Thermodynamics of thermal methods for rapid screening of combinatorial libraries

Abstract

General equations are developed relating the dependence of temperature on time for a closed system undergoing chemical reaction. Equations are reported for thermally insulated systems and for systems where Newton's law of cooling describes the exchange of thermal energy between system and surroundings. These equations provide the basis for analysing and modelling thermal methods for screening combinatorial libraries. Key equations describe the impact of chemical reactions having different orders and molecularities. The potential of resulting differential equations is illustrated using numerical integration to yield temperature-time plots which highlight the roles of rate constants and enthalpies of reactions.

Three important calorimetric applications of a classic thermodynamic equation

“…Equation ( 10) is rearranged as an equation for the rate of change of temperature, dT/dt. Thus, (11) An indication of the patterns 19 which can emerge is obtained if we assume that the sample cell is perfectly thermally insulated; i.e. dq/dt) is zero.…”

“…A general pattern for this calorimetric technique 19 emerges after combining equation ( 13) for a perfectly thermally insulated sample cell with equation ( 9) for the dependence of composition on time for a first order reaction. Then (14) All terms on the r.h.s.…”

“…Equation ( 15) is the general equation for the temperature dependence of the solution in the sample cell. 19 (15)…”

“…A typical pattern 19 for the dependence of T(t) on time is shown in Figure 1. The temperature rises to a limiting value in the limit (t?H).…”