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Phil Attard's research has primarily been in the field of classical statistical mechanics. His work encompasses applications and methodology, as well as exploring the foundations of the subject. One on-going theme involves the properties of liquids at the molecular level. which are characterized using various computational and mathematical techniques. This research is complemented by experimental measurements in collaboration with other laboratories. The emphasis of the theory is on the development of new methods for the treatment of more complex systems, and on specific calculations aimed at rationalizing measured data and unexplained phenomena. An example is the focus on inhomogeneous and confined liquids, and on the interactions of colloidal particles and surfaces in such liquids. This has resulted in an increased understanding of fundamental phenomena, and in direct comparison of calculated and measured surface forces. Knowledge of how the cooperative behavior of molecules determines macroscopic processes has been used to unravel a multitude of scientific and industrial problems.
Below may be found a list of specific research topics, a list of reviews, and a description of several broad research areas of current interest.
One major aim is to develop new and more efficient theoretical techniques to obtain the structure and thermodynamic properties of liquids from the interaction potentials of the molecules. Past successes have included integral equation methods, which have been developed for inhomogeneous fluids, three body correlation functions, the electric double layer, and polymer melts. Computer simulation techniques have been formulated for the chemical potential, solvation free energy, the surface tension, and shearing fluids. Asymptotic results have been obtained for the electric double layer and for near-critical and spinodal fluids. Recent work has seen the formulation of a stochastic molecular dynamics simulation algorithm that yields the correct probability distribution for constant temperature systems. This has now been extended to the case of constant chemical potential (grand canonical molecular dynamics), which will find applications in the study of fluids in pores and of phase transitions. Recent work has obtained the surface tension of small droplets or bubbles using a novel simulation algorithm.
The electric double layer, which describes the diffuse layer of counterions in the electrolyte next to a charged surface or about a charged colloid particle, is fundamental to colloid and surface science as it determines the stability of dispersions, the adhesion of particles, and the mobility in applied electric fields. Techniques have been developed to describe accurately the electric double layer taking into account the size of the ions and the correlations between them. Asymptotic analysis has shown how to correct the mean-field Poisson-Boltzmann approximation to include these effects. The results have been applied to charge titration data, electrophoretic mobility measurements, and to surface force measurements. Current work is aimed at obtaining benchmark results for the electric double layer about spherical macroions, including the ion density profiles, the surface charge, and the surface potential.
The fundamental basis of thermodynamics and statistical mechanics has been examined in depth, and this has lead to the development of a unified formulation that is based upon entropy and its maximization at equilibrium. This picture provides physical insight into the thermodynamic free energies and their derivatives, and it also provides a means to derive various approximation schemes in statistical mechanics. Very recently the theory has been extended to non-equilibrium systems. Based upon the new concept of second entropy for transitions, the form for the probability distribution for non-equilibrium systems have been obtained. The first ever non-equilibrium Monte Carlo simulation algorithm and the first non-equilibrium molecular dynamics algorithm have been developed. These have been successfully tested for steady heat flow and for driven Brownian motion.
Experimental and theoretical techniques have been developed to describe the interaction and deformation of bubbles, droplets, and soft colloid particles and films. For soft matter such as these, deformation can cause qualitatively different behaviour to that experienced by rigid particles. For purely elastic particles, a computational algorithm has been developed that self-consistently calculates the interaction force and the deformed particle shape as a function of separation. This algorithm has been generalised to viscoelastic particles, where the velocity and other time-dependence are important. Analytic formulae for the interaction of small particles with gas bubbles and liquid droplets have also been derived. On the experimental front, measurement protocols have been developed that allow the atomic force microscope to be used on soft matter. The interaction and deformation of polydimethylsiloxane droplets, agar gel layers, cellulose particles, and polystyrene films have all been measured. The theories mentioned above have been used to analyse these and other (air bubbles, decane droplets, and cryptospiridian oocytes) data, and quantitative values of various material properties have been extracted, in some case for the first time. Current work seeks to justify fundamentally the core formula for viscoelastic deformation, to optimise the theoretical algorithm for viscoelastic materials, and to obtain an analytic approximation for elastic deformation. The experimental protocol can be used in the atomic force microscope to obtain data for a range of soft materials, which can then be analysed and interpreted using the theory.
We have proposed that nanobubbles exist on hydrophobic surfaces and that their bridging is responsible for the measured long-range attraction and adhesion between such surfaces. Direct force measurements using the atomic force microscope support the idea, and the nanobubbles have also been imaged directly. The current challenge is to explain the thermodynamic stability of nanobubbles. To this end we have recently been exploring homogeneous nucleation theory and the curvature dependence of the surface tension of small vapour bubbles in a supersaturated or superheated liquid. A novel formally exact expression for the surface tension has been derived and tested with computer simulations of the planar liquid-vapour interface, and it remains to extend the study to the curved interface.
To Phil Attard's home page.