I'm involved with several academic projects at the moment, some stemming from my doctoral work in the University of Bristol (maximum entropy and ionomers) and others from my postdoctoral research at Cambridge (packing of filler particles and microtomography).

CURRENT COLLABORATIONS PAGE

Current academic collaborators can now access shared resources via http from here. You will need a password from to link to relevant resources.

The links below lead to a précis of each publically accessible project:

• Packing of filler particles in polymer composites
• X-ray microtomograpy of polyurethane foams
• Maximum entropy methods applied to small angle X-ray diffracton
• Structural characterisation of perfluorosulphonate ionomer membranes

The project for which I was recruited to my postdoctoral post is concerned with the geometrical packing of objects in space. Although at first glance this may seem a trivial problem, the physics of packing polydisperse assemblies of highly asymmetrical particles is not at all easy, and there are many valuable technological applications in the field of composite materials.

We are specifically concerned with polymer composites [1], and the project tackles issues such as how to maximise loading of filler material without compromising mechanical and elastic properties and how to introduce large volume fractions of such fillers into a polymer matrix. For example, below are two images of a glass-filled epoxy composite (taken using X-ray microtomography). On the high resolution image, the glass fibres and spheres can be clearly seen against the matrix.

The mixing of hard particles of various shapes and sizes can be studied on a computer using standard Molecular Dynamics (MD) or Monte Carlo (MC) simulation techniques. The former are particularly attractive, as the effect of dynamic perturbations (such as shear forces) can be examined. I have adapted the DL_POLY package [2] from Daresbury Laboratory to carry out such simulations, in a way which is very similar to the new technique of Dissipative Particle Dynamics (DPD) [3].

The computational work, which involved a validation of the method by comparison with analytical equations of state for hard spheres followed by extension to angular particles and mixtures of angular particles and spheres, has now been published [4].

1. Ritter, J. Appl. Polym. Symp., 15, 239-261, (1971).
2. Forester, T.R. & Smith, W. DL_POLY molecular dynamics code CCP5 of the EPSRC, (1995).
3. Hoogerbrugge, P.J. & Koelmann, J.M.V.A. Europhys. Lett., 19, 155, (1992).
4. Elliott, J.A. and Windle, A.H. J Chem Phys, 113, December (2000).

The relatively new technique of X-ray tomography relies heavily on use of high intensity beams which can be obtained from modern third generation synchrotrons, such as the ESRF in Grenoble, France. It is similar in many respects to medical tomography, but allows the detailed investigation of relatively dense solid state samples.

The essence of any tomographic technique is to generate a three dimensional density map of an object, which is reconstructed from a set of two dimensional projections over a range of orientations [1]. We are using X-ray tomography to study the compression of polyurethane foams, and link the results with the predictions of finite element mechanical models. I have also carried preliminary tomographic studies of polymer composite materials.

Results from the foam tomography experiments have now been submitted for publication [2]. These include an in-situ deformation sequence as a function of applied strain, part of which is shown in the pair of 3-D images below. The struts can be seen to bend and twist as the compressive strain is increased, from the left image to the right.

1. Herman, G.T. & Lewitt, R.M. in Image reconstruction from projections edited by G.T. Herman, Springer-Verlag, 1979.
2. Elliott, J.A., Windle, A.H., Hobdell, J.R., Eeckhaut, G., Oldman, R.J., Ludwig, W., Boller, E., Cloetens, P., Baruchel, J., submitted to J. Mat. Sci. (2001).

Maximum entropy (MaxEnt) methods enjoy widespread use in the field of inverse problems, with certain high profile applications such as the deconvolution of radioastronomical images [1]. They function on the principle of constrained maximisation of the Shannon entropy, which produces the most statistically probable solution consistent with the constraints.

The problem I was interested in during my PhD was how to extract structural information from the X-ray diffraction patterns from polymers, in particular the amorphous patterns produced by perfluorosulphonate ionomers. However, the MaxEnt method outlined here is quite general, and can be applied to any scattering problem in which the diffracted intensity can be described by an autocorrelation function [2]. It is based on the Cambridge Algorithm of Skilling and Gull [3].

1. Gull, S.F. & Daniell, G.J. (1978) Nature, 272 686-690.
2. Elliott, J.A. & Hanna, S. (1999) J. Appl. Cryst., 32, 1069-1083.
3. Skilling, J. & Gull, S.F. (1985) in Maximum entropy and Bayesian methods in inverse problems, Dordrecht-Reidel.

The main focus of my PhD work at Bristol was an investigation of the structure of perfluorosulphonate ionomers, in particular a material marketed by du Pont under the trade name "Nafion". We used small angle X-ray diffraction (SAXS) to characterise the membrane morphologies [1], combined with atomistic modelling using NVT molecular dynamics [2]. We also looked at the swelling behaviour of the membranes in conjunction with the scanning probe microscopy group at Bristol [3].

Perfluorosulphonate ionomers consist of a "Teflon" (PTFE) backbone with sulphonic acid groups periodically substituted along the chain, and are of commerical interest due to their peculiar ion transport properties. In particular, under certain conditions, these membranes are selectively conductive-passing cations, but not cations. This makes them ideal as membrane separators in liquid state redox fuel cells.

The commerical sponsors of this work, Innogy Technology Ventures Ltd, have recently announced details a new energy storage technology called Regenesys, which is crucially reliant on Nafion membranes to achieve efficiencies approaching 75% and capacities of up to 120MWh. This corresponds roughly to the output of a medium-sized power station over the course of a day!

1. Elliott, J.A.; Hanna, S.; Elliott, A.M.S. & Cooley, G.E. (2000) Macromolecules, 33, 4161-4171.
2. Elliott, J.A.; Hanna, S.; Elliott, A.M.S. & Cooley, G.E. (1999) PCCP, 1, 4855-4863.
3. James, P.J.; Elliott, J.A.; McMaster, T.J.; Newton, J.N.; Elliott, A.M.S.; Hanna, S.; Miles, M.J. (2000) J. Mat. Sci., 35, 5111-5119.