Material Propertiesand Characterization - ETH Z ETH lecture: 151-0637-00 Material Propertiesand...

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ETH lecture: 151-0637-00

Material Properties and Characterization

Manfred Heuberger

Advanced Fibers, Empa, 9014 St. Gallen

Materials Science & Technology

Material Properties and Characterization - Surfaces M. Heuberger

Manfred HeubergerManfred Heuberger

EMPA - ETH

2


8h about Surfaces8h about SurfacesIntroduction

When the material property depends on the surface1.5h Surface Properties

What are the relevant quantities?Analysis and Characterization of Surfaces (XPS, SIMS)

1.5h Intermolecular Interactionsintermolecular forces (Van der Waals, electrostatic forces, entropic forces)Integration: from intermolecular to surface forcesMacroscopic forces (Kapillary Forces, Young-Laplace equation)

1h Exercises (magnitudes, ranges, XPS spectra)

1.5h Static Surface ForcesLifschitz TheoryHamaker constantForces at solid-liquid interfaces (Hydrophilic, double-layer, depletion, structural forces)Forces at polymer interfaces (steric forces, brush, bridging,…)Forces on biological surfaces (membranes, specific interaction)

1.5h Dynamic Surface ForcesAdhesion hysteresis (dynamics of surfaces, WLF)Macroscopic friction (with / without lubrication)Introduction to NanotribologieMeasurement of surface forces (AFM, SFA)

1h Exercises (integration, Hamaker, steric repulsion)

Part 1

Part 2


Why study surfaces?Why study surfaces?

Example 1: Miniaturization – everywhere

Memory stick

Integrated circuit

Harddisk

3



Example 2: MEMS

MEMS ratchet

MEMS hinge



Example 3:Forces and Actuation

Large Force Electrostatic MEMS Comb Drive

MEMS Post Style Actuator

4



Example 4: Nano-Structures

Nanoporous Bio-Assay

E-spun nano-fiber



Example 5:Nano-Particles

Quantum Dots

V2O5 Nano-wire

Stabilized Nano-particle

5

Introduction

When the material property depends on the surface


Surface to Volume RatioSurface to Volume Ratio

500x106

400

300

200

100

0

Rat

io F

/V [m

-1]

10-10 10-5 100 105 1010

Radius of Sphere [m]

R[m-1

]

6


Playing with „Nano“Playing with „Nano“

„nano“ (greek) = dwarf


Just a piece of surface…Just a piece of surface…

Number of atoms?7x7x7=343 atoms

Number of surface atoms?210 atoms (60%)

1 nm = 10-9 m = 0.000 000 001m

7


Size matters…Size matters…

Mechanical propertiesThermodynamic propertiesElectronic propertiesMagnetic propertiesOptical propertiesChemical propertiesBiological properties

Surface Properties

What are the relevant quantities?

8


? Question !? Question !

name 3 surface properties (3‘)

How can they be measured?


Surface propertiesSurface properties

Hydrophobic/hydrophilic ratioSurface energySurface potentialSurface chemistry (functional groups)Biologic activity (receptor sites)Swelling potential (hydrogel character)Molecular mobility, relaxationsTopography (roughness, texture)Crystalline/amorphous characterOrientation (tilt angle, conformation)Domain, phase separation...

9


Analysis and Characterization

Analysis and Characterization


Devil‘s Work…Devil‘s Work…

Problem 1: Surface SensitivityProblem 2: Cleanliness

The physicist Wolfgang Pauli (1945 Nobel Prize in Physics)once remarked:

"God made solids, but surfaces were the work of the devil"

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Surface SensitivitySurface Sensitivity

Cube: 1cm x 1cm x 1cm

1cm

Question:How many atoms are in this cube?

Answer: ~1024 Atoms

Question:How many atoms are on one surface?

Answer: ~1016 Atoms

Volume to Surface Ratio: 100’000’000x


Interacting with a surfaceInteracting with a surface

photons (light, X-ray, IR)electronsionsatomsforces (touch, adhesion, friction, confinement) Liquids interfacing (spreading, wetting)chemical reactions (catalysis)specific interactions (protein activity)non-specific interactions (adsorption)...

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Surface AnalysisSurface Analysis

1. Probe (excitation)2. Interaction (surface process)3. Signal (information)

surface

1. 2. 3.


Surface SelectivitySurface Selectivity

Requirement

The Probe, Interaction or the Signal must have an exponentially (or steeper) decay within the solid.

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Detection LimitsDetection Limits


Surface CharacterizationTechniques

Surface CharacterizationTechniques

Electron spectroscopiesESCA/XPS, AES

Ion spectroscopiesSIMS, ISS

Vibrational spectroscopiesATR/FT-IR, HREELS

Direct force methodsSTM, AFM/LFM, SFA

Contact angle methodsContact angles, Wilhemly

balance

Diffraction methodsTEM, grazing-XRD

Evanescent field methodsSPR, OWLS

Interference methodsQCM

Optical techniquesSEM (e-), CLSM, Ellipsometry

(laser)

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Surface CleanlinessSurface Cleanliness

The monolayer time, τ, is the time it takes to cover a surface with a single layer of molecularadsorbates.It can be estimated from:

τ =

where t is in seconds, and P is in millibar.

This assumes unity "sticking coefficient".

3.2 x 10-6

P


Vacuum technologyVacuum technology

Idealized initial pumpdown of a 100 l system, size 50 x 50 x 40 cm, with a 6 CFM roughingpump and 200 l/s UHV pump. Typical pumpdown cycle…

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A single fingerprint can betoo much…

A single fingerprint can betoo much…

Clean surfaces are high energy surfaces

They cover themselves with adsorbents to lower energy.

Sources of Contaminants:

airborne, pump oil, plasticisers, degasing, fingerprint…

Surface specific techniques are therefore extremely sensitive to surface contamination (the more surface specific, the worse...) and this can be catastrophic for surface identification


XPS and SIMSXPS and SIMS

XPS

SIMS

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Overview: XPS and SIMSOverview: XPS and SIMS

Depth profiles

XPS, SIMS XPS, SIMS

SIMSXPS

Sample

Depth analysed

Primary beam

e-photohν

Secondary particles to detector

Sample

Ions (Ga+) Ions & molecular ions

under UHV - 10-9 mbar

vacuumtechnique

Information:

SIMS

Spectra

XPS

Imaging

X-Ray PhotoelectronSpectroscopy: XPS

Electron Spectroscopy for Chemical Analysis (ESCA)

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1921 Nobel Prize1921 Nobel Prize

In 1921 Einstein won the Physics Nobel Prize, not for relativity, but forthe photoelectric effect.

Electrons can absorb energy from photons. They follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or the energy is re-emitted. If thephoton is absorbed, some of the energy is used to liberate it from the atom, and the rest contributes to the electron's kinetic (moving) energy as a freeparticle.

Einsteins conclusion “The light is quantized” launched quantum theory.


Photoemission ExperimentPhotoemission Experiment

primary: X-Ray (~1.5KeV)interaction: photo-electric effectsecondary: electrons

photo emission

hν

Ekin

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X-Ray SourcesX-Ray Sources

CuMgAl

Crystal-Monochromator

Synchrotron

Al Kα


Using PhotoemissionUsing Photoemission

Idea!

Determination of electronic binding energies (Eb) of electrons emitted from the core levels of an atom resulting from X-ray irradiation of the sample (photoelectric effect).

The emitted photoelectrons are collected by an electrostatic energy analyzer as a function of their kinetic energy (Ekin), from which the binding energies (Eb) can be obtained using the Einstein relation

Eb = hν - Ekin - φPhotoelectron emission

e-photohν

ESCA/XPS

2p3/2 (L3)2p1/2 (L2)

2s (L1)

1s (K)

Photoelectron emission

e-photohν

ESCA/XPS

2p3/2 (L3)2p1/2 (L2)

2s (L1)

1s (K)

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Where the energy can goWhere the energy can go

2s 2p1s

1) Photoemission O1s

2s 2p1sa)

b)

2) Relaxationa) Auger e- emissionb) X-Ray fluorescencephotoelectron

Auger electron

Photon


Measuring kinetic energyMeasuring kinetic energy

Energy analyser CHA

E lectron optics

Electron detector

Sample

Mg K α1,2 source

e -h ν

Main X-ray sources

E = hν ΔEAl Kα1,2 1486.6 eV 0.85 eVMg Kα1,2 1253.6 eV 0.7 eV

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Typical XPS spectrumTypical XPS spectrum

02004006008001000

Inte

nsity

[a.u

.]

02004006008001000

Inte

nsity

[a.u

.]

Fermi level

valence band (UPS)

core levels

PMMAPMMA

oxygen KLL Auger

Binding Energy [eV]


XPS Reference DataXPS Reference DataC1s

O1s

Handbook of X-ray Photoelectron Spectroscopy; J. Chastain, R.C. King ed., 1995, Physical electronics Inc., Minnesota, US

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Secondary PeaksSecondary Peaks

• X-ray source satelites

• surface plasmons

• electron system shake-ups

•Auger electrons (shift with X-ray energy)

binding energy

equal distance

π −> π∗


Energy of Auger electronsEnergy of Auger electrons

Ekin (Auger) = 509eVAl Kα = 1486.6 eV

Apparent BE = 977.6 eV

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02004006008001000

Inte

nsity

[a.u

.]

02004006008001000

Inte

nsity

[a.u

.]

PMMAPMMA

oxygen KLL Auger

Binding Energy [eV]


Electron mean free pathElectron mean free path

M. P. Seah and W. A. Dench, Surface and Interface Analysis, 1, 2-11 (1979)S. Tanuma, C. J. Powell and D. R. Penn, Surface and Interface Analysis, 11, 577-589 (1988) and 21, 165-176 (1993).

5.02 )( kinkin

aEBEA

+=λ

As first approximation: λ = BEkin0.5

With : B = 0.087 for organicsB = 0.096 for inorganics

usually: 0.4 nm < λ < 4 nm

Example: (MgKα) λ(C1s) ≈ 34 Åλ(O1s) ≈ 29 Åλ(N1s) ≈ 32 Å

Other estimations by Tanuma et al. give similar results in the 700-1100 eV Ekin range.

Estimation of inelastic mean free path(Seah & Dench relation):

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02004006008001000

Inte

nsity

[a.u

.]

02004006008001000

Inte

nsity

[a.u

.]

PMMAPMMA

Binding Energy [eV]


Surface SensitivitySurface Sensitivity

http://www-group.slac.stanford.edu/sms/images/xps.jpg

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Quantitative XPSTheory

Quantitative XPSTheory

Samplez

e- photohν

α

The peak intensity detected for element A (IA) is a function of the corresponding element concentration distribution throughout the sample:

IA = IRXσ A f (Ekin) CA(z)exp(−z

λA sinα)dz

0

∞

∫

IA: intensity of the measured photoelectron signal

IRX : intensity of the primary X-ray sourceσA: cross section for emission of a photoelectron from an inner core shell of Af(Ekin): detection efficiency of the spectrometer for each electron emittedCA: concentration of A as a function of depth (z)λA: inelastic mean free path of a photoelectron emitted from Aα: emission angle of the photoelectron with respect to the surface of the sample.


Quantitative XPS Measurement

Quantitative XPS Measurement

The concentration of element A in a homogeneous matrix of n elements can be determined from a quantitative XPS measurement by the relation:

CA =

IAs A

Σi=1

n I isi

si: atomic sensitivity factor: accounts for instrumental factors and for the cross-section of the photon-electron collision.

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AR-XPSAR-XPS

Information depth

Primary Xray source Detector

Substrate

Grazing emission angle θ

Primary Xray source Detector

Substrate

Normal emission angle θ

θ

Information or sampling depth (95% of total signal intensity): Z = 3λ sinθ


AR-XPSDDP / Nb2O5

AR-XPSDDP / Nb2O5

Nb3d

120x10 3

100

80

60

40

20

0

coun

ts [a

.u.]

1000 800 600 400 200 0

binding energy [eV]

XPS Survey spectrum 45°

Nb3p

C1s

O1s

P2pNb4pP2s

OKLL

45°

15°

75°

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AR-XPSDDP / Nb2O5

AR-XPSDDP / Nb2O5

35x103

30

25

20

15

10

5

0

coun

ts [a

.u.]

300295290285280

binding energy [eV]

'C1s@15°' 'C1s@75°'

C1s

35x103

30

25

20

15

10

5

0

coun

ts [a

.u.]

215210205200

binding energy [eV]

'Nb3d@15°' 'Nb3d@75°'

Nb3d

40x10 3

30

20

10

0

coun

ts [a

.u.]

545540535530525

binding energy [eV]

'O1s@15°' 'O1s@75°'

O1s

45°

15°

75°


Quantitative XPSOverlayers


e- e-

e- e-

T(Ekin) is the transmission function of the XPS analyzer. β [%]: over-layer surface coverage

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OIR does NOT depend on β!

distinction of different over-layer morphologies


XPS Quiz !XPS Quiz !

1. What features in the XPS spectrum are due to elastic electrons?

2. Why has the XPS spectrum stair-steps at each peak?

3. What are the advantages / disadvantages of a monochromator?

4. Why is XPS a vacuum technique?

5. Is shake-up an alcoholic drink?

?

main Peaks

inelastic scattering of electrons

resolution / less intensity

electron scattering, Cleanliness

no, an excitation of the π electrons

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Secondary IonsMass Spectroscopy: SIMS

Time-of-flight Secondary Mass Spectroscopy – Tof-SIMS


The three modes of SIMSThe three modes of SIMS

Static SIMS (S-SIMS)Minimal sample degradation, topmost surface atomsStatic limit: total primary ion dose < 1013 ions/cm2

Sampling depth < 1 nm

Dynamic SIMS (D-SIMS)Depth profiling applications (sputtering rates ≥ 100 Å/min)Sampling depth 1-5 nm

Imaging SIMS (I-SIMS)Chemical imagingSampling depth 3-10 nm

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Secondary Ions fromIon Bombardement

Secondary Ions fromIon BombardementPrimary ions

1012 ions cm-2 max.

BC+C+

A+

ABCABCAB+

ABCAB+ABC+

ABCABCAB+

1 monolayer ≈ 1015 atoms cm-2

Cs+Cs+


Mass SpectroscopyMass Spectroscopy

Electrodynamic Buncher

Cs+ ion gun

ESA 1

ESA 3ESA 2Energy slit

DetectorLiquid Metal Ion Gun

Electron Neutraliser

Sec. El. Detector

Laser

IL

sampleTL 1 TL 2 Contrast Diaphragm

High Speed DeflectorIL

Deflector Plates

Animation:(Forschungszentrum Jülich)

Tofsim.swf

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Typical SpectrumTypical Spectrum


I-SIMSI-SIMS

Si

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Comparing XPS and SIMSComparing XPS and SIMS

ESCA/XPSElemental analysis (Z>2, 0.1-1% monolayer)Determination of oxidation state of elementsFunctional group identification (± 0.3 eV)Surface quality controlQuantification (± 5-10%)Composition vs depth

2-10 nm (AR-XPS)> 10 nm (depth profiling)

Determination of oxide or SAM thicknessesChemical imaging (± 5-1000 µm)Sample chargingStudy of surface reorganisation (with or without cold-stage)

ToF-SIMSElemental analysis (10-3 monolayer, mass range easlily up to 10000 amu)IsotopesChemical structure (m/Δm > 3000)Surface quality controlLimited quantification (matrix effects)Composition vs depth

Sampling depth < 10 Å (static mode)> 1 nm (dynamic SIMS)

Chemical imaging (> 100 nm)Sample charging very problematicStudy of surface reorganisation (with cold-stage)


Sample charging effectsSample charging effects

Problem related to insulating samples (bio-polymer, ceramics...)

Cherging mechanismXPS:

charging via emission of photoelectronsa positive charge builds up at the surfaceaffects emission efficiency and the binding energy (drift to higher Eb).

SIMS: charging due to positive primary ions bombardmentSpecial problem for negative ions mass spectrumloss of intensity and high-mass fragments detection

Charging generally not stable with time and not homogeneous throughout the sample (depends on chemical, morphological, ..., heterogeneity).

Neutralization with low energy electron flood gun: help but not ideal; can also induce significant sample damage.

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XPS Quiz !XPS Quiz !?

1. Why is XPS surface-selective?

2. Why is SIMS not as quantitative?

3. Why does one work in vacuum?

4. Why does Tof-SIMS use pulsed primary ions?

5. How can one realize the imaging mode (i-XPS, i-SIMS)?

Electron free path very short

Not all secondary fragments are charged

Cleanliness, Scattering of electrons and ions

To measure time-of-flight

i-XPS: electron optics; i-SIMS primary ion beam

Intermolecular Interactions

What are the forces between two molecules?

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Forces in NatureForces in Nature

Grand Unifying Theory (GUT)

Strong nuclear interaction(gluons)

Electro-weak interaction(kaons)

Electrostatic Interaction(photons)

-> (vacuum) surface forces

Gravitational interaction(tachions)

The nature of Surface ForcesThe nature of Surface ForcesThe nature of Surface ForcesQ: Are Surface Forces “fundamental” forces?

A: No, except charged surface interaction in vacuum. (Surface Forces are structure and thermodynamics)

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Thermodynamic ForcesThermodynamic ForcesThermodynamic ForcesThermodynamics

Steric forcesOsmotic forcesEntropic forces

important in colloid science

What exactly are Surface Forces?What exactly are Surface Forces?

Range of Surface Forces?Surface: Interface ±10nmSurface Forces <-> Intermolecular Forces

Strength of Surface Forces?Where are Surface Forces important?

What is a Dynamic Surface Force?How can one measure a Surface Force?

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Who is studying SurfaceForces?

Who is studying SurfaceForces?

Prof. B. Derjaguin, Moscow (50‘s)Prof D. Tabor, Cambridge, UK (70‘s)

Prof. Jacob Israelachvili, UCSB, USA

Other labs

Historic opinionsHistoric opinions“One of the fundamental problems of science is to establish the effective ranges of

molecular attractions:

1) The classical physicists of the 19th century considered that there were direct forces of attraction over distances... up to many microns.

2) During the first decades of the 20th century, however, the recognition of the electrical structure of matter influenced scientific opinion to assume, without new evidence, that the direct range of molecular attraction amounted to only a few Ångstrom units; and an extreme view, under the influence of Langmuir, held that not adjacent molecules, but only their adjacent atoms had any important influence upon each other.

3) A third point of view recognizes the short range of direct attraction but considers that it must be relayed from molecule to neighboring molecule through impressive distances. The conflicting consequences of these beliefs are of the greatest importance.”

McBain in Colloid Science, (1950)

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First direct measurement

Range ≈ 1µmRoughnessSurface charging problematic

Derjaguin, 1951

Intermolecular forcesearly concepts

Van der Waals forces in gas equation, 1873 (P +a

V 2 ) ⋅ (V − b) = R ⋅ T

w(r) = −C1

r n +C2

rmEmpiric potential by Mie, 1903

Intermolecular forces Surface Forces

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Power laws and decay lengths

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

pair

pote

ntia

l [a.

u.]

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

distance [m]

n=1

n=2n=3

n=4n=5

n=6

y=10-10n

/xn

Surface forcesStarting point: w(r) = −

Cr n

z

x

z=0 z=D

dzdx

xr = (z2+x2)1/2

D

dV

dV = 2π ⋅ x ⋅ dx ⋅ dz

assumption:pair additive

Wms (D) =−2π ⋅C ⋅ ρ

(n − 2)(n −3)Dn−3 Wms (D) =−π ⋅ C ⋅ ρ

6D3

n=6

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Electrostatic Surface Forces8.2.1 Electrostatic Interactions

Coulomb Potential

wCb (r) =Q1 ⋅ Q2

4π ⋅ ε0 ⋅ ε ⋅r=

z1 ⋅ z2 ⋅ e2

4π ⋅ε0 ⋅ε ⋅ r

Interaction charge-surface

Fcs(r) =d

dDwcs(r ) =

σ ⋅ e2π ⋅ε0ε

⋅D

D2 + R2−1

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

R→∞⎯ → ⎯ ⎯ −σ ⋅ e

2π ⋅ε0ε

Integration:additivity

strong interactionNearly independent of Dstrong interactionNearly independent of D

surface charge density, σ

point charge, Q1distance, D

Rr

D2+r22

dA=2πrdr D2+r22

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Experimental Consequences

ProblemsDifficult to measure other (weaker) interactionsHigh electric fields in contact area

SolutionsScreening of charges by ionsRemoval of charges by conductance

Electrostatic Surface Forces8.2.2 Van der Waals forces and potentials

e-

p-

Electrostatic Nature of matter

polarizability, αpermittivity, εdispersion, ε(λ)permanent charges, σpermanent dipoles, µ

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Van der Waals forceVan der Waals force

Johannes Diderik van der Waals (1837 - 1923 )

Gecko and ist feet

Van der Waals - many faces

strongubiquitous(always) attractive

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The three most important contributions to

Van der Waals interactions

Dispersion interaction (London)Dipole-induced dipole interactions (Debye)Rotating dipole-dipole interactions (Keesom)

The London interaction

Descriptionpolarizability, α

London interaction energy(quantum mechanics)

rαα

w(r) = −3hυα 2

4(4πε0ε)2 ⋅r 6

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The Debye interactionDescription

dipole moment µrotational angle Θ1

polarizability, α

Electric dipole field

µΘ

rα

E(r,Θ) =μ 1+ 3cos2 Θ

4πε0ε ⋅ r3

The Debye interaction

w(r,Θ) = −12

α ⋅ E2 (r) = −μ 2 ⋅α ⋅(1+ 3cos2 Θ)

2(4πε0ε)2 ⋅ r6

w(r,Θ) = −μ2 ⋅ α

(4πε0ε)2 ⋅ r6After angular integration:

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The Keesom interaction

µ1 µ2

Θ1 Θ2r

Θ3

Description

dipole moments µ1 and µ2

rotational angles Θ1, Θ2 and Θ3

w(r,Θ1,Θ2,Θ3) = −μ1 ⋅ μ2

4πε0ε ⋅ r3 (2cosΘ1 ⋅ cosΘ2 − sinΘ1 ⋅ sinΘ2 ⋅ cosΘ3)

w(r,0,0,Θ3) =2μ1 ⋅ μ2

4πε0ε ⋅ r3Maximum interaction

The Keesom interaction

µ1 µ2

Θ1 Θ2r

Θ3

Angular-spatial Integration

Integral Zero for free rotationBoltzmann distribution favors attractive angles

w(r) ≅ −μ1

2 ⋅ μ22

3(4πε0ε)2 kT ⋅ r6for kT >

μ1μ 2

4πε0ε ⋅ r3

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Van der Waals Surface ForcesExperimental evidence of retardation effects

range <10nmretardation >5nm

-> Hamaker constant


What is surface energy?What is surface energy?

Broken symmetry at the surfaceSurface molecules have higher energyless interactions

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Minimum system energy at equilibrium

Minimum system energy at equilibrium

smallest surface to volume ratiospherecurvature 1/r

r


Lowering surface energyLowering surface energy

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Surfactants can lowersurface energy

Surfactants can lowersurface energy

polar

polar

non-polar


Surface energy and surface tension

Surface energy and surface tension

Surface energy = [J/m2] = [Nm/m2] = [N/m] = surface tension

J/m2

1m1m

1N

1m

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Surface tension of waterSurface tension of water

1 dyne = 10-5 Newton

[dyne/cm] = [mN/m] = [mJ/m2]


Young-Laplace equationYoung-Laplace equation

r1

r2

dr

pressure, pi

outside pressure, p0

area: A = 4 π R2 dA = 8 π R dR

volume: V=4/3 π R3 dV = 4 π R2 dR

work: ΔW = 0 = γ dA – (pi-p0) dV = γ 8 π R dR – Δp 4 π R2 dR

Δp = 2 γ / R = γ (1/r1 + 1/r2)

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1805 independent derivation of equation

1805 independent derivation of equation

Thomas Young (1773-1829)Pierre-Simon Laplace (1749-1827)

Exercises1) Plot the Lennard-Jones pair-potential and the resulting pair- force in a graph. At what separation, r, is the equilibrium distance (F=0)? Below which separation does the repulsive term start to dominate?

2) To directly measure Lennard-Jones-type forces between macroscopic bodies, does one need the entire bodies to be present? What is the critical exponent, n, in a potential of type w(r)=-A/rn , below which the total energy of interaction starts to depend on the entire body?

3) Compare the Keesom energy to kT. Up to what distance are dipolar typically molecules oriented?The dipole moment of water is µ=1.854D (Debye), where 1D=3.33564*10-30Cm, the relative permittivity of water is ε=78.54 and the permittivity of vacuum is ε0=8.854*10–

12As/Vm, the Boltzmann constant is k=1.38*10-23J/K.

4) The DLVO theory is known to fail at high salt concentrations and/or small distances. What could be the reason(s) for this, and, in which sense do you expect the real forces to deviate from the theory?

5) Using Archimedes law, show that two bodies of mass m1=V1*ρ1 and m2=V2*ρ2 are experiencing a repulsive gravitational force if immersed in a medium of density ρ3 when either one of the conditions ρ1<ρ3<ρ2 or ρ2<ρ3<ρ1 applies.

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? Question ! ? Question !

What objects are shown in the background?

What are their properties?


Answer!Answer!

Multi-walled carbon nano tubes (CNT)

high tensile strengthel. conductive1nm-10nm diameter

-> use in Advanced Fibers

Material Propertiesand Characterization - ETH Z ETH lecture: 151-0637-00 Material Propertiesand...

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