The Response of a Viscoelastic System to Sinusoidal Stress

Consider an applied stress varying as a function of time according to the relationship (7 = (To sin CO, where co is the stress frequency. If the material were wholly elastic, and obeyed Hooke s law, the strain would then vary as e = e, sin cur. 

However, for a viscoelastic material the strain lags behind the stress. Let this lag be denoted by 3, which may be called the phase angle or the phase lag, and is the relative angular displacement of the stress and strain. 

The strain can therefore be considered in terms of two components, one of which, o sin at cos 5, is in phase with the strain, and the other, cos cot sin 3, is out of phase with the strain by nil. It is therefore possible to define two dynamic moduli, i in phase with the stress and fj, which is 7t/2 out of phase with the stress. i = aje cosd and = ( To/ o)sin 

dynamic mechanical measurements are usually made over a range of temperature and frequencies in order to cover the various types of molecular motion that may occur. The oscillatory strain amplitudes used are very small, typically below 1.0% ofthe total sample dimension, to ensure a linear viscoelastic response. 

Molecular motions in polymers, particularly those types that involve some reorganization of functional groups such as branches, should be amenable to study by vibrational spectroscopy. The spatial movement of functional groups involves a change in the directions of dipole moment and polarizability changes during molecular vibrations. Hence, the measurement of linear dichroism using 

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