^{1}and E. Yu. Kramarenko

^{1,a)}

### Abstract

We report a theoretical study of micelles from diblock copolymers with an insoluble core-forming block and an amphiphilic ionic corona-forming block. We calculate the micelle structural parameters depending on the composition of the coronal block (ratio between the non-polar and ion-containing groups) as well as solvent quality and polarity for the coronal block. We focus on the effect of ion pair formation in a low polar corona medium and predict the existence of novel micelles with ionomer-type coronae. In these micelles most part of counterions is bound with ions in polymer chains. Two consecutive jump-like first-order phase transitions between different-type micelles can take place in the solution upon change of hydrophobic/polyelectrolyte balance within the micelle corona: large micelles with polyelectrolyte collapsed coronae → large micelles with ionomer-type coronae → small micelles with polyelectrolyte swollen coronae. These transitions are accompanied by non-monotonous change in the micelle aggregation number. New insight into the role of counterions is important for design of stimuli responsive systems.

I. INTRODUCTION

II. THEORETICAL MODEL

III. RESULTS AND DISCUSSION

A. Micelles in the absence of ion pair formation

B. Effects of ion pairing

C. Diagrams of micelle states

IV. CONCLUSION

##### B01J13/00

## Figures

Schematic representation of a micelle with a charged corona. Three types of counterion states are distinguished: bound counterions forming ion pairs, free counterions within the micelle corona and in the outer solution.

Schematic representation of a micelle with a charged corona. Three types of counterion states are distinguished: bound counterions forming ion pairs, free counterions within the micelle corona and in the outer solution.

Corona thickness R B (a) and core radius R A (b) in a units, polymer volume fraction Φ in corona (c), fraction of counterions in the outer solution α (d) and aggregation number m (e) as functions of β for N A = N B = 100, u 0 = 2, γa 2/kT = 4.1, and C = 10−5. Curves correspond to χ = 0.5 and χ = 0.8.

Corona thickness R B (a) and core radius R A (b) in a units, polymer volume fraction Φ in corona (c), fraction of counterions in the outer solution α (d) and aggregation number m (e) as functions of β for N A = N B = 100, u 0 = 2, γa 2/kT = 4.1, and C = 10−5. Curves correspond to χ = 0.5 and χ = 0.8.

Aggregation number m (a), fraction of counterions in the outer solution α (b), fraction of ion pairs p (c), volume fraction of the polymer in corona Φ (d), and total micelle charge in e units (e) as the functions of β for N A = N B = 100, u 0 = 2, γa 2/kT = 4.1, χ = 0.55, C = 10−5. Curves correspond to the case of no ion binding p = 0 (1) and δε = 0.67 (2), δε = 0.69 (3), and δε = 0.7 (4).

Aggregation number m (a), fraction of counterions in the outer solution α (b), fraction of ion pairs p (c), volume fraction of the polymer in corona Φ (d), and total micelle charge in e units (e) as the functions of β for N A = N B = 100, u 0 = 2, γa 2/kT = 4.1, χ = 0.55, C = 10−5. Curves correspond to the case of no ion binding p = 0 (1) and δε = 0.67 (2), δε = 0.69 (3), and δε = 0.7 (4).

Schematic representation of two consecutive transitions in micelles induced by corona block charging.

Schematic representation of two consecutive transitions in micelles induced by corona block charging.

Aggregation number m (a) and fraction of ion pairs p (b) as functions of β for N A = N B = 100, δε = 0.7, γa 2/kT = 4.1, χ = 0.55, C = 10−5. Curves correspond to u 0 = 1.8 (1), u 0 = 1.9 (2), u 0 = 2 (3), u 0 = 2.1 (4).

Aggregation number m (a) and fraction of ion pairs p (b) as functions of β for N A = N B = 100, δε = 0.7, γa 2/kT = 4.1, χ = 0.55, C = 10−5. Curves correspond to u 0 = 1.8 (1), u 0 = 1.9 (2), u 0 = 2 (3), u 0 = 2.1 (4).

Aggregation number m (a) and fraction of ion pairs p (b) as functions of β for N A = N B = 100, u 0 = 2, δε = 0.7, γa 2/kT = 4.1, C = 10−5. Curves correspond to χ = 0.55, χ = 0.9.

Aggregation number m (a) and fraction of ion pairs p (b) as functions of β for N A = N B = 100, u 0 = 2, δε = 0.7, γa 2/kT = 4.1, C = 10−5. Curves correspond to χ = 0.55, χ = 0.9.

Aggregation number m (a) and fraction of ion pairs p (b) as functions of χ for N A = N B = 100, u 0 = 1, δε = 0.78, γa 2/kT = 4.1, β = 0.25, C = 10−5.

Aggregation number m (a) and fraction of ion pairs p (b) as functions of χ for N A = N B = 100, u 0 = 1, δε = 0.78, γa 2/kT = 4.1, β = 0.25, C = 10−5.

β − u 0 diagram of micelle states for the fixed value of Flory-Huggins interaction parameter χ = 0.7. Micelle types (large PE, small PE, ionomer-type) are depicted on the diagram.

β − u 0 diagram of micelle states for the fixed value of Flory-Huggins interaction parameter χ = 0.7. Micelle types (large PE, small PE, ionomer-type) are depicted on the diagram.

First-order phase transition lines of the solution for different values of Flory-Huggins interaction parameter χ. Curves correspond to χ = 0.55, χ = 0.7, χ = 0.9. Critical points are depicted by bold dots.

First-order phase transition lines of the solution for different values of Flory-Huggins interaction parameter χ. Curves correspond to χ = 0.55, χ = 0.7, χ = 0.9. Critical points are depicted by bold dots.

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