measurements with millisecond resolution on the formation of star-like micelles after
stopped-flow mixing of molecularly dissolved block copolymers with a selective
solvent. The micellization process could be modelled as a nucleation & growth
process with unimer exchange as the elemental mechanism. The resulting scenario
could be described as a three step process that includes a fast nucleation event, a
region of micellar growth, and a final equilibration to thermodynamically stable
micelles. In summary, this review demonstrates the importance of small angle
scattering techniques for studying fundamental aspects of kinetics in block copolymer
micelles and in soft matter materials in general.
Keywords Block copolymer micelles Á Contrast variation Á Equilibrium and nonequilibrium kinetics Á Morphology Á Small-angle neutron and X-ray scattering Á
Time-resolved SAXS/SANS
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.1 Structure and Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2 Chain Exchange Kinetics in Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 Non-equilibrium Micellization Kinetics . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . 77
3 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.1 Small-Angle Scattering Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2 Time-Resolved Small-Angle Scattering as a Technique for Studying Micellar
Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Equilibrium Kinetics in Block Copolymer Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.1 Quasi-equilibrium Kinetics of PEO-PPO-PEO in Temperature-Jump Experiments 110
4.2 PEP-PEO Block Copolymers in Aqueous Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3 Block Copolymer Micelles in Organic Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 n-Alkyl-PEO Polymeric Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.5 Chain Exchange in Soft Solids: Effect of Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.6 Cylinders Versus Spheres: Effect of Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 Non-equilibrium Kinetics in Block Copolymer Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Formation and Micellization Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 Morphological Transition Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6 Concluding Remarks and Future Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 152
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Symbols
dΣ
dΩ
Macroscopic differential scattering cross-section per unit volume
in cm
À1
k
þ
p
Rate constant for unimer insertion from micelle of size P
k
À
p
Rate constant for unimer expulsion from micelle of size P
52
R. Lund et al.
stopped-flow mixing of molecularly dissolved block copolymers with a selective
solvent. The micellization process could be modelled as a nucleation & growth
process with unimer exchange as the elemental mechanism. The resulting scenario
could be described as a three step process that includes a fast nucleation event, a
region of micellar growth, and a final equilibration to thermodynamically stable
micelles. In summary, this review demonstrates the importance of small angle
scattering techniques for studying fundamental aspects of kinetics in block copolymer
micelles and in soft matter materials in general.
Keywords Block copolymer micelles Á Contrast variation Á Equilibrium and nonequilibrium kinetics Á Morphology Á Small-angle neutron and X-ray scattering Á
Time-resolved SAXS/SANS
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.1 Structure and Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2 Chain Exchange Kinetics in Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 Non-equilibrium Micellization Kinetics . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . 77
3 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.1 Small-Angle Scattering Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2 Time-Resolved Small-Angle Scattering as a Technique for Studying Micellar
Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Equilibrium Kinetics in Block Copolymer Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.1 Quasi-equilibrium Kinetics of PEO-PPO-PEO in Temperature-Jump Experiments 110
4.2 PEP-PEO Block Copolymers in Aqueous Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3 Block Copolymer Micelles in Organic Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 n-Alkyl-PEO Polymeric Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.5 Chain Exchange in Soft Solids: Effect of Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.6 Cylinders Versus Spheres: Effect of Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 Non-equilibrium Kinetics in Block Copolymer Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Formation and Micellization Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 Morphological Transition Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6 Concluding Remarks and Future Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 152
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Symbols
dΣ
dΩ
Macroscopic differential scattering cross-section per unit volume
in cm
À1
k
þ
p
Rate constant for unimer insertion from micelle of size P
k
À
p
Rate constant for unimer expulsion from micelle of size P
52
R. Lund et al.