  Brownian motion and viscoelasticity of semiflexible polymers is a subject
that has been studied for many years. Still, rigorous analysis has been
hindered due to the difficulty in handling the constraint that polymer chains
cannot be stretched along the contour. Here, we show a straightforward method
to solve the problem. We consider a stiff polymer that has a persistent length
$L_p$ much larger than the contour length $L$. We express the polymer
configuration using three types of variables: the position vector of the center
of mass $R_c$, the unit vector $n$ along the main axis, and the normal
coordinates $u_p$ for bending. Solving the Smoluchowski equation for the
distribution function of these variables, we calculate the equilibrium time
correlation function $ \langle P(t)\cdot P(0) \rangle$ of the end-to-end vector
$P$ and the complex modulus $G^*(\omega)$ of dilute solution. They include the
bending effect to the first order in $\theta \equiv L/L_p$ and reduce to the
exact results for the rigid rod in the limit of $\theta \to 0$. The rotational
diffusion coefficient increases slightly by the semiflexibility because the
equilibrium length of the semiflexible polymer is smaller than that of the
rigid rod with the same contour length. The storage modulus shows the same
asymptotic dependence $G'(\omega) \sim \omega^{3/4}$ predicted by Shankar,
Pasquali, and Morse [J. Rheol. 2002, 46, 1111--1154]. The high-frequency
viscosity is predicted to be dependent on the thickness of the semiflexible
polymers.
