Statistical mechanical deconvolution of thermal transitions in macromolecules. I. Theory and application to homogeneous systems

The theoretical basis for the statistical mechanical deconvolution of a thermally induced macromolecular melting profile is presented. It is demonstrated that all the thermodynamic quantities characterizing a multistate macromolecular transition can be obtained from the average excess enthalpy function, 〈ΔH〉, of the system, without any assumption of the particular model or mechanism of the reaction. Experimentally, 〈ΔH〉 is obtained from scanning calorimetric data by direct integration of the excess apparent molar heat capacity function, ΦCp. Once 〈ΔH〉 is known as a continuous function of the temperature, the partition function, Q, of the system can be calculated by means of the equation (Formula Presented.) From the partition function all the thermodynamic quantities of the system can be obtained. It is shown that the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.