Critical micelle concentration from standard chemical potentials
= Critical micelle concentration from standard chemical potentials
With $\mu=\mu_1^0+k_BT\ln x_1$, large aggregates become abundant when monomer <chemical potential> approaches the favorable aggregate standard value $\mu_*^0$. This gives $x_{1,*}\simeq\exp[(\mu_*^0-\mu_1^0)/(k_BT)]$ in the large-aggregation approximation. For one finite preferred size $n$, equal molecular populations $x_n=x_1$ instead give $\ln x_{1,*}=[n(\mu_n^0-\mu_1^0)/(k_BT)-\ln n]/(n-1)$.