A model for viscosity coefficients of gases with potentials differing in form FERNANDO DEL RI ´ O*, BENJAMI ´ N IBARRA and LUIS MIER Y TERA ´ N Laboratorio de Termodina´mica, Depto de Fı´sica, Universidad Auto´ noma Metropolitana, Iztapalapa, Apdo 55 534, Me´xico, DF Me´xico (Received 14 May 2003; accepted 27 May 2003) A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters—energy  and distance r m —a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient . It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for  (T, , r m , s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of  for the heavier noble gases (Ar, Kr and Xe), diatomics (H 2 ,N 2 , O 2 and Cl 2 ) and a dozen small polyatomics. It is found that the ANC model  (T, , r m , s), with only three substance-dependent parameters, reproduces experimental  data within their estimated error. 1. Introduction Gas viscosity coefficients and intermolecular forces are closely related concepts of great interest in chemical physics. Shear viscosity coefficients of gases at zero pressure  (T,[u]) depend on temperature T and (func- tionally) on the intermolecular potential u [1]. Experi- mental values of  (T ) have been used in conjuction with virial coefficient data, quantum mechanical ab initio calculations and values of other thermodynamic proper- ties in determining pair interaction potentials u [2]. The use of experimental  (T ) data in obtaining or comple- menting information about u enhances the importance of  beyond its intrinsic interest as a transport property; for example, for the spherical noble-gas molecules, the combination of  (T ) data with other sources of infor- mation has permitted one to determine highly accurate pair potentials u(r) as functions of the centre-to-centre distance r [3–5]. As occurs with other thermodynamic properties in the classical regime, it is well known that viscosity coefficients follow the principle of corresponding states (PCS). Two gases with different but conformal inter- molecular potentials u 1 and  2 will have the same value of the reduced viscosity coefficient   (T  ) when their reduced temperatures are equal, T  1 ¼ T  2 ¼ T  , namely,   1 ðT  1 Þ¼   2 ðT  2 Þ. Quantities are reduced with appropri- ate energy and length scale parameters  i and r mi for substance i; here  i is taken as the depth of u i (r) at its minimum located at the diameter r mi . Hence T  i ¼ kT = i , u  i ¼ u i ðr=r mi Þ= i and   i T  i   ¼ r 2 mi  i ðT Þ  i m i ð Þ 1=2 , ð1Þ where m i is the molecular mass. Lastly, two interaction potentials are called conformal if they have the same form, i.e. if their reduced versions are identical: u  1 ¼ u  2 . However, since most substances of interest have non- conformal potentials, use of the PCS in its restricted sense is very limited [6]. In view of this fact, several empirical extensions of the PCS have been used to correlate or estimate values of  (T ) for a particular type of gas [7]. Here we present a treatment of viscosity coefficients that arises from a rigorous extension of the PCS to deal with non-conformal changes in the potential. The approach is based on a theory recently introduced to generate models for the pressure virial coefficient B(T ) of a gas. The approximate non-conformal (ANC) theory has been proposed to deal with non-conformality of pair potentials [8–10]. The theory introduces a set of spherical potentials u ANC (r; s) whose form in r varies in a simple and systematic way with a form factor s, called the softness of the interaction. Two softness factors s R and s A are introduced to measure the (inverse) steepness of the repulsive and attractive wings of the potential function, and are defined in relation to a reference potential function u 0 (r). One of the main features of ANC theory is that B(T ) is written explicitly in terms of the potential parameters *Author for correspondence. e-mail: fdr@xanum.uam.mx MOLECULAR PHYSICS, 10 OCTOBER 2003, VOL. 101, NO. 19, 2997–3007 Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00268970310001605732