STOCHASTIC DYNAMICS OF N-NONANE AND RELATED MOLECULES IN SOLUTION COMPARED WITH NUCLEAR-MAGNETIC-RESONANCE COUPLED RELAXATION-TIMES

The motion of chain molecules in solution has been analyzed using both generalized Langevin equation (GLE) and ordinary Langevin equation (OLE) simulations. A numerical algorithm for solving the GLEs is developed in which the integrations over various forces have been performed explicitly. It is shown in the GLE simulations that the motion of chain segments is correlated closely with solvent relaxation giving significantly reduced friction forces. At temperatures higher than 233 K, a hydrodynamic description with a structure relaxation mode in the solvent (diglyme) is sufficient to yield Cartesian correlation times in good agreement with the NMR coupled relaxation results on n-nonane. The relative contributions of both overall tumbling and internal motion to the Cartesian and end-to-end direction relaxation and the possible couplings of these two motions are analyzed by calculating apparent activation energies for various motional modes and by using a harmonic approximation. It is found that the OLE model underestimates the contribution of internal motion to the relaxation of local Cartesian modes. The finite structural relaxation rate in the solvent can substantially alter not only the correlation times, but the dynamic features of the relevant relaxation processes in a full GLE calculation. In particular, it is shown that the short-time decay of the Cartesian correlation functions is underdamped oscillation in contrast with the overdamped behavior found from the OLE simulations.