Abstract

Total Internal Reflection Microscopy (TIRM) is a sensitive non-invasive technique to measure the interaction potentials between a colloidal particle and a wall with femtonewton resolution. The equilibrium distribution of the particle-wall separation distance z is sampled monitoring the intensity I scattered by the Brownian particle under evanescent illumination. Central to the data analysis is the knowledge of the relation between I and the corresponding z, which typically must be known a priori. This poses considerable constraints to the experimental conditions where TIRM can be applied (short penetration depth of the evanescent wave, transparent surfaces). Here, we introduce a method to experimentally determine I(z) by relying only on the distance-dependent particle-wall hydrodynamic interactions. We demonstrate that this method largely extends the range of conditions accessible with TIRM, and even allows measurements on highly reflecting gold surfaces where multiple reflections lead to a complex I(z).

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
    [CrossRef]
  8. S. G. Bike and D. C. Prieve, "Measurements of double-layer repulsion for slightly overlapping counterion clouds," Int. J. Multiphase Flow 16, 727-740 (1990).
    [CrossRef]
  9. 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]
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    [CrossRef]
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    [CrossRef]
  12. M. A. Bevan and P. J. Scales, "Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO," Langmuir 18, 1474-1484 (2002).
    [CrossRef]
  13. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
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    [CrossRef]
  19. R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (1999).
    [CrossRef]
  20. C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
    [CrossRef]
  21. L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
    [CrossRef] [PubMed]
  22. N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
    [CrossRef]
  23. 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]
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    [CrossRef]
  25. O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
    [CrossRef]
  26. G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
    [CrossRef]
  27. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
    [CrossRef] [PubMed]
  28. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
    [CrossRef]
  29. A. Ulman, "Formation and structure of self-assembled monolayers," Chem. Rev. 96, 1533-1554 (1996).
    [CrossRef] [PubMed]
  30. C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
    [CrossRef] [PubMed]
  31. 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]
  32. H. Brenner, "The slow motion of a sphere through a viscous fluid towards a plane surface," Chem. Eng. Sci. 16, 242-251 (1961).
    [CrossRef] [PubMed]
  33. R. J. Oetama and J. Y. Walz, "A new approach for analyzing particle motion near an interface using total internal reflection microscopy," J. Colloid. Interfac. Sci. 284, 323-331 (2005).
    [CrossRef]
  34. M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
    [CrossRef] [PubMed]
  35. M. A. Bevan and D. C. Prieve, "Hindered diffusion of colloidal particles very near to a wall: Revisited," J. Chem. Phys. 113, 1228-1236 (2000).
    [CrossRef] [PubMed]
  36. G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
    [CrossRef]

2008 (3)

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

2007 (5)

M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
[CrossRef] [PubMed]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
[CrossRef]

G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

2006 (3)

D. Kleshchanok, R. Tuinier, and P. R. Lang, "Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy," Langmuir 22, 9121-9128 (2006).
[CrossRef] [PubMed]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[CrossRef]

2005 (3)

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]

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

R. J. Oetama and J. Y. Walz, "A new approach for analyzing particle motion near an interface using total internal reflection microscopy," J. Colloid. Interfac. Sci. 284, 323-331 (2005).
[CrossRef]

2004 (1)

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

2003 (1)

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 (2)

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[CrossRef]

M. A. Bevan and P. J. Scales, "Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO," Langmuir 18, 1474-1484 (2002).
[CrossRef]

2001 (1)

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 (2)

C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
[CrossRef]

M. A. Bevan and D. C. Prieve, "Hindered diffusion of colloidal particles very near to a wall: Revisited," J. Chem. Phys. 113, 1228-1236 (2000).
[CrossRef] [PubMed]

1999 (3)

R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (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, "Measurement of colloidal forces with TIRM," Adv. Colloid. Interfac. Sci. 82, 93-125 (1999).
[CrossRef]

1997 (1)

J. Walz, "Measuring particle interactions with total internal reflection microscopy," Curr. Opin. Colloid. Interfac. Sci. 2, 600-606 (1997).
[CrossRef]

1996 (1)

A. Ulman, "Formation and structure of self-assembled monolayers," Chem. Rev. 96, 1533-1554 (1996).
[CrossRef] [PubMed]

1995 (1)

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

1993 (3)

1992 (1)

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]

1991 (1)

W. Ducker, T. Senden, and R. Pashley, "Direct measurement of colloidal forces using an atomic force microscope," Nature 353, 239-241 (1991).
[CrossRef]

1990 (1)

S. G. Bike and D. C. Prieve, "Measurements of double-layer repulsion for slightly overlapping counterion clouds," Int. J. Multiphase Flow 16, 727-740 (1990).
[CrossRef]

1986 (1)

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

1979 (1)

1961 (1)

H. Brenner, "The slow motion of a sphere through a viscous fluid towards a plane surface," Chem. Eng. Sci. 16, 242-251 (1961).
[CrossRef] [PubMed]

Arauz-Lara, J. L.

M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
[CrossRef] [PubMed]

Babic, D.

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

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[CrossRef]

Bechinger, C.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

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

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Bevan, M. A.

M. A. Bevan and P. J. Scales, "Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO," Langmuir 18, 1474-1484 (2002).
[CrossRef]

M. A. Bevan and D. C. Prieve, "Hindered diffusion of colloidal particles very near to a wall: Revisited," J. Chem. Phys. 113, 1228-1236 (2000).
[CrossRef] [PubMed]

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

Bielefeldt, H.

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

Bike, S. G.

S. G. Bike and D. C. Prieve, "Measurements of double-layer repulsion for slightly overlapping counterion clouds," Int. J. Multiphase Flow 16, 727-740 (1990).
[CrossRef]

Binnig, G.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Blickle, V.

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

Brenner, H.

H. Brenner, "The slow motion of a sphere through a viscous fluid towards a plane surface," Chem. Eng. Sci. 16, 242-251 (1961).
[CrossRef] [PubMed]

Carbajal-Tinoco, M. D.

M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
[CrossRef] [PubMed]

Chew, H.

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]

Dietrich, S.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Ducker, W.

W. Ducker, T. Senden, and R. Pashley, "Direct measurement of colloidal forces using an atomic force microscope," Nature 353, 239-241 (1991).
[CrossRef]

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]

Eremin, Y.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

Eremina, E.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Gambassi, A.

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Gerber, C.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Ghislain, L. P.

Girard, C.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

Hecht, B.

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

Helden, L.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

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]

Herminghaus, S.

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

Hertlein, C.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

Kaiser, T.

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

Kerker, M.

Kleshchanok, D.

D. Kleshchanok, R. Tuinier, and P. R. Lang, "Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy," Langmuir 22, 9121-9128 (2006).
[CrossRef] [PubMed]

Koenderink, G. H.

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]

Kozyreff, G.

G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Lang, P. R.

D. Kleshchanok, R. Tuinier, and P. R. Lang, "Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy," Langmuir 22, 9121-9128 (2006).
[CrossRef] [PubMed]

Lange, S.

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

Leiderer, P.

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]

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

Liu, C.

C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
[CrossRef]

Liu, C. C.

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

Lopez-Fernandez, R.

M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
[CrossRef] [PubMed]

Marti, O.

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[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]

Mlynek, J.

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

Oetama, R. J.

R. J. Oetama and J. Y. Walz, "A new approach for analyzing particle motion near an interface using total internal reflection microscopy," J. Colloid. Interfac. Sci. 284, 323-331 (2005).
[CrossRef]

Pack, A.

R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (1999).
[CrossRef]

Pashley, R.

W. Ducker, T. Senden, and R. Pashley, "Direct measurement of colloidal forces using an atomic force microscope," Nature 353, 239-241 (1991).
[CrossRef]

Petrov, D.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
[CrossRef]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[CrossRef]

Piech, M.

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[CrossRef]

Prieve, D. C.

M. A. Bevan and D. C. Prieve, "Hindered diffusion of colloidal particles very near to a wall: Revisited," J. Chem. Phys. 113, 1228-1236 (2000).
[CrossRef] [PubMed]

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

D. C. Prieve, "Measurement of colloidal forces with TIRM," Adv. Colloid. Interfac. Sci. 82, 93-125 (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]

S. G. Bike and D. C. Prieve, "Measurements of double-layer repulsion for slightly overlapping counterion clouds," Int. J. Multiphase Flow 16, 727-740 (1990).
[CrossRef]

Quate, C. F.

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

Quidant, R.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[CrossRef]

Quinten, M.

R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (1999).
[CrossRef]

Riefler, N.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

Righini, M.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

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]

Scales, P. J.

M. A. Bevan and P. J. Scales, "Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO," Langmuir 18, 1474-1484 (2002).
[CrossRef]

Schweiger, G.

C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
[CrossRef]

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

Senden, T.

W. Ducker, T. Senden, and R. Pashley, "Direct measurement of colloidal forces using an atomic force microscope," Nature 353, 239-241 (1991).
[CrossRef]

Tuinier, R.

D. Kleshchanok, R. Tuinier, and P. R. Lang, "Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy," Langmuir 22, 9121-9128 (2006).
[CrossRef] [PubMed]

Ulman, A.

A. Ulman, "Formation and structure of self-assembled monolayers," Chem. Rev. 96, 1533-1554 (1996).
[CrossRef] [PubMed]

Volpe, G.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
[CrossRef]

G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
[CrossRef]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[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.

J. Walz, "Measuring particle interactions with total internal reflection microscopy," Curr. Opin. Colloid. Interfac. Sci. 2, 600-606 (1997).
[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]

R. J. Oetama and J. Y. Walz, "A new approach for analyzing particle motion near an interface using total internal reflection microscopy," J. Colloid. Interfac. Sci. 284, 323-331 (2005).
[CrossRef]

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[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]

Wang, D.-S.

Wannemacher, R.

R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (1999).
[CrossRef]

Webb, W. W.

Weigel, T.

C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
[CrossRef]

Weronski, P.

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[CrossRef]

Wriedt, T.

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

L. Helden, E. Eremina, N. Riefler, C. Hertlein, C. Bechinger, Y. Eremin, and T. Wriedt, "Single-particle evanescent light scattering simulations for total internal reflection microscopy," Appl. Opt. 45, 7299-7308 (2006).
[CrossRef] [PubMed]

Wu, X.

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[CrossRef]

Zelenina, A. S.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

Adv. Colloid. Interfac. Sci. (1)

D. C. Prieve, "Measurement of colloidal forces with TIRM," Adv. Colloid. Interfac. Sci. 82, 93-125 (1999).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

R. Wannemacher, A. Pack, and M. Quinten, "Resonant absorption and scattering in evanescent fields," Appl. Phys. B 68, 225-232 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

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

Chem. Eng. Sci. (1)

H. Brenner, "The slow motion of a sphere through a viscous fluid towards a plane surface," Chem. Eng. Sci. 16, 242-251 (1961).
[CrossRef] [PubMed]

Chem. Rev. (1)

A. Ulman, "Formation and structure of self-assembled monolayers," Chem. Rev. 96, 1533-1554 (1996).
[CrossRef] [PubMed]

Curr. Opin. Colloid. Interfac. Sci. (1)

J. Walz, "Measuring particle interactions with total internal reflection microscopy," Curr. Opin. Colloid. Interfac. Sci. 2, 600-606 (1997).
[CrossRef]

Int. J. Multiphase Flow (1)

S. G. Bike and D. C. Prieve, "Measurements of double-layer repulsion for slightly overlapping counterion clouds," Int. J. Multiphase Flow 16, 727-740 (1990).
[CrossRef]

J. Appl. Phys. (1)

G. Volpe, G. Kozyreff, and D. Petrov, "Backscattering position detection for photonic force microscopy," J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

J. Chem. Phys. (2)

M. A. Bevan and D. C. Prieve, "Hindered diffusion of colloidal particles very near to a wall: Revisited," J. Chem. Phys. 113, 1228-1236 (2000).
[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]

J. Colloid Interfac. Sci. (1)

M. Piech, P. Weronski, X. Wu, and J. Y. Walz, "Prediction and measurement of the interparticle depletion interaction next to a flat wall," J. Colloid Interfac. Sci. 247, 327-341 (2002).
[CrossRef]

J. Colloid. Interfac. Sci. (1)

R. J. Oetama and J. Y. Walz, "A new approach for analyzing particle motion near an interface using total internal reflection microscopy," J. Colloid. Interfac. Sci. 284, 323-331 (2005).
[CrossRef]

J. Quantum Spectr. Rad. Transfer (1)

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, "Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy," J. Quantum Spectr. Rad. Transfer 106, 464-474 (2007).
[CrossRef]

Langmuir (6)

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]

C. Hertlein, N. Riefler, E. Eremina, T. Wriedt, Y. Eremin, L. Helden, and C. Bechinger, "Experimental verification of an exact evanescent light scattering model for TIRM," Langmuir 24, 1-4 (2008).
[CrossRef] [PubMed]

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]

D. Kleshchanok, R. Tuinier, and P. R. Lang, "Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy," Langmuir 22, 9121-9128 (2006).
[CrossRef] [PubMed]

M. A. Bevan and P. J. Scales, "Solvent quality dependent interactions and phase behavior of polystyrene particles with physisorbed PEO-PPO-PEO," Langmuir 18, 1474-1484 (2002).
[CrossRef]

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

Nature (2)

W. Ducker, T. Senden, and R. Pashley, "Direct measurement of colloidal forces using an atomic force microscope," Nature 353, 239-241 (1991).
[CrossRef]

C. Hertlein, L. Helden, A. Gambassi, S. Dietrich, and C. Bechinger, "Direct measurement of critical Casimir forces," Nature 451, 172-175 (2008).
[CrossRef] [PubMed]

Nature Phys. (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nature Phys. 3, 477-480 (2007).
[CrossRef] [PubMed]

Opt. Commun. (3)

O. Marti, H. Bielefeldt, B. Hecht, S. Herminghaus, P. Leiderer, and J. Mlynek, "Near-field optical measurement of the surface plasmon field," Opt. Commun. 96, 225-228 (1993).
[CrossRef]

C. Liu, T. Weigel, and G. Schweiger, "Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave," Opt. Commun. 185, 249-261 (2000).
[CrossRef]

C. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, "Structural resonances in a dielectric sphere illuminated by an evanescent wave," Opt. Commun. 117, 521-531 (1995).
[CrossRef]

Opt. Lett. (1)

Phys Rev. Lett. (1)

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, "Surface plasmon radiation forces," Phys Rev. Lett. 96, 238101 (2006).
[CrossRef]

Phys. Rev. E (1)

G. Volpe, G. Volpe, and D. Petrov, "Brownian motion in a nonhomogeneous force field and photonic force microscope," Phys. Rev. E 76, 061118 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

G. Binnig, C. F. Quate, and C. Gerber, "Atomic force microscope," Phys. Rev. Lett. 56, 930-933 (1986).
[CrossRef] [PubMed]

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]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, "Surface plasmon optical tweezers: tunable optical manipulation in the femto-newton range," Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

M. D. Carbajal-Tinoco, R. Lopez-Fernandez, and J. L. Arauz-Lara, "Asymmetry in colloidal diffusion near a rigid wall," Phys. Rev. Lett. 99, 138303 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Total Internal Reflection Microscopy (TIRM). (a) Schematic of a typical TIRM setup: a Brownian particle moves in the evanescent electromagnetic field generated by total internal reflection of a laser beam; its scattering is collected by an objective lens; and the scattering intensity is recorded using a photomultiplier (PMT). (b) Typical experimental scattering intensity time-series (polystyrene particle in water, R=1.45µm). (c) Exponential intensity-distance relation (β=120nm). (d) Particle position distribution (acquisition time 1200s, sampling rate 500Hz). (e) Experimental (dots) and theoretical (line) potential obtained from the position distribution using the Boltzmann factor.

Fig. 2.
Fig. 2.

Vertical diffusion coefficient D (z) near a wall [Eq. (1)].

Fig. 3.
Fig. 3.

Relation between position distributions and intensity distributions. Brownian diffusion of a particle around a point is symmetric, leading for small Δt to a gaussian distribution h(z; z 0t) (bottom). According to I(z) this leads to the scattered intensity histograms h(I; I 0t) (left): in the linear region of I(z), h(I; I 0t) is also gaussian with the width depending on I′ [Eq. (4)]; in the nonlinear region of I(z) (central histogram), h(I; I 0t) deviates from a gaussian and has a finite skewness depending on I″ [Eq. (5)].

Fig. 4.
Fig. 4.

Various intensity-distance relations and their effect on MSD(I) (black) and skewness S(I) (red). Both theoretical values (solid lines) and the results from the analysis of numerically simulated data (dots) using Eq. (4) and Eq. (5) are presented (R=1.45µm, ρp =1.053g/cm 3, samples 106, frequency 100Hz). (a)-(b) Linear I(z). (c)-(d) Exponential I(z). (e)-(f) Exponential I(z) modulated by a sinusoidal function.

Fig. 5.
Fig. 5.

TIRM with exponential intensity-distance relation. (a) The experimental (dots) and theoretical (solid line) potential. Inset: the diffusion coefficient on the position data (black dots) fits well Eq. (1) (black solid line), while the absolute value of the Brownian motion skewness S(z) is small (red dots). (b) Experimental MSD(I) (black dots) and skewness S(I) (red dots) for a scattering intensity time-series (polystyrene particle, R=1.45µm, ρp =1.053g/cm 3, np =1.59 suspended in water nm =1.33 with 300µM NaCl background electrolyte, κ -1=17nm, near a glass surface ns =1.52, acquisition time 1800s, sampling frequency 500Hz) calculated using Eq. (4) and Eq. (5). Given the short penetration depth (β=120nm), the theoretical MSD(I) (black solid line) and S(I) (red solid line) for an exponential I(z) fit the experimental ones and the conditions in Eqs. (6) are fulfilled.

Fig. 6.
Fig. 6.

TIRM with large penetration depth. (a) The experimental potential (black dots) obtained using the fitted intensity-distance relation and the theoretical one (black solid line). The green dots represent the faulty potential obtained using the exponential I(z). (b) The fitted I(z) (black line) and the exponential one (green line) corresponding to the penetration depth β=720nm. (c) Experimental intensity MSD(I) (black dots) and skewness S(I) (red dots) for a scattering intensity time-series (same particle and acquisition parameters as in Fig. 5) calculated using Eq. (4) and Eq. (5). Due to the large penetration depth, the I(z) diverges from an exponential; the theoretical MSD(I) (black solid line) and S(I) (red solid line) correspond to the fitted I(z).

Fig. 7.
Fig. 7.

TIRM in front of a reflective surface. (a) The experimental potential (black dots) obtained using the fitted intensity-distance relation and theoretical one (solid black line). The green dots represent the faulty potential obtained using the exponential I(z) with β=244nm. (b) The fitted I(z) (black line) and the exponential one (green line) corresponding to the evanescent field penetration depth β=244nm. (c) Experimental intensity MSD(I) (black dots) and skewness S(I) (red dots) for a scattering intensity time-series (same particle and acquisition parameters as in Fig. 5, except for background electrolyte 50µM, κ -1=42nm) calculated using Eq. (4) and Eq. (5). Due to the presence of a 20nm-thick gold layer on the surface, the I(z) deviates from an exponential; the theoretical MSD(I) (black solid line) and S(I) (red solid line) correspond to the fitted I(z).

Equations (6)

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D ( z ) = D S E l ( z ) ,
D ( z ) = lim Δ t 0 1 2 Δ t ( z t + Δ t z t ) 2 z t = z .
S ( z ) lim Δ t 0 1 Δ t 2 ( z t + Δ t z t M ( z , Δ t ) 2 D ( z ) ) 3 z t = z = 0 ,
MSD ( I ) lim Δ t 0 1 Δ t ( I t + Δ t I t ) 2 I t = I = I 2 ( z ) 2 D ( z ) ,
S ( I ) lim Δ t 0 1 Δ t 2 ( I t + Δt I t M ( I , Δ t ) MSD ( I ) ) 3 I t = I = 9 2 I ( z ) I ( z ) 2 D ( z ) ,
{ MSD ( I ( z ) ) = I ' 2 ( z ) 2 D ( z ) S ( I ( z ) ) = 9 2 I ( z ) I ' ( z ) 2 D ( z ) ,

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