Mode-coupling theory of the slow dynamics of polymeric liquids: Fractal macromolecular architectures

Abstract

Recently a mode coupling theory for the dynamics of solutions and melts of entangled linear chain polymers has been developed. We report the extension of this approach to macromolecular architectures different from linear chains. Specifically, this work addresses recent experimental findings on melts of ring shaped polymers, small spherical micro-networks, and linear chains in two dimensions. The mechanical and dielectric response, diffusion, and molecular relaxation times of macromolecules modeled by fractal mass distributions are studied. The distribution is chosen to be Gaussian and then is uniquely determined from the experimentally measured scaling of macromolecular size (R g ) with degree of polymerization (N), i.e., R g ϰ N . The exponent and the spatial dimension d determine the large N scaling of the transport coefficients and the exponents describing intermediate time anomalous diffusion. Within the theory, entanglement corrections to the single polymer Rouse dynamics are effective for Ͻ2/d only. There, we find D ϰ N 2dϪ5 for the diffusion coefficient and that the ratio D D /R g 2 is almost constant, where D is the terminal relaxation time. Using independent input from equilibrium liquid state theories, the magnitude and scaling with macromolecular density and segment length of the dynamical properties is determined. It is also found that macromolecular interpenetration requires progressively higher densities and consequently entanglements become less effective with fractal dimension 1/ approaching the spatial dimension. © 1997 American Institute of Physics. ͓S0021-9606͑97͒50901-9͔

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

“…More importantly, it places additional constraints on our theory by requiring the same set of parameters simultaneously explain the center-of-mass diffusion and conformational (stress) relaxation aspects of entangled dynamics. (vi) Finally, our suggestions 60 for new experiments at nonzero frequencies, and for transport coefficients, of entangled fluids composed of macromolecules of variable fractal dimensionality (e.g., rings) and in variable spatial dimension. Computer simulation could potentially play a critical role here, although proper treatment of heavily entangled systems remains in the future.…”

“…As discussed previously, 1,60 by comparing PMC theory with the reptation/tube theory in the asymptotic limit the parameter R is easily shown to be approximately 3. Of course, this is only obviously relevant in polymer melts since it is the only case where the asymptotic N-scaling of the diffusion coefficient is observed.…”

“…As is evident from eq I.64, the effect of a small parameter r can also be interpreted as a change in N e , Θ ∝ rN e -5/2 , and without further independent experimental information a closer identification of the PMC model parameters is impossible. Also, the errors introduced into the PMC results by the neglect of chain end corrections 60 are unknown at present. In Figure 6, the reported change 9,10 from Rouse to reptation-like molecular weight scaling of τ is qualitatively correctly reproduced by the PMC results, but with quantitative deviations.…”

“…Note that these results, more strongly than our results for the internal or the center-of-mass dynamics, depend on the technical approximations made when diagonalizing the equations of motion, eq I.1, where chain end effects have been neglected. 60 Also, for a PI tracer in a PBD matrix, system-specific polymer interactions could strongly influence these results, especially the parameters characterizing the tracer dynamics. Whereas the parameters, P e , R m , and δ, specifying the dynamics of the entangled melt correspond to the ones found (for example) from independent viscosity measurements, the tracer parameters, N e and R tr , must differ from the corresponding values found for the one-component system of tracer polymers.…”

Intermolecular structure factors of macromolecules in solution: Integral equation results

“…The low density limit of PRISM theory shall be worked out in detail in this contribution in order to discuss the density correlations on the mesh size length scale. This works either extends [13][14][15], or complements [16,17] previous studies.…”