Physics of the Jagla model as the liquid-liquid coexistence line slope varies

The slope of the coexistence line of the liquid-liquid phase transition can be positive, negative, or zero. All three possibilities have been found in Monte-Carlo simulations of a modified spherically symmetric two-scale Jagla model. Since the liquid-liquid critical point frequently lies in a region of the phase diagram that is difficult to access experimentally, it is of great interest to study critical phenomena in the supercritical region. We therefore study the properties of the Widom line, defined in the one-phase region above the critical point as an extension of the coexistence line near which the loci of various response functions extrema asymptotically converge with each other. This phenomenon is predicted by the scaling theory according to which all response functions can be expressed asymptotically in the vicinity of a critical point as functions of the diverging correlation length. We find that the method of identifying the Widom line as the loci of heat capacity maxima becomes unfruitful when the slope of the coexistence line approaches zero in the T-P plane. In this case, the specific heat displays no maximum in the one-phase region because, for a horizontal phase coexistence line, according to the Clapeyron equation, the enthalpy difference between the coexisting phases is zero, and thus the critical fluctuations do not contribute to enthalpy fluctuations. The extension of the coexistence line beyond the critical point into the one-phase region must in this case be performed using density fluctuations. Although the line of compressibility maxima bifurcates into a symmetrical pair of lines, it remains well-defined. We also study how the glass transition changes as the slope of the coexistence line in the T-P plane approaches zero. We find that for the case of positive slopes, diffusivity shows a fragile-to-strong transition upon crossing the Widom line, while for horizontal slope, diffusivity shows the behavior typical for fragile liquids.