Intermolecular potential parameters and combining rules determined from viscosity data

Abstract

The Law of Corresponding States has been demonstrated for a number of pure substances and binary mixtures, and provides evidence that the transport properties viscosity and diffusion can be determined from a molecular shape function, often taken to be a Lennard-Jones 12-6 potential, that requires two scaling parameters: a well depth ε ij and a collision diameter σ ij , both of which depend on the interacting species i and j. We obtain estimates for ε ij and σ ij of interacting species by finding the values that provide the best fit to viscosity data for binary mixtures, and compare these to calculated parameters using several "combining rules" that have been suggested for determining parameter values for binary collisions from parameter values that describe collisions of like molecules. Different combining rules give different values for σ ij and ε ij and for some mixtures the differences between these values and the best-fit parameter values are rather large.There is a curve in (ε ij, σ ij ) space such that parameter values on the curve generate a calculated viscosity in good agreement with measurements for a pure gas or a binary mixture. The various combining rules produce couples of parameters ε ij , σ ij that lie close to the curve and therefore generate predicted mixture viscosities in satisfactory agreement with experiment. Although the combining rules were found to underpredict the viscosity in most of the cases, Kong's rule was found to work better than the others, but none of the combining rules consistently yields parameter values near the best-fit values, suggesting that improved rules could be developed.Keywords: viscosity, transport properties, combining rules, intermolecular potential parameters 3 I -IntroductionMany important phenomena that occur in gas mixtures depend on molecular transport processes including viscosity, diffusion, and thermal conductivity. Transport properties are often critically important in engineering applications and for understanding phenomena like combustion processes, hypersonic flows, and chemical vapor deposition. A recent trend in engineering design is to use modeling to reduce design times, and combustion is an area benefitting from this approach. Modeling combustion processes requires accurate values of transport properties over a wide range of temperatures and pressures. It is not possible to measure all the requisite transport properties, so we must have models to calculate them. This requires adequate information about the intermolecular potential and the underlying dynamics. The shape function, φ, is frequently taken to be a Lennard-Jones 12-6 potential, where the energy scaling parameter ε ij is the well depth, and σ ij is the length scaling parameter that defines the intermolecular separation at which the potential is zero. Viscosity measurements of a single chemical species allow direct estimation of the parameters that describe the interaction between two molecules of the same species, ε ii and σ ii . The situation is more complicated for even the si...

Transport Properties for Systems with Deep Potential Wells: H + O2

“…The parameters specifying this potential for H−O 2 were estimated with conventional combining rules: The well depth ε and length parameter σ for H−O 2 were taken as the geometric and arithmetic means, respectively, of the corresponding parameters for the like systems A″ and 4 A″ PESs was taken. We see that the collision integrals computed with the LJ potential are larger than those from the quantum scattering calculation, except for Ω (2,2) at low temperatures. Moreover, the LJ estimate has a temperature dependence that is much steeper than that of the quantum scattering calculation.…”

“…These collision integrals are larger for collisions on the 4 A″ PES, reflecting the differences in the magnitudes of the transport cross sections plotted in Figures 3 and 4. The Q n i (2,2) collision integrals for both PESs show a similar dependence upon the rotational level n i and are not plotted here. We see in Figure 5 that the dependence of Q n i (1,1) upon n i is relatively weak at 300 K.…”

“…This difference results from the weighting factor Φ n (E) in eq 6 for the transport cross section. 20 The state-specific transport cross section Q n i (2) for the lowest rotational level n i = 1 displays a collision energy dependence similar to that for the corresponding Q n i (1) cross section. We see, however, in Figure 3d that Q n i (2) is very large in magnitude and negative at low collision energies.…”

Transport properties for combustion modeling

“…Bastien et al [61] collected recent viscosity data for a number of substances and temperatures and used Powell's method as described by Press et al [62] with a brute force fitting approach to determine ε and ζ. They found a nearly linear -trough‖ in ε, ζ space, such that any parameter pair in the trough yields a viscosity that agrees with experiment within about 1%, as as shown on Figure 2.…”

Exact quantum scattering calculations of transport properties: CH2($\tilde{X}^3$X̃3B1, $\tilde{a}^1$ã1A1)–helium

“…15 For unlike systems, the parameters are typically estimated by combination rules. [16][17][18] a) Electronic mail: pjdagdigian@jhu.edu b) Electronic mail: mha@umd.edu Investigations of several systems have shown that the repulsive wall of the LJ 12-6 potential is steeper than predicted by more accurate methods. 1,14 This results in inaccuracies in the prediction of the temperature dependence of the transport properties.…”