Part I: Multi-Valent Ion Effects on Polyelectrolyte Structure and Thermodynamics & Part II: Hydrodynamic Self-Propulsion

Citation

Glisman, Alec Gregory (2025) Part I: Multi-Valent Ion Effects on Polyelectrolyte Structure and Thermodynamics & Part II: Hydrodynamic Self-Propulsion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/gf6m-gs53. https://resolver.caltech.edu/CaltechTHESIS:07092024-204040190

Abstract

Part I: Polyelectrolytes are a class of charged polymers that have found widespread utility in water treatment, drug delivery, and scale inhibition, among other applications. For many of these applications, it is crucial to control the phase stability of the polyelectrolyte solution. The long-ranged nature of the electrostatic interactions in polyelectrolyte solutions and the polyelectrolyte's connectivity lead to a rich phase behavior that can be challenging to study, especially in the presence of other ions or surfaces. In scale inhibition applications, polyelectrolytes such as poly(acrylic acid) (PAA) are used to prevent the dissolution of sparingly soluble salts, such as calcium carbonate, in water. While the significant influence of small ions on polyelectrolyte solution phase behavior is recognized, the precise molecular mechanisms driving the resulting phase stability remain largely elusive.

Polyelectrolyte theory suggests that a polyelectrolyte's behavior and adsorption properties in solution are strongly tied to the polymer chain conformation and charge distribution, which in turn is influenced by solution ionic strength and ionic valency. Consequently, we expect the polyelectrolyte performance to be highly dependent on the solution conditions and the molecular features of the polyelectrolyte. Previous computational studies have studied general polyelectrolytes in solution with coarse-grained and implicit solvent models and provided insights into the chain conformational transitions. However, they disagree on the mechanisms underlying aqueous polyelectrolytes salting out of suspension and are unable to yield chemically specific insights. We seek to better understand the antiscalant mechanisms of polyelectrolytes using all-atom molecular dynamics to capture solvation and polymer chemistry effects on the mechanisms of polyelectrolytes preventing scale nucleation and slowing growth.

The current work investigates the structure and thermodynamics of polyelectrolytes in bulk solution and at crystalline interfaces with added multi-valent ions. The presence of multi-valent ions, such as Ca2+, can significantly influence polyelectrolyte conformation via ion bridging non-neighboring charged monomers as well as screening the electrostatic interactions. We employ all-atom molecular dynamics simulations to investigate the binding modes of Ca2+ onto a PAA chain, Ca2+–PAA complex aqueous stability, and PAA adsorption onto a crystalline CaCO3 surface. In each of these cases, we find that the balance between ion bridging, electrostatic screening, and water-mediated interactions plays a crucial role in determining the polyelectrolyte's behavior in solution and at an interface.

Part II: Active bodies undergo self-propulsive motion in a fluid medium and span a broad range of length and time scales. Many active systems spontaneously self-organize into visually striking structures: fish schooling, birds flocking, and bacterial colonies growing. Current models of this emergent behavior in the inertial regime are mainly phenomenological and lack consideration of the fluid-mediated interactions between bodies.

To address this limitation, we seek to advance physics-based models of swimmers by explicitly incorporating the fluid mechanical interactions between bodies. We aim to discern the fluid medium's role in group dynamics and determine whether it can reproduce the observed emergent phenomenon without resorting to phenomenologically based interaction rules. To that end, we focus specifically on swimming in high Reynolds number flows, where inertial forces dominate, and draw comparisons to the well-studied low Reynolds number (Stokes) regime. We begin by deriving the equations of motion for a collection of unconstrained spherical particles in potential flow and extend the model to include viscous dissipation and rigid body motion constraints for many bodies with arbitrary kinematics.

We then consider the case of a single swimmer consisting of three linked spheres in potential flow. Through this, we find self-propulsion without needing external forces or momentum transfer via vortex shedding. We compare the inertial swimmer to an identical swimmer in the Stokes regime—where fluid inertia is neglected—and find that the structure of the equations of motion is identical in both flow regimes. Notably, the Stokes hydrodynamics are longer-ranged at leading order, leading to a more significant net displacement of the swimmer after one period of articulation. Finally, our study provides analytical insight into the swimming of a deformable body through an expansion of the non-linear spatial dependence of the hydrodynamic interactions.

Thesis Files