Critical phenomena of anomalous liquids
Liquids such as water, silicon, silica, and germanium possess thermodynamic anomalies: at sufficiently low temperature, the specific heat Cp, the compressibility KT and the thermal expansion ap increase upon cooling. Studies have shown the possibility for anomalous liquids to have a liquid-liquid phase transition (LLPT), terminating at a liquid-liquid critical point (LLCP). The existence of the LLCP would explain the anomalies of these systems. However the LLCP is difficult to access experimentally due to crystallization. Here we study the properties of the Widom line, defined as the locus of the maximum correlation length in the one-phase region. The Widom line is approximately an extension of the LLPT line. For different systems, the slope of the LLPT line may vary from positive to negative, so the behavior of the Widom line may also differ. To gain a complete picture of the critical phenomena, we study the behavior of the Widom line for systems with different slopes of the LLPT line. In both computer simulations and linear scaling theory, we find the Widom line can be identified by maxima in either entropy or volume fluctuations for systems with non-zero slope of the LLPT line. The loci of Cp, Kt or αp maxima converge as the critical temperature is approached. However, when the slope of the LLPT line approaches zero, the method of identifying the Widom line by entropy fluctuations as the loci of Cp or αp maxima becomes unfruitful. The locus of Cp maxima approaches the LLCP from below the critical temperature in linear scaling theory and cannot be observed in simulations. The response function maxima in terms of volume fluctuations are still well-defined, and it is possible to identify the Widom line by following the locus of Kt maxima. Our findings should help guide the experimental search for the LLCP in liquid water. We also study the effect of confinement (i) within a fixed matrix of nanoscopic particles, and (ii) inside a cylindrical pore. We find the LLCP shifts to lower temperatures and higher pressures, but the behavior of the Widom line is unaffected by confinement.
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