Characterization of the Young's Modulus and Equation of State for Crystalline Polytetrafluoroethylene Chain through Density-Function Theory

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The Young’s modulus and equation of state for crystalline polytetrafluoroethylene (PTFE ) is characterized by using the framework of the density function theory , with the local density approximation and ultrasoft psuedopotentials. Phonon modes are calculated by using the density functional perturbation theory (DFPT). The structure is optimized first to find the equilibrium geometry. Then the direct elongation relaxation method is implemented and the elastic constant s of PTFE are obtained. I. Introduction RIVEN by an increasing interest in th e mechanical properties of the polymers under high pressure and shock loading condition s, many attempts are made to evaluate the Young’s modulus and equation of state (EOS) of polymer chains. The classical experiment al methods includ e mechanical stress -str ain measurement , X -ray diffraction , gas -gun, and flyer plate tests . Aside from the experiment al method s, the theoretical evaluation method o f the structural properties of a bulk system has gain ed a significant amount of attention in recent years as a low -cost method of prediction of mechanical behavior of polymer s. Without introducing the sample impurities and imperfection s, the elastic constants obtained with first principle method will be different . First -principle (or ab initio) methods is widely used du ring the past three decades for crystalline metals . This progress is indebted partially to the powerful computer simulation tool s. However, the application of ab initio methods in the structural characterization of complex polymeric materials is relatively new . In the work of Miao, Camp, et al. (1996) 1 the structural and electronic properties of PTFE systems are calculated for several different dihedral angles. They use two different local density approximations for exchange correlation function and optimiz e the geometrical parameters. The dihedral angle corresponding to the minimum torsional potential is also discuss ed. In the work of Hageman, Meier, et al. (1997) 2 the Young’s modulus for crystalline polyethylene are calculated using ab initio molecular dyn amics , based on density functional theory with the local density approximation. For the first time the modulus is evaluated by ab initio method with no bias from experimental data. In the paper by Bartha, Bagar, et al. (2000) 3 the force constants and elast ic properties of some polymers are calculated with density functional theory. Calculations are on single helical chains of polyethylene, PTFE, polyglycine and Nylon -3. They showed that it is possible to omit some degrees of freedom of the polymer from such theoretical calculation s without a considerable loss of accuracy . In a paper by Miao, Zhang and Doren (2001) 4 the structure of crystalline polyethylene under high pressures is obtained by density function theory. The geometry, elastic moduli and band stru ctures of the crystalline polyethylene are studied by a pseudopotential plane wave method as a function of applied pressure. In the paper by D’Amore, Talarico and Barone (2006) 5 the main results represent a successful attempt of prediction of some macrosco pic properties of PTFE both in regular and disordered forms by using first principle quantum mechanical approaches . A statistical approach is applied to obtain the thermal concentration of defects and to reproduce the thermal behavior of PTFE. Several att empts are also made to experimentally measure the equation of state and lattice vibration property of PTFE. Morris and Fritz (1984) 6 present the Hugoniot equation of state of PTFE. Shock -recovery experiments are performed to investigate the high -pressure e quation of state. Bourne and Gray (2003) 7 present the measurement of five different production PTFE materials. The equation of state of these variants are quantified by conducting a series of shock impact experiments in which both pressure -particle velocit y and shock velocity -particle velocity dependencies ar e measured. Piseri and Powell (1972) 8 discuss the normal modes of vibration propagating along the