Finding the Missing Physics: Mapping Polydispersity into Lattice-Based Simulations

Polydispersity plays an important role in polymer physics influencing both processing approaches and final properties. Despite the obvious physical importance of polydispersity, studies usually simulate monodisperse chains or occasionally, a few different chain lengths. This work presents a comprehensive methodology for mapping various molecular weight distributions onto a finite number of lattice chains. The use of a lattice in the present derivation enables a variety of lattice-based simulations to incorporate polydispersity. Examples are provided by extending the cooperative motion (COMOTION) algorithm for polydispersity to create the “polydisperse cooperative motion algorithm” (p-COMOTION). The dynamic version of p-COMOTION captures the dynamics of entangled polydisperse melts. For the same weight-averaged molecular weight, polydispersity gives a lower Rouse time and introduces a broadening of the reptation transition. In addition, when adapted into the cooperative motion with flow (COMOFLO) algorithm the resulting p-COMOFLO algorithm captures important polydispersity effects including the suppression of wall slip. Equilibrium results for confined geometries provide evidence that polydispersity modifies wall effects through reduced perturbation of chain dimensions and legth-based migration effects. These and other important effects associated with including the missing physics of polydispersity can be addressed using the newly developed formalism.