Rotational Diffusion of Sphericalhyphen;Top Molecules in Liquids

摘要

The extension of the classical rotational diffusion model proposed by Gordon in his study of linear molecules is applied to the evaluation of the reorientational correlation functions, their Fourier transforms, and correlation times for fluids composed of sphericalhyphen;top moelcules. The reorientational correlation timestgr;thgr;lpar;jrpar;, describing the time correlation of ajthhyphen;order spherical harmonic, are expressed as functions of the correlation timetgr;Jfor the angular momentum of the molecules. These expressions are valid for all values ofohgr;macr;tgr;J, whereohgr;macr;is the roothyphen;meanhyphen;square angular frequencylpar;kTthinsp;sol;thinsp;Irpar;1thinsp;sol;thinsp;2for a sphericalhyphen;top molecule with moment of inertiaI. In the Debye limitlpar;ohgr;macr;tgr;Jthinsp;Lt;thinsp;1rpar;, tgr;thgr;lpar;jrpar;thinsp;Gt;thinsp;tgr;J, andtgr;thgr;lpar;jrpar;are proportional totgr;Jminus;1thinsp;sol;thinsp;ohgr;macr;2; in the perturbedhyphen;freehyphen;rotor limitlpar;ohgr;macr;tgr;Jthinsp;Gt;thinsp;1rpar;, tgr;thgr;lpar;jrpar;is proportional totgr;Jand is of comparable magnitude.tgr;thgr;lpar;jrpar;goes through a minimum value whentgr;thgr;lpar;jrpar;, tgr;J, andohgr;macr;minus;1are approximately equal. Magnetic spin relaxation due to motional modulation of anisotropic spinndash;rotational interactions is also considered in the framework of this extended diffusion model. The resulting expression for the spin relaxation times involves a correlation function containing both the time correlation of the orientation of the molecule and the angular momentum of the molecule simultaneously. This correlation function and hence the spinhyphen;relaxation times, can be calculated on the basis of the extended diffusion model for all values ofohgr;macr;tgr;Jwithout assuming any separability or independence of the correlations of the molecular orientation and angular momentum. In the Debye limit, the expression for the spinhyphen;relaxation times reduces to that of Hubbard, and in the perturbedhyphen;freehyphen;rotor limit, it reduces to the result previously obtained by Bloomet al.