Introduction to Dynamic Mechanical Analysis (4)
DMA is also used to study the behaviour of thermosetting polymers that are undergoing cross-linking due to chemical reaction. The curves below show the overlaid DMA and DSC response of a carbon fibre-epoxy composite undergoing isothermal curing at 120°C. The large peak in heat flow at the start is due to the chemical reaction. The mechanical properties do not start to change until about 5 minutes into the crosslinking process as a network of polymer molecules begins to form (gel point). Even after nearly an hour, the DMA detects that curing is still continuing although the DSC response has subsided.
Results from such experiments can be used to construct diagrams showing the changes in a thermoset’s properties which occur as a function of cure time and temperature. Such a "time-temperature-transformation" diagram is shown below:
Such diagrams are usually obtained by impregnating inert glass fibre braids with the (often low viscosity) uncured resin in order to provide sufficient stiffness for the instrument to work against at the start of the eperiment. It is not generally possible to measure the absolute mechanical modulus of the polymer using this technique. When a material is sufficiently cross-linked to form a solid with a reasonable degree of mechanical integrity above the glass rubber transition then DMA can be used to estimate its cross link density using the formula:
G = rRT/Mc
Where G is the equilibrium shear modulus, r is the density, R is the gas constant, T the thermodynamic temperature and Mc the average molecular weight between cross-links. The storage modulus at low frequencies approximates to the equilibrium modulus and can be used in these calculations. In this way, the mechanical properties can be related to the polymer structure.