where R is the gas constant, V2 is the specific volume of the polymer, V1 is the molar volume of the solute, P10 is the vapor pressure, and B11 is the second

virial coefficient of the solute in the gaseous state.

A measure of protein-protein interactions known as the osmotic second

virial coefficient, or [B.

They give rise to a third term in the so-called virial expansion of the pressure of the system in terms of the density, and therefore, it is named the "third

virial coefficient.

w], and second

virial coefficient which is a quantification of the polymer-solvent interaction for polymer chains, [A.

11]=second

virial coefficient of the standard substance at column operating temperature [d[m.

We employ state-of-the-art pair and three-body potentials with path-integral Monte Carlo (PIMC) methods to calculate the third density

virial coefficient C(T) for helium.

The equation contains

virial coefficients up to the third

virial coefficient.

But, it represents poorly the supercritical state: the properties of the fluids in this region are inaccurately predicted, in particular, derived properties such as the second

virial coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the Joule-Thomson inversion curve.

Two tested submodels, which closely resemble the real gas model, were based on substitution of the

virial coefficient contribution to property values in favor of a simple correlation.

Intermolecular Potentials and the Evaluation of the Second

Virial Coefficient.

where R is the gas constant, T is the column temperature, M1 is the molecular mass of the probe, P1 is the saturated vapor pressure of the probe at temperature T, and B11 is the second

virial coefficient of the probe in the gaseous state and can be determine from Equation 15.

Knowledge of the pair and three-body potential-energy surfaces of helium is now sufficient to allow calculation of the third density

virial coefficient, C(T), with significantly smaller uncertainty than that work, we employ the best available pair and three-body potentials for helium and calculate C(T) with path-integral Monte Carlo (PIMC) calculations supplemented by semiclassical calculations.