Non-linear hydrophobic relationships

Hansch [66] and his co-workers soon found that curved free-energy correlation plots were frequent and equations of the type shown in Eqn. 81 were found. 

Pauling and Pressman [73] attempted to correlate binding constants of haptens and antibodies with molar refractivity of substrates (Eqn. 82) 

An interesting example of the application of molecular polarisabihty comes from data of this laboratory on papain analysed by Hansch and Calef [75]. The papain-catalysed hydrolysis of substituted phenyl methanesulphonylglycinates gave relatively poor correlations between k /K and a, m, MR and tt and a. The correlation of ko/K with MR and a is significant (Eqn. 83) indicating that inductive and polarisable effects are involved so far as substitution on the phenyl-leaving group is concerned. 

Like the inductive effect and unlike the steric effect E ) hydrophobic and molecular polarisability parameters are additive thus it is possible to calculate partition 

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