Unimer exchange

Recent developments in SANS methodology include time-resolved SANS and time-involved SANS (TISANE). These developments have arisen from the desire to minimize the SANS data collection time to enable the study of rapid kinetic reactions such as solubilization of PC vesicles by bile salt ° and unimer exchange kinetics in polymeric micelles. Time-resolved SANS enables time resolution down to 50-100 ms, while the technique of TISANE obtains an even better time resolution of 50-100 ps, although TISANE is still largely at the experimental stage. 

Willner, L. Poppe, A. Allgaier, J. Monkenbusch, M. Richter, D. Time-resolved SANS for the determination of unimer exchange kinetics in block copolymer micelles. Europhysics Letters 2001, 55, 661-613. 

Micelles can attain and maintain their global equilibrium by constantly redistributing their chains. This can predominantly occur via two main mechanisms unimer exchange and fusion/fission, as schematically illustrated in Fig. 2. These two mechanisms will be discussed in the context of different thermodynamic and kinetic models. 

Fig. 2 Illustration of two important mechanisms involved in various kinetic processes in micellar systems, (a) Unimer exchange, single surfactant/block copolymer chains are interchanged one by one via the solvent medium, (b) Fusion/fission, where two micelles fuse or are fragmented to...

Aniansson and Wall Mechanism Unimer Exchange and Linear Relaxation Experiments... 

The second relaxation time T2, is related to a change in the number of micelles and is much slower because the surfactants have to be rearranged between the micelles in a cooperative fashion (formation/dissociation of micelles limited by unimer exchange). Again under the assumption of unimer exchange, this can be written as ... 

Thus, this simple result suggests that the rate of unimer exchange is governed by the expulsion rate constant. We will see later that this approximation is indeed a good assumption when we compare with the proposed models for unimeric expul-sion/insertion. 

Hence, the most important process for the equilibrium kinetics is the unimer exchange mechanism which, as expected from the Aniansson-WaU scenario, is mainly governed by the expulsion rate constant. In the model of Halperin and Alexander this release of a single unimer from the micelle is pictured to go through two stages ... 

Unimer Exchange Kinetics at Higher Concentrations Effect of Osmotic Pressure... 

So far, we have considered unimer exchange as the only (main) equilibration mechanism. However, other important mechanism may come into play. As depicted in Fig. 2, the most likely candidates are fusion and fission mechanisms ... 

The question is, however, with what probability does fusion or fission occur in comparison with unimer exchange, i.e., how important are they Halperin and Alexander performed a rather straightforward calculation of the activation energy for fusion of two micelles of size Pi and P2 under the assumption that the corOTia free energy (star-like) of the micelle dominates. For star-like micelles they obtained ... 

Considering the results of Halperin and Alexander [60] and of Nyrkova and Semenov [68] presented above, fusion and fission events between polymeric micelles appear to be rather rare. In any case, unimer exchange will always be an important if not completely dominating mechanism as a consequence of the low activation barrier of the process compared to other mechanisms. 

Independently of the evaluation method, a KZAC TR-SANS experiment allows the kinetics to be evaluated through the decay of either R(t) or /exc(0- The unimer exchange rate constant in simple labeling experiment will now be discussed. 

A kinetic model for unimer exchange mechanism has been presented by Thilo [105] as well as by Cantu et al. [106]. According to Thilo [105], the following kinetic scheme can be used. Here, we use the terminology of proteated (H) and deuterated (D) chains or surfactants because in the present review the focus is on scattering experiments. 

In other words, R(t) and/ xc would, in the case where the mechanism of unimer exchange is dominant, give rise to a simple exponential decay. 

Lejeune et al. [153] employed a chemical approach to lowering of interfacial tension in poly( -butyl acrylate)-(polyacrylic acid) (PnBA-PAA). PnBA-PAA forms kinetically frozen micelles in water that are not able to reorganize over a month. By statistical incorporation of hydrophilic acrylic acid (AA) units into the hydrophobic PnBA block, P(nBA5o%-stat-AA5o%)-PAA, they could moderate the hydrophobicity of the core block such that unimer exchange was promoted and thermodynamic equilibrium was reached at shorter times. 

Stop-flow experiments have been performed by Tuzar and Kratochvil [7] and more recently by Kositza et al. [128]. In analogy to low molar weight surfactants, it could be shown that two relaxation processes have to be considered for block copolymer micellar systems the first in the time scale of tens of microseconds, associated to unimer exchange between micelle and bulk solution, and the second, in the millisecond range, attributed to the rearrangement of the micelle size distribution. Major differences were observed between A-B diblock and A-B-A triblock copolymers, which could be explained by the fact that the escape of a unimer, which has to disentangle from the micellar core, might be much easier in a diblock than in a triblock structure. 

A very different scenario emerged in the case of simrd-taneous unimer exchange and fusion/fission. No quasi-equilibrium was observed and association proceeded quickly. Odd i-mers never prevailed and dimers turned into tetramers, then hexamers, octamers, and so on. At the beginning of the miceUization process, the micelle fusion mechanism was practically the only active one, until unimer expulsion from micelles became active. It is only toward the end of the process that unimer exchange became significant, in conjrmction with micelle fusion, particrdarly between rmequal micelles. 

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