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In this paper, we report on nontrivial results of our investigations ofdynamic and thermodynamic moduli in search of invariants for viscous liquids inthe density scaling regime by using selected supercooled van der Waals liquidsas representative materials. Previously, the dynamic modulus $M_{p-T}$ (definedin the pressure-temperature representation by the ratio of isobaric activationenergy and activation volume) as well as the ratio $B_{T}/M_{p-T}$ (where $B_T$is the thermodynamic modulus defined as the inverse isothermal compressibility)have been suggested as some kind of material constants. We have establishedthat they are not valid in the explored wide range of temperatures $T$ overdozen decades of structural relaxation times $\tau $. The temperaturedependences of $M_{p-T}$ and $B_T/M_{p-T}$ have been elucidated by comparisonwith the well-known measure of the relative contribution of temperature anddensity fluctuations to molecular dynamics near the glass transition, i.e., theratio of the isochoric and isobaric activation energies,$E^{act}_{V}/E^{act}_{p}$. Then, we have implemented an idea to transform thedefinition of the dynamic modulus $M_{p-T}$ from the p-T representation to theV-T one. This idea relied on the disentanglement of combined temperature anddensity fluctuations involved in isobaric parameters has resulted in finding aninvariant for viscous liquids in the density scaling regime, which is the ratioof the thermodynamic and dynamic moduli, $B_{T}/M_{V-T}$. In this way, we haveconstituted a characteristic of thermodynamics and molecular dynamics, whichremains unchanged in the supercooled liquid state for a given material, themolecular dynamics of which obeys the power density scaling law.

In search of invariants for viscous liquids in the density scaling regime: Investigations of dynamic and thermodynamic moduli