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Molecular Dynamics Simulations (ME 850Z):
Introductions
Gisuk Hwang, Ph.D.
Department of Mechanical Engineering
2015 Fall
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OUTLINE
1. Course Overview
2. Introductions
3. Why Molecular Dynamics Simulations?
4. Applications: Examples
5. Review of Thermodynamics
6. Statistical Thermodynamics
ME 325 (Computer Applications)
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Introduction
• Education & Research
– Assistant Professor, ME, WSU, 2013/Sep - Present
– Post-doctoral Fellow, Lawrence Berkeley National Lab., 2010-13
– University of Michigan, Ph.D., Mechanical engineering, 2010• Water/thermal management in polymer electrolyte fuel cell
• Thermal/fluid science and engineering in porous media, heat pipe
• Micro thermoelectric cooler
– Handong University Mechanical engineering, 2002
• Two-phase flow (nuclear power plant safety)
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Introductions
http://blogs.rep-am.com/
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Why Molecular Dynamics (MD) Simulation?
Molecular-level scientific
understandings
Molecular-level
engineering for desired
functionalities
J. Phys. Chem. C, 113, 4597, 2009
Ice meting
Phys. Rev. Lett. . 111, 118103, 2013
Water transport in
nanotube
Optimal nanostructure for desired
water wetting
J. Chem. Phys., 140, 114704, 2014
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What is MD Simulation?
• Atomic force
– van der waals, electrostatic, ionic bond, covalent bond …
• Equation of motion
– Force → acceleration → velocity → displacement → force …
+-
+ -
2
2ij ij ij
d rF r E m
dt
D. Frenkel and B. Smit, “Understanding Molecular Simulation”, Academic Press, 2002
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What MD Simulation can do?
• Diffusivity (ensemble average), <D>
• Heat flux (ensemble average), q
r
H2O
2
1 1 1 1 1
1 1( )
2
N N N N N
i i i ij i ij i i
i i j i j
q m u u E u uV
r F
2
6
rD
t
• Other transport and equilibrium states
– Viscosity, density, Young’s modulus, saturation curve ….D. Frenkel and B. Smit, “Understanding Molecular Simulation”, Academic Press, 2002
• Temperature and pressure2
1
B
1
2
3( 1)
N
i i
i
m u
TN k
B
1
1( )
3
N N
ij ij
i j i
Nk Tp
V V
x F
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Why Molecular Scale Modeling?
• To fundamentally understand the physical behaviors in science and engineering?
• Expand the understanding of the phenomena where the experiments could not or are challenging to measure
• Develop predictive model and optimal design
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Regime Diagram Approaches
• Molecular dynamics simulation is ideal for ~10 -1 mm and ~0.1 – 1 ms
Macroscale
Microscale
Mesoscale
Molecular
Scale
Electrochemical System
Thermal System
Atomic
Scale
t
LmmmnmÅ
fs
ps
ns
ms
pm
s
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Example: Molecular Dynamics Simulation Water/Proton Transport in Nafion®
• Need clean energy systems for sustainable energy and environmental future
www.universetoday.com
addins.waow.com
www.worldofstock.com
H21/2O2
e-
H2O
e.g., Polymer Electrolyte Membrane Fuel Cell (PEMFC)
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1-D
Sandwich
Gas
Channel
Rib
1-D
Sandwich
Gas
Channel
Rib
Anatomy of a Polymer-Electrolyte-Membrane Fuel Cell (PEMFC)
1-D
Sandwich
Gas
Channel
Rib
1-D
Sandwich
Gas
Channel
Rib
1-D
Sa
nd
wic
h
Ga
s
Ch
an
nel
Rib
1-D
Sa
nd
wic
h
Ga
s
Ch
an
nel
Rib
Air flow field
Hydrogenflow field
PEM
Catalyst layersDiffusionmedia
Currentcollectors
150-250 mm 10-20 mm 50 - 177 mm
cell area: 5-300 cm2
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How a PEMFC Works andOptimal Water Management
Air flow field
Hydrogenflow field
PEM
Catalyst layersDiffusionmedia
Currentcollectors
Anode: 4e4H2H2
4e
4e
4e
2H2
2O
4H 4e
Cathode:
O2HO4e4H 22
O2H2O2H2
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PEM: Nafion® membrane
• Nafion® (Dupont) membrane: state-of-the-art PEM
– High proton conductor upon hydrated and good separator
• fuel cells, flow battery, solar-driven electrolysis, humidifiers, electrochemical sensors …
– PTFE backbone + side chain with functional sulfonic acid group
Hydrophobic
HydrophilicCF2)x[(CF2 CF2)]y(CF2
O CF2
CF2
CF O CF2 CF2 SO3−
z
H2O
Water Content
λ =N(H2O)
N(SO3H)
Side Chain
PTFE backbone
H+
• Nafion® nanostructures
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Water Uptake/Diffusivity/Proton Condcutivity in Nafion®
• Water uptake ~ f(RH)
A. Kusoglu and A. Z. Weber, ACS Symposium Series, 175, 2012
Relative Humidity (RH)
• Water diffusivity
• Proton conductivity
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Transport Channels of Hydrated Nafion®
• Hydration of Nafion® results in phase separation to have transport pathways
Dry
SO3−
Membrane Matrix
Low Humidity High Humidity or Liquid
K.A. Mauritz and R.B. Moore, Chem. Rev., 104, 4535, 2004
~4 nm
Microscopic phenomenological description (need further details on atomic-level description)
Atomic-level description (e.g., molecular dynamics): limited to very small region ~ 10 nm
Need multiscale approach: molecular dynamics and pore network model
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Bimodal Nanoscale Pore Size Network• Bimodal pore size
network
– Mesh-type pore structure using 1 and 4 nm water fillable nanogaps
– Nanogaps are used for molecular dynamics (MD) simulation(CF2)n
(CF2)n
(CF2)n
(CF2)n
1 nm 4 nm
G.S. Hwang et al., Polymer, 52, 2584, 2011.
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Water State/Transport in Nanopore
• State and self-diffusivity of water in nanopore
D = <r2>/6t
<f> = f e/t
G.S. Hwang et al., Polymer, 52, 2584, 2011.
r H2O
(CF2)n
(CF2)n
Transport hindrance(Debye length, ~ 0.4 nm)
Bulk-like
• Effective water transport in pore network
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Water Filling in Nanopores
• Bimodal water filling in two size nanopores
– Early water filling at smaller pores due to stronger surface interaction
G.S. Hwang et al., Polymer, 52, 2584, 2011.
RH = 1% 30 % 100 %
1 nm
4 nm
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Molecular Dynamic Simulation Movie
• Sluggish water movements near surfaces compared to the central region
4 nm
Water
Nanopores
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Bimodal Water Uptake
• Low RH
– Only adsorbed-water
• High RH:
– Transition from adsorption to capillary, resulting in capillary flow and significant increase of transport properties
G.S. Hwang and et.al, J. Electrochemical Soc., 156, B1192-B1200, 2009.
Relative Humidity (RH)
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Water Transport:Diffusivity
T.A. Zawodzinski et al., J. Electrochem. Soc., 140, 1981, 1993
Transport properties can be optimized by the nanostructure and surface wetting structure
for desired functionalities G.S. Hwang et al., Polymer, 52, 2584, 2011
Atomic-level and macroscopic network model successfully elucidates water transport
phenomena
Small pore: early filling but sluggish transport due to surface hindrance
Large pore: delayed filling but fast transport due to less surface hindrance
Large pore dominant
Small pore dominant
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Proton Transport
• Proton transport mechanism
– Diffusive
– Hopping (Grotthuss)
G.S. Hwang et al., Polymer, 52, 2584, 2011.
H3O+
H+ H+
3
+3 3
2
H O
H H H ,G H O H O ,B
( )D
en D n D
k T
Nernst-Planck Relation
wikipedia.com
T.A. Zawodzinski et al., J. Electrochem. Soc., 140, 1981, 1993
• Proton conductivity
• Atomic-level and macroscopic network model successfully elucidates proton transport
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Ex: Heat Transfer in Atomic Scale
• Thermal conductivity (continuum): Fourier Law
nf : fluid particle number density
cv,f: specific heat per particle
uf: average velocity of particles
λf: mean free path
M. Kaviany, “Heat Transfer Physics”, Cambridge, 2008
𝑘𝑓 = −𝑞𝑘
𝜕𝑇/𝜕𝑧
=1
3𝑛𝑓𝑐𝑣,𝑓𝑢𝑓𝜆𝑓 (atomic scale)
λf
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Thermal Conductivity in Nanopores
M. Kaviany, “Heat Transfer Physics”, Cambridge, 2008
Knf
LL
λf
𝑘𝑓,𝑓𝑚 =𝑝 𝑐𝑣,𝑓 + 𝑅𝑔/2
𝑎𝑇,1−1 + 𝑎𝑇,2
−1 − 1(2𝜋𝑀𝑅𝑔𝑇)
−1/2𝐿
aT,1
aT,2
thermal accommodation
coefficientL
• Knudsen number
• Free-molecular regime (KnL >> 1)
,1 ,2 1
, ,
,1 ,2 ,1 ,2
4 1(1 )
15 Kn
T T
f t f fm
L T T T T
a ak k
a a a a
• Transition regime (KnL ~ 1)
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Visualization of NEMD in Nanogap
• High Temperature Nanogap at <Tg> = 155 K (close to critical T) at DT = 10 K
• Low Temperature Nanogap at <Tg> = 90 K (close to triple point)
Pt surfacePt surface
L = 20 nm L = 20 nm
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Ex: Deposition of a Single Cu on Cu
• Example of a molecular dynamics simulation in a simple system: deposition of a single Cu atom on a Cu surface
ME 850Z (Molecular Dynamics Simulation)
Cu Layer
https://en.wikipedia.org/wiki/Molecular_dynamics
Cu Atom
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Ex: Capillary Filling in Carbon Nanotube
• Different water filling with respect to different Carbon Nanotube (CNT) size
ME 850Z (Molecular Dynamics Simulation)
Water (H2O) Molecules
CNT, d = 5 nm
Capillary filling with giant liquid/solid slip: Dynamics of water uptake by carbon
nanotubes, L. Joly, THE JOURNAL OF CHEMICAL PHYSICS, 135, 214705
(2011)
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Ex: Evaporation Self-Assembly
• Evaporation-induced nanoparticle assembly
ME 850Z (Molecular Dynamics Simulation)
Molecular dynamics simulations of evaporation-induced nanoparticle assembly,
S. Cheng and G. S. Grest, J Chem Phys, 138, 064701 (2013)
Vapor Zone
Liquid Zone
Nanoparticles
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Ex: Capture of Volatile Iodine using Zeolite-based Nanostructures
• Using grand-canonical Monte-Carlo method, the “filling” of Iodine is predicted
ME 850Z (Molecular Dynamics Simulation)
Capture of Volatile Iodine, a Gaseous Fission Product, by Zeolitic Imidazolate Framework-8, Sava, Dorina F. and Rodriguez, Mark A.
and Chapman, Karena W. and Chupas, Peter J. and Greathouse, Jeffery A. and Crozier, Paul S. and Nenoff, Tina M., JOURNAL OF THE
AMERICAN CHEMICAL SOCIETY, 133, 12398-12401 (2011)
Zeolite based Nanostructures
Zeolite based Nanostructures
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Ex: Brazing of Two-Metal System
• Cu and Ni atoms are simulated upon brazing
ME 850Z (Molecular Dynamics Simulation)
Molecular dynamics study of liquid metal infiltration during brazing, E. B. Webb
III and J. J. Hoyt, Acta Materialia, 56, 1802-1812 (2008)
Ni Cu
Brazing Interface
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Ex: Slip Flow of Polymer in Nanostructures
• Polymer fluid flow is studied in nanostructures with different solid-fluid interactions
ME 850Z (Molecular Dynamics Simulation)
Rheological study of polymer flow past rough surfaces with slip boundary
conditions, A. Niavarani and N. V. Priezjev, J Chem Phys, 129, 144902 (2008)
LJ Fluid
(Rigid) Nanostructures
(Rough Surface) NanostructuresLJ Fluid
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Ex: Ice Melting
• Ice Melting can be simulated using molecular dynamics simulations
ME 850Z (Molecular Dynamics Simulation)
https://www.youtube.com/watch?v=6s0b_keOiOU
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Ex: Dynamics of an isolated edge dislocation
• The propagation of an isolated edge dislocation in FCC aluminum under shear deformation
ME 850Z (Molecular Dynamics Simulation)
Molecular-dynamics simulation of edge-dislocation dynamics in aluminum, A. Y.
Kuksin, V. V. Stegailov, and A. V. Yanilkin, Doklady Physics, 53, 287-291 (2008)
Isolated Dislocation
Aluminum
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Ex: Cavitation Growth in Liquid Metal
• Cavitation evolution in liquid Pb is studied under negative pressure
ME 850Z (Molecular Dynamics Simulation)
Cavitation in liquid metals under negative pressures. Molecular dynamics modeling and simulation, T. T. Bazhirov, G. E.
Norman, and V. V. Stegailov, J Phys - Condensed Matter, 20, 114113:1-11 (2008)
Pb Liquid MetalCavitation
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Ex: RuBisCO Protein Simulations
• Properties of Ribulose-1,5-bisphosphate carboxylase/oxygenase, (RuBisCO) enzyme (protein) are studied for optimal CO2 to organic form
ME 850Z (Molecular Dynamics Simulation)
http://lammps.sandia.gov/movies.html
CO2
Protein
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