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Characterization of Optical Properties and Surface Roughness Profiles: The Casimir Force Between Real Materials

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Casimir Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 834))

Abstract

The Lifshitz theory provides a method to calculate the Casimir force between two flat plates if the frequency dependent dielectric function of the plates is known. In reality any plate is rough and its optical properties are known only to some degree. For high precision experiments the plates must be carefully characterized otherwise the experimental result cannot be compared with the theory or with other experiments. In this chapter we explain why optical properties of interacting materials are important for the Casimir force, how they can be measured, and how one can calculate the force using these properties. The surface roughness can be characterized, for example, with the atomic force microscope images. We introduce the main characteristics of a rough surface that can be extracted from these images, and explain how one can use them to calculate the roughness correction to the force. At small separations this correction becomes large as our experiments show. Finally we discuss the distance upon contact separating two rough surfaces, and explain the importance of this parameter for determination of the absolute separation between bodies.

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Notes

  1. 1.

    This correlation was not noted in [15] and stressed here for the first time.

References

  1. Casimir, H.B.G.: On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793–795 (1948)

    MATH  Google Scholar 

  2. Lifshitz, E.M. (1955) Zh. Eksp. Teor. Fiz. 29, 894 [Soviet Phys. JETP 2, 73 (1956)]

    Google Scholar 

  3. Dzyaloshinskii, I.E., Lifshitz, E.M., Pitaevskii, L.P.: General theory of van der Waals’ forces. Usp. Fiz. Nauk 73, 381–421 (1961) [Soviet Phys. Usp. 4, 153–176 (1961)]

    Google Scholar 

  4. Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics, Part 2. Pergamon, Oxford (1980)

    Google Scholar 

  5. Lamoreaux, S.K.: The Casimir force: background, experiments, and applications. Rep. Prog. Phys. 68, 201–236 (2005)

    Article  ADS  Google Scholar 

  6. Capasso, F., Munday, J.N., Iannuzzi, D., Chan, H.B.: Casimir Forces and Quantum Electrodynamical Torques: Physics and Nanomechanics. IEEE J. Sel. Top. Quantum Electron. 13, 400–414 (2007)

    Article  Google Scholar 

  7. Palik, E.D.: Handbook of Optical Constants of Solids. Academic Press, New York (1995)

    Google Scholar 

  8. Weaver,J.H., Krafka, C., Lynch, D.W., Koch, E.E.:(1981) Optical properties of metals, Part II, Physics Data No. 18-2. Fachinformationszentrum Energie, Physik, Mathematik, Karsruhe

    Google Scholar 

  9. Lambrecht, A., Reynaud, S.: Casimir force between metallic mirrors. Eur. Phys. J. D 8, 309–318 (2000)

    Article  ADS  Google Scholar 

  10. Lamoreaux, S.K.: Calculation of the Casimir force between imperfectly conducting plates. Phys. Rev. A 59, R3149–R3153 (1999)

    Article  ADS  Google Scholar 

  11. Lamoreaux, S.K.: Comment on “Precision Measurement of the Casimir Force from 0.1 to 0.9 \(\upmu\hbox{m}\)”. Phys. Rev. Lett. 83, 3340 (1999)

    Article  ADS  Google Scholar 

  12. Svetovoy, V.B., Lokhanin, M.V.: Do the precise measurements of the Casimir force agree with the expectations?. Mod. Phys. Lett. A 15, 1013–1021 (2000)

    Article  ADS  Google Scholar 

  13. Svetovoy, V.B., Lokhanin, M.V.: Precise calculation of the Casimir force between gold surfaces. Mod. Phys. Lett. A 15, 1437–1444 (2000)

    Article  ADS  Google Scholar 

  14. Pirozhenko, I., Lambrecht, A., Svetovoy, V.B.: Sample dependence of the Casimir force. New J. Phys. 8, 238 (2006)

    Article  ADS  Google Scholar 

  15. Svetovoy, V.B., van Zwol, P.J., Palasantzas, G., DeHosson, J.Th.M.: Optical properties of gold films and the Casimir force. Phys. Rev. B 77, 035439 (2008)

    Article  ADS  Google Scholar 

  16. van Zwol, P.J., Palasantzas, G., De Hosson, J.Th.M.: Influence of dielectric properties on van der Waals/Casimir forces in solid-liquid systems. Phys. Rev. 79, 195428 (2009)

    Article  Google Scholar 

  17. Genet, C., Lambrecht, A., Maia Neto, P., Reynaud, S.: The Casimir force between rough metallic plates. Europhys. Lett. 62, 484–490 (2003)

    Article  ADS  Google Scholar 

  18. Maia Neto, P., Lambrecht, A., Reynaud, S.: Roughness correction to the Casimir force: Beyond the Proximity Force Approximation. Europhys. Lett. 69, 924–930 (2005)

    Article  ADS  Google Scholar 

  19. Maia Neto, P., Lambrecht, A., Reynaud, S.: Casimir effect with rough metallic mirrors. Phys. Rev. A 72, 012115 (2005)

    Article  ADS  Google Scholar 

  20. Derjaguin, B.V., Abrikosova, I.I., Lifshitz, E.M.: Direct measurement of molecular attraction between solids separated by a narrow gap. Q. Rev. Chem. Soc. 10, 295–329 (1956)

    Article  Google Scholar 

  21. DelRio, F.W., de Boer, M.P., Knapp, J.A., Reedy, E.D. Jr, Clews, P.J., Dunn, M.L.: The role of van derWaals forces in adhesion of micromachined surfaces. Nat. Mater. 4, 629–634 (2005)

    Article  ADS  Google Scholar 

  22. Maboudian, R., Howe, R.T.: Critical review: Adhesion in surface micromechanical structures. J. Vac. Sci. Technol. B 15, 1 (1997)

    Article  Google Scholar 

  23. Houston, M.R., Howe, R.T., Maboudiana, R.: Effect of hydrogen termination on the work of adhesion between rough polycrystalline silicon surfaces. J. Appl. Phys. 81, 3474–3483 (1997)

    Article  ADS  Google Scholar 

  24. van Zwol, P.J., Palasantzas, G., De Hosson, J.Th.M.: Influence of random roughness on the Casimir force at small separations. Phys. Rev. B 77, 075412 (2008)

    Article  ADS  Google Scholar 

  25. Lamoreaux, S.K.: Demonstration of the Casimir force in the \(0.6\text{--}6\,\upmu\hbox{m}\) range. Phys. Rev. Lett. 78, 5–8 (1997)

    Article  ADS  Google Scholar 

  26. Harris, B.W. et al.: Precision measurement of the Casimir force using gold surfaces. Phys. Rev. A. 62, 052109 (2000)

    Article  ADS  Google Scholar 

  27. Decca, R.S. et al.: Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates. Phys. Rev. D 75, 077101 (2007)

    Article  ADS  Google Scholar 

  28. Aspnes, D.E., Kinsbron, E., Bacon, D.D.: Optical properties of Au: Sample effects. Phys. Rev B 21, 3290–3299 (1980)

    Article  ADS  Google Scholar 

  29. Chen, F., Mohideen, U., Klimchitskaya, G.L., Mostepanenko, V.M.: Investigation of the Casimir force between metal and semiconductor test bodies. Phys. Rev. A 72, 020101 (2005)

    Article  ADS  Google Scholar 

  30. Dold, B., Mecke, R.: Optische Eigenschaften von Edelmetallen, Übergangsmetallen und deren Legierungen im Infratot. Optik 22, 435–446 (1965)

    Google Scholar 

  31. Motulevich, G.P., Shubin, A. A.: Influence of Fermi surface shape in gold on the optical constants and hall effect. Zh. Eksp.Teor. Fiz. 47, 840 (1964) [Soviet Phys. JETP 20, 560–564 (1965)]

    Google Scholar 

  32. Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media. Pergamon Press, Oxford (1963)

    Google Scholar 

  33. Zhou, F., Spruch, L.: van der Waals and retardation (Casimir) interactions of an electron or an atom with multilayered walls. Phys. Rev. A 52, 297–310 (1995)

    Article  ADS  Google Scholar 

  34. Iannuzzi, D., Lisanti, M., Capasso, F.: Effect of hydrogen-switchable mirrors on the Casimir force. Proc. Natl. Acad. Sci. U.S.A. 101, 4019–4023 (2004)

    Article  ADS  Google Scholar 

  35. Lisanti, M., Iannuzzi, D., Capasso, F.: Observation of the skin-depth effect on the Casimir force between metallic surfaces. Proc. Natl. Acad. Sci. U.S.A. 102, 11989–11992 (2005)

    Article  ADS  Google Scholar 

  36. de Man, S., Heeck, K., Wijngaarden, R.J., Iannuzzi, D.: Halving the Casimir force with Conductive Oxides. Phys. Rev. Lett. 103, 040402 (2009)

    Article  Google Scholar 

  37. Azzam, R.M.A., Bashara, N.M.: Ellipsometry and Polarized Light. North Holland, Amsterdam (1987)

    Google Scholar 

  38. Tompkins, H.G., McGahan, W.A.: Spectroscopic Ellipsometry and Reflectometry. Wiley, New York (1999)

    Google Scholar 

  39. Hofmann, T. et al.: Terahertz Ellipsometry Using Electron-Beam Based Sources. Mater. Res. Soc. Symp. Proc. 1108, A08–04 (2009)

    Google Scholar 

  40. Feng, R., Brion, C.E.: Absolute photoabsorption cross-sections (oscillator strengths) for ethanol (5–200 eV). Chem. Phys. 282, 419–427 (2002)

    Article  ADS  Google Scholar 

  41. Tompkins, H.G., Irene, E.A.: Handbook of ellipsometry William Andrew (2005)

    Google Scholar 

  42. van Zwol, P.J., Palasantzas, G., van de Schootbrugge, M., De Hosson, J.Th.M.: Measurement of dispersive forces between evaporated metal surfaces in the range below 100 nm. Appl. Phys. Lett. 92, 054101 (2008)

    Article  ADS  Google Scholar 

  43. http://www.JAWoollam.com

  44. Thèye, M.-L.: Investigation of the Optical Properties of Au by Means of Thin Semitransparent Films. Phys. Rev. B 2, 3060–3078 (1970)

    Article  ADS  Google Scholar 

  45. Munday, J.N., Capasso, F., Parsegian, A.: Measured long-range repulsive CasimirLifshitz forces. Nature 457, 170–173 (2009)

    Article  ADS  Google Scholar 

  46. Dagastine, R.R., Prieve, D.C., White, L.R.: The Dielectric Function for Water and Its Application to van der Waals Forces. J. Colloid Interface Sci. 231, 351–358 (2000)

    Article  Google Scholar 

  47. Munday, J.N., Capasso, F., Parsegian, A., Bezrukov, S.M.: Measurements of the Casimir-Lifshitz force in fluids: The effect of electrostatic forces and Debye screening. Phys. Rev. A 78, 032109 (2008)

    Article  ADS  Google Scholar 

  48. Kitamura, R. et al.: Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature. Appl. Optics 46, 8118 (2007)

    Article  ADS  Google Scholar 

  49. Segelstein, D.J.: The complex refractive index of water. PhD thesis, University of Missouri, Kansas City, USA (1981)

    Google Scholar 

  50. Nguyen, A.V.: Improved approximation of water dielectric permittivity for calculation of hamaker constants. J. Colloid Interface Sci. 229, 648–651 (2000)

    Article  Google Scholar 

  51. Parsegian, V.A., Weiss, G.H.: Spectroscopic parameters for computation of van der Waals forces. J. Colloid Interface Sci. 81, 285–289 (1981)

    Article  Google Scholar 

  52. Roth, C.M., Lenhoff, A.M.: Improved parametric representation of water dielectric data for Lifshitz theory calculations. J. Colloid Interface Sci. 179, 637–639 (1996)

    Article  Google Scholar 

  53. van Oss, C.J., Chaudhury, M.K., Good, R.J.: Interfacial Lifshitz-van der Waals and polar interactions in macroscopic systems. Chem. Rev. 88, 927–941 (1988)

    Article  Google Scholar 

  54. Milling, A., Mulvaney, P., Larson, I.: Direct measurement of repulsive van der Waals interactions using an atomic force microscope. J. Colloid Interface Sci. 180, 460465 (1996)

    Article  Google Scholar 

  55. Ogawa, M., Cook, G.R.: Absorption Coefficients of Methyl, Ethyl, N-Propyl and N-Butyl Alcohols. J. Chem. Phys 28, 747–748 (1957)

    Article  ADS  Google Scholar 

  56. Salahub, D.R., Sandorfy, C.: The far-ultraviolet spectra of some simple alcohols and fluoroalcohols. Chem. Phys. Lett. 8, 71–74 (1971)

    Article  ADS  Google Scholar 

  57. Koizumi, H. et al.: VUV-optical oscillator strength distributions of \(\hbox{C}_2\hbox{H}_6\hbox{O}\) and \(\hbox{C}_3\hbox{H}_8\hbox{O}\) isomers. J. Chem. Phys. 85, 4276–4279 (1986)

    Article  ADS  Google Scholar 

  58. Sethna, P.P., Williams, D.: Optical constants of alcohols in the infrared. J. Phys. Chem. 83, 405–409 (1979)

    Article  Google Scholar 

  59. Bertie, J.E., Zhang, S.L., Keefe, C.D.: Measurement and use of absolute infrared absorption intensities of neat liquids. Vib. Spectro. 8, 215–229 (1995)

    Article  Google Scholar 

  60. van Zwol, P.J., Palasantzas, G., DeHosson, J.Th.M.: Weak dispersion forces between glass and gold macroscopic surfaces in alcohols. Phys. Rev. E. 79, 041605 (2009)

    Article  ADS  Google Scholar 

  61. Meakin, P.: The growth of rough surfaces and interfaces. Phys. Rep. 235, 189–289 (1993)

    Article  ADS  Google Scholar 

  62. Palasantzas, G., Krim, J.: Experimental Observation of Self-Affine Scaling and Kinetic Roughening at Sub-Micron Lengthscales. Int. J. Mod. Phys. B, 9, 599–632 (1995)

    Article  ADS  Google Scholar 

  63. Zhao, Y., Wang, G.-C., Lu, T.-M.: Characterization of Amorphous and Crystalline Rough Surfaces-principles and Applications. Academic Press, New York (2001)

    Google Scholar 

  64. Palasantzas, G.: Power spectrum and surface width of self-affine fractal surfaces via the k-correlation model. Phys. Rev. B 48, 14472–14478 (1993)

    Article  ADS  Google Scholar 

  65. Palasantzas, G.: Phys. Rev. B 49, 5785 (1994)

    Article  ADS  Google Scholar 

  66. Klimchitskaya, G.L., Pavlov, Yu.V.: The correction to the Casimir forces for configurations used in experiments: the spherical lens above the plane and two crossed cylinders. Int. J. Mod. Phys. A 11, 3723–3742 (1996)

    Article  ADS  Google Scholar 

  67. Rodriguez, A., Ibanescu, M., Iannuzzi, D., Capasso, F., Joannopoulos, J.D., Johnson, S.G.: Computation and Visualization of Casimir Forces in Arbitrary Geometries: Nonmonotonic Lateral-Wall Forces and the Failure of Proximity-Force Approximations. Phys. Rev. Lett. 99, 080401 (2007)

    Article  ADS  Google Scholar 

  68. van Zwol, P.J., Palasantzas, G., De Hosson, J.Th.M.: Influence of roughness on capillary forces between hydrophilic sur-faces. Phys. Rev. E 78, 031606 (2008)

    Article  ADS  Google Scholar 

  69. DelRio, F.W., Dunn, M.L., Phinney, L.M., Bourdon, C.J.: Rough surface adhesion in the presence of capillary condensation. Appl. Phys. Lett. 90, 163104 (2007)

    Article  ADS  Google Scholar 

  70. van Zwol, P.J., Palasantzas, G., De Hosson, J.Th.M.: Influence of random roughness on the adhesion between metal surfaces due to capillary condensation. Appl. Phys. Lett. 91, 101905 (2007)

    Article  ADS  Google Scholar 

  71. Israelachvili, J.: Intermolecular and Surface Forces. Academic, New York (1992)

    Google Scholar 

  72. Palasantzas, G., Svetovoy, V.B., van Zwol, P.J.: Influence of water adsorbed on gold on van der Waals/Casimir forces. Phys. Rev. B 79, 235434 (2009)

    Article  ADS  Google Scholar 

  73. van Zwol, P.J., Svetovoy, V.B., Palasantzas, G.: Distance upon contact: Determination from roughness profile. Phys. Rev. B 80, 235401 (2009)

    Article  ADS  Google Scholar 

  74. Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. A 295, 300–319 (1966)

    Article  ADS  Google Scholar 

  75. Coles, S.: An Introduction to Statistical Modelling of Extreme Values. Springer, Berlin (2001)

    Google Scholar 

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Acknowledgements

The research was carried out under Project No. MC3.05242 in the framework of the Strategic Research Programme of the Materials Innovation Institute M2i (the former Netherlands Institute for Metals Research NIMR) The authors benefited from exchange of ideas by the ESF Research Network CASIMIR.

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Authors and Affiliations

  1. Materials Innovation Institute and Zernike Institute for Advanced Materials, University of Groningen, AG, 9747, Groningen, The Netherlands

    P. J. van Zwol & G. Palasantzas

  2. MESA+ Institute for Nanotechnology, University of Twente, PO 217, AE, 7500, Enschede, The Netherlands

    V. B. Svetovoy

Authors
  1. P. J. van Zwol
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  2. V. B. Svetovoy
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  3. G. Palasantzas
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Correspondence to P. J. van Zwol .

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Editors and Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Diego Dalvit

  2. , Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Peter Milonni

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    David Roberts

  4. , Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Felipe da Rosa

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van Zwol, P.J., Svetovoy, V.B., Palasantzas, G. (2011). Characterization of Optical Properties and Surface Roughness Profiles: The Casimir Force Between Real Materials. In: Dalvit, D., Milonni, P., Roberts, D., da Rosa, F. (eds) Casimir Physics. Lecture Notes in Physics, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20288-9_10

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