Self-consistent field theory of micelle formation by block copolymers

Abstract

A self-consistent field theory was developed to account for the micellization of block copolymers in selective solvents. The mean-field expression used successfully by Edwards in treating the polymer excludedvolume problem was modified to enable it to be applied to chains in bad solvents without the generation of unrealistically high segment densities. Full consideration was given to the issue of standard states so that a meaningful comparison could be made between theoretical and experimental results. The theory was able to account in a consistent and satisfactory manner for the thermodynamics of micellization of two polystyreneblock-polyisoprene copolymers in n-hexadecane which is a selectively bad solvent for polystyrene.

On the Theory of Micellization Kinetics

“…Their relaxation involve two essentially different processes: a relatively fast exchange of molecules between the micelles and the ‘gas’ of unimers [relaxation of the micelle aggregation number, Figure 16(a)] and a slow relaxation of the number of micelles involving micelle formation or dissociation [Figure 16(b)]. The prediction of the two qualitatively different relaxation channels is in agreement with the previous theoretical and simulation studies 8–13…”

“…Our theoretical model based on the activation kinetics provides a simpler and physically more clear picture of relaxation processes, and therefore it allows to also consider more complicated non‐linear dynamical effects. In the linear regime, we predict two essential relaxation processes (fast, unimer exchange and slow, variation of the number of micelles) in agreement with experimental data and with earlier theoretical (mostly numerical) results 8–13. We also show that (in the case of sufficiently large micelles) the terminal slow relaxation time may be extremely long, i.e.…”

“…Kinetics of micellization attracted considerable attention in the past, both experimental and theoretical 1,8–17. Nevertheless, in our opinion there are certain important points concerning the kinetics that are either not clarified or not sufficiently emphasized.…”

Theory of copolymer micellization

“…4,5 The use of self-consistent theories for copolymer micelles has a long history, beginning with the work of Yuan et al in 1992. 6 Our approach differs from previous ones in that we are not primarily interested in the calculation of properties of isolated micelles, but rather in how to include this information in a thermodynamic description of the micellar fluid. Even though the importance of the excess free energy of the micelles in defining a proper CMC and distinguishing between competing structures has been recognized since the first works, 7 we feel the connection between it and the concentration of micelles, which can lead to differences between possible definitions of the CMC, has not been explored in detail.…”

Design of block copolymer membranes using segregation strength trend lines

“…Yuan et al used self--consistent field theory to estimate the energy involved in the micellization of block copolymers. 56 The term , used in this work, is a simplified and semi--empirical ratio, estimated only from solubility parameters and polymerization degree. This information is easily available for the copolymers and solvents and should be used a fast indicator of the most suitable cast solution composition.…”