Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods

  • Reidar LundEmail author
  • Lutz WillnerEmail author
  • Dieter Richter
Part of the Advances in Polymer Science book series (POLYMER, volume 259)


This article reviews recent progress in studying the kinetics of block copolymer micellar systems by time-resolved small angle scattering techniques. The review includes an overview of the theoretical background concerning block copolymer micellar structure and kinetics, with a clear distinction between equilibrium and non-equilibrium processes. Basic principles of both static and time-resolved small-angle X-ray and neutron scattering (TR-SAXS and TR-SANS) techniques are summarized, with a special emphasis on the characterization of block copolymer micellar systems. In particular, the principle of SANS in combination with hydrogen/deuterium (H/D) contrast variation for the determination of chain exchange under equilibrium conditions is highlighted. In the experimental part, we first review results on equilibrium kinetics obtained within the last decade by the TR-SANS/H/D labeling technique. In general, the experimental results strongly indicate that the component exchange between different micelles proceeds via the exchange of single unimers. In agreement with the theoretical prediction, chain expulsion is the rate-determining step. The corresponding activation energy is mainly governed by the interfacial tension and the length of the insoluble block, which determine the exchange rate with a double exponential dependence. Thus, due to this extremely strong dependence, even synthetic polymers with modest chain length distribution show a logarithmic time dependence instead of the theoretically expected single exponential decay. In the second part, the kinetic results obtained under non-equilibrium conditions, i.e., relaxation processes obtained after perturbations from equilibrium, are reviewed. This part covers formation kinetics as well as reorganization and morphological transition kinetics. We present, as a special highlight, TR-SAXS 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.


Block copolymer micelles Contrast variation Equilibrium and non-equilibrium kinetics Morphology Small-angle neutron and X-ray scattering Time-resolved SAXS/SANS 


\( \frac{{\mathrm{ d}\varSigma }}{{\mathrm{ d}\varOmega }} \)

Macroscopic differential scattering cross-section per unit volume in cm−1

\( k_p^{+} \)

Rate constant for unimer insertion from micelle of size P

\( k_p^{-} \)

Rate constant for unimer expulsion from micelle of size P

|Q| = Q

Scattering vector in Å−1




Elementary lattice size


Scattering amplitude in cm

A2, A3

Second and third virial coeffcient


Scattering length in cm


Numerical prefactors


Density in g/cm3


Diffusion coefficient


Fractal dimension


Activation energy


Free energy


Ratio between degree of polymerization of soluble and insoluble block


The mixing term of free block copolymers and solvent


Free energy of mixing

G(P, ϕ1)

Chemical potential




Flux of unimers to micelle of size P


Boltzmann constant: 1.38 × 10−23 J/K


Cylinder length in Å


Monomer segment length of block i


Weight average molecular weight in g/mole


Density profile


Degree of polymerization of soluble block


Avogadro’s number: 6.022 × 1023 mole−1


Degree of polymerization of insoluble block


Total particle number


Micellar aggregation number


Form factor


Relaxation function (TR-SANS)


Micellar core radius in Å


Radius of gyration


Total micellar radius in Å


Grafting density (area available per chain)


Structure factor


Translational entropy of micelles


Dead time of mixing


Flory exponent


Volume of component i


Sample volume in cm3


Interfacial tension in mN/m


Fraction of block copolymer in the micellar state


Corona density


Blob radius/correlation length


Scattering length density in cm−2


Gaussian width of core–corona interface


Smearing parameter for micellar radius


Slow relaxation time (Aniansson and Wall)


Fast relaxation time (Aniansson and Wall)


Solvent fraction in micellar core


Total amphiphile volume fraction


Unimer concentration


Concentration of micelle of size p


Flory–Huggins interaction parameter



The authors are thankful to all colleagues on the beamlines, in particular Dr. Peter Lindner, Dr. Isabelle Grillo, Dr. Vitaliy Pipich, Dr. Aurel Radulescu, Dr. Theyencheri Narayanan, and Dr. Jeremie Gummel for fruitful collaborations. We are also indebted to Dr. Michael Monkenbusch, Dr. Jörg Stellbrink, and Thomas Zinn for numerous fruitful discussions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of OsloOsloNorway
  2. 2.Jülich Centre for Neutron Science JCNS and Institute for Complex Systems ICSForschungszentrum Jülich GmbHJülichGermany

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