Investigation of the microscopic mechanism of H₂O adsorption by low-rank coal slit pores through GCMC and MD simulations

2.1 Model building and optimization

The coal molecule comprises a continuous polycyclic aromatic hydrocarbon structure composed of carbon atoms and containing various heteroatoms. In this study, the Wender coal model, illustrated in Fig. 1(a), was selected to represent the LRC molecule (Xia et al., 2019). The molecular formula of the Wender coal model is C₄₃H₄₆O₁₂, with a molecular weight of 754 and elemental content of 25.46 % O, 6.10 % H, and 68.44 % C. The abundant OFGs and fewer branched chains of the Wender coal model are consistent with the structural features of the LRC. Extensive research has demonstrated the congruence of the Wender coal model with LRC properties (Zhao and Liu, 2023; Zhang et al., 2020), confirming its suitability for investigating the adsorption-diffusion characteristics of H₂O in LRC slit pores. Geometry Optimization tasks were conducted using the Materials Studio software to optimize the structural energy of individual coal molecules. Periodic boundary conditions were applied to these molecules to simulate realistic coal behavior. Subsequently, the single coal molecules were arranged within a crystal cell measuring 10.15 × 10.15 × 10.15 Å using the Amorphous Cell module. The cell model was simulated with geometry optimization and annealing kinetics at temperatures ranging from 298 K to 1498 K. Upon simulation, the density stabilized at 1.12 g/cm³, the energy was minimized and stabilized, and the optimal configuration was achieved, as depicted in Fig. 1(b). Geometry optimization and annealing were performed with medium accuracy, employing the COMPASS II force field to assign corresponding force field parameters to the atoms in the model. Details of the force field parameters are provided in the Appendix, along with the use of Forcefield assigned to assign charges (Meng et al., 2021; Xia et al., 2019). The COMPASS II force field was selected for its broader applicability and higher accuracy compared to the Dreiding force field. Numerous scholars have employed the COMPASS II force field to investigate coal adsorption characteristics with various gas molecules, yielding results consistent with experimental findings (Tan et al., 2022; Wang et al., 2020). Long-range electrostatic interactions were analyzed using Ewald summation with an accuracy of 1.0 × 10^-3 kcal/mol, while van der Waals interactions were examined via Atom-based analysis with a truncation radius of 12.5 Å (You et al., 2019). Detailed parameter settings are outlined in Table 1. Finally, the single-cell model underwent cell expansion to construct the slit-pore model, as illustrated in Fig. 1(c). The structure of the H₂O molecule is presented in Fig. 1(d), with an optimized bond length of 0.93 Å and a bond angle of 104.55°.

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Fig. 1

Structure of coal and H₂O molecules: (a) Wender coal molecule, (b) single-coal cell model, (c) slit pore model, and (d) H₂O molecule.

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Coal possesses a natural porous structure characterized by complexity. According to the International Union of Pure and Applied Chemistry (IUPAC), pores are categorized into macropores, mesopores, and micropores, with size boundaries set at 50 nm and 2 nm, while micropores smaller than 1 nm are referred to as nanopores (Sharon et al., 2015). Microporous pores constitute the majority of coal pores, whereas macroporous pores are less prevalent. In this study, we investigate the H₂O adsorption mechanism in coal by establishing models of LRC with nanopores of 0.5 and 1 nm, micropores of 1.5 and 2 nm, and mesopores of 2.5 and 3 nm. First, the single-cell model was expanded to 3 × 3 × 2 cells. Subsequently, slit-shaped pore structures with varying pore diameters were constructed by introducing vacuum layers with different thicknesses between the two layers of expanded cell models using the Build Layers tool. Fig. 2 illustrates the different slit hole models and cell parameters. The model conforms to the orthorhombic crystal system with interprong angles α, β, and γ set at 90°, prong lengths a and b measuring 3.12 nm, and prong lengths c measuring 5.39/5.89/6.39/6.89/7.39/7.89 nm, respectively. To ensure comparability with the LRC slit-pore model (b)(c)(d)(e)(f) depicted in Fig. 2, model (a) does not impose restrictions such as rotations on the H₂O molecular configuration. Additionally, the empty space above the LRC model contains H₂O molecules during the simulation. However, the impact of these molecules on H₂O adsorption in the slit pores is minimal and can be disregarded.

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Fig. 2

LRC molecular slit pore model illustrating free volume (blue areas) and volume occupied by the atomic skeleton (gray areas) at various pore sizes: (a) 0.5 nm, (b) 1 nm, (c)1.5 nm, (d) 2 nm, (e) 2.5 nm, and (f) 3 nm.

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2.2 Simulation and calculation methods

3.1 Adsorption isotherms

The adsorption isotherms of H₂O molecules within the LRC slit-pore model, featuring various pore sizes, are illustrated in Fig. 3(a). Additionally, the Freundlich isothermal adsorption model was employed for fitting, yielding satisfactory results as depicted in Fig. 3(b). Analysis of Fig. 3 reveals that, at the same fugacity, larger apertures of the slit pores corresponded to higher H₂O adsorption amounts. For instance, at a fugacity of 100 kPa, the adsorption amounts of H₂O by 0.5, 1, 1.5, 2, 2.5, and 3 nm LRC slit pores were 16.55, 22.05, 27.74, 33.51, 38.43, and 44.23 mmol/g, respectively. Compared with the 0.5 nm nanopore slit model, the other five LRC slit-pore models exhibited increased adsorption by 33.19 %, 67.56 %, 102.44 %, 132.15 %, and 167.20 %, respectively. This phenomenon can be attributed to the dependency of H₂O adsorption in the LRC model on both the kinetic diameter of the H₂O molecule itself and the aperture of the slit pore. The kinetic diameter of the H₂O molecule was 0.28 nm, with pore diameters greater than 0.28 nm serving as effective adsorption pore diameters within the determined LRC model. Hence, the pore diameters of the slit pores primarily dictate the adsorption amount. Below a fugacity of 10 kPa, the adsorption of H₂O in the LRC slit pores of varying sizes exhibited gradual increases, indicating monomolecular layer adsorption. Beyond 10 kPa, a sharp increase in H₂O molecule adsorption was observed, signifying the formation of multilayer adsorption and the appearance of numerous water clusters until the slit pores of low-rank coal reached saturation. An increase in fugacity leads to adsorption saturation, reaching adsorption equilibrium at a specific fugacity point where the adsorption rate stabilizes. Notably, the fugacity point of adsorption equilibrium varied across the LRC slit-pore models of different pore sizes. For instance, adsorption equilibrium occurred at approximately 50 kPa for a pore diameter of 0.5 nm, at 60 kPa for pore diameters of 1 and 1.5 nm, and at approximately 80 kPa for a pore diameter of 2 nm. Moreover, no equilibrium was observed even at fugacities exceeding 80 kPa for pore diameters of 2.5 and 3 nm. The greater the pore size of the LRC slit-pore model, the higher the fugacity point of adsorption equilibrium, making adsorption saturation more challenging. The existence of multilayer adsorption of H₂O molecules on the LRC slit-pore model was indicated by the energy distribution (Fig. 6) and the interaction energy of H₂O molecules with the LRC slit-pore model in Fig. 10. Notably, the formation of potential energy bimodal peaks at low fugacities and the increasing interaction energy of individual H₂O molecules with the LRC pore model with increasing pore diameter confirmed the occurrence of multilayer adsorption of H₂O molecules. Yang et al. analyzed the adsorption behavior of low-rank coal and high-rank coal using water vapor isothermal adsorption tests and analyzed them using the Freundlich model (Yang et al., 2021). Their findings revealed a transition from monolayer adsorption of H₂O molecules to multilayer adsorption with increasing water content, eventually leading to capillary condensation. They concluded that the difference in coal water absorption was primarily related to the degree of pore development, aligning with the conclusions drawn from the adsorption of H₂O molecules in different LRC slit-pore models in this paper.

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Fig. 3

Adsorption amounts of H₂O molecules at various pore diameters. (a) adsorption isotherm (b) Freundlich fit.

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3.2 Isosteric heat of adsorption

H₂O adsorption by the LRC slit-pore model was assessed from an energy perspective by analyzing the isosteric adsorption heat. Fig. 4 illustrates the relationship between the adsorbed H₂O amount and the corresponding isosteric adsorption heat across different pore diameters. As depicted in Fig. 4, within the same LRC slit-pore model, the adsorption heat exhibited an exponential increase with rising H₂O molecular adsorption capacity, exhibiting an average growth rate of approximately 160.56 %. When the adsorption amount remained below 0.56 mmol/g, the isosteric adsorption heat measured less than 42 kJ/mol, indicating physical adsorption where H₂O primarily adsorbed onto LRC molecules at the main adsorption site (Zhao and Liu, 2022; Wang et al., 2020). However, upon surpassing the 0.56 mmol/g threshold, the isosteric adsorption heat increased sharply before stabilizing, consistently exceeding 42 kJ/mol. For example, a 3 nm slit pore adsorption of 44.23 mmol/g, the isosteric adsorption heat peaked at 70.40 kJ/mol, surpassing the range of physical adsorption. This notable increase suggests a shift in the adsorption site, where the H₂O adsorbed on the LRC acts as the active site for adsorption (the second adsorption site) and thus adsorbs the H₂O molecules. As the isosteric adsorption heat stabilized, it indicated saturation of the second adsorption site, with an accumulation of H₂O molecules forming water clusters within the LRC slit pores. At this stage, the H₂O-H₂O interaction outweighed the interaction between LRC and H₂O. Notably, there was no direct correlation between adsorption heat and LRC slit pore diameter. In summary, the adsorption mechanism of H₂O by the LRC slit-pore model differs from that of other gases, characterized by multilayer adsorption, changing active adsorption sites, and a sharp increase in isosteric adsorption heat.

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Fig. 4

Correlation between adsorption amount and isosteric adsorption heat.

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3.3 Probability density field distribution

Visualizing the adsorption of H₂O within the LRC slit pores is facilitated by the probability density field distribution (Wu et al., 2019). Fig. 5 illustrates the fluctuation in H₂O adsorption density within 0.5 nm LRC slit pores across eight fugacities: 1, 5, 10, 20, 30, 50, 70, and 100 kPa. The closer to the blue area in the figure, the higher the density of H₂O molecules. At a fugacity of 1 kPa, H₂O predominantly occupied the adsorption sites on the LRC surface, particularly the OFGs, which are inclined to form hydrogen bonds with H₂O, while the presence of H₂O within the slit pores was minimal. With an increase in fugacity to 5 kPa, albeit with the adsorbed H₂O on the LRC escalated, a lower density within the slit pores, where the interaction between LRC and H₂O prevailed. Subsequently, at 10 kPa fugacity, the density of H₂O within both the LRC and the slit pores experienced a moderate increase, accompanied by a slight aggregation of H₂O within the pores. By the time the fugacity reached 20 kPa, H₂O concentration within the slit pores increased substantially, forming denser water clusters. When the fugacity increased to 50 kPa, the LRC slit pores approached saturation with H₂O, exhibiting a very high density, signifying saturation of adsorption where H₂O molecules occupied the second adsorption site. However, due to the aperture limitation of the slit pores, there was no substantial increase in H₂O density when the fugacity was further increased to 100 kPa, akin to the degree of H₂O aggregation observed at 50 kPa. This study comprehensively analyzed the probability density field of H₂O within 0.5 nm slit pores across different fugacities, with the distribution of the probability density field of H₂O in slit pores of other aperture sizes demonstrating similar patterns.

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Fig. 5

Probability density field distribution of H₂O at different fugacities: (a) 1 kPa, (b) 5 kPa, (c) 10 kPa, (d) 20 kPa, (e) 30 kPa, (f) 50 kPa, (g) 70 kPa, and (h) 100 kPa.

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3.4 Energy distribution

The number of adsorption sites and the strength of adsorption were determined based on the energy distribution of H₂O during adsorption within the LRC slit-pore model. Fig. 6 depicts the energy distribution of H₂O adsorption within 0.5 nm LRC slit pores at varying fugacities. The number of peaks indicated the number of adsorption sites, with lower energies suggesting stronger adsorption. At a fugacity of 1 kPa, a distinct potential energy peak around −27 kJ/mol, corresponding to the preferred adsorption site of H₂O, was observed, indicating that all H₂O molecules were adsorbed on the LRC. With increasing fugacity, the energy of H₂O adsorption within the LRC slit pores exhibited a bimodal distribution, signifying the presence of two adsorption sites for H₂O, each with different interaction regions. When the fugacity increased to 5 kPa, the potential energy peak at −27 kJ/mol gradually diminished, while the peak at −45 kJ/mol increased, indicating the emergence of a second adsorption site alongside the preferred one, although most H₂O molecules were still adsorbed at the preferred site. The formation of the second adsorption site evolved gradually with increasing adsorption, with adsorbed H₂O molecules serving as new adsorption sites. When the fugacity reached to 10 kPa, the potential energy peaks at −27 kJ/mol and −45 kJ/mol were close to each other, and the preferred and second adsorption sites occupied the same ratio. The emergence of potential energy bimodal peaks at low fugacity indicated the multilayer adsorption of H₂O within the LRC slit-pore model and the existence of two adsorption sites for H₂O molecules. Given that H₂O molecules exhibit a Boltzmann distribution, the ratio of H₂O molecules between the potential bimodal peaks at low fugacity was approximately 1:5, as revealed by the simulation of the RDF between H₂O and H₂O, with the peak area of the RDF_H2O-H2O bimodal peaks being roughly 1:5. When the fugacity increased to 20 kPa, a peak in the −27 kJ/mol energy region was absent, and the only peak existed in the −45 kJ/mol potential energy region, shifting to a lower energy region (-50 kJ/mol). Thus, H₂O saturated the preferred adsorption site, and all adsorption shifted to the second adsorption site, leading to enhanced H₂O-H₂O interactions and a substantial increase in the amount of H₂O adsorbed within the LRC slit pores. When the fugacity increased to the range of 50 kPa to 100 kPa, the peak potential energy ranged from approximately −66 kJ/mol to −68 kJ/mol in the low-energy region, indicating a higher concentration of H₂O adsorption in this region where the H₂O-H₂O interaction was the strongest. Specifically, at 50 kPa, the adsorption of H₂O at the second adsorption site reached saturation, leading to the filling of the LRC slit pores with H₂O. Svabova et al. conducted isothermal water vapor adsorption tests using three coal samples and concluded that adsorption primarily occurred at the primary adsorption site at lower pressures. However, with increasing pressure, H₂O molecules gradually shifted to the secondary adsorption site, wherein secondary adsorption became more prominent (Svabova et al., 2011). These findings aligned with the simulation results.

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Fig. 6

Energy distribution of H₂O in the LRC slit-pore model.

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A comparison of the energy distribution of H₂O adsorbed in the LRC slit pores at various fugacities revealed a shift in adsorption sites for H₂O molecules. Increasing fugacity resulted in a shift of the potential energy distribution of H₂O toward lower potential energy, with the high energy region representing the preferred adsorption site. Conversely, in the case of CO₂ gas adsorption in coal, the potential energy distribution occurred in the region with the lowest interaction energy, indicating the preferential adsorption site for CO₂. The position of the potential energy peak shifted to the right with increasing fugacity. These differences in the direction of potential energy movement and the preferential adsorption sites of H₂O molecules and CO₂ gas indicated notable variations in their adsorption properties. The adsorption mechanism of H₂O in coal was assessed based on the energy distribution of H₂O in the LRC slit-pore model, confirming the conclusions drawn from the adsorption amount of H₂O molecules, the distribution of probability density field, and the adsorption heat. These findings provided a deeper understanding of the adsorption behavior of H₂O molecules in coal.

3.5 Kinetic properties of H₂O molecules

3.5.1

3.5.1 Diffusion properties of H₂O

The size of the LRC pore diameter influenced the migratory diffusion characteristics of H₂O. The mean square displacement (MSD) and the self-diffusion coefficient (D) helped elucidate the diffusion rate of H₂O within the slit pores of varying pore diameters. Stable data from 0 to 250 ps were selected to analyze the MSD and calculate the self-diffusion coefficient using the following expression (Hao et al., 2022):

(1)

$$\text{MSD}=\frac{1}{N}\sum _{i=1}^N{[r_i(t)-r_i(0)]}^2$$ where N denotes the number of molecules, and $r_i(t)$ and $r_i(0)$ represent the position vectors of the center of mass of the molecules at moments t and t = 0, respectively.

The self-diffusion coefficient was derived from the Einstein equation with the following expression (Hao et al., 2022):

(2)

$$D=\frac{1}{6N}\underset{t\to \infty }{\lim }\frac{d}{\mathit{dt}}\sum _{i=1}^N[r_i(t)-r_i{(0)]}^2$$

(3)

$$D=\underset{t\to \infty }{\lim }(\frac{\text{MSD}}{6t})=\frac{1}{6}{K}_{\text{MSD}}$$ where D denotes the self-diffusion coefficient of H₂O molecules, and K_MSD is the slope of the MSD curve. Fig. 7 depicts the MSD of H2O over time in different LRC slit-pore models, exhibiting a linear correlation between the MSD curves and time within the selected 250 ps, with an R² value exceeding 0.99 in all instances. The fitted MSD curves are summarized in Table 2. The magnitude of the slope of the MSD curve positively correlated with the diffusion strength of the H₂O molecules. As depicted in Fig. 7, the larger the pore diameter, the easier the migration of H₂O in the LRC slit pores, with the mobility of H₂O in mesopores notably higher than that in micropores. The self-diffusion coefficients of H₂O in different LRC slit pores were obtained using expression (3), with the results presented in Table 2. As indicated by the data in Table 2 the self-diffusion coefficient of H₂O tended to increase with the aperture of the slit pores, but the rate of increase had a tendency to increase first and then slow down. The self-diffusion coefficient of H₂O in the 0.5 nm slit pore was 1.21 × 10^-5 cm²/s, whereas it was 3.75 × 10^-5 cm²/s in the 3 nm slit pore, indicating approximately a threefold increase in the self-diffusion coefficient·H₂O exhibited a greater propensity to migrate and diffuse in mesopores, attributed to the strong adsorption on the LRC and the binding effect of the pores on the H₂O molecules, which had a more notable influence only within a certain distance range. Beyond this range, the effect of adsorption on H₂O was diminished. The greater the pore diameter of the slit pores, the closer the diffusion of H₂O was to that of pure water. Low-rank coal mesopores retained more H₂O than micropores, with the influence of OFGs and pores on the migration and diffusion of H₂O being less notable, resulting in a larger self-diffusion coefficient. The self-diffusion coefficient of H₂O in the 3 nm slit pore did not substantially increase compared to that in the 2.5 nm slit pore, because the self-diffusion coefficient of H₂O in the 2.5 nm slit pore closely resembled that of pure water, leading to a decrease in the rate of increase of the self-diffusion coefficient in the 3 nm slit pore.

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Fig. 7

Self-diffusion coefficients of H₂O in the LRC slit-pore model.

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Table 2 MSD fitting curves and self-diffusion coefficients of H₂O in different LRC slit pores.

Slit pore aperture	MSD fitting curves	R2	Self-diffusion coefficient (D, cm2/s)
0.5 nm	Y = 0.7232 X  + 9.7789	0.9981	1.21 × 10-5
1 nm	Y = 1.1497 X  + 15.2632	0.9975	1.92 × 10-5
1.5 nm	Y = 1.6386 X  + 12.7939	0.9992	2.73 × 10-5
2 nm	Y = 1.7497 X  + 20.6512	0.9969	2.92 × 10-5
2.5 nm	Y = 2.1140 X  + 20.7099	0.9978	3.52 × 10-5
3 nm	Y = 2.2496 X  + 21.5591	0.9974	3.75 × 10-5

3.5.2

3.5.2 Radial distribution function (RDF)

The RDF characterizes the distribution of one class of atoms or molecules in the system relative to another class of atoms or molecules within a specific distance r + dr (Zhao and Liu, 2022; Xiang et al., 2014). It responds to the level of ordering of H₂O within the LRC slit pores of varying pore sizes using the following expression (Zhou et al., 2022):

(4)

$$g_{x-y}(r)=\frac{1}{4\pi {\rho }_y{r}^2}\times \frac{d{N}_{x-y}}{\mathit{dr}}$$ where x and y represent the two classes of atoms, ${\rho }_y$ denotes the density of class y atoms, and dN_x-y denotes the average number of class y atoms within a certain distance of class x atoms. To further elucidate the diffusion distribution of H₂O within the LRC slit pores, the RDFs between hydrogen atoms, oxygen atoms in the H₂O molecule, and H₂O molecules within the slit pores of different aperture diameters were calculated at an analytical distance of 12 Å. The results are illustrated in Fig. 8 and Fig. 9. Higher peaks in the RDF curve indicated a higher degree of ordering between atoms or molecules. As depicted in Fig. 8 and Fig. 9, for different pore sizes of LRC slit-pore models, the peak-out distances between hydrogen atoms, oxygen atoms, and H₂O molecules in the H₂O remained consistent, with only the heights of the peaks differing. The position of the first peak of the RDF between hydrogen atoms in an H₂O molecule was at 1.5 Å, representing the distance between two hydrogen atoms within an H₂O molecule, while the position of the second peak was at 2.5 Å. The position of the RDF peak between oxygen atoms of an H₂O molecule was approximately 2.7 Å. Comparing the heights of the inter-atomic oxygen peaks in H₂O revealed that the smaller the pore size, the higher the RDF peaks between oxygen atoms in the LRC slit pores. This indicated a tighter arrangement between oxygen atoms in H₂O molecules within smaller aperture slit pores, resulting in more organized H₂O molecules with lower diffusion rates, consistent with conclusions drawn from the height of the peaks between hydrogen atoms in H₂O molecules. The RDF between H₂O molecules exhibited two peaks, at 0.9 Å and 1.5 Å. Given that H₂O molecules follow a Boltzmann distribution, the ratio of H₂O molecules between the two peaks was 1:5, consistent with the ratio of peak areas obtained from the RDF calculations, affirming the accuracy of the calculations. At r = 0.9 Å, this corresponded to the bond length between oxygen and hydrogen atoms within the H₂O molecule, whereas at r = 1.5 Å, it represented the hydrogen bond formed between H₂O molecules. The height of the hydrogen bonding peak decreased with the increase in the aperture of the LRC slit pores, indicating that with an increase in the pore diameter, the hydrogen bonding force between H₂O molecules diminished, the degree of ordering weakened, and the diffusion rate increased. This can be attributed to the adsorption of OFGs in the LRC and the binding effect of pores; with an increase in pore diameter, more H₂O is adsorbed in the slit pores, resulting in weaker binding effects of the LRC pores and stronger H₂O diffusion. The diffusion performance of H₂O molecules was the most pronounced when the pore size of the slit holes was 3 nm, consistent with the results of the calculated diffusion coefficients.

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Fig. 8

RDF between atoms in H₂O molecule.

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Fig. 9

RDF between H₂O molecule and H₂O molecule.

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3.5.3

3.5.3 Effect of pore size of slit pores on the adsorption of LRC/H₂O

The strength of H₂O adsorption was evaluated by calculating the interaction energies between different LRC slit-pore models and H₂O. The script was utilized to analyze 101 frames of interaction energy post-model adsorption equilibrium, focusing on the last 80 frames to calculate the average interaction energy. The expression for each frame of interaction energy/adsorption energy is as follows (Ding et al., 2023):

(5)

$$E_{\text{int}}=E_{\text{LRC}/{\text{H}}_{\text{2}}\text{O}}-E_{\text{LRC}}-E_{{\text{H}}_{\text{2}}\text{O}}$$ where E_LRC/H2O represents the total energy of the optimized H₂O/LRC slit-pore system (kcal/mol); E_LRC and E_H2O denote the energies of LRC and H₂O, respectively (kcal/mol). A lower interaction energy value indicates stronger H₂O molecule adsorption. The calculation results of the interaction energy and non-covalent interaction force between the LRC slit-pore model with different pore diameters and H₂O/single H₂O molecule are presented in Fig. 10. As illustrated in Fig. 10(a), the interaction energy between the LRC pore model and H₂O gradually decreases with the increase in the pore diameter of the slit pores, indicating an enhanced adsorption capacity of H₂O with larger pore diameters, aligning with the results of adsorption isotherm analysis. From the perspective of non-covalent interaction force, electrostatic force constitutes a higher percentage of the interaction energy of the H₂O-LRC slit pore model, approximately 60 %, in both micropores and mesopores. Hence, the adsorption of H₂O in the LRC slit pores was predominantly controlled by electrostatic force. Notably, as depicted in Fig. 10(b), the interaction energy between a single H₂O molecule and the 0.5-nm pore model was −2.08 kcal/mol, whereas for the 8-nm pore model, it was −0.88 kcal/mol, representing a 57.69 % increase over the 0.5 nm pore model. The interaction between a single H₂O molecule and the LRC slit pore model gradually decreases with increasing pore diameter, with electrostatic forces still dominating the interaction energy. Thus, when the pore diameter increases, the number of H₂O molecules also increases, and the farther the H₂O molecules are from the LRC, the weaker the adsorption of individual H₂O molecules with the LRC pore model. This can be attributed to the adsorption of H₂O molecules with those already adsorbed at the primary adsorption site, forming secondary adsorption sites. Subsequently, the adsorption between H₂O molecules facilitates re-adsorption to form secondary adsorption layers, thus weakening the interaction of the LRC slit-pore model with individual H₂O molecules. The larger the LRC slit pore, the more secondary adsorption layers are formed, confirming multilayer adsorption of H₂O in the LRC slit-pore model, as indicated by the energy analysis in Fig. 10.

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Fig. 10

Interaction energy between H₂O (individual H₂O molecules) and LRC slit-pore models.

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Fig. 11 illustrates the relative concentration distribution of H₂O molecules along the Z-axis in the LRC slit-pore/H₂O system. The adsorption rate of H₂O in the LRC slit pores was 33.36 % when the pore diameter was 0.5 nm. With an increase in pore diameter, the adsorption rate of H₂O gradually rises, exceeding 50 % for all pore diameters exceeding 1 nm. When the pore diameter reaches 3 nm, the adsorption rate peaks at 74.75 %. A substantial amount of H₂O is adsorbed in the LRC slit with larger pore sizes, weakening the interaction of individual H₂O molecules with the LRC. Conversely, fewer H₂O molecules are adsorbed in small aperture slit pores, resulting in greater force exerted by low-rank coal in micropores compared to mesopores on individual H₂O molecules. The pore diameter magnitude significantly influences H₂O adsorption in the LRC slit-pore model, which is pivotal for the investigation of coal pore wetting.

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Fig. 11

Relative concentration distribution of H₂O molecules along the Z-axis: (a) 0.5 nm, (b) 1 nm, (c) 1.5 nm, (d) 2 nm, (e) 2.5 nm, and (f) 3 nm.

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