## 4 Evolution Mechanism of Unfrozen Water Content in Pore
### Effect of Potential Energy between Pore Wall and Unfrozen Water on Unfrozen Water Content  
In the slit pores, the intermolecular potential energy exists between the fluid molecules and the coal pore wall, which affects the pore pressure, thus weakening the interaction between water molecules and affecting the freezing process of pore water. The interaction between H\({}_{2}\)O molecule and coal pore wall adopts the two-body potential energy model. If the distance between \(f\) molecule and one side pore wall is \(z_{f}\), then  
\[\Phi_{sf}(z_{f})=\frac{5}{3}\Phi_{0}\left\{\frac{2}{5}\left(\frac{\sigma_{sf}} {z_{sf}}\right)^{10}-\left(\frac{\sigma_{sf}}{z_{sf}}\right)^{4}-\left[\frac{ \sigma_{sf}^{4}}{3\Delta\left(0.61\Delta+z_{sf}\right)^{3}}\right]\right\} \tag{15}\]  
where \(\Phi_{0}\) represents the minimum interaction energy between molecules and carbon atoms, \(\Phi_{0}=\left(\frac{5}{3}\right)\pi\rho_{b}\varepsilon_{sf}\sigma_{sf}^{2}\Delta\); \(\rho_{s}\) is the number density of carbon atoms; \(\Delta\) represents the layer distance of carbon atom crystal (0.335 nm); \(\varepsilon_{sf}\) and \(\sigma_{sf}\) are interaction parameters between fluid molecules and carbon pore walls and represent the depth and effective diameter of potential energy well between fluid molecules and carbon atoms, respectively. The interaction parameters between solid (coal) and fluid (H\({}_{2}\)O molecules) were calculated using the Lorentz-Berthelot mixing rule, as follows:  
\[\sigma_{sf}=\sqrt{\varepsilon_{ss}\varepsilon_{ff}} \tag{16}\]  
\[\sigma_{sf}=\frac{\sigma_{ss}+\sigma_{ff}}{2} \tag{17}\]  
Equation (15) only describes the potential energy between fluid molecules and one side of the pore wall, but in fact, fluid molecules will interact with both sides of the pore wall. Assuming the pore width is \(w_{p}\), the total potential energy between a single fluid molecule \(f\) and the pore wall is:  
\[\Phi_{sf,f(z_{f})}=\Phi_{si(z_{f})}+\Phi_{sf}\Big{(}w_{p}-z_{f}\Big{)} \tag{18}\]  
The effect of pore size on the potential energy between fluid molecules and coal pore wall molecules was further analyzed using the actual pore size combined with the 10-4-3 two-body potential energy model. Within slit-type pores with a pore diameter of less than 0.1 \(\upmu\)m, there was a large intermolecular potential energy between water molecules and carbon atoms, which gradually decreases as the pore diameter table increases. Unfrozen water existed mainly in the form of thin film water in the slit-type pore; a very small gap existed between the H\({}_{2}\)O molecules and the coal pore wall, creating a large potential energy between two different molecules, so that the coal wall generated some pressure on the water molecules, affecting the freezing point of the pore water. In other words, the smaller the pore diameter was, the lower the ice melting point in the pore was, which is also consistent with the above results. At extremely low temperatures, the free water in the pores of coal was completely frozen, and under the influence of pore pressure, there was still bound water that could not be completely frozen in some micropores, as shown in Figure 10. As the melting temperature increased, the ice in the pores began to melt gradually, and there were two kinds of fluids, bound water and free water, and a large amount of free water existed in the pores after the positive temperature. Figure 10b,c show the phase transition evolution process of ice water and the relationship between the intermolecular potential energy in the pore with the pore size. With the decrease of temperature, the pore pressure gradually increased, and there was a great intermolecular potential energy in the pores of small size, and both affected the melting point of the ice in the pores, resulting in the difference of unfrozen water content at different melting temperatures. In addition, the temperature at the site and the pore structure of different quality coals themselves can affect the unfrozen water content within the pores.