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The experimental evidence for the existence of nanobubbles is summarized. The paradox represented by their stability and the apparent contradiction with the Laplace-Young equation is discussed in detail. A review of surface thermodynamics is given, which shows that nanobubbles are only stable in water super-saturated with air, and also that the surface tension of the water-air interface decreases with increasing super-saturation. Computer simulation evidence for this reduction is reviewed. Experimental measurements showing the reduction in surface tension in the case of nanobubbles are given. The consequences of this novel physical phenomenon are discussed for nanobubbles, as well as more broadly.

The experimental evidence for the existence of nanobubbles is summarized. The paradox represented by their stability and the apparent contradiction with the Laplace-Young equation is discussed in detail. A review of surface thermodynamics is given, which shows that nanobubbles are only stable in water super-saturated with air, and also that the surface tension of the water-air interface decreases with increasing super-saturation. Computer simulation evidence for this reduction is reviewed. Experimental measurements showing the reduction in surface tension in the case of nanobubbles are given. The consequences of this novel physical phenomenon are discussed for nanobubbles, as well as more broadly.

This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is notan extremum. The relationships of the new theory to Onsager’s regression hypothesis, Prigogine’s minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life.

A formally exact Kirkwood–Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood–Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood–Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.

A summary is given of the authors’ recent research on viscoelastic theory and its application to colloid probe atomic force microscopy. A general computational approach for the interaction of viscoelastic colloids interacting with realistic surface forces of extended range is outlined, and the origins of velocity- and time-dependent effects including hysteresis are discussed. A general method for establishing the zero of separation in atomic force microscopy of deformable bodies is described and utilized in force measurements made on viscoelastic poly(dimethylsiloxane) colloid particles. A quantitative analysis of the velocity and load dependence of the hysteresis in the measurements yields the viscoelastic parameters of the colloid.

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.

Charge titration data for silver iodide, titanium dioxide, aluminum oxide, silica dioxide and ferric hydroxide are analyzed using a generic site binding model that has the Nernst equation as a limiting form. Both the hypernetted chain and the nonlinear Poisson–Boltzmann approximations are used to relate the diffuse double-layer potential to the surface charge, and a zeroth-order Stern layer is used to give the surface potential. In all cases it is shown that in the vicinity of the point of zero charge the Nernst equation accurately gives the surface charge.

By making use of the recently derived asymptotic expansion to the Mie forward-scattering amplitude, we are able to employ complex contour-integration techniques to derive three sum rules in the case of a constant real refractive index. The results are in good agreement with numerical calculation. Extension to complex refractive indices may be possible under certain analyticity conditions.

Rigid site-site molecular fluids are analysed, and a formally exact expression for the virial pressure is obtained that involves the triplet site correlation function, which may be evaluated using a superposition approximation. Numerical results for a Lennard-Jones dimer are obtained using the hypernetted chain (HNC) closure with all bridge diagrams with two field points. The bridge diagrams induce the secondary peak in the site-site distribution function that is missing in the HNC. Although the internal energy and the pressure are improved by the inclusion of bridge functions, the latter is most reliably given by the bare HNC and the compressibility route.

The second moment of the Lennard-Jones local field distribution in a hard-sphere fluid is evaluated using the PY3 three-particle distribution function. An approximation due to Lado that avoids the explicit calculation of the latter is shown to be accurate. Partial results are also given for certain cavity-hard-sphere radial distribution functions that occur in a closest particle expansion for the local field.

A surprisingly simple ansatz is given which greatly improves the Kirkwood superposition approximation for the three-particle distribution function when two atoms are in contact with a third. This geometry occurs in a number of theories of the liquid state, and is the one for which the Kirkwood approximation is most inaccuate. Results are given for hard sphere and for Lennard-Jones fluids.

A force-balance simulation method is introduced, where the volume of the cell and the size and shape of inhomogeneities fluctuate in the presence of external potentials. Equilibrium corresponds to the balance of internal and external forces, which allows mechanical quantities such as the pressure and surface tension to be found directly. The technique also enables the geometry to be changed while the confined fluid remains in equilibrium with a bulk reservoir. Here the appropriate ensembles for bulk and inhomogeneous fluids are analysed, including planar, spherical, and cylindrical cavities, cylindrical pores, and interacting planar walls. A method for finding the chemical potential from a fluctuating, partially coupled solvent is discussed. Monte Carlo results are presented for the surface free energy and the adsorption excess of a hard-sphere fluid at a hard wall. It is found that the scaled particle theory remains accurate at quite high densities.

The six-vertex lattice model is augmented with ionic vertices and bonding effects. These represent sources and sinks for hydrogen atoms, and the extra vertices account for the pH of water. This 14-vertex lattice model with Bjerrum bond defects represents a not unrealistic model of ice, and possibly also of structured water next to a surface. Such surfaces polarise the adjacent molecules, which greatly restricts the possible patterns of hydrogen bonds. The polarisation is screened by the defective vertices and bonds, which leads to a strong exponentially decaying repulsion between two similar surfaces. The model is solved in mean field approximation, and the relevance to the experimentally measured hydration forces is discussed.

The asymptotic form of the Mie-scattering amplitude is of interest for a number of reasons, perhaps the most important of which is to reduce significantly the computational effort involved when the size parameter becomes large. Recently, Nussenzveig and Wiscombe [ Phys. Rev. Lett.45, 1490 ( 1980)] published an asymptotic expansion for the Mie extinction efficiency based on complex-angular-momentum theory. In this paper, we show how this result may be generalized to the full forward-scattering amplitude.