Modeling the Non-Linear Rheology of Linear Polymers and Associating Telechelic Polymers

The non-linear rheology of ordinary linear polymers and linear polymers with associable end-group has been examined by means of modeling. This work is motivated by discrepancies between experiments and existing theoretical expectations in the non-linear regime. In the case of associating polymers, we aim at understanding the break-down of Cox-Merz rule, shear thickening, and strain hardening of shear startup, while for conventional linear polymers we focus on the discrepancies typically encountered in the fast uniaxial extensional flows. It is appropriate to mention that most efforts are related to developing a stochastic simulation of associating telechelic polymers (part 1) while the studies of linear polymers in the fast flows (part 2) is rather limited in the persepectives of nematic interactions of oligomer-type solvent. For reference sample of associating telechelic polymers, the hydrophobically modified ethoxylated urethane (HEUR) is selected because of plenty of experimental data have been reported in the past. This information is collected into chapter 1 considering both morphology and dynamical aspects. HEUR is made up by poly(ethylene oxide) (PEO) end-capped with short hydrophobic groups. Above the so-called critical micelle concentration, HEUR in aqueous solutions forms flower-like micelles where the core is composed of aggregated hydrophobic end-groups. Since the aggregation is physically reversible, chain ends can detach from the core, and attach to neighboring micelles (thus forming bridges). The probability of bridge formation increases with increasing HEUR concentration, and a transient network eventually builds up. The linear viscoelastic behavior of HEUR systems is somehow simple since they exhibit a single-mode Maxwell-like response with a dominant relaxation time (related to the association/dissociation dynamics), exhibiting a power-law dependence on HEUR concentration and molar mass. On the contrary, HEUR solutions exhibit a complex nonlinear rheological behavior. The Cox-Merz rule is often violated since the steady shear viscosity can reveal shear thickening while the dynamic viscosity only shows shear thinning. In the shear rate range of the viscosity thickening, the first normal stress coefficient remains at its LVE value. As regards the shear startup response at high shear rates, strain hardening is often observed both for the viscosity and for the first normal stress coefficient. Remarkably, the overshoot of stress growth function is well beyond linear viscoelastic envelope. Motivated by these experimental observations, new stochastic simulation is proposed where its coarse-graining level is the consequence of trade off between computation time (within few days for non-equilibrium simulation) and availability to capture detailed mechanism behind rheological observations, especially for number of elastically active chains. This newly developed stochastic simulation is based on Langevin dynamics coupled with an additional stochastic step for topological renewal. Parameters of the simulations are size of micelles and chains, stiffness of micelle structure, micelle aggregation number, length being related to micelle core, and time ratio between micelle diffusion time and loop-dissociation time. After detailing the algorithm in chapter 2, chapter 3 explores the effect of various parameters on static and dynamical observables. Selected samples are examined in chapter 4 both under equilibrium and non-equilibrium conditions. Results show scaling exponents consistent with experimental data, understanding strain hardening of shear startup in the way of finite extensibility of chains, confirm break-down of Cox-Merz rule due to persistence of bridges, and capture shear-thickening. Details of simulations are reported in the appendix together with the theoretical background and strategy of code development. In part 2, we examined entangled linear polymers in the extensional flows at flow rates higher than the reciprocal Rouse time. In the classical molecular models, the steady-state extensional viscosity is characterized by four regimes: (i) the linear regime with Trouton ratio equal to 3, (ii) viscosity thinning with exponent -1, (iii) upturn due to chain stretch, and (iv) approach to an asymptotic value due to finite extensibility. The advent of data from extensional rheology, however, reveals that the theoretical expectation is not strictly true, and the tendency depends on the details of chemistry. To be specific, polystyrene (PS) melt shows the spontaneous decrease even beyond the reciprocal Rouse time with an exponent of -1/2, while polyisoprene (PI) and poly(n-butyl acrylate) (PnBA) shows the upturn around reciprocal Rouse time. These differences are believed to be due to the sensitivity of the monomeric friction coefficient to alignment in the statistical segments of polymer chain when the flow rate is larger than reciprocal Rouse time. This is confirmed by measuring components for friction tensor and order parameter of oligomer-type molecular simulations in the simple shear where shear rate is higher than reciprocal self-diffusion time (chapter 6). In this context, we also analyze PS solutions in its oligomeric solvents, all having the same linear-viscoelasticity (chapter 7). The suggested model uses the frictional change due to the change of order parameter that accounts for the nematic interactions. The results quantitatively predict the experimental data from extensional flow.