Anisotropy of static and dynamic orientational correlations in N-alkanes

Abstract

Static and dynamic orientational correlations in n-alkanes are analyzed using the rotational isomeric states formalism and its newly introduced adaptation to local chain dynamics. For systems in equilibrium, the anisotropy of directional correlations is investigated in relation to the respective orientations of two coordinate frames rigidly attached to the terminal bonds. The resulting static correlations exhibit a strong odd–even effect depending on the number of intervening bonds between the two frames. Dynamic correlations, on the other hand, necessitate the analysis of the time-dependent autocorrelation of a single reorienting frame rigidly embedded in the motional molecule. Expressions for both the first and second orientational correlation functions—identified according to the order of the associated Legendre polynomials—are formulated, for static and dynamic systems. Dynamic correlations are mathematically related to static correlations through the limiting values to which they asymptotically converge, as time goes to infinity. The orientational correlations are calculated to be strongly anisotropic in all cases.