New Correlation for the Critical Amplitude of the Critical Isotherm

The correlation dependence $$D = D(\omega ,{{Z}_{c}},\delta )$$ was established between the critical amplitude of the critical isotherm $$D$$ , the acentric factor ω, the critical compressibility factor $${{Z}_{c}}$$ , and the critical index of the critical isotherm $$\delta $$ . The parameters of the proposed correlation $$D = D(\omega ,{{Z}_{c}},\delta )$$ are established using the universal set of critical amplitudes $${{R}_{\chi }} = {{\Gamma }^{ + }}D{{B}^{{\delta - 1}}}$$ , where $${{\Gamma }^{ + }}$$ and $$B$$ are the critical amplitudes of the isothermal compressibility coefficient and the liquid–vapor system coexistence curve, respectively. The values $${{R}_{\chi }}$$ are chosen in accordance with the 3D Ising model ( $${{R}_{\chi }} = 1.57$$ ), the Landau crossover model ( $${{R}_{\chi }} = 1.73$$ ), and the renormalization group theory of Abbaci ( $${{R}_{\chi }} = 1.74$$ ). It is shown that the correlation $$D = D(\omega ,{{Z}_{c}},\delta )$$ most accurately describes D(e) at $${{R}_{\chi }} = 1.57$$ when using the description of 32 substances by the critical amplitude $$D = {{D}^{{(e)}}}$$ as an example. In this case, the correlations of Ivanov [7], Behnejad et al. [16], and the Abbaci crossover model [1, 41] are significantly inferior in accuracy to the proposed correlation $$D = D(\omega ,{{Z}_{c}},\delta )$$ . The use of the proposed correlation $$D = D(\omega ,{{Z}_{c}},\delta )$$ for calculating the critical amplitude D of liquid sodium is discussed.