Probing the critical nucleus size in tetrahydrofuran clathrate hydrate formation using surface-anchored nanoparticles

Controlling the formation of clathrate hydrates is crucial for advancing hydrate-based technologies. However, the microscopic mechanism underlying clathrate hydrate formation through nucleation remains poorly elucidated. Specifically, the critical nucleus, theorized as a pivotal step in nucleation, lacks empirical validation. Here, we report uniform nanoparticles, e.g., graphene oxide (GO) nanosheets and gold or silver nanocubes with controlled sizes, as nanoprobes to experimentally measure the size of the critical nucleus of tetrahydrofuran (THF) clathrate hydrate formation. The capability of the nanoparticles in facilitating THF clathrate hydrate nucleation displays generally an abrupt change at a nanoparticle-size-determined specific supercooling. It is revealed that the free-energy barrier shows an abrupt change when the nanoparticles have an approximately the same size as that of the critical nucleus. Thus, it is inferred that THF clathrate hydrate nucleation involves the creation of a critical nucleus with its size being inversely proportional to the supercooling. By proving the existence and determining the supercooling-dependent size of the critical nucleus of the THF clathrate hydrates, this work brings insights in the microscopic pictures of the clathrate hydrate nucleation.

respectively.g The typical DSC thermograph of THF mixed in water with 28 wt% in weight.h The melting peak analysis of formed ice and hydrate from (g) solution, respectively.The quantity of ice decreases as increasing the concentration, but reach zero until the concentration is a larger value than the expected 19%, (e.g., 28%), consisting with the argument that the remained water molecules inside the liquid droplet are excessed after the hydrate due to the evaporation of water molecules to the gas space less than the 17 times (the value in the clathrate) of that of THF molecules.5a.When the sample is cooled to -40 o C with rate of 1 o C min -1 (see Methods), there are two exothermic peaks beginning at about -14 °C and -17 o C, which distinguished to be assigned as hydrate and ice formation, respectively.Once all of the sample is frozen at -40 o C, the final heating with rate of 5 o C min -1 produces two peaks: the ice peak at 0 °C and the hydrate peak at about 4.4 °C, which is in fair agreement with the published value.The middle row in Supplementary Figure 5b shows the DSC thermographs obtained when THF/water with 31 nm (average lateral size) GOs is cooled to -40 o C and then heated.It is observed that both of hydrate and ice are formed at higher nucleation temperature compared with the pure THF aqueous solution (Supplementary Figure 5a) under the experimental conditions.This indicates that the GOs can facilitate the formation of hydrate and ice, which is consistent with the previous results.Moreover, the addition of GO nanosheets with 38 nm can trigger the hydrate nucleation with a much higher temperature.This demonstrates that the size of GO can affect the hydrate nucleation, as the larger GO nanosheets facilitate the clathrate formation.Furthermore, the nucleation of hydrate always occurs before the ice with cooling the experimental sample due to the equilibrium melting temperature of THF hydrate is higher than ice, as shown in Fig. 1.It illustrates that clathrates cannot heterogeneously nucleate ice, which agree with previous reports.

Supplementary Figure 4 .
Ice formation during cooling the THF solution with various THF/water ratio.a The typical DSC thermograph of THF mixed in water with 15 wt% in weight.b The melting peak analysis of formed ice and hydrate from (a) solution, respectively.c The typical DSC thermograph of THF mixed in water with 19 wt% in weight.d The melting peak analysis of formed ice and hydrate from (c) solution, respectively.e The typical DSC thermograph of THF mixed in water with 23 wt% in weight.f The melting peak analysis of formed ice and hydrate from (e) solution,

Figure 6 .
Nucleation temperature of THF/water mixture containing GOs of controlled sizes.a The average nucleation temperature of THF clathrate tuned by GOs with various average sizes and different cooling rates, at the scaled GO coverage of n = 0.18.Each nucleation temperature on the substrate without GOs was averaged from 85 independent experiments.Error bars are the standard error of the mean (SEM).Data are shown as mean ± SEM.Each nucleation temperature on the substrate with GOs was averaged from 100 independent experiments.Data are mean ± SEM. b The average nucleation temperature of THF clathrate tuned by GOs with various average sizes and different cooling rates, at the scaled GO coverage of n = 0.25.Each nucleation temperature on the substrate without GOs was averaged from 85 independent experiments.Data are shown as mean ± SEM.Each nucleation temperature on the substrate with GOs was averaged from 100 independent experiments.Data are mean ± SEM. c The average nucleation temperature of THF clathrate tuned by GOs with various average sizes and different cooling rates, at the scaled GO coverage of n = 1.Each nucleation temperature on the substrate without GOs was averaged from 85 independent experiments.Data are shown as mean ± SEM.Each nucleation temperature on the substrate with GOs was averaged from 100 independent experiments.Data are mean ± SEM.Supplementary Figure 7.The capability of GOs in facilitating the THF hydrate nucleation versus temperature.a The induction time of THF hydrate on GOs with coverage at lateral size of L = 31 nm, and the (supercooling) temperature occurring the hydrate nucleation versus the applied coverage of GOs.Every average clathrate hydrate nucleation delay time shows mean ± SEM.For the GO coverage of n = 0.14, the mean values were averaged from 36 measurements.For every other GO coverage, the mean values were averaged from 39 measurements.The clathrate hydrate nucleation delay time was independently measured with more than 35 valid nucleation events.b the induction time of THF hydrate on GOs with coverage at lateral size of L = 38 nm, and the (supercooling) temperature occurring the hydrate nucleation versus the applied coverage of GOs.The clathrate hydrate nucleation delay time was independently measured with more than 35 valid nucleation events.Every average clathrate hydrate nucleation delay time shows mean ± SEM.For the GO coverage of n = 0.14, the mean values were averaged from 36 measurements.For every other GO coverage, the mean values were averaged from 39 measurements.c the induction time of THF hydrate on GOs with coverage at lateral size of L = 46 nm, and the (supercooling) temperature occurring the hydrate nucleation versus the applied coverage of GOs.Every average clathrate hydrate nucleation delay time shows mean ± SEM.For the GO coverage of n = 0.14, the mean values were averaged from 36 measurements.For every other GO coverage, the mean values were averaged from 39 measurements.The dashed lines in (a) -(c) give ΔTL for all the three-size GOs.

Table 3 . The amount of nitrogen and carbon element on APTES vs the grafting reaction time of GOs with the average size 31 nm.
The results show mean ± s.e.m. from 3 samples.

Table 4 . The relative grafting densities of 38 nm GOs anchored on substrates, calculated by ΔC/Max ΔC.
DSC) was the direct calorimetric measurement used to study the formation of THF hydrates.One typical DSC thermograph of 19 wt% THF in water solution is illustrated in Supplementary Figure