# Differential Scanning Calorimeter (DSC)

Linseis Chip DSC 10 [SOP]
Temperature: Range: -180°C (using LN2) to 500°
Heating and cooling rates: 0.001 up to 250 K/min
Resolution: 0.03 µW
Measuring range: +/-2.5 up to +/-250 mW

The Linseis Differential Scanning Calorimeter (DSC) is a thermal testing instrument used for measurements of material properties such as transformation temperatures, enthalpies of transformation, and heat capacities. It is capable of measuring temperatures up to 500°C and can use both solid and liquid specimens.

## Thermal Properties & Transitions

### Heat Capacity

The heat capacity ($\displaystyle{ Cp }$) of a system is the amount of heat needed to raise its temperature 1°C [1]. It is usually given in units of Joules/°C and can be found from the heat flow and heating rate. The heat flow is the amount of heat ($\displaystyle{ q }$) supplied per unit time ($\displaystyle{ \frac{q}{t} }$). The heating rate is the time rate change of temperature $\displaystyle{ \frac{\Delta T}{t} }$ where $\displaystyle{ \Delta T }$ is the change in temperature. One can obtain the heat capacity from these quantities $\displaystyle{ Cp = \frac{q/t}{\Delta T/t} = \frac {q}{\Delta T} }$. This means the heat capacity can be found by dividing the heat flow by the heating rate. If the $\displaystyle{ Cp }$ of a material is constant over some temperature range, then the plot of heat flow against temperature will be a line with zero slope as shown in the figure. If the heating rate is constant, the distance between the line and the x axis is proportional to the heat capacity. If heat is plotted against temperature, the heat capacity is found from the slope.

Schematics of a glass transition. The glass transition results in a kink in the heat versus temperature plot due to the change in heat capacity (A). In a plot of heat flow versus temperature it is a gradual transition that occurs over a range of temperatures (B). The glass transition temperature is taken to be the middle of the sloped region.

### Glass Transition

Example of a crystallization ‘peak’ in a plot of heat flow against temperature. Crystallization is an exothermic process, so the heat flow to the sample must be decreased to maintain a constant heating rate.

If a molten polymer is cooled it will at some point reach its glass transition temperature ($\displaystyle{ T_g }$). At this point, the mechanical properties of the polymer change from those of an elastic material to those of a brittle one due to changes in chain mobility. $\displaystyle{ C_p }$ of polymers is usually higher above $\displaystyle{ T_g }$. DSC is a valuable method to determine $\displaystyle{ T_g }$. It is important to note that the transition does not occur suddenly at one unique temperature but rather over a range of temperatures. The temperature in the middle of the inclined region is taken as the $\displaystyle{ T_g }$.

### Crystallization

Above the glass transition temperature the polymer chains have high mobility. At some temperature above $\displaystyle{ T_g }$, the chains have enough energy to form ordered arrangements and undergo crystallization. Cold crystallization is an exothermic process that occurs during heating and consists of previously amorphous regions rearranging themselves into new crystallites from the thermal energy being put into the polymer during heating. Such a crystallization 'peak' can be used to confirm that crystallization occurs in the sample, find the crystallization temperature ($\displaystyle{ T_c }$), and determine the latent heat of crystallization. The crystallization temperature is defined as the lowest point of the dip. The latent heat (enthalpy) of crystallization is determined from the area under the curve. Cold crystallization can occur when a semi-crystalline polymer has been rapidly quenched during processing, so it has been frozen in an amorphous state. Re-crystallization is also exothermic, but occurs during cooling and arranges molten polymer chains into ordered crystalline structures.

### Melting

The polymer chains are able to move around freely at the melting temperature ($\displaystyle{ T_m }$) and thus do not have ordered arrangements. Melting is an endothermic process, requiring the absorption of heat. The temperature remains constant during melting despite continued heating. The energy added during this time is used to melt the crystalline regions and does not increase the average kinetic energy of the chains that are already in the melt. In a plot of heat against temperature this appears as a jump discontinuity at the melting point. The heat added to the system during the melting process is the latent heat (enthalpy) of melting and can be calculated from the area of a melting peak observed in a plot of heat flow against temperature. The $\displaystyle{ T_m }$ is defined as the temperature at the peak apex. After melting, the temperature again increases with heating.

Typical DSC heating plot for a polymer that undergoes a glass transition, crystallization and melting.

## DSC Heating Curves of Polymers

It is worth noting that not all polymers undergo all three of the aforementioned transitions during heating. The crystallization and melting peaks are only observed for polymers that can form crystals. While purely amorphous polymers will only undergo a glass transition, crystalline polymers typically possess amorphous domains and will also exhibit a glass transition. The amorphous portion only undergoes the glass transition while the crystalline regions only undergo melting. The exact temperatures at which the polymer chains undergo these transitions depend on the structure of the polymer. Subtle changes in polymer structure can result in huge changes in $\displaystyle{ T_g }$. In a perfectly crystalline polymer, the plot of heat against temperature has a jump discontinuity at the melting point. The plot of heat against temperature is continuous for the glass transition, but plot is not smooth (the slope at $\displaystyle{ T_g }$ is different depending on if you approach the point from the right or the left).

DSC curve showing phase transitions of iron [2]

## DSC Curves of Metals

In metals, heat capacity and melting/solidification information can be determined through DSC, as well as other solid-solid transitions such as the Curie transition (where magnetic properties change from ferromagnetic to paramagnetic) and transitions between different types of crystal structure.

## Test Parameters

DSC Plot showing multiple heatings of a PLA sample (exothermic up)

DSC has several test parameters that are crucial to set to proper values based on the sample(s) being tested in order to obtain the best data possible. These include the endpoints, ramp rate, and number of heating/cooling cycles. The endpoints when testing an unknown polymer should be determined by the maximum temperature that the DSC model is capable of and the degradation temperature of that polymer (can be found from TGA). Changing the ramp rate of the DSC can affect the sensitivity and resolution of the measurements and the appearance of the curves. A high ramp rate (such as 50°C/min) increases sensitivity at the cost of resolution, while a very low ramp rate (0.1°C/min) could cause the sample to undergo unwanted annealing/crystallization. Multiple heating/cooling curves are used when a polymer has undergone processing to find its intrinsic values, while the first heating curve shows any processing the polymer has undergone.

In a situation where the initial heating curve of a semi-crystalline polymer such as PET shows a certain $\displaystyle{ T_g }$, $\displaystyle{ T_c }$, and $\displaystyle{ T_m, }$ the cooling rate can have a significant effect on the values of these parameters found in the following heating cycle. For a slow cool (~1°C/min) these values would be expected to decrease, while they would be expected to increase due to a very fast cool (~1000°C/min). $\displaystyle{ \Delta H_c }$ would be expected to decrease while $\displaystyle{ \Delta H_m }$ would be expected to increase in the slow cool and while the opposite would be expected in the fast cool.

The enthalpy values of cold crystallization ($\displaystyle{ \Delta H_c }$), melting ($\displaystyle{ \Delta H_m }$), and recrystallization ($\displaystyle{ \Delta H_{rc} }$) transitions (where applicable) for each sample can be determined from trapezoidal Riemann sums which calculate the area under each peak. The heat capacity of each sample ($\displaystyle{ C_p }$) at a certain temperature can be calculated by dividing the heat flow at that temperature by the heating rate (typically 10 degrees/min). The percentage crystallinity ($\displaystyle{ X_C }$) can be calculated from the following equation:
$\displaystyle{ X_C = \frac{\Delta H_m}{\Delta H^\circ_m} \cdot 100\% }$
where $\displaystyle{ \Delta H^\circ_m }$ is the melting enthalpy for a 100% crystalline sample (found in literature).