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

TLDR

The paper presents the theoretical basis for statistically deconvolving thermally induced macromolecular melting profiles. The method derives the average excess enthalpy from calorimetric data, uses it to compute the partition function, and then obtains all thermodynamic properties. The approach shows that all thermodynamic quantities, including discrete energy states, enthalpy/entropy changes, and temperature‑dependent populations, can be calculated recursively without assuming a specific model.

Abstract

Abstract 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, 〈Δ H 〉, of the system, without any assumption of the particular model or mechanism of the reaction. Experimentally, 〈Δ H 〉 is obtained from scanning calorimetric data by direct integration of the excess apparent molar heat capacity function, Φ Cp . Once 〈Δ H 〉 is known as a continuous function of the temperature, the partition function, Q , of the system can be calculated by means of the equation 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.