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Abstract
Recently, it has been shown that an asymmetric gradient term should be added to the Landau-Ginzburg type Hamiltonian for one-component fluids to produce the correct critical asymmetry of vapour–liquid equilibrium. However, the coefficient of the asymmetric gradient was treated as an adjustable parameter. In this work, we show this asymmetric gradient is related to the local part of the effective Hamiltonian and its coefficient should also be determined according to the effective Hamiltonian. We develop a self-consistent method and apply it to various one-component fluid systems. The calculated vapour–liquid coexistence diameters and the isochoric heat capacities are in good agreement with the simulation and the experimental data. Furthermore, the RG treatment yields another major field-mixing coefficient which is very close to the prediction of the classical equation of state, implying that our RG calculations preserve the critical asymmetry intrinsic to the classical equation of state and the effective Hamiltonian is correctly constructed.
Given the coefficient of the asymmetric gradient modification, i.e. u1, one can perform RG calculations to get the value of the field-mixing coefficient a3 that depends on u1. Considering that the classical EOS also predicts reasonable accurate value of a3, we tune the value of u1 to make the a3 obtained from RG calculations identical to that from the classical EOS. Thus, we fix the parameter u1. Then the calculations of thermodynamic properties can be accomplished without difficulty.
GRAPHICAL ABSTRACT
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.