OptiMelt Automated Melting Point System - Stanford Research ...

80 Pharmacopeia vs. Thermodynamic Melting Points Appendix Aclear point (pharmacopeia melting point, MP pharma ). The thermodynamic correction isdefined as:() r = MP pharma −MPthermo∆ T(eqn. 1)and must be expresed as a function of the ramping rate, r.In order to obtain the thermodynamic melting temperature of a pure substance, it isnecessary to calculate and subtract a thermodynamic correction from the detected clearpoint. This calculates back to the temperature at the beginning of the melt, so that thevalue obtained has virtually no dependence on the temperature ramping rate.Instruments with automated melting point determination facilities (such as OptiMelt),often pack enough data analysis infrastructure to automate the thermodynamic correctionprocedure: (1) the clear point is accurately identified and recorded, (2) the ramping rate isknown and carefully controlled, and (3) the thermodynamic correction algorithm can beprogrammed and stored in memory. Knowledge of the functional dependence of thethermodynamic correction, ∆T(r), on r is the only requirement to automate thethermodynamic correction process. A parametric derivation of that functional dependenceis presented in the following section.Thermodynamic CorrectionAt any given time, t, during a melt, the amount of heat, dQ(t), transferred from theheating stand to the sample during a time dt is:where,dQ()= t α ⋅ ( T −MP thermo )⋅ dt (eqn. 2)T is the temperature of the heating stand, [°C]t is the time variable, [min]α is the heat transfer constant for the melting point apparatus, [calories/(°C · min)]r = dT/dt is the temperature ramping rate of the instrument, [°C/min].Substituting dt with dT/r in eqn. 2, leads to:( T − MP ) dTα ⋅dQ()t = thermo ⋅(eqn. 3)rIntegration of the heat transferred from the block to the sample, over the entire meltingprocess, provides the “heat of fusion” of the sample, ∆H f [Calories], which is dependenton its mass but independent of the ramping rate, r:( T − MP )MPpharma⎡α ⋅thermo ⎤∆Hf=∫⋅ dTMP ⎢thermo ⎣ r ⎥(eqn. 4)⎦Calculation of the integral term leads to the analytical expression:OptiMelt Automated Melting Point System