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

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

Abstract

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.

Keywords

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

Symbols

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

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

A

Area

a

Elementary lattice size

A(Q)

Scattering amplitude in cm

A2, A3

Second and third virial coeffcient

b

Scattering length in cm

CF, CH

Numerical prefactors

d

Density in g/cm3

D

Diffusion coefficient

df

Fractal dimension

Ea

Activation energy

F

Free energy

f

Ratio between degree of polymerization of soluble and insoluble block

Fmicelle

The mixing term of free block copolymers and solvent

Fmix

Free energy of mixing

G(P, ϕ1)

Chemical potential

H/D

Hydrogen/deuterium

jP

Flux of unimers to micelle of size P

kB

Boltzmann constant: 1.38 × 10−23 J/K

L

Cylinder length in Å

li

Monomer segment length of block i

Mw

Weight average molecular weight in g/mole

n(r)

Density profile

NA

Degree of polymerization of soluble block

NAvo

Avogadro’s number: 6.022 × 1023 mole−1

NB

Degree of polymerization of insoluble block

Nm

Total particle number

P

Micellar aggregation number

P(Q)

Form factor

R(t)

Relaxation function (TR-SANS)

Rc

Micellar core radius in Å

Rg

Radius of gyration

Rm

Total micellar radius in Å

s

Grafting density (area available per chain)

S(Q)

Structure factor

Sm

Translational entropy of micelles

tdead

Dead time of mixing

v

Flory exponent

Vi

Volume of component i

Vs

Sample volume in cm3

γ

Interfacial tension in mN/m

ζ

Fraction of block copolymer in the micellar state

η

Corona density

ξ

Blob radius/correlation length

ρ

Scattering length density in cm−2

σint

Gaussian width of core–corona interface

σm

Smearing parameter for micellar radius

τ1

Slow relaxation time (Aniansson and Wall)

τ2

Fast relaxation time (Aniansson and Wall)

Φ0

Solvent fraction in micellar core

ϕ0

Total amphiphile volume fraction

ϕ1

Unimer concentration

Φp

Concentration of micelle of size p

χ

Flory–Huggins interaction parameter

Notes

Acknowledgements

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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