Fluid Dynamics Issues in Synthesis of Nanotubes

1
Fluid Dynamics Issues in Synthesis of Nanotubes

• By
• Dr. Alex Povitsky
• Department of Mechanical Engineering
• University of Akron
• E-mail povitsky_at_uakron.edu

2

3
Carbon nanotube-polymer of pure carbon

• Stiffness-to-weight ratio forty times higher than
  that of aluminum
• Strength-to-weight ratio five hundred times
  higher than that of aluminum
• Thermal conductivity as high as diamond
• Electrical conductivity six orders-of-magnitude
  higher than copper

4
Nanotubes Properties Uses

• Conductive plastics
• Energy storage
• Molecular electronics
• Thermal materials
• Fibers and fabrics
• Catalyst supports

5
Scope of the presentation

• Considered processes of synthesis of nanotubes
  are decomposition of high-pressure carbon oxide
  (HiPco), laser ablation (LA), and chemical vapor
  deposition (CVD).
• We discuss the required modeling tools including
  combined Eulerian and Lagrangian approach and
  Burnett equations for higher Kn number flow.
• Based on modeling, we find a thermal regime of
  catalyst particles that is critical for formation
  of carbon nanotubes.

6
Mathematical problems

• Classification of catalyst particles
  trajectories. Trajectory-based optimal design of
  the apparatus for synthesis of nano-tubes
• Multi-scale modeling and interaction of molecular
  dynamics and continuous aerodynamics. Examples
  include solid-to-gas ablation (1 microsec) and
  plume dynamics (1 millisec) Rigorous model is
  needed to switch between MD, DSMC, and CGD
• Use of micro-fluidic boundary conditions and
  Burnett equations to obtain heat and mass
  transfer coefficients between the feedstock gas
  and a single nanotube for Kngt0.1. Example
  synthesis of nano-tubes by chemical vapor
  deposition.

7
(No Transcript)
8
(No Transcript)
9
HiPco reactor and showerhead
10
Various mixing scenario
90O
30O
11
Temperature of catalyst particles versus time
30O
30O
60O
60O
Hot-to-cold Mass ratio31
Hot-to-cold Mass ratio61
90O
90O
12
Improved Showerhead of the HiPco Reactor
60O
13
Temperature of catalyst particles along their
trajectories

• Basic configuration one cold and three hot jets

• Improved showerhead

14
Typical trajectories of catalyst particles for
high-incidence jet mixing
1-trajectory bends inwards 2-trajectory bends
outwards 3-particle rotates upstream of the jet
intersection point
Can we design a mixing device to achieve as much
trajectories (2) as possible?
15
Random Walk model for turbulent flow
One central jet, 60 degrees
New design, 60 degrees
New design, 90 degrees
16
Journal publications about CFD modeling of HiPco

• C. Scott, A. Povitsky, C. Dateo, T. Gokcen, P.
  Willis and R.E. Smalley, Iron Catalyst Chemistry
  in Modeling a High Pressure Carbon Monoxide
  Nanotube Reactor, Journal of Nanoscience and
  Nanotechnology, Vol. 3, No. 2, 2003, pp. 63-73.
• A. Povitsky and M. Salas, Trajectory-based
  Approach to Jet Mixing and Optimization of the
  Reactor for Production of Carbon Nanotubes,
  AIAA Journal , Vol. 41, No. 11, November 2003,
  pp. 2130-2143 preliminary version ICASE Report
  2001-04
• A. Povitsky, Improving Jet Reactor Configuration
  for Production of Carbon Nanotubes, Computers and
  Fluids, Vol. 31, No. 8, April 2002, preliminary
  version ICASE Report 2000-18

17
Laser-Ablation SWNT Process at NASA Johnson Space
Center

• Dual concentric quartz tubes
• Pulse laser at 532 nm wavelength and 5mm beam
  diameter
• Target graphite and catalyst (Ni and Co)
• Non-reacting surrounding argon flow at T1473 K

18
Plume formation in laser ablation
19
Ablation
20
Evolution of plume and formation of nanotubes
21
2-D CONSERVATION LAWS Euler Equations
22
Numerical discretization

• The second-order upwind scheme(MUSCL)
• Second-order explicit RK scheme integrates in
  time
• Minmod TVD limiter is used
• Relaxing TVD scheme is employed
• Kurganov Tadmor, J Comp. Physics, 160 241-282,
  2000
• S. Jin and Z. Xin, The Relaxation Schemes for
  Systems of Conservation Laws in Arbitrary Space
  Dimensions, Comm. Pure Appl. Math., 1995, Vol.
  48, pp. 235-276

23
Validation of the code
2-D shock tube problem
24
Sedov-Taylor analytical solutionL. I. Sedov,
Similarity and Dimensional Methods in Mechanics,
Academics Press, New York, 1959
25
Effect of Injection Velocity on Plume Motion
26
Propagation of plumeunder standard atmospheric
pressure
27
Low chamber pressure (p0.01atm)
28
Temperature of catalyst particles emerging with
the doubled plume
1
2
29
Influence of injection velocity on multi-pulse
plume
30
10th plume
31
Geometry of the laser furnace
32
Target is located in the middle section of the
bulb-shape furnace
30 µs
60 µs
pressure
90 µs
30 µs
33
Effects of viscosity and turbulence

• For a single plume, effective viscous
  length-scale can be defined as

For t200µsec, l100µ (typical figures for laser
ablation in production of carbon nanotubes). This
scale is two orders of magnitude smaller than
cross-section of the plume and two orders of
magnitude larger than the particle size.
For multiple plume injection, viscous effects may
be more important since the flow is more close to
continuous jet For turbulent surrounding flow,
the effective viscosity is much higher and
viscous effects are more prominent Viscous/turbule
nt effects are important for motion of catalyst
particles
34
Multi-domain approach

• The multi-domain approach will be developed for
  concurrent rendering of different areas of
  computational domain by different models (MD,
  DSMC, and CGD) and/or different time steps for
  the same model.
• For multiple plume ejection, the near-target area
  will be rendered by MD or DSMC whereas the CGD
  algorithm is employed to simulate plume dynamics
  of previously ejected plumes apart of the target.
  
• The jet mixing occurs by formation of
  Raleigh-Taylor instabilities at the plume-gas
  interface due to interaction with reflected shock
  waves, and the local fine grid should be used
• For the first 180 time steps after ablation
  CFL0.0001 and the time step is

35
Adopting grid and shock wave interaction with
Vortical Density Inhomogeneity (VDI)
Povitsky Ofengeim, 1999
36
Laser ablation conclusions

• Non-monotonic temperature of catalyst particles
  is caused by (i) interaction of particles with
  reflected shock waves and (ii) circular motion of
  the particles caused by formation of vortical
  zones, stagnation points, and slip-lines. While
  both reasons are important for the standard
  atmospheric pressure of furnace gas, the latter
  reason plays the key role for near-vacuum ambient
  pressure.
• The plume propagation is much slower than that
  of the leading shock wave especially for low
  injection rate and/or low ambient pressure. For
  the given pressure in a laser furnace, the
  position of the front of the plume primarily
  depends on the plume injection velocity. A
  refined laser melting and vaporization model is
  needed to determine the injection velocity.

37

• The location of the carbon target in the middle
  section of the bulb (semi-bulb furnace geometry)
  produces relatively smooth temperature profile of
  catalyst particles required for synthesis of
  carbon nanotubes.
• Modeling of multiple plume is important for
  technological applications where laser hits
  target many times. Behavior of catalyst particles
  for multiple injected plumes shows substantial
  difference in comparison to a single plume
  model.
• On one hand, the temperature of catalyst
  particles for multi-plume injection has been
  increased substantially in comparison to the
  single and double pulse cases. On the other hand,
  there is a broad spread of the temperature for
  catalyst particles emerging from different zones
  of the target.

38
Related Journal Papers

• D. Lobao and A. Povitsky, Single and Multiple
  Plume Dynamics in Laser Ablation for Nanotube
  Synthesis, accepted for publication in AIAA
  Journal, preliminary version AIAA Paper
  2003-3923.
• D. Lobao and A. Povitsky, Furnace Geometry
  Effects on Plume Dynamics in Laser Ablation, to
  appear in Mathematics Computers in Simulation
  (Special Issue on Wave Propagation), short
  version in Proceedings of ICCSA-2003, Lecture
  Notes in Computer Science 2668, pp. 871-880, 2003.

39
Chemical Vapor Deposition method (CVD) for
synthesis of nanotubes
Base growth model
40
CFD modeling of CVD process

• Knudsen number is 0.1-1.0 (based on the nanotubes
  diameter)
• Slip/No-slip boundary conditions
• Navier-Stokes/Burnett equations

Purpose to compute mass transfer between the
feedstock gas and catalyst particles
41
Slip boundary conditionsStocks Equations (low
Re, Knlt0.1)
Single Isolated Cylinder
For slip boundary conditions D ?0!
42
Computational framework for CVD process
43
Micro-fluids aspects of feedstock gas flow at
the nanotubes base
Slip boundary conditions
No-slip boundary conditions
44
Conclusions and Future Research

• CFD modeling of nanotubes synthesis requires
  multi-scale approach to combine
• continuous mechanics of multi-species flow of
  feedstock gas or plume
• micro-fluidic flow model that is needed to find
  heat and mass transfer coefficients about
  isolated nanotubes
• molecular dynamics of formation of plume in laser
  ablation. The obtained distribution of plume
  injection velocity will be used by continuous
  model

45
Collaboration with Prof. Zhigiley(U. of Virginia)
Proposal Title Combined mathematical model of
plume dynamics in laser ablation of nanosecond
to millisecond temporal scale During the first
nanoseconds, fast laser energy deposition leads
to overheating of the surface and ejection of
atoms, molecules, ions, and clusters. This
initial fast part of the ablation process is
followed by a slower expansion of the ablation
plume. The large disparity of the processes
occuring at different stages of laser ablation
does not allow one to describe this phenomenon
within a single computational approach

46
Collaboration with Profs. Tsukerman (Akron) and
Friedman (Drexel)
Proposal Magnetically Driven Self-Assembly of
Nano- and Micro- particles in Fluids
During the last decade, substrates patterned with
many different chemical species or other
materials have found applications in
combinatorial chemistry, chemical sensors and
genetic testing (DNA chips). Fluid agitation by
impulsive flows can induce much more ordered
patterns of particles on the substrate. Flow
motion may be used to disperse undesirable chains
or clouds of particles.
47
References