[For M.Sc. Chemistry (Physical Ch Specialization) students at Cotton College. By Rituraj Kalita.]

Differential Scanning Calorimetry (DSC):

In this method, the specific heat of the polymer sample is estimated over a wide range of temperature scanned, by noting the difference in the heating power supplied to the sample and the reference holders, where the heating powers are supplied in such a rate so that the sample and the reference always maintain the equal temperature. Here an average-temperature circuit goes on measuring and controlling the temperature of both so that it conforms to a pre-programmed linear (uniform) rate of rise of temperature with time. On the other hand, a temperature- difference circuit goes on comparing the temperatures of the sample and reference holders, and distributes the power to each holder in such a way so that their temperatures remain equal. Now, The difference of the supplied heating power to the two holders is continuously plotted against the increasing temperature by using an automated recorder. When the sample undergoes a thermal transition such as glass transition or melting, the sample holder requires a greater heating power, and there's a peak in the curve. In such a case, the excess area coming under the curve is a direct measure of the heat of transition. On the other hand, if there occurs an onset on crystallinity above the glass transition temperature, there's a drop in the curve. Thus, though with a moderate accuracy, DSC can speedily measure the thermal characteristics of a sample over a large range of temperature.

As an example, the DSC curve of quenched (amorphous) PETP sample is shown in figure. With increasing temperature, the curve rises slowly at low temperature, then steeply during the glass transition, 60-80 degree centigrade. With the onset of mobility of molecular chains above this temperature, crystallization occurs as is indicated by the sharp drop. At still higher temperatures, 220-270 C, the crystalline form melts which is indicated by the corresponding steep rise.

Thermogravimetric Analysis (TGA):

Most polymer samples undergo some chemical reactions and physical changes when heated to different temperatures. Many such chemical reactions lead to formation of volatile products that go away, decreasing the residual mass of the sample. In some cases, all the products are volatile, so that no residual mass remains. Thermogravimetric analysis is a fast and convenient method for getting information about such behaviour on heating. In it, the temperature is increased continuously, and the consequent mass change is followed by using a sensitive balance that continuously monitor the residual mass, and is plotted against the rising temperature. It is obvious that this plot offers valuable information about the thermal stability and thermal decomposition behaviour, as those chemical reactions are bound to destroy the utility of the polymer. As the temperatures of the reactions and the change in mass depend on the exact chemical structure in the polymer, this method can also be used to assess the extent of cure in condensation polymers, and the composition in copolymers. As the filler materials are generally thermally stable, TGA can also be used to assess composition of filled polymers.

In the figure TGA plots of percent remaining mass versus the increasing temperature (in nitrogen atmosphere) are shown for several polymeric materials. Here it is seen that PVC first loses HCl at around 270 C, later the mixture of resulting unsaturated carbon-carbon backbone and unchanged PVC partly chars and partly volatilize to small fragments, leaving a small amount of char. On the other hand, PMMA, HPPE and PTFE degrade completely during three small but different ranges of temperatures, while a polyimide (PI) partly decomposes, forming an almost non-volatile char above 800 C.

Viscoelastic behavior of polymers with associated models:

                When placed under stress, the polymers show different forms of flow or deformation behavior, depending on the structure and composition of the individual polymer used, and also on temperature. In general, the deformation behavior of any polymer is more or less complicated, and is a combination of both a permanent flow (viscous) and a temporary deformation (elastic) behavior, and so the rheological behavior of polymers is known as viscoelasticity.

                Viscoelastic behavior of polymers can be understood in terms of several models derived using two simple models called the Hooke and the Newton models, respectively of elasticity and viscosity. The Hooke model is about the simple elastic behavior of reversible deformation with a stress-strain proportionality and an instantaneous recovery upon release of stress. It is obeyed in the case of amorphous polymers below the glass transition temperature, and partially also in case of crystalline polymers such as fibers. The other basic model i.e., the Newton model is about the simple viscous behavior of irreversible deformation as observed in a liquid, with a proportionality between stress and the time rate of change of strain. It is obeyed in polymer melts and also approximately in non-crosslinked amorphous polymers such as raw rubber and latex, when kept above their glass transition temperature. The Newton model is expressed by drawing a dashpot, and Hooke model by a spring, as shown in the figure. Under a constant temporary stress between time t₁ and t₂, the strain vs. time plot.

                However, polymers in general show rheological behavior more complicated than these two models, and such behaviors are viscoelastic ones. Fiber forming polymers such as nylon shows a small irreversible strain combined with an elastic reversible deformation associated with a high tensile strength. To express such behavior, the Maxwell model is used, which is composed of a spring and a dashpot connected in series (as in figure). So, in this model the strain is shared: it's a linear combination of an irreversible and a reversible strain, with the strain vs. time curve showing the two types of strain superimposed.

                On the other hand, the elastomers, i.e., the crosslinked amorphous polymers above the glass transition temperature show a large reversible strain, but the strain is time-dependent (i.e., non-instantaneous) unlike the Hooke model. Such a delayed elongation with a delayed but complete recovery can be explained with the help of Kelvin-Voigt model, which comprises of a spring and a dashpot connected in parallel (as in figure), so that here the stress is shared or divided. The strain is common to both the spring and dashpot element, and so the strain is reversible but delayed. The Kelvin-Voigt model is suitable for an mathematical understanding of the phenomena of strain retardation or creep (under constant stress), while the Maxwell model is suitable for an mathematical understanding of the phenomena of stress relaxation (upon constant strain), both common in polymeric materials.

                However, the majority of the polymers show an even more complicated viscoelastic behavior with a combination of instantaneous elongation, delayed elongation, instantaneous recovery, delayed recovery and permanent set. To describe such phenomena, a series combination of a Hooke model, a Kelvin-Voigt model and a Newton model is necessary; such a complicated model (shown in figure) is called a Burger model. It can be shown that this model can explain the most generalized strain vs. time curve for polymeric materials shown in figure.

(Figures to be added. Mathematical Treatments for the Mentioned Models to be added later.)