Soft Matter under Exogenic Impacts pp 305-323 | Cite as

# Fluctuational equation of state and slopes of critical curves near the critical point of solvent

## Abstract

A simple, yet reliable, equation of state was developed for fluids ranging from inert gases Ar, Kr, Xe to polar substances NH_{3} and H_{2}O. The equation consists of the van der Waals generalized term as a reference system and a closed-form term approximating a coupling of the molar volume and entropy fluctuations near a phase boundary. Only the coexistence-curve data P_{S}(T), ρ_{l}(T),ρ_{g}(T) and the second virial coefficient B(T) are necessary to determine three temperature dependent coefficients a(T), b(T), c(T) in the wide ranges of P and T. Proposed equation of state is not global and does not incorporate the Maxwell construction to locate a phase boundary. Critical point constraints were used only to obtain the asymptotic values \({\rm (a}_{\rm c}^{\rm 0}, {\rm b}_{\rm c}^{\rm 0}, {\rm c}_{\rm c}^{\rm 0} {\rm )}\) from the side of supercritical region. No critical point constraints were used in the subcritical region, where the asymptotic values (a_{c}, b_{c}, c_{c}) are determined by the true critical parameters (P_{c}, ρ_{c}, T_{c}) and by the real reduced critical slope A_{c}=(T_{c}/P_{c})(dP_{S}/dT)_{c}. This parameter is interrelated for the binary systems with the known Krichevskii parameter and with the initial slopes of the critical curve for a mixture in (P, x)- and (T, x)-planes. A method of analysis for the different type with the near critical solvent has been developed. The accurate description of the critical point and coexistence curve data for the pure components provides the correct estimation of binary cross-interaction coefficient by utilizing of the single experimental point of a critical line for the given mixture. The proposed strategy is to determine the correlation between the Krichevskii parameter and the binary cross-interaction coefficient k_{12} in equation a_{12}=(1−k_{12})(a_{1}(T)a_{2}(T))^{1/2}. The initial slopes of the critical curves near the critical point of solvent have been used to predict reliable values of k_{12}.

### Keywords

supercritical solvent cosolvent local phase diagram solubility critical curve phase behavior## Preview

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### References

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