Refractive-index gas thermometry.

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.

Progress towards the determination of thermodynamic temperature with ultra-low uncertainty.

Previous research effort towards the determination of the Boltzmann constant has significantly improved the supporting theory and the experimental practice of several primary thermometry methods based on the measurement of a thermodynamic property of a macroscopic system at the temperature of the triple point of water. Presently, experiments are under way to demonstrate their accuracy in the determination of the thermodynamic temperature T over an extended range spanning the interval between a few kelvin and the copper freezing point (1358 K). We discuss how these activities will improve the link between thermodynamic temperature and the temperature as measured using the International Temperature Scale of 1990 (ITS-90) and report some preliminary results obtained by dielectric constant gas thermometry and acoustic gas thermometry. We also provide information on the status of other primary methods, such as Doppler broadening thermometry, Johnson noise thermometry and refractive index gas thermometry. Finally, we briefly consider the implications of these advancements for the dissemination of calibrated temperature standards.

Second osmotic virial coefficient from the two-component van der Waals equation of state.

The second osmotic virial coefficient is in principle obtained from the second-order term in the expansion of the osmotic pressure Π or solute activity z(2) in powers of the solute density ρ(2) at fixed solvent activity z(1) and temperature T. It is remarked that the second-order terms in the analogous expansions at fixed pressure p or at liquid-vapor coexistence instead of at fixed z(1) also provide measures of the effective, solvent-mediated solute-solute interactions, but these are different measures. It is shown here how the function z(2)(ρ(2), z(1), T) required to obtain the second osmotic virial coefficient B from an expansion in ρ(2) may be obtained from an equation of state of the form p = p(ρ(1), ρ(2), T) with ρ(1) the solvent density, and also how the analogous coefficient B' in the fixed-p expansion may be so obtained. The magnitude of the difference B - B' is often much smaller than that of B and B' separately, so B' is sometimes an acceptable approximation to B. That is not true of the analogous coefficient in the expansion at liquid-vapor coexistence. These calculations are illustrated with the van der Waals two-component equation of state and applied to solutions of propane in water as an example.

Communication: Length scale dependent oil-water energy fluctuations.

Interfacial fluctuations in the cohesive (van der Waals) interaction energy of spherical oil-drops with water provide evidence of a length scale dependent transition from linear to non-linear response behavior. For sub-nanometer oil-drop sizes, energy fluctuations are found to be independent of the van der Waals coupling strength, while nanometer (and larger) size oil drops experience highly non-linear energy fluctuations. The latter behavior is linked to enhanced hydrophobic density fluctuations and the emergence of entropic contributions to oil-water cohesive interaction free energies.

Are long-chain alkanes hydrophilic?

Although short n-alkane chains are classic examples of hydrophobic solutes, mounting evidence points to a hydrophilic crossover for the hydration free energies (DeltaG) of sufficiently long n-alkane chains. Experimental and simulation results for the hydration of n-alkanes from methane (C1) to docosane (C22) are combined with fundamental thermodynamic relations to elucidate intermolecular contributions to DeltaG. Theoretical bounds on the influence of solute conformation on DeltaG are inferred by considering the hydration of idealized linear (all-trans) and globular (spherical) model solutes. More detailed theoretical extrapolations of experimental and simulation results imply that the water-mediated free energy change associated with collapsing an all-trans C100 chain is on the order of -100 kJ/mol and thus that n-alkane chains of this length and longer may be hydrophilic (DeltaG < 0).

Unraveling water's entropic mysteries: a unified view of nonpolar, polar, and ionic hydration.

[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.