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Thermophoresis and Capillary
Filling of Water in Nanochannels
Harvey A Zambrano
Jens H Walther*
Department of Mechanical Engineering,
Technical University of Denmark, Denmark
*Also at Chair of Computational Science, ETH Zurich, Switzerland
Introduction
•
Goal: study flow in pipes and channels
Image from the Tecnai Transmission Electron Microscope (TEM) operated at 200kV
at DTU CEN, DTU. By Cavalca, Jensen and Zambrano, April, 2010.
.
Page 2
Carbon nanotubes
Graphite sheet
Carbon Nanotube
Threadlines through different types of
CNTs
Schoen et al. Applied Physics Lett. 2007, 90, 253116(1-3)
Zig-zag CNT
Armchair CNT
Chiral CNT
Page 3
Introduction
Driving Mechanism for liquids
1-Electrophoresis
2-Osmosis and Marangoni effect
3-Pressure Gradients
4-Thermophoresis/Soret
5-Capillary filling
Osmosis
Kalra et al. PNAS, U.S.A. 2003, 100, 10175-10180
Thermophoresis
Zambrano et al. Nano Lett. 2009 9(1), 66-71,
Page 4
Molecular dynamics
Newton’s equations:
∂ 2 xi
,
Fi = mi
∂ 2t
∂U i
Fi =
∂x
Interactions potentials:
• Water: rigid SPC/E water.
• Carbon Nanotube: Morse, Harmonic angle and
torsions potentials.
• Carbon-water: Lennard-Jones
 σ
=
U LJ (rij ) 4ε CO  CO
 rij


 σ CO  
 − 
  ,

 rij  
12
U
6
r
Page 5
FASTTUBE MD package
MD simulation of water on a graphite sheet in order to calibrate the governing potential
Werder et al J. Phys. Chem. B 2003, 107, 1345-1352
MD Simulations using Fasttube
package
Walther et al. Carbon 2004, 42, 1185-1194
Werder et al. Nanolett. 2001, 1(12), 697-702
Page 6
Thermophoresis of water nano-droplets inside CNT
Schematic of the water nanodroplet confined inside a zig-zag carbon nanotube
Zambrano et al. Nano Lett. 2008, 9(1), 66-71.
Three different thermal gradients imposed:
red 1.97 K/nm, green 1.58 K/nm and blue,
1.05 K/nm
A thermal gradient of 1.05K/nm
Page 7
Thermophoresis of water nano-droplets inside CNT
Axial flow profile
Tangential flow profile
Page 8
Introduction
•
Molecular linear motors
subnanometer cargo motion driven by thermal gradients
along carbon nanotubes
Barreiro et al. Science 320, 775 (2008).
Experimental study of a molecular linear motor
Somada et al. Nanolett. 9, 62-65, (2009).
Page 10
Thermally driven molecular linear motors
Schematic of the computational setup.
Zambrano et al. J. Chem. Phys. 2009, 131, 241104
COM position and velocity for three different thermal
gradients: 1.18 K/nm, green 1.58 K/nm and blue, 3.16 K/nm
Page 11
Thermally driven molecular linear motors
16 nm/ns
4 nm/ns
Zambrano et al. J. Chem. Phys. 2009, 131, 241104
Page 12
Capillary filling of silica nanochannels
Set up of the experiments of water filling nanochannels
liquid
gas
Thamdrup et al. Appl. Phys. Lett. 91, 2007
Page 13
Simulation details
•
Interaction potentials
1-Silica Model: Born-Huggins-Mayer form parameterized from
Guissani et al. 1996.
2-Water model: rigid SPC/E (Berendsen et al. 1987).
3-Air-water: LJ potential (Jiang et al for air and Werder et al. for OW).
-Parameterization using the air solubility
4-Silica-Water: Buckingham potential + Coulomb potential
- Partial charges: soft potential by Takada et al. 2007
(qsi = 1.3e and qo = 0.65e)
-Parameterization using the WCA.
Method by Werder et al. J. Phys. Chem.B.107(6), 2003
Page 14
Potential calibration
~ 4000 CPU hours/simulation
Top view of a full equilibrated
nanodroplet on a 38nm x 38nm
silica surface
Relation between the Buckingham parameter
Cij and water contact angle.
Snapshots of the silica-water system at vacuum, WCA 20°
Page 15
Potential calibration
Density profiles and solubility of N2 and O2
Inside a water slab for different air pressures
Page 16
Results
Density profiles water and air on silica at high
air pressure and solubility of air inside the water
Axial flow profile
Silica-water-air system
Capillary filling of water in a silica nanochannel
Page 17
Acknowledgement
DCSC - nilfheim.fysik.dtu.dk
Danish Center for Scientific Computing
Grant No. FTP-274-06-0465
Danish Research Council
Prof. P. Koumoutsakos
CSE Lab. - ETH Zurich, Switzerland
Assistant Prof. Ivo F. Sbalzarini
CSE Lab. - ETH Zurich, Switzerland
Prof. D. Poulikakos
Institute of Energy Technology, ETH Zurich, Switzerland
Prof. E. Kaxiras
Department of Physics, Harvard University, USA
Dr. R. L. Jaffe
NASA Ames Research Center, USA