md simulation introductions

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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)

3

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)

4

Introductions

http://blogs.rep-am.com/

5

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

6

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

8

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

9

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

10

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


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


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)


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


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


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


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


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


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


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


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


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


http://lammps.sandia.gov/movies.html

CO2

Protein

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