^{1}and Monica Olvera de la Cruz

^{2,a)}

### Abstract

We investigate the equilibrium properties and the underlying dynamics of emulsions formed in asymmetric A-B copolymers in matrices of immiscible B and C molecular fluids using coarse-grained molecular dynamics simulations. The emulsions are generated by introducing net attractions among the A units of the copolymers and the C molecules. They coexist with an absorbed copolymermonolayer. We determine the interfacial properties as the emulsions are forming. In general, highly asymmetric copolymersself-assemble within the B-matrix phase into swollen micelles; the cores of which are composed of C-component material. Less asymmetric copolymers, however, after initially budding and eventually fissioning from the interfacialcopolymermonolayer, generate emulsified “inverse swollen micelles” within the C-matrix phase. These stable inverse (crew-cut) swollen micelles, which form under the inward bending of the saturated or oversaturated interfaces toward the longer B-block due to the attraction between the A and C units, can encapsulate large amounts of B-matrix component in their cores. This monolayer collapse mechanism can be exploited to generate nanoreactors or containers that enhance the delivery of molecular components into immiscible molecular fluid environments.

This work was supported by the Non-equilibrium Energy Research Center (NERC), which is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0000989. H.G. would like to thank support of NSF China (Grant No. 20874110).

I. INTRODUCTION

II. MODEL AND METHOD

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Copolymers
- 87.0
- Micelles
- 60.0
- Monolayers
- 33.0
- Block copolymers
- 21.0
- Micellar systems
- 10.0

## Figures

An asymmetric A-B copolymer monolayer formed at interfaces that separate immiscible C and B matrix-components (center cartoon) in the presence of attractive interactions among A-block and C-matrix units can lead to two types of emulsions present in either one or both of the matrices coexisting with the adsorbed copolymer monolayer: inverted or crew-cut swollen micelles (left cartoon) and swollen micelles (right cartoon). Swollen micelles in the B-matrix phase (right cartoon) results in systems with highly asymmetric copolymers. Meanwhile in ternary systems with less asymmetric copolymers, a monolayer collapse transition induces the formation of inverse swollen micelles in the C-matrix phase (left cartoon). The process occurs via budding and fission from the metastable copolymer monolayer at the interface between the C-matrix and B-matrix components. These inverse swollen micelles permit the encapsulation of more cargo for delivery than conventional swollen micelles.

An asymmetric A-B copolymer monolayer formed at interfaces that separate immiscible C and B matrix-components (center cartoon) in the presence of attractive interactions among A-block and C-matrix units can lead to two types of emulsions present in either one or both of the matrices coexisting with the adsorbed copolymer monolayer: inverted or crew-cut swollen micelles (left cartoon) and swollen micelles (right cartoon). Swollen micelles in the B-matrix phase (right cartoon) results in systems with highly asymmetric copolymers. Meanwhile in ternary systems with less asymmetric copolymers, a monolayer collapse transition induces the formation of inverse swollen micelles in the C-matrix phase (left cartoon). The process occurs via budding and fission from the metastable copolymer monolayer at the interface between the C-matrix and B-matrix components. These inverse swollen micelles permit the encapsulation of more cargo for delivery than conventional swollen micelles.

Phase diagram showing the regions where swollen micelles or inverse swollen micelles are in equilibrium with the adsorbed copolymer monolayer at the interface between the matrix and phases at fixed interaction parameter, defined in Eq. (1), and copolymer concentration . Filled circles define molecular parameters required to generate stable swollen micelles. Filled squares define molecular parameters required to generate stable inverse swollen micelles. Crosses define molecular parameters where free copolymers in the bulk phase are in equilibrium with adsorbed copolymer monolayer at the interface.

Phase diagram showing the regions where swollen micelles or inverse swollen micelles are in equilibrium with the adsorbed copolymer monolayer at the interface between the matrix and phases at fixed interaction parameter, defined in Eq. (1), and copolymer concentration . Filled circles define molecular parameters required to generate stable swollen micelles. Filled squares define molecular parameters required to generate stable inverse swollen micelles. Crosses define molecular parameters where free copolymers in the bulk phase are in equilibrium with adsorbed copolymer monolayer at the interface.

(a) The time evolution of the interfacial tension calculated by averaging instant interfacial tension over the sub-run of the length of 20 time steps , and (b) the typical configuration sequences for a system with and [see Eq. (1)] and copolymer concentration . The big black dot in (a) indicates the value of at time zero. For clarification, there is a break in the Y axis of (a). In (b), the copolymers stabilize swollen micelles in the matrix in the presence of adsorbed copolymer monolayer at the interface between the matrix and phases. For clarification, is shown in green, block in orange, and the matrix components and blocks are not shown. The starting configuration is described in the text.

(a) The time evolution of the interfacial tension calculated by averaging instant interfacial tension over the sub-run of the length of 20 time steps , and (b) the typical configuration sequences for a system with and [see Eq. (1)] and copolymer concentration . The big black dot in (a) indicates the value of at time zero. For clarification, there is a break in the Y axis of (a). In (b), the copolymers stabilize swollen micelles in the matrix in the presence of adsorbed copolymer monolayer at the interface between the matrix and phases. For clarification, is shown in green, block in orange, and the matrix components and blocks are not shown. The starting configuration is described in the text.

(a) The time evolution of the interfacial tension calculated by averaging instant interfacial tension over the sub-un of the length of 20 time steps , and (b) the typical configuration sequences for a system with and [see Eq. (1)] and copolymer concentration . In (b), the copolymers stabilize inverse swollen micelles in the matrix in the presence of adsorbed copolymer monolayer at the interface between the matrix and phases. For clarification, the same configuration is shown by the left and right images with different sets of monomers. Here is shown in green, block in orange, in red and block in blue. The remaining details is the same as Fig. 3.

(a) The time evolution of the interfacial tension calculated by averaging instant interfacial tension over the sub-un of the length of 20 time steps , and (b) the typical configuration sequences for a system with and [see Eq. (1)] and copolymer concentration . In (b), the copolymers stabilize inverse swollen micelles in the matrix in the presence of adsorbed copolymer monolayer at the interface between the matrix and phases. For clarification, the same configuration is shown by the left and right images with different sets of monomers. Here is shown in green, block in orange, in red and block in blue. The remaining details is the same as Fig. 3.

The interfacial copolymer excess , as function of the interaction parameters defined in Eq. (1) for the studied ternary blends at fixed and copolymer concentration .

The interfacial copolymer excess , as function of the interaction parameters defined in Eq. (1) for the studied ternary blends at fixed and copolymer concentration .

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