new perspectives on van der waals – london dispersion interactions of materials: wetting, graded...

New Perspectives on van der Waals – London Dispersion

Interactions of Materials: Wetting, Graded Interfaces and Carbon Nanotubes

R. H. French1,2, R. Rajter3

1. DuPont Company, Central Research & Development, Wilmington, DE U.S.A.

2. University of Pennsylvania, Materials Science Department, Philadelphia, PA, U.S.A.

3. Mass. Inst. Of Tech., Materials Science Department, Cambridge, MA, USA

http://www.lrsm.upenn.edu/~frenchrh/index.htm

2

DuPont Co. Central Research, Univ. of Pennsylvania, Materials Science, R. H. French © 2007 April 19, 2023 VuGraph 2

Acknowledgements

Spectroscopy• G. L. Tan (UPenn)• M. K. Yang (DuPont)• M. F. Lemon (DuPont)• D. J. Jones (DuPont)

Polystyrene• K. I. Winey (UPenn)• W. Qiu (DuPont)

SiO2: Amorphous & Quartz• G. L. Tan (UPenn)

SrTiO3

• K. van Benthem (ORNL)• M. Ruhle (MPI-Stuttgart)• C. Elsasser (MPI-Stuttgart)• Manfred Rühle (MPI-Stuttgart)

Carbon Nanotubes• R. Rajter (MIT)• W. C. Carter (MIT)• Y. M. Chiang (MIT)• W. Y. Ching (Univ. Missouri–Kansas City)• L. K. Denoyer (Deconvolution.com)• V. A. Parsegian (NIH)• R. Podgornik (Slovenia)

3


Dispersion Contribution to Surface Free EnergyLondon Dispersion Energy

• Thermodynamic Free Energy Arising From• London Dispersion Interaction

• Dispersive Component Of Surface Free Energy

Electrodynamic &

Polar Interactions

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1arccos

123

121

A

Aθ

DiiodomethaneNon-polar

Polystyrene

WaterPartially Polar

PolarDisp ã+ã=ã .

Polystyrene R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, 251-63, (2007).

4


vdW-Ld Interactions: Outline

Optically Isotropic, Plane Parallel Morphology• Polystyrene

• SrTiO3: 5 And 13 Grain Boundaries

Optically Anisotropic, Plane Parallel Morphology• [6,5,s] and [9,3,m] Carbon Nanotubes:

• Plates Of Close Packed CNTs

Optically And Morphologically Anisotropic• [6,5,s] and [9,3,m] Carbon Nanotubes

• Cylinder – Cylinder Interactions

• Cylinder – Substrate Interactions

Conclusions

Optically IsotropicPlane Parallel Morphology

Hamaker Constants and Coefficients

London Dispersion Energies

With Effects Of Retardation

Arbitrary Numbers Of Layers (Add-A-Layer)

6


Origin of The vdW-London Dispersion InteractionLondon Dispersion Interactions• Of the Van der Waals Interaction• Thermodynamic Free Energy

Arises From Oscillating Dipoles• Interatomic Bonds of Elect. Struc.

Jcv => London Disp. Spectra

A - Hamaker Constant• Interaction Scaling Constant

Fdisp - Dispersion Force

Attractive Force: Nonwetting• Positive Hamaker Constant

Repulsive Force: Wetting• Negative Hamaker Constant

zJ = zeptoJoule = 10-21 Joules

A123

71 zJ

8 zJ

Water AirPS

PS

Disp. Force

Air PS

Water

Disp. Force

PS PS

212

)(

l

lAE DispersionLondon π

−=

-16 zJ

Mat. 1. Mat. 2.s

p p

s

p p

7


VUV Reflectance and Interband Transitions VUV Reflectance

• Linear Response Function

Obeys Kramers Kronig Dispersion

Interband Transition Strength • Complex Optical Property

• Related To Dielectric Function

( ) ( ){ }θ

πρ

EE E

E EE= −

−

∞

∫2

2 20

Pln '

d'

'

M. L. Bortz, R. H. French, Appl. Phys. Lett., 55, 19, 1955-7, Nov. 8, (1989).

R. H. French, Phys. Scripta, 41, 4, 404-8, (1990).

M. L. Bortz, R. H. French, , Appl. Spect., 43, 8, 1498-1501, (1989).

*212

2

)(8

π

iE

iJ cv +=

0

5

10

15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Energy (eV)

0

5

10

15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Energy (eV)

File 2 = E:\STUTT\X\POLYMERSESOP\AUS\PMMAD.SPCFile 1 = E:\STUTT\X\POLYMERSESOP\AUS\PESTD.SPC

0

1

2

3

4

0

2

4

6

8

10

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Energy (eV)

File 3 = E:\STUTT\X\POLYMERSESOP\AUS\PSD.SPC

Reflectance of PS

Interband Transition Strength: Im [Jcv] of PS

Interband Transition Strength: Re [Jcv] of PS

n

PS

Im[J

cv]

(eV

2 )

R

e[Jc

v] (

eV2 )

8


Electronic Structure Of PolystyreneHierarchy Of Interband Transitions

• Aromatic π→ π*

• Nonbonding: n→ *

• Saturated: → *

File 2 = E :\STUTT\X\POLYMERSESOP\AUS\PMMAD.SPCFile 1 = E :\STUTT\X\POLYMERSESOP\AUS\PESTD.SPC

0

.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10 12 14 16 18 20

File 3 = E :\S TUTT\X\P OLYME R SE S OP \AUS \PS D.S P C

E1: Aromatic pi - pi*

E3: C-C sigma - sigma*

E1'

E1

E2

E3E3'

Energy (eV)

Interband Transition Strength - Re[Jcv] (eV )

2

n

PS

R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, 251-63, (2007).

9


London Dispersion Spectra

Using Lifshitz Theory, QED• Acquire Exp. Spectra• Calc. London Disp. Spectrum

• Kramers Kronig Transform

• Then Hamaker Constant• Calc’d by Spectral Differences• of London Disp. Spectra

ωξωωω

πξ di ∫

∞

++=

022

)("21)("

0

.5

1

1.5

2

2.5

3

3.5

Im[Jcv] (eV^2) / Energy (eV) Overlay X-Zoom CURSORFile #14 : PSTY6T

Res= 1 #568,POLYSTYRENE,ALTHOR,,300,NO,SAMBOX ROUGHBK

PSWater

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Energy (eV)

Im[Jcv] (eV^2) / Energy (eV) Overlay X-Zoom CURSORFile #14 : PSTY6T

Res= 1 #568,POLYSTYRENE,ALTHOR,,300,NO,SAMBOX ROUGHBK

PSWater

R. H. French, J. Am. Ceram. Soc., 83, 2117-46 (2000). R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, 251-63, (2007).

)(" ξ i

10


Optically Isotropic, Plane Parallel: vdW-Ld Formalism

Example: A123 Non-retarded

G(l): Thermodynamic Free Energy

Are Spectral Difference Function• Between Half Space Material L or R• And Interlayer Material m

Represent The Optical Contrast

Also Implemented: • Add-A-Layer: Up To 99 Layers• Graded Interfaces• Full Effects Of Retardatio

11


Gecko Hamaker: Open Source Hamaker Program

Full Spectral, Retarded Hamaker, Coefficientshttp://geckoproj.sourceforge.net/

12


-18

-16

-14

-12

-10

-8

-6

-4

-2

0

0 5 10 15 20 25 30 35 40 45 50

Zeptojoule / nm Overlay X-Zoom CURSORFile #25 : PSWATVACA Res=None

Non-Retarded

PS | Water | Air

Wetting

Distance (nm)

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30 35 40 45 50

Zeptojoule / nm Overlay X-Zoom CURSORFile #26 : PSWATERPSA Res=None

Non-Retarded

PS | Water | PSNon-Wetting

Distance (nm)

Speed of Light Plays a Role• Transit Time Important

Higher Energy Bonds• Induced Dipoles De-Phase• Contribution Drops

Nonwetting• Attractive Dispersion Force

Wetting• Repulsive Dispersion Force

Retardation Length • Can Exceed 300 nm• Depending On Details Of System

Retarded Hamaker Coefficients

Water

Force

PS PS

AirWaterPS

13


Compare Energies From Hamaker Const. & Contact Angles Use Hamaker Constants

=> Surface Energy

Interface Energy

Fowkes Method• Using Non-polar & Polar Liquids

Experimental Uncertainties• Polar Components Retract Into Free Surface

2.11

1.1. 242

1

o

vMatMat d

AE

πγ =−=

2.31

3.1.3.1. 242

1

o

vMatMatMatMat d

AE

πγ =−=

1PS

1PS

2Air

Force

1PS

1PS

3Water

Force

Surface Energy Of Polystyrene (mJ/m2)

Full Spectral Hamaker Polymer Handbook Fowkes Method

Dispersive Component 34.7 32.5 - 33.9 40.6 – 43.2

Polar Component 6.8 – 8.2 0 - 1.8

Surface Free Energy 37.5 - 40.7 41.2- 43.8

DiiodomethaneNon-polar

Polystyrene

PolarDisp ã+ã=ã .

R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, 251-63, (2007).

14


Gradient Properties in Grain Boundaries of SrTiO3

Index of Refraction • 5 Grain Boundary = 1.56• n13 Grain Boundary = 1.29

n=2.37 for bulk SrTiO3,

• Spectroscopic Ellipsometry.1

Valence Electron Density Variations• From Oscillator Strength Sum Rule

Units of Electrons Per nm3

• for bulk SrTiO3 5 and n13 GB

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

-12 -8 -4 0 4 8

re [jcv / energy (ev)File #20 : STOS5GT

Index of Refraction [n]

Distance (nm)

13

5

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80

File # 3 : STOS13BS

SrTiO3:Fe, Sigma13, Klaus,,KK(c00431o)n2.37(1 ,42)n2.37(62,92)tr0 -93Hew3 ,C00436T

Energy (eV)

Oscillator Strength Sum Rule (electrons/nm )

3

Bulk

5

13

K. van Benthem, C. Elsässer, R. H. French, J. Appl. Phys, 90, 12, 6156-64, (2001), K. van Benthem, et al., Phys. Rev. Lett., 93, 227201, (2004), K. van Benthem, et al., Phys. Rev. B, 74, 205110, (2006).

15


A Graded Interface Approach

The Sharp Interfaces of a 1|2|1 Type Model• Have Unrealistic Infinite Property Gradients

Are These Sharp Interface Results • Applicable To Grain Boundaries?

Nanoscale Approach To Apply • Bulk Continuum Dispersion Theory

Use Graded Interface Model• Interfaces With Finite Property Gradients

• [ 1 | gradient | 2 | gradient | 1 ]

Define Finest Length Scale For Gradients• Use A Characteristic Interatomic Bond Length

• For SrTiO3 Use do = 0.19525

• The Ti-O Bond Length in SrTiO3

Finest Scale Property Gradients Are Interatomic

K. van Benthem , G. Tan, R. H. French, L. K. Denoyer, R. Podgornik, V. A. Parsegian, Phys. Rev. B, 74, (2006). R. Podgornik, R. H. French, V.A. Parsegian, J. Chem. Phys., 124, 044709, (2006)

16


Hamaker Coefficients: 5 & n13 SrTiO3 GBs

Compare 3 Layer, Gradient Model• Using Quadroid Gradient

Graded Interface Approach• Doesn’t Change Findings• Small Reduction in Edisp.

Limiting Behavior Correct• For 0 nm Core Width• Dispersion Interaction Approaches 0

K. van Benthem, et al., Phys. Rev. Lett., 93, 227201, (2004). K. van Benthem, et al., Phys. Rev. B, 74, 205110, (2006).

17


vdW-L Dispersion Energies Of GBs

GB Stabilization Energy• Due To Dispersion

Abrupt Model ResultsE ( n13) = 169 – 73 = 96 mJ/m2

E ( n5) = 169 – 24 = 145 mJ/m2

Quadroid Graded Interface ModelE ( n5) = 119 – 14 = 69 mJ/m2

E ( n13) = 119 – 50 = 105 mJ/m2

London Dispersion Stabilization EnergiesFor These Atomically Abrupt Grain Boundaries Are Appreciable

Compare To Chemical Energies3 GB = 520 mJ/m2

• Surface Energy ~ 1100/mJ/m2

Optically AnisotropicPlane Parallel Morphology

Hamaker Constants and Coefficients

vdW-Ld Normal Forces

And

vdW-Ld Torques

19


Metallic and Semiconducting SWCNTs

[9,3 Metallic] [6,5 Semiconducting]

Diameter To Atomic Cores 0.423 nm 0.373 nm

Build CNT’s By Rolling Graphene Shift With m,n Chirality• Graphite Interlayer Spacing Is 0.167 nm

• Used to Define Cylinder Diamters

Much Interest In Manipulating CNTs• London Dispersion Interactions: Universal, Long Range

Can Dispersion Interaction Be Used For SWCNT Processing?• Focus On Aqueous Dispersions

20


ab initio Band Structures Of [6,5,s] & [9,3,m] SWCNT

ab initio Band Structures and Optical Properties• To Calculate Dielectric Function • To Calculate London Dispersion Spectra

R. F. Rajter, R. H. French, W. Y. Ching, W. C. Carter, Y. M. Chiang, J. Appl. Phys., 101, 054303, p. 1-5, (2007).R. Rajter, R. Podgornik, V. A Parsegian, R. H. French, W. Y. Ching, to be published, Phys. Rev. B., 75, (2007).

21


Uniaxial Optical Properties Of [6,5,s] & [9,3,m] SWCNT

Radial Directions Have Similar Properties

Axial Directions Very Different• Due To Metallic Axial Property Of [9,3,m]

• [9,3,m] Max of 933 at 0.04 eV

22


London Disp. Spectra Of [6,5,s] & [9,3,m] CNTs

LDS Crossings => Complex Behavior• e.g. Surficial Films Of Water On Ice

Water Max of 78 at 0 eV

[9,3,m] Peaks of 333 at 0 eV

)(" ξ i

23


Optically Anisotropic vdW-Ld Formalism

Example: A123 Non-retarded• Uniaxial Optical Properties

Is Optical Contrast • With Interlayer Medium

γ Is Optical Anisotropy• Of Material

Torques Due To γ

• In Addition To Normal Forces

Still To Do:• Opt. Anisotropic Add-A-Layer

A(0) Is Rotation Independent Part: f(l)

A(2) Is Rotation Dependent Part: f(θ)

• Of vdW-Ld Interaction

24


vdW-Ld Spectra On Log Axes

LDS Crossings Yield Repulsive And Attractive Dispersion Contributions• Due To The Spectral Difference Functions,

• The Optical Contrast Among Component Materials

25


Dispersion Torques From Optical Anisotropy

Optical Anisotropy γ Produces Torques• To Align The Axial Axes Of The Metallic CNT’s

vdW-Ld Torques: Hamaker Coefficient versus Angle

45

45.5

46

46.5

47

0 15 30 45 60 75 90

angle (degrees)

Hamaker Coefficient (zJ)

A121 [ 9,3,m] Aniso Substrates

Parallel

Optically AnisotropicAnd

Morphologically Anisotropic (Solid Cylinders)

27


Still To Do:• Add-A-Layer

• Coated Cylinders• Multi-wall CNTs• Hollow Cylinders

Optically & Morpholigically Anisotropic vdW-Ld Formalism

Example: A123, Optically Uniaxial, Cylinder-Cylinder• In The Far Limit• Isotropic Interlayer Medium m

Also Implemented:• Optically Anisotropic Cylinder Substrate• Near and Far Limits: Cyl. Cyl., Cyl. Sub.• Transition Region Between Near And Far Limits

28


Hamaker Coefficients Versus distance

Near Limit Is < 2 Diameters, And Far Limit Is > 2 Diameters

Semiconducting CNT’s Hamaker Coefficient Larger Than Metallic

Far Limit Hamaker Coeff.s Larger Than Near Limit• Due To parallel

Near Limit Far Limit

29


Versus Angle

Hamaker Torques Small In Near Limit, Larger In Far Limit

Large Torques Arise For Metallic CNT’s

Arise From Large Differences In parallel and perpendicular, or γ

30


vdW-Ld Torques Of Metallic CNT’s

Optical And Morphological Anisotropy Both Essential For Dispersion Torques

vdW-Ld Torques: Hamaker Coefficient versus Angle

0

20

40

60

80

100

120

140

160

0 15 30 45 60 75 90angle (degrees)

Hamaker Coefficient (zJ)

A121 Polystyrene H 2OA121 Alumina H2OA121 [9,3 ,m] Aniso SubstratesA121 [9,3 ,m] Aniso Cylinders

Parallel

31


Three Major Cases: Optical, Morphological Anisotropy

Morphology: Plane Parallel Plane Parallel Cylinder

Optically: Isotropic Uniaxial Uniaxial

32


Conclusions

Long Range Interactions In Nanoscale Science• Electrodynamics: vdW-L Dispersion, Debye, Keesom• Electrostatics• Polar Interactions

Polystyrene/Water• Interface Energy From Both vdW-Ld and Polar Interactions

SrTiO3 Grain Boundary Dispersion Energies• Due To Reduced Physical, Electron Density, Index of Refr.• ~ 5 to 10% of Chemical GB Energy

New Non-Plane Parallel Hamaker Development

Carbon Nanotubes• ab initio Optical Properties From Band Structures

CNT Optical Properties Differ• Produce Different Hamaker Coefficients• Method For CNT Separation By Type

Optical & Morphological Anisotropy• Produces Strong Dispersion Torques

• Optical Anisotropy γ And Optical Contrast • An Interaction For Alignment Of CNT’s

ab initio:LDA Band Structure

Optical Properties & Electronic Structure:

Interband Transition Strength

vdW-Ld Interaction:Hamaker Coefficients

Electrodynamics

Bulk:VUV

Reflectance

Interfacial:Trans. EELS

TEM

Surficial:Refl. EELSSurf. Sci.

Probes

Polystyrene

SrTiO3 Grain Boundaries

CarbonNanotubes

33


"Controlled Two-Dimensional Pattern of Spontaneously Aligned Carbon Nanotubes", R.S. McLean, X. Huang, C. Khripin, A. Jagota, M. Zheng, Nanoletters, 6 [1] 55-60 (2006)

Observation of Aligned Adsorption Of CNTs

34


new perspectives on van der waals – london dispersion interactions of materials: wetting, graded...

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