Inertial and bias effects in the rotational Brownian motion of rodlike molecules in a uniaxial potential

Inertial effects in the rotational Brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a Brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h , both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.