Density scaling in viscous liquids: from relaxation times to four-point susceptibilities.

We present numerical calculations of a four-point dynamic susceptibility, chi(4)(t), for the Kob-Andersen Lennard-Jones mixture as a function of temperature T and density rho. Over a relevant range of T and rho, the full t-dependence of chi(4)(t) and thus the maximum in chi(4)(t), which is proportional to the dynamic correlation volume, are invariant for state points for which the scaling variable rho(gamma)/T is constant. The value of the material constant gamma is the same as that which superposes the relaxation time tau of the system versus rho(gamma)/T. Thus, the dynamic correlation volume is a unique function of tau for any thermodynamic condition in the regime where density scaling holds. Finally, we examine the conditions under which the density scaling properties are related to the existence of strong correlations between pressure and energy fluctuations.