# Hydrates for Cold Storage: Formation Characteristics, Stability, and Promoters
## 3 Results and Discussion  
### Characteristics of Hydrate Formation  
Hydrate formation is a crystallization process that includes two consecutive steps: nucleation (formation of crystal nuclei) and formation of crystals through the growth of crystal nuclei [31]. [PERSON] et al. defined the induction time as the time to obtain a visible hydrate or to reach the onset of rapid hydrate growth (depending on resolution of the monitoring method) [32]. In this study, the induction time is considered to be the time from the beginning of the experiment to the appearance of the hydrate crystals visible to the naked eyes. The hydrate formation time is considered to be the time from the appearance of visible hydrate crystals to the time when the morphology of hydrate formed in the reaction vessels no longer changed. The data on characteristics of hydrate formation experiments was listed in Table 3, and the comparison of three guest molecules before and after hydrate formation was shown in Figure 2.  
In this study, for the pure water system (without any promotion method), R141b and TBAB/TBAC failed to form hydrates within 48 h, as shown in Figure 2(b1,b5). By contrast, for the TME solution, hydrate crystals were formed at the air-water interface at  
Figure 2: Comparison of three guest molecules before and after hydrate formation. (**a**) Before hydrate formation; (**b**) after hydrate formation; experimental conditions for hydrate formation by R141b in pure water (1), R141b with 1 cm\({}^{3}\) ice cube addition (2), TME in pure water (3), TME with 1 cm\({}^{3}\) ice cube addition (4), TBAB/TBAC in pure water (5), TBAB/TBAC with 1 cm\({}^{3}\) ice cube addition (6), TBAB/TBAC with 500 rpm stirring (7) and TBAB/TBAC with 500 rpm stirring and 0.1 g graphene addition (8). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Whether There Is Formation** & **Induction Time (h)** & **Formation Time (h)** \\ \hline Case 1 & No & — & — \\ Case 2 & Yes & 0.17 & 0.58 \\ Case 3 & Yes & 3.00 & 1.17 \\ Case 4 & Yes & 0.17 & 0.33 \\ Case 5 & No & — & — \\ Case 6 & Yes & 0.08 & 0.25 \\ Case 7 & Yes & 9.01 & 0.62 \\ Case 8 & Yes & 9.67 & 0.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The data on characteristics of hydrate formation experiments. 3 h, and grew rapidly thereafter. The hydrates were concentrated on the bottom layer of the reaction vessel, and visible remaining water was still present in the upper layer, as shown in Figure 2(b3). The excess of water in the TME solution, rather than the excess of TME solute, may result in less water being consumed for hydrate formation. This may be the reason for the presence of clearly visible remaining water in the system. Subcooling is small in the experiment with R141b, moderate in the experiments with TBAB/TBAC, and strong with TME. This may be one of the reasons why only TME hydrates formed in the pure water system (without any promotion method) within 48 h. And in the previous study, the formation of any hydrate was associated with co-existing phases. The stability of hydrate can be expressed as a complex function of the temperature and concentration (and corresponding chemical potential) of all components in all coexisting phases [33]. For the hydrate nucleation process, a certain amount of free guest molecules must be evenly distributed with the water molecules, and the free energy of the guest and water molecules should be relatively low. Only under these conditions can be the nuclei of the hydrate crystals can stabilize and continue to grow [34; 35; 36; 37]. However, because of its very low solubility in water, R141b cannot diffuse uniformly in water molecules [19]. Accordingly, under the effect of the free energy of the water molecules and the R141b molecules, the formation of hydrates by the nucleate may be hindered. Although the guest molecules in free state were evenly distributed in the water molecules, the Gibbs free energy of the system could reach its maximum value, and the formation of a new phase (crystal nucleus) in the system was severely hindered [31].