Is it possible for more than one glass transition range for a thermoplastic polymer. If so why and how? I need the exact answer of this question. Please help.
There is no reason why you need to call this transition other than the glass transition as this name is so widely known and accepted, though sometimes you might call it glassy to rubbery transition. You can observe more than one glass transition when you see slightly different degree of mobility in the non-crystalline phase. For example, multiple transitions, crystal to smectic, smectic to nematic, and nematic to isotropic transition in liquid crystalline polymers. For some rigid polymers, there is another transition near the main glass transition peak caused by a rigid amorphous phase at the crystal to amorphous interphase. Classic definition of a crystal is the order in all three directions. This perfect packing will be disturbed as soon as defects are introduced. Depending on the defect concentration, the chain mobility and range of those chains moving can change and when the range becomes large enough, then it can show glass transition. When the range of the chain moving is short, it influences the beta transition (glass transition being the alpha transition). For some time, glass transition was explained by the ability of the polymer chains go in and out of the free volume, though the free volume theory is not considered good enough to explain the glass transition today. The glass transition is considered classically as the second order thermodynamic transition. However, more modern understanding is that the glass transition is more than a simple thermodynamic transition. Unfortunately, there is no widely accepted molecular level interpretation of glass transition available today, despite the fact that it is so easy to observe it.
Some sceintists think that there is a phenomenon called "polyamorphousness", which may lead to multiple glass transitions even within a single component amorphous or liquid material:
Article Polyamorphism and Liquid-Liquid Phase Transitions: Challenge...
https://en.wikipedia.org/wiki/Polyamorphism
Article Polyamorphous Transformation in Bulk Metallic Glass-forming ...
https://www.it.cas.cz/en/featured-articles/polyamorphous-liquids-and-waters-secrets/ and much more ...
which is also linekd with the much debated existence of liquid-liquid transitions in polymer melts:
Article Free volume dependence of polymer viscosity