Molecular Insights into Adsorption and Diffusion Mechanism of N-Hexane in MFI Zeolites with Different Si-to-Al Ratios and Counterions

: The effect of the silicon to aluminum ratio (SAR) and alkali metal cations on adsorption and diffusion properties of ZSM-5 and silicate-1 zeolites was investigated using n-hexane as the model probe via giant canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. A wide range of SAR was considered in this study to explore the possible adsorption sites in the zeolites. The ﬁndings show that, at 298 K and 423 K, adsorption and diffusion of n-hexane on/in low SAR ( ≤ 50) H-ZSM-5 models were promoted due to the preferable distribution of n-hexane in straight channels and enhanced interaction between protons and n-hexane molecules (about 24 kcal · mol − 1 ). In alkali metal cation (i.e., Na + and K + ) exchanged ZSM-5, the alkali metal cations affected transport of molecules, which led to signiﬁcant differences in their adsorption and diffusion properties compared to HZSM-5. In the Na + and K + systems, lower saturated adsorption capacities were predicted compared to that of silicate-1, which could be attributed to the decrease in effective void size posed by alkali–metal cations. In addition, simulation results also suggested that the T9 and T3 are the most likely sites for n-hexane adsorption, followed by T2, T5, and T10. Findings of the work can be beneﬁcial to the rational design of high-performance zeolite n-hexane


Introduction
Zeolites are important catalysts and adsorbents that are widely used by many fields such as oil refining, petrochemical conversions and environmental remediation [1][2][3]. Both the chemical and physical properties of zeolites (such as acid sites and pore structures) are crucial for their performance in different applications [4][5][6][7].
MFI frameworks especially aluminum-substituted ZSM-5 show excellent catalytic activity due to their unique structural properties and acidity [8][9][10][11][12]. The MFI framework has 12 distinct crystallographic tetrahedral framework sites; isomorphous substitution of silicon (Si) with aluminum (Al) can generate acidic sites [8,13]. These sites are mostly located within the porous frameworks of zeolites, which offer distinct steric access for guest molecules, controlling the reaction mechanism and diffusion of both reactants and products inside the framework. Thus, it can be expected that the locations and distributions of aluminum atoms would be one of the most important parameters to affect the properties and performance of zeolites.
Hence, significant efforts have been made via both experimental and numerical studies to gain insights into this topic. For example, experimental techniques, such as Fourier transform infrared (FT-IR) spectroscopy [14,15], 27 Al nuclear magnetic resonance (NMR) and then adsorption increased sharply with an increase in pressure and reached saturation when p > 3 × 10 −1 kPa; therefore, higher pressures are required to reach the saturated adsorption capacity at higher temperatures. At 298 K, the saturation adsorption amount of each case is significantly higher than that at 423 K; that is, higher temperature corresponds to a lower saturation adsorption amount, being consistent with the reported findings [43]. At 298 K, we see three clusters of isotherms: one contains the three lowest SARs (12.47, 5.86 and 2.43) has a saturation limit ca. 40 and a half-saturation pressure value of about 10 −9 kPa; the second, with SAR 30 and 50, has values near 32 and 10 −8 kPa; and the third with SAR 100 and 300 has values near 28 and 10 −6 kPa. At 423 K, the effect of different SAR on n-hexane adsorption shows the same trend with 298 K. Compared with silicate-1 zeolite, the adsorption limit of n-hexane on HZSM-5 decreases (30 molecules vs. 25 molecules) and then rises (30 molecules vs. 35 molecules) with the decrease in SAR. When the SAR is less than 30, the adsorption amount would exceed that of silicate-1 zeolite. It is interesting that the untreated silicate-1 has value in the second cluster, which may be attributed to a strong proton environment, resulting in a higher saturated limit of zeolites with low SARs (12.47, 5.86 and 2.43) than that of silicate-1 [44]. These differences in the adsorption behavior could be not only seen in the adsorption isotherms but reflected in the distribution of n-hexane molecules. Figure 2 depicts the density distribution of n-hexane on silicate-1 and HZSM-5 with different SAR at 298 K. In this display, the green region represents the lowest energy, preferred adsorption positions for n-hexane molecules. It can be seen that the green region in silicate-1 zeolite and HZSM-5 zeolites with high SAR (300, 100 and 50) is mainly located in the sinusoidal channels, indicating that n-hexane molecules are mainly distributed in the sinusoidal channels. At a SAR below or equal to 30, the green region in HZSM-5 zeolites almost covered both straight and sinusoidal channels, implying that the increase in proton sites promotes the adsorption of n-hexane molecules in straight channels. The blue shadow in the picture is used to provide much more information for the density distribution of n-hexane in a straight channel. We also see three clusters of density distribution: one contains the three lowest SARs (12.47, 5.86 and 2.43) has the highest probability distribution (i.e., maximum blue shaded area) of n-hexane in the straight channel and the second one is a group of SAR 30 and 50 and silicate-1, and the third with SAR 100 and 300 has the lowest probability distribution (i.e., minimum blue shaded area) of n-hexane in the straight channel. Distribution characteristics of n-hexane on silicate-1 and HZSM-5 with different SAR at 423 K are similar to that at 298 K (cf. Figure S1). Specific quantities of n-hexane in HMFI and silicate-1 models used for MD calculations for further evidence are shown in Figure S4 (20 molecules per cell). The numbers of n-hexane in the straight channels and sinusoidal channels of zeolites (SAR = 300 and 100) are 2~3 and 17~18, respectively. Whilst the numbers of n-hexane in the straight channels and sinusoidal channels of zeolites (silicate-1 and SAR = 50, 30, 12.47, 5.86 and 2.43) is 7~10 and 10~13, respectively. These results show that the HZSM-5 zeolites with SAR less than or equal to 50 are more favorable for the distribution of n-hexane molecules in the straight channels than that with SAR 300 and 100 and improve the molecular adsorption performance.
The MSD of isotropic diffusion coefficient for the n-hexane molecules on these HMFI models is characterized in Figure 3. The diffusion properties of n-hexane molecules on silicate-1 and HZSM-5 zeolites with different SAR have the same trend as the adsorption properties. The order of diffusion coefficients, can be computed by taking the slope of the MSD, is as follows: HZSM-5 (SAR = 12.47, 5.86, 2.43) > HZSM-5(SAR = 50, 30), silicate-1 > HZSM-5(SAR = 300, 100). Combined with Figure 2, it can be concluded that controlling the adsorption of n-hexane in the straight channel would increase the diffusion of n-hexane molecules. These findings demonstrate that the decrease in the SAR is conducive to the adsorption and diffusion of n-hexane molecules, resulting in a distribution transformation from localization to dispersion.

Figure 2.
Density distribution of n-hexane on silicate-1 (a) and HZSM-5 with different SAR of (b), 100 (c), 50 (d), 30 (e), 12.47 (f), 5.86 (g) and 2.43 (h) at 298 K. The X-axis direction (vertical di tion in picture) represents the sinusoidal channels; the Y-axis direction (horizontal direction in ture) represents the straight channels (blue shadow area). green region represents the lowest ener preferred adsorption positions for n-hexane molecules.
The MSD of isotropic diffusion coefficient for the n-hexane molecules on these HM models is characterized in Figure 3. The diffusion properties of n-hexane molecules silicate-1 and HZSM-5 zeolites with different SAR have the same trend as the adsorpt properties. The order of diffusion coefficients, can be computed by taking the slope of MSD, is as follows: HZSM-5 (SAR = 12.47, 5.86, 2.43) > HZSM-5(SAR = 50, 30), silicate-HZSM-5(SAR = 300, 100). Combined with Figure 2, it can be concluded that controll the adsorption of n-hexane in the straight channel would increase the diffusion of n-h ane molecules. These findings demonstrate that the decrease in the SAR is conducive the adsorption and diffusion of n-hexane molecules, resulting in a distribution transf mation from localization to dispersion.   The MSD of isotropic diffusion coefficient for the n-hexane molecules on these HMFI models is characterized in Figure 3. The diffusion properties of n-hexane molecules on silicate-1 and HZSM-5 zeolites with different SAR have the same trend as the adsorption properties. The order of diffusion coefficients, can be computed by taking the slope of the MSD, is as follows: HZSM-5 (SAR = 12.47, 5.86, 2.43) > HZSM-5(SAR = 50, 30), silicate-1 > HZSM-5(SAR = 300, 100). Combined with Figure 2, it can be concluded that controlling the adsorption of n-hexane in the straight channel would increase the diffusion of n-hexane molecules. These findings demonstrate that the decrease in the SAR is conducive to the adsorption and diffusion of n-hexane molecules, resulting in a distribution transformation from localization to dispersion.  12.47 (f), 5.86 (g) and 2.43 (h) at 298 K. The X-axis direction (vertical direction in picture) represents the sinusoidal channels; the Y-axis direction (horizontal direction in picture) represents the straight channels (blue shadow area). green region represents the lowest energy, preferred adsorption positions for n-hexane molecules. Figure 4 illustrates that adsorption isotherms of n-hexane molecules on silicate-1 and alkali metal cation exchanged ZSM-5 zeolites (i.e., NaZSM-5 and KZSM-5) at 298 K and 423 K. For NaZSM-5 and KZSM-5 zeolites, the temperature has little effect on the saturated adsorption amounts, but higher pressure is still required to achieve saturated adsorption at high temperatures. The lower saturated adsorption capacity than silicate-1 can be found in Na + and K + systems due to the decrease in effective void size posed by alkali-metal cations. Na + exchanged ZSM-5 with high SAR (SAR = 300, 100) have higher saturated adsorption capacity than that with low SAR (SAR = 50, 30, 5.86 and 2.43). A suitable Na + cationic environment (SAR = 12.47) is conducive to the n-hexane adsorption. The saturated adsorption amounts for KZSM-5 decrease with the SAR decreasing from 100 to 2.43, especially, saturated adsorption amounts of n-hexane on KZSM-5 zeolites have been reduced to 6 and 0 molecules per cell, when the SAR is at 5.86 and 2.43. These results suggest that the alkali-metal cations not only can reduce the effective void size of the system but also provide a cationic environment for the n-hexane molecules at the same time, leading to a significant difference in the adsorption performance of NaZSM-5 and KZSM-5 compared with HZSM-5.  Figure 4 illustrates that adsorption isotherms of n-hexane molecules on silicate-1 alkali metal cation exchanged ZSM-5 zeolites (i.e., NaZSM-5 and KZSM-5) at 298 K 423 K. For NaZSM-5 and KZSM-5 zeolites, the temperature has little effect on the s rated adsorption amounts, but higher pressure is still required to achieve saturated sorption at high temperatures. The lower saturated adsorption capacity than silicate-1 be found in Na + and K + systems due to the decrease in effective void size posed by alk metal cations. Na + exchanged ZSM-5 with high SAR (SAR = 300, 100) have higher s rated adsorption capacity than that with low SAR (SAR = 50, 30, 5.86 and 2.43). A suit Na + cationic environment (SAR = 12.47) is conducive to the n-hexane adsorption. The urated adsorption amounts for KZSM-5 decrease with the SAR decreasing from 10 2.43, especially, saturated adsorption amounts of n-hexane on KZSM-5 zeolites have b reduced to 6 and 0 molecules per cell, when the SAR is at 5.86 and 2.43. These res suggest that the alkali-metal cations not only can reduce the effective void size of the tem but also provide a cationic environment for the n-hexane molecules at the same t leading to a significant difference in the adsorption performance of NaZSM-5 and KZ 5 compared with HZSM-5. Figures 5 and 6 present the density distribution of n-hexane molecules on silica NaZSM-5 and KZSM-5 with different SAR at 298 K. The density distribution in Fig  5a-h and 6a-h can also be divided into three clusters. For Na + systems together with cate-1, the first cluster of panels 5a-c has the highest density distribution in both chan of zeolite, the second group of panels 5d-f and the last group of panels g and h has lowest density distribution. There are some differences in the distribution of n-hexan K + systems. The green area in panel f of Figure 6 (KMFI, SAR = 12.71) decreases sig cantly compared to that in panel f of Figure 5 (NaMFI, SAR = 12.71). Noticeably, n-hex molecules have almost no density distribution on KZSM-5 with the SAR of 5.86 and 2 which is in good agreement with the change of the above adsorption isotherm. Distr tion characteristics of n-hexane on silicate-1, NaZSM-5 and KZSM-5 with different SA 423 K is basically similar to that at 298 K (cf. Figures S2 and S3). Specific quantities o hexane in NaMFI, KMFI and silicate-1 models used for MD calculations for further dence are shown in Figures S5 and S6. The numbers of n-hexane in the straight chan (eight molecules per cell) and the sinusoidal channels (12 molecules per cell) of Na zeolite (silicate-1 and SAR = 300, 100, 50 and 30) are the same. The numbers of n-hex in the straight channels (6~9 molecules per cell) and the sinusoidal channels (14~11 m cules per cell) of KMFI zeolite (silicate-1 and SAR = 300, 100, 50 and 30) are similar.   and 6a-h can also be divided into three clusters. For Na + systems together with silicate-1, the first cluster of panels 5a-c has the highest density distribution in both channels of zeolite, the second group of panels 5d-f and the last group of panels g and h has the lowest density distribution. There are some differences in the distribution of n-hexane in K + systems. The green area in panel f of Figure 6 (KMFI, SAR = 12.71) decreases significantly compared to that in panel f of Figure 5 (NaMFI, SAR = 12.71). Noticeably, n-hexane molecules have almost no density distribution on KZSM-5 with the SAR of 5.86 and 2.43, which is in good agreement with the change of the above adsorption isotherm. Distribution characteristics of n-hexane on silicate-1, NaZSM-5 and KZSM-5 with different SAR at 423 K is basically similar to that at 298 K (cf. Figures S2 and S3). Specific quantities of n-hexane in NaMFI, KMFI and silicate-1 models used for MD calculations for further evidence are shown in Figures S5 and S6. The numbers of n-hexane in the straight channels (eight molecules per cell) and the sinusoidal channels (12 molecules per cell) of NaMFI zeolite (silicate-1 and SAR = 300, 100, 50 and 30) are the same. The numbers of n-hexane in the straight channels (6~9 molecules per cell) and the sinusoidal channels (14~11 molecules per cell) of KMFI zeolite (silicate-1 and SAR = 300, 100, 50 and 30) are similar. The differences of n-hexane distribution in straight and sinusoidal channels are inapparent and irregular in Figure 5,    Based on the above results, we only analyze and discuss the diffusion properties of n-hexane molecules on silicate-1, NaZSM-5 and KZSM-5 with typical SAR (300, 100, 50 and 30). MSD of isotropic diffusion coefficient for the n-hexane on these NaMFI and KMFI models are represented in Figure 7. From Figure 7a, the diffusion coefficient of n-hexane molecules on the NaZSM-5 zeolites with high SAR of 300 and 100 is the highest (maximum values of MSD are ca. 90 Å 2 ), followed by silicate-1 (maximum values of MSD is ca. 60 Å 2 ) and then the NaZSM-5 zeolites with SAR of 50 and 30 showed a much lower diffusion coefficient (maximum values of MSD are ca. 10 Å 2 ), which is mainly attributed to the differences in properties of alkali-cations and the distribution of n-hexane molecules (cf. Figure 5). The Na + cations on the NaZSM-5 zeolites with high SAR of 300 and 100 increase the diffusion rate of n-hexane molecules. This is all due to the negligible space-confined posed by the small amount of Na + . As the amount of Na + cations increases, that is, a decrease in SAR, the rate of diffusion decreases. We found that the diffusion coefficient of silicate-1 is the highest when the temperature is increased to 423 (maximum values of MSD are ca. 90 Å 2 ). Maximum values of MSD with SAR 300, 100 and with SAR 50, 30 are near 50 Å 2 and 70 Å 2, respectively. Contrary to 298 K, the diffusion coefficient of the NaZSM-5 with SAR of 300 and 100 is lower than that of 50 and 30, which is mainly due to the increase in mobility in channels at high temperature to affect interaction mode between host and guest. In order to explain the nature of these differences, we conducted an in-depth analysis of the anisotropic MSD with X-axis, Y-axis and Z-axis direction (cf. Figures S7 and S8). X-axis and Y-axis directions represent the sinusoidal and the straight channels, respectively. There are no channels in the Z-axis direction, which is why the diffusion coefficient in this direction is basically zero. At 298 K and 423 K, the diffusion coefficient of n-hexane molecules in the X-axis and Y-axis directions of NaZSM-5 with high SAR of 300 and 100 shows completely opposite trends, suggesting that high temperatures tip a balance so that transport in sinusoidal channels is enhanced over that in straight channels. For KZSM-5 zeolites at 298 K and 423 K (cf. Figure 7c,d), the maximum values of MSD show the following pattern: silicate-1 > KZSM-5 (SAR = 300) > KZSM-5 (SAR = 100 > KZSM-5(SAR = 50) > KZSM-5 (SAR = 30), indicating that the diffusion coefficient of n-hexane molecules decreases with the decrease in SAR. The reason is that K+ cations pose nonnegligible diffusional limitations due to their larger size, which slows the diffusion of n-hexane molecules. Moreover, it should be noted that in the KZSM-5, in high temperatures (423 K), appears a second slow process; it may be attributed to the process of molecules approaching cations. When molecules are close to the molecules with high mobility, an opposite effect immediately occurs to accelerate the diffusion of molecules and then appear a second slow process. The second slow process does not occur in the zeolite with low SAR (i.e., higher K + cation content) because n-hexane would approach another K + cation with high mobility when it is close to one K + cation with high mobility, which would limit the transport of hexane molecules. The properties of alkali cations in MFI models are closely related to the adsorption and diffusion performance of n-hexane molecules, and the alkali cations with low electronegativity and large size are unfavorable to the adsorption and diffusion of n-hexane molecules. Based on the above results, we only analyze and discuss the diffusion properties of n-hexane molecules on silicate-1, NaZSM-5 and KZSM-5 with typical SAR (300, 100, 50 and 30). MSD of isotropic diffusion coefficient for the n-hexane on these NaMFI and KMFI models are represented in Figure 7. From Figure 7a, the diffusion coefficient of n-hexane and then appear a second slow process. The second slow process does not occur in the zeolite with low SAR (i.e., higher K + cation content) because n-hexane would approach another K + cation with high mobility when it is close to one K + cation with high mobility, which would limit the transport of hexane molecules. The properties of alkali cations in MFI models are closely related to the adsorption and diffusion performance of n-hexane molecules, and the alkali cations with low electronegativity and large size are unfavorable to the adsorption and diffusion of n-hexane molecules.

Comparative Analysis of Energy Distribution of N-Hexane Molecules on the HMFI, NaMFI and KMFI Zeolites with Typical SAR
In order to further explore the essence of the change of adsorption state, the isosteric heats and the interaction energy distribution curves of n-hexane molecules on the HMFI, NaMFI and KMFI zeolites with typical SAR are analyzed in Figures 8-11. Figure 8 illustrates the isosteric heats of n-hexane molecules on the HMFI, NaMFI and KMFI zeolites with typical SAR at 298 K and 423 K. These figures make it clear that increasing temperature would reduce the isosteric heats of n-hexane molecules over these MFI zeolites. This trend agrees well with the interaction energy distribution curves; interactions between nhexane molecules and these MFI zeolites were decreased with the increase in temperature corresponding to the right shift of the energy distribution curve (cf. Figures 9-11). Figure  8a,b refer to HZSM-5 and silicate-1 show a roughly linear increase in strength as loading increases, curves for the range of SAR values (300, 100 and 50) seem noisier. The results

Comparative Analysis of Energy Distribution of N-Hexane Molecules on the HMFI, NaMFI and KMFI Zeolites with Typical SAR
In order to further explore the essence of the change of adsorption state, the isosteric heats and the interaction energy distribution curves of n-hexane molecules on the HMFI, NaMFI and KMFI zeolites with typical SAR are analyzed in Figures 8-11. Figure 8 illustrates the isosteric heats of n-hexane molecules on the HMFI, NaMFI and KMFI zeolites with typical SAR at 298 K and 423 K. These figures make it clear that increasing temperature would reduce the isosteric heats of n-hexane molecules over these MFI zeolites. This trend agrees well with the interaction energy distribution curves; interactions between n-hexane molecules and these MFI zeolites were decreased with the increase in temperature corresponding to the right shift of the energy distribution curve (cf. Figures 9-11). Figure 8a,b refer to HZSM-5 and silicate-1 show a roughly linear increase in strength as loading increases, curves for the range of SAR values (300, 100 and 50) seem noisier. The results of linear fitting the data are listed in Table S1. The values of R2 for HZSM-5 and silicate-1 are 0.65 (SAR = 300), 0.90 (SAR = 100), 0.93 (SAR = 50), 0.97 (SAR = 30) and 0.94 (silicate-1). The localized and uneven distribution of n-hexane in the HZSM-5 with SAR of 300, 100 and 50 can be seen as the cause of the fact that curves occur some degree of deviation from the regression line. The distribution of n-hexane delocalizes well with a low SAR of 30, presenting a better linear relationship than silicate-1. The same trend also can be found in high temperatures (cf. Table S1). The order of isosteric heats at 298 K is as follows: HZSM-5 (SAR = 30) > silicate-1 > HZSM-5 (SAR = 300, 100 and 50). The temperature rises to 423 K, the adsorption heat on silicate-1 is higher than that on the HZSM-5 due to the reduction in the interaction between the proton adsorption site and the n-hexane molecules. It is important to note that the more acidic sites, the more significant the effect of high temperature weakening interaction (cf. Figure 8b). From Figure 9, there are two kinds of interactions, which are distributed on the left and right of 24 kcal·mol −1 , Catalysts 2022, 12, 144 9 of 16 respectively. In Figure 9a-d, the higher-pressure (>10 −5 kPa or >5 × 10 −7 kPa) cluster refers to relatively strong interaction around about −24.5 kcal/mol and the low-pressure cluster (<5 × 10 −7 kPa or <10 −8 ) refers to weaker interaction, at most −24 kcal. There is considerable overlap of the several distributions. At the higher temperature, the clustering is less evident and there seems to be a shift toward lower adsorption energy. There is at least a hint that the two peak values may refer to the straight and sinusoidal channels.      Figure 8c,d referring to NaZSM-5 represent a slight linear increase in strength as loading increases, especially at high temperatures. The synergistic mechanism of multiple Na+ sites at low SAR may be seen as the cause for the departure from linearity. The isosteric heats of n-hexane molecules on NaMFI zeolites at 298 K are almost identical, with the exception of the NaZSM-5 with SAR of 30 (see Figure 8c). Interaction energy distribution curves of n-hexane molecules on NaZSM-5 with SAR of 30 present the special peak at 25 kcal·mol −1 , indicating the stronger interactions between the n-hexane molecules and the Na + sites (see Figure 10d), which can account for the higher isosteric heat in Figure 8c at 30 SAR. At 423 K, isosteric heats curves on NaZSM-5 zeolites are all lower than on silicate-1, possibly because kinetic energy in high temperature overcome the attraction between n-hexane and the zeolites. The specific difference for different SAR mainly depends on the interaction mode between Na + cation sites and n-hexane and the distribution of n-hexane molecules, which will cause the completely opposite trend of the anisotropic MSD (cf. Figure 7, Figures S7 and S8). Figure 8e,f refer to KMFI that depict further scatter, that is, the lack of linear correlation between isosteric heat and loading. The isometric heats are much higher than that of the HMFI and NaMFI, and the order is basically followed, the lower the SAR, the higher the isometric heat (see Figure 8e,f). The interaction mode of host-guest is similar to the NaMFI, but K + has a larger size and lower electronegativity, resulting in stronger diffusion limitation and interaction energy; therefore, the decrease in adsorption amount of n-hexane and the increase in complexity of interaction mode are the reasons for the erratic data. This trend keeps with the energy distribution curve in the K + systems that show quite different behavior in detail. The new cluster is shown in Figure 11b-d, which refers to the stronger interaction around about −26 kcal, which should be linked to the synergistic mechanism between K + cations, which is much stronger than Na + systems. This interaction is greatly improved with the decrease in the SAR that is also according to the change in adsorption and diffusion properties of n-hexane molecules. These findings show that the interactions between the n-hexane molecules and proton sites are favorable to the adsorption and diffusion of n-hexane molecules (about −24 kcal·mol −1 ), while the strong interactions between the n-hexane molecules and alkali-cation sites are not conducive to the adsorption and diffusion of n-hexane molecules (above −25 kcal·mol −1 ).

Identification of Adsorption Sites of N-Hexane Molecules on HZSM-5
HZSM-5 model with the SAR of 2.43, which contains substituted Al atoms at all 12 T sites, was selected for exploring the adsorption site of n-hexane. RDFs can clearly identify the relative locations of particles by calculating the possibility of the presence of other particles surrounding a particular particle. Figure 12 gives the RDFs of COM-H (COM refers to the mass of the center of the n-hexane molecules; H refers to a proton in the Si-O(H)-Al) on HZSM-5 with the SAR of 2.43. It can be seen that the acid sites in T9 and T3 have the highest adsorption probability with the r (Å) of 3.5 Å, followed by T2, T5 and T10. The result reported here agrees well with previous related studies that suggest that T2, T3, T5 and T10 sites are all stable acidic sites in MFI structure and should represent the active site for sorption and reaction [8,20,22]. For T9 site, it is a very promising nhexane adsorption site, although it may not be easily replaced by aluminum.

Identification of Adsorption Sites of N-Hexane Molecules on HZSM-5
HZSM-5 model with the SAR of 2.43, which contains substituted Al atoms at all 12 T sites, was selected for exploring the adsorption site of n-hexane. RDFs can clearly identify the relative locations of particles by calculating the possibility of the presence of other particles surrounding a particular particle. Figure 12 gives the RDFs of COM-H (COM refers to the mass of the center of the n-hexane molecules; H refers to a proton in the Si-O(H)-Al) on HZSM-5 with the SAR of 2.43. It can be seen that the acid sites in T9 and T3 have the highest adsorption probability with the r (Å) of 3.5 Å, followed by T2, T5 and T10. The result reported here agrees well with previous related studies that suggest that T2, T3, T5 and T10 sites are all stable acidic sites in MFI structure and should represent the active site for sorption and reaction [8,20,22]. For T9 site, it is a very promising n-hexane adsorption site, although it may not be easily replaced by aluminum.
have the highest adsorption probability with the r (Å) of 3.5 Å, followed by T2, T5 an T10. The result reported here agrees well with previous related studies that suggest tha T2, T3, T5 and T10 sites are all stable acidic sites in MFI structure and should represen the active site for sorption and reaction [8,20,22]. For T9 site, it is a very promising n hexane adsorption site, although it may not be easily replaced by aluminum.

Discussion
The adsorption and diffusion of n-hexane on/in low SAR (<50) H-ZSM-5 models were enhanced by the preferable distribution of n-hexane in straight channels and enhanced interaction between protons and n-hexane molecules (about 24 kcal·mol −1 ). In Na + /K + exchanged ZSM-5, the presence of alkali metal cations in the framework affects the transport of molecules, which alters the adsorption and diffusion properties of the alkali metal cations exchanged ZSM-5 in comparison to HZSM-5. The cations not only can reduce the effective void size of the system but also provide a cationic environment for the n-hexane molecules at the same time. The lower saturated adsorption capacity than silicate-1 can be found in Na + and K + systems due to the decrease in effective void size posed by alkalimetal cations. Na + exchanged ZSM-5 with high SAR (SAR = 300 and 100) have higher saturated adsorption capacity than that with low SAR (SAR = 50, 30, 5.86 and 2.43). A suitable cationic environment (SAR = 12.47) is beneficial to the n-hexane adsorption. The various ionic environments will lead to differences in the interaction mode between the host and the guest, thereby changing the molecular diffusion. The existence of optimal amount of Na + (SAR = 300, 100 at 298 K or SAR = 50, 30, at 423 K) is beneficial to the diffusion of n-hexane molecules. This phenomenon is not seen in the K + system. The adsorption-diffusion performance of n-hexane gradually decreases with the increase in K + concentration. It was found that the strong interaction between n-hexane molecules and alkali-metal cations (above 25 kcal·mol −1 ) is not beneficial to the adsorption and diffusion of n-hexane molecules on/in the zeolite framework. The effect of temperature on the adsorption and diffusion behavior of n-hexane molecules in the zeolite models was also studied, which shows that kinetic energy in high temperature possibly overcome the attraction between n-hexane and the zeolites, easing diffusion. In addition, simulation results also suggested that the T9 and T3 are the most likely sites for n-hexane adsorption, followed by T2, T5 and T10. The findings of the work provide a theoretical basis for the rational design and synthesis of zeolites with the tailored SAR for processes involving adsorption and diffusion of alkane molecules.
The MFI models with different SAR and counterions (proton and alkali-cations) used in this study were all established from the MFI supercell mentioned above. The ZSM-5 models with typical and considered SAR of 300, 100, 50 and 30 are constructed for the calculation of this work. Moreover, we also considered ZSM-5 models with smaller SAR of 12.47, 5.86 and 2.43, in which the 12 kinds of T positions of Si atoms were all replaced by Al atoms to obtain the possible adsorption sites to active n-hexane molecules. The Al atoms are randomly introduced by the program, following Lowenstein s rule [45,46]. After substitution, protons (H + ) and metal ions (Na + and K + ) with positive charge compensate the negatively charged aluminosilicate framework, forming Brønsted and Lewis acid sites, respectively. The computational models are shown in Figures S10-S12.
Methods: All calculations were performed using the Sorption and Forcite software package (5.5, Accelrys, San Diego, CA, USA, 2010), contained in the Materials Studio 5.5 of Accelrys, based on giant canonical Monte Carlo (GCMC) and molecular dynamics (MD). Adsorption behavior and properties were calculated by the Sorption module. The Forcite module was used to calculate structural optimization and diffusion properties. For all the simulations, the consistent valence force field (CVFF), successfully utilized with silicate, aluminosilicate and other inorganic systems, was used in this study to measure the valence and nonbonding interactions of zeolite frameworks with adsorbates (host-guest) and adsorbates with adsorbates (guest and guest) [47]. The interactions were modeled by Lenard-Jones (LJ) potential plus Coulomb potential, as shown in the following part: where σ ij and ε ij are the LJ parameters, r ij is the distance between i and j sites, q i and q j are the charges on the interaction center. Ewald summation method [48][49][50] is used to deal with the electrostatic interactions with a calculation accuracy of 4.184 J/mol; the Atom-based method is selected for van der Waals force interactions. The cutoff radius is 12.5 Å. During the GCMC calculation process, the equilibrium steps were set to l × 10 5 , followed by other production steps of l × 10 7 . Each of the steps attempted to move every adsorbate once. The distribution of movement was chosen randomly with a fixed probability, which was 40% exchange, 20% translation, 20% rotation and 20% conformation [51]. The isosteric heat equation used in the adsorption process was calculated as follows: where N ad is the loading of n-hexane, E intra is the intramolecular energy of n-hexane molecules, E ad is the sum of all interactions among adsorbate molecules (E ads−ads ) and all adsorbate interactions with the framework of the MFI zeolites (E ads−zeo ). For the calculation process of MD, one simulation time step of 1.0 fs was employed, which was short enough to ensure good energy conservation. The system was performed using 1000 ps NVE-MD simulations and a Nose-Hoover thermostat was used for temperature control. The mean square displacement (MSD) of alkanes was used in analyzing the diffusion coefficients and is defined by the following equation Further, radial distribution functions (RDFs) are mainly used for confirming the adsorption sites of n-hexane molecules on MFI models. The relative equation is g ij (r) = ∆N ij (r, r + ∆r) V where i and j stand for two particles, r is the distance between these two species, V is volume of the system, ∆N ij (r, r + ∆r) represents the ensemble-averaged number of the species j around i within a shell of ∆r, and N i and N j are the number of i and j species.

Data Availability Statement:
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.