cores. The kinetics was observed using a light scattering instrument at a fixed angle
θ ¼ 90
, thus limiting the experimental outcome to a net scattered intensity without
structural resolution in terms of the radius of gyration, R g , or similar quantities. For
micelle formation, the data were best fitted with a sum of two simple exponential
decay functions. The individual relaxation time constants, τ 1 and τ 2 , were not given
but an “average” value was defined by τ ¼ a 1 τ 1 + a 2 τ 2 where a 1 and a 2 ¼ 1 À a 1
are the normalized amplitudes. The mean relaxation time was found to be about
40 and 70 ms for the diblock and triblock copolymer micelles, respectively. For the
decomposition kinetics, the process was observed to be too fast for the diblock
copolymer (< 1 ms) whereas for the triblock copolymer micelle a mean relaxation
time of about 140 ms was found. Although a theoretical analysis was not performed,
the authors speculate that the finding of two relaxation times probably reflects a
continuous spectrum of relaxation times.
In a study by Kositza el al. [129] on Pluronic micelles, the kinetics was
investigated using both the laser temperature jump and a stopped-flow method. The
results after adding salt to a solution originally below cmt showed that micellization
could be induced. The associated intensity was characterized by a double or single
relaxation time constant depending on concentration. Despite the fact that the initial
conditions were completely different, the stopped-flow results seem to indicate a
terminal relaxation time similar to the T-jump experiments (τ 2 ) for certain
temperatures. No quantitative correspondence was found for the fast process. A
similar dependence, where τ 2 decreased with concentration, was observed and
interpreted as a redistribution process by which the micelles might undergo fusion
or fission.
Johnson and Prud’homme [174] investigated the micellization kinetics indirectly by applying an analytical confined impinging (CIJ) mixer to induce micelles
and studied the effect of the mixing speed on particle size ( a process coined “flash
nanoprecipitation”). By using poly(butyl acrylate)–poly(acrylic acid) (PBA-PAA)
diblock copolymers, the system could be molecularly dissolved in methanol. By
adding water, which is selective towards the PPA block, micelles can be induced.
Once formed, the micelles were expected to be kinetically frozen, i.e., further
ripening of the micelles was inhibited by the high interfacial tension and the
aggregates could be regarded as stable particles. By applying various mixing
times, τ mix , the supersaturation as well as the so-called Darmko ¨hler number were
varied. The latter is defined here as Da mixing time/micellization time, τ mix /τ mic .
The dependence of Da on concentration and mixing time is given in Fig. 34.
As can be seen from Fig. 34, below certain mixing times of between 20 and
60 ms, depending on concentration, the micellar dimensions were independent of
both mixing time and concentration. At the breakpoints, the characteristic time was
taken as the micellization time, hence Da 1. For Da > 1, the measured radii were
found to be a function of concentration [generally R ¼ R(conc)], as well as to
depend on τ mix . The latter regime is characterized by large inhomogeneities in the
solvent mixture that homogenize at time scales longer than the time it takes to form
the particles, i.e., the system can fuse and exchange unimers for a long time, leading
to larger particles. It is also likely that the particles in this regime would be much
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
139
θ ¼ 90
, thus limiting the experimental outcome to a net scattered intensity without
structural resolution in terms of the radius of gyration, R g , or similar quantities. For
micelle formation, the data were best fitted with a sum of two simple exponential
decay functions. The individual relaxation time constants, τ 1 and τ 2 , were not given
but an “average” value was defined by τ ¼ a 1 τ 1 + a 2 τ 2 where a 1 and a 2 ¼ 1 À a 1
are the normalized amplitudes. The mean relaxation time was found to be about
40 and 70 ms for the diblock and triblock copolymer micelles, respectively. For the
decomposition kinetics, the process was observed to be too fast for the diblock
copolymer (< 1 ms) whereas for the triblock copolymer micelle a mean relaxation
time of about 140 ms was found. Although a theoretical analysis was not performed,
the authors speculate that the finding of two relaxation times probably reflects a
continuous spectrum of relaxation times.
In a study by Kositza el al. [129] on Pluronic micelles, the kinetics was
investigated using both the laser temperature jump and a stopped-flow method. The
results after adding salt to a solution originally below cmt showed that micellization
could be induced. The associated intensity was characterized by a double or single
relaxation time constant depending on concentration. Despite the fact that the initial
conditions were completely different, the stopped-flow results seem to indicate a
terminal relaxation time similar to the T-jump experiments (τ 2 ) for certain
temperatures. No quantitative correspondence was found for the fast process. A
similar dependence, where τ 2 decreased with concentration, was observed and
interpreted as a redistribution process by which the micelles might undergo fusion
or fission.
Johnson and Prud’homme [174] investigated the micellization kinetics indirectly by applying an analytical confined impinging (CIJ) mixer to induce micelles
and studied the effect of the mixing speed on particle size ( a process coined “flash
nanoprecipitation”). By using poly(butyl acrylate)–poly(acrylic acid) (PBA-PAA)
diblock copolymers, the system could be molecularly dissolved in methanol. By
adding water, which is selective towards the PPA block, micelles can be induced.
Once formed, the micelles were expected to be kinetically frozen, i.e., further
ripening of the micelles was inhibited by the high interfacial tension and the
aggregates could be regarded as stable particles. By applying various mixing
times, τ mix , the supersaturation as well as the so-called Darmko ¨hler number were
varied. The latter is defined here as Da mixing time/micellization time, τ mix /τ mic .
The dependence of Da on concentration and mixing time is given in Fig. 34.
As can be seen from Fig. 34, below certain mixing times of between 20 and
60 ms, depending on concentration, the micellar dimensions were independent of
both mixing time and concentration. At the breakpoints, the characteristic time was
taken as the micellization time, hence Da 1. For Da > 1, the measured radii were
found to be a function of concentration [generally R ¼ R(conc)], as well as to
depend on τ mix . The latter regime is characterized by large inhomogeneities in the
solvent mixture that homogenize at time scales longer than the time it takes to form
the particles, i.e., the system can fuse and exchange unimers for a long time, leading
to larger particles. It is also likely that the particles in this regime would be much
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
139