Decoding a Percolation Phase Transition of Water at ~330 K with a Nanoparticle Ruler

Liquid water, despite its simple molecular structure, remains one of the most fascinating and complex substances. Most notably, many questions continue to exist regarding phase transitions and anomalous properties of water, which are subtle to observe experimentally. Here, we report a sharp transition in water at 330 K unveiled through experimental measurements of the instantaneous Brownian velocity of NaYF 4 :Yb/Er upconversion nanoparticles in water. Our experimental investigations, corroborated by molecular dynamics simulations, elucidate a geometrical phase transition where a low-density-liquid (LDL) phase becomes percolated below 330 K. Around this critical temperature, we find that the sizes of the LDL clusters to be similar to the nanoparticles, confirming the role of upconversion nanoparticle as a powerful ruler for measuring the extensiveness of the LDL hydrogen-bond network and nanometer-scale spatial changes (20 to 100 nm) in liquids. Additionally, a new order parameter that unequivocally classifies water molecules into two local geometric states is introduced, providing a new tool for understanding and modelling water’s many anomalous properties and phase transitions.

Brownian velocity is sensitive to the local liquid environment, we use this method to measure the LDL motif that is known as a large tetrahedral network featuring strong cooperativity 27 . As a proof-of-concept experiment, we prepared and measured the instantaneous Brownian velocity of luminescent nanofluids containing NaYF4:Yb/Er@NaYF4 and NaYF4:Lu/Yb/Er upconversion nanocrystals of 24 and 106 nm in diameter, respectively, dispersed in water, cyclohexene, and toluene with volume fractions (ϕ) of 0.085% and 0.066%, for the smaller and bigger nanocrystals, respectively (Figures S1,2 and Tables S1,2 in Supporting Information).
The experimental set-up is similar to that in Ref. 26 and is detailed in Supporting Information.
Whereas for cyclohexene and toluene the Brownian velocities increase linearly with increasing temperature, for water a bilinear behaviour with a crossover temperature Tc=329.  (Table S3 in Supporting Information). These values of Tc are within the range of those reported for different physical properties of liquid water: thermal conductivity (337±5 K), proton spin-lattice relaxation time (323±5 K), refractive index (323±5 K), conductivity (326±5 K), surface tension (330±5 K), and kinetic viscosity (323±6 K), 11 as described in Figure S12 in Supporting Information. Moreover, this bilinear trend was also observed in studies involving metallic nanoparticles, 28 colloidal Ln 3+ -based nanocrystals, 29 Eu 3+ aqueous complexes, [30][31] and organic molecules. [32][33]  (d) Effective diffusivity and enhancement factor of the nanofluid with 24 nm nanoparticles (pH=5.10±0.01) with respect to pure water. All lines are the best fits to straight lines (slopes and correlation coefficients r 2 shown in Table S3 in Supporting Information).
The bilinear behaviour observed in the instantaneous velocity of nanoparticles in water indicates two regimes of nanoparticle motion, where the nanoparticles exhibit a different effective mass * , signaling a change in the water-nanoparticle interaction. For a nanoparticle 24 nm in diameter, * changes drastically at Tc, since the slope of 2 vs. T for T>Tc increases 4-to 5-fold relative to that for T<Tc ( Figure 2a and Table S4   To rationalize the transition observed in the nanoparticles' effective mass, we investigate the underlying local order of the liquid water through molecular dynamics (MD) simulation based on the polarizable SWM4-NDP water model. 34 Since tetrahedral geometry is key to distinguish the two different structures as the low-density water is thought to be more "ice-like", 35 we first examine a tetrahedral orientational order parameter q for each water molecule 36-37 , given by: This q-value considers the relative angular positions in the four nearest neighbors around each water molecule. The summations run over all six pairs among the four nearest neighbors.
denotes the angle extended from the oxygen atom of the molecule to the oxygen atoms of neighbours and (inset of Figure 2a). The q-value grows with the tetrahedral order around a molecule, with its average value equal to one for ordinary ice and zero for an ideal gas. At ambient conditions, the probability density function f(q) exhibits two overlapping peaks ( Figure   2a), one at higher q that decreases with temperature, and the other at lower q that increases with temperature. 37 These two peaks suggest the existence of two local structural states of water with different tetrahedral orders but, to date, their origin has not been elucidated.
Here, we introduce a new method to classify water molecules into two local structural states that give rise to the two peaks in f(q). Since the peak at higher q indicates a state with a higher tetrahedral order, the positions of the four nearest neighbours are close to the vertices of a regular tetrahedron ( Figure 2b). We denote this state as the locally tetrahedral (TH) state. The peak at lower q, on the other hand, indicates a state with less tetrahedral order.
Owing to the open configuration in the TH-state, the second state involves an additional water molecule at an interstitial site that makes the liquid structure more tightly packed. We denote this state as the locally distorted (DT) state (Figure 2c). For a molecule in the DT-state, as the newly added molecule may become one of the four nearest neighbours, greater tetrahedral order may be found when the fifth nearest neighbour is taken into account. Therefore, we consider a generalized tetrahedral orientational order parameter q5 to be given by the maximum value of q for any 4 out of the 5 nearest neighbours (see Supporting Information for detailed description): where the summation runs over all pairs jk among the 4 chosen neighbours. A comparison between q and q5 allows us to distinguish the two local structural states. In the TH state, the 4 nearest neighbours give the maximal tetrahedral order, and thus 5 = . In contrast, in the DT state, the maximal tetrahedral order arises when the 5 th nearest neighbour is considered, and Connected TH-state molecules can form a long-ranged hydrogen-bond network, consistent with the LDL liquid structure as a large tetrahedral network featuring strong cooperativity. 27 In contrast, such cooperativity is much weaker in the HDL motif formed by the DT-state molecules, in which the hydrogen bond network is less structured and shorter-ranged. Due to the two-state nature of the hydrogen-bond network, there is necessarily a geometric percolation transition that is not thermodynamic in origin. Although the two motifs interpenetrate with each other, the network formed by TH-state molecules is long-ranged and is consequential for transport properties on a larger length scale that might be discernible. It should be noted that the TH-state defined here is not equivalent to the low-density state that is defined elsewhere, 7, 42-43 and the connection between different two-state classifications is a subject in future work.
With nanoparticles of different sizes, the difference between Tc values of smaller and bigger nanocrystals is, in all the pH range tested, around 3 degrees (Figure 1c), suggesting a drastic change in the length scale of the LDL motif around Tc ( Figure S11 in Supporting Information).
This suggests that the fluctuations of LDL motifs become correlated and grow in spatial extent below Tc, 2, 44 and this could be due to the underlying percolation transition such that the LDL motif formed by TH-state molecules becomes percolated below Tc. While liquid water has been known to be a large cluster of connected hydrogen-bonded network, [45][46][47] here, we are concerned with the more tetrahedrally-structured network formed by TH-state molecules. Although individual hydrogen bonds in the network have short lifetime, they are likely to reform because of the favourable tetrahedral geometry. Therefore, the network formed by TH-state molecules would be more cooperative over a longer range and more persistent. Moreover, it should be noted that the LDL motifs cannot be thought as density heterogeneities measured by smallangle X-ray scattering (SAXS) measurements (dimensions of the order of 1 nm at ambient conditions). 16,[48][49] The LDL motifs are formed by a tetrahedral (ice-like) network of TH-state molecules with many empty pockets in between for the less-ordered, shorter-ranged HDL water network (dominant in ambient conditions) and, thus, are larger than the density heterogeneities measured by SAXS measurements (regions occupied by TH-state molecules exclusively). On computing the fraction of TH-state molecules (Figure 3c), TH , we notice that the fraction at   In a further set of experiments, we measured the temperature dependence of the Brownian velocity of colloidal nanocrystals in the water at pH values in the range 2.70−8.50, as illustrated in Figure 1b. Notably, for both NaYF4:Yb/Er@NaYF4 and NaYF4:Lu/Yb/Er nanocrystals, while for T>Tc the rate of increase of the Brownian velocity with temperature is independent of the nanofluid's pH, for T<Tc that rate changes with the pH in such a way that the Brownian velocity increases with decreasing pH (Figure 1b). Furthermore, Tc increases with decreasing pH (Figure 1c), suggesting H3O + increases the size of the LDL motif because its oxygen atoms is sp 3 -hybridized and, thus, geometrically similar to TH-state water molecules. However, the observed increase of the Brownian velocity with decreasing pH for T<Tc suggests that H3O + destabilizes the hydrogen-bond network in the LDL motif, making the network motion less cooperative.
Using a two-plate thermal diffusion model, we can accurately describe our measured instantaneous Brownian velocity with thermal diffusion (see Supporting Information). The twoplate model predicts a linear trend of t0 versus xi in Figure S3 in Supporting Information and shows a linear relationship between thermal diffusivity and the predicted velocity ( Figures S15-18 in Supporting Information). Extrapolating this relation using the thermal diffusivity for pure water, 51-53 we predict the thermal diffusivity for the 24 nm nanoparticles suspended in water to be enhanced more than two times, as compared to that of pure water in the same temperature range (Figure 1d). Though this large enhancement is a prediction based on thermal modelling, it is within the range of enhancements observed experimentally in some nanofluids. [54][55] It is worth noting that our numerical model highlights the fact that the temperature detected by luminescence nanocrystals obeys macroscopic thermal transport. However, to understand the exact nature of the Brownian motion at nonequilibrium conditions, comprehensive models accounting for nanoconvection and other nanoscale effects are required. Additionally, effects of ions and the surface water structure on nanoparticles may be considered in a more comprehensive model of the system.
Using suspended nanocrystals as rulers, we have been able to detect a crossover temperature in the nanoparticle's instantaneous Brownian velocity in water, at which temperature the size of the nanoparticle and the LDL motif are comparable. This rapid change of the size of the LDL motif at around 330 K is a result of an underlying percolation transition. Since the long-range hydrogen-bond network in LDL motif is the key to decipher the behaviour of water, 56 understanding the temperature dependence of its length scale will provide insight into the properties, as well as the mechanisms, functions, and roles of water, for instance, in influencing the stability of proteins [57][58] Figures S3 and S4 in Supporting Information). For each time instance, the absolute temperature T is calculated through the intensity ratio (the thermometric parameter ) between the 2 H11/2→ 4 I15/2 (IH, 510−535 nm) and 4 S3/2→ 4 I15/2 (IS, 535−565 nm) Er 3+ emission bands, as 26 : where 0 is the thermometric parameter at a reference temperature T0, kB is the Boltzmann Preparation of upconversion nanocrystals. NaYF4:Yb/Er(18/2%)@NaYF4 (average diameter 24 nm) and NaYF4:Lu/Yb/Er (50/18/2%) (average diameter 106 nm) nanocrystals were synthesized by a standard co-precipitation or modified hydrothermal method according to Ref. 60 . Further experimental details are available in Supporting Information.
Operating procedure for temperature mapping. In a typical experiment, a Thorlabs quartz cuvette (CV10Q1400) was used as the container and filled with 0.50 mL of nanofluid at an initial temperature between 300 and 355 K. For water suspensions, the pH ranges from 2. Molecular dynamics simulation of water. Molecular dynamics simulation for the polarizable SWM4-NDP water model 34 was carried out using an extended Lagrangian dynamics with a dual-Langevin thermostat 61 with OpenMM package 62 . At each temperature, the size of the cubic simulation box was set such that the density of water molecules in the simulation box matched the density of water at atmospheric pressure (Table S6 in Supporting Information). Periodic boundary conditions are applied. For the dual-Langevin thermostat, the friction coefficients for the center-of-mass and for the internal Drude-pair degrees of freedom were 20 ps -1 and 1 ps -1 , respectively, and the temperature set for the internal Drude-pair was 1 K. The time step for the integration was 1 fs. For each randomly generated initial configuration, the system was first annealed from 373.15 K to the desired temperature in 100 equal-interval temperature steps and 1 ps per step, followed by equilibration at the desired temperature for 1 ns. Then, the configuration state of the water was sampled every 10 ps for 70 ns. The sampling was repeated independently for 8 times for each system size and temperature.

ASSOCIATED CONTENT
Supporting Information. Nanoparticle synthesis; materials characterizations; computational methods; study of the effective mass of the nanoparticles; and investigation of instantaneous Brownian velocity and thermal diffusivity.

AUTHOR INFORMATION
The authors declare no competing financial interests.