GATE (TF) Textile 2015 Question Paper Solution | GATE/2015/TF/41

Tg, Tc, and Tm are terms commonly used in the field of polymer science and materials engineering, and they refer to different temperature-related properties of polymers. The relationships between Tg, Tc, and Tm can vary depending on the specific polymer being considered.
Glass Transition Temperature (Tg): Tg is the temperature at which an amorphous polymer transitions from a glassy, brittle state to a rubbery, more flexible state. It is the temperature below which the polymer transitions from a rigid, glass-like material to a more mobile, rubbery material. Tg is an important parameter in understanding the mechanical, thermal, and processing properties of polymers, as it can affect their stiffness, brittleness, and dimensional stability. Tg is typically determined using techniques such as differential scanning calorimetry (DSC) or dynamic mechanical analysis (DMA).
Crystallization Temperature (Tc): Tc is the temperature at which a polymer undergoes crystallization, which is the process of forming an ordered, crystalline structure from a disordered, amorphous state. Polymers that are capable of crystallization, such as polyethylene and polypropylene, can exhibit a sharp increase in crystallinity as the temperature is lowered below Tc. Crystallization can affect the mechanical, thermal, and barrier properties of polymers, and it is an important parameter in processing techniques such as melt extrusion and injection molding.
Melting Temperature (Tm): Tm is the temperature at which a crystalline polymer transitions from a solid to a liquid state upon heating. It is the temperature at which the polymer’s crystalline regions lose their ordered structure and become more mobile, resulting in a decrease in the material’s stiffness and an increase in its flowability. Tm is typically determined using techniques such as DSC or thermomechanical analysis (TMA).
The relationship between Tg, Tc, and Tm can vary depending on the specific polymer. In some cases, Tg and Tc may be close or even overlapping, indicating that the polymer’s glass transition and crystallization occur in a similar temperature range. In other cases, Tg and Tc may be distinctly separated, with a significant temperature difference between them. Tm, on the other hand, is typically higher than Tg and Tc, as it represents the temperature at which the polymer’s crystalline regions melt and lose their ordered structure.
It’s important to note that not all polymers exhibit crystallization, and not all polymers have a distinct melting temperature. Amorphous polymers, for example, do not have a well-defined Tc or Tm, as they do not exhibit crystalline regions. Additionally, the presence of additives, molecular weight, polymer composition, and processing conditions can also affect the values of Tg, Tc, and Tm for a given polymer. Therefore, the relationship between Tg, Tc, and Tm can vary widely depending on the specific polymer system being considered.