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

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)

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, 251-63, (2007).

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 Isotropic Plane Parallel Morphology Hamaker Constants and Coefficients London Dispersion Energies With Effects Of Retardation Arbitrary Numbers Of Layers (Add-A-Layer)

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 = 10-21 Joules A123 71 zJ PS Disp. Force Air Mat. 1. Mat. 2. s p Water Disp. Force PS 8 zJ Water Air PS -16 zJ

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, 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).

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, 251-63, (2007).

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

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

Gecko Hamaker: Open Source Hamaker Program Full Spectral, Retarded Hamaker, Coefficients http://geckoproj.sourceforge.net/

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

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

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, 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).

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)

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

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

Optically Anisotropic Plane Parallel Morphology Hamaker Constants and Coefficients vdW-Ld Normal Forces And vdW-Ld Torques

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

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).

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

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

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

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

Dispersion Torques From Optical Anisotropy Optical Anisotropy  Produces Torques To Align The Axial Axes Of The Metallic CNT’s

Optically Anisotropic And Morphologically Anisotropic (Solid 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 Still To Do: Add-A-Layer Coated Cylinders Multi-wall CNTs Hollow Cylinders

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

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 

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

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

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

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] 55-60 (2006)