Molecular Simulation Study of the Effect of Pressure on the Vapor-Liquid Interface of the Square-Well Fluid Jayant K. Singh and David A. Kofke* Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200 Received November 15, 2004. In Final Form: February 28, 2005 We examine a model system to study the effect of pressure on the surface tension of a vapor-liquid interface. The system is a two-component mixture of spheres interacting with the square-well (A-A) and hard-sphere (B-B) potentials and with unlike (A-B) interactions ranging (for different cases) from hard sphere to strongly attractive square well. The bulk-phase and interfacial properties are measured by molecular dynamics simulation for coexisting vapor-liquid phases for various mixture compositions, pressures, and temperatures. The variation of the surface tension with pressure compares well to values given by surface-excess formulas derived from thermodynamic considerations. We find that surface tension increases with pressure only for the case of an inert solute (hard-sphere A-B interactions) and that the presence of A-B attractions strongly promotes a decrease of surface tension with pressure. An examination of density and composition profiles is made to explain these effects in terms of surface-adsorption arguments. I. Introduction The effect of pressure, p, on interfacial tension, γ, is an issue of longstanding interest. 1-7 The behavior is captured by the derivative where a change that occurs along the saturation curve (subscript σ) at constant temperature, T, and interfacial area, A, is indicated. From the phase rule, there is only one degree of freedom for two coexisting phases of a pure substance and thus one cannot vary saturation pressure at a fixed temperature; for a pure substance, τ is not defined. To proceed, it is necessary to consider a two- component system, for which the phase rule permits isothermal variation of the pressure while maintaining the presence of two phases. However, in this case, one still does not get a description of the purely mechanical effects that pressure has on surface tension. It is not possible to effect the change in pressure without also changing the species composition of the coexisting phases, which in turn can modify the composition and structure of the interfacial region. Thus, the effect of pressure on surface tension, when measured this way, is necessarily a result of the combined mechanical (pressure) and chemical (composition) effects. In the best case, an “inert” gas (insoluble in the liquid) is added to pressurize the system, which then produces changes in the vapor-phase composition only. A Maxwell relation provides some insight that can be used to predict and understand the effect of pressure for a two-component system containing N 1 and N 2 molecules of species 1 and 2, respectively: The right-hand side describes the change in total volume that results from a change in the amount of interfacial area between the phases, keeping the overall mole numbers fixed. Rice 5 has discussed the effects giving rise to the change of volume. On one hand, movement of material from the bulk liquid to form the new surface (where the density is less) will result in an increase in the volume and tend to make the derivative positive. On the other hand, if vapor-phase molecules adsorb to some degree on the surface, then as new surface forms, it adsorbs more material from the vapor, causing the volume there to decrease and thus tend to make the derivative negative. In practice, both positive and negative values of τ have been observed in experiments involving the pressurization of a vapor-liquid interface using an inert gas, although negative values are much more prevalent. 7 Hansen 8 presented a general formulation of interfacial thermodynamics, developed such that the pressure re- mains a relevant independent variable, while making both species chemical potentials into dependent variables. Turkevich and Mann 6 also showed how Hansen’s con- struction could be used to determined τ strictly in terms of the volume and moles of the two-phase system and the densities of the bulk phases. Considering henceforth a mixture of two species only, a Gibbs-Duhem equation can be written for the composite liquid + vapor + interface system where S, V, and N i are the total entropy, volume, and number of moles of species i in the two-phase system, respectively, and µ i is the chemical potential of component i. To maintain equilibrium between the phases, an isothermal change in pressure must be accompanied by changes in the chemical potentials that permit them to (1) Gibbs, J. W. Collected Works (Yale University Press: New Haven, 1906); Dover: New York, 1961; Vol. 1, p 236. (2) Lewis, G. N.; Randall, M. Thermodynamics and the Free Energy of chemical substances; McGraw-Hill: New York, 1923; Chapter 21. (3) Bridgman, P. W. The Physics of High Pressure; Beel: London, 1952. (4) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; Wiley: New York, 1966; p 89. (5) Rice, O. K. J. Chem. Phys. 1947, 15, 333. (6) Turkevich, L. A.; Mann, J. A. Langmuir 1990, 6, 445. (7) Turkevich, L. A.; Mann, J. A. Langmuir 1990, 6, 457. (8) Hansen, R. S. J. Phys. Chem. 1962, 66, 410. τ ≡ ( ∂γ ∂p ) σ,T,A (1) ( ∂γ ∂p ) T,A,N 1 ,N 2 ) ( ∂V ∂A ) T,p,N 1 ,N 2 (2) -S dT + V dp - N 1 dµ 1 - N 2 dµ 2 - A dγ ) 0 (3) 4218 Langmuir 2005, 21, 4218-4226 10.1021/la0471947 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/30/2005