A general fractal structure approach to the study of the thermodynamic properties of liquids and its applications

Abstract

The calculation of liquid heat capacity in its general form is one of the most challenging subjects in condensed matter physics due to the dynamical disorder of liquids, in contrast to the solid phase, and the strong interactions involved, unlike the gas phase. Despite these difficulties, a phonon theory of liquids has been proposed, although the discussion has been limited to a Debye-type density of states. In the present paper, we adopt a new approach: rather than focusing on the Debye model, we extend the Debye-type density of states to fractal spaces and obtain an expression for the liquid heat capacity based on a fractal model. We develop a new method for calculating the heat capacity of liquids using the fractal concept of substances. To verify the proposed approach, formulas are derived for the temperature dependence of the heat capacity of liquid Hg for various fractal dimensions. Our approach can be applied to both the quantum and classical regimes and can be reduced to the phonon theory of liquids and solids in the limiting cases.