This thesis is concerned with the dynamics and rheology of polymers, and in particular on the influence of entanglements and supramolecular “sticky” groups. The text is organised as follows:
In Part I, we consider these effects in isolation. We begin with an introductory chapter detailing established theory for unentangled polymers, unentangled sticky polymers, and entangled polymers.
In Chapter 2, we develop a stochastic model for linear rheology of unentangled polymers with stickers along the backbone that we then compare with experimental data and the “classic” sticky Rouse model.
In Chapter 3, we explore the nonlinear rheology of a mixture of entangled polymeric chains of various lengths (polydisperse) based on coupled equations of similar form the to Rolie-Poly model [Likhtman and Graham, J. Nonnewton. Fluid Mech. 114, 1–12 (2003)].
Part II of this thesis describes the development and testing of a “toy” nonlinear rheology model for entangled supramolecular polymeric materials. We describe three stages in development and testing of this model [Boudara and Read, J. Rheol. 61, 339–362 (2017)]:
Chapter 4, presents a simplified stochastic model for the rheology of entangled telechelic star polymers. In both linear and nonlinear regimes, we produce maps of the whole parameter space, indicating the parameter values for which qualitative changes in response to the applied flow are predicted. Preaveraging the stochastic equations described above, we obtain a set of non-stochastic coupled equations that produce very similar predictions. This is detailed in Chapter 5.
Finally, in Chapter 6, we use the preaveraged model to explore complex flow behaviour. In Chapters 4 and 5, we observed that for some parameter values, the steady state stress versus shear rate curve is non-monotonic, which is a signature of shear banding [Fielding, J. Rheol. 60, 821–834 (2016)]. Our simulations confirm shear banding. Surprisingly, for some parameter values, the system never reaches a steady state but instead it oscillates in time between homogeneous state and recoil (coexistence of positive and negative shear rates). We investigate the mechanism behind this oscillatory behaviour.
