The behavior of aqueous solutions of poly(ethylene oxide) (PEO) is studied theoretically by applying a mean field-like approach which includes the effect of the competition of PEO and water as proton acceptors in hydrogen bond formation. Accounting for this effect is of crucial importance for a correct description of all solution properties. We calculate the temperature and concentration dependence of the average fraction of hydrogen bonds between PEO and water and find very good agreement between our predictions and experimental or MD simulation data. We also make predictions concerning the temperature behavior of the second virial coefficient A 2 and the effective interaction parameter χeff and compare it with experimental data. We found that the decrease of A2 with temperature is caused by the delicate balance of the opposing effects of water-PEO and water-water hydrogen bonding. The phase diagram for PEO of different molecular weights in water is calculated using experimentally reported data for the energy and entropy of association. We achieved very good quantitative agreement with most of the experimental data reported, in particular reproducing the closed loop regions of phase coexistence. We also compare our findings with results of other theoretical models.

The kinetics of micelle evolution of diblock copolymers from unimers toward the equilibrium state is studied analytically on the basis of consideration of the kinetic equations. The association/dissociation rate constants for unimer insertion/expulsion and micelle fusion/fission are calculated by applying Kramers' theory combined with a scaling approach. It is shown that the difference in the intermediate results and the rate of association for the “unimer exchange” mechanism and the joint “micelle fusion/fission + unimer exchange” mechanism is remarkable, with the latter being much more effective. According to this mechanism, at the beginning of the micellization, after coupling of free unimers is completed, fusion of micelles becomes dominant, whereas unimer exchange is effectively frozen by the high activation energy required for unimer release. The later stages of micelle evolution involve both unimer exchange and micelle fusion, which is considerably slowed with time as the average micelle size increases. Micelle fission is also a relatively slow process that however plays an important role in micelle reequilibration occurring with a decrease in the equilibrium aggregation number (as e.g., during T-jump experiments). Applications of the theory to experimental results are discussed in detail.

A systematic study of the equilibrium chain exchange kinetics of a tunable model system for starlike polymeric micelles is presented. The micelles are formed by well-defined highly asymmetrical poly-(ethylene-propylene)-poly(ethylene oxide) (PEP-PEO) diblock copolymers. Mixtures of N,N-dimethylformamide (DMF) and water are used as selective solvents for PEO. With respect to PEP this solvent mixture allows the interfacial tension, γ, to be tuned over a wide range. The equilibrium chain exchange between these micelles has been investigated using a novel time-resolved small-angle neutron scattering (TR-SANS) technique. The results show that the exchange kinetics is effectively frozen for large interfacial tensions but can be readily tuned to accessible time scales (minutes to hours) by lowering γ. Independent of temperature and concentration, the corresponding relaxation functions show an extremely broad and heterogeneous logarithmical decay over several decades in time. We explicitly show that such broad relaxation cannot be explained by polydispersity or a classical distribution of activation energies. Instead, the logarithmic time dependence points toward a complex relaxation picture where the chains are slowed down due to mutual topological and geometrical interactions. We propose that the behavior stems from constrained core dynamics and correlations between the expulsion probability of a chain and its conformation.

The order-disorder transition in a melt of asymmetric micelle-forming diblock copolymers is studied analytically in the strong segregation limit. In contrast to previous calculations by Semenov and by self-consistent mean-field theory, both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy are taken into account. This enables us to locate the order-disorder transition, ODT, where the long-range order (or lattice) of micelles disappears. In agreement with some experimental observations, the ODT occurs between body-centered-cubic spheres and disordered micelles. A face-centered-cubic sphere phase remains thermodynamically unstable, as it is superseded by the disordered micelle regime due to the gain in the translational entropy of micelles. The ODT is accompanied by a decrease in the micelle volume fraction and, more importantly, in the number density of micelles. The aggregation number and the average distance between micelles also change at the ODT, but only slightly. At higher temperatures the number of micelles decreases, but some small fraction of micelles may persist to very high temperatures. A "critical micelle temperature" (cmt) may be estimated, which separates the disordered micelle regime (with a finite micelle concentration) from a disordered melt (with exponentially small micelle fraction), but it is not a true phase transition. Thus, the disordered micelle regime is part of the disordered phase. The composition dependence of the ODT is also analyzed. We compare the predictions of this model with experimental data for poly(styreneb-isoprene) diblock copolymers, with encouraging agreement.

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