The functional properties of colloidal materials can be tailored by tuning the shape of their constituent particles. Unfortunately, a reliable, general methodology for purifying colloidal materials solely based on shape is still lacking. Here we exploit the single-particle analysis and sorting capabilities of the fluorescence-activated cell sorting (FACS) instrument, a commonly used tool in biomedical research, and demonstrate the ability to separate mixtures of synthetic microparticles based solely on their shape with high purity. We achieve this by simultaneously obtaining four independent optical scattering signals from the FACS instrument to create shape-specific ‘scattering signatures’ that can be used for particle classification and sorting. We demonstrate that these four-dimensional signatures can overcome the confounding effects of particle orientation on shape-based characterization. Using this strategy, robust discrimination of particles differing only slightly in shape and an efficient selection of desired shapes from mixtures comprising particles of diverse sizes and materials is demonstrated.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Data availability

Flow cytometry data are available as FCS files in FlowRepository with accession code FR-FCM-ZYR6. All the other data that support the findings of this study are available within the article and its supplementary information files or available from the corresponding authors upon reasonable request.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Champion, J. A., Katare, Y. K. & Mitragotri, S. Making polymeric micro- and nanoparticles of complex shapes. Proc. Natl Acad. Sci. USA 104, 11901–11904 (2007).

  2. 2.

    Mitragotri, S. & Lahann, J. Physical approaches to biomaterial design. Nat. Mater. 8, 15–23 (2009).

  3. 3.

    Mitragotri, S., Burke, P. A. & Langer, R. Overcoming the challenges in administering biopharmaceuticals: formulation and delivery strategies. Nat. Rev. Drug Discov. 13, 655–672 (2014).

  4. 4.

    Chen, H. H. et al. MR imaging of biodegradable polymeric microparticles: a potential method of monitoring local drug delivery. Magn. Reson. Med. 53, 614–620 (2005).

  5. 5.

    Subramanian, G., Manoharan, V. N., Thorne, J. D. & Pine, D. J. Ordered macroporous materials by colloidal assembly: a possible route to photonic bandgap materials. Adv. Mater. 11, 1261–1265 (1999).

  6. 6.

    Velikov, K. P., Van Dillen, T., Polman, A. & Van Blaaderen, A. Photonic crystals of shape-anisotropic colloidal particles. Appl. Phys. Lett. 81, 838–840 (2002).

  7. 7.

    Kim, S.-H., Lee, S. Y., Yang, S.-M. & Yi, G.-R. Self-assembled colloidal structures for photonics. NPG Asia Mater. 3, 25–33 (2011).

  8. 8.

    Yang, S.-M., Kim, S.-H., Lim, J.-M. & Yi, G.-R. Synthesis and assembly of structured colloidal particles. J. Mater. Chem. 18, 2177 (2008).

  9. 9.

    Sacanna, S. & Pine, D. J. Shape-anisotropic colloids: building blocks for complex assemblies. Curr. Opin. Colloid Interface Sci. 16, 96–105 (2011).

  10. 10.

    Kruglova, O., Demeyer, P.-J., Zhong, K., Zhou, Y. & Clays, K. Wonders of colloidal assembly. Soft Matter 9, 9072 (2013).

  11. 11.

    Phillips, C. L. et al. Digital colloids: reconfigurable clusters as high information density elements. Soft Matter 10, 7468–7479 (2014).

  12. 12.

    Kong, T. et al. Droplet based microfluidic fabrication of designer microparticles for encapsulation applications. Biomicrofluidics 6, 34104 (2012).

  13. 13.

    Dendukuri, D. & Doyle, P. S. The synthesis and assembly of polymeric microparticles using microfluidics. Adv. Mater. 21, 4071–4086 (2009).

  14. 14.

    Xu, Q. et al. Preparation of monodisperse biodegradable polymer microparticles using a microfluidic flow-focusing device for controlled drug delivery. Small 5, 1575–1581 (2009).

  15. 15.

    Min, N. G. et al. Anisotropic microparticles created by phase separation of polymer blends confined in monodisperse emulsion drops. Langmuir 31, 937–943 (2015).

  16. 16.

    Dendukuri, D., Pregibon, D. C., Collins, J., Hatton, T. A. & Doyle, P. S. Continuous-flow lithography for high-throughput microparticle synthesis. Nat. Mater. 5, 365–369 (2006).

  17. 17.

    Wu, C. Y., Owsley, K. & Di Carlo, D. Rapid software-based design and opticaltransient liquid molding of microparticles. Adv. Mater. 27, 7970–7978 (2015).

  18. 18.

    Bhaskar, S., Pollock, K. M., Yoshida, M. & Lahann, J. Towards designer microparticles: simultaneous control of anisotropy, shape, and size. Small 6, 404–411 (2010).

  19. 19.

    Sansdrap, P. & Moës, A. J. Influence of manufacturing parameters on the size characteristics and the release profiles of nifedipine from poly(DL-lactide-co-glycolide) microspheres. Int. J. Pharm. 98, 157–164 (1993).

  20. 20.

    Yin, Y. & Xia, Y. Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures. Adv. Mater. 13, 267–271 (2001).

  21. 21.

    Campos, E. et al. Designing polymeric microparticles for biomedical and industrial applications. Eur. Polym. J. 49, 2005–2021 (2013).

  22. 22.

    Sharma, V., Park, K. & Srinivasarao, M. Shape separation of gold nanorods using centrifugation. Proc. Natl Acad. Sci. USA 106, 4981–4985 (2009).

  23. 23.

    Akbulut, O. et al. Separation of nanoparticles in aqueous multiphase systems through centrifugation. Nano Lett. 12, 4060–4064 (2012).

  24. 24.

    Meloy, T. P. & Durney, T. E. Particle shape chromatography—he sieve cascadograph. Int. J. Miner. Process. 11, 101–113 (1983).

  25. 25.

    Hanauer, M., Pierrat, S., Zins, I., Lotz, A. & Sönnichsen, C. Separation of nanoparticles by gel electrophoresis according to size and shape. Nano Lett. 7, 2881–2885 (2007).

  26. 26.

    Sugaya, S., Yamada, M. & Seki, M. Observation of nonspherical particle behaviors for continuous shape-based separation using hydrodynamic filtration. Biomicrofluidics 5, 024103 (2011).

  27. 27.

    Ranjan, S., Zeming, K. K., Jureen, R., Fisher, D. & Zhang, Y. DLD pillar shape design for efficient separation of spherical and non-spherical bioparticles. Lab Chip 14, 4250–4262 (2014).

  28. 28.

    Masaeli, M. et al. Continuous inertial focusing and separation of particles by shape. Phys. Rev. X 2, 031017 (2012).

  29. 29.

    Lu, X. & Xuan, X. Elasto-inertial pinched flow fractionation for continuous shape-based particle separation. Anal. Chem. 87, 11523–11530 (2015).

  30. 30.

    Lu, X., Zhu, L., Hua, R. & Xuan, X. Continuous sheath-free separation of particles by shape in viscoelastic fluids. Appl. Phys. Lett. 107, 264102 (2015).

  31. 31.

    Nho, H. W., Yang, N., Song, J., Park, J. S. & Yoon, T. H. Separations of spherical and disc-shaped polystyrene particles and blood components (red blood cells and platelets) using pinched flow fractionation device with a tilted sidewall and vertical focusing channels (t-PFF-v). Sensors Actuators B 249, 131–141 (2017).

  32. 32.

    Latimer, P., Brunsting, A., Pyle, B. E. & Moore, C. Effects of asphericity on single particle scattering. Appl. Opt. 17, 3152–3158 (1978).

  33. 33.

    Kaye, P. H. Spatial light-scattering analysis as a means of characterizing and classifying non-spherical particles. Meas. Sci. Technol. 9, 141–149 (1998).

  34. 34.

    Jones, A. R. Light scattering for particle characterization. Prog. Energy Combust. Sci. 25, 1–53 (1999).

  35. 35.

    Melamed, M. R., Lindmo, T. & Mendelsohn, M. L. Flow Cytometry and Sorting (Wiley, New York, 1990).

  36. 36.

    Mätzler, C. MATLAB Functions for Mie Scattering and Absorption Research Report 2002-08 (IAP, 2002).

  37. 37.

    Mishchenko, M. I. Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation. Appl. Opt. 39, 1026 (2000).

  38. 38.

    Doornbos, R. M. P. et al. Lissajous-like patterns in scatter plots of calibration beads. Cytometry 16, 236–242 (1994).

  39. 39.

    Salzman, G. C. Light scatter: detection and usage. Curr. Protoc. Cytom. 9, 1.13.1–1.13.8 (2001).

  40. 40.

    Rotstein, R., Berges, A., Mitragotri, S., Morse, D. E. & Moskovits, M. Angle-dependent light scattering by highly uniform colloidal rod-shaped microparticles: experiment and simulation. J. Polym. Sci. B 54, 1889–1895 (2016).

  41. 41.

    Hoffman, R. A. Pulse width for particle sizing. Curr. Protoc. Cytom. 50, 1.23.1–1.23.17, doi:https://doi.org/10.1002/0471142956.cy0123s50 (2009).

  42. 42.

    Tzur, A., Moore, J. K., Jorgensen, P., Shapiro, H. M. & Kirschner, M. W. Optimizing optical flow cytometry for cell volume-based sorting and analysis. PLoS ONE 6, e16053 (2011).

  43. 43.

    Sharpless, T. K., Bartholdi, M. & Melamed, M. R. Size and refractive index dependence of simple forward angle scattering measurements in a flow system using sharply-focused illumination. J. Histochem. Cytochem. 25, 845–856 (1977).

  44. 44.

    Amir, E. D. et al. viSNE enables visualization of high dimensional single-cell data and reveals phenotypic heterogeneity of leukemia. Nat. Biotechnol. 31, 545–552 (2013).

  45. 45.

    Meehan, S. et al. AutoGate: automating analysis of flow cytometry data. Immunol. Res. 58, 218–223 (2014).

  46. 46.

    Yu, J. S., Pertusi, D. A., Adeniran, A. V., Tyo, K. E. J. & Wren, J. CellSort: a support vector machine tool for optimizing fluorescence-activated cell sorting and reducing experimental effort. Bioinformatics 33, 909–916 (2017).

  47. 47.

    Rens, W., Welch, G. R. & Johnson, L. A. A novel nozzle for more efficient sperm orientation to improve sorting efficiency of X and Y chromosome-bearing sperm. Cytometry 33, 476–481 (1998).

  48. 48.

    Stovel, R. T., Sweet, R. G. & Herzenberg, L. A. A means for orienting flat cells in flow systems. Biophys. J. 23, 1–5 (1978).

  49. 49.

    BD FACSAria III Cell Sorter Technical Specifications (BD, 2010).

  50. 50.

    Jones, S. H., King, M. D. & Ward, A. D. Determining the unique refractive index properties of solid polystyrene aerosol using broadband Mie scattering from optically trapped beads. Phys. Chem. Chem. Phys. 15, 20735 (2013).

  51. 51.

    Velazco-Roa, M. A. & Thennadil, S. N. Estimation of optical constants from multiple-scattered light using approximations for single particle scattering characteristics. Appl. Opt. 46, 8453–8460 (2007).

  52. 52.

    Leinonen, J. High-level interface to T-matrix scattering calculations: architecture, capabilities and limitations. Opt. Express 22, 1655–1660 (2014).

Download references


We thank D. Wu, C. Gordon, C. Wang, P. Coffey and M. Radeke for helpful discussion and technical flow cytometry support. This work was financially supported by DARPA (N66001-14-2-4055). H.T.S. is a Chan Zuckerberg Biohub investigator. The content of the information does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.

Author information

Author notes

    • Peter L. Mage

    Present address: BD Biosciences, San Jose, CA, USA

    • Daniel Klinger

    Present address: Institut für Pharmazie, Freie Universität Berlin, Berlin, Germany


  1. Materials Department, University of California, Santa Barbara, CA, USA

    • Peter L. Mage
    • , Craig Hawker
    •  & H. Tom Soh
  2. Department of Electrical Engineering, Stanford University, Stanford, CA, USA

    • Peter L. Mage
    • , Michael Eisenstein
    •  & H. Tom Soh
  3. Institute for Collaborative Biotechnologies, University of California, Santa Barbara, CA, USA

    • Andrew T. Csordas
    • , Craig Hawker
    •  & H. Tom Soh
  4. Interdepartmental Program in Biomolecular Science and Engineering, University of California, Santa Barbara, CA, USA

    • Tyler Brown
  5. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    • Tyler Brown
    •  & Samir Mitragotri
  6. Materials Research Laboratory, University of California, Santa Barbara, CA, USA

    • Daniel Klinger
    •  & Craig Hawker
  7. Department of Radiology, Stanford University, Stanford, CA, USA

    • Michael Eisenstein
    •  & H. Tom Soh
  8. Department of Chemical Engineering, University of California, Santa Barbara, CA, USA

    • Samir Mitragotri


  1. Search for Peter L. Mage in:

  2. Search for Andrew T. Csordas in:

  3. Search for Tyler Brown in:

  4. Search for Daniel Klinger in:

  5. Search for Michael Eisenstein in:

  6. Search for Samir Mitragotri in:

  7. Search for Craig Hawker in:

  8. Search for H. Tom Soh in:


P.L.M., D.K., C.H. and H.T.S. conceived the project. P.L.M., A.T.C. and D.K. designed the experiments. T.B. synthesized the microparticles and performed scanning electron microscopy. P.L.M. and A.T.C. performed the FACS. P.L.M. analysed the data, designed the sort gates, wrote the analysis and simulation code, performed scattering simulations and performed optical microscopy and image analysis. P.L.M., H.T.S. and M.E. co-wrote and edited the manuscript. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Samir Mitragotri or Craig Hawker or H. Tom Soh.

Supplementary information

  1. Supplementary Information

    Supplementary Discussion 1–2, Supplementary Figures 1–12, Supplementary Tables 1–2, Supplementary References 1–4

  2. Supplementary Software 1

    MATLAB code for simulating the forward scattering (FSC) and side scattering (SSC) intensities of spheres using Mie theory

  3. Supplementary Software 2

    Python code for simulating the forward scattering (FSC) and side scattering (SSC) intensities of ellipsoids using the T-matrix method

About this article

Publication history




Issue Date