There has been discussion of this in the literature since the early 1950's when a number of papers showed that there is an empirical relationship such that Tg/Tm is approx equal to 2/3 (when expressed in K) for many polymers. Later work (Lee and Knight, 1970) showed that this ratio varies widely depending on the polymer in question. This has more recently been summarized by Van Krevelen, to show that a majority of polymers that crystallize (about 80%) have a Tg/Tm ratio of between 0.56 and 0.76, with a large majority of those with a ratio of 2/3. There are of course exceptions to this general rule, and it has been found that polymers with Tg/Tm ratios below 0.5 are highly symmetrical, i.e. have two identical substituents, and have short repeating units consisting of up to two main-chain atoms, and also have single atom substituents, ie PE, PTFE etc. Polymers which have Tg/Tm ratios above 0.67 are unsymmetrical, and they can also be highly crystalline if they contain long sequences of methylene groups or are highly stereo regular. To date there has not been a direct correlation determined between Tg and Tm, so these empirical relationships remain the best there is at present.

It is really difficult to correlate between Tg and Tm of a particular polymer. The glass transition is the chain mobility and influenced by plasticizer, MW, PDI etc. and many other factors whereas the Tm is the thermal transition and very specific for a polymer with a little change. Tg is very distinct for amorphous polymer whereas Tm is only found for crystalline polymer. We can correlate Tg and Tm based on MW or %of plasticizer for a particular polymer. 

 Abdul:

If you have not yet, see this RG link on your topic can be helpful in finding some valuable research and comments for you: https://www.researchgate.net/topic/glass_transition

Best regards,

Debra

We may want to consider the well-known Williams-Landel-Ferry (WLF) viscosity model: μ = μº·exp [-C1·ΔT / (C2 + ΔT)]. Here μº stands for the dynamic viscosity of the polymer at the reference temperature, Tº ≥ Tg, while μ refer to the actual temperature being considered (T), taken as exceeding Tº by a ΔT gap (ΔT = T-Tº), while C1 and C2 are empiric (fitting) parameters. For our present purpose we may identify Tº with Tg, while we shall also accept to extend the WLF to the melting temperature, Tm, with a corresponding viscosity, μ*. The viscosities at Tg and Tm, respectively μº and μ*, can usually be taken as corresponding to widely accepted generic values, independent of the actual polymer being considered. Hence, we can write: ln (μ* / μº) = -C1·ΔT* / (C2 + ΔT*), with ΔT* = Tm - Tg. This rewrites itself as: Tm - Tg = - C2 ·ln (μ* / μº) / [ln (μ* / μº) + C1]. The C1 and C2 fitting parameters can in principle be determined from viscosity measurements at intermediate temperatures between Tm and Tg. 

Most of the parameters such as, hydrogen bonding, polar interaction, aromaticity etc. affect both Tg and Tm in same direction.

There has been discussion of this in the literature since the early 1950's when a number of papers showed that there is an empirical relationship such that Tg/Tm is approx equal to 2/3 (when expressed in K) for many polymers. Later work (Lee and Knight, 1970) showed that this ratio varies widely depending on the polymer in question. This has more recently been summarized by Van Krevelen, to show that a majority of polymers that crystallize (about 80%) have a Tg/Tm ratio of between 0.56 and 0.76, with a large majority of those with a ratio of 2/3. There are of course exceptions to this general rule, and it has been found that polymers with Tg/Tm ratios below 0.5 are highly symmetrical, i.e. have two identical substituents, and have short repeating units consisting of up to two main-chain atoms, and also have single atom substituents, ie PE, PTFE etc. Polymers which have Tg/Tm ratios above 0.67 are unsymmetrical, and they can also be highly crystalline if they contain long sequences of methylene groups or are highly stereo regular. To date there has not been a direct correlation determined between Tg and Tm, so these empirical relationships remain the best there is at present.

Jürn W. P. Schmelzer

Glass Selected Properties and Crystallization

Book (2014)

this book can answer your question

Tg is for  amorphous polymers and Tm is for crystaline polymers

Tm is always higher than Tg.