### Abstract

Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

Original language | English (US) |
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Article number | 062501 |

Journal | Physical Review E |

Volume | 100 |

Issue number | 6 |

DOIs | |

State | Published - Dec 11 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics