The speed of sound and derived thermodynamic properties of pure water at temperatures between (253 and 473) K and at pressures up to 400 MPa

Analytic Correlation for the Thermodynamic Properties of Water at Low Temperatures (200-300 K) and High Pressures (0.1-400 MPa)

Water is vital to all facets of life and is anomalously behaving in its condensed states, making it continually a substance of interest to researchers. Therefore, attempting to capture its properties via correlations and equations of state is extremely valuable. Liquid water has not been studied as extensively in the low-temperature and high-pressure region as in other regions. Some key applications for correlations in this region are cryopreservation (specifically in certain methods of cryopreservation such as hyperbaric (high-pressure) and isochoric (constant-volume) cryopreservation), deep oceans, hydrospheres, clouds, and precipitation. Although there are not nearly as many models for water at low temperatures and high pressures as there are in other temperature and pressure ranges, there are some models that do currently exist. However, these either do not extend to temperatures and pressures as extreme as the data that exist, or they are complex with large numbers of parameters making them more difficult for application. Herein, we present a new correlation for liquid water valid for the temperature range of 200-300 K (-73-27 °C) and pressure range of 0.1-400 MPa that can analytically calculate volume, isothermal compressibility, isobaric expansivity, constant pressure heat capacity, and speed of sound, using only 17 adjustable parameters. The analytical expressions that we derived, and the fitting method that we used can also be applied to other fluids of interest in the future.

Phase behavior of metastable water from large-scale simulations of a quantitatively accurate model near ambient conditions: The liquid-liquid critical point

The molecular mechanisms of water's unique anomalies are still debated upon. Experimental challenges have led to simulations suggesting a liquid-liquid (LL) phase transition, culminating in the supercooled region's LL critical point (LLCP). Computational expense, small system sizes, and the reliability of water models often limit these simulations. We adopt the CVF model, which is reliable, transferable, scalable, and efficient across a wide range of temperatures and pressures around ambient conditions. By leveraging the timescale separation between fast hydrogen bonds and slow molecular coordinates, the model allows a thorough exploration of the metastable phase diagram of liquid water. Using advanced numerical techniques to bypass dynamical slowing down, we perform finite-size scaling on larger systems than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, demonstrating the existence of the LLCP in the 3D Ising universality class in the low-temperature, low-pressure side of the line of temperatures of maximum density, specifically at TC = 186 ± 4 K and PC = 174 ± 14 MPa, at the end of a liquid-liquid phase separation stretching up to ∼200 MPa. These predictions align with recent experimental data and sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. We also observe substantial cooperative fluctuations in the hydrogen bond network at scales larger than 10 nm, even at temperatures relevant to biopreservation. These findings have significant implications for nanotechnology and biophysics, providing new insights into water's behavior under varied conditions.

Isotope effects in supercooled H2O and D2O and a corresponding-states-like rescaling of the temperature and pressure

Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H2O and D2O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations-with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a "corresponding-states-like" rescaling for water properties in three classical water models that all exhibit a liquid-liquid transition and critical point [Uralcan et al., J. Chem. Phys. 150, 064503 (2019)], the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H2O and D2O is investigated here. Utilizing previously published data and equations-of-state for H2O and D2O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid-liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water's anomalies.

Speed of Sound Measurements in Helium at Pressures from 15 to 100 MPa and Temperatures from 273 to 373 K

The speed of sound in helium was measured along five isotherms in a temperature range from 273 to 373 K at pressures from 15 to 100 MPa with a relative expanded uncertainty (k = 2) from 0.02 to 0.04%. A dual-path pulse-echo system was utilized to conduct these measurements. The data were compared with the reference equation of state developed by Ortiz Vega et al. At pressures up to 50 MPa, relative deviations were within the uncertainty of our measurements, while, at higher pressures, increasing negative deviations were observed up to -0.26%. We also compared the results with predictions based on the virial equation of state correct to the seventh virial coefficient, using the ab initio virial coefficients reported recently by Gokul et al., finding agreement to within the experimental uncertainty at all investigated states.

Absorption of pressurized methane in normal and supercooled p-xylene revealed via high-resolution neutron imaging

Supercooling of liquids leads to peculiarities which are scarcely studied under high-pressure conditions. Here, we report the surface tension, solubility, diffusivity, and partial molar volume for normal and supercooled liquid solutions of methane with p-xylene. Liquid bodies of perdeuterated p-xylene (p-C₈D₁₀), and, for comparison, o-xylene (o-C₈D₁₀), were exposed to pressurized methane (CH₄, up to 101 bar) at temperatures ranging 7.0-30.0 °C and observed at high spatial resolution (pixel size 20.3 μm) using a non-tactile neutron imaging method. Supercooling led to the increase of diffusivity and partial molar volume of methane. Solubility and surface tension were insensitive to supercooling, the latter substantially depended on methane pressure. Overall, neutron imaging enabled to reveal and quantify multiple phenomena occurring in supercooled liquid p-xylene solutions of methane under pressures relevant to the freeze-out in the production of liquefied natural gas.

Synchronization of RF Data in Ultrasound Open Platforms (UOPs) for High-Accuracy and High-Resolution Photoacoustic Tomography Using the "Scissors" Programming Method

Synchronization is important for photoacoustic (PA) tomography, but some fixed delays between the data acquisition (DAQ) and the light pulse are a common problem degrading imaging quality. Here, we present a simple yet versatile method named "Scissors" to help synchronize ultrasound open platforms (UOPs) for PA imaging. Scissors is a programed function that can cut or add a fixed delay to radio frequency (RF) data and, thus, synchronize it before reconstruction. Scissors applies the programmable metric of UOPs and has several advantages. It is compatible with many setups regardless of the synchronization methods, light sources, transducers, and delays. The synchronization is adjustable in steps reciprocal to the UOPs' sampling rate (20-ns step with a 50-MHz sampling rate). Scissors works in real-time PA imaging, and no extra hardware is needed. We programed Scissors in Vantage UOP (Verasonics, Inc., Kirkland, WA, USA) and then imaged two 30- [Formula: see text] nichrome wires with a 20.2-MHz central frequency transducer. The PA image was severely distorted by an 828-ns delay; over 90% delay was caused by our Q -switch laser. The axial and lateral resolutions are 112 and [Formula: see text], respectively, after using Scissors. We imaged a human finger in vivo, and the imaging quality is tremendously improved after solving the 828-ns delay by using Scissors.

Dual-capillary dilatometer for density measurements of supercooled water

An apparatus tailored to accurate density measurements of supercooled water, i.e. liquid water in a metastable state below the freezing point temperature, was recently developed at the Institute of Thermomechanics of the Czech Academy of Sciences. The apparatus, dual-capillary dilatometer, is described, together with the measurement procedure and the evaluation methodology. The primary result of the dual-capillary method are relative densities with respect to the density at a reference temperature and given pressure. In order to calculate absolute densities, densities at the reference temperature as a function of pressure are needed. For calculation of such pressure dependence of density, so called thermodynamic integration involving literature thermodynamic data and our experimental results is used. The dual-capillary dilatometer was successfully employed in density measurements of ordinary water, heavy water and seawater. The data in the temperature range from 238.15 to 303.15 K at pressures from atmospheric up to 200 MPa are presented and compared with respective IAPWS formulations of thermodynamic properties. The data for ordinary water are also compared with an accurate equation of state for supercooled water of Holten et al. (2014) revealing good mutual agreement. The expanded uncertainty of relative densities acquired by means of the dual-capillary method is estimated to be lower than 50 ppm.

Speed of Sound Measurements of Binary Mixtures of 1,1,1,2-Tetrafluoroethane (R-134a), 2,3,3,3-Tetrafluoropropene (R-1234yf), and trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E)) Refrigerants

Speed of sound data measured using a dual-path pulse-echo instrument are reported for binary mixtures of 1,1,1,2-tetrafluoroethane (R-134a), 2,3,3,3-tetrafluoropropene (R-1234yf), and trans-1,3,3,3-tetrafluoropropene (R-1234ze(E)). For each binary mixture, the speed of sound is studied at two compositions of approximately (0.33/0.67) and (0.67/0.33) mole fraction. The conditions covered in this study range in temperature from 230 to 345 K and from pressures slightly above the bubble curve up to a maximum pressure of 51 MPa. However, to avoid potential polymerization reactions, data for mixtures containing R-1234yf are limited to a maximum pressure of 12 MPa at temperatures below 295 K and 8 MPa at temperatures above 295 K. The mean uncertainty of the measured speed of sound is less than 0.1%, where relative combined expanded uncertainties at individual state points range from 0.04 to 0.4% of the measured speed of sound value. The greatest combined expanded uncertainties are encountered as the state point approaches the mixture critical region where weakened echo signals and lower speed of sound values are observed. The reported data are compared to available REFPROP mixture models, which are not adjusted using the data reported here, with average absolute deviations ranging from 0.27 to 0.75% with maximum deviations as high as 1.1%. The comparisons to the REFPROP correlations show that further adjustments to the mixture models are needed to provide a representation of the data within its experimental uncertainty.

Bubble Point Measurements of Mixtures of HFO and HFC Refrigerants

Bubble point pressures of six binary mixtures at two compositions each have been measured utilizing a static method. The performance of the apparatus was characterized from bubble point measurements of R32 + R125 for which 19 literature studies are available for comparison. The mixtures studied were as follow: R1234yf + R134a, R134a + R1234ze (E), R1234yf + R1234ze (E), R125 + R1234yf, R1234ze (E) + R227ea and R1234yf + R152a. For each mixture measurements were conducted from 270 K to 360 K or to within approximately 10 K of the critical temperature of the pure component with the lower critical temperature. A total of 196 bubble point pressures are reported with combined expanded uncertainties (k = 2) ranging from 0.1% - 0.6%. The measured data are graphically compared to available literature data.

Water above the spinodal

The liquid spinodal has long been discussed alongside the elusive liquid-liquid critical point hidden behind the limit of homogeneous nucleation. This has inspired numerous scenarios that attempt to explain water anomalies. Despite recent breakthrough experiments doubting several of those scenarios, we lacked a tool to localize the spinodal and the liquid-liquid critical point. We constructed a unique equation of state combining Speedy's well known expansion and the liquid-liquid critical point to remove that deficit and to review these explanations. For the first time, the proposed equation of state independently depicts the spinodal in the presence of the liquid-liquid critical point and demonstrates that the explanation for water anomalies based on the reentrance of the spinodal is not valid; this feature (reentrance of the spinodal) was predicted because the density surface is curved by the presence of the second critical point. However, the critical point alone is not sufficient to explain the shape of the density surface of water. In the new equation, hydrogen bond cooperativity is important to force the critical point to exist outside of zero temperature. Together with the recent discovery of a compressibility maximum behind the homogeneous nucleation limit at positive pressure, the findings argue in favor of excluding all explanations for water anomalies except for the existence of the liquid-liquid critical point at positive pressure. Finally, an extensive study of heat capacity demonstrated profound disagreement between the two major experimental heat capacity datasets and identified the more accurate dataset.

Thermodynamics of supercooled and stretched water: Unifying two-structure description and liquid-vapor spinodal

We have applied a two-structure approach to the description of the thermodynamic properties of supercooled and stretched water, metastable toward vapor, ice, or both, by incorporating the stability limit of liquid with respect to vapor at negative pressures. In addition to the properties of water considered in previous studies, we include new data recently obtained in deeply supercooled and stretched regions. Our model reproduces the experimentally observed anomalies in metastable water up to 400 MPa and down to -140 MPa, and can provide a physically based extrapolation in regions where no measurements are available yet. Moreover, we are able to elucidate the thermodynamic nature of the alternative "states" of liquid water, namely, high-temperature denser water (state A) and "mother-of-ice" lighter water (state B). Based on the internal consistency of the described anomalies and new data on the isothermal compressibility, we exclude the critical-point-free scenario in which the first-order liquid-liquid transition line would continue into the stretched liquid state (doubly metastable) crossing the vapor-liquid spinodal. A "singularity-free" scenario remains an option for explaining supercooled water's anomalies within the framework of two-state thermodynamics; however, the extreme case of the singularity-free scenario, ideal mixing of A and B, seems improbable. We have also clarified the concept of fast interconversion of alternative states in supercooled water as a phenomenological representation of distribution of short-ranged local structures.

Direct measurement of the sound velocity in seawater based on the pulsed acousto-optic effect between the frequency comb and the ultrasonic pulse

We present a new method to measure the velocity of sound in pure water and seawater using the Raman-Nath diffraction caused by acousto-optic effect between the optical frequency comb and the ultrasonic pulse. In the Mach-Zehnder interferometry system we established, the measurement and reference arms are tagged with sharp negative pulses caused by the pulsed ultrasound passing through them. The difference in optical path between the two parallel beams is twice the flight distance of the ultrasonic waves. The span between the two negative pulses reflects the time interval. At the same time, the distance between the two arms can be measured precisely using the femtosecond laser interferometry. Consequently, the time interval and the distance can be used to measure the sound velocity. The experimental results show that, the uncertainty of the sound speed measurement can achieve 0.03m/s@1482m/s in pure water and 0.029m/s@1527m/s in seawater, respectively, compared with the commercial sound velocity profiler (SVP). More importantly, benefiting from the faster and cleaner response of the acousto-optic effect than the piezoelectric effect which is widely adopted in direct sound velocity measurement method, our method provides a new idea for the metrology of sound velocity in seawater.

Activity of Supercooled Water on the Ice Curve and Other Thermodynamic Properties of Liquid Water up to the Boiling Point at Standard Pressure

A simple model for thermodynamic properties of water from subzero temperatures up to 373 K was derived at ambient pressure. The heat capacity of supercooled water was assessed as lambda transition. The obtained properties for supercooled water such as heat capacity, vapor pressure, density and thermal expansion are in excellent agreement with literature data. Activity of water on ice curve, independent of used electrolyte and Debye-Hückel constant applied in modeling, is also calculated. Thus, the ice curve activity of supercooled water can be used as a universal basis for thermodynamic modeling of aqueous solutions, precipitating hydrated and anhydrous solids. A simple model for heat capacity, density and thermal expansion of ice are also derived from 170 K up to melting point.

Amplification of pressure waves in laser-assisted endodontics with synchronized delivery of Er:YAG laser pulses

When attempting to clean surfaces of dental root canals with laser-induced cavitation bubbles, the resulting cavitation oscillations are significantly prolonged due to friction on the cavity walls and other factors. Consequently, the collapses are less intense and the shock waves that are usually emitted following a bubble’s collapse are diminished or not present at all. A new technique of synchronized laser-pulse delivery intended to enhance the emission of shock waves from collapsed bubbles in fluid-filled endodontic canals is reported. A laser beam deflection probe, a high-speed camera, and shadow photography were used to characterize the induced photoacoustic phenomena during synchronized delivery of Er:YAG laser pulses in a confined volume of water. A shock wave enhancing technique was employed which consists of delivering a second laser pulse at a delay with regard to the first cavitation bubble-forming laser pulse. Influence of the delay between the first and second laser pulses on the generation of pressure and shock waves during the first bubble’s collapse was measured for different laser pulse energies and cavity volumes. Results show that the optimal delay between the two laser pulses is strongly correlated with the cavitation bubble’s oscillation period. Under optimal synchronization conditions, the growth of the second cavitation bubble was observed to accelerate the collapse of the first cavitation bubble, leading to a violent collapse, during which shock waves are emitted. Additionally, shock waves created by the accelerated collapse of the primary cavitation bubble and as well of the accompanying smaller secondary bubbles near the cavity walls were observed. The reported phenomena may have applications in improved laser cleaning of surfaces during laser-assisted dental root canal treatments.

An absolute instrument for determination of the speed of sound in water

An apparatus for the absolute determination of the sound speed in water based on the time-of-flight technique is described. The time measurement is realized by hardware circuits and the distance measurement by a double-beam plane-mirror interferometer. A highly accurate time chip, with a resolution of approximately 90 ps, is employed for time measurements. The acoustic path length is adjustable and can be measured directly. Two transducers are used for transmitting and receiving ultrasonic signals without reflection. The transducers are immersed in a thermostatic vessel that maintains bath temperature with high stability. The speed of sound in pure water was measured at ambient pressure and at the temperatures 308 K, 303 K, 298 K, and 293 K. The achieved measurement uncertainties are 2 mK for temperature and 0.045 m/s for speed of sound. The results are compared to data from the literature, equation of state models, and measurements by two commercial sensors in the same experiment, showing excellent agreement among them.

Capability of pure water calibrated time-of-flight sensors for the determination of speed of sound in seawater

Results from a laboratory investigation of commercial time-of-flight sensors designed for oceanographic in situ speed-of-sound measurements are presented. An older analog model and three modern digital units were calibrated in pure water in the temperature range of 1 °C to 50 °C. The speed of sound (w) was measured in salt solutions of varying concentration (NaCl, MgCl2, Na2SO4) and in samples of original and diluted North Atlantic seawater at atmospheric pressure. A high reproducibility of the time-of-flight readings was found, resulting in sound speed standard deviations in pure water between 0.033 m s(-1) and 0.015 m s(-1), depending on the individual instruments. This depicts the potential of the time-of-flight method. However, although simultaneously calibrated, the measurements revealed systematic speed-of-sound differences between the different sensors which exceeded the reproducibility by about 1 order of magnitude. As the cause of these deviations could not be determined within this study, this exhibits a constraint for the uncertainty of measurements in seawater relative to pure water. In comparison with recent equations this has been estimated at 0.3 m s(-1) (200 ppm) in original seawater. In seawater at temperatures >40 °C and in diluted seawater the results indicate relevant differences from the recent Thermodynamic Equation of Seawater-2010 equation of state.

Burst design and signal processing for the speed of sound measurement of fluids with the pulse-echo technique

The pulse-echo technique determines the propagation time of acoustic wave bursts in a fluid over a known propagation distance. It is limited by the signal quality of the received echoes of the acoustic wave bursts, which degrades with decreasing density of the fluid due to acoustic impedance and attenuation effects. Signal sampling is significantly improved in this work by burst design and signal processing such that a wider range of thermodynamic states can be investigated. Applying a Fourier transformation based digital filter on acoustic wave signals increases their signal-to-noise ratio and enhances their time and amplitude resolutions, improving the overall measurement accuracy. In addition, burst design leads to technical advantages for determining the propagation time due to the associated conditioning of the echo. It is shown that the according operation procedure enlarges the measuring range of the pulse-echo technique for supercritical argon and nitrogen at 300 K down to 5 MPa, where it was limited to around 20 MPa before.

The thermodynamical response functions and the origin of the anomalous behavior of liquid water

The density maximum of water dominates the thermodynamics of the system under ambient conditions, is strongly P-dependent, and disappears at a crossover pressure P(cross) approximately 1.8 kbar. We study this variable across a wide area of the T-P phase diagram. We consider old and new data of both the isothermal compressibility K(T)(T, P), the pressure constant specific heat C(P)(T) and the coefficient of thermal expansion alpha(P) (T, P). We observe that K(T)(T) shows a minimum at T* approximately 315 +/- 5 K for all of the studied pressures, whereas, at the same temperature, C(P)(T) has the minimal variation as a function of P in the interval 1 bar-4 kbar. We find the behavior of alpha(P) also to be surprising: all the alpha(P)(T) curves measured at different P cross at T*. The experimental data show a "singular and universal expansivity point" at T* approximately 315 K and alpha(P)(T*) = 0.44 10(-3) K(-1). Unlike other water singularities, we find this temperature to be thermodynamically consistent in the relationship connecting the three response functions. By considering also the P-T behavior of the self-diffusion coefficient D(S) and of the NMR proton chemical shift delta we have the information that at T* the water local order points out, with decreasing T, the crossover from a normal fluid to the anomalous and complex liquid characterized by the many anomalies.

Apparatus for the measurement of the speed of sound of ammonia up to high temperatures and pressures

An apparatus for the measurement of the speed of sound based on the pulse-echo technique is presented. It operates up to a temperature of 480 K and a pressure of 125 MPa. After referencing and validating the apparatus with water, it is applied to liquid ammonia between 230 and 410 K up to a pressure of 124 MPa. Speed of sound data are presented with an uncertainty between 0.02% and 0.1%.

Convergence and low temperature adaptability analysis of the high temperature series expansion of the free energy

By appealing to the coupling parameter series expansion to calculate the first seven perturbation coefficients of the high temperature series expansion (HTSE) of the free energy, analysis of convergence and low temperature adaptability of the HTSE in calculating fluid thermodynamic properties is performed for the first time; the fluid thermodynamic properties considered include critical parameters, vapor-liquid coexistence curve, thermodynamic characteristic functions, chemical potential, pressure, and constant volume excess heat capacity. To proceed with the analysis, a well known square well model is used as sample; the well widths considered range over a wide interval, and the relevant temperatures amenable to simulation calculations (used as "exact" results to analyze the HTSE) can be both very high and very low. The main discoveries reached are summarized as follows: (1) The HTSE usually converges at the 4th-order truncation, but with decrease of the temperature considered, the lowest truncation order, which makes the HTSE to converge, tends to rise. As a conservative estimate, it is considered that the HTSE always converges for reduced temperature T* higher than 0.25, whereas for T* < 0.25 there appear signs indicating that the HTSE may diverge from the 7th-order truncation. (2) Within the temperature interval with T* ≥ 0.5, the HTSE converges approximately to the correct solution, and the HTSE can be reliably used to calculate the fluid thermodynamic properties, and within this temperature interval, the 4th-order truncation is enough; whereas for T* < 0.5, such as within the temperature interval with 0.275 ≤ T* ≤ 0.355, although the HTSE does converge, it does not converge to the correct solution, and the deviations between the HTSE calculations and MC simulations become an ever-prominent issue with the rising of the density, and the slopes of the thermodynamic properties over density are not satisfactorily represented. As a result, the HTSE is not suited for calculations for temperature interval T* < 0.5.

Volumes of aqueous hydrogen and hydroxide ions at 0 to 200 °C

The electrostriction of aqueous hydrogen and hydroxide ions at infinite dilution was calculated by the shell-by-shell method over the temperature range 0 to 200 °C. The calculation required an estimate of the ionic radius of these ions, and comparison with data for aqueous lithium, sodium, and fluoride ions provided values for the nominal sizes of the hydrogen and hydroxide ions in solution. From the volumetric standpoint, these sizes are surprisingly smaller than the size of a water molecule.