The effects of hydrodynamic interactions on translational and rotational relaxation

Abstract

A theory of coupled translational and rotational relaxation in solution including the effects of hydrodynamic interaction is presented. The translational, translational–rotational, and rotational diffusion tensors are computed using the method of hydrodynamic reflections. The correlation functions C_lm(t) =〈Y_lm*[u(0)] Y_lm[u(t)]〉 and C_lm(q,t) =〈exp iq⋅[r(t)−r(0)] Y_lm*[u(0)] Ylm[u(t)]〉 are found from a coupled translational–rotational diffusion equation. C_lm(t) is shown to reduce to the Debye result under conditions relevant to magnetic resonance experiments. The concentration dependence of the rotational diffusion coefficient is calculated and compared with experiment. The failure of the results to account for the dynamical correlations seen in recent NMR studies of protein solutions by Koenig and co‐workers is discussed.