exchange as the dominant mechanism for chain exchange in agreement with the
theoretical picture of Halperin and Alexander. Exchange due to other mechanisms,
e.g., fusion/fission or fragmentation/defragmentation, if at all existent can play only
a minor role because they would show a clear concentration dependence.
Recently, Choi et al. [152] measured the molecular exchange in ordered diblock
copolymer micelles, employing the same PS-PEP micelles in squalane as already
studied before in dilute solution by TR-SANS. At 15% polymer volume fraction,
the spherical micelles are packed on body centered cubic (bcc) lattices. Individual
micellar solution with 15 vol% of h-PS-PEP or d-PS-PEP were annealed far above
T g , resulting in soft solids after cooling to room temperature. Blending of the soft
solids on a nanoscale level with a complete statistical arrangement of micelles was
achieved by a special cup-rotor mixer device [94]. The efficiency of this technique
was demonstrated by a combination of SANS and SAXS measurements. While the
SAXS data confirmed the bcc structure of the mixture, the SANS data showed the
single micellar form factor since intraparticle contributions were canceled out due
to the applied ZAC. Notable was the observation that in comparison to dilute
solution, individual micelles had increased aggregation numbers and core radii.
This was attributed to the system’s tendency to avoid energetically unfavorable
corona overlap by reducing the number density of micelles, as discussed in the
mean-field model of Grason [164]. The kinetic studies were carried out at different
temperatures above the glass transition of PS in an isotopic mixtures of squalane
(T g % 70
C). In order to account for the temperature dependence, individual master
curves were derived by the principle of time–temperature superposition. A comparison of the master curves at dilute solution and at 15% polymer volume fraction
are shown in Fig. 29 at a reference temperature T ref ¼ 110
C for PS-PEP-1 and
T ref ¼ 145
C for PS-PEP-2. We note that time-temperature superposition for the
higher concentrations does not work as well as for the dilute solutions. The data do
not exactly superimpose by using the shift factors, a T , shown in the inset of Fig. 29.
Nevertheless, the obtained curves show the typical logarithmic time decay consistent with the finding at dilute solution. The relaxation curves obtained for the soft
solids are, however, shifted to longer times by more than one order of magnitude.
Because of the logarithmic form of R(t), the molecular exchange kinetics could be
described by the same theoretical model as already used for the dilute solutions (see
Eqs. 119, 120, and 121). Reasonable fits were obtained by increasing the activation
barrier through an increase in the parameter αχ and by slightly adjusting the
polydispersity of the core block.
The authors postulated several reasons for the slowing down of the exchange rate
at higher concentrations. These include weaker mobility arising from a higher glass
transition of the core polymer. A higher T g was assumed because the tendency of
solvent to penetrate the core is reduced at higher block copolymer concentration.
However, this effect was considered to be too small to account for the dramatic
change observed for the chain exchange dynamics. It was also suggested that
increased core chain stretching arising from increased micellar sizes in the bcc
state could lead to altered Rouse dynamics. It was, however, estimated that core
block stretching cannot be so significant in the low entanglement regime to
reasonably explain the slowdown of the kinetics. As the most probable explanation,
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
129
theoretical picture of Halperin and Alexander. Exchange due to other mechanisms,
e.g., fusion/fission or fragmentation/defragmentation, if at all existent can play only
a minor role because they would show a clear concentration dependence.
Recently, Choi et al. [152] measured the molecular exchange in ordered diblock
copolymer micelles, employing the same PS-PEP micelles in squalane as already
studied before in dilute solution by TR-SANS. At 15% polymer volume fraction,
the spherical micelles are packed on body centered cubic (bcc) lattices. Individual
micellar solution with 15 vol% of h-PS-PEP or d-PS-PEP were annealed far above
T g , resulting in soft solids after cooling to room temperature. Blending of the soft
solids on a nanoscale level with a complete statistical arrangement of micelles was
achieved by a special cup-rotor mixer device [94]. The efficiency of this technique
was demonstrated by a combination of SANS and SAXS measurements. While the
SAXS data confirmed the bcc structure of the mixture, the SANS data showed the
single micellar form factor since intraparticle contributions were canceled out due
to the applied ZAC. Notable was the observation that in comparison to dilute
solution, individual micelles had increased aggregation numbers and core radii.
This was attributed to the system’s tendency to avoid energetically unfavorable
corona overlap by reducing the number density of micelles, as discussed in the
mean-field model of Grason [164]. The kinetic studies were carried out at different
temperatures above the glass transition of PS in an isotopic mixtures of squalane
(T g % 70
C). In order to account for the temperature dependence, individual master
curves were derived by the principle of time–temperature superposition. A comparison of the master curves at dilute solution and at 15% polymer volume fraction
are shown in Fig. 29 at a reference temperature T ref ¼ 110
C for PS-PEP-1 and
T ref ¼ 145
C for PS-PEP-2. We note that time-temperature superposition for the
higher concentrations does not work as well as for the dilute solutions. The data do
not exactly superimpose by using the shift factors, a T , shown in the inset of Fig. 29.
Nevertheless, the obtained curves show the typical logarithmic time decay consistent with the finding at dilute solution. The relaxation curves obtained for the soft
solids are, however, shifted to longer times by more than one order of magnitude.
Because of the logarithmic form of R(t), the molecular exchange kinetics could be
described by the same theoretical model as already used for the dilute solutions (see
Eqs. 119, 120, and 121). Reasonable fits were obtained by increasing the activation
barrier through an increase in the parameter αχ and by slightly adjusting the
polydispersity of the core block.
The authors postulated several reasons for the slowing down of the exchange rate
at higher concentrations. These include weaker mobility arising from a higher glass
transition of the core polymer. A higher T g was assumed because the tendency of
solvent to penetrate the core is reduced at higher block copolymer concentration.
However, this effect was considered to be too small to account for the dramatic
change observed for the chain exchange dynamics. It was also suggested that
increased core chain stretching arising from increased micellar sizes in the bcc
state could lead to altered Rouse dynamics. It was, however, estimated that core
block stretching cannot be so significant in the low entanglement regime to
reasonably explain the slowdown of the kinetics. As the most probable explanation,
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
129