Experimental determination of the third derivative of G. I. Enthalpic interaction

The solute (i)-solute interaction in terms of enthalpy, H-i-i(E)=N(partial derivative H-2(E)/partial derivative n(i)(2))=(1-x(i))(partial derivative H-2(E)/partial derivative n(i)partial derivative x(i)), the third derivative of G, was experimentally determined using a Thermal Activity Monitor isothermal titration calorimeter for aqueous solutions of 2-butoxyethanol (BE) and 1-propanol (1P). This was done using both calorimetric reference and sample vessels actively. We simultaneously titrate small and exactly equal amounts of solute i (=BE or 1P) into both cells which contain the binary mixtures at an average mole fraction, x(i), which differs by a small amount Delta x(i). The appropriate amount of titrant delta n(i) was chosen so that the quotient (delta H-E/delta n(i)) can be approximated as (partial derivative H-E/partial derivative n(i)), and so that the scatter of the results is reasonable. delta H-E is the thermal response from an individual cell on titration, and we measure directly the difference in the thermal response between the two cells, Delta(delta H-E). The resulting quotient, Delta(delta H-E)/delta n(i)/Delta x(i), can be approximated as (partial derivative H-2(E)/partial derivative n(i)partial derivative x(i)) and hence provides a direct experimental avenue for the enthalpy interaction function. We varied the value of Delta x(i) to seek its appropriate size. Since H-E contains the first derivative of G with respect to T, the result is the third derivative quantity. Thus we present here a third derivative quantity directly determined experimentally for the first time.