The nature of the rectilinear diameter singularity

Abstract

The rigorous explanation for the term $|t{|}^{2\beta }$ in the rectilinear diameter equation is given ($t=(T_c-T)/T_c$, $\beta$ is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric is constructed within the canonical formalism. It is shown that the ratio of the amplitudes $\f{D_{2β}}{D_{1-α}}$ before $|t{|}^{2\beta }$ and $|t{|}^{1-\alpha }$ where $\alpha$ determines the behavior of the heat capacity, takes the universal character. The analysis of entropy for argon and water leads to $\beta =0.33$ and $\f{D_{2-β}}{D_{1-α}}\approx - 3.5$.

arXiv comment6 pages, 1 figure

References in corpus (4)

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• "Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions
• Singular Coexistence-curve Diameters: Experiments and Simulations
• Is the thermodynamic behavior of the noble fluids consistent with the Principle of Corresponding States?

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