Dynamics of Polydisperse Polymer Mixtures

Abstract

We develop a general analysis of the diffusive dynamics of polydisperse polymers in the presence of chemical potential gradients, within the context of the tube model (with all species entangled). We obtain a set of coupled dynamical equations for the time evolution of the polymeric densities in a form proposed phenomenologically in recent work by N. Clarke, but with explicitly derived coefficients. For the case of chemical polydispersity (a set of chains that are identical except for having a continuous spectrum of enthalpic interaction strengths) the coupled equations can be fully solved in certain cases. For these we study the linearised mode spectrum following a quench through the spinodal, with and without a passive (polymeric) solvent. We also study the more conventional case of length polydisperse chains in a poor solvent. Here the mode structure is more complicated and exact analysis difficult, but enough progress can still be made to gain some qualitative insight. We briefly discuss the modifications required to allow for the presence of unentangled, low molecular weight species in the system.

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

“…It is worth noting that previous support for the two-stage scenario, both in Warren's original paper 48 and in the study by Pagonabarraga and Cates, 51 was obtained in the context of polymers, whereas here we have polydispersity in the interaction strength in a context that is more easily connected with the physics of colloids. This indicates that Warren's scenario may be a general feature of the non-equilibrium dynamics of dense fluid mixtures.…”

“…Summarizing the discussion in this section thus far, our meanfield theory for the spinodal dynamics of polydisperse colloids provides strong support for Warren's two-stage hypothesis, in the appropriate regime of high densities. It is worth noting that previous support for the two-stage scenario, both in Warren's original paper 48 and in the study by Pagonabarraga and Cates, 51 was obtained in the context of polymers, whereas here we have polydispersity in the interaction strength in a context that is more easily connected with the physics of colloids. This indicates that Warren's scenario may be a general feature of the non-equilibrium dynamics of dense fluid mixtures.…”

“…Determining such an entire mobility matrix from an offlattice model is a considerable challenge, also because the results might differ for size versus interaction polydispersity (similarly to the differences found in the mobility coefficients between systems with length and chemical polydispersity, in ref. 51). One route to deriving such Cahn-Hilliard-like equations would be dynamical density functional theory (DDFT); it should be possible to adapt this to a fully polydisperse scenario and then use it to test Warren's two-stage scenario.…”

“…n 0 i = 1 indicates the presence of a vacancy at site i, or, equivalently, a solvent particle. Note that the solvent particles are 'passive' 51 in this framework, in such a way that any non-hydrodynamic effect caused by them has already been effectively included in the interaction between the particles as described by the model Hamiltonian. We also neglect the fact that colloidal particles may interact with one another via hydrodynamic interactions mediated by the solvent.…”

Theory of Polydisperse Inhomogeneous Polymers

“…42 Thus, we expect that the present formalism and numerical methods for treating polydisperse equilibrium systems will ultimately be applicable to polydisperse polymers out of equilibriumsa subject of current research interest. 43,44…”