Polymer physics theory
The mucus layer is a matrix of biopolymers that dynamically associate and form a physical barrier against harmful pathogens to the body. Understanding the behavior of dynamic polymer networks, polymers with chemical groups that form temporary bonds, is paramount in determining the mechanism behind the biophysics of infection in the mucus layer. Current experimental rheological measurements of polymer networks rely on time-temperature superposition, an assumption that is invalid for dynamic and, especially, biological polymer networks. Additionally, existing theoretical models are limited by parameters that do not shed light on the molecular details of dynamic polymer systems due to their inherent coarse-graining. I developed a new polymer theory called brachiation theory that incorporates molecular-level parameters (i.e. polymer chain length, number of chemical groups, association rates). I chemically modified hyaluronic acid, a biopolymer that contributes to the viscoelasticity of lung mucus during inflammation, with host-guest molecules to form a supramolecular network and used dynamic light scattering microrheology to characterize its rheological behavior. The remarkable agreement between the experimental rheological data and the theoretical prediction of the model demonstrates the utility of brachiation theory for modeling the mechanism of polymer interactions in biological polymer fluids. In the case of the mucus layer, the molecular parameters of the theory could reveal the length scale at which the biopolymers present exhibit enough elasticity to hinder pathogen diffusion to the epithelium as well as the biopolymer concentrations at which the mucus layer becomes unable to disperse pathogens.
Articles
PC Cai, BA Krajina, AJ Spakowitz. “Brachiation of a polymer chain in the presence of a dynamic network.” Physical Review E.
The viscoelastic behavior of a physically crosslinked gel involves a spectrum of molecular relaxation processes, which at the single-chain level involve the chain undergoing transient hand-to-hand motion through the network. We develop a self-consistent theory for describing transiently associating polymer solutions that captures these complex dynamics. A single polymer chain transiently binds to a viscoelastic background that represents the polymer network formed by surrounding polymer chains. The viscoelastic background is described in the equation of motion as a memory kernel, which is self-consistently determined based on the predicted rheological behavior from the chain itself. The solution to the memory kernel is translated into rheological predictions of the complex modulus over a wide range of frequencies to capture the time-dependent behavior of a physical gel. Using the loss tangent predictions, a phase diagram is shown for the sol-gel transition of polymers with dynamic association affinities. This theory provides a predictive, molecular-level framework for the design of associating gels and supramolecular assemblies with targeted rheological properties.
PC Cai, B Su, L Zou, MJ Webber, SC Heilshorn, AJ Spakowitz. “Rheological Characterization and Theoretical Modeling Establish Molecular Design Rules for Tailored Dynamically Associating Polymers.” ACS Central Science.
Dynamically associating polymers have long been of interest due to their highly tunable viscoelastic behavior. Many applications leverage this tunability to create materials that have specific rheological properties, but designing such materials is an arduous, iterative process. Current models for dynamically associating polymers are phenomenological, assuming a structure for the relationship between association kinetics and network relaxation. We present the Brachiation model, a molecular-level theory of a polymer network with dynamic associations that is rooted in experimentally controllable design parameters, replacing the iterative experimental process with a predictive model for how experimental modifications to the polymer will impact rheological behavior. We synthesize hyaluronic acid chains modified with supramolecular host–guest motifs to serve as a prototypical dynamic network exhibiting tunable physical properties through control of polymer concentration and association rates. We use dynamic light scattering microrheology to measure the linear viscoelasticity of these polymers across six decades in frequency and fit our theory parameters to the measured data. The parameters are then altered by a magnitude corresponding to changes made to the experimental parameters and used to obtain new rheological predictions that match the experimental results well, demonstrating the ability for this theory to inform the design process of dynamically associating polymeric materials.