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Fundamentals of Polarization and Polarizability

Fundamentals of Polarization and Polarizability. Seth R. Marder Joseph W. Perry Department of Chemistry. Polarizability: A Microscopic View. F = qE (1). Polarization = µ =   (2). Effect of Application of an Oscillating Electric Field such as Light.

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Fundamentals of Polarization and Polarizability

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  1. Fundamentals of Polarization and Polarizability Seth R. Marder Joseph W. Perry Department of Chemistry

  2. Polarizability: A Microscopic View F = qE (1) Polarization = µ =  (2)

  3. Effect of Application of an Oscillating Electric Field such as Light • Application of an oscillating electric field will induce an oscillating polarization in a material. • For linear polarization, this electric field will have the same frequency as the applied electric field, although its phase may be shifted (not shown). • This induced electric field is, itself, light and in the absence of scattering will propagate through the material in the same direction as the light beam that created it.

  4. Mechanisms of Polarization • The oscillating electric field of light affects all charges in the optical medium, not only the electron. • Vibrational polarization and involves nuclear motion • In dipolar materials molecular rotation can create polarization • In ionic materials, the ions move relative to one another

  5. Dipoles in Electric Fields • For materials that contain electric dipoles, such as water molecules, the dipoles themselves stretch or reorient in the applied field.

  6. Anisotropic Nature of Polarizability • The polarization of a molecules need not be identical in all directions.

  7. Each entry of the tensor is a component of the polarizability The balloon diagram illustrates this point crudely. If a balloon is stretched in one direction (z) then the dimension of the balloon will change in all three directions. Tensorial Nature of Polarization Polarizability is a tensor quantity as shown below:

  8. Polarizability: A Macroscopic View In bulk materials, the linear polarization is given by: Pi() = ij( Ej( (4) i,j where ij() is the linear susceptibility of an ensemble of molecules The total electric field (the "displaced" field, D) within the material becomes: D = E + 4P = (1 + 4E (5) Since P = E (Equation (4)), 4E is the internal electric field created by the induced displacement (polarization) of charges

  9. The Dielectric Constant The dielectric constant and the refractive index n(w) are two bulk parameters that characterize the susceptibility of a material. e(w) in a given direction is defined as the ratio of the displaced internal field to the applied field (e = D/E) in that direction. ij() = 1 + 4ij() . (6) The frequency dependence of the dielectric constant provides insight into the mechanism of charge polarization.

  10. The Index of Refraction The ratio of the speed of light in a vacuum, c, to the speed of light in a material, v, is called the index of refraction (n): n = c/v. (7) At optical frequencies the dielectric constant equals the square of the refractive index: e∞(w) = n2(w). (8) Consequently, we can relate the refractive index to the bulk linear (first-order) susceptibility: n2(w) = 1+ 4pc(w). (9) Index of refraction depends therefore on chemical structure.

  11. Role for Materials Chemists

  12. Bond Length Alternation

  13. Resonance Structures and BLA

  14. Electric Field Perturbation of Structure

  15. Linear Polarizability and BOA

  16. First Hyper-polarizability and BOA

  17. Factors Affecting Charge Separation

  18. Manipulation of BLA Through Topology

  19. Good, But Not Good Enough

  20. Second Hyper-polarizability and BOA

  21. S n S 2 h  Electron Transfer A Energy Transfer S h  A 1 Photochemistry Two-photon Absorptivity Fluorescence  h  F  h  fl A S 0 Two-Photon Excited Processes

  22. -2 z I  2 TPA  I -4 TPA  z Two-Photon Processes Provide 3-D Resolution Excitation by two photons is confined to a volume very close to focus where intensity is highest, giving rise to pinpoint 3D resolution Excitation by one photon results in absorption along the entire path of the laser beam in the cuvette.

  23. TPA Provides Improved Penetration Into Absorbing Materials Excitation by two photons of half the energy allows for penetration through the material, and then two photons can be absorbed by the sample Excitation by one photon results in absorption by surrounding medium before beam reaches sample

  24.  ≈ 10 x 10-50 cm4 s photon-1  ≈ 200 x 10-50 cm4 s photon-1 Effect of bis-Donor Substitution

  25. 0.1 0.05 0 -Charge Difference -0.05 -0.1  -0.15 N Phenyl Vinyl Phenyl N Proposed Model to Enhance TPA in Symmetrical Molecules • BDAS has large and symmetrical charge transfer from nitrogens to central vinyl group that is associated with large transition moment between S(1) and S(2). • These results suggest that a large change in quadrupole moment between S(0) and S(1) is leads to enhanced  Group

  26. Strategies for the Design of New Materials D--D Increase conjugation length Add electron acceptors to the backbone DD ADA Also:

  27. Chain-Length Dependence • Method: Two-photon induced fluorescence (TPF) • Pulse duration: ≈ 5 ns I II III • With increasing chain length: •  increases • (2)max red-shifts IV

  28. Design of TPA Chromophores p D-p-D D-A-D A-D-A 210 12 4700 995 1940 53 1250 2300 Albota et al., Science 1998 d in 10-50 cm4 s/photon

  29. Photochemistry Generated via an Intramolecular Electron Transfer

  30. Media: Negative Tone Resist Unexposed Exposed Developed Two-photon negative resist Two-photon radical initiator 70% polymer precursor 30% binder 0.1% 2hn radical initiator 100 x more sensitive than commerical radical initiators

  31. Why 3D Micro and Nanofabrication • Technology pull towards miniaturization of devices and patterned materials. • Need to free form fabricate 3 dimensional structures • Increasing need for ability to pattern a variety of materials • Need to couple nano-scale object with micro-scale objects • Areas impacted by 3D micro- and nano-fabrication Tissue engineering MEMS Microfluidics Photonics

  32. Design of a Donor-Acceptor Linked Two-Photon Dye Photoacid Generator 1. Non-basic Electron Donor: Ar3N (Ph3N+H, pKa = -5) 2. Electron Acceptor Sulfonium group Separated from a π-Conjugation System of Two-Photon Dye (π* > s*) 3. Decrease of Perturbation of Sulfonium Group on Electron Donor 4. Non-nucleophilic Anions (X- = BF4-, PF6-, AsF6-, SbF6-, (Ph-F5)4B- , etc.) R’ = π-Conjugation System R = methyl, benzyl

  33. Quantum Yields of Acid Generation Rhodamine B as an Indicator

  34. Media: Positive Tone Resist Unexposed Exposed Developed Two-photon positive resist 1% 2hn photoacid generator 99% positive resist 50 x more sensitive than commercial photoacid initiators

  35. 20 20 100 8 m 50 m Vertical cross-section Grating plane: 10 m below surface Film surface Positive-Tone Resist Grating with buried channels

  36. Acknowledgments

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