Dynamic Mechanical Analysis (DMA) is particularly useful for measuring transitions in polymers that cannot be detected by other techniques. For example, the DMA curve of polycaprolactone measured at a meachnical vibration frequency of 1 Hz is shown below:
The drop in storage modulus (E') and peak in damping factor (tan delta) between -60 and -30°C is due to the glass transition (Tg) of the amorphous polymer in this semi-crystalline material. Above 50°C the sample begins to melt and flow, thus loosing all mechanical integrity. Below the Tg small peaks are evident in the tan delta curve at -80 and -130°C. These are the beta and gamma transtions in this polymer (the glass transition is known also as the alpha transition) and are caused by local motion of the polymer chains as opposed to large scale co-operative motion that accompanies the Tg. These small transitions are very difficult to observe by DSC but are often very important in determining the impact resistance of the polymer.
The viscoelatic behaviour of polymers means that there is often a time dependence of their properites in addition to any temperature effects. An example of this is shown for poly(ethylene terephalate) measured at different mechanical oscillation frequencies:
As the mechanical frequency is increased the position of the glass-rubber transtion moves to a higher temperature since the polymer chains need more energy (i.e. the sample needs to be hotter) to respond to the shorter timescale stresses imposed at higher frequencies. Thus time and temperature can be seen to be interchangable. This can be demonstrated by plotting the data from the curve above on a frequency axis:
Then all the curves except those gathered at some particular reference temperature (in this case 100°C) can be shifted in time (or frequency) so as to overlap:
The temperature dependence of the shift factors can often follow an Arrhenius relationship over a narrow temperature range so that a plot of log[shift factor] versus reciprocal absolute temperature is linear with a slope corresponding to the activation energy of the viscous flow that accompanies the glass transition:
Close inspection of the above plot shows that there is some curvature of the apparently linear relationship between the log[shift factor] and 1/temperature. The Williams-Landel-Ferry (WLF) equation is most often used to describe this time-temperature superposition more accurately:
log[aT] = C1(T-Tref)/(C2 + T - Tref)
Where aT is the temperature dependant shift required to allign the cuves above, Tref is the reference temperature at which the master curve is constructed (often Tg) and C1 & C2 are constants. This approach enables one to predict the mechanical properties of polymers outside the experimental timescales usually available in conventional DMA equipment (10-2 to 102 Hz)