Singular-Enthalpic Limits in Polymer Morphology

Michigan State University, East Lansing MI

Investigators

Abstract

Polymers are among the most mutable and dynamic structures in nature and science. Their uses range from the strongest components on airplanes to the smallest sensors and proteins in living materials. When polymers are suspended in solvent with ionic materials such as salt, as is typical in biological applications, the resulting interactions are among the most complex in all of nature. This investigation will derive and analyze models for the entropic and enthalpic interaction of diblock polymers in suspensions as a prototype of lipids in biology. It aims to identify the role of polymer substructure on the self-adhesion tendencies of charged polymers that lead to self-assembly of complex biological organelles, such as the thylakoid membranes that drive photosynthesis in plants and the Golgi apparatus that is vital to protein manufacture and transport in humans. The project is intended to illuminate the role of hydrophobic-hydrophilic phase separation on the detailed structure of lipid bilayers and its impact on membrane permeability. Most significantly, new methods will be investigated for the casting of lamellar membranes destined for water purification applications that combine microfluidic flow with the systems’ natural phase separation tendencies. The project includes training for undergraduate and graduate students through involvement in the research. Functional polymers contain charged or polarizable groups that induce strong interactions with solvent and with other polymers. System behaviors become increasingly complex when several types of polymers or multiple solvents are combined. This project addresses a broad scaling limit that renders fundamental systems amenable to analysis. This arises from free energy landscapes of polymer systems that combine entropy, enthalpy, and pressure. Pressure is large and enforced through incompressibility. Enthalpy is smooth, entropy is singular in key regions. The singular enthalpy limit is an approach that resolves the connection problem for optimal packings of diblock polymers by patching linear enthalpic flows to the stable and unstable manifolds of fixed points from a vicinity of the singular entropy domain to find points of intersection. Robust families of connection solutions lead to novel interface flows in the sharp-interface limits, including adhesion effects. Establishing linear convexity will allow for rigorous sharp-interface reduction. Incorporation of flux leads to weakly heteroclinic connections that parameterize the response of bilayers to pressure gradients, leading to determination and control of membrane permeability. The focus on self-assembly of charged polymers and the stacking behavior of the associated bilayer vesicles have broad application to photosynthesis, through thylakoid membranes, and the behavior of organelles such as the Golgi apparatus. The formation of lamellar membranes at interfaces between immiscible fluids is relevant to membranes for water purification systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.