The persistence length of a wormlike micelle composed of ionic surfactants
CnEmXk in an aqueous solvent ispredicted b
y means of the self-consistent-field theor
y where
CnEm is the conventional nonionic surfactant and
Xk is an additional sequence of
k weakl
y charged (pH-dependent) segments. B
y considering a toroidal micelleat infinitesimal curvature, we evaluate the bending modulus of the wormlike micelle that corresponds to thetotal persistence length, consisting of an elastic/intrinsic and an electrostatic contribution. The total persistencelength increases with pH and decreases with increasing background salt concentration. We estimate that theelectrostatic persistence length
![](/isubscribe/journals/jpcbfk/111/i28/eqn/jp071756oe10001.gif)
scales with respect to the Deb
ye length
-1 as
![](/isubscribe/journals/jpcbfk/111/i28/eqn/jp071756oe10002.gif)
~
-p where
p ![](/images/entities/ap.gif)
1.98for wormlike micelles consisting of
C20E10X1 surfactants and
p ![](/images/entities/ap.gif)
1.54 for wormlike micelles consisting of
C20E10X2 surfactants. The total persistence length
![](/isubscribe/journals/jpcbfk/111/i28/eqn/jp071756oe10003.gif)
is a weak function of the head group length
m but scaleswith the tail length
n as
![](/isubscribe/journals/jpcbfk/111/i28/eqn/jp071756oe10004.gif)
~
nx where
x ![](/images/entities/ap.gif)
2-2.6, depending on the corresponding head group length.Interestingl
y,
![](/isubscribe/journals/jpcbfk/111/i28/eqn/jp071756oe10005.gif)
varies nonmonotonicall
y with the number of charged groups
k due to the opposing trends inthe electrostatic and elastic bending rigidities upon variation of
k.