Abstract

A method is described for measuring the potential energy of nanoparticles in an optical trap by trapping an ensemble of particles with a focused laser beam. The force balance between repulsive osmotic and confining gradient-force pressures determines the single-particle trapping potential independent of interactions between the particles. The ensemble nature of the measurement permits evaluation of single-particle trapping energies much smaller than kBT. Energies obtained by this method are compared to those of single-particle methods as well as to theoretical calculations based on classical electromagnetic optics.

© 2011 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
    [CrossRef] [PubMed]
  2. H. D. Ou-Yang and M.-T. Wei, Annu. Rev. Phys. Chem. 61, 421 (2010).
    [CrossRef] [PubMed]
  3. J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352(1994).
    [CrossRef] [PubMed]
  4. L. Hough and H. Ou-Yang, J. Nanopart. Res. 1, 495 (1999).
    [CrossRef]
  5. M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
    [CrossRef] [PubMed]
  6. C.-H. Lien, M.-T. Wei, T.-Y. Tseng, C.-D. Lee, C. Wang, T.-F. Wang, H. D. Ou-Yang, and A. Chiou, Opt. Express 17, 20376 (2009).
    [CrossRef] [PubMed]
  7. M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
    [CrossRef] [PubMed]
  8. R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
    [CrossRef] [PubMed]
  9. K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
    [CrossRef]
  10. J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
    [CrossRef]
  11. Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 2005).
  13. The confining pressure exerted on a system of noninteracting particles in an isotropic Gaussian potential U(r)=U0exp⁡(−r2/R2) is found by integrating the product of the force per particle F(r)=−dU/dr and the particle number density N(r)=N∞exp⁡(−U(r)/kBT). ΔP≈∫0RF(r)N(r)dr≈0.7N∞U0≈0.65NU0 for U0/kBT in the range 0.1–0.2, where R is the estimated radius of our detection volume and N is the average particle number density in the detection volume. Because of experimental uncertainties , we approximate the prefactor as ≈1/2.
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    [CrossRef]
  15. A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
    [CrossRef] [PubMed]
  16. J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
    [CrossRef] [PubMed]
  17. A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
    [CrossRef]
  18. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  22. M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
    [CrossRef] [PubMed]

2010 (3)

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
[CrossRef] [PubMed]

H. D. Ou-Yang and M.-T. Wei, Annu. Rev. Phys. Chem. 61, 421 (2010).
[CrossRef] [PubMed]

2009 (3)

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

C.-H. Lien, M.-T. Wei, T.-Y. Tseng, C.-D. Lee, C. Wang, T.-F. Wang, H. D. Ou-Yang, and A. Chiou, Opt. Express 17, 20376 (2009).
[CrossRef] [PubMed]

2008 (1)

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

2007 (1)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

2006 (1)

2005 (1)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

2004 (2)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

C. Hosokawa, H. Yoshikawa, and H. Masuhara, Phys. Rev. E 70, 061410 (2004).
[CrossRef]

2003 (2)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
[CrossRef]

M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
[CrossRef] [PubMed]

1999 (1)

L. Hough and H. Ou-Yang, J. Nanopart. Res. 1, 495 (1999).
[CrossRef]

1996 (2)

R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef] [PubMed]

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

1994 (1)

J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352(1994).
[CrossRef] [PubMed]

1986 (1)

Arsenault, M. E.

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

Asakura, T.

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Ashkin, A.

Baba, Y.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Bau, H.

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Bjorkholm, J. E.

Block, S.

M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 2005).

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
[CrossRef] [PubMed]

Chiou, A.

Chu, S.

Crocker, J. C.

J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352(1994).
[CrossRef] [PubMed]

Dziedzic, J. M.

Finer, J.

R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Fordyce, P.

M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
[CrossRef] [PubMed]

Goldman, Y.

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

Grier, D. G.

J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352(1994).
[CrossRef] [PubMed]

Harada, Y.

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Hosokawa, C.

C. Hosokawa, H. Yoshikawa, and H. Masuhara, Phys. Rev. E 70, 061410 (2004).
[CrossRef]

Hough, L.

L. Hough and H. Ou-Yang, J. Nanopart. Res. 1, 495 (1999).
[CrossRef]

Hu, Y.

Y. Hu and H. D. Ou-Yang, “Dynamics of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” presented at American Physical Society March Meeting 2010 (March 15–19, 2010).

Junio, J.

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Kaji, N.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Kawata, S.

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

Kim, M.-W.

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Lang, M.

M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
[CrossRef] [PubMed]

Lee, C.-D.

Lien, C.-H.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
[CrossRef] [PubMed]

Maia Neto, P. A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
[CrossRef]

Masuhara, H.

C. Hosokawa, H. Yoshikawa, and H. Masuhara, Phys. Rev. E 70, 061410 (2004).
[CrossRef]

Mazolli, A.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
[CrossRef]

Mesquita, O. N.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

Murata, M.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
[CrossRef] [PubMed]

Nussenzveig, H. M.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
[CrossRef]

Okamoto, Y.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Ou-Yang, H.

L. Hough and H. Ou-Yang, J. Nanopart. Res. 1, 495 (1999).
[CrossRef]

Ou-Yang, H. D.

H. D. Ou-Yang and M.-T. Wei, Annu. Rev. Phys. Chem. 61, 421 (2010).
[CrossRef] [PubMed]

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

C.-H. Lien, M.-T. Wei, T.-Y. Tseng, C.-D. Lee, C. Wang, T.-F. Wang, H. D. Ou-Yang, and A. Chiou, Opt. Express 17, 20376 (2009).
[CrossRef] [PubMed]

Y. Hu and H. D. Ou-Yang, “Dynamics of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” presented at American Physical Society March Meeting 2010 (March 15–19, 2010).

Park, S.

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Park, Y.-S.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Rocha, M. S.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

Rodgers, T.

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

Rohrbach, A.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Schmidt, C. F.

Sekkat, Z.

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

Shoji, S.

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

Simmons, R.

R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef] [PubMed]

Spudich, J.

R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef] [PubMed]

Stienen, G. J. M.

Sun, Y.

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

Tokeshi, M.

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Tseng, T.-Y.

Vermeulen, K. C.

Viana, N. B.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

Wang, C.

Wang, T.-F.

Wei, M.-T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 2005).

Wuite, G. J. L.

Yoshikawa, H.

C. Hosokawa, H. Yoshikawa, and H. Masuhara, Phys. Rev. E 70, 061410 (2004).
[CrossRef]

Anal. Bioanal. Chem. (1)

M. Murata, Y. Okamoto, Y.-S. Park, N. Kaji, M. Tokeshi, and Y. Baba, Anal. Bioanal. Chem. 394, 277 (2009).
[CrossRef] [PubMed]

Annu. Rev. Phys. Chem. (1)

H. D. Ou-Yang and M.-T. Wei, Annu. Rev. Phys. Chem. 61, 421 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (1)

R. Simmons, J. Finer, S. Chu, and J. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef] [PubMed]

J. Biol. (1)

M. Lang, P. Fordyce, and S. Block, J. Biol. 2, 6 (2003).
[CrossRef] [PubMed]

J. Nanopart. Res. (1)

L. Hough and H. Ou-Yang, J. Nanopart. Res. 1, 495 (1999).
[CrossRef]

Opt. Commun. (1)

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

M. E. Arsenault, Y. Sun, H. Bau, and Y. Goldman, Phys. Chem. Chem. Phys. 11, 4834 (2009).
[CrossRef] [PubMed]

Phys. Rev. E (2)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Phys. Rev. E 75, 021914(2007).
[CrossRef]

C. Hosokawa, H. Yoshikawa, and H. Masuhara, Phys. Rev. E 70, 061410 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601(2010).
[CrossRef] [PubMed]

J. C. Crocker and D. G. Grier, Phys. Rev. Lett. 73, 352(1994).
[CrossRef] [PubMed]

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, Phys. Rev. Lett. 101, 127402 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, Proc. R. Soc. A 459, 3021 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Solid State Commun. (1)

J. Junio, S. Park, M.-W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 2005).

The confining pressure exerted on a system of noninteracting particles in an isotropic Gaussian potential U(r)=U0exp⁡(−r2/R2) is found by integrating the product of the force per particle F(r)=−dU/dr and the particle number density N(r)=N∞exp⁡(−U(r)/kBT). ΔP≈∫0RF(r)N(r)dr≈0.7N∞U0≈0.65NU0 for U0/kBT in the range 0.1–0.2, where R is the estimated radius of our detection volume and N is the average particle number density in the detection volume. Because of experimental uncertainties , we approximate the prefactor as ≈1/2.

Y. Hu and H. D. Ou-Yang, “Dynamics of nanoparticles in an optical trap studied by fluorescence correlation spectroscopy,” presented at American Physical Society March Meeting 2010 (March 15–19, 2010).

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Figures (4)

Fig. 1
Fig. 1

Δ N / N for 100 nm particles in 5 mM NaCl at six different particle concentrations. I laser = 1.0 × 10 10 W / m 2 corresponds to a laser power of 8 mW . The legend gives N in terms of volume percent for each data set.

Fig. 2
Fig. 2

( 2 × initial slope of Δ N / N vs . I laser ) 1 for 100 nm particles at different NaCl concentrations, fitted with polynomials. The heavy curve refers to data from Fig. 1.

Fig. 3
Fig. 3

( 2 × initial slope of Δ N / N vs . I laser ) 1 for each particle size as a function of volume fraction in 5 mM NaCl. The intercepts determine U 0 per milliwatt of laser power for each particle size, shown in Fig. 4.

Fig. 4
Fig. 4

Experimental and calculated values of U 0 per milliwatt of laser power versus particle size. The refractive-index mismatch between the coverslip and the water was accounted for in the calculation [19].

Equations (2)

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Δ N / N ( β I laser / 2 k B T ) ( 1 + 2 B 2 N + · · · ) 1 .
U ( r ) = ( Re ( α ) / 4 ) | E in ( r ) | 2 ,

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