A direct observation of counterion condensation around cylindrical micelles

Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) techniques have been used to confirm and determine the size and shape of cylindrical micelles formed by a comb-shaped copolymer, poly(1-octadecene-co-maleic anhydride), abbreviated as PODMA, in aqueous solution. Upon full neutralization by the addition of alkaline hydroxide, PODMA becomes a polyelectrolyte carrying two negative charge per repeating unit. SANS measurement gives the dimension of the cylinder with a radius of 20 Å, and a length of 110 Å in D₂O solutions with Cs as counterion. SAXS measurements were made for a series of 1% PODMA solutions fully neutralized by CsOH. Linear charge density at the micellar surface was varied by adding an ionic surfactant, sodium dodecyl sulfate (SDS). The dimensionless linear charge density parameter, ξ ≡ l_B/b, where l_B is the Bjerrum length (l_B = 7.15 Å for water solvent at 295 K) and b is the linear spacing between unit charges on the micellar surface, varies from 32.96 to 67.21. Since the electron densities of the micellar core and the aqueous solvent are nearly equal, the SAXS intensity distribution function is a Bessel transform of the Cs counterion distribution around the cylindrical micelles. Comparison is made between the results obtained from SAXS intensity distribution analyses and the prediction of Manning's condensation theory.