Abstract

We propose an alternative approach to the use of dynamic light scattering (DLS) for the analysis of particle sizes ranging from 5 nm to 100 nm. This approach employs a combination of 1) diffusion, 2) density grating, and 3) dielectrophoresis (DEP), and measures the diffusion coefficient from the decay rate of the diffracted light intensity in the relaxation process of particle density modulation generated by DEP. Both the experiments and the theoretical analysis confirm the reliable determination of particle size independently of the refractive index. The new method records a decay signal directly without an autocorrelator and is expected to have a less extreme sensitivity dependence on particle size than DLS.

© 2006 Optical Society of America

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References

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  1. ISO Reference, Particle size analysis -Laser diffraction methods-Part 1, ISO 13320-1 (1999).
  2. M. Kerker, The scattering of light, (Academic, New York, 1969), pp. 31-39.
  3. H. G. Barth and R. B. Flippen, "Particle size analysis," Anal. Chem. 67, 257R-272R (1995).
    [CrossRef]
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).
  5. ISO Reference, Particle size analysis - Photon correlation spectroscopy, ISO 13321 (1996).
  6. B. J. Berne and R. Pecora, Dynamic Light Scattering With Application to Chemistry, Biology, and Physics (General Publishing Company, Toronto, 1976).
  7. C. S. Johnson, Jr. and D. A. Gabriel, Laser Light Scattering, (Dover, New York, 1994).
  8. H. A. Pohl, Dielectrophoresis, (Cambridge University Press, 1978).
  9. J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
    [CrossRef] [PubMed]
  10. M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
    [CrossRef]
  11. H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
    [CrossRef]
  12. M. Terajima, "Translational diffusion of intermediate species in solutions," Res. Chem. Intermed. 23, 853-901 (1997).
    [CrossRef]
  13. For example, see E. Hecht, Optics fourth edition, (Addison Wesley, San Francisco 2002) pp 449-457.
  14. D. E. Koppel, "Analysis of macromolecular polydispersity in intensity correlation Spectroscopy: The method of cumulants," J. Chem. Phys. 57, 4814-4820 (1972).
    [CrossRef]
  15. R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
    [CrossRef]
  16. R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
    [CrossRef]
  17. E. R. Pike and B. McNally, "Theory and design of photon correlation and light-scattering experiments, "Appl. Opt. 36, 7531-7538 (1997).
    [CrossRef]

2001 (1)

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

1997 (3)

H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
[CrossRef]

M. Terajima, "Translational diffusion of intermediate species in solutions," Res. Chem. Intermed. 23, 853-901 (1997).
[CrossRef]

E. R. Pike and B. McNally, "Theory and design of photon correlation and light-scattering experiments, "Appl. Opt. 36, 7531-7538 (1997).
[CrossRef]

1995 (1)

H. G. Barth and R. B. Flippen, "Particle size analysis," Anal. Chem. 67, 257R-272R (1995).
[CrossRef]

1994 (1)

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

1993 (1)

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

1992 (1)

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

1972 (1)

D. E. Koppel, "Analysis of macromolecular polydispersity in intensity correlation Spectroscopy: The method of cumulants," J. Chem. Phys. 57, 4814-4820 (1972).
[CrossRef]

Barth, H. G.

H. G. Barth and R. B. Flippen, "Particle size analysis," Anal. Chem. 67, 257R-272R (1995).
[CrossRef]

Braff, R. A.

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

Clauwaert, J.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

De Jaeger, N.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

De Wispelaere, W.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Demeyere, H.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Deriemaeker, L.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Finsy, R.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

Flippen, R. B.

H. G. Barth and R. B. Flippen, "Particle size analysis," Anal. Chem. 67, 257R-272R (1995).
[CrossRef]

Gelade, E.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

Gillioen, P.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Gray, M. L.

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

Haestier, A.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Koppel, D. E.

D. E. Koppel, "Analysis of macromolecular polydispersity in intensity correlation Spectroscopy: The method of cumulants," J. Chem. Phys. 57, 4814-4820 (1972).
[CrossRef]

Kurosawa, O.

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

McNally, B.

Nishizaka, T.

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

Pike, E. R.

Sakamoto, T.

H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
[CrossRef]

Schmidt, M. A.

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

Shinohara, T.

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

Sneyers, R.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

Steyfkens, S.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Stone-Masui, J.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Suzuki, S.

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

Terajima, M.

M. Terajima, "Translational diffusion of intermediate species in solutions," Res. Chem. Intermed. 23, 853-901 (1997).
[CrossRef]

Toner, M.

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

Tsukahara, S.

H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
[CrossRef]

Van der Meeren, P.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Vanderdeelen, J.

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Voldman, J.

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

Washizu, M.

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

Watarai, H.

H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
[CrossRef]

Anal. Chem. (1)

H. G. Barth and R. B. Flippen, "Particle size analysis," Anal. Chem. 67, 257R-272R (1995).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (1)

J. Voldman, R. A. Braff, M. Toner, M. L. Gray, and M. A. Schmidt, "Holding forces single-particle dielectrophoretic traps," Biophys. J. 80, 531-541 (2001).
[CrossRef] [PubMed]

IEEE Trans. Ind. Appl. (1)

M. Washizu, S. Suzuki, O. Kurosawa, T. Nishizaka, T. Shinohara, "Molecular dielectrophoresis of biopolymers," IEEE Trans. Ind. Appl. 30, 835-843 (1994).
[CrossRef]

J. Chem. Phys. (1)

D. E. Koppel, "Analysis of macromolecular polydispersity in intensity correlation Spectroscopy: The method of cumulants," J. Chem. Phys. 57, 4814-4820 (1972).
[CrossRef]

Langmuir (1)

H. Watarai, T. Sakamoto, and S. Tsukahara, "In situ measurement of dielectrophoretic mobility of single polystyrene microparticles," Langmuir 13, 2417-2420 (1997).
[CrossRef]

Part. Part. Syst. Charact. (2)

R. Finsy, N. De Jaeger, R. Sneyers, and E. Gelade, "Particle sizing by Photon Correlation Spectroscopy. Part III: Mono and bimodal distributions and data analysis," Part. Part. Syst. Charact. 9, 125-137 (1992).
[CrossRef]

R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, "Particle sizing by photon correlation Spectroscopy. Part IV: Resolution of bimodals and comparison with other particle sizing methods," Part. Part. Syst. Charact. 10, 118-128 (1993).
[CrossRef]

Res. Chem. Intermed. (1)

M. Terajima, "Translational diffusion of intermediate species in solutions," Res. Chem. Intermed. 23, 853-901 (1997).
[CrossRef]

Other (8)

For example, see E. Hecht, Optics fourth edition, (Addison Wesley, San Francisco 2002) pp 449-457.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

ISO Reference, Particle size analysis - Photon correlation spectroscopy, ISO 13321 (1996).

B. J. Berne and R. Pecora, Dynamic Light Scattering With Application to Chemistry, Biology, and Physics (General Publishing Company, Toronto, 1976).

C. S. Johnson, Jr. and D. A. Gabriel, Laser Light Scattering, (Dover, New York, 1994).

H. A. Pohl, Dielectrophoresis, (Cambridge University Press, 1978).

ISO Reference, Particle size analysis -Laser diffraction methods-Part 1, ISO 13320-1 (1999).

M. Kerker, The scattering of light, (Academic, New York, 1969), pp. 31-39.

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Figures (8)

Fig. 1.
Fig. 1.

Schematics of the overall system.

Fig. 2.
Fig. 2.

Schematics of arrangement of electrodes.

Fig. 3.
Fig. 3.

Density grating illuminated by a collimated beam and viewed at an angle θ. The density grating (shown in red color) turns in a short time to be a simple sinusoid according to Eq. (6) of m=1.

Fig. 4.
Fig. 4.

Dependence of |E|2 on δ. Three values of φ are calculated for the case of N=10, µ=0.

Fig. 5.
Fig. 5.

Graph of the deviation factor.

Fig. 6.
Fig. 6.

Typical raw trace of the diffraction intensity for silica particles 8 nm in diameter. The ordinate is the response of the photodiode (in arbitrary units).

Fig. 7.
Fig. 7.

Normalized changes in intensity for silica particles. The nominal diameter of the particle given by the manufacturer is shown for each curve.

Fig. 8.
Fig. 8.

Summary of the measurement by comparison of diameters; nominal vs. measured. To indicate the repeatability of measurements four plots (for silica) or three plots (for polystyrene) are presented for each nominal diameter. Some of them are overlapped in cases when the ordinate values are very close to each other.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

I = I 0 exp ( 2 D q 2 t ) ,
q = 2 π Λ = π a ,
D = k B T 3 π η d ,
u ( x ) = c o + m = 1 c m cos 2 m π x Λ ,
u ( x , t ) t = D 2 u ( x , t ) 2 x .
u ( x , t ) = c o + m = 1 c m exp ( m 2 q 2 Dt ) · cos ( mqx ) .
E = constant × ( e μ + i φ + e μ i φ e i δ 2 ) · ( sin N δ 2 sin δ 2 ) ,
where δ = 2 π n λ 0 Λ sin θ .
sin θ = λ 0 n Λ .
I = E 2 = constant × N 2 ( e μ + i φ e μ i φ ) ( e μ + i φ e μ i φ ) ¯ .
I = 4 N 2 ( μ 2 + φ 2 ) [ 1 + 1 3 ( μ 2 φ 2 ) ] .
I = 4 N 2 [ ( μ 0 2 + φ 0 2 ) exp ( 2 q 2 Dt ) ] · F ,
where F = [ 1 + 1 3 ( μ 0 2 + φ 0 2 ) exp ( 2 q 2 Dt ) ] .
exp ( 2 K 2 D τ ) ,
K = 4 π n λ 0 sin θ s 2 ,
2 q 2 D = 2.42 sec 1
and 2 K 2 D = 3.8 × 10 4 sec 1 .
S G = C 1 ( ρ V + ρ V ) 2 C 1 ( ρ V ) 2 ( 1 + 2 . ρ V ρ V ) = C 1 ( ρ V ) 2 ( 1 + 0.002 ) ,
S s = C 2 ( ρ V 2 + ρ V 2 ) = C 2 ρ V 2 ( 1 + ρ V ρ V · V V ) = c 2 ρ v 2 ( 1 + 10 3 · 10 3 ) .

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