New Perspectives on van der Waals London Dispersion Interactions of Materials: Wetting, Graded Interfaces and Carbon Nanotubes

Transcription

1 New Perspectives on van der Waals London Dispersion Interactions of Materials: Wetting, Graded Interfaces and Carbon Nanotubes R. H. French 1,2, R. Rajter 3 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 2 Spectroscopy G. L. Tan (UPenn) M. K. Yang (DuPont) M. F. Lemon (DuPont) D. J. Jones (DuPont) SrTiO 3 K. van Benthem (ORNL) M. Ruhle (MPI-Stuttgart) C. Elsasser (MPI-Stuttgart) Manfred Rühle (MPI-Stuttgart) Polystyrene K. I. Winey (UPenn) W. Qiu (DuPont) SiO 2 : Amorphous & Quartz G. L. Tan (UPenn) 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) VuGraph 2

3 Dispersion Contribution to Surface Free Energy 3 London Dispersion Energy Thermodynamic Free Energy Arising From London Dispersion Interaction Dispersive Component Of Surface Free Energy Diiodomethane Non-polar & A # 121 = arccos $ ' 1! % A123 " (! liq.! sol.! sol.-liq. Polystyrene Electrodynamic & Polar Interactions Water Partially Polar ã= ã Disp. + ã Polar Polystyrene R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007). VuGraph 3

4 vdw-ld Interactions: Outline 4 Optically Isotropic, Plane Parallel Morphology Polystyrene SrTiO 3 : Σ5 And Σ13 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 VuGraph 4

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 s s Mat. 1. p p Mat. 2. p p Arises From Oscillating Dipoles Interatomic Bonds of Elect. Struc. Attractive Force: Nonwetting Positive Hamaker Constant PS PS Air Disp. Force Water Disp. Force PS PS 6 A zj 8 zj J cv => London Disp. Spectra A - Hamaker Constant Interaction Scaling Constant E London Dispersion F disp - Dispersion Force A( l) = " 12! l 2 Repulsive Force: Wetting Negative Hamaker Constant PS Water Air zj = zeptojoule = Joules -16 zj VuGraph 6

7 VUV Reflectance and Interband Transitions VUV Reflectance Linear Response Function! ( E) 2E = $ " % & {# ( E )} P ln ' de' 2 2 E' $ E 0 Obeys Kramers Kronig Dispersion Refl. (%) n PS 5 Reflectance of PS Energy (ev) 4 Interband Transition Strength Complex Optical Property Related To Dielectric Function ε 2 E J cv = i (! i! 8" 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). 2 ) * Im[Jcv] Re[Jcv] (ev^2) 2 ) Re[Jcv] Im[Jcv] (ev^2) 2 ) Interband Transition Strength: Re [Jcv] of PS Interband Transition Strength: Im [Jcv] of PS Energy (ev) VuGraph 7

8 8 Electronic Structure Of Polystyrene Hierarchy Of Interband Transitions Aromatic p p* Nonbonding: n s* Saturated: s s* band Transition Strength - Re[Jcv] (ev ) R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007) E1: Aromatic pi - pi* E1' E1 PS E2 n E3' E3: C-C sigm VuGraph 8

9 " ( i! ) London Dispersion Spectra 9 Using Lifshitz Theory, QED Acquire Exp. Spectra Calc. London Disp. Spectrum Kramers Kronig Transform 2!#"(!) #"( i " ) = 1+ % d! 2 2 $! + " Then Hamaker Constant Calc d by Spectral Differences of London Disp. Spectra & 0 Im[Jcv] (ev^2) Im[Jcv] (ev^2) PS Water PS Water R. H. French, J. Am. Ceram. Soc., 83, (2000). File #14 : PSTY6T Im[Jcv] (ev^2) / Energy (ev) #568,POLYSTYRENE,ALTHOR,,300,NO,SAMBOX ROUGHBK R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007). VuGraph Energy (ev) Overlay X-Zoom CURSOR Res= 1

10 10 Optically Isotropic, Plane Parallel: vdw-ld Formalism Example: A 123 Non-retarded G(l): Thermodynamic Free Energy Δ Are Spectral Difference Function Between Half Space Material L or R And Interlayer Material m Also Implemented: Add-A-Layer: Up To 99 Layers Graded Interfaces Full Effects Of Retardatio Δ Represent The Optical Contrast VuGraph 10

11 Gecko Hamaker: Open Source Hamaker Program 11 Full Spectral, Retarded Hamaker, Coefficients VuGraph 11

12 Speed of Light Plays a Role Transit Time Important Higher Energy Bonds Induced Dipoles De-Phase Contribution Drops Nonwetting Attractive Dispersion Force Wetting Retarded Hamaker Coefficients PS Repulsive Dispersion Force PS Water Force Water Retardation Length PS Air Can Exceed 300 nm Depending On Details Of System Hamaker Coefficient (Zeptojoules) Hamaker Coefficient (Zeptojoules) Distance (nm) PS Water PS Non-Wetting Wetting PS Water Air Non-Retarded Non-Retarded Distance (nm) 12 VuGraph 12

13 Compare Energies From Hamaker Const. & Contact Angles Use Hamaker Constants => Surface Energy Fowkes Method Using Non-polar & Polar Liquids 13 1 PS 2 Air Force 1 " Mat.1 = # EMat.1 = 2 ÞInterface Energy A 24! 1v1. 2 d o 1 PS Diiodomethane Non-polar ã= ã Disp. + ã Polar 1 PS 3 Water 1 PS Polystyrene Force 1 " Mat.1 Mat.3 = # EMat.1 Mat.3 = 2 A 24! 1v3. 2 d o Experimental Uncertainties Polar Components Retract Into Free Surface Surface Energy Of Polystyrene (mj/m 2 ) Full Spectral Hamaker Polymer Handbook Fowkes Method Dispersive Component Polar Component Surface Free Energy R. H. French, K. I. Winey, M. K. Yang, W. Qiu, Aust. J. Chem.,60, , (2007). VuGraph 13

14 14 Gradient Properties in Grain Boundaries of SrTiO Index of Refraction [n] !13!5 Oscillator Strength Sum Rule (electrons/nm ) Bulk!5! Distance (nm) Energy (ev) Index of Refraction S5 Grain Boundary = 1.56 ns13 Grain Boundary = 1.29 n=2.37 for bulk SrTiO 3, Spectroscopic Ellipsometry. 1 Valence Electron Density Variations From Oscillator Strength Sum Rule Units of Electrons Per nm 3 for bulk SrTiO 3 S5 and ns13 GB K. van Benthem, C. Elsässer, R. H. French, J. Appl. Phys, 90, 12, , (2001), K. v an Benthem, et al., Phys. Rev. Lett., 93, , (2004), K. v an Benthem, et al., Phys. Rev. B, 74, , DuPont Co. Central Research, Univ. of Pennsylvania, Materials Science, R. H. French 2007 (2006). August 15, 2007 VuGraph 14

15 A Graded Interface Approach 15 The Sharp Interfaces of a 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 SrTiO 3 Use d o = The Ti-O Bond Length in SrTiO 3 Finest Scale Property Gradients Are Interatomic K. v an Benthem, G. Tan, R. H. French, L. K. Denoy er, R. Podgornik, V. A. Parsegian, Phys. Rev. B, 74, (2006). R. Podgornik, R. H. French, V.A. Parsegian, J. Chem. Phys., 124, , (2006) VuGraph 15

16 16 Hamaker Coefficients: S5 & ns13 SrTiO 3 GBs Compare 3 Layer, Gradient Model Using Quadroid Gradient Graded Interface Approach Doesn t Change Findings Small Reduction in E disp. 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). VuGraph 16

17 vdw-l Dispersion Energies Of GBs 17 GB Stabilization Energy Due To Dispersion Abrupt Model Results ΔE ( nσ13) = = 96 mj/m 2 ΔE ( nσ5) = = 145 mj/m 2 Quadroid Graded Interface Model ΔE ( nσ5) = = 69 mj/m 2 ΔE ( nσ13) = = 105 mj/m 2 Interface SrTiO 3 vac. SrTiO 3 d o =0.195 nm SrTiO 3 n! 13 SrTiO 3 d o =0.195 nm SrTiO 3! 5 SrTiO 3 d o =0.195 nm SiO 2 vac. SiO 2 d o =0.165 nm Abrupt Gradient A 121 NR (zj) E London (mj.m -2 ) Double-Quadratic Gradient a A 121 R (zj) (L=0.9 nm) (L=0.9 nm) (L=0.6 nm) E London (mj.m -2 ) London Dispersion Stabilization Energies For These Atomically Abrupt Grain Boundaries Are Appreciable Compare To Chemical Energies Σ3 GB = 520 mj/m 2 Surface Energy ~ 1100/mJ/m 2 VuGraph 17

18 Optically Anisotropic Plane Parallel Morphology Hamaker Constants and Coefficients vdw-ld Normal Forces And vdw-ld Torques

19 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 DuPont Co. Central Research, Univ. of Pennsylvania, Materials Science, VuGraph 19 R. H. French 2007 August 15, 2007

20 ab initio Band Structures Of [6,5,s] & [9,3,m] SWCNT 20 ab initio Band Structures and Optical Properties To Calculate Dielectric Function ε 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). VuGraph 20

21 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 VuGraph 21

22 " ( i! ) London Disp. Spectra Of [6,5,s] & [9,3,m] CNTs 22 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 VuGraph 22

23 Optically Anisotropic vdw-ld Formalism 23 A (0) Is Rotation Independent Part: f(l) A (2) Is Rotation Dependent Part: f(θ) Of vdw-ld Interaction Example: A 123 Non-retarded Uniaxial Optical Properties Δ 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 VuGraph 23

24 vdw-ld Spectra On Log Axes 24 LDS Crossings Yield Repulsive And Attractive Dispersion Contributions Due To The Δ Spectral Difference Functions, The Optical Contrast Among Component Materials VuGraph 24

25 Dispersion Torques From Optical Anisotropy 47 vdw-ld Torques: Hamaker Coefficient versus Angle 25 Hamaker Coefficient (zj) A121 [ 9,3,m] Aniso Substrates Parallel angle (degrees) Optical Anisotropy γ Produces Torques To Align The Axial Axes Of The Metallic CNT s VuGraph 25

26 Optically Anisotropic And Morphologically Anisotropic (Solid Cylinders)

27 Optically & Morpholigically Anisotropic vdw-ld Formalism 27 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 VuGraph 27

28 Hamaker Coefficients Versus distance 28 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 Δ parallel VuGraph 28

29 Versus Angle 29 Hamaker Torques Small In Near Limit, Larger In Far Limit Large Torques Arise For Metallic CNT s Arise From Large Differences In Δ parallel and Δ perpendicular, or γ VuGraph 29

30 vdw-ld Torques Of Metallic CNT s 30 Hamaker Coefficient (zj) Parallel vdw-ld Torques: Hamaker Coefficient versus Angle A121 Polystyrene H 2O A121 Alumina H 2O A121 [9,3,m] Aniso Substrates A121 [9,3,m] Aniso Cylinders angle (degrees) Optical And Morphological Anisotropy Both Essential For Dispersion Torques VuGraph 30

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

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 SrTiO 3 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 Δ An Interaction For Alignment Of CNT s Bulk: Polystyrene VUV Reflectance Interfacial: Trans. EELS TEM Probes SrTiO 3 Grain Boundaries 32 ab initio: Carbon LDA Nanotubes Band Structure Surficial: Refl. EELS Surf. Sci. Optical Properties & Electronic Structure: Interband Transition Strength vdw-ld Interaction: Hamaker Coefficients Electrodynamics VuGraph 32

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

34 VuGraph 34 34