Journal of Materials Science Research; Vol. 8, No. 3; 2019 ISSN 1927-0585 E-ISSN 1927-0593 Published by Canadian Center of Science and Education 31 Flexibility of Polymers Defined and Related to Dynamic Friction Witold Brostow 1, 2 , Haley E. Hagg Lobland 1 , Hee Jae Hong 1 , Sven Lohse 1 & Allison T. Osmanson 1 1 Laboratory of Advanced Polymers & Optimized Materials (LAPOM), Department of Materials Science and Engineering and Department of Physics, University of North Texas, Denton, USA 2 College of Mechanics and Robotics, AGH University of Science and Technology, Aleja Adama Mickiewicza, Krakow, Poland Correspondence: Witold Brostow, Laboratory of Advanced Polymers & Optimized Materials (LAPOM), Department of Materials Science and Engineering and Department of Physics, University of North Texas, 3940 North Elm Street, Denton, TX 76207, USA. E-mail: wkbrostow@gmail.com Received: July 5, 2019 Accepted: July 24, 2019 Online Published: July 31, 2019 doi:10.5539/jmsr.v8n3p31 URL: https://doi.org/10.5539/jmsr.v8n3p31 Abstract We have quantitatively defined flexibility of polymers. Flexibility Y is not an inverse of the brittleness B, rather, the two equations are compared. The expression for flexibility includes the specific volume and the summation of the strengths of chemical bonds-a concept introduced by Linus Pauling. The flexibility is plotted as a function of dynamic friction, resulting in a representative single curve for polymers. Keywords: Polymer Brittleness, Polymer Flexibility, Polymer Dynamic Friction, Strength of Chemical Bonds, Linus Pauling 1. Scope and Definitions Polymers are characterized in terms of a variety of properties, including “brittleness” and “flexibility”. Such characterizations help one to choose a polymer for a specific application. For instance, Wang and coworkers (2018) declare that “flexible materials are very attractive because of easy integration into various industrial processes”. They have created polymer-containing composite films “feasible to act as self-powered wearable devices by utilizing body’s heat or other heat source to generate electricity, wearable temperature sensors, and flexible solid-state coolers, which are very difficult to achieve for inorganic thermoelectric materials since they are intrinsically brittle and rigid”. However, in order to better navigate among intrinsic material properties and to find materials with suitable combinations of properties, an equation defining polymer brittleness B has been formulated by two of us and Narkis (Brostow, Hagg Lobland, & Narkis, 2006), and B has been related to several other properties (Brostow & Hagg Lobland, 2017). By contrast, there has been no quantitative definition of polymer flexibility, call it Y. We provide such a definition in this paper. Let us mention a few more examples of the importance of Y. Chinaglia and coworkers (2007) developed much improved light-emitting devices, putting green phosphor compounds in a conductive polymer blend; flexibility is a requirement in such devices. Rubbers and rubber-like materials are known for high flexibilities. Yu and Selvadurai (2007) note that large strains can be achieved in rubbers with little energy dissipation while large deformations of a polyurea elastomer were studied by Amirkhizi and coworkers (2006). Relaxation times of chains in polymers studied through molecular dynamics simulations by Bedrov, Liu and Colby (2008) are important for the polymer properties-and necessarily related to flexibility. Dong-Yu Kim and coworkers (2008) have created organic solar cells on flexible polymeric substrates—with much better mechanical properties than ITO (indium tin oxide) solar cells. Polymer based energy storage devices developed by Nyholm and coworkers at the University of Uppsala (2011) require flexible polymers. Being able to predict and quantify the flexibility of such polymeric materials would improve the ease of development of novel flexible materials as well as create a clear method for comparison of the materials. As mentioned before, flexibility is not an inverse of brittleness. We first provide a definition of brittleness  (Brostow, Hagg Lobland, & Narkis, 2006) so as to contrast it with the definition of flexibility later: = ଵ ா ᇲ ∗ఌ  (1)