Interestingly, the study showed that both the fluorescence and light scattering
signals exhibited a similar single exponential growth law, with a relaxation time of
about 0.1–1 ms after a temperature jump ΔT % 1 K close to the cmt. A single time
constant was interpreted in terms of the unimer insertion rate constant, k + , and
discussed within the Aniansson and Wall theory (c.f. Sect. 2.2.5). The absence of a
slower relaxation process could be related to a restricted total time interval of only
100 ms.
Other Temperature-Jump Studies
The temperature jumps achieved by lasers and capacitor discharge Joule heating are
usually very small; of the order of some few degrees Kelvin, limiting the techniques
to marginally segregated systems close to cmt. In addition, the temperature will
typically follow a pulse-like time dependence and will decay to the initial temperature after a relative short time (typically 100 ms [171]) due to energy dissipation.
An alternative method can overcome this problem by using a stopped-flow apparatus with a rapid mixing temperature jump system (mT-Jump from BioLogic
Scientific Instruments, France). This set-up achieves temperature changes by
mixing two solutions of different initial temperatures T 1 and T 2 . The final temperature of the mixture (T 3 ) is calculated from the initial temperatures and the mixing
ratio of the two solutions and can be kept stable over a long period after mixing. In
this way, the initial solution can be quenched rapidly through fast mixing to a
different temperature with relatively large temperature jumps, ΔT.
Liu and coworkers employed this method to study the micellization kinetics of a
double hydrophilic diblock poly(N-isopropylacrylamide)–poly(2-diethylamino ethyl
methacrylate) (PNIPAM-PDEA) in aqueous solution [172]. The results obtained after
a temperature jump from 20
C (unimers) to different final temperatures are shown in
Fig. 33.
As seen in Fig. 33, the micellization occurs increasingly rapidly with the amplitude for moderate ΔT, reflecting deeper quench and thus increasingly unstable
unimers. For the largest ΔT, the intensity is smaller and the terminal relaxation is
actually slower than for the lower temperatures. This might indicate that the micelles
are trapped in smaller aggregates and the terminal kinetics is slower at higher
temperatures where the segregation between the core PNIPAM block and the solvent
is larger. Interestingly, at intermediate ΔT the size of the initial micelles are larger
than the terminal ones. The resulting intensity curves (reflecting both a change in
aggregation number and number of micelles as well as distribution) could be tentatively fitted to a double exponential growth model. The fit results show that the fast
relaxation time (τ 1 ) decreased with the micellar concentration while the second,
slower relaxation time, τ 2 , was found to be virtually independent of the concentration,
in line with the observations by Honda et al. [169]. The results were discussed in
terms of a dominating unimer exchange mechanism.
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
137
signals exhibited a similar single exponential growth law, with a relaxation time of
about 0.1–1 ms after a temperature jump ΔT % 1 K close to the cmt. A single time
constant was interpreted in terms of the unimer insertion rate constant, k + , and
discussed within the Aniansson and Wall theory (c.f. Sect. 2.2.5). The absence of a
slower relaxation process could be related to a restricted total time interval of only
100 ms.
Other Temperature-Jump Studies
The temperature jumps achieved by lasers and capacitor discharge Joule heating are
usually very small; of the order of some few degrees Kelvin, limiting the techniques
to marginally segregated systems close to cmt. In addition, the temperature will
typically follow a pulse-like time dependence and will decay to the initial temperature after a relative short time (typically 100 ms [171]) due to energy dissipation.
An alternative method can overcome this problem by using a stopped-flow apparatus with a rapid mixing temperature jump system (mT-Jump from BioLogic
Scientific Instruments, France). This set-up achieves temperature changes by
mixing two solutions of different initial temperatures T 1 and T 2 . The final temperature of the mixture (T 3 ) is calculated from the initial temperatures and the mixing
ratio of the two solutions and can be kept stable over a long period after mixing. In
this way, the initial solution can be quenched rapidly through fast mixing to a
different temperature with relatively large temperature jumps, ΔT.
Liu and coworkers employed this method to study the micellization kinetics of a
double hydrophilic diblock poly(N-isopropylacrylamide)–poly(2-diethylamino ethyl
methacrylate) (PNIPAM-PDEA) in aqueous solution [172]. The results obtained after
a temperature jump from 20
C (unimers) to different final temperatures are shown in
Fig. 33.
As seen in Fig. 33, the micellization occurs increasingly rapidly with the amplitude for moderate ΔT, reflecting deeper quench and thus increasingly unstable
unimers. For the largest ΔT, the intensity is smaller and the terminal relaxation is
actually slower than for the lower temperatures. This might indicate that the micelles
are trapped in smaller aggregates and the terminal kinetics is slower at higher
temperatures where the segregation between the core PNIPAM block and the solvent
is larger. Interestingly, at intermediate ΔT the size of the initial micelles are larger
than the terminal ones. The resulting intensity curves (reflecting both a change in
aggregation number and number of micelles as well as distribution) could be tentatively fitted to a double exponential growth model. The fit results show that the fast
relaxation time (τ 1 ) decreased with the micellar concentration while the second,
slower relaxation time, τ 2 , was found to be virtually independent of the concentration,
in line with the observations by Honda et al. [169]. The results were discussed in
terms of a dominating unimer exchange mechanism.
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
137