The generalized scaling laws based on some deductions from the van der Waals equation

Abstract

Some thermodynamic relations that follow from the van der Waals equation are considered. It is shown that they are applicable to real substances and model systems described by absolutely different equations of state. These relations are associated with definite geometric lines on the density-temperature plane.The data for the model systems that substantiate the derived regularities were calculated by numerical simulation methods. For real substances, the relevant databases constructed according to experiments were used. It has also been established by numerical simulation that the limitations of the regularities under investigation are related to the nature of attraction in the interparticle interaction potential.

The Zeno Line for Al, Cu, and U

“…However, in reality, only the Zeno-line is straight (at least in liquid phase). So in our previous investigations, we have offered an algorithm to find the critical point coordinates, which are based on the linearity of the Zeno-line. ,− We have found the following relation connecting the critical and the Zeno-line parameters: …”

“…(Here P is the pressure, T is the temperature, measured in the units of energy, n is the particle density.) This line has been considered in many studies. − Below we will refer to it as the Z-line as well. The key property of this contour is that it is appeared to be the straight line over all density temperature plane n – T .…”

“…The key property of this contour is that it is appeared to be the straight line over all density temperature plane n – T . The number of substances for which this property can be confirmed experimentally are wider than for many other regularities, although there are exclusions. , Another useful property of the Z-line is that, at T → 0, it is tangent to the liquid binodal branch. , In refs − , we have taken into account these properties to construct the coexistence liquid–gas curve and to find possible relation between the critical point coordinates and the Zeno-line parameters. The latter values (Boyle temperature T B and Boyle density n B ) are defined by the points where the Zeno line is crossing with the axes on the density–temperature plane.…”

“…For instance, in the NIST database there are about 70 different substances for which the Zeno line is straight. The exclusions , among them are only the quantum liquids (hydrogen, helium) and water (see also ref ). So it was interesting to apply considered similarities to metals, which occupy most of the periodic table.…”

On metal-dielectric transition in laser ablation modeling

“…Laser-matter interaction gives possibility to obtain rather high temperature and pressure values which include values of liquid-vapor critical parameters for any element. However critical parameters of most metals remain badly known and this fact is mentioned in many papers [1][2][3][4]. From [1] it follows that the difference between critical pressure values for Al in scientific literature is about an order of magnitude.…”