https://doi.org/10.1351/goldbook.15385
Temperature above which, in a given chain polymerization, polymer of high molar mass is not formed.
Notes:
- A ceiling temperature is only observed for enthalpy-driven chain polymerizations in which \(\Delta H_{\rm{m}} \lt 0\) and \(\Delta S_{\rm{m}} \lt 0\), where \(\Delta H_{\rm{m}}\) and \(\Delta S_{\rm{m}}\) are respectively the enthalpy and entropy change per mole of monomer reacted.
- For most chain polymerizations, \(\Delta H_{\rm{m}} \lt 0\) and \(\Delta S_{\rm{m}} \lt 0\).
- Below \(T_{\rm{c}}\), \(\Delta G_{\rm{m}} (= \Delta H_{\rm{m}} - T\Delta S_{\rm{m}}) \lt 0\); at \(T_{\rm{c}}\), \(\Delta G_{\rm{m}} = 0\); and above \(T_{\rm{c}}\), \(\Delta G_{\rm{m}} \gt 0\).
- Because \(\Delta G_{\rm{m}} = 0\) at the ceiling temperature, \(T_{\rm{c}} = \Delta H_{\rm{m}}/\Delta S_{\rm{m}}\). If \(\Delta H_{\rm{m}}^{\circ}\) and \(\Delta S_{\rm{m}}^{\circ}\) are the enthalpy and entropy changes in the standard state, and the monomer behaves ideally, then \[T_{\rm{c}} = \Delta H_{\rm{m}}^{\circ}/\{\Delta S_{\rm{m}}^{\circ} + R\ln ([{\rm{M}}]_{0}/c^{\circ})\}\] where \(c^{\circ} = \pu{1 mol dm-3}\) is the standard concentration and \([{\rm{M}}]_{0}\) is the initial monomer concentration. Thus, \(T_{\rm{c}}\) depends on the initial monomer concentration.
- The symbol \(T_{\rm{c}}(c^{\circ})\) is used to denote the ceiling temperature when the initial monomer concentration, \([{\rm{M}}]_{0}\), is equal to \(c^{\circ}\).
- The symbol \(T_{\rm{c}}({\rm{bulk}})\) is used to denote the ceiling temperature when the initial monomer concentration is equal to its undiluted concentration.
See also: floor temperature