Phase behavior of a fluid with a double Gaussian potential displaying waterlike features

Cristina Speranza, Santi Prestipino, Gianpietro Malescio, and Paolo V. Giaquinta

Phys. Rev. E 90, 012305 – Published 18 July 2014

Abstract

Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we reconstruct the equilibrium phase diagram of a system of particles interacting through a potential that brings together a Gaussian repulsion with a much weaker Gaussian attraction, close to the thermodynamic stability threshold. Compared to the purely repulsive model, only the reentrant branch of the melting line survives, since for lower densities solidification is overridden by liquid-vapor separation. As a result, the phase diagram of the system recalls that of water up to moderate (i.e., a few tens of MPa) pressures. Upon superimposing a suitable hard core on the double-Gaussian potential, a further transition to a more compact solid phase is induced at high pressure, which might be regarded as the analog of the ice I-to-ice III transition in water.

Received 28 April 2014

DOI:https://doi.org/10.1103/PhysRevE.90.012305

Authors & Affiliations

Cristina Speranza^*, Santi Prestipino^†, Gianpietro Malescio^‡, and Paolo V. Giaquinta^§

Università degli Studi di Messina, Dipartimento di Fisica e di Scienze della Terra, Contrada Papardo, I-98166 Messina, Italy

^*csperanza@unime.it
^†Corresponding author: sprestipino@unime.it
^‡malescio@unime.it
^§paolo.giaquinta@unime.it

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Vol. 90, Iss. 1 — July 2014

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Images

Figure 1
Numerical phase diagram of the DGM system in the $T − P$ plane. We show the liquid-vapor coexistence points obtained from Gibbs-ensemble simulations (high- $T$ black dots), along with the estimated critical point (black asterisk); the solid-liquid coexistence points obtained from the “exact” free-energy calculations described in the text (low- $T$ black dots); the structural-anomaly locus (red open diamonds), the volumetric-anomaly locus (red open triangles), the diffusion-anomaly locus (red open squares), and the minimum- $c_{P}$ locus (red open inverted triangles). The lines through the points are plotted as a guide for the eye. On the scale of the figure, the bcc-vapor coexistence line is invisible.
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Figure 2
Numerical phase diagram of the DGM system in the $ρ − T$ plane. We show a number of points along the liquid-vapor binodal line obtained by Gibbs-ensemble simulations (black dots), along with the estimated critical point (black asterisk); a number of points along the line (dubbed “HNC pseudospinodal” in the figure) enclosing the region where the HNC equation could not be solved (blue open dots); the solid-liquid coexistence points obtained from the “exact” free-energy calculations described in the text (black diamonds and squares); some points on the $P = 0$ isobar of the bcc solid (black right-pointing triangles). The lines through the points are plotted as a guide for the eye. Note that the low-density region of the plot (i.e., the one enclosed in the red frame) is shown magnified in the next Fig. 3.
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Figure 3
DGM phase diagram in the $ρ − T$ plane: Magnification of the low-density region. We show two points on the liquid-vapor binodal line obtained by Gibbs-ensemble simulations (black dots); two points along the line enclosing the region where the HNC equation could not be solved (blue open dots); a few solid-liquid coexistence points obtained from the “exact” free-energy calculations described in the text (black diamonds and squares); some points on the bcc sublimation line, obtained from MC simulations of the bcc crystal at $P = 0$ (black right-pointing triangles); the HUIM melting points obtained by heating (in steps of $Δ T = 0.0002$ close to melting) an originally perfect bcc crystal along isochoric and isobaric paths until it melted (blue plusses and crosses, respectively); the variational-theory (VT) coexistence points (blue open diamonds and squares); the locus of zero- $Δ s$ points (blue open triangles). The lines through the points are plotted as a guide for the eye. The yellow-shaded regions denote two-phase coexistence regions. In the inset, a zoom on the triple-point region is provided.
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Figure 4
DGM-system RMPE, i.e., $Δ s = s^{ex} - s_{2}$ , defined as the difference between the excess and two-body entropies per unit particle, plotted as a function of the density along a number of isotherms (see legend).
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Figure 5
Schematic phase diagram of the DGM fluid with $ε_{2} = 0.02 ε$ (left) and of the modified DGM (mDGM) system defined in the text (right). These diagrams were obtained using the HNC approximation in combination with a Lindemann-type criterion of melting [34]. The region delimited from above by the black dots is the $(ρ, T)$ set of points where the HNC equation has no solution. It turns out that this region is almost insensitive to the inner part of the core. The lines are tentative melting loci for the fcc (blue dotted line), the bcc (red solid line), and the hcp crystals (cyan dashed line). More realistically, the actual values of $T_{m}$ are roughly a half of those shown. The inclusion of an inner “hard” core has led to the stabilization of the fcc crystal at high pressure.
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