Modulated Temperature Thermogravimetry is a way of obtaining information about the kinetics of thermal degradation processes. The temperature dependence of chemical processes may be readily expressed in terms of the Arrhenius equation:
k = A exp (-Ea/RT)
where k is the rate constant, R the gas constant and T the thermodynamic (Kelvin) temperature. Values of the Arrhenius parameters (Ea and A) provide measures of the magnitude of the energy barrier to reaction (the activation energy, Ea) and the frequency of the occurrence of a condition that may lead to reaction (the frequency factor, A). The rate constant k is defined by the relationship between the rate of reaction (da/dt) and the extent of conversion or fraction reacted (a). Polymer decompositions are generally heterogeneous reactions since the sample is solid (or molten) and the products are gases.
A useful method of determining Ea is temperature jump thermogravimetry. The rate of decomposition is measured either side of a change in temperature and the activation energy determined by:
Ea= R ln[dm/dt(T1)/dm/dt(T2)][1/T1-1/T2]
Where dm/dt(T1) and dm/dt(T2) are the rates of mass loss at T1 and T2 either side of the temperature jump.
Another approach is to studying degradation kinetics using data from conventional linear rising temperature thermogravimetry. Many such methods have been proposed, but the most popular strategy is that described by Ozawa, Flynn and Wall which has been incorporated into an American Society for Testing and Materials standard method. Essentially, separate measurements are carried out at different linear heating rates and the temperatures at which a set percentage mass loss occurs noted. These are then plotted as a function of heating rate (dT/dt) and the activation energy determined by an iterative process. These algorithms have been incorporated into a number of commercially available software packages, although the user should always question the predictions of such "black box" methods especially since they often assume, without appropriate justification, that the polymer decomposition reactions are "first order" processes i.e.:
da/dt = k (1- a)
Modulated Temperature Thermogravimetry employs a temperature profile in which a sinusoidal temperature fluctuation is superimposed upon a conventional linear rising temperature program. The raw data from such an experiment are shown below for an ethylene-co-vinyl acetate copolymer. The curves showing the heating rate (dT/dt) and rate of mass loss (-dm/dt) make the effect of the temperature modulations apparent.
Ea for the chemical decomposition is then calculated according to:
Ea = R(Tav.2-(0.5 Tamp.)2)L/Tamp.
where Tav. is the average thermodynamic temperature, Tamp. is the amplitude of the temperature modulation and L is the logarithm of the amplitude of the rate of mass loss over one modulation. Plots of mass and Ea as a function of temperature from the data are shown below.
- T. Ozawa, "A New Method of Analyzing Thermogravimetric Data" Bulletin of the Chemical Society of Japan 38 (1965) 1881-1886
- J. H. Flynn, L. A. Wall, "A Quick, Direct Method for the Determination of Activation Energy from Thermogravimetric Data" Polymer Letters 4 (1966) 323-328
- J. H. Flynn, B. Dickens, "Steady-State Parameter-Jump Methods and Relaxation Methods in Thermogravimetry" Thermochimica Acta 15 (1976) 1-16
- "Standard Test Method for Decomposition Kinetics by Thermogravimetry" ASTM Test Method E1641 ASTM Book of Standards 14.02, 1042-1046, American Society for Testing and Materials (1994)
- R. L. Blaine, B. K. Hahn, "Obtaining Kinetic Parameters by Modulated Temperature Thermogravimetry" Journal of Thermal Analysis 54 (1998) 695-704