Potenciales de Interacción electroquimico

1Ren Overney / UW Molecular Tribology NME 498A / A 2010

From Classical to

Molecular TRIBOLOGY Contact Forces

- Van der Waals

- Capillary Forces

Contact Mechanics

- Fully Elastic Contact Model (Hertz Theory)

- Elastic-Adhesive Contact Model (JKR)

Tribology Basics

- Amontons Laws, Reynolds Lubrication, Adhesive Model

Molecular Motion, Energetics and Time Temperature Superposition

Eyring Model, Intrinsic Friction Analysis

Molecular Tribology

Ren Overney / UW Molecular Tribology NME 498A / A 2010

Table 1: Short Range Interaction Forces

significant in the range of a few to hundreds of

1.(CH4)

(i) dipole-dipole force(ii) dipole-induced dipole force(iii) dispersion forces(charge fluctuation)

Van der Waals

7 (HF)a strong type of directional dipole-dipole interactionHydrogen Bond

4.3 2.9 3.1

26 (Na)96 (Fe)210 (W)

free valency electron sea interaction(sometimes also partially covalent (e.g., Fe and W)

Metallic bond

N/A170 (Diamond)283 (SiC)Electrostatic force(wave function overlap)Covalent bond

2.8 2.0

180 (NaCl)240 (LiF)Coulombic forceIonic bond

DistanceEnergy (kcal/mol)Type of ForceNature of Bond

Interaction Potentials


Interactions and Surface Forces Van der Waals Interaction (Point Particles)

dipole-dipole or induced-dipole interaction

( ) 6222

21

43)(

Trkuurw

Bo=

Keesom Interaction(rotating dipole interaction)

( ) 622

443)(

rh

rwo

o

=

London Interaction(QED fluctuation)

r

( ) 622

4)(

r

urw

o

o

=

Debye Interaction(induced dipole interaction)

r r

Dipole Dipole Interactions Potential: 1/r6 Potential

6rC)r(w vdwVDW =

w(r

)

Short range VdW 1/r6

attractive (they can also be repulsive)

Long range Electrostatic 1/r

Interactions (sketch)


Cl H+ -

Polar Molecule:Hydrogen Chloride (HCl)

l = 0.127 nm

Permanent Dipole Moment:

u = q l

Induced Dipole Moment:

uind = E

uHCl = 1.08 D(ebye)

1.08HCl

1.85Polar: H2O

0.00Non-polar: CO2

Dipole Moment (D)Chemical

Interactions and Surface Forces Dipole Moment and Polarizability

--

l

+ -+ -

electronic polarizability [C2m2/J]

+/- q charge

1 D = 3.3310-30 C m CO2 = 3.110-40 C2m2/J

Non-Polar Molecule:Carbon Dioxide (CO2)

CO2-E


Interactions and Surface Forces Semi-empirical Potential: Lennard Jones (LJ)

6-12 Potential

=+=

612

126 4 rrrC

rC)r( repvdw

r

()

0

r()

-

Characteristic Parameters collision paramter energy of interaction


Van der Waals InteractionInteractions between 2D and 3D Objects 6r

C)r(w vdwVDW = ( ) DARDW

6

=

R

D

( )DARDW

6

=

Interaction Potential (W)

Two Atoms

Atom-Surface

Sphere-Sphere

Plane-Sphere

Two Cylinders

Two Crossed Cylinders

Plane-Plane

Two Parallel Chain Molecules

Poin

t Int

erac

tion

Bod

y In

tera

ctio

n

Geometry of Interaction

6rC

36DC

)(6 2121

RRRR

DA

+

DAR

6

21

21

2123 )(212

+ RRRR

DAL

DRRA

621

212 DA

5283

rCL

per unit area

Interaction Potential (W)

Two Atoms

Geometry of Interaction

6rC

A = 2 12CHamaker Constant

. molecular number density

w(r

)



Long range VdW 1/D

Point Interaction

Integral Interaction

w(r

)



Long range VdW 1/D

w(r

)



Long range VdW 1/D

Point Interaction

Integral Interaction


1.3592.1PTFE1.67Mica

1.453.78Silicon Oxide (SiOx)3.4512Silicon (Si)

n (refractive index) (dielectric constant)Solid Material

1.4262.03Cyclohexane

n (refractive index) (dielectric constant)

Fluid Environment

( )( )( ) ( ) ( ) ( ){ }2322232123222321

23

22

23

21

32

32

31

31

283

43

nnnnnnnnnnnnhkTA e

+++++

+

+

+

( )DARDW

6

=Van der Waals Interaction Parameter expressed by Field Properties Lifshitz Equation

Lifshitz Eq.

absorption frequency e (e.g., for H2O: e = 3 x 1015 Hz)


Surface Energy

Lifshiz Theory

A/24 Do2

(10 -20) {Do=0.165nm} (20oC)

Liquid helium 0.057 0.28 0.12 - 0.35(at 4-1.6K)

Water 3.7 18 73

Acetone 4.1 20.0 23.7Benzene 5.0 24.4 28.8CCl4 5.5 26.8 29.7H2o2 5.4 26 76Formamide 6.1 30 58

Methanol 3.6 18 23Ethanol 4.2 20.5 22.8Glycerol 6.7 33 63Glycol 5.6 28 48

n- Pentane 3.75 18.3 16.1n -Hexadecane 5.2 25.3 27.5n -Octane 4.5 21.9 21.6n -Dodecane 5.0 24.4 25.4Cyclohexane 5.2 25.3 25.5

PTFE 3.8 18.5 18.3Polystyrene 6.6 32.1 33Polyvinyl chloride 7.8 38.0 39

Material A

Surface Energy, (mJ/m2)

Experimental*

Surface energies based on Lifshitz theory and experimental values.(Source: intermolecular & Surface Forces, J. Israelachvili, Academic Press)


Adhesion and Surface EnergyThe energy of adhesion (or just adhesion), W", i.e., the energy per unit area necessary to separate two bodies (1 and 2)

12 interfacial energy 1/2 surface energy of surface 1 and 2

21211212 22 +== ;W ''

1221

( ) ( )212 o

o

DA

DWDWW

=

==

Do ~ 0.165 nm 212 24 oDA

=


Capillary ForcesCapillary forces are meniscus forces due to third media condensation.

=

s

LK

pplogRT

Vr

cosRF dRmax 4=>>


Capillary Forces

[N]AR.D

RAFFo

stvtotal ==18

2 105124

+= cosDARF water

ototal 424 2

RH < 35%

RH > 40 %

Capillary will dominate

VdW only


Contact Mechanics

Contact Mechanical Models1: Hertz: fully elastic model, JKR: fully elastic model considering adhesion in the contact zone, Bradley: purely Van der Waals model with rigid spheres, DMT: fully elastic, adhesive andVan der Waals model.


Contact Mechanics

Fully Elastic Hertz Model

31

43

= *E

LRa

32

*2

43

==

ELRaA

=

232

321

aa

Ra o 0== Lo aa

Hertz contact radius:

Hertz area of contact:

Mutual approach: with

Hertz pressure:

1

2

22

1

21 11

+

=

EEE*

Youngs Modulus1

21

11

+=

RRR

Combined Radius of Curvature

L Load

( ) 3123

2

26

23

23

=

=

RELp

aLp

*

mmax


( )

+++= 23 363

43 RRLRLERa *

Contact Mechanics

Elastic-Adhesive JKR Model

JKR contact radius:

surface tension

== *JKRadh RLL 23


A system in which only the sample material is compliant

Approach: At "A" two surfaces during approach deform suddenly towards each other and form an adhesive interfacial junction at "B".Retraction: At "C" the adhesive junction is suddenly lost and the force jumps from the upper branch to the lower LJ branch.

The area described by (ABCD) corresponds to the energy dissipated during the approach-retraction cycle.

We assumed an infinitely stiff holding system.

LJ Adhesive Branch (out of contact)

Elastic Contact JKR Branch


A system in which the sample and the probe (cantilever) is compliant

A

B C

D

LJ Adhesive Branch (out of contact)


TribologyThe science of Tribology (Greek tribos: rubbing) concentrates on Contact Mechanics of Moving Interfaces that generally involve energy dissipation


Tribology

Prehistoric to Ancient Times~ 7000 B.C. Northern Norway Skier in rock carving

1880 B.C. Egypt Transport of Eqyptiancolossus on the tomb of Tehuti-Hetep. El-Bersheh.

10


Tribology

Dry and Wearless Friction

Leonardo da Vinci

1. The force of friction is directly proportional to the applied load. (Amontons 1st Law)

2. The force of friction is independent of the apparent area of contact. (Amontons 2nd Law)

3. Kinetic friction is independent of the sliding velocity. (Coulomb's Law)

The classical Laws of unlubricated Friction


Tribology

Dry and Wearless Friction

x

F Fstat

Fstat(x)= kc x Fpull v = 0

L

Fpull

- Fpull xo x1

Fstat Static Friction

0

Fkin Kinetic Friction

Fkin

Fkin Fpull

L

v = const

Def.: Friction Coefficient

LFkin

=

L Load (normal force)

11


Desanguliers (1734) proposed Adhesion Idea

Eulers (18th century) Asperity Interlocking Model

Hardys (1922) Theory of Boundary Lubrication

Bowden and Tabors (~1950) Plastic Adhesive Model

Mode Coupling Entropic Model (Overney, Silss, Knorr ~2004)

Tribology Dry Friction

Friction Theoretical Models


Eulers (18th century) Asperity Interlocking Model


Friction Theoretical Models

NanometerBoundary Regime(ultra thin film regime)

Even Liquids behavesolid-like

Hardys (1922) Theory of Boundary Lubrication

= F/A= G (stress strain relationship)v

12



Friction Theoretical Models Bowden and Tabors (~1950) Plastic Adhesive Model

(i) Real Contact Area defies Amontons second law, i.e., friction is dependent on contact area

Spherical Real Contact

Apparent contact

real contact area

Y.pApA

LF crit

crit,m

crit

rcrit,m

rcritkin 82

===

(ii) Contact Zones (Asperities) are plastically deformed

Y material specificplastic yield stress

Contact radius a determined from Contact Mechanics


vx

y

vo

0

no-slip condition

Tribology

Lubrication Reynolds HL(stress strain rate relationship)

Newtons law of viscosity

yx xdvdy

=

viscosity

Fx, vo

x

y

0

A

yx= = Fx/A

Reynolds Lubrication Assumption for Hydrodynamic Lubrication (HL):

1. The height of the fluid film y is very small compared to the dimensions of the contact area, the pressure is constant across the fluid film,

2. the flow is laminar, i.e., no turbulence occur,3. the inertia of the fluid is small compared to the viscous shear (examples of

inertia forces are fluid gravity and acceleration of the fluid),4. no external forces act on the film.

Fx Drag Force

13


( ) ( ) ( )

x

h px z

h pz

U Uh

xh

xU U V

3 3

1 2 1 26 6 12

+

= + + +

Reynolds Equation of Lubrication

Tribology

Lubrication Reynolds HL

DF vSimplified for parallel plates at close distance D:

V is directly correlated to DGumbel Number NG = P-1

Friction or Drag Force

Hydrodynamic Regime

D

D

D


Tribology

Molecular Atomistic Phenomena

Fluid behavior

StartupPhase

Steady ShearPhase stop

D;t

ADexp oo

v

=

Debye Relaxation

Stick-slip PhenomenaObserved for Ultrathin LiquidsIsraelachvili J.

solid liquid

Model concept: Solid-liquid phase transition

Observed for Molecularly Smooth Surfaces E

x)t(

x)t,x(Ex Mx M =

++

14


Prandtl - Tomlinson Model (1920)


Molecular Stick-Slip

SFM/AFMon bilayerLipid Film

Fave=24 nN

Fave=32 nN

Experimental Verification (1994 Overney)


Eyring Model: Kinetic Jump ModelFriction depends logarithmically

on velocityContrary to Newtons Law (linear)

(for liquids)Contrary to Coulombs Law (constant)

(for solids)

Tribology

Rate Dependence of Friction

+= PQE

P

Q

P

Q

P

Q

E po +=To = '

vln'' += o

Polystyrene

15


Tribology Intrinsic Friction Analysis (IFA)

Superposition of Friction Rate Isotherms

ln(aT) shift

arb. chosen reference line (temperature)

resulting MASTER CURVE

Ea2

1

2

1

T

T

T

TTa

=

Time-Temperature Equivalence

t

log G

log t

log aT2

GT1 GT2

t

log G

log t

log aT2

GT1 GT2



Friction: Relaxation vs. Probing Rate

70

80

90

100

110

120

130

140

1 5 9 13ln( aT * v [nm/s] )

F +

F(

T)

[nN

]

377 K380 K384 K388 K392 K395 K398 K403 K -5

-4-3-2-101234

2.45 2.50 2.55 2.60 2.65 2.70

1000 / T (K)

ln( a

T )

Ea = 88 kcal / mol

The bell shape of F(v)|T originates from the interplay of two dominating time scales (Deborah Number):

e extrinsic experimental time

m material intrinsic time

m

eDe

=

-Segmental Motion

Phenyl Rotation

although distinctively different origin for dissipation, the qualitative difference (log vs. bell-shaped) is not reflecting a fundamental difference

Rubber Melt

Glass

Tg

16



Superposition of Friction Rate Isothermspoly(tert-butyl acrylate) (PtBA)

R

R

H

Cooperative Motion

zero

high for backbones

Backbonerelaxation

E1

E2

Side chainrelaxationEnergetics

'*

STFF



Mode CouplingSlider couples with thermally active modes controlled externally with

Pressure and Temperature

E.g., Pressure addressed Mode Coupling

Side ChainRelaxation

Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol

Side ChainRelaxationSide ChainRelaxation

Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol



Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol

BackboneRelaxation


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol

BackboneRelaxationBackboneRelaxation

Polystyrene

17



Mode CouplingSlider couples with thermally active modes controlled externally with

Pressure and Temperature

E.g., Pressure addressed Mode Coupling


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol



Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol

BackboneRelaxation


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol


Ea = 7 kcal / mol

BackboneRelaxation

Ea = 88 kcal / mol

BackboneRelaxationBackboneRelaxation

Polystyrene

Coupling with Thermally Active ModesCoupling with Thermally Active Modes

Thermally active modes(rotational , translational, vibrational)

Slider 1D motion couples with thermally available mode(s) in sample

Entropy Reduction a Energy Dissipative Process Heat generation follows (coupling of rotational with vibrational modes)

TOP View

SIDE View

Slider Tip

18


Millipede (NEMS) Project a Tribological Challenge

Shear Force Analysis with Hot Tip of Adhesive Forces in Nanocomposites

Flux and Transition Analysis using Friction Forces

Related Topics


Discussed contact forces, in particular adhesion forces and capillary forces.

Introduced contact mechanics, which considers the deformation aspect of contact. Limited discussion to elastic contact.

Addressed dry and lubricated friction in classical phenomenological terms.

Introduced the Eyring activation model a first step towards a molecular description of friction dissipation.

Discussed Molecular stick-slip phenomena and logarithmic friction-velocity behavior directed.

Considered molecular modes of rotation and translation that couple to the sliding motion and extract energy from it.

We concluded that frictional heating is a consequence of a two step process:

(i) slider coupling with intrinsic modes, which leads to entropic cooling (alignment) of molecular modes, which gives rise to energy dissipation,

(ii) followed by mode coupling of the entropically cooled modes with modes of vibrations.

Summary

19

BIT INDENTATIONS30-50 nm

CANTILEVERED READ / WRITE

PROBEQ

SUBSTRATE

POLYMER FILM

20-50 nm

Data storage via small indents in thin polymer films

Thermomechanical Data Storage (TDS)Thermomechanical Data Storage (TDS)

1 Vettiger, et al., IEEE Transactions on Nanotechnology, 1 (2002)

Density well beyond the superparamagnetic limit. (Tb/in2 vs 100 Gb/in2)1

Data rates comparable to todays magnetic devices. (Mb/s)1

A 2D Array of probes is operated in a parallel /

multiplexed manner.

Indentation:

NanoScience & Information StorageNanoScience & Information Storage

Millipede Storage Concept

2 mm 200 m 20 m 2 m

A 2D ARRAY OF LOCAL PROBES IS OPERATED IN A PARALLEL / MULTIPLEX FASHION.

Cantilever Array: (7 14 mm2)

32 32 (1024) Cantilevers

Vettiger, et al., IEEE Transactions on Nanotechnology, 1 (2002)

20

Thermomechanical Data Storage (Millipede)Thermomechanical Data Storage (Millipede)

Modulus and Tg profiles coincide.

0

10

20

30

40

0 50 100 150 200 250

Film Thickness, (nm)

Rel

ativ

e M

odul

us1.00

1.01

1.02

1.03

1.04

1.05

1.06

Rel

ativ

e T

g

Modulus (Si substrate)Modulus (PS-BCB)Tg

MAX ~ 60 nm

Modulus vs. Film ThicknessEffective modulus profile compared to glass transition profile.(normalized with corresponding value

at =150 nm)

Eeff = pm / tan

CANTILEVERED READ /

WRITE PROBE

Q

SUBSTRATE

POLYMER FILM

20-50 nm

15 nm

250 nm

z

d

DRDi

0

Glass Transition and Device Performance:

-200 0 200 400 600 800 1000 1200 1400 1600-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

Late

ral D

ispl

acem

ent (

nA)

Distance (nm)

TEMP

Adhesion Analysis of Silicon Adhesion Analysis of Silicon PTMSP NanocompositesPTMSP Nanocomposites

Fmax

Laser T

B

RL

Fmax

Laser T

B

RL

adhesive interaction energy per unit area PTMSP 180 mJ/m2

21

Water Transport in Proton Exchange Membrane (PEM)

Working principle illustrated on N2 diffusive flux through a Ceramic Zeolite Membrane, measured in-situ with surface morphology.

Local Flux Measurements Relaxations in PEMA: poor water

transportA/B: polymer re-

organizationpromoteswater transport

B: evaporationB/C: Tg=116 oC

1 m

Water Transport Through Nafion (PEM)

J.H. Wei et al., J. Membr. Sci. 279 (2006) 60)

Membrane 1 (M1)

0.0001 0.0002 0.0003 0.0004 0.0005

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

Forc

e-Pr

essu

re G

radi

ent (

nN/k

Pa)

Permeation Flux (mol*s-1*m-2*kPa-1)Fric

tion

/ N2

Pre

ssur

e

Permeation Flux

M1

M3

M2Fluid:Humidified N2(90% RH)

Potenciales de Interacción electroquimico

Documents

surface forces dipole

nmpermanent dipole moment

repulsive long range

q linduced dipole moment

surface forces van

empirical potential

waals capillary forces

c2m2jnonpolar molecule