Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited

Abstract

We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264-6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r(c) = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r(c) = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as the cutoff distance is larger. We have also checked the effect of the impulsive contribution to the pressure due to the discontinuity of the intermolecular interaction potential when it is cut. If this contribution is not accounted for in the calculation of the microscopic components of the pressure tensor, incorrect values of both components as well as a wrong structure along the vapour-liquid interface are obtained.

Liquid-liquid interfacial properties of a symmetrical Lennard-Jones binary mixture

“…We use periodic boundary conditions and minimum image convention in all three directions of the simulation box. To be consistent with simulations performed using the NP z AT ensemble for preparing the definitive simulation box, we use inhomogeneous LRC to the intermolecular energy of MacDowell and Blas 7,44 methodology for the intermolecular potential energy and the recipe presented in our previous paper 34 for the evaluation of the LRC for the components of the pressure tensor, both of them based on the Janecek's method. 6 We have obtained the normal and tangential microscopic components of the pressure tensor from the mechanical expression or virial route following the same procedure as in our previous works 34,35 and used the well-known IK recipe 8,57 for determining the microscopic components of the pressure tensor, P N (z) ≡ P z z (z) and…”

“…For further details, we recommend the original work 3 and the most important applications. 7,9,16,[19][20][21][22][23][24]27,28,33,34,44,[60][61][62] The implementation of the TA technique involves performing virtual or test area deformations of relative area changes defined as ξ = ∆A/A during the course of the simulation at constant N, V , and T every five MC cycles. Note that the procedure for calculating the surface tension is similar to that used to evaluate the components of the pressure tensor, but in this case the changes in the normal and transverse dimensions are coupled to keep the overall volume constant.…”

“…Standard homogeneous LRC to both magnitudes 37 are used in NPT simulations of bulk phases. In addition to that, inhomogeneous LRC using the MacDowell and Blas 7,44 methodology for the intermolecular potential energy and the recipe presented in our recent paper, 34 based on the Janecek's method 6,43 for the evaluation of the LRC for the components of the pressure tensor, are used. Results obtained using these LRC are equivalent to use the full potential or a potential with infinite truncation distance.…”

“…Fortunately, this problem seems to be solved satisfactorily recently in cases in which the system exhibits planar symmetry. Different authors have contributed to the establishment of appropriate and standard inhomogeneous LRC, including Blokhius, 38 Mecke, 39, 40 Daoulas, 41 Guo and Lu, 42 and finally, Janecek,6,43 and the recent improved methods proposed by MacDowell and Blas, 7 de Gregorio et al, 33 and Martínez-Ruiz et al 34,35 Despite the great number of studies carried out during the last 10 years for determining the interfacial tension and pressure tensor from Monte Carlo and molecular dynamics methodologies, most of them have focused on using the mechanical or virial route for determining these properties. Little work, however, has been developed to determine the interfacial properties, and particularly the surface tension and pressure tensor, from perturbative and thermodynamic methods for binary mixtures involving liquid-liquid (LL) separation.…”

“…In addition to that, we also analyze the effect of the cut-off distance on other thermodynamics properties, such as coexistence density and pressure-composition projection of the phase diagram. The second objective is to check the accuracy of the improved versions of the inhomogeneous LRC of Janecek 6 recently proposed by MacDowell and Blas 7 for the intermolecular energy and Martínez-Ruiz et al 34,35 for the microscopic components of the pressure tensor. In order to check the effectiveness of these methods in the case of a mixture that exhibits liquid-liquid phase separation, we also determine the interfacial tension and the components of the pressure tensor using two different perturbative methods, the TA technique and the VP methodology.…”