### Multi-Scale Modeling, Simulations and Experiments of Coating Growth on Nanofibers

Dr. Clemons, Dr. Kreider, Dr. Young, and others

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.