Halperin and Alexander

Halperin and Alexander extended the theory of the Aniansson and Wall approach to calculate the detailed rate constants and the associated activation energies for polymeric materials, i.e., block copolymer micelles. We briefly review the central results in the following section. 

Exchange Kinetics in Block Copolymer Micelles Halperin and Alexander Theory... 

The theory proposed by Halperin and Alexander (H-A theory) [60] is based on the structural scaling description of polymeric micelles outlined in Sect. 2.1.2. Using a combination of scaling theory and Kramers rate theory for diffusirai in an external potential [61], the expulsion rate for both crew-cut and star-like spherical micelles was derived. Moreover, Halperin and Alexander discussed different scenarios of chain exchange between micelles. 

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 ... 

In a recent work, the original Halperin and Alexander model was, in light of new experimental data, extended for the case of high cOTicentrations and particularly for the case of overlapping coronal A-chains [64]. As noted, Eq. 34 is only approximately correct and several corrections should be included. In particular, as is evident from Fig. 4, Eq. 34 does not give a complete description of the activation barrier. In addition to the surface free energy of the exposed insoluble B-block, the expulsion process involves interactions with the corona chains. The free energy of the activated state must therefore be calculated in more detail. 

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. 

Figure 4.8 Variation of the entry rate constant t with N(POF as suggested by Halperin and Alexander theory for triblock EOn(eo)POn(po)EOn(eo) copolymers. The solid line is a best fit of the data.

The analysis of Rabin and Alexander was elaborated by Barrat" in order to ex-plain shear induced swelling of brushes immersed in good solvents. The stretching of brushes in poor solvents was considered by Halperin and Zhulina. Ross and Pincus considered the role of lateral inhomogeneities in this problem. Finally, in this regime shear is expected to induce brush shrinkage as was shown by Williams. ... 

Hall and Alexander (1940) Brodskii and Sulima (1953) Brodskii and Sulima (1953) Brodskii and Sulima (1953) Halperin and Taube (1952) Hoering et al. (1956)... 

Douglas JF, Kent MS, Satija SK, Karim A (2001) Polymer Brushes Structure and Dynamics. In Buschow KHJ (ed) Encyclopedia of Materials Science and Technology. Elsevier, Amsterdam Alexander S (1977) J Phys France 38 983 Halperin A, TirreU M, Lodge TP (1991) Adv Polym Sci 100 31 Singh C, Picket GT, Balazs AC (1996) Macromolecules 29 7559 Currie EPK, Norde W, Cohen Stuart MA (2003) Adv Colloid Inter Sci 100-102 205 Meredith JC, Karim A, Amis EJ (2002) MRS Bull 27 330... 

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