1. 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

2. Acknowledgements Spectroscopy Polystyrene SiO2: Amorphous & Quartz
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
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 Energy
Diiodomethane Non-polar
Polystyrene
London Dispersion Energy
Thermodynamic Free Energy Arising From
London Dispersion Interaction
Dispersive Component Of Surface Free Energy
Electrodynamic &
Polar Interactions
Water
Partially Polar
Polystyrene
R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (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

5. Optically Isotropic Plane 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 Interaction
London 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 = Joules
A zJ PS
Disp. Force
Air
Mat. 1.
Mat. 2. s p
Water
Disp. Force PS
8 zJ
Water
Air PS
-16 zJ

7. VUV Reflectance and Interband Transitions
Linear Response Function
Obeys Kramers Kronig Dispersion
Interband Transition Strength
Complex Optical Property
Related To Dielectric Function 
Im[Jcv] (eV2) Re[Jcv] (eV2)
M. L. Bortz, R. H. French, Appl. Phys. Lett., 55, 19, , Nov. 8, (1989).
R. H. French, Phys. Scripta, 41, 4, 404-8, (1990).
M. L. Bortz, R. H. French, , Appl. Spect., 43, 8, , (1989).

8. Electronic Structure Of Polystyrene
Hierarchy Of Interband Transitions
Aromatic p→ p*
Nonbonding: n→ s*
Saturated: s→ s*
R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (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
R. H. French, J. Am. Ceram. Soc., 83, (2000).
R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007).

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, Coefficients

12. Retarded Hamaker Coefficients
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
Water
Force PS
Air
Water PS

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
Diiodomethane Non-polar
Polystyrene
1 PS
2 Air
Force
1 PS
3 Water
Force
Surface Energy Of Polystyrene (mJ/m2)
Full Spectral Hamaker
Polymer Handbook
Fowkes Method
Dispersive Component
34.7
40.6 – 43.2
Polar Component
6.8 – 8.2
Surface Free Energy
R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007).

14. Gradient Properties in Grain Boundaries of SrTiO3
Index of Refraction
S5 Grain Boundary = 1.56
nS13 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 S5 and nS13 GB
K. van Benthem, C. Elsässer, R. H. French, J. Appl. Phys, 90, 12, , (2001), K. van Benthem, et al., Phys. Rev. Lett., 93, , (2004), K. van Benthem, et al., Phys. Rev. B, 74, , (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 =
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, , (2006)

16. Hamaker Coefficients: S5 & nS13 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, , (2004).
K. van Benthem, et al., Phys. Rev. B, 74, , (2006).

17. vdW-L Dispersion Energies Of GBs
GB Stabilization Energy
Due To Dispersion
Abrupt Model Results
E ( n13) = 169 – 73 = 96 mJ/m2
E ( n5) = 169 – 24 = 145 mJ/m2
Quadroid Graded Interface Model
E ( n5) = 119 – 14 = 69 mJ/m2
E ( n13) = 119 – 50 = 105 mJ/m2
London Dispersion Stabilization Energies For These Atomically Abrupt Grain Boundaries Are Appreciable
Compare To Chemical Energies
3 GB = 520 mJ/m2
Surface Energy ~ 1100/mJ/m2

18. Optically Anisotropic Plane 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 nm nm
Build CNT’s By Rolling Graphene Shift With m,n Chirality
Graphite Interlayer Spacing Is 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, , 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

23. Optically Anisotropic vdW-Ld Formalism
Example: A123 Non-retarded
Uniaxial Optical Properties
 Is Optical Contrast
With Interlayer Medium
 Is Optical Anisotropy
Of Material
Torques Due To 
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()
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  Produces Torques
To Align The Axial Axes Of The Metallic CNT’s

26. Optically Anisotropic And Morphologically Anisotropic (Solid Cylinders)

27. 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
Still To Do:
Add-A-Layer
Coated Cylinders
Multi-wall CNTs
Hollow Cylinders

28. Hamaker Coefficients Versus distance
Near Limit
Far Limit
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

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 

30. vdW-Ld Torques Of Metallic CNT’s
Optical And Morphological Anisotropy Both Essential For Dispersion Torques

31. Three Major Cases: Optical, Morphological Anisotropy
Morphology: Plane Parallel Plane Parallel Cylinder
Optically: Isotropic Uniaxial Uniaxial

32. Optical Properties & Electronic Structure:
Conclusions
Polystyrene
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. EELS Surf. Sci.
Probes
Carbon Nanotubes
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  And Optical Contrast 
An Interaction For Alignment Of CNT’s
SrTiO3 Grain Boundaries

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