We study the Stell-Hemmer potential using both analytic (exact 1d and approximate 2d) solutions and numerical 2d simulations. We observe in the liquid phase an anomalous decrease in specific volume and isothermal compressibility upon heating, and an anomalous increase in the diffusion coefficient with pressure. We relate the anomalies to the existence of two different local structures in the liquid phase. Our results are consistent with the possibility of a low temperature/high pressure liquid-liquid phase transition.PACS numbers: 61.20. Gy, 61.25.Em, 65.70.+y, 64.70.Ja In their pioneering work, Stell and Hemmer proposed the possibility of a new critical point in addition to the normal liquid-gas critical point for potentials that have a region of negative curvature in their repulsive core (henceforth referred to as core-softened potentials) [1]. They also pointed out that for the 1d model with a long long range attractive tail, the isobaric thermal expansion coefficient, α P ≡ V −1 (∂V /∂T ) P (where V, T and P are the volume, temperature and pressure) can take an anomalous negative value. Debenedetti et al., using thermodynamic arguments, pointed out that the existence of a "softened core" can lead to α P < 0 [2].Here we further investigate properties of core-softened potential fluids. We first study the properties of the 1D fluid using an exact solution. We then investigate the behavior of the 2D fluid, initially by an approximate solution provided by cell theory method and finally by performing molecular dynamics simulation of the fluid.The discrete form of the potential that we study iswith r being the inter-particle distance and λ < 1 ( Fig. 1(a)) [3]. The model is exactly solvable in 1d, following the methods of [4][5][6][7], and the equation of state is| Here V /N ≡ ℓ is the average distance between nearest neighbors, Π x ≡ e −βP x (x = a, b, c), W ≡ e βǫ and β ≡ k B T . The isobars ( Fig. 1(b)) exhibit two different types of behavior. For all P larger or equal to an upper boundary pressure P up , ℓ = a at T = 0, and ℓ increases monotonically with T . For P < P up , ℓ = b at T = 0. The isobars show a maximum and a minimum in ℓ, which correspond respectively to points of minimum and maximum density [8], bounding a density anomaly (α P < 0) region [9,10]. There is a discontinuity in ℓ at P = P up along the T = 0 isotherm. Next we study the isothermal compressibility K T ≡ −V −1 (∂V /∂P ) T,N . We use Eq.(2) to calculate K T along isobars (Fig. 1(c)). The graphs show an anomalous region in which K T decreases upon heating (for simple liquids K T increases with T ). We find the maximum value of K T grows as P increases towards P up , and K T diverges as 1/T when we approach the point C ′ with coordinates (T = 0, P = P up ) which we interpret as a critical point [11]. Further, the locus of K T extrema joins the point C ′ (Fig. 1(d)).We also study the T MD locus (Fig. 1(d)) and note that the locus of K T extrema intersects the T MD locus at its infinite slope point, a result that is thermodynamically require...

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We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The coresoftened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T = 0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point C ′ at a positive pressure, which is the analog of the T = 0 "critical point" in the 1d Ising model. The existence of point C ′ leads to anomalous behavior of the isothermal compressibility K T and the isobaric specific heat C P .

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