Probing the critical nucleus size for ice formation with graphene oxide nanosheets


Water freezing is ubiquitous and affects areas as diverse as climate, the chemical industry, cryobiology and materials science. Ice nucleation is the controlling step in water freezing1,2,3,4,5 and has, for nearly a century, been assumed to require the formation of a critical ice nucleus6,7,8,9,10. But there has been no direct experimental evidence for the existence of such a nucleus, owing to its transient and nanoscale nature6,7. Here we report ice nucleation in water droplets containing graphene oxide nanosheets of controlled sizes and show that they have a notable impact on ice nucleation only above a certain size that varies with the degree of supercooling of the droplets. We infer from our experimental data and theoretical calculations that the critical size of the graphene oxide reflects the size of the critical ice nucleus, which in the case of sufficiently large graphene oxides sits on their surface and gives rise to ice formation behaviour consistent with classical nucleation theory. By contrast, when the graphene oxide size is smaller than that of the critical ice nucleus, pinning at the periphery of the graphene oxide deforms the ice nucleus as it grows. This gives rise to a much higher free-energy barrier for nucleation and suppresses the promoting effect of the graphene oxide11. The results provide experimental information on the existence and temperature-dependent size of the critical ice nucleus, which has previously only been explored theoretically and through simulations12,13,14,15,16. As pinning of a pre-critical nucleus at a nanoparticle edge is not specific to the ice nucleus on graphene oxides, we expect that our approach could be extended to probe the critical nuclei in other nucleation processes.

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Fig. 1: GOs of controlled sizes.
Fig. 2: Ice nucleation activities of GOs with different sizes and oxidation degrees.
Fig. 3: Transitions in the ice nucleation activity of nanosheets.
Fig. 4: Abrupt change in the free-energy barrier of ice nucleation on GO nanosheets.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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The work is supported by the National Natural Science Foundation of China through grant nos 21733010, 11574310 and 21534007, the National Key R&D Program of China 2018YFA0208502, and the Strategic Priority Research Program of Chinese Academy of Sciences, grant no. XDB28000000. We thank B. Guan and Y. Liu for help in cryo-TEM experiments.

Author information

G.B., X.Z. and J.W. conceived the project and designed the experiments. G.B., D.G. and Z.L. performed the experiments. G.B., D.G., Z.L., X.Z. and J.W. analysed the data. G.B., D.G., X.Z. and J.W. prepared the manuscript.

Correspondence to Xin Zhou or Jianjun Wang.

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The authors declare no competing interests.

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Peer review information Nature thanks Niall English, Christoph Salzmann and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data figures and tables

Extended Data Fig. 1 Characterizations of GOs of controlled sizes.

a, AFM images of GOs of five controlled sizes and the corresponding height profiles along the lines marked. b, Cryo-TEM images of GOs of various sizes before size fractionation, showing the shape of the GOs in water. The upper image is the original; the lower panel is the image with enhanced contrast by colouring the GO domains to help the visibility. Scale bar, 10 nm. c, Photographs of 0.04 mg ml−1 GO aqueous dispersions. From left to right, the average lateral sizes of GO are <1 kDa, 3 nm, 8 nm, 11 nm, 21 nm and 50 nm, respectively. All the GO aqueous dispersions are clear and transparent, indicating the good dispersibility of various-sized GOs in water.

Extended Data Fig. 2 Influence of the substrate on the ice nucleation measurement.

a, Optical microscopic images of frozen water droplets on glass coverslip coated with a thin layer of silicone oil (left) and without silicone oil (right) during the ice nucleation assays. The other experimental conditions for these two images are identical (see Methods). The frozen water droplets on a glass coverslip coated with a thin oil film are independent. In contrast, on the glass coverslip without a thin oil film, the freezing events of the water droplets are not independent. b, Ice nucleation temperatures of water droplets on glass coated with silicone oil, glass without oil, silicon wafer and highly oriented pyrolytic graphite (HOPG). Data are means ±s.e.m. For each mean, the total number of the measurements is not less than 50. The volume of the water droplet is 0.2 µl. Cooling rate, 5 °C min−1. TIN of water droplets on different substrates shows different values, suggesting that the ice nucleation is initiated at the water/substrate interface.

Extended Data Fig. 3 Ice nucleation probability distribution of water droplets containing GOs of controlled sizes at three different concentrations.

The distributions are fitted by Gaussian functions. For each distribution, the total number of ice nucleation measurements is about 150. The results show that the change in concentration (from 0.52 to 13 μmol l−1) of GOs with sizes smaller than 8 nm does not affect the TIN of water droplets; however, TIN increases with the concentration of GOs when the GO size is above 11 nm.

Extended Data Fig. 4 Ice nucleation temperatures of droplets of GO aqueous dispersions at cooling rates ranging from 1 °C min−1 to 15 °C min−1.

a, Cooling rate dependence of TIN of water droplets containing GO samples of controlled sizes. Data are means ±s.e.m. For each mean, the total number of measurements is about 150. b, Ice nucleation probability distribution of the blank control (water droplets) at various cooling rates with Gaussian fitting. c, Ice nucleation probability distribution (Gaussian fitting) of water droplets containing GOs with a series of average lateral sizes at various cooling rates. For each distribution, the total number of measurements is about 150. The concentration of GO aqueous dispersion is 5.2 µmol l−1. All the volumes of water droplets are 0.2 µl.

Extended Data Fig. 5 The transitions of the ice nucleation activity of GOs.

a, The mean ice nucleation (supercooling) temperature −ΔT ≡ TIN − Tm versus the number of GOs in the water droplet, n = CV (for concentration, C and volume, V), for three degrees of oxidation of GOs with the same lateral size of 11 nm. Here the cooling rate is always 5 °C min−1. Data are means ±s.e.m. For each mean, the total number of the measurements is about 50. b, The scaled delay time of ice nucleation of water droplets containing GOs, τ = ntD(Tn), versus ΔT. The three curves for each GO size come from different n (the same as Fig. 3b in the main text) and collapse into the same curve. Data are means; error bars are standard deviation estimated by the jackknife resampling technique. For each mean, the total number of measurements varies from 20 to 150 to ensure that the nucleation event number m is typically not less than 10 (see Methods).

Extended Data Fig. 6 Characterization and ice nucleation activity of laponite.

a, AFM characterization of the prepared laponite. The insets show the lateral size distribution, the thickness and the hydrodynamic diameter of laponite. The size distribution is obtained by averaging the lateral sizes of more than 100 laponite nanosheets imaged by AFM. The hydrodynamic diameter of laponite nanosheets is measured by a Malvern Zetasizer. b, The ice nucleation (supercooling) temperature −ΔT ≡ TIN − Tm versus the number of laponites contained in the water droplet (for concentration, C and volume, V). Here the cooling rate is always 5 °C min−1. Data are means ±s.e.m. For each mean, the total number of the measurements is about 50.

Extended Data Fig. 7 Characterization and ice nucleation temperature investigations of GOs anchored on silicon water surface.

a, Schematic illustration showing the preparation process of the anchored GOs on Si wafer surfaces. b, AFM characterizations of the prepared surfaces without GOs and with GOs of controlled sizes. c, The ice nucleation (supercooling) temperature −ΔT ≡ TIN − Tm versus the contact area between the water droplets and the surface to which the GOs are anchored. The contact area, measured by optical microscopy, is proportional to the number of nucleation active sites (see Methods). Here the cooling rate is always 5 °C min−1. Data are means ±s.e.m. For each mean, the total number of measurements is about 50.

Extended Data Fig. 8 Theoretical analysis of ice nucleation on finite-sized nanosheet.

a, Free-energy barrier of ice nucleation on a thin-disk GO versus the normalized size of GOs. The inset shows the schematic illustration of thin-disk-shaped GOs with a smooth hemispherical edge. Its major diameter (lateral size) is L, and the thickness is H. b, Schematic diagram showing three typical shapes of ice nucleus on GO when L ≈ 2Rc. The first and the third are the critical ice nuclei corresponding to two different free-energy barriers (see Methods). c, The calculated dimensionless free energy, radius of ice nucleus (in units of Rc) and the apparent contact angle ψ versus the volume of ice nucleus (in units of (4π/3)Rc3) on the thin-disk GO nanosheet when L ≈ 2Rc . Here the dimensionless thickness of GO disk h = H/2Rc = 0.1, and θ (=30°) is the intrinsic contact angle between ice nucleus and the GO. The obtained results are not sensitive to these details of GO and the applied parameters (see Methods and Supplementary Section PS6).

Extended Data Table 1 Summary of characterization of GOs of controlled sizes
Extended Data Table 2 Ice nucleation temperatures of water droplets containing GOs of controlled sizes and decreasing degrees of oxidation

Supplementary information

Supplementary Information

This file contains parts PS1−PS7 with 20 Supplementary Figures and one Supplementary Table showing characterizations of GOs, TIN data about GOs, the size effect of Au nanoparticles on ice nucleation, theoretical analysis of ice nucleation on nanoparticles and Supplementary References.

Video 1

Freezing process of a water droplet containing GOs with an average lateral size of 8 nm. Volume of the water droplet, 0.2 µl. Cooling rate, 5 °C min−1. The concentration of GOs in the water droplet, 13 µmol l−1. The video shows that the freezing of the droplet occurs at the temperature of −27.6 °C.

Video 2

Freezing process of a water droplet containing GOs with an average lateral size of 11 nm. Volume of the water droplet, 0.2 µl. Cooling rate, 5 °C min−1. The concentration of GOs in the water droplet, 13 µmol l−1. The video shows that the freezing of the droplet occurs at the temperature of −17.7 °C.

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Bai, G., Gao, D., Liu, Z. et al. Probing the critical nucleus size for ice formation with graphene oxide nanosheets. Nature 576, 437–441 (2019).

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