Deciphering Density Fluctuations in the Hydration Water of Brownian Nanoparticles via Upconversion Thermometry

Liquid water is the main constituent of the human body and covers a majority of the Earth’s surface. It plays a vital role in a myriad of biological, chemical, physical, geological, industrial, and environmental processes.¹⁻⁷ In addition to its chemical properties as a solvent, proton transfer medium, and active component of reactions, the physical properties of water are also fundamentally relevant.⁸ Although water is the most commonly used liquid, its complex behavior under varying pressure and temperature conditions leads to numerous anomalies in its properties that differ significantly from those of other commonly used liquids. To date, more than 60 anomalous properties have been reported for water,⁹⁻¹² including a minimum specific heat at 308 K, a negative thermal expansion coefficient below 277 K, and a minimum isothermal compressibility at 319 K.

The underlying reason for these anomalous characteristics is related to water’s remarkable ability to form strong and directional hydrogen bonds (H-bonds). As these hydrogen bonds are constantly breaking and re-forming on a picosecond time scale, fluctuations occur in the local structure of water, leading to the emergence of water motifs (or patches) with different densities.^11,12 Today, two contrasting schools of thought seek to explain the anomalous properties of water by investigating its structural fluctuations. The continuous distribution models of water propose a homogeneous structural distribution caused by thermal fluctuations.¹³⁻¹⁵ The two-state model, on the contrary, argues that the anomalies stem from the coexistence of two distinct preferred local structural arrangements of water molecules that have different physical properties (e.g., the density differs by ∼20%⁴): a low-density liquid (LDL) and a high-density liquid (HDL). These local structures become increasingly well-defined upon supercooling and begin to contribute around the compressibility minimum.^4,8,11,16 While LDL is an open tetrahedral configuration with predominantly low-energy H-bonds, HDL is a network with shorter and highly disordered H-bonds.¹⁶⁻²²

This two-state scenario appears today to be very likely, as both theoretical²³⁻²⁸ and experimental results²⁹⁻⁴⁰ support the existence of a liquid–liquid critical point located in the supercooled liquid region of the water phase diagram, separating a one-phase region from a two-phase region where the LDL and HDL patches coexist, separated by a first-order transition line^4,11,41−43 (Supporting Information and Figure S1). The coexistence of these two structural motifs of water has been observed both in silico(41,44−46) and in experimental^21,47−53 works, especially upon supercooling. Although further experimental evidence for inhomogeneous structures of liquid water and fluctuations between HDL and LDL patches was provided by the isosbestic point in the temperature-dependent OH stretching Raman signal,^54,55 temperature-dependent infrared spectra of liquid water,⁵⁶ optical Kerr effect measurements,⁵⁷ and X-ray absorption and emission spectroscopy,^{42,47−49,58} the coexistence of these fluctuations under ambient conditions and their implications remain elusive and controversial.^{14,16,21,59−66} Nonetheless, showcasing two distinct arrangements of water molecules and their fluctuations is crucial, as it has the potential to revolutionize our understanding of biochemistry and reveal that life-supporting conditions may hinge on the presence of two kinds of H-bond organization in liquid water.^1,3,67

Little is known about the topology of liquid water, specifically regarding the existence of motifs forming the H-bond networks such as rings, clathrates, and clusters, which, although numerically proposed through molecular dynamics,^45,68−70 have not been experimentally observed. This knowledge gap arises because techniques commonly employed to investigate density fluctuations in liquid water and H-bond network structures are limited to a length scale of ∼1 nm (Figure 1). Therefore, there is a strong demand for experimental techniques for microscopically deciphering H-bond structures in liquid water as well as in aqueous solutions of electrolytes, suspensions of biomolecules, and inorganic materials. These systems have garnered more attention due to their potential to unveil the intricate relationship among charged interfaces, high- to low-density liquid fluctuations, and their role in the formation of large-scale H-bond supramolecular structures, as suggested by molecular dynamics simulations of the hydration shell of the lysozyme protein.⁷¹ Supramolecular structures of orientationally ordered water as large as 1 μm have been reported in light scattering measurements of aqueous solutions of low-molar mass compounds⁷²⁻⁷⁴ and in wide-field second harmonic (SH) microscopy of divalent cations interacting with water and negatively charged free-standing lipid bilayers,^75,76 although not explicitly connected to HDL and LDL domains.

In recent years, there has been extensive research into the temperature dependence of the optical properties of a wide range of water-suspended materials such as quantum dots,⁵² plasmonic⁷⁷ and luminescent⁷⁸ nanoparticles, organic molecules,⁷⁹⁻⁸¹ and trivalent lanthanide-based materials,⁸²⁻⁸⁴ including upconverting nanoparticles (UCNPs).⁸⁵⁻⁸⁷ The temperature (T) at which these materials exhibit a notable change in their optical properties is often termed the crossover temperature (T_c).⁵² It predominantly falls within the range of 320–340 K and coincides with the minimum of the isothermal compressibility of water.⁵⁰ Surprisingly, although some of these measurements have been interpreted in light of the two-state model of water,^52,80 the observed bilinear trend has not been explicitly attributed to the presence of HDL and LDL motifs or the fluctuations between them. To the best of our knowledge, only one research paper has explored the intriguing relationship between the bilinear temperature dependence of the instantaneous Brownian velocity of NaYF₄:Yb/Er UCNPs suspended in water and the high- to low-density liquid fluctuations.⁸⁷ These experimental data, corroborated by molecular dynamics simulations, elucidated a geometric phase transition in which the LDL phase percolates below 330 K. T_c, in this context, was interpreted as the onset of fluctuations between high- and low-density liquid water.⁸⁷

In this work, we delve into the unique ability of upconversion nanothermometry⁸⁸ to measure the temperature and pH dependence of the Brownian velocity⁸⁹ of UCNPs of varying sizes (15–106 nm in diameter) dispersed in water [so-called nanofluids (section 2 of the Supporting Information)]. We estimate an upper-temperature threshold for the liquid water density fluctuations in the region dominated by HDL domains under ambient conditions, which agrees with the value suggested in the hypothetical phase diagram of liquid water under ambient conditions (Figure S1).^{4,8,11,23,31,90} We also show that increasing the pH of the nanofluids fragments the LDL domains (the LDL–HDL fluctuations become less favorable), similar to increasing the pressure in this phase diagram. Furthermore, our results provide new insights into the relative proportion of HDL and LDL motifs that coexist in the hydration water around the particle surface under ambient conditions. We find that the high- to low-density liquid fluctuations depend on the size of the suspended nanoparticle and the pH of the nanofluid. As the size increases, the relative proportion of HDL domains increases, while as the surface charge increases (controlled by pH), the relative proportion of LDL patches increases.

We measured the instantaneous Brownian velocity of 15 nm [diameter (d)] NaGdF₄:Yb/Er(18%/2%)@NaGdF₄ core–shell UCNPs dispersed in water (H₂O, pH 5.10), heavy water (D₂O), and ethanol (EtOH) at a volume fraction of 0.085% (Figure 2a and Table S1). The colloidal stability of the nanofluids and the size distribution of the UCNPs are presented in Figures S2–S6 and Table S2. The experimental setup, similar to that in ref (89), is described in sections 2 and 3 of the Supporting Information, Figures S7–S10, and Table S3. As the solvent density (ρ) increases, the Brownian velocity decreases because denser liquids have a higher effective mass (defined as the combined mass of the UCNPs and half of the liquid mass moving cooperatively with them).⁹¹ This is well illustrated by the difference in density between EtOH and D₂O (781 and 1105 kg m^–3, respectively, at 303 K⁹²). The lower density of EtOH facilitates the faster motion of the UCNPs within the nanofluid, whereas the higher density of D₂O results in considerably slower motion (Figure 2a). An analogous density dependence was observed in the Brownian velocity of UCNPs containing an oleic acid coating and dispersed in toluene and cyclohexane, where the increase in solvent density decelerates the motion of particles.⁸⁷

The Brownian velocity of the UCNPs depends on the particle size, decreasing by ∼20% when the size increases from 15 to 64 nm and being almost independent of size for larger values of ≤106 nm, as observed in Figure 2b and Figure S11a. Due to the same volume fraction used across all colloidal suspensions (0.085%), smaller particle sizes correspond to a greater number of UCNPs in the suspensions (Figure S11 and Table S4). Consequently, this results in an increased Brownian velocity of the UCNPs with a higher particle count in the suspension. The number of UCNPs increases by a factor of ∼4 when the particle size decreases from 106 to 64 nm. However, this increment is far more striking, reaching a factor of 40, when the size decreases from 52 to 15 nm. The observed decrease in Brownian velocity as UCNP size increases is therefore attributed to the dependence of Brownian velocity on the number of particles per unit of volume in the suspensions due to the particle–particle interactions. It is noteworthy that these findings align seamlessly with our earlier observations.⁸⁹

Notably, the Brownian velocity of the UCNPs in the aqueous nanofluids exhibits a bilinear trend, regardless of the size of the particles (Figure 2b). This behavior is attributed to the presence of two distinct motion regimes for the UCNPs. When T < T_c (300–330 K), there are HDL fluctuations into more voluminous LDL regions within the HDL dominant phase. Consequently, this gives rise to a greater effective mass of the nanoparticles, resulting in lower Brownian velocity values. Conversely, when the temperature exceeds the critical threshold (T > T_c), density fluctuations cease because all LDL motifs have already been converted into HDL ones. This leads to a liquid state characterized by localized fluctuations within the HDL phase, leading to higher Brownian velocity values. It is worth stressing that the obtained T_c value closely corresponds with the minimum value of the isothermal compressibility of liquid water, which is related to the change from a more to a less organized tetrahedral organization due to the density increase.⁵⁰ Once isothermal compressibility depends on fluctuations in density indicating a relative change in the volume, the similarity between the T_c values of the Brownian velocity of UCNPs and the minimum isothermal compressibility of liquid water is explained by the change in volume of the HDL and LDL motifs with an increase in temperature.⁹³

Compared to liquid water, the weaker hydrogen bonds in ethanol⁹⁴ result in a continuous linear increase in the Brownian velocity of UCNPs upon heating. Although the low boiling point of EtOH limits its study at temperatures above 333 K, the lack of tetrahedral arrangements means that T_c is not expected to occur.⁹⁵ While HDL and LDL motifs have also been identified in liquid D₂O,^96,97 the presence of isotopic quantum effects generates a more ordered structure that enhances thermodynamic stability,^98,99 displacing the Widom line toward higher temperatures (4 K at ∼0 bar).³¹ The melting point (4 K), maximum density (7 K), isothermal compressibility (5 K), nuclear quantum effects (5 K), and viscosity (−6.5 K) also exhibit a temperature offset in D₂O relative to the values in H₂O.^100−104 Then, T_c might be shifted by a few degrees. No crossover temperature, however, was observed in the temperature dependence of the Brownian velocity of the UCNPs in D₂O (Figure 2a).

Interestingly, recent findings on the three-dimensional confinement of light and heavy water within zwitterionic liposomes of different sizes, as determined through SH imaging and scattering experiments, have yielded a noteworthy conclusion: The H-bond networks in D₂O differ not only at subnanometer length scales but also at length scales of ≲100 nm.⁷⁶ This significantly exceeds the previously observed confinement length scales of ∼2–20 nm.⁷⁶ On the contrary, experimental¹⁰⁵ and simulation^106,107 results have shown that the dielectric constant of confined water is much lower than that of bulk water. Similarly, Kim et al.¹⁰⁸ highlighted how the confinement of interfacial water molecules caused by surface charge results in a lower dielectric constant at the hydration layer, which can be controlled by changing the temperature at the surface. Therefore, the Brownian velocity of UCNPs dispersed in heavy water displays an uninterrupted linear increase from room temperature to the boiling point, similar to the behavior observed for water at temperatures below T_c (Figure 2a), because of the much larger spatial extent over which H₂O molecules interact in the hydration water of the UCNPs, corresponding to a much larger spatial extent for low- to high-density liquid water fluctuations.

We observed a pronounced reduction in the T_c values of the nanofluids as the diameter d of the UCNPs increased (Figure 2c). This intriguing size-dependent trend shows that, as d → 0, T_c converges toward 331.2 ± 0.2 K, as nicely illustrated by the surface/volume (S/V) ratio of the UCNPs [quasi-spherical morphology (Figure S5)] in the inset of Figure 2c. This temperature should therefore correspond to the onset temperature of the fluctuations between high- and low-density liquid states in pure water (d = 0 in Figure 2c). Interestingly, this upper-temperature threshold for fluctuations in the HDL domain-dominated region under ambient conditions agrees with the value (325.0 ± 1.0 K) estimated based on data from the hypothetical phase diagram of water under ambient conditions published in refs (4) and (8) (Figure 3).

Furthermore, we hypothesize that the decrease in the T_c of the aqueous nanofluids derived from Figure 2c compared to pure water stems from a decrease in the high- to low-density liquid water fluctuations as a consequence of the prevalence of a higher concentration of HDL patches relative to LDL regions in the volume of nanofluid moving cooperatively with UCNPs. Notably, this hypothesis corroborates previous findings, both in silico(71) and in experiments,¹⁰⁹ about the hydration water of the lysozyme protein. This hydration water (defined as the water molecules encompassing the protein within a 0.6 nm shell)⁷¹ exhibits local distortions when compared to bulk water. For instance, its density is much higher than that of the bulk¹¹⁰ and the dielectric constant of interfacial water in the double layer is much lower than that of bulk water.¹⁰⁸ These distortions induce a different ordering of water molecules at the interface, characterized by a higher concentration of HDL domains than LDL domains, compared to bulk water.^71,109 Like the impact of the lysozyme protein in liquid water, the presence of UCNPs also influences the local structure of water within the aqueous nanofluids. Consequently, nanofluids with larger UCNPs (lower S/V ratios) contain a relatively higher proportion of HDL domains in the hydration shell of the nanoparticles, leading to lower T_c values (Figure 2c). When d > 78 nm, T_c reaches a plateau at ∼327.5 K. This occurs because the S/V ratio changes negligibly beyond this size threshold. Remarkably, the T_c of ligand-free and silica-coated UCNPs of comparable size is similar (Figure 2c), suggesting an analogous relative HDL/LDL proportion at the particle surface, in agreement with an identical charge density of the water–silica and water NaYF₄ interfaces [|ζ| ∼ 35 mV (Figures S3 and S4)].

The vicinity of the UCNPs can be sensitively influenced by local ions and ligands, with effects already occurring at extremely low concentrations.¹¹¹ Fine-tuning the pH of suspensions at the water–silica interface was found to induce changes in charge density, impacting the orientation of water molecules.^110,112 Recent surface-enhanced IR absorption spectroscopy results have also shed light on the influence of pH on hydrogen and water binding energies on platinum surfaces.¹¹³ Also, a pH dependence of the onset temperature of the anomaly related to the minimum isothermal compressibility of liquid water was reported for aqueous suspensions, including 1-methyl-5-nitroindoline,⁸⁰ Eu³⁺ complexes,^82,83 and NaYF₄:Yb/Er UCNPs.⁸⁶ These findings suggest a potential role of pH in influencing high- to low-density fluctuations within aqueous nanofluids.

To explore this possibility, we evaluated the temperature-dependent Brownian velocity of the UCNPs dispersed in aqueous nanofluids while systematically varying the pH values from 2.70 to 8.50 (Figure 4a for d values of 15, 64, and 78 nm and Figure S12 for d values of 24, 52, and 106 nm). Except for pH values between 7.0 and 8.0, the measured absolute ζ potential values (|ζ| > 20 mV) indicate stability with no UCNP aggregation (Figures S3 and S4).

pH exerts a notable influence on Brownian velocity, with an increase in pH leading to a reduction in Brownian velocity when T < T_c, while the pH dependence becomes negligible when T > T_c. This impact is primarily on LDL domains, present only when T < T_c. Increasing the pH weakens the H-bond network due to an increased concentration of OH^– ions, disrupting the tetrahedral organization of LDL domains due to their voluminous planar structure.¹¹⁴ Increasing the pH triggers the fragmentation of LDL domains into smaller ones,⁸ while keeping the HDL/LDL ratio, leading to a deceleration of the motion of the UCNPs. This effect mirrors the application of high pressures, as suggested by previous neutron diffraction measurements^114,115 and Monte Carlo simulations.¹¹⁶ As the pressure increases at a constant temperature, the LDL–HDL fluctuations become less favorable.⁸ This can be visualized as the fragmentation of the LDL domains (Figure 3 and Figure S1). However, recent machine learning-based molecular dynamics simulations of ions in salt water have shown that the ions do not homogeneously distort the structure of water but instead have localized structural effects in the first solvation shell.¹¹⁷ Our results agree with this scenario as increasing the pH of the nanofluids is an ingenious strategy for simulating a pressure-like effect and evaluating microscopic changes in H-bond networks.

The decrease in Brownian velocity with an increase in pH results in a concomitant decrease in T_c values (Figure 4b), indicating that low- to high-density liquid fluctuations at nanoparticle surfaces cease at lower temperatures in basic media compared to acidic media. To explain this dependence, we consider the influence of pH on the surface charge of UCNPs, with experiments demonstrating how surface charge controls the water structure near the interface. The fine-tuning of pH affects the extent of orientation of water molecules near the interface, as reported for water–silica interfaces.^108,110 Therefore, to study the effect of pH on the electric double layer of UCNPs, we measured the ζ potential of the distinct aqueous nanofluids. Our results show a decrease in |ζ| as pH increases (Figure S4), in good accordance with previous reports on upconverting¹¹⁸ and plasmonic¹¹¹ nanoparticles. This mirrors the trend observed for T_c (Figure 4b and Figure S13), highlighting how the presence of ions in the medium can affect the surface charge of the UCNPs. The increase in the extent of electrostatic repulsion of the UCNPs causes a higher T_c value (Figure 4c). As higher T_c values correspond to larger amounts of LDL patches, as discussed above, we propose that a greater surface charge (or the electrical potential at the slipping plane) increases the proportion of LDL patches in the hydration water of the nanoparticles. This hypothesis agrees with simulations conducted by Gallo’s group, indicating a slower decrease in the rate of LDL domains at the biomolecule interface with an increase in temperature.⁷¹ Moreover, for a constant |ζ| value, nanofluids with smaller UCNPs exhibit a higher T_c, consistent with the findings depicted in Figure 2c. It is noteworthy that the same conclusion can be drawn exclusively from upconversion thermometry and by combining upconversion thermometry with ζ potential measurements. Similar results were reported by Kim et al.,¹⁰⁸ demonstrating how temperature changes the interfacial structure of water by mitigating the effect of surface charge at water–oil interfaces.

Interestingly, Barisik et al.¹¹⁹ showed that, at a constant pH, the surface charge density of Si-NPs decreases with an increase in particle size until it stabilizes after reaching a critical diameter of 100 nm. A similar trend was observed for metal oxide nanoparticles.¹²⁰ These findings align with our T_c size dependence results (Figure 2c), revealing a decrease in T_c with an increase in particle size up to a critical value (>78 nm), beyond which it remains constant.

In summary, our study systematically investigated the impact of temperature and pH on Brownian velocity in a range of UCNPs (15–106 nm diameter) dispersed in water. We consistently observed a decrease in the onset temperature of high- to low-density liquid water fluctuations with an increase in nanoparticle size, indicative of an increased presence of HDL domains at nanoparticle surfaces. UCNPs, therefore, behave as nanorulers for assessing the HDL/LDL proportion in surrounding hydration water. Moreover, the upper-temperature threshold for these fluctuations, as predicted by our experiments, agrees with values proposed in the hypothetical phase diagram of water under ambient conditions based on the two-state model. Additionally, we have shown that increasing the pH decreases T_c and decreasing the T_c decreases the relative amount of LDL patches, akin to external pressure on pure water. By precisely controlling the UCNP size and pH levels, we have simulated the effects of temperature and pressure on HDL and LDL hydrogen bonding networks, mirroring predictions in the hypothesized phase diagram. Within nanofluids, the local environment around nanoparticles exerts a significant influence on their physical–chemical properties, being different from the bulk due to interaction with the particle surface.¹¹¹ This work elegantly underscores the substantial impact of these interactions, serving as compelling evidence of this effect for a specific example of luminescent nanoparticles.

These findings resonate with the intricate interplay between water and various nonpolar media, metals, oxides, and biomembranes, emphasizing the importance of the water charge-asymmetrical molecular configuration at interfaces.^75,108,110 In conclusion, our results provide compelling experimental evidence regarding the significance of the size of suspended nanoparticles or biomolecules in understanding the dynamics of high- to low-density liquid fluctuations and water behavior at charged interfaces.