1
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
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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
Why study surfaces?Why study surfaces?
Example 1: Miniaturization – everywhere
Memory stick
Integrated circuit
Harddisk
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Material Properties and Characterization - Surfaces M. Heuberger
Why study surfaces?Why study surfaces?
Example 2: MEMS
MEMS ratchet
MEMS hinge
Material Properties and Characterization - Surfaces M. Heuberger
Why study surfaces?Why study surfaces?
Example 3:Forces and Actuation
Large Force Electrostatic MEMS Comb Drive
MEMS Post Style Actuator
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Material Properties and Characterization - Surfaces M. Heuberger
Why study surfaces?Why study surfaces?
Example 4: Nano-Structures
Nanoporous Bio-Assay
E-spun nano-fiber
Material Properties and Characterization - Surfaces M. Heuberger
Why study surfaces?Why study surfaces?
Example 5:Nano-Particles
Quantum Dots
V2O5 Nano-wire
Stabilized Nano-particle
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Introduction
When the material property depends on the surface
Material Properties and Characterization - Surfaces M. Heuberger
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
]
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Material Properties and Characterization - Surfaces M. Heuberger
Playing with „Nano“Playing with „Nano“
„nano“ (greek) = dwarf
Material Properties and Characterization - Surfaces M. Heuberger
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
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Material Properties and Characterization - Surfaces M. Heuberger
Size matters…Size matters…
Mechanical propertiesThermodynamic propertiesElectronic propertiesMagnetic propertiesOptical propertiesChemical propertiesBiological properties
Surface Properties
What are the relevant quantities?
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Material Properties and Characterization - Surfaces M. Heuberger
? Question !? Question !
name 3 surface properties (3‘)
How can they be measured?
Material Properties and Characterization - Surfaces M. Heuberger
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...
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Material Properties and Characterization - Surfaces M. Heuberger
Analysis and Characterization
Analysis and Characterization
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
Surface AnalysisSurface Analysis
1. Probe (excitation)2. Interaction (surface process)3. Signal (information)
surface
1. 2. 3.
Material Properties and Characterization - Surfaces M. Heuberger
Surface SelectivitySurface Selectivity
Requirement
The Probe, Interaction or the Signal must have an exponentially (or steeper) decay within the solid.
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Material Properties and Characterization - Surfaces M. Heuberger
Detection LimitsDetection Limits
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
XPS and SIMSXPS and SIMS
XPS
SIMS
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Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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.
Material Properties and Characterization - Surfaces M. Heuberger
Photoemission ExperimentPhotoemission Experiment
primary: X-Ray (~1.5KeV)interaction: photo-electric effectsecondary: electrons
photo emission
hν
Ekin
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Material Properties and Characterization - Surfaces M. Heuberger
X-Ray SourcesX-Ray Sources
CuMgAl
Crystal-Monochromator
Synchrotron
Al Kα
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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]
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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∗
Material Properties and Characterization - Surfaces M. Heuberger
Energy of Auger electronsEnergy of Auger electrons
Ekin (Auger) = 509eVAl Kα = 1486.6 eV
Apparent BE = 977.6 eV
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Material Properties and Characterization - Surfaces M. Heuberger
Typical XPS spectrumTypical XPS spectrum
02004006008001000
Inte
nsity
[a.u
.]
02004006008001000
Inte
nsity
[a.u
.]
PMMAPMMA
oxygen KLL Auger
Binding Energy [eV]
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
Typical XPS spectrumTypical XPS spectrum
02004006008001000
Inte
nsity
[a.u
.]
02004006008001000
Inte
nsity
[a.u
.]
PMMAPMMA
Binding Energy [eV]
Material Properties and Characterization - Surfaces M. Heuberger
Surface SensitivitySurface Sensitivity
http://www-group.slac.stanford.edu/sms/images/xps.jpg
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Material Properties and Characterization - Surfaces M. Heuberger
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.
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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°
Material Properties and Characterization - Surfaces M. Heuberger
Quantitative XPSOverlayers
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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Material Properties and Characterization - Surfaces M. Heuberger
Quantitative XPSOverlayers
Quantitative XPSOverlayers
OIR does NOT depend on β!
distinction of different over-layer morphologies
Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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+
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
Typical SpectrumTypical Spectrum
Material Properties and Characterization - Surfaces M. Heuberger
I-SIMSI-SIMS
Si
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Material Properties and Characterization - Surfaces M. Heuberger
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)
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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
Material Properties and Characterization - Surfaces M. Heuberger
What is surface energy?What is surface energy?
Broken symmetry at the surfaceSurface molecules have higher energyless interactions
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Material Properties and Characterization - Surfaces M. Heuberger
Minimum system energy at equilibrium
Minimum system energy at equilibrium
smallest surface to volume ratiospherecurvature 1/r
r
Material Properties and Characterization - Surfaces M. Heuberger
Lowering surface energyLowering surface energy
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Material Properties and Characterization - Surfaces M. Heuberger
Surfactants can lowersurface energy
Surfactants can lowersurface energy
polar
polar
non-polar
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
Surface tension of waterSurface tension of water
1 dyne = 10-5 Newton
[dyne/cm] = [mN/m] = [mJ/m2]
Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
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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Material Properties and Characterization - Surfaces M. Heuberger
? Question ! ? Question !
What objects are shown in the background?
What are their properties?
Material Properties and Characterization - Surfaces M. Heuberger
Answer!Answer!
Multi-walled carbon nano tubes (CNT)
high tensile strengthel. conductive1nm-10nm diameter
-> use in Advanced Fibers