Molecular interpretation of low-temperature heat capacity of aliphatic oligo-urethane

Abstract

The low-temperature heat capacity of semi-crystalline aliphatic oligo-urethane obtained from the reaction between butane-1,4-diol and hexamethylene 1,6-diisocyanate was measured using a Quantum Design PPMS (Physical Property Measurement System) in the temperature range of (2.04–292.38) K. The experimental heat capacity data below the glass transition temperature of 280.2 K (7.05 °C) were interpreted in terms of molecular motion and were linked to the vibrational spectrum of oligo-urethane structure. The presented approach applies the classical Einstein, Debye and Tarasov treatments using the ATHAS Scheme. The low-temperature solid heat capacity was estimated by separately approximating the group and skeletal heat capacities from their vibrational spectra. The group vibrational heat capacity was calculated based on the chemical structure and molecular vibrational motions (Ngr = 90) derived from infrared and Raman spectroscopy. The skeletal vibrational heat capacity contribution was estimated by a general Tarasov equation with thirty skeletal modes (Nsk = 30). The solution of this equation gave the values of characteristic Debye temperatures as: Θ1 = 493.6 K, Θ2 = 133.9 K, and Θ3 = 51.6 K. The result indicates the existence of planer (Θ2) interactions in the oligo-urethane molecules, in addition to linear (Θ1) and special (Θ3) interactions, which are attributed to a possible branched structure mixed with the linear form of the oligomer. The total vibrational heat capacity, being the sum of the group and skeletal heat capacities, was extended to higher temperatures and analysed further.

The liquid heat capacity of semi-crystalline aliphatic oligo-urethane was approximated from experimental data by a linear regression and was compared with the estimated linear contributions of polymers that have the same constituent groups and were expressed as Cp(liquid) = 0.406T + 428.5 in J·K−1·mol−1. The solid and liquid heat capacities of oligo-urethane were applied as equilibrium baselines for advanced thermal analysis of the experimental, apparent heat capacity data.

Using estimated parameters of transitions and solid and liquid heat capacities at equilibrium, the integral thermodynamic functions of enthalpy, entropy and free enthalpy as functions of temperature were calculated.