Soft Confinement for Polymer Solutions

As a model of soft confinement for polymers, we investigated equilibrium shapes of a flexible vesicle that contains a phase-separating polymer solution. To simulate such a system, we combined the phase field theory (PFT) for the vesicle and the self-consistent field theory (SCFT) for the polymer solution. We observed a transition from a symmetric prolate shape of the vesicle to an asymmetric pear shape induced by the domain structure of the enclosed polymer solution. Moreover, when a non-zero spontaneous curvature of the vesicle is introduced, a re-entrant transition between the prolate and the dumbbell shapes of the vesicle is observed. This re-entrant transition is explained by considering the competition between the loss of conformational entropy and that of translational entropy of polymer chains due to the confinement by the deformable vesicle. This finding is in accordance with the recent experimental result reported by Terasawa, et al. Phase separated structures of polymer melts and polymer solutions induced by a confinement into a narrow space are actively investigated both experimentally and theoretically. For example, Wu et al. reported experimental observations of helical structures of diblock-copolymers induced by a confinement into a nano-sized cylindrical tube [1]. In theoretical studies, self-consistent field theory (SCFT) is a powerful method to obtain the equilibrium structure of polymer solutions, because SCFT can take the polymer conformations into account [2, 3]. In preceding studies, using the SCFT, effects of confinement on polymer melts and solutions have been investigated for various types of containers, such as those with spherical and cylindrical shapes [1,4–6]. However, these studies are limited to the cases with hard confinements of polymer solutions by rigid containers. In the present article, we study a gsoft confinementh of polymer solutions, where the polymer solutions are enclosed by flexible containers. As a target system of this soft confinement, we study equilibrium structures of a flexible vesicle that encloses a polymer solution. Such polymer-containing vesicles can be frequently found in biological systems such as endocytosis and exocytosis, and are expected to be applicable to industrial science, for example the drug-delivery system. Recently, Terasawa et al. and Nakaya et al. showed shape deformations of vesicles [7] or closed membranes [8] induced by enclosed polymers. They suggested an important effect of the translational entropy of the enclosed polymers. In the present article, to study the deformation of polymer-containing vesicles theoretically, we apply our field-theoretic approach [9] where SCFT for polymers [2,3] and phase field theory (PFT) for the vesicle shape [10–12] are combined. In our previous publication [9], we discussed a transition of a polymer-containing vesicle between a prolate shape and an oblate shape, where we limited our discussions to the cases with polymers swollen by a good solvent and vesicles that have no spontaneous curvature. However, in realistic situations, enclosed polymers are often in a globular state (i.e. the solvent is a poor solvent) and the vesicle has non-zero spontaneous curvature due to the asymmetric composition between the inner and outer leaflets of the bilayer membrane. In the present article, we will show remarkable effects of these two features on the vesicle deformation. Let us describe our theoretical model for polymercontaining vesicles. In our model, the vesicle is modeled by PFT, where a scalar field ψ(r) which is called the ”phase field” [10–12] specifies the inside and the outside regions of the vesicle by its positive and negative regions. Using an analogy to the Ginzburg-Landau theory for phase separating binary mixtures, the density distribution of the surfactant molecules that compose the vesicle, denoted as φm(r), and the total surface area of the vesicle S are rep-