Senior Design Expo 2023

Applied Physics & Applied Mathematics
Phase initiation and Evolution using Surface Evolver
Juan Baek ‘23
Phase initiation and evolution play a crucial role in research and manufacturing,
particularly in areas such as polycrystalline thin films and displays. However, investigating the
fundamental theory behind these processes has been challenging due to the complexity of
mathematical calculations and the difficulty of observing phase transformations in condensed
phases experimentally.
Fortunately, Professor Ken Brakke of Susquehanna University has developed a program
called Surface Evolver, originally designed to study capillarity physics of microdroplets. We can
utilize this program for simulating evolution of a new phase beyond the simple classical
Nucleation Theory. By minimizing the energy of the “inter-phase” interface as it undergoes a
transformation subject to constraints, Surface Evolver uses various mathematical tools, including
Green's Theorem and vector calculus to simulate the evolution of a new phase. However, before
conducting a simulation, we must explicitly identify the shape and constraints of the solid/liquid
interface.
By understanding the relationship between contact angles on surfaces and interfacial
energies, we can accurately simulate the evolution of a solid. We also develop a thermodynamic
analysis by recognizing that curvature is a property of solid/liquid interfaces in mechanical
equilibrium, resulting in the derivation of a critical curvature where the Gibbs-Thomson
condition holds. We further demonstrate the effectiveness and efficiency of this method by
showing that free-energy evolution plots that are normally sought after by researchers, are
readily available from our curvature-volume evolution diagrams with fewer restrictions.
A Simple Model for Optimizing Magnetic Loss During Microwave Heating of
Superparamagnetic Fe3O4 Nanoparticles
Ethan Burkley
Advisors: Dr. Mengqi Shen, Dr. Xiaoyang Shi, and Dr. Ah-Hyung Alissa Park
Rosenwieg’s phenomenological model for inductive heating of colloidal magnetic particles is
used to guide the optimization of magnetic loss in superparamagnetic magnetite (Fe2O4) for use
in the regeneration of a novel CO2 capture material. Thermal regeneration of CO2 capture
materials is energetically costly and microwave induction has shown promise as a way to
improve the efficiency of regeneration by embedding magnetic nanoparticles alongside
functionalized nanoparticle organic hybrid materials (NOHMs) in a CO2 permeable matrix.
While the magnetic properties of magnetite vary significantly with size, the Rosenwieg model
illustrates why size is not a conclusive parameter. Ultimately, this analysis demonstrates how to
tune nanoparticle size for a given microwave frequency as well as how to optimize the efficiency
of magnetic loss.
Keywords: Superparamagnetism, Microwave Induction, Magnetite, CO2 Capture
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