Relaxation counterion displacements

Finally, in this section, the possible role of counterion displacements in relaxation of globular proteins should be mentioned. These can result in fluctuating dipole moments in addition to permanent moments p. along principal molecular axes. If their relaxations are independent and separately exponential with rate constants k and k, response theory formulation gives the complex permittivity in the form... 

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. 

Among the early examples of the successful use of electric fields to probe ionic structures and electrical and optical anisotropies are the linear polyelectrolytes. Basic information about macromolecular dimensions, size, and shape have been derived from the relaxation of field-induced changes in optical properties and in electrical parameters of the electrically and optically anisotropic systems. The analysis of electric conductivity measurements has demonstrated that linear polyelectrolytes are electrically anisotropic. It was established that the extremely large dipole moments, which the electric field produces by displacement of the counterion atmosphere parallel to the long axis of the polyions, are responsible for their orientations in the direction of the external field. 

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