Multiscale Modeling of Polymer-Colloid Interactions in Waterborne Coatings

Abstract

Formulations containing rheology modifying polymers and nanometer sized colloids have widespread use in pharmaceuticals, personal care products, and waterborne coatings. When combined in solution, hydrophobic endcaps of the polymers temporarily adsorb to the colloids and act as bridges, forming a dynamic network with characteristic timescales spanning many orders of magnitude. It is computationally infeasible to capture the full range of relaxation times while maintaining atomistic resolution, but the coarse-grained hybrid population balance-Brownian dynamics model (Pop-BD) has been shown to capture qualitative behavior consistent with more fine-grained models[10, 11]. In this work, we detail efforts to improve Pop-BD to be more accurate, simulate experimentally relevant system sizes, and capture long timescale behavior. In the chapter 2, we quantify the inter-colloidal repulsions induced by adsorbed polymers using a combination of Brownian dynamics simulations and self-consistent field theory. With predictions of particle interactions that account for polymer defects and non-uniform surface coverages, we can predict phase behavior of these mixtures and inform the inter-colloidal potentials used in Pop-BD. In chapter 3, we use Brownian dynamics simulations to quantify bridge-to-loop and loop-to-bridge transition rates that are crucial to capturing dynamic behavior in Pop-BD. We show that the ratio of the fraction of polymers in the bridge configuration to the fraction of those in the loop configuration is equal to the ratio of the bridge-to-loop time to loop-to-bridge time, so that by using the equilibrium bridge and loop configuration information from the self-consistent field theory approach in chapter 2, we can easily compute the slower loop-to-bridge time from the bridge-to-loop time. In studying bridge-to-loop transition times, we observe two distinct regimes, one where the polymer relaxation time dominates for weak hydrophobes and long chains, and another, for strong hydrophobes and short chains, where the hydrophobe desorption time dominates and transitiontime scales exponentially with the hydrophobic strength. The complexities seen in the scaling of the bridge-to-loop times indicate that Brownian dynamics simulations are currently necessary for experimentally-relevant parameters, and so we present bridge-to-loop and the corresponding loop-to-bridge transition times for the systems of interest. Chapter 4 contains a thorough investigation of existing theories for modeling the escape of a particle from an adsorptive surface along with a general equation for predicting this escape time across all damping regimes. The Brownian (overdamped) escape times from this study are additionally used to understand the bridge-to-loop transition in Chapter 3. In Chapter 5, we drastically improve the computational efficiency of Pop- BD by integrating it into HOOMD-blue, adopting on-the-fly correlator, and introducing dynamic bonding functionality. We also incorporate the findings from the smaller-scale models in chapters 2-4 into the Pop-BD model so that it may capture the complexities of polymer-colloid interactions more accurately. In doing so, we have made significant progress toward developing the first multiscale model to understand and predict the behavior of these formulations with the ultimate goal of aiding the formulation development process for waterborne coatings.