Fig. 2: Transitions in the THF clathrate hydrate nucleation activity of GO nanosheets at a specific value of the product of GOs’ size and the supercooling.

a Relationship between the average nucleation temperature and L ΔT for the THF clathrate hydrate, and the nucleation temperature displays one abrupt change around L ΔT ≈ 650 nm °C for various GO nanosheets with different coverage, n = 0.18, 0.25, and 1, and under different cooling rates (Black-ramp of 1 °C min⁻¹, Red-ramp of 2 °C min⁻¹, Blue-ramp of 4 °C min⁻¹, Magenta-ramp of 8 °C min⁻¹). Black – cooling rate 1 °C min⁻¹, red – cooling rate 2 °C min⁻¹, blue –cooling rate 4 °C min⁻¹, and magenta – cooling rate 8 °C min⁻¹. Each nucleation temperature was averaged from 100 independent experiments. Error bars are the standard error of the mean (SEM). Data are shown as mean ± SEM. b The average nucleation temperature of THF clathrate tuned by GOs with various average sizes and different coverage of GO nanosheets. The white histograms are the glass substrates without anchored GOs. Cyan – GO coverage of n = 0.18, magenta – GO coverage of n = 0.25, and gray – GO coverage of n = 1. Each nucleation temperature on the substrate without GOs was averaged from 85 independent experiments. Data are mean ± SEM. Each nucleation temperature on the substrate with GOs was averaged from 100 independent experiments. Data are mean ± SEM. c The THF nucleation temperature raises as increasing the coverage of GOs with the lateral size L = 31 nm, 38 nm and 46 nm, respectively, but has a size-dependent saturated value T_L (the dashed lines). Black – 31 nm GO, red – 38 nm G, blue –46 nm GO. Each nucleation temperature was averaged from 100 independent experiments. Data are shown as mean ± SEM. d The product of the saturated supercooling nucleation temperature ΔT_L = T_m−T_L with the different GO sizes (L) of s is almost a constant, equal to 650 nm °C (the dashed line), for all the GOs with various L. Black – 31 nm GO, red – 38 nm G, blue –46 nm GO. Each nucleation temperature was averaged from 100 independent experiments. Data are mean  ±  SEM.