Rheological characterization of polymers via dissipative particle dynamics

Abstract

Dissipative particle dynamics (DPD) is a mesoscale simulation technique which uses soft potentials between large particles to reproduce liquid behavior. In form, DPD is similar to molecular dynamics, as all matter is represented by point particles which interact with each other via, pairwise forces. The method was first introduced in the early 1990's, and has since undergone a number of refinements which have put it on a firm thermodynamic footing. DPD is notable for the flexibility it presents the modeler for building complex fluid systems. DPD has been used to study simple molecular liquids, polymer and colloid solutions, and phase behavior of block copolymer melts. Recently, a number of workers have used DPD to study the flow of polymer solutions in various geometries such as microchannels, pores, and sudden contractions. While these types of flows are well-suited to DPD's relative strengths, an important step has been skipped. Before the results of these complex flows can be accepted, it is necessary to demonstrate that the rheological predictions made by DPD are generally reliable. The principle aim of this thesis is to demonstrate that the rheology of polymer solutions can be simulated successfully with DPD. The rheology of a solution of DPD dumbbells using a FENE spring force law is studied in the first part of this thesis via simulation of steady shear flow and steady planar elongational flow. The rheological results are compared to dilute Brownian dynamics simulations of the same FENE dumbbell model. The level of coarse-graining of the DPD fluid is varied by changing the length of the DPD dumbbell relative to the particle size, while maintaining a constant extensibility parameter. Broadly speaking, the viscosity, first normal stress coefficient, and dumbbell extension in shear flow calculated with DPD are in agreement with the BD results. The two methods are not perfectly alike however, and two systematic differences between the DPD and BD results are observed. An excluded volume effect which occurs naturally in DPD and is not present in the BD simulations results in elevated viscosity and dumbbell extension in the zero-shear-rate regime.

(cont.) The effect is more powerful in DPD dumbbells which are more coarse-grained. At high shear rates in the power-law regime, DPD systematically overpredicts the rate of shear-thinning, with the greatest deviation occurring in the most coarse-grained dumbbells. This is hypothesized to be a result of hydrodynamic interaction which comes naturally out of DPD's explicit treatment of the solvent. The HI effect is analyzed using the Giesekus anisotropic drag tensor. Shortly after its introduction, the complaint was made that DPD's dynamic results are suspect because it has a very low, gas-like Schmidt number, meaning that momentum and mass are transported through the DPD medium at similar rates. This is in contrast with physical liquids, which have large Schmidt numbers. The use of the Lowe-Anderson formulation of DPD allows the Schmidt number of a solution to be varied for the same polymer model. Shear flow simulations of identical dumbbells under different Schmidt number conditions give results in excellent agreement with each other, indicating that the Schmidt number is not an important factor in determining polymer rheology with DPD. Steady planar elongational flow is simulated for the first time in DPD using the Kraynik and Reinelt boundary conditions, which are periodic in both space and time, allowing for simulations of planar elongational flow for an unlimited period of time. The planar elongational flow results of FENE dumbbells are also in agreement with BD, butshow the same systematic deviations observed in shear flow. The second portion of this thesis examines a more complex polymer solution using DPD, with simulations of semidilute solutions of longer N = 20 bead-spring chain polymers undergoing shear and planar elongational flow. In addition to concentration effects, the importance of the solvent quality is also examined with simulations of polymer solutions in both good and theta solvents. In order to capture concentration dependency, a spring -spring repulsion force is added to the DPD model to prevent polymer springs from passing though each other. A strong concentration dependence on the longest relaxation time is observed.

(cont.) In planar elongational flow, each solution goes through a coil-stretch transition at the theoretically predicted strain rate De = 0.5. In shear flow, the rheological results are in qualitative agreement with theory, showing a plateau at low De, and a transition into a shear-thinning regime beginning at De = 1. While the planar elongational flow results show clear dependence on the solution relaxation time, the shear results show a mixed dependence on the overall solution relaxation time, which reflects the concentration dependence, and the relaxation rate of an isolated chain, suggesting that only some aspects of the shear rheology are affected by the concentration. The conclusion of this thesis is that DPD is able to faithfully reproduce reliable rheological behavior with bead-spring polymer models. We find however, that the computational costs associated with the explicit simulation of the solvent put DPD at a disadvantage for systematic rheology studies when compared to Brownian dynamics. The high costs of the spring-spring repulsion force implementation are particularly limiting. In complex systems where DPD's natural flexibility in molecular architecture and chemistry make it the best choice, rheological results can now be accepted with more confidence.