Bifurcation and competitive evolution of network morphologies in the strong functionalized Cahn-Hilliard equation
Kraitzman, Noa
Separation (Technology)--Mathematical models
Boundary value problems
Applied mathematics
Thesis Ph. D. Michigan State University. Applied Mathematics 2015
The Functionalized Cahn-Hilliard (FCH) energy is a higher-order free energy that has been proposed to describe phase separation in blends of amphiphilic polymers and solvent. It balances interfacial solvation energy of ionic groups and volumetric counter-ion and polymer chain self-interaction energy against elastic energy of the underlying polymer backbone. It is hoped that its gradient flows describe the formation of solvent accessible network structures, such as found in polymer electrolyte membranes, lipid membranes, and amphiphlic diblock copolymers. The FCH gradient flows possess long-lived network morphologies of distinct co-dimension and we characterize their geometric evolution, bifurcation and competition through a formal asymptotic reduction. This reduction encompasses a broad class of coexisting network morphologies with different inner structure, such as bilayers and pores. The stability of the different network morphologies is characterized by the meandering and pearling modes associated to the linearized system. For the H^{-1} gradient flow of the FCH energy, using functional analysis and asymptotic methods, we derive a sharp-interface geometric motion which couples the flow of co-dimension 1 and co-dimension 2 network morphologies, in R^3, through the spatially constant far-field chemical potential. In particular, we rigorously characterize the pearling eigenvalues for a class of admissible co-dimension 1 and co-dimension 2 networks.
Includes bibliographical references (pages 185-188)
Description based on online resource; title from PDF title page (ProQuest, viewed March 13, 2018)
Promislow, Keith S
Bates, Peter W
Schenker, Jeffrey H
Yan, Baisheng
Liu, Di
2015
text
Electronic dissertations
Academic theses
application/pdf
1 online resource (xiii, 188 pages) : color illustrations.
isbn:9781321983142
isbn:132198314X
umi:3718475
local:KRAITZMAN_grad.msu_0128D_13817
en
In Copyright
Ph.D.
Doctoral
Applied Mathematics - Doctor of Philosophy
Michigan State University