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.
- Statistical Mechanics
- Computer Simulations
(Monte Carlo techniques, sampling schemes, free energy methods,
stochastic molecular dynamics)
- Integral Equations
(inhomogeneous, singlet, triplet correlations,
bridge functions, three body potentials,
(electrolytes and the electric double layer, droplet nucleation,
phase transitions, genomics and proteomics)
probability, the arrow of time)
(steady state flows, second entropy, probability density, transition probability)
- Surface Forces
- Measurement Techniques
(deformable substrates, dynamic force measurement, friction)
- Electric Double Layer
- Electrostatic Correlations
(ionic, dipolar, van der Waals)
- Hydration Forces
- Hydrophobic Attraction, Nanobubbles
- Entropic and Structural Forces
(oscillatory, packing, depletion)
- Colloid Science
'Electrolytes and the Electric Double Layer',
Adv. Chem. Phys. 92, 1-159 (1996).
pdf (792kB, 88 pages).
© Academic Press 1996.]
`Recent Advances in the Electric Double Layer in Colloid Science',
Current Opinion in Colloid and Interface Science,
6, 366-371 (2001)
© Elsevier 2001.]
P. Attard and G. Gillies,
``Deformation and Adhesion of Viscoelastic Particles:
Theory and Atomic Force Microscopy'',
Aust. J. Chem. 54, 477-485 (2001)
© CSIRO 2001.]
``Friction, Adhesion, and Deformation:
Dynamic Measurements with the Atomic Force Microscope'',
J. Adhesion Sci. Technol. 16, 753-791 (2002)
pdf (1.3MB, 19pages).
© VSP 2002.]
``Nanobubbles and the Hydrophobic Attraction'',
Adv. Colloid Interface Sci. 104, 75-91 (2003)
© Elsevier 2003.]
``Theory for Non-equilibrium Statistical Mechanics'',
Phys. Chem. Chem. Phys. 8, 3585-3611 (2006)
© The Owner Societies 2006.]
``Measurement and Interpretation of Elastic and Viscoelastic Properties
with the Atomic Force Microscope'',
J. Phys.: Condens. Matter 19, 473201 (2007)
© Institute of Physics 2007.]
``The Second Law of Non-equilibrium Thermodynamics:
How Fast Time Flies'',
Adv. Chem. Phys. 140, 1-87 (2008)
© John Wiley & Sons 2008.]
``The Second Entropy: A General Theory for Non-equilibrium
Thermodynamics and Statistical Mechanics'',
Annu. Rep. Prog. Chem., Sect. C 105, 63-173 (2009)
© The Royal Society of Chemistry 2009.]
From Molecular Interactions to Macroscopic Properties
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.
- P. Attard,
Spherically Inhomogeneous Fluids.
I. Percus-Yevick Hard-Spheres:
Osmotic Coefficients and Triplet Correlations,
J. Chem. Phys. 91, 3072-3082 (1989).
First algorithm and solution of the spherical Ornstein-Zernike equation,
with accurate results for the hard-sphere triplet correlation function.
Extended to spherical solutes, the algorithm was used to obtain the first molecular-level results for the depletion force.
P. Attard, D. R. Berard, C. P. Ursenbach, and G. N. Patey,
The Interaction Free Energy between Planar Walls in Dense Fluids.
An Ornstein-Zernike Approach with Results for Hard-Sphere,
Lennard-Jones, and Dipolar Systems,
Phys. Rev. A 44, 8224-8234 (1991).
The original derivation of the wall-wall Ornstein-Zernike equation,
and also of the Derjaguin approximation in statistical mechanics.
- P. Attard,
Polymer Born-Green-Yvon Equation
with Proper Triplet Superposition Approximation.
Results for Hard-Sphere Chains,
J. Chem. Phys. 102, 5411-5426 (1995).
Gives the correct superposition approximation
for the polymer BGY equation and obtains the first self-consistent
results for the inter- and intra-site pair correlation functions.
- P. Attard,
Stochastic Molecular Dynamics: A Combined Monte Carlo
and Molecular Dynamics Technique for Isothermal Simulations,
J. Chem. Phys. 116, 9616-9619 (2002).
Yields the canonical probability distribution in a constant
temperature molecular dynamics simulation.
Electric Double Layer
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.
Asymptotic Analysis of Primitive Model Electrolytes
and the Electrical Double Layer,
Phys. Rev. E 48, 3604-3621 (1993).
Exact asymptote for Coulomb systems, with direct correlation
function expressions for the effective charge and decay length.
W. Briscoe and P. Attard,
Counterion-only Electric Double Layer: A Constrained Entropy Approach,
J. Chem. Phys. 117, 5452-5464 (2002).
Poisson-Boltzmann analysis of pressure and interaction free energy of counter-ions only double layer using constrained entropy approach.
Foundations of Statistical Mechanics
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.
The Explicit Density Functional and its Connection with
J. Stat. Phys. 100, 445-473 (2000).
Contains a generalization of Boltzmann's entropy
to unequal microstates,
and a physical interpretation of thermodynamics and statistical
mechanics that is based upon entropy.
The Second Entropy: A General Theory for Non-equilibrium
Thermodynamics and Statistical Mechanics ,
Annu. Rep. Prog. Chem., Sect. C 105, 63--173 (2009)
Generalizes the Boltzmann distribution to non-equilibrium systems.
Presents the first Monte Carlo results
and the first stochastic molecular dynamics results for a non-equilibrium system.
P. Attard, Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation, (448 pages, Academic Press, London, 2002).
Comprehensive coverage of modern techniques of statistical mechanics
presented from the viewpoint of constrained entropy.
Characterisation of Soft Matter
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.
P. Attard and J. L. Parker,
Deformation and Adhesion of Elastic Bodies in Contact,
Phys. Rev. A 46, 7959-7971 (1992).
Numerical and analytic results for the mutual elastic deformation
of soft solids that interact with realistic surface forces of extended range.
- P. Attard,
Interaction and Deformation of Viscoelastic Particles.
I. Non-adhesive Particles,
Phys. Rev. E 63, 061604 (2001).
First soft contact theory for viscoelastic particles.
- P. Attard and S. J. Miklavcic,
Effective Spring Constant of Bubbles and Droplets,
Langmuir 17, 8217-8223 (2001).
First analytic approximation for bubble and droplet
interaction and deformation and expression for the interfacial
G. S. Gillies, C. A. Prestidge and P. Attard,
An AFM Study of the Deformation and Nano-rheology of Cross-Linked PDMS Droplets,
Langmuir 18, 1674-1679 (2002).
First nanoscopic measurement of material parameters using viscoelastic theory.
Nanobubble Existence and Stability
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.
J. L. Parker, P. M. Claesson, and P. Attard,
Bubbles, Cavities, and the Long-Ranged Attraction
between Hydrophobic Surfaces,
J. Phys. Chem. 98, 8468-8480 (1994).
First evidence for nanobubbles and identification of them
as the source the long range hydrophobic attraction.
A. Carambassis, L. C. Jonker, P. Attard, and M. W. Rutland,
Forces Measured Between Hydrophobic Surfaces
due to a Sub-microscopic Bridging Bubble,
Phys. Rev. Lett. 80, 5357-5360 (1998).
First measurement of the force due to a
single bridging nanobubble.
J. W. G. Tyrrell and P. Attard,
Images of Nanobubbles on Hydrophobic Surfaces and their Interactions, Phys. Rev. Lett. 87, 176104 (2001).
First images of nanobubble networks.
M. P. Moody and P. Attard,
Curvature-dependent Surface Tension of a Growing Droplet,
Phys. Rev. Lett. 91, 056104 (2003)
Formally exact formula for the surface tension, and the first computer simulation results showing that the surface tension decreases with increasing supersaturation.
To Phil Attard's home page.