[Figure: see text]. Most chemical processes on earth are intimately linked to the unique properties of water, relying on the versatility with which water interacts with molecules of varying sizes and polarities. These interactions determine everything from the structure and activity of proteins and living cells to the geological partitioning of water, oil, and minerals in the Earth's crust. The role of hydrophobic hydration in the formation of biological membranes and in protein folding, as well as the importance of electrostatic interactions in the hydration of polar and ionic species, are all well known. However, the underlying molecular mechanisms of hydration are often not as well understood. This Account summarizes and extends emerging understandings of these mechanisms to reveal a newly unified view of hydration and explain previously mystifying observations. For example, rare gas atoms (e.g., Ar) and alkali-halide ions (e.g., K+ and Cl-) have nearly identical experimental hydration entropies, despite the significant charge-induced reorganization of water molecules. Here, we explain how such previously mysterious observations may be understood as arising from Gibbs inequalities, which impose rigorous energetic upper and lower bounds on both hydration free energies and entropies. These fundamental Gibbs bounds depend only on the average interaction energy of a solute with water, thus providing a deep link between solute-water interaction energies and entropies. One of the surprising consequences of the emerging picture is the understanding that the hydration of an ion produces two large but nearly perfectly cancelling, entropic contributions: a negative ion-water interaction entropy and a positive water reorganization entropy. Recent work has also clarified the relationship between the strong cohesive energy of water and the free energy required to form an empty hole (cavity) in water. Here, we explain how linear response theory (whose roots may also be traced to Gibbs inequalities) can provide remarkably accurate descriptions of the process of filling aqueous cavities with nonpolar, polar, or charged molecules. The hydration of nonpolar molecules is well-described by first-order perturbation theory, which implies that turning on solute-water van der Waals interactions does not induce a significant change in water structure. The larger changes in water structure that are induced by polar and ionic solutes are well-described by second-order perturbation theory, which is equivalent to linear response theory. Comparisons of the free energies of nonpolar and polar or ionic solutes may be used to experimentally determine electrostatic contributions to water reorganization energies and entropies. The success of this approach implies that water's ability to respond to solutes of various polarities is far from saturated, as illustrated by simulations of acetonitrile (CH 3CN) in water, which reveal that even such a strongly dipolar solute only produces subtle changes in the structure of water.

The Comité international des poids et mesures (CIPM) has projected a major revision of the International System of Units (SI) in which all of the base units will be defined by fixing the values of fundamental constants of nature. In preparation for this we have carried out a new, low-uncertainty determination of the Boltzmann constant, k B , in terms of which the SI unit of temperature, the kelvin, can be re-defined. We have evaluated k B from exceptionally accurate measurements of the speed of sound in argon gas which can be related directly to the mean molecular kinetic energy, 3 2 k B T . Our new estimate is k B = 1.380 651 56 (98) × 10 −23 J K −1 with a relative standard uncertainty u R = 0.71 × 10 −6 .

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamondturned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k B , which differ by 0.9 parts in 10 6 , and have an average value of k B = (1.380 649 6 ± 0.000 004 3) × 10 −23 J · K −1 . The relative uncertainty is 3.1 parts in 10 6 , and the average value is 0.58 parts in 10 6 below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.

The perturbing effect of a waveguide on the boundary of a quasispherical cavity resonator is investigated both theoretically and experimentally. Expressions for the frequency perturbation to the triply degenerate TM1mn and TE1mn modes are derived using cavity perturbation theory. The fields in and around the waveguide are calculated in the static limit using finite-element software. Experiments performed using quasispherical and cylindrical cavity resonators confirm the accuracy and generality of the approach. The impact of this study on attempts to re-determine the Boltzmann constant (kB) by an acoustic resonance technique is briefly considered.

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10−6 to 3.5 × 10−5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10−5 and 4.6 × 10−5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10−5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.

We describe the dimensional characterization of copper quasisphere NPL-Cranfield 2. The quasisphere is assembled from two hemispheres such that the internal shape is a triaxial ellipsoid, the major axes of which have nominal radii 62.000 mm, 62.031 mm and 62.062 mm. The artefact has been manufactured using diamond-turning technology and shows a deviation from design form of less than ±1 µm over most of its surface. Our characterization involves both coordinate measuring machine (CMM) experiments and microwave resonance spectroscopy.We have sought to reduce the dimensional uncertainty below the maximum permissible error of the CMM by comparative measurements with silicon and Zerodur spheres of known volume. Using this technique we determined the equivalent radius with an uncertainty of u(k = 1) = 114 nm, a fractional uncertainty of 1.8 parts in 106. Due to anisotropy of the probe response, we could only determine the eccentricities of the quasihemispheres with a fractional uncertainty of approximately 2%.Our microwave characterization uses the TM11 to TM18 resonances. We find the equivalent radius inferred from analysis of these modes to be consistent within ±4 nm with an overall uncertainty u(k = 1) = 11 nm. We discuss corrections for surface conductivity, waveguide perturbations and dielectric surface layers.We find that the CMM radius estimates derived from each hemisphere cannot be used to accurately predict the equivalent radius of the assembled resonator for two reasons. Firstly, the equatorial flanges are flat only to within ±1 µm, leading to an equatorial ‘gap’ whose dimension cannot be reliably estimated. Secondly, the resonator undergoes significant elastic distortion when the bolts connecting the hemispheres are tightened. We provide CMM and microwave measurements to support these conclusions in addition to finite-element modelling.Finally, we consider the implications of this work on a forthcoming experiment to determine the Boltzmann constant with a relative uncertainty below 1 part in 106.

In 2013, a team from NPL, Cranfield University and SUERC published an estimate of the Boltzmann constant based on precision measurements of the speed of sound in argon. A key component of our results was an estimate of the molar mass of the argon gas used in our measurements. To achieve this we made precision comparison measurements of the isotope ratios found in our experimental argon against the ratios of argon isotopes found in atmospheric air. We then used a previous measurement of the atmospheric argon isotope ratios to calibrate the relative sensitivity of the mass spectrometer to different argon isotopes. The previous measurement of the atmospheric argon isotope ratios was carried out at KRISS using a mass spectrometer calibrated using argon samples of known isotopic composition, which had been prepared gravimetrically.We report here a new measurement made at KRISS in October 2014, which directly compared a sample of our experimental gas against the same gravimetrically-prepared argon samples. We consider that this direct comparison has to take precedence over our previous more indirect comparison. This measurement implies a molar mass which is 2.73(60) parts in 10 6 lighter than our 2013 estimate, a shift which is seven times our 2013 estimate of the uncertainty in the molar mass.In this paper we review the procedures used in our 2013 estimate of molar mass; describe the 2014 measurement; highlight some questions raised by the large change in our estimate of molar mass; and describe how we intend to address the inconsistencies between them. We also consider the effect of a new estimate of the low pressure thermal conductivity of argon at 273.16 K. Finally we report our new best estimate of the Boltzmann constant with revised uncertainty, taking account of the new estimates for the molar mass and the thermal conductivity of the argon.

Using exceptionally accurate measurements of the speed of sound in argon, we have made estimates of the difference between thermodynamic temperature, T, and the temperature estimated using the International Temperature Scale of 1990, T90, in the range 118 K to 303 K. Thermodynamic temperature was estimated using the technique of relative primary acoustic thermometry in the NPL-Cranfield combined microwave and acoustic resonator. Our values of (T-T90) agree well with most recent estimates, but because we have taken data at closely spaced temperature intervals, the data reveal previously unseen detail. Most strikingly, we see undulations in (T-T90) below 273.16 K, and the discontinuity in the slope of (T-T90) at 273.16 K appears to have the opposite sign to that previously reported.