Micellization kinetics of diblock copolymers in a homopolymer matrix: a self-consistent field study

Abstract

Self-consistent field theory is used to calculate free energy barriers and reaction rates for the spontaneous association and dissociation of micelles formed of block copolymers in a homopolymer matrix. The barriers are prohibitively large for copolymers of typical molecular weights when the unimer (free surfactant) concentration is near the equilibrium critical micelle concentration (CMC). As a result, polymeric micelles normally cannot reach true thermodynamic equilibrium. The rates of association and dissociation are, however, sensitive to unimer concentration, making it possible to form or destroy micelles at observable rates in sufficiently highly supersaturated or subsaturated solutions, respectively, even when both reactions are suppressed near the equilibrium CMC. The barrier to dissociation is particularly sensitive to unimer concentration, and vanishes when the unimer concentration is only slightly (for example, a percentage of a few tens) below the equilibrium CMC.

Mechanism of Micelle Birth and Death

“…The more important factor in the increase in τ d is the increase in the Arrhenius factor exp(−∆W d /k B T ), which decreases by a factor of nearly 10 5 as a result of the increase in the barrier ∆W d . The magnitude of the increase in τ d is not surprising in light of previous predictions for polymeric micelles [15,16]. What we find more surprising is how much less τ f changes with α.…”

“…This theory assumes that both fast and slow processes arise from strictly stepwise changes in micelle size, by insertion and expulsion of individual free molecules, and that rates of fission and fusion are negligible. The resulting theory [11][12][13][14][15][16][17][18][19][20] is closely analogous to the classical Becker-Döring theory of stepwise nucleation of liquid from a vapor [21].…”

“…3, while τ f appears to increase by 2-4 orders of magnitude. The theory of step-wise dissociation [11,[15][16][17] predicts a dissociation rate…”

Interfacial Tension Measurement and Micellization in a Polymer Blend with Copolymer Surfactant: A False Critical Micelle Concentration

“…Self-consistent field theory (SCFT) , has been used to estimate the magnitude of the barrier to dissociation of diblock copolymer micelles in a polymer matrix via this stepwise process. The results suggest that the barrier to dissociation should generally be prohibitive for AB diblock copolymers in a B homopolymer in systems near equilibrium, with c f ≃ c c , except under rather special circumstances.…”

“…SCFT calculations also predict, however, that the barrier to dissociation is surprisingly sensitive to decreases in the concentration c f of free molecules. This barrier is predicted to disappear when c f drops below a critical value that for experimentally relevant parameters is only a few tens of percent lower than the CMC.…”