Molecular fields and statistical field theory of fluids: Application to interface phenomena

Abstract

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained, along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density and parameters of inter-molecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation -it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad-hoc or fitting parameters are in a good agreement with available simulation data. arXiv:2004.00283v1 [cond-mat.stat-mech] 1 Apr 2020

On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications

“…Both modifications are relevant to describe the charge-charge correlations between charged particles in the one component plasma (OCP) at strong coupling, concentrated electrolytes, and room temperature ionic liquids. It has also been found that these two modifications explain the deviation from the PB solution for counterion distribution over a wide range of from the intermediate to strong coupling [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…( 9). Modified PB equations for the Coulomb potential Ψ(r) [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].-Lastly, we mention two types of modified PB equations (see Appendix A for the details). Both modifications are relevant to describe the charge-charge correlations between charged particles in the one component plasma (OCP) at strong coupling, concentrated electrolytes, and room temperature ionic liquids.…”

“…This section investigates the modified PB equations, or the SC equations for the Coulomb potential Ψ(r) created by Coulomb interactions between point charges. We consider two types of the modified PB equations: the finite-spread PB equations [14,[20][21][22][23][24] based on the charge smearing model and the higher-order PB equations [15][16][17][18][25][26][27][28][29][30]. We show below that both forms can be derived from the Poisson equation for Ψ(r) defined by eq.…”

“…( 35), we use m = 1.08 according to the HNC approximation [38], the soft MSA [22,39,40] signifies the mean spherical approximation (MSA) [1,41] for soft spheres, and the smeared interaction potential is identified with the DCF in the Bessel smoothed model [35] that supposes a smeared charge distribution expressed by the modified Bessel function K 1 (see Appendix A.2 for the details). [14,[20][21][22][23][24] In the real-space representation of the electrostatic DCF given by eq. ( 34), we have…”

“…Our concern here is with the following two types of the modified PB equations. One type is derived from the charge smearing model [14,[20][21][22][23][24][35][36][37][38][39][40] and the other adds higher-order gradient terms to the original PB equation [15][16][17][18][25][26][27][28][29][30]. Both types of modifications have coexisted as complementary to each other, and the direct connections of these different types of the modified PB equations with the liquid-state theory, or the vast knowledge on correlation functions [1,41], remain to be clarified.…”