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Glass Transition Theory

Explains the discontinuous change in properties observed in amorphous polymers as a function of temperature, driven by segmental motion.
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The statement of the theorem

Define the specific enthalpy H(T)H(T) and specific volume V(T)V(T) of an amorphous polymer as functions of temperature TT. The glass transition temperature, TgT_g, is mathematically characterized by the discontinuity in the slope of the enthalpy or volume curve: \begin{equation*} \lim_{T \to T_g^-} \frac{d H}{d T} \neq \lim_{T \to T_g^+} \frac{d H}{d T} \end{equation*} This discontinuity reflects the change in the heat capacity CpC_p: \begin{equation*} C_p(T) = \frac{d H}{d T} \end{equation*} Specifically, the jump in heat capacity is ΔCp=Cp(Tg+)−Cp(Tg−)\Delta C_p = C_p(T_g^+) - C_p(T_g^-). The transition is driven by the onset of large-scale segmental motion, which activates the relaxation time τ\tau such that τ(T)∝exp⁡(EakBT)\tau(T) \propto \exp\left(\frac{E_a}{k_B T}\right).