Communications in Mathematical Sciences
Volume 17 (2019)
Bubble assemblies in ternary systems with long range interaction
Pages: 2309 – 2324
A nonlocal diffuse interface model, based on the Nakazawa–Ohta density functional theory for triblock copolymers, is used to study bubble assemblies in ternary systems. The model has three parameters weighing three types of long-range interaction and two parameters that fix the total area of each constituent. As the parameters vary, a large number of morphological phases appear as stable stationary states. One open question related to the polarity direction of double bubble assemblies is answered numerically. Moreover, it is shown that the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent areas and the long-range interaction coefficients. One further identifies the ranges for area fractions and the long-range interaction coefficients for double bubble assemblies.
diffuse interface model, Nakazawa–Ohta density functional, triblock copolymers, morphological phases, long-range interaction
2010 Mathematics Subject Classification
35R35, 70E55, 74N20, 82D60, 92C15
X.R. is supported by National Science Foundation, DMS-1714371. Y.Z. is supported by a grant from the Simons Foundation through Grant No. 357963.
Received 16 September 2018
Accepted 3 September 2019
Published 3 February 2020