Exciton States and Optical Rotatory Dispersion in Helical Polymers

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Abstract
A general formula for the optical rotatory dispersion (ORD) of oriented solute molecules is used to discuss the optical properties of helical polymers. When periodic boundary conditions are applied to both the electromagnetic field and to the excitation of the polymer the results previously obtained by Moffitt, Fitts, and Kirkwood are recovered. The procedure used, although different in appearance, is essentially that recently employed by Ando. It is shown that these results are rigorously correct in the limit of infinite polymer length. Furthermore, it may be seen that the absorption band with polarization perpendicular to the helix axis is, in fact, the sum of two bands at very slightly different frequencies having rotational strengths of opposite sign and nearly equal magnitudes. It is this splitting which was overlooked in Moffitt's original treatment of the problem and which was implicitly included, although not explicitly recognized, by Moffitt, Fitts, and Kirkwood. Finally, when the results for an infinite, arbitrarily oriented polymer are averaged over all angles the conditions under which familiar formulas for ORD of polymer solutions are valid may be seen.