Transport properties of chain molecules and the theorem of corresponding states

Abstract

Prigogine's corresponding states approach to equilibrium properties of pure r‐mers is extended to include transport properties. For r‐mer molecules, besides the alike element pair potential parameters, additional quantities are required to characterize the geometrical structure of the molecule and thereby describe more adequately pair potential interactions. As an example, the theory is applied to the homologous series of liquid n‐alkanes. The characteristic parameters for each member of the homologous series are determined using pure component viscosity data at one atmosphere and pure component denstiy data at one temperature and atmospheric pressure. The technique correlates pure component r‐mer transport properties (viscosity — 981 points, thermal conductivity — 216 points) over a wide range of temperature and pressure within experimental error. Using the present technique, available self‐diffusion coefficients are also correlated.

Transport Properties of Liquid Mixtures (n-Paraffins) and the Theorem of Corresponding States

“…In the work of Doan and Brunet (1972) a theorem of corresponding states was proposed for pure r-mers. Their theorem was stated through two equations of state.…”

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Prigogine, et al (1957), developed theorems of corresponding states for thermodynamic properties. Their approach has recently been extended to include transport properties of mixtures of spherical molecules (Brunet and Doan, 1970) as well as pure r-mers (Doan and Brunet, 1972). In the present paper the method is extended to mixtures of r-mer molecules.

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“…In the present theory the only quantities required are pair elemental interactions between alike species. In principle, pure component data are not required since a generalized correlation is available from the work of Doan and Brunet (1972). The present work amounts to an extension of earlier works of Brunet and Doan (1970), Tham and Gubbins (1969), Preston, et a/.…”

“…Recently, Doan and Brunet (1972) have shown that transport properties of pure r-mers could be correlated within experimental error (% RMS deviation = 2.8) using Prigogine's method of parameterization of r-mer molecules. This is done with the help of two elemental potential parameters e,, , and three structural dimensional numbers: (a) the number of segments (elements) per molecule r (r = 0.5 (n + 1)); (b) the number of external degrees of freedom 3(7,; and (c) the number of intermolecular contacts qrz which is calculated using eq 1. q,zr(z -2) + 2…”

“…The above parameters have been calculated from experimental viscosity and density data for pure r-mers at atmospheric pressure and are tabulated in the publication of Doan and Brunet (1972). Their technique has been tested over a wide range of temperature and pressure and has been found successful.…”