polymers Article Identification of the Temperature Dependence of the Thermal Expansion Coefficient of Polymers Igor N. Shardakov 1,2 and Aleksandr N. Trufanov 2, *   Citation: Shardakov, I.N.; Trufanov, A.N. Identification of the Temperature Dependence of the Thermal Expansion Coefficient of Polymers. Polymers 2021, 13, 3035. https://doi.org/10.3390/ polym13183035 Academic Editors: Sofiane Guessasma and Diego Antonioli Received: 8 August 2021 Accepted: 2 September 2021 Published: 8 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, 614013 Perm, Russia; shardakov@icmm.ru 2 Department of Computational Mathematics, Mechanics and Biomechanics, Perm National Research Polytechnic University, 614990 Perm, Russia * Correspondence: ant@pstu.ru Abstract: In this paper, we proposed an approach to study the strain response of polymer film samples under various temperature effects and note their corresponding effects. The advantages of the developed approach are determined by the fact that thin films of material are used as samples where it is possible to generate a sufficiently uniform temperature field in a wide range of temperature change rates. A dynamic mechanical analyzer was used for the experimental implementation of the above approach for two UV-curable polymers and one type of epoxy resin. Experimental results have shown that the thermal expansion coefficients for these polymers depend significantly not only on the temperature but also on its change rate. The strain response of the polymer to heating and cooling, with the same absolute values of the rate of temperature change, differs significantly, and this dissimilarity becomes stronger with its increasing. The results of thermomechanical experiments for massive samples on traditional dilatometer are shown to compare with the results for film samples. The discovered dependences of the temperature expansion coefficient on the temperature and its change rate can be used for mathematical modeling of thermomechanical processes arising during the operation of products made of polymers. Keywords: thermal properties; coefficient of thermal expansion; glass transition; thermal expansion behavior; polymer film sample; thermal cycles 1. Introduction Structural polymeric materials are widely used in various fields [1–3]. Modern ap- proaches to designing the thermomechanical behavior of products made of them require the completeness of information about the dependence of physical and mechanical properties of materials on the temperature. It is known that temperature changes significantly affect the thermomechanical properties of polymers [4,5]. At the same time, when thermal relaxation transitions take place, some parameters can change by times and even by orders of magni- tude [6,7]. Thus, the development of approaches that allow establishing thermomechanical properties of polymers in a wide range of temperatures is relevant. An important place among these properties is occupied by the coefficient of thermal expansion (CTE). Several works are devoted to the study of dependence of CTE on the parameters char- acterizing the temperature effect. In the article of A.I. Slutsker et al. [8], the temperature dependence of thermal expansion of polyvinyl acetate (PVA) in the region of relaxation transition at small harmonic temperature fluctuations relative to basic values was studied. The authors found that in the region of glass transition, a phase shift is observed between the expansion of the sample and the temperature, the magnitude of which depends on the frequency of temperature fluctuations. In order to explain the observed effect, the authors assumed that the temperature strain is determined not only by anharmonic vibrations of the atoms but also by the kinetics of conformational transitions. In the monograph of R. Houwink and A. Staverman [9], the dependences of the specific volume on temperature Polymers 2021, 13, 3035. https://doi.org/10.3390/polym13183035 https://www.mdpi.com/journal/polymers