Advertisement

Macromolecular Research

, Volume 25, Issue 3, pp 282–289 | Cite as

Analytical calculations of optical trapping forces for drag calibration: Effects of mismatch between beam focus and particle center

Article
  • 82 Downloads

Abstract

We present analytical calculations of optical forces for drag calibrations via the geometrical optics approximation (GOA) for the case in which a single laser beam is strongly focused on a polystyrene microsphere dispersed in an aqueous phase. When the beam focus is mismatched with the particle center owing to the presence of vertical forces, such as gravity, buoyancy, and the radiation force caused by the laser beam, the trapped particle would be displaced in a radial direction when the lateral drag force is applied. Based on the analytical calculations of optical trapping forces and the force balance upon dragging, we found that the critical laser power at which the beam focus matches the particle center exhibits a power-law relationship with the particle radius a according to the empirical expression log(P crit (mW)) = 2.899 log(2a (µm)) - 2.316. We also found an empirical expression for the mechanical equilibrium position of the vertical displacement Δz eq 0 y=0) as functions of the laser power P and the particle radius, \(\Delta z_{eq}^0 = \frac{{\left[ {{F_{gb}}\left( {pN} \right) - 0.068P\left( {mW} \right)} \right]\left[ {2.7a\left( {\mu m} \right) - 0.252} \right]}}{{P\left( {mW} \right)}}\), where F gb is the sum of the gravitational and buoyant forces.

Keywords

polymer microsphere optical trap colloid drag calibration ray optics approximation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

13233_2017_5027_MOESM1_ESM.pdf (868 kb)
Supporting Information

References

  1. (1).
    A. Ashkin and J. M. Dziedzic, Science, 235, 1517 (1987).CrossRefGoogle Scholar
  2. (2).
    K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophys. J., 77, 2856 (1999).CrossRefGoogle Scholar
  3. (3).
    S. M. Block, D. F. Blair, and H. C. Berg, Nature, 338, 514 (1989).CrossRefGoogle Scholar
  4. (4).
    M. T. Valentine, L. E. Dewalt, and H. D. Ou-Yang, J. Phys. Conden. Matter, 8, 9477 (1996).CrossRefGoogle Scholar
  5. (5).
    A. Meyer, A. Marshall, B. G. Bush, and E. M. Furst, J. Rheol., 50, 77 (2006).CrossRefGoogle Scholar
  6. (6).
    A. Ashkin, Biophys. J., 61, 569 (1992).CrossRefGoogle Scholar
  7. (7).
    K. C. Neuman and S. M. Block, Rev. Sci. Instrum., 75, 2787 (2004).CrossRefGoogle Scholar
  8. (8).
    B. J. Park, J. P. Pantina, E. M. Furst, M. Oettel, S. Reynaert, and J. Vermant, Langmuir, 24, 1686 (2008).CrossRefGoogle Scholar
  9. (9).
    B. J. Park and E. M. Furst, Soft Matter, 7, 7676 (2011).CrossRefGoogle Scholar
  10. (10).
    S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett., 99, 018303 (2007).CrossRefGoogle Scholar
  11. (11).
    B. J. Park and E. M. Furst, Langmuir, 30, 11055 (2014).CrossRefGoogle Scholar
  12. (12).
    B. J. Park and E. M. Furst, Macromol. Res., 21, 1167 (2013).CrossRefGoogle Scholar
  13. (13).
    B. J. Park and E. M. Furst, Langmuir, 24, 13383 (2008).CrossRefGoogle Scholar
  14. (14).
    P. A. Kralchevsky and K. Nagayama, Langmuir, 10, 23 (1994).CrossRefGoogle Scholar
  15. (15).
    D. Stamou, C. Duschl, and D. Johannsmann, Phys. Rev. E, 62, 5263 (2000).CrossRefGoogle Scholar
  16. (16).
    V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, Opt. Express, 16, 13831 (2008).CrossRefGoogle Scholar
  17. (17).
    J. C. Crocker and D. G. Grier, J. Colloid Interface Sci., 179, 298 (1996).CrossRefGoogle Scholar
  18. (18).
    C. A. Schneider, W. S. Rasband, and K. W. Eliceiri, Nat. Meth., 9, 671 (2012).CrossRefGoogle Scholar
  19. (19).
    J. Y. Walz and D. C. Prieve, Langmuir, 8, 3073 (1992).CrossRefGoogle Scholar
  20. (20).
    M. Giot, Optics Guide 4, Melles Griot, Irvine, CA, 1988.Google Scholar
  21. (21).
    J.-H. Park and S. Y. Yang, Macromol. Res., 24, 95 (2016).CrossRefGoogle Scholar
  22. (22).
    S. Hwang, C.-H. Choi, and C.-S. Lee, Macromol. Res., 20, 422 (2012).CrossRefGoogle Scholar
  23. (23).
    K.-S. Park, C. Kim, J.-O. Nam, S.-M. Kang, and C.-S. Lee, Macromol. Res., 24, 529 (2016).CrossRefGoogle Scholar
  24. (24).
    B. J. Park, M. Lee, and E. M. Furst, Soft Matter, 11, 8701 (2015).CrossRefGoogle Scholar
  25. (25).
    X. Wang, S. Chen, M. Kong, Z. Wang, K. D. Costa, R. A. Li, and D. Sun, Lab Chip, 11, 3656 (2011).CrossRefGoogle Scholar

Copyright information

© The Polymer Society of Korea and Springer Sciene+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Chemical EngineeringKyung Hee UniversityYongin, GyeonggiKorea

Personalised recommendations