MSci Project Proposal Form 2009-2010
Project Code: CMTH-Tangney-2
Project title: Nanoscale electromagnetism
Supervisor: Dr Paul Tangney
Assessor: Dr Peter Haynes
Telephone: Ex. 4 8155
Telephone: Ex. 4 5158
E-mail: p.tangney
E-mail: p.haynes
Research group: CMTH
Research group: CMTH
Project Summary: The macroscopic Maxwell equations describe electromagnetic behaviour in the
presence of a medium of free and bound charges. These equations are generally derived from the
microscopic Maxwell equations, which describe the behaviour of charges in vacuum, by spatially
averaging the influences of charges in the medium [1]. Implicit in this procedure is the assumption that
the macroscopic Maxwell equations will only be applied at length scales that are large compared to the
distances characterizing the distribution of charges (electrons and ions) that make up the medium.
The validity of this assumption is questionable for many problems that arise in nanoscience and in the
application of computer simulations to bulk materials. Commonly used concepts such as the
polarization density, P, rely on the distribution of electrons and ions being expressed in terms of point
multipole expansions – and therefore have limited validity at the nanoscale.
The goal of this project will be to explore, both theoretically and computationally, the limitations of
concepts and quantities of macroscopic electromagnetism on small length scales, to understand the
most meaningful ways in which these quantities can be applied at these scales, and to apply this
understanding to important systems in nanoscience and nanotechnology.
Depending on the interests and aptitudes of the student, the project can be mostly analytical, mostly
computational, or a balance of both. There are several specific topics that could be studied, including:
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
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A detailed examination of the approximations introduced when spatial averaging is used to
derive the macroscopic Maxwell equations. A derivation of correction terms to be included
when measurements are made using small probes and/or at small distances from a charge
distribution[1].
An investigation of the importance of electostatic interactions in the binding of nanoparticle
superlattices[2].
Development of improved methods of data analysis in electrostatic force microscopy[3]
Experimental component:
0%
Computational component: 0 to 80%
Theoretical component:
0 to 80%
Is the MSci Project eligible for students on the MSci
Physics with Theoretical Physics Degree: YES
Suggested reading:
1. G. Russakoff, “A derivation of the macroscopic Maxwell equations,” Am. J. Phys. 38, 1188 (1970)
2. E. V. Shevchenko et al. “Structural diversity in binary nanoparticle superlattices,” Nature 439, 55 (2006);
E. V. Shevchenko et al. “Structural Characterization of Self-Assembled Multifunctional Binary
Nanoparticle Superlattices,” J. Am. Chem. Soc. 128, 3620 (2006).
3. P. Girard, “Electrostatic force microscopy: principles and some applications to semiconductors”,
Nanotechnology 12, 485 (2001); R. Krishnan et al. , “Polarization Surface-Charge Density of Single
Imperial College of Science, Technology, and Medicine
Semiconductor
Quantum Rods,” Phys. Rev. Lett. 92, 216803 (2004).
lattices,” J. Am. Chem. Soc. 128, 3620 (2006).