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OVERVIEW:
Many industrial materials are grown from a substrate or seed rather than
homogeneously synthesized in a bulk reactor. One can think for instance of the
standard method for coating a metal piece with another metal, the
electrodeposition of the second metal from a salt of it in solution [1]; but also
the growth of large silicon monocrystals by deposition of a vapor on a substrate,
from which silicon wafers are then sliced to manufacture chips; and a large
variety of polymeric coatings and films ubiquitous in new and specialized
materials. Porous polymeric membranes can be produced by liquid-liquid extraction:
a non-solvent buffer is allowed to diffuse into a polymeric solution, which
triggers the precipitation and solidification of the polymer to form the membrane
[2]. The domains thus formed also grow in time leading to a complex
microstructure. This complexity can be desired (like in this case the pores are)
or not (coatings should be smooth), but in any case the basic properties of the
material (here its pore size distribution and morphology) strongly depend on
the growth process. In turn, each application (here microfiltration,
ultrafiltration, reverse osmosis...) requires a specific microstructure, so that
controlling the growth process is crucial.
In this project we will study growth phenomena [3] by phase-field (see
methodology) and/or other numerical simulation and theoretical methods,
based on an appropriate description at the microscopic/mesoscopic level. We will
be particularly interested in membranes, a hot topic with the additional
advantage that in-house experiments are available. Collaboration with
experimentalists or at least exposure to experiments is important and
very formative for the `modeler', and is foreseen.
BACKGROUND AND STATE OF THE ART:
Growth processes are still poorly understood. The coupling of chemical
and physical processes at the interface between the growing domains and their
environment make such problems quite complex, not the least because of
difficulties associated with handling moving, deformable surfaces numerically,
especially in three dimensions or whenever topology changes (for instance the
crucial pore formation in the mentioned membranes). Therefore, most progress to
tailor the end-product to a given specific application is made by trial-and-error
experiments. However, phase-field and (other) mesoscopic methods, together with
the increase of computer power, make the development of predictive tools
envisageable.
PROJECT CONTRIBUTION AND METHODOLOGY:
Experiments, predictability and design could be greatly helped by the
development of simulation schemes, and that is what we propose. Our group has
developed mesoscopic models, suited to bridge the gap between microscopic
phenomena and the macroscopic end result [4], and, in the macroscopic scale, this
is also becoming feasible for the first time thanks to the development of the
phase-field method [5]. Originally proposed to describe the solidification of
metals, it encodes the growing surface as the contour line of an auxiliary field,
whose dynamics are then simulated. This can then naturally handle the appearance
of new interfaces like in pore formation. The project supervisor is one of the
pioneers in this field [5,6], which is currently booming [6]; some attempts in
similar directions are already showing up.
THE IDEAL CANDIDATE:
will have the possibility to develop his/her own models to simulate these
problems (some creative, theoretical work), with the full support from the
supervisor. She/he will program the models (not less creative), run simulations
and analyze the results and compare them to experiments, always with the
assistance of the supervisor. Interaction with the experimentalists and the
group will be particularly encouraged. The emphasis on one or other aspects of
the work can be flexible to match the candidate's abilities and interests and the
progress of the project. Curiosity to understand what is going on in these
problems, together with a sense for abstract reasoning / programming are
important. Candidates with a degree in physics, chemistry, applied maths and the
engineering sciences (obviously including chemical engineering!) are very welcome.
FINISHING THIS PROJECT:
The balance of skills acquired during this project are very suitable to
work as a more independent researcher in academia, in departments ranging from
mechanical to chemical engineering, materials science, physics and chemistry. A
good `modeler' is in a privileged position to bring theory and experiments
together in any of these fields, and hence much in demand. This and the soft
skills related to the fruitful interaction with colleagues and to team work are
also very demanded in the private sector, with the applied side of the project
helping make the candidate attractive for the industry in particular.
Finally, the programming work can also be very appreciated in software, IT and
consultancy firms.
REFERENCES
[1] For a 'classical' point of view see for instance W. Schmickler, Interfacial
Electrochemistry, Oxford University Press (Oxford 1996).
[2] M. Mulder, Basic Principles of Membrane Technology, Kulwer Academic
Publishers (The Netherlands, 1992).
[3] P. Pelce, Dynamics of Curved Fronts, Perspectives in Physics, Academic
Press (1988); E. Ben Jacob and H. Levine, Adv. Phys. 49: 395 (2000).
[4] J. Bonet Avalos and A. D. Mackie, Dynamic and Transport Properties of
Dissipative Particle Dynamics with Energy Conservation, J. Chem. Phys.
111: 5267 (1999); I. Pagonabarraga and D. Frenkel,
Dissipative particle dynamics for interacting systems, ibid. 115:
5015 (2001).
[5] R. Gonzalez-Cinca, R. Folch, R. Benitez, L. Ramirez-Piscina, J. Casademunt, A.
Hernandez-Machado, Phase-field models in interfacial pattern formation out of
equilibrium, in Advances in Condensed Matter and Statistical Mechanics, ed.
by E. Korutcheva and R. Cuerno, Nova Science Publishers: 203-236 (New York, 2004),
also available at http://xxx.arxiv.org/abs/cond-mat/0305058.
B. Echebarria, R. Folch, A. Karma and M. Plapp, Quantitative phase-field model
of alloy solidification, Phys. Rev. E 70: 061604 (2004);
R. Folch and M. Plapp, Quantitative phase-field modeling of two-phase growth,
ibid. 72 (1): 011602 (2005).
[6] R. Folch et al., Phase-field model for Hele-Shaw flows with arbitrary
viscosity contrast. I. Theoretical approach Phys. Rev. E 60 (2):
1724-1733 (1999); ibid. II. Numerical results, ibid.: 1734-1740 (1999);
T. Biben, K. Kassner and C. Misbah, Phase-field approach to three-dimensional
vesicle dynamics, Phys. Rev. E 72: 041921 (2005);
W. J. Boettinger, J. A. Warren, C. Beckermann and A. Karma, Annu. Rev. Mater. Res.
32: 163 (2002); L.-Q. Chen, ibid.:113 (2002);
R. Trivedi, S. Liu and S. Williams, Nature Materials 1: 157 (2002).
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