We consider the calculation of the surface tension from simulations of several models of water, such as the traditional TIP3P, SPC, SPC/E, and TIP4P models, and the new generation of TIP4P-like models including the TIP4P/Ew, TIP4P/Ice, and TIP4P/2005. We employ a thermodynamic route proposed by Gloor et al. ͓J. Chem. Phys. 123, 134703 ͑2005͔͒ to determine the surface tension that involves the estimate of the change in free energy associated with a small change in the interfacial area at constant volume. The values of the surface tension computed from this test-area method are found to be fully consistent with those obtained from the standard mechanical route, which is based on the evaluation of the components of the pressure tensor. We find that most models do not reproduce quantitatively the experimental values of the surface tension of water. The best description of the surface tension is given by those models that provide a better description of the vapor-liquid coexistence curve. The values of the surface tension for the SPC/E and TIP4P/Ew models are found to be in reasonably good agreement with the experimental values. From the present investigation, we conclude that the TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature. We also conclude that the test area is an appropriate methodological choice for the calculation of the surface tension not only for simple fluids, but also for complex molecular polar fluids, as is the case of water.

A novel test-area ͑TA͒ technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface ͑the relation of Kirkwood and Buff ͓J. Chem. Phys. 17, 338 ͑1949͔͒͒. For particles interacting through discontinuous intermolecular potentials ͑e.g., hard-core fluids͒ this involves the determination of ␦ functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two ͑or more͒ systems with different interfacial areas ͑the method of Bennett ͓J. Comput. Phys. 22, 245 ͑1976͔͒͒, which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo ͑TAMC͒ simulations are compared with the data obtained with other techniques ͑e.g., mechanical and free-energy differences͒ for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo ͑TAMC͒ or molecular-dynamics ͑TAMD͒ algorithms for different types of interfaces ͑vapor-liquid, liquid-liquid, fluid-solid, etc.͒ of pure systems and mixtures consisting of complex polyatomic molecules.

The vapor-liquid phase equilibria of square-well systems with hard-sphere diameters o, welldepths E, and ranges il = 1.25, 1.375, 1.5, 1.75, and 2 are determined by Monte Carlo simulation. The two bulk phases in coexistence are simulated simultaneously using the Gibbs ensemble technique. Vapor-liquid coexistence curves are obtained for a series of reduced temperatures between about T,. = T/T, = 0.8 and 1, where T, is the critical temperature. The radial pair distribution functions g(r) of the two phases are calculated during the simulation, and the results extrapolated to give the appropriate contact values g(a), g(/Za-), and g(;la-I-). These are used to calculate the vapor-pressure curves of each system and to test for equality of pressure in the coexisting vapor and liquid phases. The critical points of the squarewell fluids are determined by analyzing the density-temperature coexistence data using the first term of a Wegner expansion. The dependence of the reduced critical temperature Tr = kT,/q pressure P r = P,o-'/E, number density p: = pE d, and compressibility factor Z = P /(pkT), on the potential range il, is established. These results are compared with existing data obtained from perturbation theories. The shapes of the coexistence curves and the approach to criticality are described in terms of an apparent critical exponent 8. The curves for the square-well systems with il = 1.25, 1.375, 1.5, and 1.75 are very nearly cubic in shape corresponding to near-universal values ofp (flzO.325). This is not the case for the system with a longer potential range; when ;1 = 2, the coexistence curve is closer to quadratic in shape with a nearclassical value of p (PzO.5). These results seem to confirm the view that the departure of fl from a mean-field or classical value for temperatures well below critical is unrelated to longrange, near-critical fluctuations.

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In this paper we present a computer simulation study of the phase behavior of the Gay-Berne liquid crystal model, concentrating on the effects of varying the molecular elongation . We study a range of length-to-width parameters 3рр4, using a variety of molecular dynamics and Monte Carlo techniques, obtaining a guide to the phase behavior for each shape studied. We observe vapor (V), isotropic liquid (I), nematic (N), smectic-A (S A ) and smectic-B (S B ) liquid crystal phases. Within the small range of elongation studied, the phase diagram shows significant changes. On increasing , the liquid-vapor critical point moves to lower temperature until it falls below the I-S B coexistence line, around ϭ3.4, where liquid-vapor coexistence proves hard to establish. The liquid-vapor critical point seems to be completely absent at ϭ4.0. Another dramatic effect is the growth of a stable S A ''island'' in the phase diagram at elongations slightly above ϭ3.0. The S A range extends to both higher and lower temperatures as is increased. Also as is increased, the I-N transition is seen to move to lower density ͑and pressure͒ at given temperature. The lowest temperature at which the nematic phase is stable does not vary dramatically with . On cooling, no S B -crystal transition can be identified in the equation of state for any of these elongations; we suggest that, on the basis of simulation evidence, S B and crystal are really the same phase for these models.