermediate scattering function of entangled, binary homopolymer blends are presented. The calculations are based on the reptation model of polymer dynamics and employ the dynamic random-phase approximation for inferring collective blend behavior from single-chain characteristics. The relaxation spectra found here for blendsincluding the relaxation rates and amplitudes of higher-order modesare contrasted with those for melts and are given for the entire range of length scales from the diffusive to the nondiffusive regime of polymer dynamics. Analytical limits of the intermediate scattering function are successfully compared to numerical results. The dominance of higher-order relaxation modes in specific, experimentally feasible, asymmetric blend systems is indicated, and the possibility of significant deviations of the expected time−correlation functions from a single-exponential decay is noted.

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

“…Using this formula we can find the desired structural susceptibility if we calculate the single-chain structure factors (3.6) for a chosen model of polymer dynamics. Within the original DRPA such a procedure was demonstrated in refs [18][19][20][21][22][23][24][25][26][27][31][32][33] when working with the dynamic structure factor…”

“…In particular, it is within the DRPA that the "breathing" mode in block copolymers [19] and large-scale "composition" relaxation in polydisperse blends of homopolymers [20] were predicted and described as consistent with the experimental data (see Refs. [21][22][23][24][25][26][27] and references therein). (Some authors [28][29][30] claimed that the DRPA couldn't explain the "fast mode diffusion behavior", which is sometimes observed experimentally.…”

Reptation Dynamics of Asymmetric Diblock Copolymer Melts via the Dynamic Random Phase Approximation

“…The goal of the current paper is to extend the calculation of the ISF given in ref to include asymmetric diblock copolymers for comparison to future PCS, XPCS, or even neutron spin-echo (NSE) experiments. In the asymmetric case, it turns out, first, that a new family of dynamic modes emerges, which is not present in the symmetric case and, second, that the ISF becomes increasingly non-single-exponential at the peak of the static structure factor for increasingly asymmetric compositions. Our results suggest that careful scattering studies, performed on asymmetric block copolymers, may afford an excellent opportunity to evaluate quantitatively the reptation model's detailed predictions for the higher-order mode relaxation rates and relative mode amplitudes.…”

Polymers: When S(Q,t) is not what you think! The role of dynamic RPA

“…While in the last decades some approaches on the use of dynamical RPA have been made [5][6][7][8][9][10] these did not directly yield a way to routinely describe the full resulting intermediate scattering curves as e.g. obtained in NSE experiments and allow model fitting within this framework.…”