Modeling of Isomeric Structure of Diphenyl Urethane by FT-IR Spectroscopy During Synthesis from Phenylisocyanate and Phenol as an Inverse Kinetic Problem

Abstract

Isomeric structure of diphenyl urethane during synthesis from phenylisocyanate and phenol has been investigated by modeling the reaction extent as an inverse kinetic problem, using FT-IR difference spectroscopy, to obtain structural information on the formation of the isomeric structure. The aim of this study was to determine the primary algebraic structures (an inverse problem), which describe the chemical reaction system in terms of spectroscopic observables. Moreover, a conventional description of the evolution of chemical species and of the change of moles of the observable species, as a function of time, was explored, defined in terms of the extent of reaction ξ and the reaction stoichiometries ν, based on the Jouguet-de Donder equation, for an invariant system in batch experiments. Two processes for diphenyl urethane with hydrogen bonding and their free form were identified. Experimental input for the identification is a matrix of in situ spectroscopic data A (FT-IR/ATR spectra measured during the reaction process) and a matrix of initial moles (N(0)). Subsequently, (1) the number of observable reactions present, (2) the change of moles and their extent of reactions ξ, (3) the reaction stoichiometries v, (4) the concentration of all observable species (C), and finally (5) the kinetic rate constants were determined. Meaningful extraction of such algebraic system information (an inverse algebraic problem) is a mandatory prerequisite for the subsequent detailed kinetic modeling (an inverse kinetic problem). This research opens up the possibility of modeling the extent of the reaction and performing a kinetic analysis of the hydrogen bonding in an organic system. Important information could be extracted, for understanding of different functions and interactions of hydrogen bonding in a supramolecular system.