stopped-flow apparatus. Typical time-resolved scattering curves were obtained using
a high-brilliance synchrotron SAXS instrument (ID02, at the European Synchrotron
Radiation Facility, ESRF) and show the increase in scattered intensity associated with
the formation of micelles (see Fig. 36a). The scattering could be described with a
core–shell micellar scattering model (c.f. Sect. 3.1.6), thereby allowing the extraction
of detailed parameters of the internal structure of the micelles at all times.
Fig. 36b shows the aggregation number, P mean , plotted against the corresponding
thickness of the micellar corona, R corona ¼ R m À R c for three concentrations in a
double logarithmic representation. The data agree well with the prediction [38, 40]:
R corona $ P
1=5
mean expected for star-like micelles. The results thus show that the
micelles grow like well-defined star-like micellar entities. No regime where the
size grows faster than the molecular weight, which was observed on a less
segregated system by Honda et al. [169], were observed in this case. This probably
reflects the fact that the initial time range of the micellization in this is too fast to be
captured (t < 2–3 ms). Also, for star-like micelles only a few chains are necessary
to achieve a star-like structure [38].
The time dependence of the aggregation number, P mean , deduced from the
core–shell model fits (Sect. 3.1.6) for three concentrations, is given in Fig. 37.
The observed growth behavior shown in Fig. 37 could be approximately fitted
using a phenomenological model in the form of a stretched exponential P mean
% 1 – exp[À(kt)
β ]. This yields in all cases an exponent β of about 0.2. A trial fit to
a sum of two exponentials did not give satisfactory fits, in contrast to other results
[169, 171, 176]. The broad relaxation suggests an intrinsically broadly distributed
kinetic growth process that cannot be described with a finite number (typically
1–3) of relaxation times An approximate two-exponential behavior is expected
for micelle relaxation kinetics after a sudden external disturbance, but only very
close to equilibrium [55, 60] that is not the case for micellization kinetics
observed deep in the micelle region. The data at the shortest times suggest the
existence of a fast initial aggregation (t < %5 ms) that cannot be entirely resolved
experimentally. This process seems to become exhausted at intermediate times
leading to a “shoulder” of P mean that changes with concentration. The terminal
relaxation towards a common equilibrium then appears to slow down with time,
the overall rate increasing with concentration.
The concentration dependence of the terminal relaxation has been observed
earlier in light scattering experiments and sometimes qualitatively attributed to
fusion/fission processes [176]. In [183], however, the relaxation curves could be
described using the nucleation and growth model highlighted in Sect. 2.3.3 where
growth was only allowed to occur unitarily through unimer exchange kinetics. The
corresponding size distribution extracted from the fits are displayed in Fig. 38.
The size distribution of micelles gives a very detailed view of the micellization
process. Extracted parameters such as the unimer concentration and the Gaussian
width are correlated with the mean aggregation number, giving a complete view of
the process in Fig. 38b. The results reveal the following scenario: First, the initial free
unimers are consumed rapidly in a nucleation-like event that leads to the formation of
144
R. Lund et al.
a high-brilliance synchrotron SAXS instrument (ID02, at the European Synchrotron
Radiation Facility, ESRF) and show the increase in scattered intensity associated with
the formation of micelles (see Fig. 36a). The scattering could be described with a
core–shell micellar scattering model (c.f. Sect. 3.1.6), thereby allowing the extraction
of detailed parameters of the internal structure of the micelles at all times.
Fig. 36b shows the aggregation number, P mean , plotted against the corresponding
thickness of the micellar corona, R corona ¼ R m À R c for three concentrations in a
double logarithmic representation. The data agree well with the prediction [38, 40]:
R corona $ P
1=5
mean expected for star-like micelles. The results thus show that the
micelles grow like well-defined star-like micellar entities. No regime where the
size grows faster than the molecular weight, which was observed on a less
segregated system by Honda et al. [169], were observed in this case. This probably
reflects the fact that the initial time range of the micellization in this is too fast to be
captured (t < 2–3 ms). Also, for star-like micelles only a few chains are necessary
to achieve a star-like structure [38].
The time dependence of the aggregation number, P mean , deduced from the
core–shell model fits (Sect. 3.1.6) for three concentrations, is given in Fig. 37.
The observed growth behavior shown in Fig. 37 could be approximately fitted
using a phenomenological model in the form of a stretched exponential P mean
% 1 – exp[À(kt)
β ]. This yields in all cases an exponent β of about 0.2. A trial fit to
a sum of two exponentials did not give satisfactory fits, in contrast to other results
[169, 171, 176]. The broad relaxation suggests an intrinsically broadly distributed
kinetic growth process that cannot be described with a finite number (typically
1–3) of relaxation times An approximate two-exponential behavior is expected
for micelle relaxation kinetics after a sudden external disturbance, but only very
close to equilibrium [55, 60] that is not the case for micellization kinetics
observed deep in the micelle region. The data at the shortest times suggest the
existence of a fast initial aggregation (t < %5 ms) that cannot be entirely resolved
experimentally. This process seems to become exhausted at intermediate times
leading to a “shoulder” of P mean that changes with concentration. The terminal
relaxation towards a common equilibrium then appears to slow down with time,
the overall rate increasing with concentration.
The concentration dependence of the terminal relaxation has been observed
earlier in light scattering experiments and sometimes qualitatively attributed to
fusion/fission processes [176]. In [183], however, the relaxation curves could be
described using the nucleation and growth model highlighted in Sect. 2.3.3 where
growth was only allowed to occur unitarily through unimer exchange kinetics. The
corresponding size distribution extracted from the fits are displayed in Fig. 38.
The size distribution of micelles gives a very detailed view of the micellization
process. Extracted parameters such as the unimer concentration and the Gaussian
width are correlated with the mean aggregation number, giving a complete view of
the process in Fig. 38b. The results reveal the following scenario: First, the initial free
unimers are consumed rapidly in a nucleation-like event that leads to the formation of
144
R. Lund et al.