Debye Perrin theory

In such a case, no conclusion about the mechanisms can be reached from the form of 4(t) and the observed rate will be determined primarily by the fastest process. By extension of the argument, one easily sees that marked deviation of any of the parallel processes from exponential decay will be reflected in the overall rate with possible change in the functional form. Thus, if the rotation is described by exp(-2D t) as in Debye-Perrin theory, and the ion displacements by a non-exponential V(t), one finds from eq 5 that 4(t) = exp(-2D t)V(t) and the frequency response function c(iw) = L4(t) = (iai + 2D ) where iKiw) = LV(t). This kind of argument can be developed further, but suffices to show the difficulties in unambiguous interpretation of observed relaxation processes. Unfortunately, our present knowledge of counterion mobilities and our ability to assess cooperative aspects of their motion are both too meagre to permit any very definitive conclusions for DNA and polypeptides. 

Perrin [223] extended Debye s theory of rotational relaxation to consider spheroids and ellipsoids. Using Edwards analysis [224] of the torque on such bodies, Perrin found two or three rotational relaxation times, respectively. However, except for bodies very far from spherical, these times are within a factor of two of the Debye rotational times [eqn. (108)] for stick boundary conditions. 

Finally, it may be noted that the rotational relaxation time, rrot of eqn. (108) is reduced by (1 + 3r]/P) times when considering the rotational relaxation of spheres. When test molecules of shapes far from spherical are considered, liquid is displaced by rotation (paddle wheel effect) and the Debye or Perrin theory should be a better approximation. 

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