Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Measuring the size and charge of single nanoscale objects in solution using an electrostatic fluidic trap


Measuring the size and charge of objects suspended in solution, such as dispersions of colloids or macromolecules, is a significant challenge. Measurements based on light scattering are inherently biased to larger entities, such as aggregates in the sample1, because the intensity of light scattered by a small object scales as the sixth power of its size. Techniques that rely on the collective migration of species in response to external fields (electric or hydrodynamic, for example) are beset with difficulties including low accuracy and dispersion-limited resolution2,3,4. Here, we show that the size and charge of single nanoscale objects can be directly measured with high throughput by analysing their thermal motion in an array of electrostatic traps5. The approach, which is analogous to Millikan's oil drop experiment, could in future be used to detect molecular binding events6 with high sensitivity or carry out dynamic single-charge resolved measurements at the solid/liquid interface.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Experimental set-up and device geometry.
Figure 2: Analysis of the three-dimensional motion of particles trapped in a harmonic potential well.
Figure 3: Dependence of trapping free energy on particle charge.
Figure 4: MSD measurements and deducing the charge on a single particle.


  1. Bowen, W. R., Hall, N. J., Pan, L. C., Sharif, A. O. & Williams, P. M. The relevance of particle size and zeta-potential in protein processing. Nature Biotechnol. 16, 785–787 (1998).

    Article  CAS  Google Scholar 

  2. Varenne, A. & Descroix, S. Recent strategies to improve resolution in capillary electrophoresis—a review. Anal. Chim. Acta 628, 9–23 (2008).

    Article  CAS  Google Scholar 

  3. Laue, T. M. & Stafford, W. F. Modern applications of analytical ultracentrifugation. Annu. Rev. Bioph. Biom. 28, 75–100 (1999).

    Article  CAS  Google Scholar 

  4. Giddings, J. C. Field-flow fractionation—analysis of macromolecular, colloidal and particulate materials. Science 260, 1456–1465 (1993).

    Article  CAS  Google Scholar 

  5. Krishnan, M., Mojarad, N., Kukura, P. & Sandoghdar, V. Geometry-induced electrostatic trapping of nanometric objects in a fluid. Nature 467, 692–695 (2010).

    Article  CAS  Google Scholar 

  6. Anker, J. N. et al. Biosensing with plasmonic nanosensors. Nature Mater. 7, 442–453 (2008).

    Article  CAS  Google Scholar 

  7. Millikan, R. A. The isolation of an ion, a precision measurement of its charge, and the correction of Stokes's law. Science 32, 436–448 (1910).

    Article  CAS  Google Scholar 

  8. Daaboul, G. G. et al. High-throughput detection and sizing of individual low-index nanoparticles and viruses for pathogen identification. Nano Lett. 10, 4727–4731 (2010).

    Article  CAS  Google Scholar 

  9. Sharp, K. A. & Honig, B. Calculating total electrostatic energies with the nonlinear Poisson–Boltzmann equation. J. Phys. Chem. 94, 7684–7692 (1990).

    Article  CAS  Google Scholar 

  10. Overbeek, J. T. G. The role of energy and entropy in the electrical double-layer. Colloid Surf. 51, 61–75 (1990).

    Article  CAS  Google Scholar 

  11. Ospeck, M. & Fraden, S. Solving the Poisson–Boltzmann equation to obtain interaction energies between confined, like-charged cylinders. J. Chem. Phys. 109, 9166–9171 (1998).

    Article  CAS  Google Scholar 

  12. Keen, S., Leach, J., Gibson, G. & Padgett, M. J. Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers. J. Opt. A 9, S264–S266 (2007).

    Article  Google Scholar 

  13. Howard, J. Mechanics of Motor Proteins and the Cytoskeleton 19 (Sinauer Associates, 2001).

    Google Scholar 

  14. Tothova, J., Vasziova, G., Glod, L. & Lisy, V. Langevin theory of anomalous Brownian motion made simple. Eur. J. Phys. 32, 645–655 (2011).

    Article  Google Scholar 

  15. Li, T., Kheifets, S., Medellin, D. & Raizen, M. G. Measurement of the instantaneous velocity of a Brownian particle. Science 328, 1673–1675 (2010).

    Article  CAS  Google Scholar 

  16. Savin, T. & Doyle, P. S. Role of a finite exposure time on measuring an elastic modulus using microrheology. Phys. Rev. E 71, 041106 (2005).

    Article  Google Scholar 

  17. Wong, W. P. & Halvorsen, K. The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur. Opt. Express 14, 12517–12531 (2006).

    Article  Google Scholar 

  18. Savin, T. & Doyle, P. S. Static and dynamic errors in particle tracking microrheology. Biophys. J. 88, 623–638 (2005).

    Article  CAS  Google Scholar 

  19. Eichmann, S. L. & Bevan, M. A. Direct measurements of protein-stabilized gold nanoparticle interactions. Langmuir 26, 14409–14413 (2010).

    Article  CAS  Google Scholar 

  20. Hoang, H. T. et al. Analysis of single quantum-dot mobility inside 1D nanochannel devices. Nanotechnology 22, 275201 (2011).

    Article  CAS  Google Scholar 

  21. Hunter, R. J. The significance of stagnant layer conduction in electrokinetics. Adv. Colloid Interface Sci. 100–102, 153–167 (2003).

    Article  Google Scholar 

  22. Zhang, H., Hassanali, A. A., Shin, Y. K., Knight, C. & Singer, S. J. The water-amorphous silica interface: analysis of the Stern layer and surface conduction. J. Chem. Phys. 134, 024705 (2011).

    Article  Google Scholar 

  23. Beunis, F., Strubbe, F., Neyts, K. & Petrov, D. Beyond Millikan: the dynamics of charging events on individual colloidal particles. Phys. Rev. Lett. 108, 016101 (2012).

    Article  Google Scholar 

  24. Kirkwood, J. G. & Shumaker, J. B. Forces between protein molecules in solution arising from fluctuations in proton charge and configuration. Proc. Natl Acad. Sci. USA 38, 863–871 (1952).

    Article  CAS  Google Scholar 

  25. Novo, C., Funston, A. M. & Mulvaney, P. Direct observation of chemical reactions on single gold nanocrystals using surface plasmon spectroscopy. Nature Nanotech. 3, 598–602 (2008).

    Article  CAS  Google Scholar 

  26. Semrau, S., Pezzarossa, A. & Schmidt, T. Microsecond single-molecule tracking (μsSMT). Biophys. J. 100, L19–L21 (2011).

    Article  CAS  Google Scholar 

  27. Sahl, S. J., Leutenegger, M., Hilbert, M., Hell, S. W. & Eggeling, C. Fast molecular tracking maps nanoscale dynamics of plasma membrane lipids. Proc. Natl Acad Sci. USA 107, 6829–6834 (2010).

    Article  CAS  Google Scholar 

  28. Ueno, H. et al. Simple dark-field microscopy with nanometer spatial precision and microsecond temporal resolution. Biophys. J. 98, 2014–2023 (2010).

    Article  CAS  Google Scholar 

  29. Celebrano, M., Kukura, P., Renn, A. & Sandoghdar, V. Single-molecule imaging by optical absorption. Nature Photon. 5, 95–98 (2011).

    Article  CAS  Google Scholar 

  30. De Jonge, N. & Ross, F. M. Electron microscopy of specimens in liquid. Nature Nanotech. 6, 349–356 (2011).

    Article  Google Scholar 

Download references


M.K. acknowledges support from the European Commission in the form of a Marie Curie Research Fellowship. T. Savin and R. Klemm are thanked for fruitful discussions and D. Weitz for hospitality at the time of writing. The authors thank V. Sandoghdar for sustained support.

Author information

Authors and Affiliations



N.M. performed the experiments, analysed data and participated in writing of the manuscript. M.K. conceived the project, performed the theoretical analysis, analysed data and wrote the manuscript.

Corresponding author

Correspondence to Madhavi Krishnan.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 866 kb)

Supplementary information

Supplementary movie (AVI 204 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mojarad, N., Krishnan, M. Measuring the size and charge of single nanoscale objects in solution using an electrostatic fluidic trap. Nature Nanotech 7, 448–452 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research