Diffusion models for the dynamics of flexible molecules

Abstract

A theoretical analysis based on a multivariate diffusion equation is developed to study the rotational and internal dynamics of molecules undergoing conformational changes in liquid and liquid-crystalline phases. Numerically exact solutions are obtained for the case of a single degree of freedom, while for more complex systems a rotational isomeric state approximation, in connection with a Kramers procedure generalized to multidimensional problems, is adopted to treat the torsional variables. Hydrodynamic models including interactions between centres of frictional resistance are used to compute diffusion tensors, and ‘size and shape’ models are derived to account for the torques exerted by anisotropic environments on the flexible molecules. Torsional potential profiles are selected from experimental data or structural calculations. The effects resulting from coupling between internal and rotational motions and from recoils following configurational jumps, as well as the features of the saddle-point crossings, are discussed in detail. The analysis is applied to molecular systems exhibiting conformational processes in the ground or in the excited state, to typical mesogenic moieties characterized by flexible chains, and to phospholipid model membranes.