Cavitation rate in elastomers: A geometric free volume analysis approach - Κουρνόπουλος, Σπύρος (Σχολή Χημικών Μηχανικών, 2016)
Under certain modes of deformation rubbers cavitate in their interior to form enclosed cavities. Those cavities result in a rapid deterioration of mechanical properties, as their surface will tear open to form a running crack when the maximum extensibility of the material is reached. Rubber cavitation can be examined as a phase separation phenomenon. The expansion is not very different from the process of liquid evaporation, where a dilute vapor phase coexists with the liquid. In a polymeric network of subchains, however, vapor molecules are not present inside the formed bubble to any appreciable extent. Thus, in such systems bubbles can be approximated as void regions. Nucleation theory states that, when a phase reaches the equilibrium point of transition, the formation of the new phase does not usually take place immediately, but instead a trigger is needed. This trigger is a sufficiently large density fluctuation that is driven by molecular motion and is called the critical nucleus. The formation of the critical nucleus helps the system “escape” its intermediate metastable state and reach a stable state, which is characterized by thermodynamic equilibrium. Moreover, the rate at which bubbles are formed is called nucleation rate and in a rubber material is the same as the cavitation rate. The aim of this thesis is to analyze computer models of perfect polyethylene networks subjected to hydrostatic tension and calculate their cavitation rate at various values of the tension (negative pressure). To perform this task, a geometric analysis based on quantifying the free volume between atoms is developed. The main idea is that the free space among molecules is an excellent tool to track the appearance of cavities within the material. In Chapter 1 a brief introduction is presented. All basic molecular simulation techniques used in the context of this thesis are discussed. In addition, we provide a detailed account of how to construct and effectively simulate perfect polyethylene networks. Furthermore, a section is dedicated to describing the basic thermodynamics behind phase separation phenomena. Finally, the Sanchez-Lacombe equation of state is presented, as it has been used in a related previous work to describe the behavior of the studied elastomer. In Chapter 2 we turn to the problem of constructing a Periodic Delaunay triangulation (PDT) and briefly describe important features of the open-source Computational Geometry Algorithms Library (CGAL). After discussing the methods implemented to compute the PDT, results for a test Polyethylene system are presented. In particular, emphasis is placed on correlating various geometrical distributions of the PDT with certain features of the underlying atomistic structure of the material. In Chapter 3 a new method to analyze liquid-vapor transitions is presented. One of the most fundamental questions in computational studies of phase transition phenomena is the definition of a cluster, which is a term used to refer to small occurrences of a second phase within the original one. In the scientific community this has proved to be a difficult task, both theoretically and computationally. At the beginning of the chapter, we conduct a brief literature review on other popular methods. Then we outline our methodology, which is based on quantifying the free volume among atoms. This is followed by a detailed discussion of the algorithms that were developed to utilize the PDT, which was discussed in the previous chapter, in order to solve the problem of detecting a cavity within the material. At the end of the chapter, two result sections are included. The first one contains a free volume analysis of an equilibrated state, while the second presents several free volume distributions to support the efficiency of the proposed approach. In chapter 4 we provide estimations of various cavitation properties, including the critical cavity size and the cavitation rate. This is accomplished by implementing the mean first passage time method (MFPT), which was developed to analyze activated processes. Before displaying the final results, a brief explanation is provided for how the methodology we developed in chapters 2 and 3 is utilized. Moreover, we investigate how statistics and free parameter values affect the final results. Finally, an attempt to predict the cavitation rate for a negative pressure equal to the material’s saturation pressure is presented.