Vibrational spectra, deduction

The potential energy U(r) of the solute determims the spectrum of the normal mode frequencies v that characterize the vibrations of solute molecules in the vicinity of the local minima of U(r). To obtain this spectrum, at each local minimum of U(r) the components of the Hessian matrix at the local minimum can be computed and the spectrum of v can be determined from its eigenvalues. It has been found that for different small molecule dissolved in the rigid-microstructures of both glassy and rubbery polymers at 300 K, the spectrum of Va has its maximum at about 10 s (see Fig. 1), in impressive agreement with the above-mentioned deduction by Barrer from solubility data, more than 40 years ago. It has also been established that the condition hv < 3 kT holds at... 

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