Prediction of the heat capacity of main-chain-type polymers below the glass transition temperature

• Published in: Polymer journal 2020-09, Vol.52 (9), p.1113-1120
• Main Authors: Yokota, Marika, Tsukushi, Itaru
• Format: Article
• Language: English
• Subjects: 639/301/923/1028; 639/638/440; Benzoates; Biomaterials; Bioorganic Chemistry; Chains (polymeric); Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Einstein equations; Formulas (mathematics); Functional groups; Glass transition temperature; Heat; High temperature; Mathematical analysis; Monomers; Original Article; Polymer Sciences; Specific heat; Surfaces and Interfaces; Thin Films; Vibration mode
• ISSN: 0032-3896; 1349-0540
• DOI: 10.1038/s41428-020-0365-2

This study predicts the absolute values of heat capacities from the molecular formula per monomer for main-chain-type polymers below the glass transition temperature. The frequencies of the skeletal and group-vibration modes are calculated using the Tarasov and Einstein equations, respectively, and the heat-capacity differences at constant pressure and constant volume are used to correct the predicted heat capacity. The contributes of skeletal vibrations to the heat capacity can be expressed by one- and three-dimensional Tarasov equations, and the contribution of group vibrations can be determined by summing the group-vibration heat capacities for functional groups and atoms constituting the monomer as obtained from the Einstein equation. The absolute value of the heat capacity is predicted from this combination of equations. The heat capacities of poly(4-methyl-1-pentene) are predicted within an error range of 8.0% from 90 to 180 K and ±2.0% from 180 to 300 K. The heat capacities of poly(vinyl benzoate) are within ±2.0% agreement from 190 to 350 K, while for poly(1,4-butylene adipate), the agreement is within ±2.0% from 80 to 200 K. This study predicted the absolute values of the heat capacities from the molecular formula per monomer for a main-chain-type polymer below the T g . The calculations combined the Tarasov equation, the Einstein equation, and the ( C p  −  C V ) correction term, accounting for the degrees of freedom of the monomer unit. The difference of predicted and experimental heat capacities of poly(4-methyl-1-pentene) was within 8.0% from 90 to 180 K and within ±2.0% agreement from 180 to 300 K. For poly(vinyl benzoate), the values were within ±2.0% from 190 to 350 K, and for poly(1,4-butylene adipate), they were within ±2.0% from 80 to 200 K. The predicted heat capacity was accurate, especially in the high-temperature region above 180 K.