Long-Range Crossover and "Nonuniversal" Exponents in Micellar Solutions

Observations of apparently nonuniversal exponents at the lower consolute points of micellar solutions of $n$-dodecyl-octaoxyethylene glycol monoether in ${\mathrm{H}}_2$O, ${\mathrm{D}}_2$O, etc., are analyzed by use of crossover scaling-theory and Ising-model results. The data quantitatively sustain a picture of stable micelles of radius $R$ undergoing ordinary criticality with crossover to Ising behavior delayed by an increasing range of interaction measured by ${\xi }_0$, the observed correlation-length amplitude: The crossover points, $t_{\times }\equiv \frac{(T_c-T_{\times })}{T_c}\sim {\left(\frac{R}{{\xi }_0}\right)}^6$, vary by a factor ≳ ${10}^2$ correlating with the changes seen in ${\gamma }_{\mathrm{eff}}$ and ${\nu }_{\mathrm{eff}}$.