^{1,a),b)}, Samiul Amin

^{1,a),c)}, Christopher J. Kloxin

^{1,a),d)}and John H. van Zanten

^{1,e)}

### Abstract

Tracer particle microrheology using diffusing wave spectroscopy-based microrheology is demonstrated to be a useful method to study the dynamics of aqueous Pluronic™ F108 solutions, which are viewed as solutions of repulsive soft spheres. The measured zero-shear microviscosity of noncrystallizing micellar dispersions indicates micelle corona dehydration upon increasing temperature. Colloidal sphere thermal motion is shown to be exquisitely sensitive to the onset of crystallization in these micellar dispersions. High temperature dynamics are dominated by an apparent soft repulsive micelle–micelle interaction potential indicating the important role played by lubrication forces and ultimately micelle corona interpenetration and compression at sufficiently high concentrations. The measured microscopic viscoelastic storage and loss moduli are qualitatively similar to those experimentally observed in mechanical measurements on colloidaldispersions and crystals, and calculated from mode coupling theory of colloidal suspensions. The observation of subdiffusive colloidal sphere thermal motion at short time-scales is strong evidence that the observed microscopic viscoelastic properties reflect the dynamics of *individual*micelles rather than a dispersion of micellar crystallites.

This paper is based upon work supported by the National Science Foundation (NSF) under Grant Nos. CTS-00960219 (originally CTS-9702413) and CTS-9700170. S.A.T. also acknowledges the support of the ONR-HBEC Future Engineering Faculty Fellowship Program.

I. INTRODUCTION

II. MATERIALS AND METHODS

A. Materials

B. Diffusing wave spectroscopy

C. Microrheology

III. RESULTS AND DISCUSSION

A. Colloidal sphere thermal motion in aqueous Pluronic F108 solutions

B. Microscopic creep of aqueous Pluronic F108 solutions

C. Zero shear microviscosity of aqueous Pluronic F108 solutions

D. Complex microviscosity of aqueous Pluronic F108 solutions

E. Microviscoelasticity of aqueous Pluronic F108 solutions

IV. CONCLUSIONS

### Key Topics

- Colloidal systems
- 52.0
- Micelles
- 28.0
- Viscoelasticity
- 19.0
- Elastic moduli
- 18.0
- Viscosity
- 18.0

## Figures

Colloidal sphere thermal motion in an aqueous 20 wt. % Pluronic F108 solution-effect of temperature. The mean squared displacement of 420 nm diameter polystyrene spheres diffusing in an aqueous 20 wt. % Pluronic F108 solution at the following temperatures increasing from left to right: 22, 25, 28, 30, 30.12, 30.25, 30.38, 30.5, 30.62, 30.75, and 31 °C. Probe motion was measured by diffusing wave spectroscopy in an ∼4.5 mm path length temperature cell. The probe sphere concentration was ∼1 vol. %.

Colloidal sphere thermal motion in an aqueous 20 wt. % Pluronic F108 solution-effect of temperature. The mean squared displacement of 420 nm diameter polystyrene spheres diffusing in an aqueous 20 wt. % Pluronic F108 solution at the following temperatures increasing from left to right: 22, 25, 28, 30, 30.12, 30.25, 30.38, 30.5, 30.62, 30.75, and 31 °C. Probe motion was measured by diffusing wave spectroscopy in an ∼4.5 mm path length temperature cell. The probe sphere concentration was ∼1 vol. %.

Colloidal sphere thermal motion in aqueous Pluronic F108 solutions-effect of concentration. The mean squared displacement of 966 nm diameter polystyrene spheres diffusing in 23 °C aqueous Pluronic F108 solutions at the following concentrations increasing from left to right: 5, 10, 15, 21, 22, 23, 24, and 25 wt. %. Probe motion was measured by diffusing wave spectroscopy in 10 mm path length optical cells. The probe sphere concentration was ∼1 vol. %.

Colloidal sphere thermal motion in aqueous Pluronic F108 solutions-effect of concentration. The mean squared displacement of 966 nm diameter polystyrene spheres diffusing in 23 °C aqueous Pluronic F108 solutions at the following concentrations increasing from left to right: 5, 10, 15, 21, 22, 23, 24, and 25 wt. %. Probe motion was measured by diffusing wave spectroscopy in 10 mm path length optical cells. The probe sphere concentration was ∼1 vol. %.

Microscopic creep of aqueous Pluronic F108 solutions. The microscopic creep of 10 (top-left), 15 (top-right), 17.5 (bottom-left), and 20 (bottom-right) wt. % aqueous Pluronic F108 solutions as determined from Eq. (1) are shown. The corresponding temperatures from left to right are as follows: 10 wt. %—23, 30, 35, 45, and 40 °C; 15 wt. %—25, 30, 35, 40, and 45 °C; 17.5 wt. %—25, 30, 35, 35.5, 36, 36.5, 36.55, 36.6, 36.61, and 36.63 °C; and 20 wt. %—22, 25, 28, 30, 30.12, 30.25, 30.38, 30.5, 30.62, 30.75, and 31 °C.

Microscopic creep of aqueous Pluronic F108 solutions. The microscopic creep of 10 (top-left), 15 (top-right), 17.5 (bottom-left), and 20 (bottom-right) wt. % aqueous Pluronic F108 solutions as determined from Eq. (1) are shown. The corresponding temperatures from left to right are as follows: 10 wt. %—23, 30, 35, 45, and 40 °C; 15 wt. %—25, 30, 35, 40, and 45 °C; 17.5 wt. %—25, 30, 35, 35.5, 36, 36.5, 36.55, 36.6, 36.61, and 36.63 °C; and 20 wt. %—22, 25, 28, 30, 30.12, 30.25, 30.38, 30.5, 30.62, 30.75, and 31 °C.

Zero-shear microviscosity determined from colloidal sphere thermal motion. The zero shear viscosity as determined from Eq. (7) in the text. For all four concentrations considered here the viscosity initially increases with temperature, owing to increasing micellization with the two highest concentrations, 17.5 and 20 wt. %, eventually forming soft micellar polycrystals at 36.7 and 31 °C, respectively. The subsequent viscosity decrease in the two noncrystallizing solutions primarily owes to dehydration of the micelle corona.

Zero-shear microviscosity determined from colloidal sphere thermal motion. The zero shear viscosity as determined from Eq. (7) in the text. For all four concentrations considered here the viscosity initially increases with temperature, owing to increasing micellization with the two highest concentrations, 17.5 and 20 wt. %, eventually forming soft micellar polycrystals at 36.7 and 31 °C, respectively. The subsequent viscosity decrease in the two noncrystallizing solutions primarily owes to dehydration of the micelle corona.

Normalized loss component of the complex microviscosity of a 20 wt. % Pluronic F108 aqueous solution. The loss component of the complex viscosity as determined from Eqs. (3)–(5) in the text. From left to right the curves correspond to (▪) 30.6, (□) 30.5, (●) 30.4, (◯) 30.2, (▲) 30.1, and (△) 30 °C.

Normalized loss component of the complex microviscosity of a 20 wt. % Pluronic F108 aqueous solution. The loss component of the complex viscosity as determined from Eqs. (3)–(5) in the text. From left to right the curves correspond to (▪) 30.6, (□) 30.5, (●) 30.4, (◯) 30.2, (▲) 30.1, and (△) 30 °C.

Normalized storage component of the complex microviscosity of a 20 wt. % Pluronic F108 aqueous solution. The storage component of the complex viscosity as determined from Eqs. (3)–(5) in the text. The symbols denote the following temperatures: (▪) 30.6, (□) 30.5, (●) 30.4, (◯) 30.2, (▲) 30.1, and (△) 30 °C.

Normalized storage component of the complex microviscosity of a 20 wt. % Pluronic F108 aqueous solution. The storage component of the complex viscosity as determined from Eqs. (3)–(5) in the text. The symbols denote the following temperatures: (▪) 30.6, (□) 30.5, (●) 30.4, (◯) 30.2, (▲) 30.1, and (△) 30 °C.

Crossover of the microscopic viscoelastic storage and loss moduli in a 20 wt. % Pluronic F108 aqueous solution. The viscoelastic storage and loss moduli as determined from Eqs. (3)–(5) and the relations *G*′ = ωη′′ and *G*′′ = ωη′ The symbols denote the storage and loss moduli, respectively, at the following temperatures: (▲, △) 29, (●, ◯) 30.12, and (▪, □) 30.75 °C.

Crossover of the microscopic viscoelastic storage and loss moduli in a 20 wt. % Pluronic F108 aqueous solution. The viscoelastic storage and loss moduli as determined from Eqs. (3)–(5) and the relations *G*′ = ωη′′ and *G*′′ = ωη′ The symbols denote the storage and loss moduli, respectively, at the following temperatures: (▲, △) 29, (●, ◯) 30.12, and (▪, □) 30.75 °C.

Dynamic phase diagram for aqueous Pluronic F108 solutions. The symbols denote the following: (▪) a micellar liquid with *G*′′ > *G*′; (×) micellar dispersions exhibiting a crossover from a *G*′′ dominated low-frequency region to a *G*′ dominated high-frequency region; and (◯) a polycrystalline solid with *G*′ > *G*′′. The frequency dependence of the viscoelastic moduli for each of these typical cases is illustrated in Fig. 7.

Dynamic phase diagram for aqueous Pluronic F108 solutions. The symbols denote the following: (▪) a micellar liquid with *G*′′ > *G*′; (×) micellar dispersions exhibiting a crossover from a *G*′′ dominated low-frequency region to a *G*′ dominated high-frequency region; and (◯) a polycrystalline solid with *G*′ > *G*′′. The frequency dependence of the viscoelastic moduli for each of these typical cases is illustrated in Fig. 7.

Storage modulus of a 20 wt. % Pluronic F108 aqueous solution. The microviscoelastic storage modulus as determined from colloidal sphere thermal motion. The symbols denote the following temperatures: (▪) 31, (□) 30.75, (●) 30.62, (◯) 30.5, (▲) 30.38, (△) 30.25, (◆) 30.12, (◊) 30, (◂) 27, and (◃) 23 °C.

Storage modulus of a 20 wt. % Pluronic F108 aqueous solution. The microviscoelastic storage modulus as determined from colloidal sphere thermal motion. The symbols denote the following temperatures: (▪) 31, (□) 30.75, (●) 30.62, (◯) 30.5, (▲) 30.38, (△) 30.25, (◆) 30.12, (◊) 30, (◂) 27, and (◃) 23 °C.

Loss modulus of a 20 wt. % Pluronic F108 aqueous solution. The microviscoelastic loss modulus as determined from colloidal sphere thermal motion. The symbols denote the following temperatures: (▪) 31, (□) 30.75, (●) 30.62, (○) 30.5, (▲) 30.38, (△) 30.25, (◆) 30.12, (◊) 30, (◂) 27, and (◃) 23 °C.

Loss modulus of a 20 wt. % Pluronic F108 aqueous solution. The microviscoelastic loss modulus as determined from colloidal sphere thermal motion. The symbols denote the following temperatures: (▪) 31, (□) 30.75, (●) 30.62, (○) 30.5, (▲) 30.38, (△) 30.25, (◆) 30.12, (◊) 30, (◂) 27, and (◃) 23 °C.

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