Page 36 - Handbook of Thermal Analysis of Construction Materials

20 Chapter 1 - Thermoanalytical Techniques

to one, a plot of dx/dt versus (1- x) yields a straight line. For reaction orders
different from one, Eq. (6) is written as: [44]

Eq. (13) ln (dx/dt) = n ln (1- x) + C

where C = constant
n = reaction order
x = fraction of decomposition or conversion
Plotting dx/dt versus (1-x) results in a line with a slope equal to the
reaction order. The stepwise approach allows the calculation of the reaction
order for each step of the multiple step decomposition from a single TG
experiment. [42]
A variation of the stepwise TG method was also developed by
Sichina. [43] The approach, called automated stepwise, consists of heating a
sample at a constant heating rate until a significant weight loss occurs, as
determined when the rate of decomposition exceeds a pre-selected “en-
trance” threshold level. Then, the instrument automatically holds the
sample isothermally until the rate of reaction decreases below a pre-
selected “exit” threshold level. The heating then is resumed at a constant
rate until the next weight loss is encountered. This sequence is repeated for
each weight loss during the experiment. The stepwise TG method has
shown to be a valuable technique in resolving transitions, which are closely
spaced with regards to temperature.

3.0 MODERN TECHNIQUES

3.1 Thermomechanical Analysis (TMA)

Thermomechanical analysis (TMA), as defined by ASTM E473-
85, is a method for measuring the deformation of a material under a constant
load as a function of temperature while the material is under a controlled
temperature program. The measuring system consists of a linear voltage
differential transformer (LVDT) connected to the appropriate probe (Fig.
7). Various probes are available and the measurements can be done in either
compression, expansion, penetration, flexure, or in tension mode. It is this
variety of probes which allows for the measurement on samples of different
configurations. Any displacement of the probe generates a voltage that is
then recorded. The dimensional change of a sample with an applied force