Mechanism of Micelle Birth and Death

In micellar surfactant solutions, changes in the total number of micelles are rare events that can occur by either of two mechanisms—by stepwise association and dissociation via insertion and expulsion of individual molecules or by fission and fusion of entire micelles. Molecular dynamics simulations are used here to estimate rates of these competing mechanisms in a simple model of block copolymer micelles in homopolymer solvent. This model exhibits a crossover with increasing degree of repulsion between solvent and micelle core components, from a regime dominated by association and dissociation to a regime dominated by fission and fusion.

Figure 1

Micelle free energy $W$ plotted versus micelle aggregation number $n$ at $\mathrm{\Delta }\mu =\mathrm{\Delta }{\mu }_c$. Results are shown for $\alpha =10$, 12, 14, and 16, from lowest to highest free energy barrier. Results are shifted so that $W_n=0$ at the micellar minimum, $n=n_e$.

Figure 2

Semilog plot of the intrinsic fission lifetime ${\tau }_n^{\text{fis}}$ in units of Lennard-Jones time as a function of micelle aggregation number $n$, for values of $\alpha =10$, 12, 14, and 16 (left to right). Error bars show root-mean-squared statistical errors. Solid lines are predictions of the global fit to Eq. (2), plotted at these four values of $\alpha$.

Figure 3

Predicted values of the dissociation lifetime ${\tau }_d$ (blue diamonds) and fission lifetime ${\tau }_f$ plotted versus $\alpha =({\alpha }_{AB}-{\alpha }_{AA})/k_{B}T$, for $\alpha =10$, 12, 14, and 16. Squares are estimates of ${\tau }_f$ computed using Eq. (2) for all values of $n$, while circles are an upper bound obtained by only accounting for fission events that occur in the range ${\tau }_n^{\text{fis}}$ for which the intrinsic lifetime was directly measured.