Equations of State and Structural Relaxation Times in Liquids

The compressibility equation of state obtained from Percus-Yevick's integral equation for hard spheres and that obtained from Significant Structure Theory by Henderson have been used in the evaluation of the structural relaxation times of some typical polar liquids. These hard sphere equations of state have been modified by including attraction terms as suggested by Longuet- Higgins and Widom. These equations have also been subjected to the same treatment to evaluate structural relaxation times. The generalised stress-strain relationship derived by Meixner which involves the time derivatives of stress and strain has been taken as the basic equation governing pure compressional deformation to obtain the ratio of high to low frequency modulus of compression. The value of τ _v as obtained for the hard sphere equations of state in the present paper give comparable values with those obtained by others by completely different methods. However it was found that the addition of an attraction term to the hard sphere equation gives high values of τ _v . This may be due to the fact that the van der Waals a parameter as used in the attraction term may not be the same in both the liquid and the vapour phases. Further in the attraction term a/Vⁿ , n may not be exactly equal to 2 as has been used in the present treatment.

On the whole it is found that hard sphere equations of state give inter-consistent results. We conclude that the present method of evaluation of rv may be of considerable importance in viscoelastic and physico-chemical studies as the structural relaxation times have been correlated with the molecular parameter of the liquids.