A general theory of spin relaxation developed by Fulton is applied to the problem of rotational relaxation of a dipole rotating in two dimensions. The model system is composed of a rotor with dipole moment (mu) at the center of a circular cavity in a continuous, infinite dielectric medium (heat bath). We write a quantum-mechanical Hamiltonian for the system which contains a term for free rotor motion and a bath-rotor interaction term. An equation of motion for the operators describing the rotor is developed using Heisenberg's equation of motion in conjunction with the theory of functionals. This equation is taken in the classical limit by assuming that the rotor's rotational spacing is small. We choose a simple form for the free motion time dependence of the classical rotor functions and thereby identify the rotor functions with the eigenfunctions of the Liouville operator. Through consideration of the bath-rotor interaction we find the relevant bath functions to be the bath's electric field components at the center of the cavity. The classical equation of motion which results from this process describes the time dependence of the probability distribution for the rotor's angular momentum. This equation resembles a Fokker-Planck equation with a diffusion coefficient which depends upon the angular momentum. We find that this coefficient is related to the fluctuations of the bath's electric field in the cavity. The equation of motion is solved numerically by finite differences. The solution, corresponding to relaxation of a small molecule from a high initial angular momentum state, shows a double-maximum or "bimodal" shape for intermediate momentum values before relaxing to the equilibrium Boltzman distribution. This behaviour is qualitatively similar to experimental time-dependent angular momentum distributions found by Polanyi and co-workers for hydrogen / halides formed in molecular beam reactions. We also derive and solve numerically an equation of motion for the orientational correlation function of the rotor. / Source: Dissertation Abstracts International, Volume: 42-06, Section: B, page: 2388. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74575 |
| Contributors | ARNETTE, JAMES KENNETH., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 134 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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