Section G – Thermal methods
G3 THERMOMECHANICAL
ANALYSIS
Principles When any solid sample is heated, it will expand. The coefficient of linear
expansion, a, is given by:
a=(1/l)dl/dT ∼(l −lo)/((T −To) •lo)where l is the length, lothe initial length and T and Tothe temperature and initial
temperature. The coefficient of expansion is not constant with temperature, and
whenever a phase change occurs, such as from one crystal form to another, it will
change. This is very important with polymer and glassy samples, which are
brittle below the glass transition temperature, Tg, but pliable and resilient above
that temperature. This is shown in Figure 2. The measurement of length, or gener-
ally of dimensions such as volume, is also referred to as dilatometry.
When a sample is subjected to a force, F, it may behave in a variety of
different ways. A large force, suddenly applied may break it, while smaller
forces deform it, and liquid samples will flow. Elastic deformations are
reversible and the sample returns to its original shape when the force is
removed. Above the elastic limit it may undergo irreversible plastic deformation
into a new shape.
For a true elastic material, the behavior is described by the elastic (or
Young’s) modulus, E,E =(stress/strain) =(F/A)/(Dl /l)where F is the applied force, A the cross sectional area, l the length and Dl the
change in length measured.
Most materials, such as polymers, metals and glasses, possess some elastic
and some viscous properties, and are described as viscoelastic. This causes theKey Notes
The mechanical changes that occur when a sample is heated or cooled
may be measured by the various techniques of thermomechanical
analysis.Accurate measurement of length is made using electrical devices.
Viscoelastic moduli are determined from measurements of stress-strain
characterized by applying an oscillatory force to a solid sample.Coefficients of expansion and transition temperatures can be measured
accurately by these techniques. Polymer cure is readily studied.Related topics Thermogravimetry (G1) Evolved gas analysis (G4)
Differential analysis and differential
scanning calorimetry (G2)PrinciplesInstrumentationApplications