Abstract

We simulate and measure light scattering of a micrometer-sized spherical particle suspended in solution close to a glass substrate. The model, based on the discrete sources method, is developed to describe the experimental situation of total internal reflection microscopy experiments; i.e., the particle is illuminated by an evanescent light field originating from the glass–solvent interface. In contrast to the well-established assumption of a simple exponential decay of the scattering intensity with distance, we demonstrate significant deviations for a certain range of penetration depths and polarization states of the incident light.

© 2006 Optical Society of America

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  1. D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
    [CrossRef]
  2. L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
    [CrossRef]
  3. J. N. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, 1991).
  4. R. M. Pashley, "Atomic force microscopy: a new method for the study of colloidal forces," Sci. Prog. (London) 78, 173-182 (1995).
  5. S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
    [CrossRef]
  6. H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
    [CrossRef]
  7. M. A. Bevan and D. C. Prieve, "Direct measurement of retarded van der Waals attraction," Langmuir 15, 7925-7936 (1999).
    [CrossRef]
  8. V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
    [CrossRef]
  9. A. Sharma and J. Y. Walz, "Direct measurements of depletion interaction in charged colloidal dispersion," J. Chem. Soc. Faraday Trans. 92, 4997-5004 (1996).
    [CrossRef]
  10. D. Rudhardt, C. Bechinger, and P. Leiderer, "Direct measurement of depletion potentials in mixtures of colloids and non-ionic polymers," Phys. Rev. Lett. 81, 1330-1333 (1998).
    [CrossRef]
  11. D. Rudhardt, P. Leiderer, and C. Bechinger, "Entropic forces beyond entropy," in Soft condensed Matter Physics. Annual Report 2000 (Universität Konstanz, 2001), report C16, pp. 50-51.
  12. L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
    [CrossRef] [PubMed]
  13. J. Y. Walz, "Measuring particle interactions with total internal reflection microscopy," Current Opinion in Colloid and Interface Science 2, 600-606 (1997).
    [CrossRef]
  14. D. C. Prieve, "Measurement of colloidal forces with TIRM," Advances in Colloid and Interface Science 82, 93-125 (1999).
    [CrossRef]
  15. S. G. Bike, "Measuring colloidal forces using evanescent wave scattering," Curr. Opin. Colloid Interface Sci. 5, 144-150 (2000).
    [CrossRef]
  16. D. C. Prieve and J. Y. Walz, "Scattering of an evanescent surface wave by a microscopic dielectric sphere," Appl. Opt. 32, 1629-1641 (1993).
    [CrossRef] [PubMed]
  17. L. Suresh, J. Y. Walz, and E. D. Hirleman, "Detection of particles on surfaces using evanescent wave scattering," in Particles on Surfaces V and VI, K. L. Mittal, ed. (Fine Particle Society, 1998), pp. 19-34.
  18. C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
    [CrossRef] [PubMed]
  19. Y. Eremin, "The method of discrete sources in electromagnetic scattering by axially symmetric structures," J. Commun. Technol. Electron. 45, S269-S280 (2000).
  20. A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis using Discrete Sources (Academic, 2000).
  21. Y. Eremin and T. Wriedt, "Large dielectric non-spherical particle in an evanescent wave field near a plane surface.," Opt. Commun. 214, 39-45 (2002).
    [CrossRef]
  22. A. Doicu, Y. Eremin, and T. Wriedt, "Scattering of evanescent waves by a sensor tip near a plane surface," Opt. Commun. 190, 5-12 (2001).
    [CrossRef]
  23. Y. Eremin, N. Orlov, and A. Sveshnikov, in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed. (Elsevier Science, 1999), p. 39.
  24. J. Rädler and E. Sackmann, "On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy," Langmuir 8, 848-853 (1992).
    [CrossRef]
  25. M. Gu and P. C. Ke, "Direct measurement of evanescent wave interference patterns with laser-trapped dielectric and metallic particles," in Optical Engineering for Sensing and Nanotechnology (ICOSN '99), I. Yamaguchi, ed. Proc. SPIE 3740, 323-326 (1999).
  26. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, 1991).
  27. J. Y. Walz and D. C. Prieve, "Prediction and measurement of the optical trapping forces on a dielectric sphere," Langmuir 8, 3073-3082 (1992).
    [CrossRef]
  28. S. C. Clark, J. Y. Walz, and W. A. Ducker, "Atomic force microscopy colloid-probe measurements with explicit measurement of particle-solid separation," Langmuir 20, 7616-7622 (2004).
    [CrossRef] [PubMed]
  29. R. Roth, R. Evans, and S. Dietrich, "Depletion potential in hard sphere mixtures: theory and applications," Phys. Rev. E 62, 5360-5377 (2000).
    [CrossRef]

2005

V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
[CrossRef]

C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
[CrossRef] [PubMed]

2004

L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
[CrossRef]

S. C. Clark, J. Y. Walz, and W. A. Ducker, "Atomic force microscopy colloid-probe measurements with explicit measurement of particle-solid separation," Langmuir 20, 7616-7622 (2004).
[CrossRef] [PubMed]

2003

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

2002

Y. Eremin and T. Wriedt, "Large dielectric non-spherical particle in an evanescent wave field near a plane surface.," Opt. Commun. 214, 39-45 (2002).
[CrossRef]

2001

A. Doicu, Y. Eremin, and T. Wriedt, "Scattering of evanescent waves by a sensor tip near a plane surface," Opt. Commun. 190, 5-12 (2001).
[CrossRef]

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

2000

Y. Eremin, "The method of discrete sources in electromagnetic scattering by axially symmetric structures," J. Commun. Technol. Electron. 45, S269-S280 (2000).

S. G. Bike, "Measuring colloidal forces using evanescent wave scattering," Curr. Opin. Colloid Interface Sci. 5, 144-150 (2000).
[CrossRef]

R. Roth, R. Evans, and S. Dietrich, "Depletion potential in hard sphere mixtures: theory and applications," Phys. Rev. E 62, 5360-5377 (2000).
[CrossRef]

1999

M. Gu and P. C. Ke, "Direct measurement of evanescent wave interference patterns with laser-trapped dielectric and metallic particles," in Optical Engineering for Sensing and Nanotechnology (ICOSN '99), I. Yamaguchi, ed. Proc. SPIE 3740, 323-326 (1999).

D. C. Prieve, "Measurement of colloidal forces with TIRM," Advances in Colloid and Interface Science 82, 93-125 (1999).
[CrossRef]

M. A. Bevan and D. C. Prieve, "Direct measurement of retarded van der Waals attraction," Langmuir 15, 7925-7936 (1999).
[CrossRef]

1998

D. Rudhardt, C. Bechinger, and P. Leiderer, "Direct measurement of depletion potentials in mixtures of colloids and non-ionic polymers," Phys. Rev. Lett. 81, 1330-1333 (1998).
[CrossRef]

1997

J. Y. Walz, "Measuring particle interactions with total internal reflection microscopy," Current Opinion in Colloid and Interface Science 2, 600-606 (1997).
[CrossRef]

1996

A. Sharma and J. Y. Walz, "Direct measurements of depletion interaction in charged colloidal dispersion," J. Chem. Soc. Faraday Trans. 92, 4997-5004 (1996).
[CrossRef]

1995

R. M. Pashley, "Atomic force microscopy: a new method for the study of colloidal forces," Sci. Prog. (London) 78, 173-182 (1995).

1993

S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
[CrossRef]

D. C. Prieve and J. Y. Walz, "Scattering of an evanescent surface wave by a microscopic dielectric sphere," Appl. Opt. 32, 1629-1641 (1993).
[CrossRef] [PubMed]

1992

J. Y. Walz and D. C. Prieve, "Prediction and measurement of the optical trapping forces on a dielectric sphere," Langmuir 8, 3073-3082 (1992).
[CrossRef]

J. Rädler and E. Sackmann, "On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy," Langmuir 8, 848-853 (1992).
[CrossRef]

1987

D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
[CrossRef]

Babic, D.

V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
[CrossRef]

Bechinger, C.

V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
[CrossRef]

L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
[CrossRef]

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

D. Rudhardt, C. Bechinger, and P. Leiderer, "Direct measurement of depletion potentials in mixtures of colloids and non-ionic polymers," Phys. Rev. Lett. 81, 1330-1333 (1998).
[CrossRef]

D. Rudhardt, P. Leiderer, and C. Bechinger, "Entropic forces beyond entropy," in Soft condensed Matter Physics. Annual Report 2000 (Universität Konstanz, 2001), report C16, pp. 50-51.

Bevan, M. A.

M. A. Bevan and D. C. Prieve, "Direct measurement of retarded van der Waals attraction," Langmuir 15, 7925-7936 (1999).
[CrossRef]

Bike, S. G.

S. G. Bike, "Measuring colloidal forces using evanescent wave scattering," Curr. Opin. Colloid Interface Sci. 5, 144-150 (2000).
[CrossRef]

S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
[CrossRef]

Blickle, V.

V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
[CrossRef]

Clark, S. C.

C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
[CrossRef] [PubMed]

S. C. Clark, J. Y. Walz, and W. A. Ducker, "Atomic force microscopy colloid-probe measurements with explicit measurement of particle-solid separation," Langmuir 20, 7616-7622 (2004).
[CrossRef] [PubMed]

Dietrich, S.

R. Roth, R. Evans, and S. Dietrich, "Depletion potential in hard sphere mixtures: theory and applications," Phys. Rev. E 62, 5360-5377 (2000).
[CrossRef]

Doicu, A.

A. Doicu, Y. Eremin, and T. Wriedt, "Scattering of evanescent waves by a sensor tip near a plane surface," Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis using Discrete Sources (Academic, 2000).

Ducker, W. A.

C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
[CrossRef] [PubMed]

S. C. Clark, J. Y. Walz, and W. A. Ducker, "Atomic force microscopy colloid-probe measurements with explicit measurement of particle-solid separation," Langmuir 20, 7616-7622 (2004).
[CrossRef] [PubMed]

Eremin, Y.

Y. Eremin and T. Wriedt, "Large dielectric non-spherical particle in an evanescent wave field near a plane surface.," Opt. Commun. 214, 39-45 (2002).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, "Scattering of evanescent waves by a sensor tip near a plane surface," Opt. Commun. 190, 5-12 (2001).
[CrossRef]

Y. Eremin, "The method of discrete sources in electromagnetic scattering by axially symmetric structures," J. Commun. Technol. Electron. 45, S269-S280 (2000).

Y. Eremin, N. Orlov, and A. Sveshnikov, in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed. (Elsevier Science, 1999), p. 39.

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis using Discrete Sources (Academic, 2000).

Evans, R.

R. Roth, R. Evans, and S. Dietrich, "Depletion potential in hard sphere mixtures: theory and applications," Phys. Rev. E 62, 5360-5377 (2000).
[CrossRef]

Flicker, S. G.

S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
[CrossRef]

Gu, M.

M. Gu and P. C. Ke, "Direct measurement of evanescent wave interference patterns with laser-trapped dielectric and metallic particles," in Optical Engineering for Sensing and Nanotechnology (ICOSN '99), I. Yamaguchi, ed. Proc. SPIE 3740, 323-326 (1999).

Helden, L.

L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
[CrossRef]

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

Hirleman, E. D.

L. Suresh, J. Y. Walz, and E. D. Hirleman, "Detection of particles on surfaces using evanescent wave scattering," in Particles on Surfaces V and VI, K. L. Mittal, ed. (Fine Particle Society, 1998), pp. 19-34.

Israelachvili, J. N.

J. N. Israelachvili, Intermolecular and Surface Forces, 2nd ed. (Academic, 1991).

Ke, P. C.

M. Gu and P. C. Ke, "Direct measurement of evanescent wave interference patterns with laser-trapped dielectric and metallic particles," in Optical Engineering for Sensing and Nanotechnology (ICOSN '99), I. Yamaguchi, ed. Proc. SPIE 3740, 323-326 (1999).

Koenderink, G. H.

L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
[CrossRef]

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

Lanni, F.

D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
[CrossRef]

Leiderer, P.

L. Helden, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Depletion potentials induced by charged colloidal rods," Langmuir 20, 5662-5665 (2004).
[CrossRef]

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

D. Rudhardt, C. Bechinger, and P. Leiderer, "Direct measurement of depletion potentials in mixtures of colloids and non-ionic polymers," Phys. Rev. Lett. 81, 1330-1333 (1998).
[CrossRef]

D. Rudhardt, P. Leiderer, and C. Bechinger, "Entropic forces beyond entropy," in Soft condensed Matter Physics. Annual Report 2000 (Universität Konstanz, 2001), report C16, pp. 50-51.

Luo, F.

D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
[CrossRef]

McKee, C. T.

C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
[CrossRef] [PubMed]

Orlov, N.

Y. Eremin, N. Orlov, and A. Sveshnikov, in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed. (Elsevier Science, 1999), p. 39.

Pashley, R. M.

R. M. Pashley, "Atomic force microscopy: a new method for the study of colloidal forces," Sci. Prog. (London) 78, 173-182 (1995).

Prieve, D. C.

D. C. Prieve, "Measurement of colloidal forces with TIRM," Advances in Colloid and Interface Science 82, 93-125 (1999).
[CrossRef]

M. A. Bevan and D. C. Prieve, "Direct measurement of retarded van der Waals attraction," Langmuir 15, 7925-7936 (1999).
[CrossRef]

D. C. Prieve and J. Y. Walz, "Scattering of an evanescent surface wave by a microscopic dielectric sphere," Appl. Opt. 32, 1629-1641 (1993).
[CrossRef] [PubMed]

J. Y. Walz and D. C. Prieve, "Prediction and measurement of the optical trapping forces on a dielectric sphere," Langmuir 8, 3073-3082 (1992).
[CrossRef]

D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
[CrossRef]

Rädler, J.

J. Rädler and E. Sackmann, "On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy," Langmuir 8, 848-853 (1992).
[CrossRef]

Roth, R.

L. Helden, R. Roth, G. H. Koenderink, P. Leiderer, and C. Bechinger, "Direct measurement of entropic forces induced by rigid rods," Phys. Rev. Lett. 90, 048301 (2003).
[CrossRef] [PubMed]

R. Roth, R. Evans, and S. Dietrich, "Depletion potential in hard sphere mixtures: theory and applications," Phys. Rev. E 62, 5360-5377 (2000).
[CrossRef]

Rudhardt, D.

D. Rudhardt, C. Bechinger, and P. Leiderer, "Direct measurement of depletion potentials in mixtures of colloids and non-ionic polymers," Phys. Rev. Lett. 81, 1330-1333 (1998).
[CrossRef]

D. Rudhardt, P. Leiderer, and C. Bechinger, "Entropic forces beyond entropy," in Soft condensed Matter Physics. Annual Report 2000 (Universität Konstanz, 2001), report C16, pp. 50-51.

Sackmann, E.

J. Rädler and E. Sackmann, "On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy," Langmuir 8, 848-853 (1992).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, 1991).

Sharma, A.

A. Sharma and J. Y. Walz, "Direct measurements of depletion interaction in charged colloidal dispersion," J. Chem. Soc. Faraday Trans. 92, 4997-5004 (1996).
[CrossRef]

Suresh, L.

L. Suresh, J. Y. Walz, and E. D. Hirleman, "Detection of particles on surfaces using evanescent wave scattering," in Particles on Surfaces V and VI, K. L. Mittal, ed. (Fine Particle Society, 1998), pp. 19-34.

Sveshnikov, A.

Y. Eremin, N. Orlov, and A. Sveshnikov, in Generalized Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed. (Elsevier Science, 1999), p. 39.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. (Wiley, 1991).

Tipa, J. L.

S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
[CrossRef]

von Grünberg, H. H.

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

Walz, J. Y.

C. T. McKee, S. C. Clark, J. Y. Walz, and W. A. Ducker, "Relationship between scattered intensity and separation for particles in an evanescent field," Langmuir 21, 5783-5789 (2005).
[CrossRef] [PubMed]

S. C. Clark, J. Y. Walz, and W. A. Ducker, "Atomic force microscopy colloid-probe measurements with explicit measurement of particle-solid separation," Langmuir 20, 7616-7622 (2004).
[CrossRef] [PubMed]

J. Y. Walz, "Measuring particle interactions with total internal reflection microscopy," Current Opinion in Colloid and Interface Science 2, 600-606 (1997).
[CrossRef]

A. Sharma and J. Y. Walz, "Direct measurements of depletion interaction in charged colloidal dispersion," J. Chem. Soc. Faraday Trans. 92, 4997-5004 (1996).
[CrossRef]

D. C. Prieve and J. Y. Walz, "Scattering of an evanescent surface wave by a microscopic dielectric sphere," Appl. Opt. 32, 1629-1641 (1993).
[CrossRef] [PubMed]

J. Y. Walz and D. C. Prieve, "Prediction and measurement of the optical trapping forces on a dielectric sphere," Langmuir 8, 3073-3082 (1992).
[CrossRef]

L. Suresh, J. Y. Walz, and E. D. Hirleman, "Detection of particles on surfaces using evanescent wave scattering," in Particles on Surfaces V and VI, K. L. Mittal, ed. (Fine Particle Society, 1998), pp. 19-34.

Wriedt, T.

Y. Eremin and T. Wriedt, "Large dielectric non-spherical particle in an evanescent wave field near a plane surface.," Opt. Commun. 214, 39-45 (2002).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, "Scattering of evanescent waves by a sensor tip near a plane surface," Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis using Discrete Sources (Academic, 2000).

Advances in Colloid and Interface Science

D. C. Prieve, "Measurement of colloidal forces with TIRM," Advances in Colloid and Interface Science 82, 93-125 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

V. Blickle, D. Babic, and C. Bechinger, "Evanescent light scattering with magnetic colloids," Appl. Phys. Lett. 87, 101102 (2005).
[CrossRef]

Curr. Opin. Colloid Interface Sci.

S. G. Bike, "Measuring colloidal forces using evanescent wave scattering," Curr. Opin. Colloid Interface Sci. 5, 144-150 (2000).
[CrossRef]

Current Opinion in Colloid and Interface Science

J. Y. Walz, "Measuring particle interactions with total internal reflection microscopy," Current Opinion in Colloid and Interface Science 2, 600-606 (1997).
[CrossRef]

Faraday Discuss. Chem. Soc.

D. C. Prieve, F. Luo, and F. Lanni, "Brownian motion of a hydrosol particle in a colloidal force field," Faraday Discuss. Chem. Soc. 83, 297-307 (1987).
[CrossRef]

J. Chem. Phys.

H. H. von Grünberg, L. Helden, P. Leiderer, and C. Bechinger, "Measurement of surface charge densities on Brownian particles using total internal reflection microscopy," J. Chem. Phys. 114, 10094-10104 (2001).
[CrossRef]

J. Chem. Soc. Faraday Trans.

A. Sharma and J. Y. Walz, "Direct measurements of depletion interaction in charged colloidal dispersion," J. Chem. Soc. Faraday Trans. 92, 4997-5004 (1996).
[CrossRef]

J. Colloid Interface Sci.

S. G. Flicker, J. L. Tipa, and S. G. Bike, "Quantifying double-layer repulsion between a colloidal sphere and a glass plate using total internal reflection microscopy," J. Colloid Interface Sci. 158, 317-325 (1993).
[CrossRef]

J. Commun. Technol. Electron.

Y. Eremin, "The method of discrete sources in electromagnetic scattering by axially symmetric structures," J. Commun. Technol. Electron. 45, S269-S280 (2000).

Langmuir

M. A. Bevan and D. C. Prieve, "Direct measurement of retarded van der Waals attraction," Langmuir 15, 7925-7936 (1999).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental situation in TIRM. A laser beam is coupled into a prism and hits the glass–water interface at an angle Θ 1 , which is larger than the angle of total internal reflection Θ 1 C . Thus an evanescent field is generated at the interface with intensity I ev , decaying exponentially into the medium. A spherical colloidal particle near the interface will scatter light from the evanescent field with a scattering intensity I sc .

Fig. 2
Fig. 2

Scattering intensity I ( Θ ) according to Eqs. (7) integrated over ϕ for a 1.6 μ m diameter polystyrene particle ( n = 1.59 ) suspended in water ( n = 1.333 ) at a distance of z = 50   nm away from a glass surface ( n = 1.515 ) and λ 0 = 658   nm . (a) Results for PP conditions. (b) Calculated for SS conditions. Solid curves, for a moderate penetration depth of ζ 1 = 180   nm ; dotted curves, for a larger penetration depth of ζ 1 = 377   nm . The two vertical lines mark the acceptance cone of a microscope objective with 0.5   NA .

Fig. 3
Fig. 3

Objective response for a 1.6 μ m diameter polystyrene particle suspended in water as a function of distance z for different penetration depths (a) ζ 1 = 132   nm , (b) ζ 1 = 180   nm , (c) ζ 1 = 377   nm . The penetration depths correspond to 5°, 2.6°, and 0.58° deviation from the critical angle Θ 1 C = 61.63 ° , respectively, and λ 0 = 658   nm . Circles, result for SS conditions ( σ S S ) squares, for PP conditions ( σ P P ) . For the sake of clarity the squares in (c) are shifted −0.005 units in the vertical direction. The solid curves are analytical functions of the form I ( z ) = A exp ( ζ z ) , showing the expectations from the exponential model. The prefactor A was chosen to allow convenient comparison with the simulation data by matching the curves for large distances. The triangles in (c) explicitly show the difference between the simulation results and the exponential curve for SS conditions, revealing the oscillatory structure of the deviations. The dotted curve that overlaps the triangles shows the empirical fit according to Eq. (11). Note that the first exponential term in Eq. (11) was subtracted in the same way as for the data.

Fig. 4
Fig. 4

Objective response for a 1.6 μ m diameter polystyrene ( n = 1.59 ) particle suspended in water as a function of distance z for PS conditions (diamonds) and SP conditions (triangles) at ζ 1 = 377   nm and λ 0 = 658   nm . The solid curves are analytical functions of the form I ( z ) = A   exp ( ζ z ) , showing the expectations from the exponential model. The prefactor A was chosen to allow convenient comparison with the simulation data by matching the curves for large distances.

Fig. 5
Fig. 5

a) Typical interaction potential of a TIRM probe particle with the substrate according to Eq. (9), using parameters B = 20 , κ 1 = 15   nm , G = 5 . b) Calculated distorted TIRM potential achieved by assuming the exponential model for data evaluation under conditions where the true intensity–distance relation is the DSM result shown in Fig. 3(c) as circles. Details are discussed in the text.

Fig. 6
Fig. 6

Standard TIRM potentials measured with a 3 μ m diameter polystyrene particle in aqueous dispersion containing c salt = 50 μ mol / l of NaCl near a glass wall at ζ 1 = 400   nm penetration depth. The upper curve (circles) was measured under SS conditions, while the lower curve (squares) was obtained under PP conditions. Since no absolute distance could be determined, the distance scale has an offset z offset chosen such that the first minimum in each standard TIRM potential appears at z z offset = 0 . The curve that overlaps the squares is a fit of Eq. (9) to the PP data by using B and Φ 0 as free parameters and the calculated values of κ 1 = 43   nm and G = 1.8 k B T μ m - 1 , equivalent to a gravity force of 7.4   fN .

Fig. 7
Fig. 7

Standard TIRM potentials measured under SS conditions with a 4 μ m diameter polystyrene particle in aqueous dispersion containing c salt = 150 μ mol / l of NaCl at various penetration depths: ζ 1 = 135   nm (diamonds), ζ 1 = 169   nm (triangles), ζ 1 = 400   nm (circles), ζ 1 = 624   nm (squares). The topmost curve is a fit of Eq. (9) to the ζ 1 = 135   nm (diamonds) data, which agrees well with the real potential shape. Again B and Φ 0 were free parameters, and the calculated values of κ 1 = 25   nm and G = 4.8 k B T μ m - 1 were used. The potentials for larger penetration depths are shifted downward, and the fitted curve is reproduced for each potential with the appropriate shift. Since no absolute distance could be determined, the distance scale has an offset ( z offset ) chosen such that the minimum of the ζ 1 = 135   nm (diamonds) potential is at z z offset = 0 . The other potentials were aligned accordingly along the z axis.

Fig. 8
Fig. 8

Standard TIRM potentials measured under SS conditions with a 3 μ m diameter polystyrene particle at a penetration depth of ζ 1 = 400   nm for three different salt concentrations: c salt = 10 μ mol / l (diamonds), 50 μ mol / l (triangles), 250 μ mol / l (circles). With increasing salt concentration the particle comes closer to the substrate. The absolute particle–wall distance was determined with the sticking method, which is subject to a large error but is consistent for all three potentials. The expected slope to which all potentials should converge for large distances is indicated by the underlying straight line.

Equations (167)

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Θ 1
Θ 1 C
ζ 1
ζ 1 = λ 0 4 π n 1 sin 2 Θ 1 sin 2 Θ 1 C .
n 1
λ 0
I sc
100   Hz
p ( z )
Φ ( z )
p ( z ) = exp ( Φ ( z ) / k B T ) ,
k B T
I ev
I ev exp ( ζ z ) .
( I sc )
I sc ( z ) = I 0   exp ( ζ z ) ,
I 0
( z = 0 )
I 0
I α ( θ , ϕ ) = | E , θ 0 , α ( θ , ϕ ) | 2 + | E , ϕ 0 , α ( θ , ϕ ) | 2 ,
α = P , S
E , θ 0 , α ( θ , ϕ )
E , ϕ 0 , α ( θ , ϕ )
E , θ 0 , P
E , ϕ 0 , P
E , θ 0 , S ( θ , ϕ ) = j k 0 / ε 0 m = 0 M sin ( m +1 ) ϕ ( j k 0 / ε 0   sin   θ ) m × n = 1 N 0 m { p n , m 0   cos   θ [ γ n + ( ν e ν sin 2 θ ) γ n ] q n , m 0 ( γ + ν h γ n ) } ,
E , ϕ 0 , S ( θ , ϕ ) = - j k 0 / ε 0 m = 0 M cos ( m +1 ) ϕ ( j k 0 / ε 0  sin   θ ) m × n = 1 N 0 m { p n , m 0  cos   θ ( γ + ν e γ n ) q n , m 0 [ γ n + ( ν h ν sin 2 θ ) γ n ] cos   θ } + j k 0 / ε 0  sin   θ n =1 N 0 0 r n     0 ( γ + ν h γ n ) .
I P P = | E 0 , P · e x | 2 = | E , θ 0 , P  cos   θ  cos   ϕ E , ϕ 0 , P  sin   ϕ | 2 ,
I P S = | E 0 , P · e y | 2 = | E , θ 0 , P  cos   θ  sin   ϕ + E , ϕ 0 , P  cos   ϕ | 2 ,
I S P = | E 0 , S · e x | 2 = | E , θ 0 , S  cos   θ  cos   ϕ E , ϕ 0 , S  sin   ϕ | 2 ,
I S S = | E 0 , S · e y | 2 = | E , θ 0 , S  cos   θ  sin   ϕ + E , ϕ 0 , S  cos   ϕ | 2 .
σ S PP , PS , SP , S S = Ω I PP , PS , SP , S S ( θ ,   ϕ ) d ω ,
Ω = { 0 ϕ 360 ° ; 0 ; 0 θ θ NA }
θ NA
θ NA = arcsin ( NA / n 0 )
0.1 %
1.6 μ m
z = 50   nm
ζ 1 = 377   nm
ζ 1 = 180   nm
Θ = 80 °
Θ = 10 °
Θ = 60 °
Θ < 60 °
Θ = 0 °
50 ×
ζ 1 = 132   nm
z > 100   nm
( z < 100   nm )
250   nm
ζ 1 = 180   nm
ζ 1 = 377   nm
ζ 1 = 180   nm
250   nm
ζ 1 = 377   nm
300   nm
( λ n = 1.333 / 2 = 247   nm )
3 %
( z = 0 )
50   nm
z = 0   nm
z = 70   nm
Φ ( z ) = B   exp ( - κ z ) + G z + Φ 0 .
κ 1 = ε k B T 2 e 2 1 c salt ,
c salt
k B T
Φ 0
100   nm
1.6 μ m
ζ 1 = 377   nm
0 < z < 1200   nm
I DSM ( z ) μ m 2 = 38.32 × 10 3   exp ( z 377   nm ) + 5.04 × 10 3   exp ( z 187.31   nm ) × sin [ π ( z + 20.86   nm ) 191.29   nm - 0 .04995 z ] ( 2.22 × 10 3 ) + ( 3.34 × 10 6 nm 1 ) z ( 1.32 × 10 9 nm 2 ) z 2 .
( > 1 k B T )
z = 350   nm
z = 650   nm
I 0
z = 0
( z < 100   nm )
50   nm
z = 0
I 0
λ 0 = 658   nm
λ / 2
50 ×
( NA  of   0.5
I 0
( z offset )
3 μ m
ζ 1 = 400   nm
Φ 0
ζ 1 = 135   nm
ζ 1 = 625   nm
4 μ m
ζ 1 = 135   nm
ζ 1 = 300   nm
3 μ m
ζ 1 = 400   nm
I 0
I 0
23 μ m
130   nm
z > 100   nm
z < 100   nm
150   nm
150   nm
SiO 2
300   nm
ζ 1 < 200   nm
ζ 1 > 377   nm
Θ 1
Θ 1 C
I ev
I sc
I ( Θ )
1.6 μ m
( n = 1.59 )
( n = 1.333 )
z = 50   nm
( n = 1.515 )
λ 0 = 658   nm
ζ 1 = 180   nm
ζ 1 = 377   nm
0.5   NA
1.6 μ m
ζ 1 = 132   nm
ζ 1 = 180   nm
ζ 1 = 377   nm
Θ 1 C = 61.63 °
λ 0 = 658   nm
( σ S S )
( σ P P )
I ( z ) = A exp ( ζ z )
1.6 μ m
( n = 1.59 )
ζ 1 = 377   nm
λ 0 = 658   nm
I ( z ) = A   exp ( ζ z )
B = 20
κ 1 = 15   nm
G = 5
3 μ m
c salt = 50 μ mol / l
ζ 1 = 400   nm
z offset
z z offset = 0
Φ 0
κ 1 = 43   nm
G = 1.8 k B T μ m - 1
7.4   fN
4 μ m
c salt = 150 μ mol / l
ζ 1 = 135   nm
ζ 1 = 169   nm
ζ 1 = 400   nm
ζ 1 = 624   nm
ζ 1 = 135   nm
Φ 0
κ 1 = 25   nm
G = 4.8 k B T μ m - 1
( z offset )
ζ 1 = 135   nm
z z offset = 0
3 μ m
ζ 1 = 400   nm
c salt = 10 μ mol / l
50 μ mol / l
250 μ mol / l

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