The interplay between liquid-liquid and ferroelectric phase transitions in supercooled water

TL;DR

The paper addresses how liquid-liquid phase transitions in supercooled water relate to ferroelectric ordering, proposing that polarization and density fluctuations are two facets of the same underlying phenomenon. It combines extensive molecular dynamics simulations of TIP4P/Ice with a classical density functional theory in mean-field form, showing that dipolar interactions couple density and polarization to produce a ferroelectric LDL and a paraelectric HDL, and predicting a tricritical point in the $P$-$\rho$ phase diagram. The work documents polarization fluctuations and collective modes (Goldstone-like and Higgs-like) accompanying the LLPT and Widom line, and suggests dielectric measurements as a practical route to validate the LLPT experimentally. Overall, it supports a unified view in which ferroelectricity and LLPT are two facets of the same underlying phenomenon and highlights polarization as a high-signal observable for experimental verification.

Abstract

The distinctive characteristics of water, evident in its thermodynamic anomalies, have implications across disciplines from biology to geophysics. Considered a valid hypothesis to rationalize its unique properties, a liquid-liquid phase transition in water's supercooled regime has nowadays been observed in several molecular dynamics simulations and is being actively researched experimentally. Here, we highlight intriguing and far-reaching implications of water: the ferroelectric and liquid-liquid phase transitions can be designed as two facets of the same underlying phenomenon. Our results are based on the analysis of extensive molecular dynamics simulations and are explained in the context of a classical density functional theory in mean-field approximation valid for a polar liquid. The theory underpins the potential role of ferroelectricity in promoting the liquid-liquid phase transition. The existence of ferroelectric order in supercooled low-density liquid water is confirmed by the observation in molecular dynamics simulations of collective modes in polarization fluctuations dynamics, traceable to spontaneous breaking of continuous rotational symmetry. Our work opens the door to new experimental investigations of the static and dynamic behavior of water polarization.

Figures (5)

• Figure 1: Temporal evolution of $\rho$ (top) $P$ (middle) and $P_i$ (bottom) across supercooled water in LDL (left), near CP (center) and in HDL (right) as obtained from MD simulations, suggesting paraelectric and ferroelectric character for HDL and LDL, respectively. It is $\bar{P}=N d$. The CP for TIP4P/Ice model has been evaluated Debenedetti to be $( \bar{p}_c=1725 \ bar, \bar{T}_c=188.6 \ K)$.
• Figure 2: a, The figure depicts $U_L$, $\rho$, $\epsilon_0$, and $K_T$ at different points in the (T, p) plane obtained from MD simulations. Color scale represents the quantities value, symbol size is proportional to the associated error, obtained through block averaging. Full and dashed black lines serve as visual guidance, marking the first-order LLPT and WL, respectively. The diamond symbol marks CP. b, $U_L$, $\langle\rho\rangle$, $\epsilon_0$, and $K_T$ as functions of $T$ along constant-$p$ lines intersecting the WL ($p$=0 bar, 1000 bar, left) and the first-order LLPT line ($p$=2500 bar, right). The values of each quantity at CP are marked by a diamond symbol. A gradual change is observed in $U_L$ and $\rho$ when crossing the WL, while a sudden shift in $U_L$ occurs at the first-order LLPT line.
• Figure 4: a. Static susceptibilities $\chi_{T\hat{p}(L\hat{p})}(k)$, in LDL as a function of $k$. Both $\chi_{T\hat{p}}$ and $\chi_{L\hat{p}}$ show significant enhancement as $k \rightarrow 0$, following trends approximately proportional to $k^{-2}$ and $k^{-1}$, respectively, as indicated by the dashed lines. This behavior is consistent with predictions for a ferroelectric phase characterized by the spontaneous breaking of the $O(3)$ symmetry group. b. The upper graph shows the static correlation between $\delta P_{L\hat{p}}$ and $\delta P_{T\hat{p}}^2$, represented by $\chi_{T\hat{p}L\hat{p}}$, over $\chi_{L\hat{p}}(k)$ in the LDL phase. The lower graph depicts the static correlation between $\delta \rho$ and $\delta P_{L\hat{p}}$, $\chi_{\rho L\hat{p}}(\textbf{k})$ over $S(k)$ in LDL. A correlation between $\delta P_{L\hat{p}}$, $\delta P_{T\hat{p}}^2$ and $\delta \rho$ emerges, in particular at moderately small $k$s.
• Figure 5: From left to right: $C_{T\hat{p}T\hat{p}}(k,t)$, $C_{L\hat{p}L\hat{p}}(k,t)$, $C_{PP}(k,t)$, $C_{\rho \rho}(k,t)$ at different $k$ values. All quantities are normalized to their value at $t=0$, being $\bar{C}(k,t)=C(k,t)/C(k,0)$. The oscillatory behavior in $C_{L\hat{p}L\hat{p}}(k,t)$ and $C_{T\hat{p}T\hat{p}}(k,t)$, whith characteristic frequency varying with k, indicates the presence of a collective propagating mode, consistent with the existence of a ferroelectric phase leading to the spontaneous breaking of the $O(3)$ symmetry group. Oscillations are significantly reduced in $C_{PP}(k,t)$, suggesting that the constant modulus principle is approximately satisfied. The appearance of a propagating collective mode in $C_{\rho \rho}(k,t)$ highlights an existing correlation between $P$ and $\rho$, as also emphasized in Panel b of Fig. \ref{['Fig8short_1']}.
• Figure 6: Non-local transverse (longitudinal) static dielectric functions, $\epsilon_{T(L)}(k)$ and static structure factor $S(k)$ in HDL, close to CP and in LDL. The black circle with the error bar, obtained by block averaging, in the upper graphs mark the value of $\epsilon_0$. The first peak in $S(k)$ corresponds to a minimum in $\epsilon_T(k)$, highlighting a possible link between the spatial arrangement of molecules' center of mass and dipole orientation.