**Participants: A. Buldum
(Physics), C.
B. Clemons (Theo and Applied Math), K. L. Kreider
(Theo and Applied Math), G. W.
Young (Theo and Applied Math), E. A.
Evans (Chemical Eng), S. I. Hariharan (Electrical Eng)**

The
coating of nanoscale structures and the evolution of
crystalline structure at the nanoscale are and will
continue to be important issues. Our efforts in this area include a coordinated
experimental and modeling program for the synthesis of core/clad and hollow nanowire structures. Physical vapor deposition techniques
are used to apply coatings to electrospun polymer nanofibers. These fibers are coated with films of copper,
aluminum, titanium, zirconium and aluminum nitride by using a
plasma enhanced physical vapor deposition (PEPVD) sputtering process.

To
aid the understanding of the deposition process on nanoscale
size structures, a comprehensive model for the coating of nanofibers
within a traditional PEPVD system has been developed. The model integrates
across atomic to continuum length scales for simulating the sputtering,
transport and deposition of coating material onto a nanoscale
substrate. The model connects macroscale phenomena to
nanoscale phenomena by linking simple models at each
length scale. The solution procedure involves many simplifying assumptions to
piece together a collection of simple models into one comprehensive model.
Solution strategies that couple continuum and atomistic models are used.
Information is passed between the various length scale models so that the
simulations are integrated together. To keep the numerical simulations at a
manageable level, asymptotic analyses are used to reduce the complex models to
simpler, but still relevant, models.

In
Part I of this series, we describe a continuum model of the sheath region at
the target and the reactor dynamics near the target surface. At the atomic
level, we use molecular dynamics (MD) simulations to study the sputtering and
deposition mechanisms at the target. Ion kinetic energies and fluxes are passed
from the continuum sheath model to the MD simulations. These simulations
calculate sputtering and sticking probabilities that in turn are used to
calculate parameters for the continuum reactor model. The reactor model
determines the concentration of the coating material.

In
Part II of this series we describe the sheath region at the holder and the
local dynamics near the substrate surface. The concentration from Part I is
input to this local model. At the atomic level, we use molecular dynamics (MD)
simulations to study the sputtering and deposition mechanisms at a curved
surface. Ion kinetic energies and fluxes are passed from the continuum sheath
model to these MD simulations. These simulations calculate sputtering and
sticking probabilities that in turn are used to calculate parameters for the
local model. The local model determines an evolution equation for the coating
surface. A polar geometry is assumed for the coating surface. In deriving the
evolution equation, we assume two levels of simplification to derive the
concentration field of the coating material. First, the concentration field is
assumed to be radially dominant and so variations in
the angular direction are neglected. This leads to a concentration field that
depends highly nonlinearly on the location of the coating surface. Hence, a
second simplification is posed. The location of the coating surface is replaced
by the radius of the uncoated nanofiber. Finally, the
coating surface is assumed to be single-valued so that some coating
morphologies are excluded from consideration. These simplifications reduce the
complexity of the numerical simulation of the evolution equation. Nevertheless,
parametric studies of this evolution equation reveal general trends that
rougher coatings develop on nanofibers with larger
radii, in systems with higher levels of concentration, and in systems
characterized by high rates of deposition.

Current work considers the axisymmetric
geometry and solves the evolution equation without the single-valued assumption
and under less restrictive assumptions on the concentration field than the
previous work.

We have also examined the emission response of a
nanotube due to an applied electric field along the
axis of the nanotube. The nanotube
was assumed to have small roughness in the azimuthal
direction. Coupled Helmholtz equations for the field emission interior and
exterior to the tube were solved by boundary perturbation methods. The strength
of the exterior field was calculated as a function of the frequency and
magnitude of the applied field. The tunneling problem for electrons at the
surface of the nanotube was investigated by the WKB
method. The critical frequency and magnitude of the applied field to initiate
tunneling was determined.

** Publications**:

- Multi-Scale
Modeling, Simulations and Experiments of Coating Growth on Nanofibers: Part I - Sputtering, A. Buldum, I. Busuladzic, C. B.
Clemons, L. H. Dill, K. L. Kreider, G. W. Young,
E. A. Evans, G. Zhang, S. I. Hariharan, and W. Keifer, J. Applied Physics, Vol. 98, (2005), pp.
044303-044303-10.

- Multi-Scale
Modeling, Simulations and Experiments of Coating Growth on Nanofibers: Part II - Deposition, A. Buldum, C. B. Clemons, L. H. Dill, K. L. Kreider, G. W. Young, X. Zheng,
E. A. Evans, G. Zhang, and S. I. Hariharan,
*J. Applied Physics*, Vol. 98, (2005), pp. 044304-044304-16.

- Field
Emission from Coated Nanowires, T. Marinov, A. Buldum, C. B.
Clemons, K. L. Kreider, G. W. Young, and S. I. Hariharan, J
*. Applied Physics*, Vol. 98, (2005), pp. 044314-044314-11.

- Modeling
and Simulation of Axisymmetric Coating Growth on
Nanofibers, K. Moore, C. B. Clemons, K. L. Kreider, and G. W. Young, Submitted to
*J. Applied Physics*.

__Funding:__

- NSF
Division of Mathematical Sciences - Multi-Scale Analysis and Simulation of
Nanofiber Coatings: Growth and Applications NSF
Grant No. DMS-03-05580, (2003 - 2004): $106,250, with C. B. Clemons, K. Kreider, E. Evans, A. Buldum,
and S. I. Hariharan.

- NSF
DMI - NIRT: Nanofiber Manufacturing for Energy
Conversion and Utilization NSF Grant No. DMI-0403835, (2004 - 2008):
$1,300,000, with D. Reneker, G. Chase, E. Evans,
D. Smith, R. Ramsier, A. Buldum,
S. I. Hariharan, K. Kreider,
and A. Yarin.