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A general theory for the stability and coexistence of nonequilibrium phases is formulated. An integral formulation of the second entropy is given, the functional maximization of which yields nonlinear hydrodynamics. Rayleigh–Bénard convection is analyzed, and analytic approximations are obtained for the second entropy for conduction and for convection. Despite the simplicity of the model, coexistence is predicted for a Rayleigh number within 5% of the known value. [ABSTRACT FROM AUTHOR]

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin’s friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic equations of motion. Setting the variance to zero but keeping the friction coefficient nonzero reduces the theory to a Hoover thermostat without explicit constraint, although such a limit violates the physical requirement of proportionality between the dissipation and the fluctuation. A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle. [ABSTRACT FROM AUTHOR]

A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A fluctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation. [ABSTRACT FROM AUTHOR]

The authors study the transport of mass and heat in simulations of a Lennard-Jones fluid and demonstrate the calculation of transport coefficients, and of both the first and second entropies. These entropies are calculated from time correlation functions, as are the transport coefficients. They discuss the role of the second entropy in providing a physical explanation for the link between dynamic fluctuations and response. They illustrate the physical significance of the various contributions to the second entropy and how they simplify in the case of relaxation by steady-state flow. Certain approximations proposed for the calculation of the first entropy, common in the literature, are shown to break down under certain circumstances, and they give an improved method of calculation. They pay particular attention to the coupling between variables of opposite time parity in the transport matrix, and show that in general this cannot be neglected. [ABSTRACT FROM AUTHOR]

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics. [ABSTRACT FROM AUTHOR]

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard’s expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed. [ABSTRACT FROM AUTHOR]

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics. [ABSTRACT FROM AUTHOR]

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results. [ABSTRACT FROM AUTHOR]

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green–Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green–Kubo expression. An ansatz for the steady-state probability distribution for heat flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is found to be accurate in the high-density regime at not too short times, but not more generally. The probability distribution is implemented in Monte Carlo simulations, and a method for extracting the thermal conductivity is given. [ABSTRACT FROM AUTHOR]

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient. [ABSTRACT FROM AUTHOR]

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes’ law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green–Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics. [ABSTRACT FROM AUTHOR]

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A novel “ghost interface” expression for the surface tension of a planar liquid–vapor interface is derived in detail from consideration of the free energy of the system, and a methodology for utilization of this new technique is given. An augmented Monte Carlo computer simulation procedure is developed specifically for the ghost interface, including derivation of long-range corrections resulting from potential truncation and a modified Gibbs ensemble technique for the simulation of adjacent coexisting phases. Results generated from the ghost interface theory for the surface tension are presented and found to be in good quantitative agreement with those resulting from the Kirkwood–Buff equation. Applications of this new approach to curved and to supersaturated systems are also discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A hybrid molecular dynamics-Monte Carlo grand canonical simulation technique is developed for systems with constant chemical potential and temperature. The method ensures that the particle number and energy fluctuate according to the standard grand canonical probability distribution. Partial coupling and fractional particles are used to enhance the success of insertion and deletion attempts, and the method is shown to be feasible in dense liquids. The method is applied to a Lennard-Jones fluid and it gives the density as a function of chemical potential in agreement with known results. It is demonstrated that the transport coefficients can be obtained with the method by analyzing the influence of the stochastic perturbation on the diffusion constant for an isothermal system. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The thermodynamic potential for fixed charges in dielectric continua is given for arbitrary values of the polarization density. Minimization of the functional gives the equilibrium polarization density (equivalently image charges) and the electrostatic potential throughout the media. The functional, which in general involves volume integrals, for the case of piecewise uniform dielectrica is reduced to surface integrals of the constrained surface charge density at the dielectric discontinuities. A linear integral equation for the induced surface charge, which can be solved by iteration, is given. The conjugate thermodynamic force for the constrained surface charge is also given. The latter formulation is suitable for Car-Parrinello or Lagrangian molecular dynamics in complex geometries. [ABSTRACT FROM AUTHOR]

An approximate semianalytic theory is developed to describe the homogeneous nucleation of droplets from a supersaturated vapor, beginning with a partition function and including rigorously the translation and surface tension contributions. The liquid and vapor phases are treated as uniform (step density profile) and may be described by any accurate equation of state. It is shown that the classical approximation for the free energy of droplet formation may be derived from the present theory by making additional approximations (ideal gas, incompressible liquid), and the two are compared for the case where the vapor phase forms a reservoir (constant supersaturation). In the case of a finite-sized vapor phase, where the supersaturation decreases as the droplet grows, a free energy minimum exists beyond the critical radius, and this stable droplet equilibrium is examined in detail. Comparison with computer simulations proves the quantitative accuracy of the present theory for a Lennard-Jones system. Also derived is a new, formally exact expression for the surface tension that is useful for computer simulations. [ABSTRACT FROM AUTHOR]

A counterion-only double-layer theory is developed taking a constrained entropy maximization approach based on an isothermal thermodynamic system. The double-layer interaction free energy per unit area between two charged planar surfaces is obtained in a consistent manner for the boundary conditions of constant surface charge density and charge regulation. Once applied to the nonpolar medium, it reveals that the electrical double-layer repulsion is weak and long-ranged. Asymptotically, the interaction decays as a power law, in contrast with that in the presence of an ion reservoir which decays exponentially at large surface separation. The applicability of the counterion-only model for describing colloidal stability in nonpolar media is discussed. [ABSTRACT FROM AUTHOR]

A hybrid Monte Carlo molecular dynamics technique is developed that gives equations of motion for an isothermal system. Test results for a Lennard-Jones fluid are shown to be in good agreement with the known equation of state. The physical interpretation of the procedure and the extension to isothermal-isobaric systems is also discussed. [ABSTRACT FROM AUTHOR]

A site–site Born–Green–Yvon (BGY) equation is derived for polymeric fluids. This relates the pair and triplet site distribution functions, and superposition approximations for the latter are analyzed. It is shown that the pair functions to be superposed are uniquely determined by the exact normalization equations and asymptotic conditions. The Kirkwood superposition of pair distribution functions is shown to be valid only for the case of sites on three different polymers; for the cases of two or three sites on the same polymer different pair functions must be superposed. The polymer BGY equation is derived for a soft bonding potential between adjacent sites; the result for infinitely stiff bonds is given as a limiting case. Numerical results are obtained for soft and stiff tangent hard-sphere chains, and comparison is made with simulations for packing fractions up to 0.4 and chains with up to 12 sites. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The wall–wall Ornstein–Zernike equation is formulated for the case of charged walls in a primitive model electrolyte. Numerical results are presented for the modified hypernetted chain (HNC) closure, which includes the effects of ion size and correlations. The bare HNC gives attractions between like-charged surfaces rather too readily, but this is ameliorated by the inclusion of the first bridge diagram. The singlet approach is shown to be accurate in divalent electrolyte, and in the large separation asymptotic regime. The method is less reliable in dilute monovalent electrolyte. [ABSTRACT FROM AUTHOR]

A Lennard-Jones fluid confined between two planar hard walls is simulated using grand canonical Monte Carlo, and capillary evaporation is found for liquid subcritical bulk states. General methods are given for simulating a metastable fluid beyond coexistence. For the systems studied, the liquid and the gas phases coexist in equilibrium at a separation of ∼5 diam, the spinodal cavitation separation is at ∼4 diam, and the spinodal condensation separation is at >=15 diam. The interaction pressure between the walls is found to be attractive and increases rapidly as the spinodal separation is approached. On the equilibrium liquid branch, the net pressure still appears significantly larger than the van der Waals attraction at separations of ∼10 diam. A simple analytic theory is given, which relates the force to the approach of the separation-induced phase transition. It is suggested that this is the microscopic origin of the measured attractions between hydrophobic surfaces in water. [ABSTRACT FROM AUTHOR]

The chemical potential of dense hard-sphere fluids, and also the work of cavity formation, are simulated directly by a force-balance Monte Carlo technique. Here the coupling between a solute and the solvent varies in the presence of an external field. For a hard-sphere fluid the variable is the cavity diameter, and the scaled particle theory proves sufficient for the applied field. The method is shown to be viable for densities as high as the freezing transition. A vectorizable Monte Carlo computer algorithm is also given. [ABSTRACT FROM AUTHOR]

It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out. [ABSTRACT FROM AUTHOR]

Bridge functions and triplet potentials of mean force are calculated for the Lennard-Jones fluid using the binodal chain closure approximation. Inclusion of the former in the hypernetted-chain closure for the pair correlation functions leads to substantially improved values for the virial pressure. The triplet function also appears reliable, being in reasonable agreement with the solution to the spherically inhomogeneous Ornstein–Zernike equation. [ABSTRACT FROM AUTHOR]

The first term in a systematic expansion of the two particle potential of mean force yields the hypernetted chain closure approximation. Here is it shown that the second term (a bridge function) consists of a convolution of two ternary correlation functions, and that these can be related by an integral equation analagous to that of Ornstein and Zernike. An expansion for the three particle potential of mean force which also retains the leading two terms completes a closed set of equations. Also discussed are methods for the numerical resolution of the equations, the asymptotic forms of the triplet total and direct correlation functions, and relations between various quaternary functions. [ABSTRACT FROM AUTHOR]

Potentials of mean force for pairs of charged and neutral macroparticles immersed in simple dipolar hard sphere and waterlike solvents are obtained using the reference hypernetted-chain theory. In general, the results depend rather strongly upon both the solvent and the size of the macroparticles. For smaller neutral macroparticles, the potential of mean force in both solvents is essentially a short-ranged hydrophobic interaction with very little structure. For larger neutral particles in water, short-ranged structural effects likely due to solvent ordering near the flatter surfaces are evident. For charged macroparticles, the potential of mean force is found to be essentially a superposition of three distinct contributions: a short-ranged structural contribution which clearly depends upon the granular nature of the solvent; a repulsive ‘‘cavity’’ term which decays asymptotically as r-4; and of course there is the long-ranged Coulombic interaction. At intermediate separations, this repulsion is the principal correction to Coulomb’s law and it is shown to be much more important in molecular solvents than predicted by comparable dielectric continuum calculations. Furthermore, it is shown that this contribution can be represented with reasonable accuracy by simple analytical approximations. [ABSTRACT FROM AUTHOR]

Methods of calculating the first two terms in the density expansion of the bridge function are given. The closure to the Ornstein–Zernike equation is now exact to two orders in density beyond the hypernetted-chain or Percus–Yevick approximations. The bridge function is resummed as a Padé approximant, and the results for hard spheres are relatively accurate over the whole density regime. The closure is shown to yield physically reasonable results for highly asymmetric mixtures. Infinitely dilute hard sphere solutes with diameters up to 30 times that of the hard-sphere solvent are also considered. The Derjaguin approximation for rescaling the force between spheres to the interaction free energy between planes is examined and found to give the dominant curvature correction. [ABSTRACT FROM AUTHOR]

For fluids in a spherically symmetric external field, it is shown that the Ornstein–Zernike convolution integral becomes a simple algebraic equation upon Legendre transformation. Applying the usual closure relations, the full inhomogeneous pair correlation functions become available. A discrete orthogonal transform pair is also derived, which, in conjunction with the Legendre factorization, makes computations feasable for these generic systems. The general method is here applied to a bulk uniform fluid of hard spheres, using the pair Percus–Yevick closure, but at the triplet level in the hierarchy of distribution functions. Consequently, the pair distribution function and the osmotic coefficient are better than the known analytic results. The method enables the accurate calculation of the triplet correlation function, and several examples are given. [ABSTRACT FROM AUTHOR]

The inhomogeneous Ornstein–Zernike equation and the Triezenberg–Zwanzwig expression for the density profile are solved using the Percus–Yevick closure for the inhomogeneous pair correlations of a hard-sphere fluid in the vicinity of an isolated hard-sphere particle. Results are presented for the solvent density profiles (solute–solvent radial distribution function) around solutes of diameter 0.01–50 times the diameter of the solvent hard spheres. At larger solute diameters, values obtained for the contact density are comparable in accuracy to those given by the scaled-particle theory, and significantly more accurate than those given by the Percus–Yevick analytic results for a bulk asymmetric mixture. A superposition approximation is introduced and this gives the effective solvent-mediated solute-solute interaction. The approximation is expected to be accurate for an asymmetric mixture at low concentrations. Two lower order approximations, the Asakura–Oosawa depletion attraction, and the Derjaguin curvature correction, are tested and found to be qualitatively correct. [ABSTRACT FROM AUTHOR]

An extension of the Poisson–Boltzmann theory of the electric double layer is applied to a symmetric electrolyte between two charged planar surfaces. This analytic treatment includes the effects of images and of ion correlations via the Debye–Hückel closure for the direct correlation function. It is demonstrated that at large separations the corrections to Poisson–Boltzmann theory appear as an effective surface charge. A means of correcting the apparent ion binding inferred from fitting experimental force data is also given. The extended theory shows good agreement with accurate numerical calculations for systems with low coupling. The generalization of the Onsager–Samaras limiting result to higher concentrations and to the case of the surface free energy of a charged dielectric interface is also presented. [ABSTRACT FROM AUTHOR]

The electrostatic fluctuation interactions between two surfaces which carry charged or dipolar, laterally mobile particles, are investigated using both a formally exact theory and approximate methods. Each surface constitutes the boundary between two dielectric continua and has no net charge. The exact analysis demonstrates the interdependence of the van der Waals interaction between the dielectric media and the electrostatic image interactions of the particles. General asymptotic laws for the pressure between the surfaces, valid at large separations, are extracted from the exact equations. Even at relatively small separations, the asymptotic expressions give surprisingly good estimates of the actual interactions, as calculated using the hypernetted chain equation and Monte Carlo techniques. A simple mean field perturbation approximation is also investigated and is shown to give good results, provided accurate pair distributions are known for the corresponding isolated, single surface. [ABSTRACT FROM AUTHOR]

The general solution to the zero size mean spherical model is found for an inhomogeneous electrolyte (with specified profile) between charged planar surfaces. The analysis includes the effects of images and correlations. It provides the primary correction to the classical mean field theory of the double layer and allows the error in that theory to be easily estimated over experimental regimes. The relationship between Lifshitz theory and primitive model theories of electrolytes is made explicit. Results obtained for the one component double layer are accurate for systems with low coupling. [ABSTRACT FROM AUTHOR]

The interaction free energy between two planar bodies interacting across a uniform dielectric, expressed as a sum over allowed electrodynamic modes, is interpreted in terms of reflection coefficients. It is proved that, within the approximations implied by this modal approach, the force between identical bodies interacting across a uniform dielectric is always attractive. Explicit electrostatic results for interacting dipolar surfaces are obtained and these are applicable to the measured long range attractive forces between polar lipid bilayers. [ABSTRACT FROM AUTHOR]

Discusses the use of grand canonical simulations with a fixed number of particles by coupling variations in the system size to the instantaneous chemical potential determined by virtual test particle methods. Testing of methods on Lennard-Jones fluids; Method's advantage for dense fluids; Suitability for confined fluids; Chemical potential of a preferential cell sampling method.

Performs extensive Monte Carlo method simulations of binary hard-sphere mixtures to determine entropic forces. Microsphere background fluid induced by an entropic force; Components of infinite dilution; Overall agreement of hypernetted chain-based theory for the entropic force.

A thermodynamic analysis of the size, shape, and stability of nanobubbles is carried out by modifying classical nucleation theory to include the supersaturation dependence of the surface tension. It is shown that the free energy of a nanobubble is a minimum at the critical radius when the contact line is pinned, that the size of the nanobubble is determined by the decrease in the surface tension caused by the degree of supersaturation, and that together these explain the increased exterior contact angle of a nanobubble compared with the corresponding angle of a macroscopic bubble or droplet on the same surface. [ABSTRACT FROM AUTHOR]

In the past decade, the slip of simple liquids on solidsurfaceshas been demonstrated by many groups. However, the slip of liquidson wettable surfaces is heavily debated. Using colloid probe atomicforce microscopy (AFM), we found the slip length of di-n-octylphthalate in a symmetric wettable system (silica) to bearound 11 nm, which raises the question of what the measured sliplength in an asymmetric hydrophilic–hydrophobic system wouldbe. To answer this question, we investigated liquid slip in one symmetricnonwettable system (hydrophobic DCDMS or OTS) and in one asymmetrichydrophilic (silica)–hydrophobic (DCDMS) system by the samemethod at driving velocities of between 10 and 80 μm/s. Theslip results obtained from the three systems are in agreement witheach other, and this comparison provides a means to self-assess theaccuracy and reproducibility of the measured force curves and thefitted slip length in our systems. Furthermore, this method providesaccess to reliable values of the actual slip length on any investigatedflat surface in an asymmetric system, avoiding the difficulty of preparinga symmetric probe/flat surface system in a colloid probe AFM forcemeasurement. [ABSTRACT FROM AUTHOR]

The photodiode sensitivity in the atomic force microscope is calibrated by relating the voltage noise to the thermal fluctuations of the cantilever angle. The method accounts for the ratio of the thermal fluctuations measured in the fundamental vibration mode to the total, and also for the tilt and extended tip of the cantilever. The method is noncontact and is suitable for soft or deformable surfaces where the constant compliance method cannot be used. For hard surfaces, the method can also be used to calibrate the cantilever spring constant. [ABSTRACT FROM AUTHOR]

A formally exact effective boundary potential is defined that can be combined with hard-wall boundary conditions to allow computer simulations to be performed that mimic an infinite system. The effective potential accounts for the interactions that would be present across the boundary if the system were truly infinite. The exact many-body potential is approximated by one- and two-body potentials. The algorithm is implemented and tested for a Lennard–Jones fluid. The advantages of the present formulation over the widely used periodic boundary conditions are discussed. [ABSTRACT FROM AUTHOR]

The evidence for nanobubbles as the origin of the long-ranged attractions measured between hydrophobic surfaces immersed in water is reviewed by focusing upon several unique features of the force curves. Also covered is the morphology of nanobubbles as revealed by direct imaging with tapping mode atomic force microscopy. A discussion of the origin, thermodynamic stability and practical implications of nanobubbles is given. [Copyright &y& Elsevier]

The capacitance of two parallel disks of finite unequal size is calculated by a variational procedure based on the electrostatic energy. It is found that effects due to the edges and the asymmetry can be substantial unless the radii of the disks are very much greater than the thickness of the dielectric interlayer. The trends predicted by the calculations are confirmed by measurements of the capacitance of electrodes deposited on polymer films and of water droplets. The implications for the electrical measurement of the contact angle or contact area of a droplet, and for the dependence of the contact angle on the applied potential in electrowetting, are discussed. [ABSTRACT FROM AUTHOR]

Nanobubbles, whose existence on hydrophobic surfaces immersed in water has previously been inferred from measurements of long-ranged attractions between such surfaces, are directly imaged by tapping mode atomic force microscopy. It is found that the nanobubbles cover the surfaces in an irregular, interconnected or close-packed network whose morphology is dependent on pH and whose lifetimes are at least of the order of hours. Their height is of the order of 30 nm and their radius of curvature is of the order of 100–300 nm. It appears that the nanobubbles form from a solution supersaturated with air. A thermodynamic and statistical mechanical analysis of the homogeneous nucleation of liquid droplets from a supersaturated vapour shows that although a single droplet can be in equilibrium with a finite volume of gas, for a gas reservoir the equilibrium state is represented by a single macroscopic droplet, which grows by collisions and by Ostwald ripening. It is concluded that the electric double-layer repulsion between neighbouring nanobubbles on the hydrophobic surface plays a role in their stabilisation. [Copyright &y& Elsevier]

A summary is given of the author's recent experimental and theoretical work involving the atomic force microscope, with the focus being upon dynamic measurements. Four topics are covered: calibration techniques for the friction force microscope, quantitative measurements of friction and the effect of adhesion, measurement and theory for the deformation and adhesion of viscoelastic particles, and the interaction and adhesion of hydrophobic surfaces due to bridging nanobubbles. [ABSTRACT FROM AUTHOR]

Part I. Measures the dynamic surface force using the van der Waals collisions. Effect of cantilever deflection on speed and magnitude of surface force; Details on the collision-induced elastic vibrations in the solids; Factors attributing the surface separation at high accelerations.

A generalized Markov superposition approximation is used for the higher order correlation functions in a systematic expansion for the entropy. The results are applicable to certain onedimensional problems, such as the information content of time series or signals, or possibly also to polymer adsorption at a wall. The case of digitization of the signal into many levels is treated in detail, and the dependence of the information content on sampling and digitization is analysed. [ABSTRACT FROM AUTHOR]

The exclusion of solvent from solute clusters provides an additional contribution to aggregation. A derivation of the well known equations for equilibrium aggregation is given, and an explicit expression for the solvent-exclusion effect is obtained for linear aggregates. The analytical result is shown to be in qualitative agreement with recent Monte Carlo simulations of model discotic solutions, which found a concentration dependence of the equilibrium constant. The latter behaviour is argued to stem from a peculiarity in the simulation protocol, namely that the total pressure was fixed, which means that the solvent pressure must increase due to the decreased osmotic pressure at lower solute concentrations. Finite size effects are shown to have a small effect in the simulations. Two further contributions to the observed increased aggregation at low temperatures and concentrations are analysed. For intracolumn aggregation it is argued that it is more appropriate to use the length of the column rather than the volume of the system in the definition of the aggregation constant. The possibility is raised that the increased aggregation seen at low solute concentrations could manifest a type of phase transition, either to one-dimensional columns, driven by feedback between the solvent pressure and the number of aggregates, or to a solvent-depleted globule. [ABSTRACT FROM AUTHOR]

The conventional implementation of the isobaric (fluctuating volume) ensemble neglects the density of volume states. Here it is shown that the latter is proportional to the inverse of the volume. It is argued that this expression should always be used, and that it has measurable consequences in simulations of small systems, in simulations that seek an accurate equation of state, and in simulations of the critical, spinodal, and coexistence regions. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A simple derivation of an expression for the chemical potential involving higher order direct correlation functions is given, and the Percus–Yevick approximation is extracted. [ABSTRACT FROM AUTHOR]

It is shown that the interaction of a particle with a liquid drop or a gas bubble may be quantitatively described over the whole distance regime by treating the fluid interface as a Hookean spring. An algorithm suitable for analyzing atomic force microscopy data suitable for a calculator or a spread-sheet is given and applied to data for oil drops. [Copyright &y& Elsevier]

A correction to the article "Variational formulation for the electrostatic potential in dielectric continua," which appeared in the previous issue is presented.