Persistence length of wormlike micelles composed of ionic surfactants: self-consistent-field predictions

The persistence length of a wormlike micelle composed of ionic surfactants C(n)E(m)X(k) in an aqueous solvent is predicted by means of the self-consistent-field theory where C(n)E(m) is the conventional nonionic surfactant and X(k) is an additional sequence of k weakly charged (pH-dependent) segments. By considering a toroidal micelle at infinitesimal curvature, we evaluate the bending modulus of the wormlike micelle that corresponds to the total persistence length, consisting of an elastic/intrinsic and an electrostatic contribution. The total persistence length increases with pH and decreases with increasing background salt concentration. We estimate that the electrostatic persistence length l(p,e)(0) scales with respect to the Debye length kappa(-1) as l(p,e)(0) approximately kappa(-p) where p approximately 1.98 for wormlike micelles consisting of C(20)E(10)X(1) surfactants and p approximately 1.54 for wormlike micelles consisting of C(20)E(10)X(2) surfactants. The total persistence length l(p,t)(0) is a weak function of the head group length m but scales with the tail length n as l(p,t)(0) approximately n(x) where x approximately 2-2.6, depending on the corresponding head group length. Interestingly, l(p,t)(0) varies nonmonotonically with the number of charged groups k due to the opposing trends in the electrostatic and elastic bending rigidities upon variation of k.