A cationic surfactant, cetyltrimethylammonium bromide, CTAB, forms lon
g and stable threadlike or wormlike micelles in aqueous solution with
sodium salicylate, NaSal. This system makes an entanglement network si
milar to concentrated polymer systems and shows profound viscoelastic
behavior highly dependent on concentration of CTAB, C-D, and NaSal, C-
s, and the system also is strongly flow birefringent. The shear stress
, sigma(xy) and the normal stress difference, sigma(xx) - sigma(yy), w
ere determined as functions of shear rates, gamma. Flow birefringence
measurements were carried out over almost the same shear rate range wi
th an apparatus capable of simultaneously measuring birefringence, Del
ta n, and orientational angle, chi. The data obtained indicate that th
e refractive index tenser and the stress tenser are linearly related,
Delta n sin(2 chi)/2 = Co, and Delta n cos(2 chi) = C(sigma(xx) - sigm
a(yy)), by a stress-optical coefficient C that is approximately -3.1 x
10(-8) cm(2) dyn(-1) and is essentially independent of CD and Cs. Thi
s linearity suggests that the origin of elasticity of the wormlike mic
ellar system is the orientation of micellar portions between entanglem
ent points as well as a Gaussian chain network. The sign and magnitude
of C are consistent with the proposed structure in which most CTA(+)
ions are arranged in a radial pattern with their molecular axis mostly
perpendicular to the axis of the wormlike micelle. We also estimated
the persistence length of the wormlike micelle as q = 26 nn through no
w birefringence data.