4.2.2 Equilibrium Kinetics in Pure Water: Frozen Micelles
Time-resolved SANS experiments using the H/D contrast scheme (KZAC) described
in Sect. 3.1.7 were first carried out on a PEP5-PEO15 block copolymer in water for
the determination of the unimer exchange kinetics [100]. However, there was no
decrease in intensity observable even at high temperatures and long time scales,
leading to the conclusion that the micelles are kinetically frozen due to the high
interfacial tension between PEP and water. The kinetics of star-like micelles formed
by a PEP1-PEO20 block copolymer with large compositional asymmetry and a short
core-forming PEP block was investigated by Lund et al. [101, 102]. Analogous to the
PEP5-PEO15 system, the TR-SANS experiment does not reveal any exchange of
polymers over an extended period of time and increased temperature. This becomes
obvious from Fig. 21 where SANS curves from the corresponding kinetic experiment
are shown. Before mixing, typical form factors of star-like micelles were obtained.
For better visibility, the arithmetic mean of the almost identical individual scattering
curves of the labeled micelles are shown. This curve has a shallow maximum at low
Q as a characteristic feature of a structure factor at 1% polymer volume fraction.
After mixing the two differently labeled micellar solutions, the maximum disappears
as a natural consequence of the ZAC condition. Details of the scattering behavior
under ZAC are described in more detail in Sect. 3.2.2. However, the main result of
this experiment is the fact that the intensity after mixing stays constant over an
extended period of time, even at elevated temperatures. From this observation it was
concluded that micelles are effectively frozen since due to chain exchange the
intensity was expected to approach the intensity of the blend sample, depicted as
black squares in Fig. 21. The blend sample consists of a random mixture of
h-PEP1–h-PEO20 and d-PEP1–d-PEO20, providing the smallest contrast identical
to the contrast of the final state of the kinetics after infinitely long time. A similar
observation was made by Won, Davis, and Bates [146], who attempted to observe
mixing kinetics or component exchange kinetics of PB-PEO micelles in water. Their
experiment relied on differences in the SANS profiles of two block copolymers
forming spherical or cylindrical micelles. Within a time period of 8 days, the
scattering profile of a post-mixed specimen did not approach the profile of a premixed
sample but rather resembled a superposition of the two micellar reservoirs. The
structure of the premixed sample was expected to be the final structure in the case
where chain exchange would lead to a reorganization of the micellar morphology. As
this was not observed the authors concluded that the structure of the micelles that
were initially formed upon dissolution were completely locked-in due to the effect of
strong amphiphilicity. In a subsequent study, Jain and Bates [6] examined binary
blends of PB-PEO block copolymers of different molecular weight and composition
forming either spheres, cylinders, or bilayers using cryo-transmission electron
microscopy (cryo-TEM). In agreement with the reorganization study by SANS, the
cryo-TEM showed no perceptible chain exchange between aggregates over a long
period of time, resulting in a non-ergodic state where equilibrium is never reached.
The failure to globally equilibrate is already evident at molecular weights as small as
116
R. Lund et al.
Time-resolved SANS experiments using the H/D contrast scheme (KZAC) described
in Sect. 3.1.7 were first carried out on a PEP5-PEO15 block copolymer in water for
the determination of the unimer exchange kinetics [100]. However, there was no
decrease in intensity observable even at high temperatures and long time scales,
leading to the conclusion that the micelles are kinetically frozen due to the high
interfacial tension between PEP and water. The kinetics of star-like micelles formed
by a PEP1-PEO20 block copolymer with large compositional asymmetry and a short
core-forming PEP block was investigated by Lund et al. [101, 102]. Analogous to the
PEP5-PEO15 system, the TR-SANS experiment does not reveal any exchange of
polymers over an extended period of time and increased temperature. This becomes
obvious from Fig. 21 where SANS curves from the corresponding kinetic experiment
are shown. Before mixing, typical form factors of star-like micelles were obtained.
For better visibility, the arithmetic mean of the almost identical individual scattering
curves of the labeled micelles are shown. This curve has a shallow maximum at low
Q as a characteristic feature of a structure factor at 1% polymer volume fraction.
After mixing the two differently labeled micellar solutions, the maximum disappears
as a natural consequence of the ZAC condition. Details of the scattering behavior
under ZAC are described in more detail in Sect. 3.2.2. However, the main result of
this experiment is the fact that the intensity after mixing stays constant over an
extended period of time, even at elevated temperatures. From this observation it was
concluded that micelles are effectively frozen since due to chain exchange the
intensity was expected to approach the intensity of the blend sample, depicted as
black squares in Fig. 21. The blend sample consists of a random mixture of
h-PEP1–h-PEO20 and d-PEP1–d-PEO20, providing the smallest contrast identical
to the contrast of the final state of the kinetics after infinitely long time. A similar
observation was made by Won, Davis, and Bates [146], who attempted to observe
mixing kinetics or component exchange kinetics of PB-PEO micelles in water. Their
experiment relied on differences in the SANS profiles of two block copolymers
forming spherical or cylindrical micelles. Within a time period of 8 days, the
scattering profile of a post-mixed specimen did not approach the profile of a premixed
sample but rather resembled a superposition of the two micellar reservoirs. The
structure of the premixed sample was expected to be the final structure in the case
where chain exchange would lead to a reorganization of the micellar morphology. As
this was not observed the authors concluded that the structure of the micelles that
were initially formed upon dissolution were completely locked-in due to the effect of
strong amphiphilicity. In a subsequent study, Jain and Bates [6] examined binary
blends of PB-PEO block copolymers of different molecular weight and composition
forming either spheres, cylinders, or bilayers using cryo-transmission electron
microscopy (cryo-TEM). In agreement with the reorganization study by SANS, the
cryo-TEM showed no perceptible chain exchange between aggregates over a long
period of time, resulting in a non-ergodic state where equilibrium is never reached.
The failure to globally equilibrate is already evident at molecular weights as small as
116
R. Lund et al.