with repetitive real-time data acquisition was not available at neutron research
facilities at that time. Application of the stopped-flow mixing technique would most
likely also allow resolving kinetics at 50% DMF by TR-SANS.
4.2.4 Equilibrium Kinetics in Water/DMF Mixtures:
Logarithmic Relaxation
The relaxation functions, R(t), of the TR-SANS experiments were quantitatively
determined as described in Sect. 3.2.2. For the PEP5-PEO15 block copolymer
micelles, R(t) could be acceptably fitted by a sum of two exponentials. This was
interpreted by the existence of two well-separated processes in time in strict conflict
to the single exponential expected from the Halperin and Alexander [60] model.
The activation energies of 29 KJ/mol for the slow and 12.2 KJ/mol for the fast
process were deduced from Arrhenius plots. By estimation of the activation energy
following the concepts of the scaling theory [60], the fast process was assigned to
the unimer release. There was, however, no explanation for the existence of the
second slow process. Different scenarios for the occurrence of two relaxation
processes were discussed, including unimer diffusion between micelles, an isotope
effect for the surface tension, the existence of two different species, and aggregation
that supports fast exchange and slow rearrangement of the micelles. However, none
of them could offer an explanation with a clear physical picture. Thus, the origin of
the second slow process remained an open question. Double exponential time
decays were also reported from TR-fluorescence measurements on various systems
with characteristic rate constants well separated in time [118–120, 122]. This
apparent bimodal distribution was either assigned to the presence of bulky labels
[118, 122] or to competing chain transfer by micellar collision [120]. It should be
pointed out that processes running in parallel, e.g., unimer exchange via micellar
collision, just add to a single faster rate that still yields single exponential mixing:
R(t) % exp (À (k 1 + k 2 )t) and, consequently, cannot a priori be identified by the
applied labeling techniques.
In continuation of the kinetic study of PEP5-PEO15 micelles, the relaxation
functions of PEP1-PEO20 star-like micelles in water/DMF mixtures with 25 and
30% DMF were determined. Similarly to the PEP5-PEO15/DMF system, slow and
heterogeneous kinetics were observed in this case but, in contrast, trial fits using a
sum of two exponentials did not produce any satisfactory results. Therefore, it was
more reasonable to assume a distribution of relaxation rates to describe the kinetics
in PEP1-PEO20/water/DMF systems. Furthermore, as there was no explanation for
the existence of two processes and no exclusive fits were performed, it was
concluded that in the previous works the double exponential was more an approximation of a continuous distribution of relaxation rates. As a first obvious reason,
a chain length distribution (polydispersity) of the core-forming polymer was taken
into account since the rate constants exponentially depend on the activation energy,
E a , which in the Halperin and Alexander model is given by E a $ N
2=3
B Á γ Á l
2 .
120
R. Lund et al.
facilities at that time. Application of the stopped-flow mixing technique would most
likely also allow resolving kinetics at 50% DMF by TR-SANS.
4.2.4 Equilibrium Kinetics in Water/DMF Mixtures:
Logarithmic Relaxation
The relaxation functions, R(t), of the TR-SANS experiments were quantitatively
determined as described in Sect. 3.2.2. For the PEP5-PEO15 block copolymer
micelles, R(t) could be acceptably fitted by a sum of two exponentials. This was
interpreted by the existence of two well-separated processes in time in strict conflict
to the single exponential expected from the Halperin and Alexander [60] model.
The activation energies of 29 KJ/mol for the slow and 12.2 KJ/mol for the fast
process were deduced from Arrhenius plots. By estimation of the activation energy
following the concepts of the scaling theory [60], the fast process was assigned to
the unimer release. There was, however, no explanation for the existence of the
second slow process. Different scenarios for the occurrence of two relaxation
processes were discussed, including unimer diffusion between micelles, an isotope
effect for the surface tension, the existence of two different species, and aggregation
that supports fast exchange and slow rearrangement of the micelles. However, none
of them could offer an explanation with a clear physical picture. Thus, the origin of
the second slow process remained an open question. Double exponential time
decays were also reported from TR-fluorescence measurements on various systems
with characteristic rate constants well separated in time [118–120, 122]. This
apparent bimodal distribution was either assigned to the presence of bulky labels
[118, 122] or to competing chain transfer by micellar collision [120]. It should be
pointed out that processes running in parallel, e.g., unimer exchange via micellar
collision, just add to a single faster rate that still yields single exponential mixing:
R(t) % exp (À (k 1 + k 2 )t) and, consequently, cannot a priori be identified by the
applied labeling techniques.
In continuation of the kinetic study of PEP5-PEO15 micelles, the relaxation
functions of PEP1-PEO20 star-like micelles in water/DMF mixtures with 25 and
30% DMF were determined. Similarly to the PEP5-PEO15/DMF system, slow and
heterogeneous kinetics were observed in this case but, in contrast, trial fits using a
sum of two exponentials did not produce any satisfactory results. Therefore, it was
more reasonable to assume a distribution of relaxation rates to describe the kinetics
in PEP1-PEO20/water/DMF systems. Furthermore, as there was no explanation for
the existence of two processes and no exclusive fits were performed, it was
concluded that in the previous works the double exponential was more an approximation of a continuous distribution of relaxation rates. As a first obvious reason,
a chain length distribution (polydispersity) of the core-forming polymer was taken
into account since the rate constants exponentially depend on the activation energy,
E a , which in the Halperin and Alexander model is given by E a $ N
2=3
B Á γ Á l
2 .
120
R. Lund et al.