This equation is used to predict the glass transition temperature of systems with different components (miscibility and immiscibility). This equation have been used for binary and ternary systems. Can any one know how to extend this equation for quaternary systems?
Dear Mahendra
I´m not an expert in G-T-equation, but I´ve worked with it (see my PLA PHBV paper). Due to my interpretation G-T descibes the deviatin of an polymer mixture (or Polymer/plasticizer mixture) from "ideality". Ideality means that the volumes covered with your components and the volumes of the so called "free volume" is mixed ideal (No volume contaction or expansion by mixing for the free volume and the covered volumess). If you have such a mixture you then can use tbe Fox equation instead of G-T especially when the Simha-Boyle rule (Delta alpha*Tg= constant) is valid and k can be calculated from the glas points of the componentes.
The k value in the G-T-equation
1) can describe the deviation from the Simha-Boyle rule (temperature induced different changes of density, alpha = expansion coefficient in Simha-Boyle rule) but
2) can also descibed deviation from ideal mixtures. (As an eample from Atkins book of physical chemistry: 70 mL of water and 30 mL of Alcohol doesn´t give 100mL of 30 vol % Alcohol-water mixture)
In the light of this you can interpretate the k-value in the G-T-equation with the interactions of your system components so the kvalue can be desrcibe as k12 in a binary system. From that point of view you will need three parameters k12, k13 and k23 in a ternary system (which may be reduced to k12 and k13 if k23 is small e.g using two plasticizer (2,3) in PVC (1) (do you know k23 is small?), and 6 parameters in a quaternary system (neglecting higher orders term like k123).
Therefor using G-T-equation in more-component systems doesn´t make sense if you don´t have more insight in your system or working with the values of k12 and k13 from the binary mixtures and adjusting then only k23.
Adjusting measured data with a multi parameter equation (by e.g. the method of lowest root mean square errors) will give a fit of the curve but can the fitting parameters be interpreted?
KR Rodion
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