Calculation of Transport Coefficients for CH 4 –N 2 and CH 4 –O 2 by the Inversion Method Ali MAGHARI  and Amir Hossain JALILI Department of Chemistry, University of Tehran, Tehran, Iran (Received September 30, 2003) Viscosities, diffusion coefficients and thermal diffusion factors for CH 4 –N 2 and CH 4 –O 2 are determined from the extended law of corresponding states for viscosity and the experimental second virial coefficient data by an iterative inversion method. The Lennard-Jones ð12; 6Þ potential energy function is used as the initial model potential required the technique. The obtained effective interaction potentials reproduce viscosity, diffusion and thermal diffusion factor within experimental accuracies. KEYWORDS: viscosity, diffusion coefficient, thermal diffusion factor, effective interaction potential, inversion method DOI: 10.1143/JPSJ.73.1191 1. Introduction Intermolecular potential energy functions are responsible for many of the bulk properties of matter, such as the density, heat capacities, viscosity, diffusion and thermal diffusion coefficients and etc., since the results of kinetic and statistical-mechanical theories provide the expressions for various equilibrium and non-equilibrium properties of matters in terms of the interaction potential between a pair of molecules. The direct measurement of the interaction potential energy between molecules is very difficult, so it seems reasonable to apply indirect methods. The theoretical source of information about the nature of intermolecular potential energy is quantum mechanics, i.e. ab initio methods. Moreover, a direct semi-empirical approach, developed by Smith and coworkers, 1–3) is the inversion technique. Strictly speaking, the aim of an inversion method is to obtain directly the potential from experimental data as a function of temperature, instead of fitting the data to a constrained potential having a few parameters. The method used in this study is iterative one and converged rapidly once a good choice has been made for initial starting potential. Direct inversion methods for the potential energy func- tions of noble gases and their mixtures from data on dilute gas viscosity have been tested in connection with the extended law of corresponding state. 4–7) It was also checked for some polyatomic gases and their mixtures by using a same principle of corresponding states for the transport coefficients of molecular gases as was used for noble gases. 8–10) However, there are some difficulties in determin- ing pair potentials for polyatomic molecules. The major problem is that the theories relating experimental properties to intermolecular potential are often more complex than for inert gases, so that the theory of Chapman–Enskog of the transport properties of polyatomic molecules is fundamen- tally different from the monatomic molecules, because a collision between two polyatomic molecules can involve a change in the rotation and vibration energies. The kinetic theory of polyatomic molecules which take into account of inelastic collision are extremely complex and there have been only a few attempts to calculate the transport properties from this theory. To the first approximation, we may regard the interaction as isotropic, and are thus able to apply the Chapman–Enskog theory of dilute gas transport proper- ties. 11) The other approximation has been proposed by Monchick and Mason, who assumed that the Chapman– Enskog theory of non-spherical molecules retains its original form, but the collision integrals must be averaged over all possible relative orientations occurring in collisions. 12) Their classical model ignores inelastic collision, restricting its applicability to viscosity and diffusion coefficients and also to translational part of thermal conductivity, and then the collision integrals can be calculated assuming that molecules collide with a fixed relative orientation during the encounter. It should be noticed that the inversion algorithm for polyatomic systems permits us to generate the isotropic effective interaction potential energy function and in our calculations of transport properties, the Chapman–Enskog theory retains its useful form, but the collision integrals, which appear, must be averaged over all possible relative orientations occurring in collisions. The transport properties of fluids are important quantities required in engineering design for production, processing and fluid transformation. The present work is concerned with determining an effective isotropic pair potential energy for CH 4 –N 2 and CH 4 –O 2 by the use of inversion of correspond- ing states correlation of viscosity and the experimental second virial coefficient data. The obtained interaction potential energies reproduced the viscosity, diffusion coef- ficient, and thermal diffusion factor for equimolar and low- density binary gas. The information obtained on the interaction between CH 4 with O 2 can profitably used in dealing with important processes such as combustion, flames, and atmospheric chemistry. For a dilute gas mixture of CH 4 –O 2 no measurements above 1025 K were possible, because spontaneous ignition of the methane in the hot oxygen occurred. In this work we have confined our attention to the determination of the effective intermolecular potential energy from transport properties, namely viscosity, using the inversion approach. Among the transport proper- ties, the measurement of viscosity is more practical than, say, diffusion measurement. 2. Kinetic Theory of Gases and Transport Properties The kinetic theory of monatomic or spherical gases at low-density relates the transport properties, such as inter- action viscosity  12 , binary diffusion coefficient D 12 and thermal diffusion factor of a binary mixture  T , to a series of  Corresponding author. E-mail: maghari@khayam.ut.ac.ir Journal of the Physical Society of Japan Vol. 73, No. 5, May, 2004, pp. 1191–1196 #2004 The Physical Society of Japan 1191