Effect of pH on CMC - https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjPkeejvOP1AhUujdgFHSlWCLEQFnoECAwQAw&url=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2Fabs%2F10.1002%2Fapp.1983.070280407&usg=AOvVaw2yUv0SxVWmFjljTmxUkWOU
If there are no weakly charged groups in the self-assembling amphiphilic molecules, there is no or hardly a pH dependence. It may be that changing pH affects solvent properties like ionic strength so then it may slightly change the degree of self-assembly.
In case of weakly charged groups, changing pH may increase or decrease the number of effectively charged groups of the amphiphiles. In general, more charged groups per amphiphile leads to a decrease of the aggregation number.
See for instance: Article Self-Consistent-Field Analysis of the Micellization of Carbo...