# A High-Temperature, Thermal Non-equilibirum Thermochemical Model for Polytetrafluoroethylene

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## Abstract

A comprehensive thermochemical model for polytetrafluoroethylene (PTFE), also known as Teflon^{®}, is developed for use with computational fluid dynamic and magnetohydrodynamic computer codes. The model computes the thermodynamic properties of PTFE for a temperature range of 500 K to 580 230 K (50 eV) and extends to density values as low as 10^{−8} kg · m^{−3}. The 23 equation nonlinear system produced under the assumptions of ideal gas and two-temperature local thermodynamic equilibrium (LTE) was solved numerically using the Newton–Raphson method. The extended thermochemical model is verified for both the composition and thermodynamic properties by comparisons to existing thermochemical models in the literature. These comparisons verify the model for the available, yet limited, temperature and density ranges. The properties display expected trends such as an increase in the degree of ionization with decreasing density, while almost independent of the electron to heavy-particle temperature ratio (*θ* _{e}/h = *T* _{e}/*T* _{h}). The specific internal energy adheres to a fairly predictable curve, i.e., the specific internal energy is linear as the mixture stays at a fairly constant composition over some *T* _{e} range. However, over the *T* _{e} range where reactions occur, it was observed that such variation shows a steeper positive slope that represents energy deposition to the internal modes of the gas as opposed to heating. That is, the density is the main factor in deviations from one curve to the next while *θ* had a slight effect. Likewise, for the specific internal energy, the density had the greatest impact.

## Keywords

Electric rocket propellant Equation of state High-temperature thermochemical model Polytetrafluoroethylene Thermal non-equilibrium## List of Symbols

*a*_{0}Bohr radius, m

*c*_{i}Mass fraction of species

*i**C*_{p},*C*_{v}Specific heats at constant pressure and volume, respectively, J · kg

^{−1}· K^{−1}*e*Specific internal energy, J · kg

^{−1}*e*^{−}Free electron

*F*Initial guess and solution vector in Newton–Raphson method

*g*Gibbs specific free energy, J · kg

^{−1}*g*_{j}Degeneracy for level

*j**h*Planck’s constant, J · s

*h*Specific enthalpy, J · kg

^{−1}*I*,*I*_{A}*I*_{B}*I*_{C}Moment of inertia of a diatomic and polyatomic molecules, kg

^{3}· m^{6}or kg · m^{2}*J*Jacobian matrix

*i*Chemical species indicia

*k*Boltzmann’s constant, J · K

^{−1}*K*_{p}Gas equilibrium constant

- \({\overline{M}}\)
Average atomic mass of gas mixture

*m*Mass of one species’ particle, kg

*N*Number of particles

*n*^{cutoff}Principle quantum number

*n*_{i}Number density for species

*i*, total number of particles per unit volume, m^{−3}*n f e*Number of free electrons per heavy particle

*P*Total pressure of gas/plasma mixture, N · m

^{−2}*P*_{i}Partial pressure of a species, N · m

^{−2}*Q*_{el}Electronic partition function

*Q*_{rot}Rotational partition function

*Q*_{trans}Translational partition function

*Q*_{vib}Vibrational partition function

*Q*^{tot}Total partition function of a species

*R*Universal gas constant, J · mol

^{−1}· K^{−1}*R*_{i}Specific gas constant, J · kg

^{−1}· K^{−1}*s*Specific entropy, J · kg

^{−1}· K^{−1}*T*_{e}Electron temperature, eV

*T*_{h}Heavy particle temperature (all species except electron), eV

*T*_{i}Species temperature, eV

*V*Total volume

*Z*Integer designating the number of elementary positive charges in an ion

*Z*_{eff}Effective charge number of nucleus acting on excited electron

*δ**x*Corrections vector in Newton-Raphson method

- Δ
*e*_{0} Change in the zero-point energy, J · kg

^{−1}- \({\left({\Delta h_{\rm f}}\right)^{0}}\)
Specific heat of formation at absolute zero, J · kg

^{−1}- \({\varepsilon_j}\)
Energy level

*γ*Ratio of specific heats (also referred to as gam and gamma)

*θ*_{e/h}Electron to heavy particle temperature ratio,

*T*_{e}/*T*_{h}*ν*_{i}Stoichiometric coefficients for balanced chemical equations

*ρ*Density, kg · m

^{−3}*σ*Symmetry number

- \({\overline{\varsigma}}\)
Average charge

*ω*Frequency of a vibrational mode in a molecule, s

^{−1}

## References

- 1.Kovitya P.: IEEE Trans. Plasma Sci.
**12**, 38 (1984)ADSCrossRefGoogle Scholar - 2.J.T. Cassibry,
*Numerical Modeling Studies of a Coaxial Plasma Accelerator as a Standoff Driver for Magnetized Target Fusion*(Ph.D. Dissertation, University of Alabama, Huntsville, 2004)Google Scholar - 3.S.C. Schmahl,
*Thermochemical and Transport Processes in Pulsed Plasma Microthrusters: A Two-Temperature Analysis*(Ph.D. Dissertation, Ohio State University, 2002)Google Scholar - 4.G.N. Cooper, SESAME ’83: Report on the Los Alamos Equation-of-State Library.
*Report No. LALP-83-4*, Los Alamos National Labratories (1983)Google Scholar - 5.S.C. Schmahl, Thermochemical and Transport Processes, in
*Pulsed Plasma Microthrusters: A Two-Temperature Analysis*(Ph.D. Dissertation, Ohio State University, 2002), p. 131Google Scholar - 6.Boulos M.I., Fauchais P., Pfender E.: Thermal Plasmas, pp. 255–259. Plenum Press, New York (1994)Google Scholar
- 7.Cramer J.C.: Essentials of Computational Chemistry: Theories and Models, 2nd edn., pp. 359–365. Wiley, Chichester (2004)Google Scholar
- 8.Anderson J.D. Jr.: Hypersonic and High-Temperature Gas Dynamics, pp. 437–438. American Institute of Aeronautics and Astronautics, Reston, VA (2000)Google Scholar
- 9.Cambel A.B., Duclos D.P., Anderson T.P.: Real Gases, pp. 42. Academic Press, New York (1963)Google Scholar
- 10.Venugopalan M.: Reactions Under Plasma Conditions, pp. 65–66. Wiley, New York (1971)Google Scholar
- 11.Couture L., Zitoun R.: Statistical Thermodynamics and Properties of Matter, pp. 125–126. Gordon and Breach Science Publishers, Amsterdam (2000)Google Scholar
- 12.Koudriavtsev A.B., Jameson R.F., Linert W.: The Law of Mass Action, pp. 57–58. Springer, Berlin (2001)CrossRefGoogle Scholar
- 13.Anderson J.D. Jr.: Hypersonic and High-Temperature Gas Dynamics, pp. 453–457. American Institute of Aeronautics and Astronautics, Reston, VA (2000)Google Scholar
- 14.Cramer J.C.: Essentials of Computational Chemistry: Theories and Models, pp. 366–370. Wiley, Chichester (2004)Google Scholar
- 15.M.W. Chase Jr.,
*NIST-JANAF Thermochemical Tables*, 4th edn., vol. 1. J. Phys. Chem. Ref. Data: Monograph No. 9 (American Chemical Society and American Institute of Physics, Washington, DC, New York, 1998)Google Scholar - 16.Boyko Y.V., Grishin Y.M., Kamrukov A.S., Kozlov N.P., Protasov Y.S., Chuvashev S.N.: Thermodynamic and Optical Properties of Ionized Gases at Temperatures to 100 eV, pp. 92–95. Hemisphere Publishing Corp., New York (1991)Google Scholar
- 17.Boyko Y.V., Grishin Y.M., Kamrukov A.S., Kozlov N.P., Protasov Y.S., Chuvashev S.N.: Thermodynamic and Optical Properties of Ionized Gases at Temperatures to 100 eV, pp. 116–122. Hemisphere Publishing Corp., New York (1991)Google Scholar
- 18.Y. Ralchenko, A.E. Kramida, J. Reader,
*NIST Atomic Spectra Database*(National Institute of Standards and Technology, Gaithersburg, MD, 2010). http://physics.nist.gov/PhysRefData/ASD/lines_form.html - 19.Humble R.W., Henry G.N., Larson W.J.: Space Propulsion Analysis and Design, 1st edn. pp. 546. McGraw-Hill, New York (1995)Google Scholar