Property Prediction and Correlation

Polymer solutions and melts are complex fluids ubiquitous in both nature (e.g. DNA, polypeptides) and technological applications (e.g. in personal care products, food processing). These materials are comprised of large macromolecules whose building blocks (molecular repeating units or monomers) are many orders of magnitude smaller than the macromolecule size. This breadth of length scales enables the design of polymers with a multitude of microstructures (physical architecture). These microstructures can give rise to vastly different transport and mechanical properties in materials that have a similar chemical composition. Further tailoring of material and flow properties of polymer solutions and melts can be achieved through suspension of hard and/or soft particles. By perturbing the polymer flow field and forming a microstructure of their own, the suspended particles create materials with enhanced viscoelastic properties. Developing theoretical models that connect the microstructure to material and flow properties in polymers solutions and melts as well as particle-polymer mixtures remains an important problem at the interface between polymer physics, statistical physics and fluid mechanics. Development of such models will enable “designer” materials for next generation technological applications and a fundamental understanding of the different physical processes (e.g. the interplay between entropic and elastic forces) that give rise to their viscoelastic properties.

My research interests focus on developing predictive models of transport and rheology in polymers and particle-polymer mixtures. Utilizing theoretical techniques such as scaling theories, dynamic simulations, micro-mechanical models, and constitutive models, my goal is to develop predictive theory connecting microscopic structure to properties near and far from equilibrium. These models aim to reveal the underlying physical mechanisms driving such behaviors and serve as a basis to design tailored materials for next generation technological applications.

As a faculty member I will begin by focusing on three research thrusts:

1) The first is the development of charged polymer elastomers with enhanced conductive and mechanical properties. Charged polymer elastomers have potential applications in energy storage and as soft actuators. However, current materials have prohibitively low conductivities, hindering their use in practical applications. My goal is to design new charged polymer elastomers with improved conductivities and predict their properties via the use of dynamic simulations and scaling theories.

2) The second item on my research agenda is to develop predictive models for the non-linear rheology of complex coacervates. Complex coacervates are formed from mixtures of oppositely charged polyelectrolytes that phase separate into a polymer rich coacervate and a polymer-depleted supernatant. Coacervates are utilized in the food and personal care industry, and have shown promise in drug and gene delivery applications. There is burgeoning interest in understanding the rheological behavior of these materials far from equilibrium, as it is the most relevant regime for many practical applications. Understanding the physical mechanisms governing their non-equilbrium behavior also allows for rational design of their viscoelastic properties. My goal is to utilize dynamic simulations to inform the development of analytical models predicting the non-linear rheology of complex coacervates.

3) My third project aims to develop predictive models for the rheological behavior of particle laden polymer flows. Despite their importance in many industrial processes, the non-linear rheological behavior of particles suspended in non-newtonian solvents, such as polymer solutions and melts, remains poorly understood. Through a combination of constitutive and micro-mechanical models, my goal is to connect solvent viscoelasticity, particle microstructure, and hydrodynamic interactions to describe the rheological properties far from equilibrium. This will enable improved industrial processing, and provide rigorous interpretations of non-linear rheological characterization techniques such as large amplitude oscillatory shear.

Research Background:

My current research, carried out as a postdoctoral associate at Duke University under the supervision of Professor Michael Rubinstein, focuses on the linear viscoelasticity of complex coacervates. I developed a scaling theory for the dynamic behavior of asymmetric liquid-like coacervates formed from oppositely charged polyelectrolyte solutions. Depending on the degree of polymerization, the asymmetric liquid coacervate can form either an interpenetrating double-semidilute structure, wherein both polyanion and polycation are found above their overlap concentration, or a dilute-semidilute structure, where only one of the polyelectrolytes is found above their overlap concentration. I developed a scaling theory for polymer dynamics, providing predictions for the relaxation modulus and steady state shear viscosity of the coacervate, and predicting the diffusivity of the polyelectrolyte chains. The scaling theory highlights the different dynamical regimes of the system, and how the dynamic properties can be tuned from experimentally controllable parameters such as the degree of polymerization, the number density of charges of the polyanion and polycation, and the strength of electrostatic interactions. To complement the scaling theory we conduct molecular dynamics simulations to determine the structure and dynamical properties of the coacervate and confirm the different dynamical regimes.

For my PhD thesis, carried out at Cornell University under the supervision of Professor Roseanna Zia, I studied the diffusion in and rheology of hydrodynamically interacting colloids confined by a spherical cavity via dynamic simulation, as a model of intracellular and other confined biophysical transport. The modeling of transport and rheology in such confined inhomogeneous soft materials requires an accurate description of the microscopic forces driving particle motion, such as entropic and hydrodynamic forces, and of particle interactions with nearby boundaries. Previous models of such micro-confined transport behavior had been limited primarily to a single particle inside a spherical cavity. Although attempts had been made to extend such models to more than one confined particle, none had yet successfully accounted for the effects of hydrodynamics, owing to the difficulties of modeling many-body long-ranged interactions. To accurately model spherically confined suspensions, we derived new far-field mobility functions and, together with the appropriate near-field resistance functions, implemented them in a Stokesian-dynamics like approach. The method fully accounts for all many-body far-field interactions and near-field interactions both between the particles themselves and between particles and the enclosing cavity. Utilizing our newly developed method, we studied short- and long- time self-diffusion at equilibrium, with a focus on the dependence of the former on particle positions relative to the cavity, and of both on volume fraction and size ratio. We found the cavity exerts qualitative changes in transport behavior, such as a position dependent and anisotropic short-time self-diffusivity and anisotropic long-time transport behavior. Such qualitative changes suggest that careful interpretation of experimental measurements in 3D confined suspensions requires accounting for such confinement induced behaviors. To elucidate the effects of confinement on inter-particle hydrodynamic interactions, we utilized our method to determine the concentrated mobility of particles in the spherically confined domain. We found that confinement induces qualitative changes in the functional dependence of particle entrainment with inter-particle separation. We developed a scaling theory to predict the effects of confinement on particle entrainment and utilized the theory to develop a more accurate framework for two-point microrheology measurements near confining boundaries.

Selected Publications

1. “Simulation of hydrodynamically interacting particles confined by a spherical cavity”, Christian Aponte-Rivera, Roseanna N. Zia. Physical Review Fluids 2016. 1(2):023301.
2. “Equilibrium structure and diffusion in concentrated, hydrodynamically interacting suspensions confined by a spherical cavity”, Christian Aponte-Rivera, Yu Su, Roseanna N. Zia. Journal of Fluid Mechanics (2018). 836:413–50

Awards and honors:

• Bouchet Graduate Honor Society, 2018
• National Science Foundation Graduate Research Fellowship, 2013
• Colman Fellow, 2012

Teaching Interests:

My teaching interests focus on engineering core courses (e.g. transport phenomena and fluid mechanics, mathematical methods) as well as interdisciplinary courses with a focus on soft matter physics (including topics such as polymer physics, micro-hydrodynamics, and colloidal suspension rheology).