I want know about the relation between Tα and Tg in both amorphous and crystalline polymers.
In amorphous polymers Tg is usually the main transition appearing at the highest temperature, accompanied by a drop in modulus. As this is the highest temperature transition, it is usually denoted as T(alpha). In semicrystalline polymers Tg is usually arounf 2/3*Tm where Tm is the melting temperature. Between Tg and Tm usually there are on or more "pre-melting" transitions detectable as a maximum (or shoulder) in tan delta (mechanical spectroscopy). There are more notations. If the highest temperature transition is denoted as alpha, Tg may be denoted as T(beta). Some others use alpha, alpha dash, alpha double dash. I personally prefer notations as Tg and Tcc where cc means crystal-crystal transition.
In amorphous polymers Tg is usually the main transition appearing at the highest temperature, accompanied by a drop in modulus. As this is the highest temperature transition, it is usually denoted as T(alpha). In semicrystalline polymers Tg is usually arounf 2/3*Tm where Tm is the melting temperature. Between Tg and Tm usually there are on or more "pre-melting" transitions detectable as a maximum (or shoulder) in tan delta (mechanical spectroscopy). There are more notations. If the highest temperature transition is denoted as alpha, Tg may be denoted as T(beta). Some others use alpha, alpha dash, alpha double dash. I personally prefer notations as Tg and Tcc where cc means crystal-crystal transition.
In order to derive relation between Tα and Tg, we first derive relation between Tα and Tm ; then Tm and Tg and ultimately between Tα and Tg (both for unsymmetrical and symmetrical polymers) as follows:
Tα(alpha relaxation temperature) is the temperature at which the hindered rotation of polymer chains inside the folded crystals can occur.
Tα/Tm ≈0.9 -----------------------[1]
[A] For Unsymmetrical polymers:
Tg/Tm ≈ 0.667 -------------- [2]
So for Unsymmetrical polymers
Tα/Tg ≈ 1.35----------------[3]
[B] For Symmetrical polymers:
Tg/Tm ≈ 0.5 -------------- [4]
So for Symmetrical polymers
Tα/Tg ≈ 1.8----------------[5]
Yes and no. Depends on the convention used by the author...unfortunately.
However, you can recognized the glass (or some subglass transitions) by their modified temperature dependence (Vogel, WLF...) or from the shape of the heat evolution versus temperature///
What about for sugar compounds, if the Tα/Tg ≈ 0.9, how do we
interpret the results ?
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