Skip to main content

Thank you for visiting nature.com. 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.

Modes of surface premelting in colloidal crystals composed of attractive particles

Abstract

Crystal surfaces typically melt into a thin liquid layer at temperatures slightly below the melting point of the crystal. Such surface premelting is prevalent in all classes of solids and is important in a variety of metallurgical, geological and meteorological phenomena1. Premelting has been studied using X-ray diffraction2 and differential scanning calorimetry3, but the lack of single-particle resolution makes it hard to elucidate the underlying mechanisms. Colloids are good model systems for studying phase transitions4 because the thermal motions of individual micrometre-sized particles can be tracked directly using optical microscopy5. Here we use colloidal spheres with tunable attractions to form equilibrium crystal–vapour interfaces, and study their surface premelting behaviour at the single-particle level. We find that monolayer colloidal crystals exhibit incomplete premelting at their perimeter, with a constant liquid-layer thickness. In contrast, two- and three-layer crystals exhibit conventional complete melting, with the thickness of the surface liquid diverging as the melting point is approached. The microstructures of the surface liquids differ in certain aspects from what would be predicted by conventional premelting theories. Incomplete premelting in the monolayer crystals is triggered by a bulk isostructural solid–solid transition and truncated by a mechanical instability that separately induces homogeneous melting within the bulk. This finding is in contrast to the conventional assumption that two-dimensional crystals melt heterogeneously from their free surfaces3,6 (that is, at the solid–vapour interface). The unexpected bulk melting that we observe for the monolayer crystals is accompanied by the formation of grain boundaries, which supports a previously proposed grain-boundary-mediated two-dimensional melting theory7. The observed interplay between surface premelting, bulk melting and solid–solid transitions challenges existing theories of surface premelting and two-dimensional melting.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Pair potentials of the 2.02-μm-diameter PMMA spheres measured from monolayer liquid structures.
Figure 2: Surface premelting.
Figure 3: Density and elastic moduli.
Figure 4: Bulk melting.

References

  1. 1

    Dash, J. G., Rempel, A. W. & Wettlaufer, J. S. The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78, 695–741 (2006)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Frenken, J. W. M. & van der Veen, J. F. Observation of surface melting. Phys. Rev. Lett. 54, 134–137 (1985)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Zhu, D.-M., Pengra, D. & Dash, J. G. Edge melting in two-dimensional solid films. Phys. Rev. B 37, 5586–5593 (1988)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Li, B., Zhou, D. & Han, Y. Assembly and phase transitions of colloidal crystals. Nature Rev. Mater . 1, 15011 (2016)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Dash, J. G. History of the search for continuous melting. Rev. Mod. Phys. 71, 1737–1743 (1999)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Chui, S. T. Grain-boundary theory of melting in two dimensions. Phys. Rev. Lett. 48, 933–935 (1982)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Elbaum, M., Lipson, S. G. & Dash, J. G. Optical study of surface melting on ice. J. Cryst. Growth 129, 491–505 (1993)

    ADS  CAS  Article  Google Scholar 

  9. 9

    van der Gon, A. W. D., Gay, J. M., Frenken, J. W. M. & van der Veen, J. F. Order–disorder transitions at the Ge(111) surface. Surf. Sci. 241, 335–345 (1991)

    ADS  Article  Google Scholar 

  10. 10

    Carnevali, P., Ercolessi, F. & Tosatti, E. Melting and nonmelting behavior of the Au(111) surface. Phys. Rev. B 36, 6701–6704 (1987)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Rogers, W. B. & Manoharan, V. N. Programming colloidal phase transitions with DNA strand displacement. Science 347, 639–642 (2015)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Savage, J. R., Blair, D. W., Levine, A. J., Guyer, R. A. & Dinsmore, A. D. Imaging the sublimation dynamics of colloidal crystallites. Science 314, 795–798 (2006)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Hertlein, C., Helden, L., Gambassi, A., Dietrich, S. & Bechinger, C. Direct measurement of critical Casimir forces. Nature 451, 172–175 (2008)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Yang, Y., Asta, M. & Laird, B. B. Solid–liquid interfacial premelting. Phys. Rev. Lett. 110, 096102 (2013)

    ADS  Article  Google Scholar 

  15. 15

    Strandburg, K. J. Two-dimensional melting. Rev. Mod. Phys. 60, 161–207 (1988)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Pluis, B., Frenkel, D. & van der Veen, J. F. Surface-induced melting and freezing II. A semi-empirical Landau-type model. Surf. Sci. 239, 282–300 (1990)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Di Tolla, F. D. Interplay of melting, wetting, overheating and faceting on metal surfaces: theory and simulation. Surf. Sci. 377–379, 499–503 (1997)

    ADS  Article  Google Scholar 

  18. 18

    Karim, O. A. & Haymet, A. D. J. The ice/water interface: a molecular dynamics simulation study. J. Chem. Phys. 89, 6889–6896 (1988)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Broughton, J. Q. & Gilmer, G. H. Interface melting: simulations of surfaces and grain boundaries at high temperatures. J. Phys. Chem. 91, 6347–6359 (1987)

    CAS  Article  Google Scholar 

  20. 20

    Lipowsky, R. Surface induced disordering at first-order bulk transitions. Z. Phys. B 51, 165–172 (1983)

    ADS  CAS  Article  Google Scholar 

  21. 21

    von Grünberg, H. H., Keim, P., Zahn, K. & Maret, G. Elastic behavior of a two-dimensional crystal near melting. Phys. Rev. Lett. 93, 255703 (2004)

    ADS  Article  Google Scholar 

  22. 22

    Still, T. et al. Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions. Phys. Rev. E 89, 012301 (2014)

    ADS  Article  Google Scholar 

  23. 23

    Lee, S. et al. Giant magneto-elastic coupling in multiferroic hexagonal manganites. Nature 451, 805–808 (2008)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Bolhuis, P. & Frenkel, D. Prediction of an expanded-to-condensed transition in colloidal crystals. Phys. Rev. Lett. 72, 2211–2214 (1994)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Alsayed, A. M., Islam, M. F., Zhang, J., Collings, P. J. & Yodh, A. G. Premelting at defects within bulk colloidal crystals. Science 309, 1207–1210 (2005)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Halperin, B. I. & Nelson, D. R. Theory of two-dimensional melting. Phys. Rev. Lett. 41, 121–124 (1978)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  27. 27

    Zahn, K., Lenke, R. & Maret, G. Two-stage melting of paramagnetic colloidal crystals in two dimensions. Phys. Rev. Lett. 82, 2721–2724 (1999)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Han, Y., Ha, N. Y., Alsayed, A. M. & Yodh, A. G. Melting of two-dimensional tunable-diameter colloidal crystals. Phys. Rev. E 77, 041406 (2008)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Kapfer, S. C. & Krauth, W. Two-dimensional melting: from liquid-hexatic coexistence to continuous rransitions. Phys. Rev. Lett. 114, 035702 (2015)

    ADS  Article  Google Scholar 

  30. 30

    Nosenko, V., Zhdanov, S. K., Ivlev, A. V., Knapek, C. A. & Morfill, G. E. 2D melting of plasma crystals: equilibrium and nonequilibrium regimes. Phys. Rev. Lett. 103, 015001 (2009)

    ADS  CAS  Article  Google Scholar 

  31. 31

    Qi, W. & Dijkstra, M. Destabilisation of the hexatic phase in systems of hard disks by quenched disorder due to pinning on a lattice. Soft Matter 11, 2852–2856 (2015)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank X. Cao and M. Liao for the discussions and Chromatech Inc. for the dye sample. This study was supported by RGC grants GRF601911, GRF16301514 and C6004-14G (Y.H.) and an NWO VENI grant 680-47-441 and the Start-Up Grant from Nanyang Technological University (R.N.).

Author information

Affiliations

Authors

Contributions

Y.H. and B.L. conceived and designed the research. B.L. carried out the experiment with help from D.Z. and Y.P., and the data analysis with help from F.W. and R.N. B.L. and Y.H. wrote the paper. Y.H. supervised the work. All authors discussed the results.

Corresponding author

Correspondence to Yilong Han.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-18 and additional references. (PDF 9576 kb)

Surface premelting process of an equilibrium bilayer crystal at four temperatures

Surface premelting process of an equilibrium bilayer crystal at four temperatures (×3 real time). (MP4 7813 kb)

Surface premelting process of an equilibrium monolayer crystal at four temperatures

In the final temperature step, we shifted the field of view containing two domains with different surface lattice orientations and a grain boundary to show that they exerted little effect on the surface liquid thickness l (×3 real time). (MP4 4200 kb)

Non-quasistatic surface premelting process of a monolayer crystal accompanied with a bulk lattice expansion

The temperature of the sample dropped rapidly from 26.5°C to 22.8°C in 30 s, making the solid–solid transition easier to visualize (×50 real time). (MP4 8621 kb)

Heterogeneous melting of a bilayer crystal inside the bulk

The white spots are smaller than the physical size of the sphere because of the high-contrast CCD camera setting (×3 real time). (MP4 6628 kb)

Homogeneous melting of a monolayer crystal inside the bulk

Homogeneous melting of a monolayer crystal inside the bulk (×3 real time). (MP4 17051 kb)

The melted monolayer is a structural liquid with polycrystalline patches

The melted monolayer is a structural liquid with polycrystalline patches (×40 real time). (MP4 20410 kb)

Premelted monolayer crystal at T = 23.1°C under equilibrium for 20 min shows no drift flow

Premelted monolayer crystal at T = 23.1°C under equilibrium for 20 min shows no drift flow (×50 real time). (MP4 14927 kb)

Epitaxial growth of a two-layer crystal under a temperature gradient of 15.0°C/mm at 32.0°C

Epitaxial growth of a two-layer crystal under a temperature gradient of 15.0°C/mm at 32.0°C (×30 real time). (MP4 9252 kb)

Image of the particles becomes sharper by increasing the contrast of the controlling software of the CCD camera under a constant brightness.

Image of the particles becomes sharper by increasing the contrast of the controlling software of the CCD camera under a constant brightness. (MP4 5947 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, B., Wang, F., Zhou, D. et al. Modes of surface premelting in colloidal crystals composed of attractive particles. Nature 531, 485–488 (2016). https://doi.org/10.1038/nature16987

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing