THEORY OF THE ROTATIONAL BROWNIAN-MOTION OF A LINEAR MOLECULE IN 3D -A STATISTICAL-MECHANICS STUDY

The Fokker-Planck-Kramers (FPK) equation for the rotational Brownian m otion of a linear rigid rotator in 3D is derived from the basic princi ples of statistical mechanics applied to the two classical model Hamil tonians: 1) The model of a rigid fixed rotor interacting with a bath o f harmonic oscillators. 2) The model of a linear rigid rodlike polymer diluted in a monoatomic solvent. An entropy formula is established fo r the rotator system allowing to formulate the second law of thermodyn amics and to analyze its implication on the form of the dielectric and Kerr functions. Finally, a general scheme is proposed to solve the FP K equation in the form of series expansion. Approximative analytical e xpressions for the dielectric and Kerr functions, are obtained up to t he third order in the electric field, considering a steady state regim e of a de field on which is superimposed an alternating field. These r esponse functions generalize and extend all the results recently publi shed on the topic. The particular case of the Debye-Smoluchowski diffu sion model is straightforwardly recovered.