MEAN-SQUARE AMPLITUDES OF THE LONGITUDINAL VIBRATIONS OF HELICAL POLYMERS

A simple model for the longitudinal acoustical vibrations of helical polymers has been developed. This model consists of a linear string of masses, M, connected by springs. The mass must be taken as that of one helical turn of the true helix. It has been found that all of the previously observed or calculated frequencies for the longitudinal acoustical modes of helical polymers can be calculated from this model using only one adjustable parameter, the force constant f, between the turns, for each type of helix. Using this simplified model it has been possible to obtain the rms amplitudes of the changes in the overall end‐to‐end length of helical polymers as a function of their chain length and temperature. At room temperatures the rms end‐to‐end length is found to vary from a few tenths of an angstrom for hydrocarbon chains of the length found in phospholipid membrane bilayers to several angstroms in a rigid α‐helix of 100 peptide residues. The damping of these α‐helical modes is not considered but may be appreciable in solution. Copyright © 1979 John Wiley & Sons, Inc.