Investigation on Water Vapor Adsorption of Silica-Phosphonium Ionic Liquids Hybrid Material

Adsorption and diffusion of water vapor in phosphonium ionic liquid modified silica gel were studied, aiming to reduce the loading of water vapor in porous materials. The modified silica gel was prepared through a grafting method and characterized by FTIR, thermal gravity analysis and X-ray photoelectron spectroscopy. N2 sorption isotherms at −196 °C and CO2 sorption isotherms at 0 °C were also measured to analyzee the porosity. Water vapor adsorption equilibriums at 25 °C up to 30 mbar were tested. The results indicate that the ionic liquids (ILs) phase acts as a protecting film which decreases water vapor adsorption. The improvement of water-resistant performance is also attributed to the decrease of micro-porosity and silanol groups on the silica surface. Diffusion behavior of water vapor on modified silica was determined on the basis of the adsorption equilibrium. The effective diffusivity of water vapor in modified silica is almost the same as in bare silica and decreases with the increasing of water vapor loading.


Introduction
Ionic liquids (ILs) are salts with a melting point below 100 • C, which are commonly composed of organic cations and inorganic or organic anions, typically. ILs have been considered as promising solvents in separation [1][2][3], chemical reaction, or catalytics, due to their unique properties, such as low volatility, chemical stability, high gas selectivity, and tunable properties [4,5]. A lot of research into imidazolium-based ILs have been reported [6][7][8], while phosphonium-based ILs are currently appear more attractive, owing to their unique advantages in many aspects. Phosphonium salts are generally more thermally stable and have lower densities than nitrogen-based ILs [9,10]. Moreover, compared with imidazolium and pyridinium ILs, phosphonium ILs have no acidic proton or aromatic ring, which makes them stable towards nucleophilic and basic conditions [11,12]. In addition, the kinetics of phosphonium salt formations are much faster than those of nitrogen-based salts, implying higher productivity and less expense than their equivalent imidazolium ILs [13][14][15]. Based on the characteristics of ILs, there have been many studies on IL-modified porous materials, such as activated silica, carbon, and alumina for CO 2 adsorption. Zhang [16] showed that CO 2 capture capacity increased markedly for grafting amino-functionalized phosphonium ILs ([aP 4443 ]AA) onto silica gel than in a bulk liquid and bare support. Balsamo [17] reported that supported [Emim][Gly] ionic liquid on mesoporous gamma-Al 2 O 3 at different loadings had better CO 2 sorption capacity. These experiments reveal that CO 2 capture performance is greatly enhanced owing to the fact that ILs were supported on the porous support.
A noticeable influence of water on the physical characteristics of adsorbents has been also reported, due to the presence of a small amount of water vapor (8-15%) in the power plant flue gas, which tends Tri-n-octylphosphine (purity: 97%) was purchased from Stream Chemicals, Inc. (Cambridge, UK). Bistrifluoromethanesulfonimide lithium (purity: 99%) was purchased from J&K Scientific (Beijing, China). 3-Chloropropyltriethoxysilane (purity: 97%) was purchased from Beijing Fengtuo Chem Co., Ltd., Beijing, China. Toluene (dried by Na), acetone, and HCl were all analytical grade. All chemicals were purchased from a commercial supplier and used as received. Silica gel with 0.5-1.5 mm in particle size was purchased from Shanghai Silica Gel Factory, Shanghai, China. Silica was pretreated before use.

Synthesis of grafted silica gel
The pretreated methods of silica affect the pore structure and hydroxyls of the silica surface, thus influencing water vapor sorption capacity. In this study, two different treatement methods were used. Silica was calcined at 150 • C for 3.5 h (coded as SiO 2 -C) or acid treated with hydrochloric acid (8 mol/g) at 70 • C for 12 h (coded as SiO 2 -H). It was then washed with distilled water until neural, and dried at 353 K under vacuum for 8 h before further use. The pretreated silica is referred to as bare silica in the following text. The preparation of phosphonium IL-modified silica using grafted method was carried out, according to a previous report [26]. In this work, another kind of silica with different pretreated methods was selected for further controlled amounts of IL. The general procedure is as follows. Tri-n-octylphosphine was added to 3-chloropropyltriethoxysilane and anhydrous toluene and stirred under nitrogen gas at 110 • C for 40 h. Phosphonium chloride was then stirred with an aqueous solution of bistrifluoromethanesulfonimide lithium at room temperature for 30 h. The resulting crude IL was extracted from the aqueous phase using dichloromethane. The dichloromethane phase was then washed with distilled water for several times until no residual chloride salt was detected with the use of AgNO 3 . The IL was dried in vacuum at 333 K for 8 h. The pretreated silica was added to the prepared grafting agent in anhydrous toluene under a nitrogen atmosphere and stirred at 90 • C for 24 h. The solid was collected and washed with acetonitrile and distilled water and then dried at 80 • C overnight under vacuum to obtain an IL-modified silica. The product prepared by calcined silica was labeled as Si-P 8 TFSI/SiO 2 -C, when the molar ration of silica and IL is 1:1. The product prepared by acid-treatment silica was coded as Si-P 8 TFSI/SiO 2 -H(I) and Si-P 8 TFSI/SiO 2 -H(II), respectively, depending on the different molar ratio of silica and the grafting agent (1:0.5 and 1:1), as illustrated in Figure 1. The preparation of phosphonium IL-modified silica using grafted method was carried out, according to a previous report [26]. In this work, another kind of silica with different pretreated methods was selected for further controlled amounts of IL. The general procedure is as follows. Trin-octylphosphine was added to 3-chloropropyltriethoxysilane and anhydrous toluene and stirred under nitrogen gas at 110 °C for 40 h. Phosphonium chloride was then stirred with an aqueous solution of bistrifluoromethanesulfonimide lithium at room temperature for 30 h. The resulting crude IL was extracted from the aqueous phase using dichloromethane. The dichloromethane phase was then washed with distilled water for several times until no residual chloride salt was detected with the use of AgNO3. The IL was dried in vacuum at 333 K for 8 h. The pretreated silica was added to the prepared grafting agent in anhydrous toluene under a nitrogen atmosphere and stirred at 90 °C for 24 h. The solid was collected and washed with acetonitrile and distilled water and then dried at 80 °C overnight under vacuum to obtain an IL-modified silica. The product prepared by calcined silica was labeled as Si-P8TFSI/SiO2-C, when the molar ration of silica and IL is 1:1. The product prepared by acid-treatment silica was coded as Si-P8TFSI/SiO2-H(I) and Si-P8TFSI/SiO2-H(II), respectively, depending on the different molar ratio of silica and the grafting agent (1:0.5 and 1:1), as illustrated in Figure 1.

Chemical Analysis
Fourier transform infrared (FTIR) spectra were recorded on a Thermo Scientific Nicolet 380 IR Spectrometer (Thermo Scientific, Massachusetts, USA), and the samples, in powder form, along with KBr, were compressed into tablets. The spectra (32 scans for the pure ionic liquid and 128 scans for the IL-modified silica) were collected with a spectral resolution of 4 cm −1 .
An x-ray photoelectron spectroscopy measurement was carried out on an X-Ray Photoelectron Spectrometer ESCALAB 250Xi (Thermo Fisher Co, Massachusetts, USA). All binding energies were referenced to the neutral C1 speak at 284.8 eV to compensate for the surface-charging effects.
Thermogravimetric analysis (TGA) was performed at a heating rate of 10 °C/min in the range from room temperature to 700 °C under nitrogen atmosphere, using a STA409C DTA/DSC-TG (Netzsch,Selb, Germany). The hydroxyl group contents were estimated by assuming that the condensation occurred based on the reaction of two hydroxyl groups on the silica surface and can be calculated as follows in Equation (1) [27]. Moreover, according to the thermogravimetric curve, the total IL load on the surface of silica gel is determined by using Equation (2).
Where n (SiO ) indicates the moles of hydroxyl groups on the silica particles W(T ) and W(T ) are the weight of the silica particles (g) at the temperatures 200 °C and 700 °C, respectively, MH2O is the molecular weight of water and GR (wt%) is the total load of ILs on the surface of silica gel.

Chemical Analysis
Fourier transform infrared (FTIR) spectra were recorded on a Thermo Scientific Nicolet 380 IR Spectrometer (Thermo Scientific, Massachusetts, USA), and the samples, in powder form, along with KBr, were compressed into tablets. The spectra (32 scans for the pure ionic liquid and 128 scans for the IL-modified silica) were collected with a spectral resolution of 4 cm −1 .
An x-ray photoelectron spectroscopy measurement was carried out on an X-Ray Photoelectron Spectrometer ESCALAB 250Xi (Thermo Fisher Co., Franklin, MA, USA). All binding energies were referenced to the neutral C1 speak at 284.8 eV to compensate for the surface-charging effects.
Thermogravimetric analysis (TGA) was performed at a heating rate of 10 • C/min in the range from room temperature to 700 • C under nitrogen atmosphere, using a STA409C DTA/DSC-TG (Netzsch, Selb, Germany). The hydroxyl group contents were estimated by assuming that the condensation occurred based on the reaction of two hydroxyl groups on the silica surface and can be calculated as follows in Equation (1) [27]. Moreover, according to the thermogravimetric curve, the total IL load on the surface of silica gel is determined by using Equation (2).
where n OH (SiO 2 ) indicates the moles of hydroxyl groups on the silica particles W(T 0 ) and W(T final ) are the weight of the silica particles (g) at the temperatures 200 • C and 700 • C, respectively, M H2O is the molecular weight of water and GR (wt%) is the total load of ILs on the surface of silica gel. The adsorption isotherm of N 2 at −196 • C and CO 2 at 0 • C were measured by an Autosorb-1-MP (Quantachrome, Florida, USA), an automatic surface area and pore size analyzer. The porous particles were dried and degassed at 100 • C under high vacuum for 5 h to remove moisture or other volatile contaminants. As for N 2 adsorption, the relative pressure (P/P 0 ) range was set between 0.001 and 0.995, and the CO 2 adsorption isotherms were collected within the relative pressure (P/P 0 ) range of 0.0001~0.03 for restricting pores narrower than 2 nm. A density functional theory (DFT) analysis was used to calculate the pore size distribution (PSD) and the pore structure parameters using Quantachrome ASiQwin software (Quantachrome, Florida, USA). based on the adsorption isotherms.

Adsorption Studies
Adsorption and diffusivity of water vapor were measured on an Intelligent Gravimetric Analyzer (IGA-003, Hiden Isochema Ltd., Manchester, UK). Detailed information on the apparatus and analyzing methods have been previously reported [28,29]. Water vapor uptake was measured in the Analyzer's Humidifier configuration, using similar methods at 25 • C. The samples were dried by circulating dry nitrogen until a constant weight was obtained. Vapor pressure was then controlled by circulating a mixture of dry nitrogen and vapor-saturated nitrogen to reach the required humidity. At a required humidity, the mass gain was measured as a function of time until reaching constant. More details have been reported in references [30,31].

FTIR Analysis
The FTIR spectra of bare and grafted silica are shown in Figure 2. The typical peaks for SiO 2 -H and SiO 2 -C were found at 1098 cm −1 for asymmetric stretching vibration and 800 cm −1 for symmetric stretching vibration of Si-O-Si. The vibration bands of OH groups are located at different frequencies, which depend on the bonding configuration. The broad band between 3800 cm −1 and 3050 cm −1 is attributed to the stretching of silanol associated with surface silanols, including isolated silanol, vicinal, and geminal groups [32]. The shoulder at 956 cm −1 indicates the existence of the Si-OH asymmetric stretching band [33]. Based on the comparison of the intensity of the characteristic peaks of Si-OH in Figure 2a,b, Figure 2 reviews that hydroxyl content on the surface of SiO 2 -H treated by hydrochloric acid and SiO 2 -C treated by calcined are a little different. The hydroxyl content was calculated in the scetion of thermogravimetry analysis.

Pore Structure Characteristics
The adsorption isotherm of N2 at −196 °C and CO2 at 0 °C were measured by an Autosorb-1-MP (Quantachrome, Florida, USA), an automatic surface area and pore size analyzer. The porous particles were dried and degassed at 100 °C under high vacuum for 5 h to remove moisture or other volatile contaminants. As for N2 adsorption, the relative pressure (P/P0) range was set between 0.001 and 0.995, and the CO2 adsorption isotherms were collected within the relative pressure (P/P0) range of 0.0001~0.03 for restricting pores narrower than 2 nm. A density functional theory (DFT) analysis was used to calculate the pore size distribution (PSD) and the pore structure parameters using Quantachrome ASiQwin software (Quantachrome, Florida, USA). based on the adsorption isotherms.

Adsorption Studies
Adsorption and diffusivity of water vapor were measured on an Intelligent Gravimetric Analyzer (IGA-003, Hiden Isochema Ltd., Manchester, UK). Detailed information on the apparatus and analyzing methods have been previously reported [28,29]. Water vapor uptake was measured in the Analyzer's Humidifier configuration, using similar methods at 25 °C. The samples were dried by circulating dry nitrogen until a constant weight was obtained. Vapor pressure was then controlled by circulating a mixture of dry nitrogen and vapor-saturated nitrogen to reach the required humidity. At a required humidity, the mass gain was measured as a function of time until reaching constant. More details have been reported in references [30,31].

FTIR Analysis
The FTIR spectra of bare and grafted silica are shown in Figure 2. The typical peaks for SiO2-H and SiO2-C were found at 1098 cm -1 for asymmetric stretching vibration and 800 cm -1 for symmetric stretching vibration of Si-O-Si. The vibration bands of OH groups are located at different frequencies, which depend on the bonding configuration. The broad band between 3800 cm -1 and 3050 cm -1 is attributed to the stretching of silanol associated with surface silanols, including isolated silanol, vicinal, and geminal groups [32]. The shoulder at 956 cm -1 indicates the existence of the Si-OH asymmetric stretching band [33]. Based on the comparison of the intensity of the characteristic peaks of Si-OH in Figure 2a,b, Figure 2 reviews that hydroxyl content on the surface of SiO2-H treated by hydrochloric acid and SiO2-C treated by calcined are a little different. The hydroxyl content was calculated in the scetion of thermogravimetry analysis. As shown in Figure 2, the infrared spectrum of Si-P 8 TFSI/SiO 2 -H(I) shows the appearance of the bands at 2924 cm −1 and 2856 cm −1 due to C-H aliphatic stretching vibration, and the peak at 1465 cm −1 belongs to P-C stretching vibration. Figure 2 appears to show that broad peak characteristic bands between 1024~1246 cm −1 , due to Si-O-Si and S=O, and the peak at 664 cm −1 belongs to S-C stretching vibration. The success of the neat phosphonium IL grafted onto the silica surface has been assessed based on the appearance of the characteristic bands for neat IL at 2926, 2855, 1466, and 1227~1060,663 cm −1 .

XPS Analysis
The XPS spectrum of SiO 2 -H, neat [Si-P 3888 ][TFSI], and Si-P 8 TFSI/ SiO 2 -H(I) is shown in Figure 3. The peaks of C 1s, O 1s, and Si 2p appear only in spectrum (a) of the bare silica. It can be seen from Figure 3b that a binding energy of 168.4 eV, 397.4 eV, and 688.9 eV is attributed to S 2p, N 1s, and F 1s for the neat IL, respectively, in [TFSI] anion [34]. In addition, there is a P 2p peak with a binding energy of 131.0 eV, which further proves the successful synthesis of the ionic liquid [Si-P 3888 ][TFSI]. Compared to spectrum (a), the C 1s peak in spectrum (c) is significantly enhanced, and two new peaks attributable to F 1s (binding energy 689.0 eV) and P 2p (binding energy 131.1 eV) appear in the XPS spectrum. This shows that the ionic liquid has been successfully immobilized on the surface of silica. belongs to P-C stretching vibration. Figure 2 appears to show that broad peak characteristic bands between 1024~1246 cm -1 , due to Si-O-Si and S=O, and the peak at 664 cm -1 belongs to S-C stretching vibration. The success of the neat phosphonium IL grafted onto the silica surface has been assessed based on the appearance of the characteristic bands for neat IL at 2926, 2855, 1466, and 1227~1060,663 cm −1 .

XPS Analysis
The XPS spectrum of SiO2-H, neat [Si-P3888][TFSI], and Si-P8TFSI/ SiO2-H(І) is shown in Figure 3. The peaks of C 1s, O 1s, and Si 2p appear only in spectrum (a) of the bare silica. It can be seen from Figure 3b that a binding energy of 168.4 eV, 397.4 eV, and 688.9 eV is attributed to S 2p, N 1s, and F 1s for the neat IL, respectively, in [TFSI] anion [34]. In addition, there is a P 2p peak with a binding energy of 131.0 eV, which further proves the successful synthesis of the ionic liquid [Si-P3888][TFSI]. Compared to spectrum (a), the C 1s peak in spectrum (c) is significantly enhanced, and two new peaks attributable to F 1s (binding energy 689.0 eV) and P 2p (binding energy 131.1 eV) appear in the XPS spectrum. This shows that the ionic liquid has been successfully immobilized on the surface of silica.    Silanol group content for silica and the total load of phosphonium ILs on the surface for modified samples determined by TGA techniques are listed in Table 1. The condensation of all kinds of silanol groups occurs by the reaction of two silanol groups on the silica surface, resulting in the release of one molecule of water and the formation of one siloxane group. It is assumed that no other groups  Silanol group content for silica and the total load of phosphonium ILs on the surface for modified samples determined by TGA techniques are listed in Table 1. The condensation of all kinds of silanol groups occurs by the reaction of two silanol groups on the silica surface, resulting in the release of one molecule of water and the formation of one siloxane group. It is assumed that no other groups than water were released from the sample. As shown in Table 1, for SiO 2 -H and SiO 2 -C, TGA shows that the hydroxyl content of SiO 2 -C is significantly higher than that of SiO 2 -H, which is probably because the H + in the hydrochloric acid activating solution destroys the hydroxyl groups on the surface of the silica gel [35]. Moreover, IL loading calculated for the Si-P 8 TFSI/SiO 2 -H(I), Si-P 8 TFSI/SiO 2 -H(II), and Si-P 8 TFSI/SiO 2 -C was 4.92 wt%, 10.62 wt%, and 10.79 wt%, respectively, whereby the ionic liquid loading depends on the limited number of active silanol groups on the supporter surface.

Pore size distribution
There is a certain correlation between pore structure and water adsorption. The use of both adsorbates, N 2 and CO 2 , provides complementary information about the porous texture of the samples. Isotherms measured with N 2 often lead to an underestimation of the microporosity due to the lower mobility of N 2 at −196 • C and whose diffusion in small size pores is inhibited. To access the microporosity, isotherms can be measured under CO 2 at 0 • C, since the CO 2 molecules are more mobile. Based on the N 2 and CO 2 adsorption isotherms at −196 • C and 0 • C, respectively, CO 2 adsorption capacity at 0 • C and the data to evaluate their surface areas and pore structures of the samples were obtained using the DFT method [36] in Table 2. The DFT model is based on the molecular statistical thermodynamics equation that calculates the specific adsorption amount in an individual pore of a given adsorbate-adsorbent system at a given experimental temperature and pressure by solving the function of the grand thermodynamic potential in terms of the distribution of gas density in a specific pore space. The cumulative pore volume (CPV) and cumulative surface area (CSA) of SiO 2 -C shown in Table 2 are considerably higher than those of SiO 2 -H, and the surface modified silica presents a significantly lower pore volume and specific surface area as compared to the bare silica, which leads to a decrease in the adsorption of CO 2 . On the basis of structural characteristics, silica impregnated with ILs results in the blockage of pores. Not surprisingly, Si-P 8 TFSI/SiO 2 -C prepared by grafting ILs on calcined supporter has a higher pore volume and specific surface area than Si-P 8 TFSI/SiO 2 -H(II).
The pore size distribution based on N 2 sorption isotherms at −196 • C and CO 2 sorption isotherms at 0 • C are shown in Figure 5. According to the pore size distribution (PSD) of the micropore in Figure 5b, the PSD of samples mainly concentrated in the range of 0.4-1.0 nm. The proportion of the micropores for Si-P 8 TFSI/SiO 2 -H(II) is lower than that of Si-P 8 TFSI/SiO 2 -H(I) and Si-P 8 TFSI/SiO 2 -C, which is mainly due to the clogging of a part of the pores after the introduction of the ionic liquid. Combined with IL loading obtained by TGA data, it is expected that the Si-P 8 TFSI/SiO 2 -H(II) with higher IL loading and less micropores should exhibit lower water adsorption capacity, which will be discussed later.
higher IL loading and less micropores should exhibit lower water adsorption capacity, which will be discussed later.

Water Vapor Adsorption
The mechanism of water adsorption on silica is very complex. It is known that the surface of silica contains silanol or siloxane groups. The Si-OH shows a specific interaction with water (hydrophilic), and it is a typical polar group and has some similar properties with water, so the hydrogen bonds were formed by the reaction of water and the hydroxyl group [37,38]. It is reasonable to think that water vapor adsorption, depending on the amount of the hydroxyl group on the silica surface and the adsorption capacity, increased with the hydroxyl content. Water vapor adsorption isotherms, corresponding to all samples, are illustrated in Figure 6. SiO2-H has better water resistance than SiO2-C. SiO2-H displays a lower quantity of the hydroxyl group, as demonstrated by the FTIR and TGA data. According to the pore structure parameters, SiO2-H also presents lower CSA and less micropores, which is unfavorable for the adsorption of water vapor.

Water Vapor Adsorption
The mechanism of water adsorption on silica is very complex. It is known that the surface of silica contains silanol or siloxane groups. The Si-OH shows a specific interaction with water (hydrophilic), and it is a typical polar group and has some similar properties with water, so the hydrogen bonds were formed by the reaction of water and the hydroxyl group [37,38]. It is reasonable to think that water vapor adsorption, depending on the amount of the hydroxyl group on the silica surface and the adsorption capacity, increased with the hydroxyl content. Water vapor adsorption isotherms, corresponding to all samples, are illustrated in Figure 6. SiO 2 -H has better water resistance than SiO 2 -C. SiO 2 -H displays a lower quantity of the hydroxyl group, as demonstrated by the FTIR and TGA data. According to the pore structure parameters, SiO 2 -H also presents lower CSA and less micropores, which is unfavorable for the adsorption of water vapor. The results in Figure 6 also indicate that water adsorption of silica modified by ionic liquid reduces significantly, and Si-P8TFSI/SiO2-H(II) with relatively higher IL content and a lower microporous structure shows better water resistance. Due to grafting the hydrophobic ionic liquid onto the silica gel, there is an ionic liquid film formed by reacting with the silanol groups on the silica surface, and the schematic is shown in Figure 7. According to the previous PSD data, the CPV, especially of the micropores, and CSA of Si-P8TFSI/SiO2-H(II) are lower, resulting in a slight decrease in water adsorption capacity.
The pore structure parameters and surface property show a correlation with water vapor The results in Figure 6 also indicate that water adsorption of silica modified by ionic liquid reduces significantly, and Si-P 8 TFSI/SiO 2 -H(II) with relatively higher IL content and a lower microporous structure shows better water resistance. Due to grafting the hydrophobic ionic liquid onto the silica gel, there is an ionic liquid film formed by reacting with the silanol groups on the silica surface, and the schematic is shown in Figure 7. According to the previous PSD data, the CPV, especially of the micropores, and CSA of Si-P 8 TFSI/SiO 2 -H(II) are lower, resulting in a slight decrease in water adsorption capacity. will be coadsorbed with CO2 at the high relative humidities than can be expected in post-combustion applications.

Water Diffusion Coefficient
The diffusion coefficient calculation presented a great significance toward the evaluation of the industrial application value of the adsorbent. The diffusion in porous solids is more complicated than in liquids. For bare silica and silica-phosphonium ionic liquid hybrid material prepared with the grafting method, the particle is considered as a uniform adsorbent. Diffusion of water vapor into a porous spherical particle can be described by Equation (3) [39].  The pore structure parameters and surface property show a correlation with water vapor sorption capacity, suggesting that porosity and the IL film play an important role in reducing a small amount of water vaporin adsorption of the power plant flue gas for the bare and modified SiO 2 , thereby resulting in decreased CO 2 adsorption capacity. The maximum adsorption capacity of water vapor on silica-phosphonium ionic liquid hybrid material is lower than that for bare silica, with a higher pore volume and quantity of the hydroxyl group, which is advantageous, as less water vapor will be coadsorbed with CO 2 at the high relative humidities than can be expected in post-combustion applications.

Water Diffusion Coefficient
The diffusion coefficient calculation presented a great significance toward the evaluation of the industrial application value of the adsorbent. The diffusion in porous solids is more complicated than in liquids. For bare silica and silica-phosphonium ionic liquid hybrid material prepared with the grafting method, the particle is considered as a uniform adsorbent. Diffusion of water vapor into a porous spherical particle can be described by Equation (3) [39].
where D e is the effective porous diffusion coefficient (m 2 /s), ε is the material porosity, q is the adsorbate concentration in the solid phase (wt%), C is the adsorbate concentration in the gas phase (wt%), R is the particle of radius (m), and t is the adsorption time(s). Initial conditions (IC) and boundary conditions (BC): The solution of the equation is given by Equation (6) [40]. where D ap is the apparent diffusion coefficient, q is the quantity adsorbed at time t, and K is the slope of adsorption isotherm. A simplified equation for the diffusion is given by Equation (8): where A is the particle surface area (m 2 ) and V is the particle volume (m 3 ). In case of spherical particles: From equation (8) it can be obtained that: where S is the slope of the curve m/m ∞ versus t 0.5 . Further, from Equation (9), D ap can be obtained as: Finally, the effective diffusion coefficient (D e ) can be calculated with the relationship: where, V p is the pore volume and ρ si is the apparent density. Examples of the experimental data and fitting curves for SiO 2 -H, SiO 2 -C, and Si-P 8 TFSI/SiO 2 -H(I) at different pressures and at 25 • C are illustrated in Figure 8. A good agreement between the experimental values and the fitting curves was obtained.
Diffusion coefficients obtained from the curve fitting are listed in Table 3. It can be obtained from Table 3 that the calculated effect diffusion coefficients of silica gel are at a level of 10 −7 and these values are close to reports on silica [41][42][43]. Comparing two kinds of bare silica, the diffusion coefficient of SiO 2 -C is lower than that of SiO 2 -H. The reason may be that the diffusion resistance of water vapor is increased by an excessive amount of water adsorbed by SiO 2 -C with a higher hydroxyl group, CPV, and CSA. Moreover, diffusion coefficients in Si-P 8 TFSI/SiO 2 -H(I) are about 10 −8~1 0 −7 m 2 /s and slightly lower than those of SiO 2 -H, which implies that the thin IL coating on the silica surface and a loss of micro-porosity impedes water diffusion. Figure 9 shows the relationship between water vapor uptake and D e . Effective diffusion coefficients of all the samples show a decreasing trend with the increase of water vapor adsorption, which, due to the porosity available for water vapor transport, decreases at higher loading as adsorbed water vapor occupies a part of porous sites. Diffusion coefficients obtained from the curve fitting are listed in Table 3. It can be obtained from Table 3 that the calculated effect diffusion coefficients of silica gel are at a level of 10 -7 and these values are close to reports on silica [41][42][43]. Comparing two kinds of bare silica, the diffusion coefficient of SiO2-C is lower than that of SiO2-H. The reason may be that the diffusion resistance of water vapor is increased by an excessive amount of water adsorbed by SiO2-C with a higher hydroxyl group, CPV, and CSA. Moreover, diffusion coefficients in Si-P8TFSI/SiO2-H(I) are about 10 -8~1 0 -7 m 2 /s and slightly lower than those of SiO2-H, which implies that the thin IL coating on the silica surface and a loss of micro-porosity impedes water diffusion.    1.38 2.13 1.84 Figure 9 shows the relationship between water vapor uptake and De. Effective diffusion coefficients of all the samples show a decreasing trend with the increase of water vapor adsorption, which, due to the porosity available for water vapor transport, decreases at higher loading as adsorbed water vapor occupies a part of porous sites.

Conclusions
Phosphonium-based ILs were successfully immobilized on bare silica pretreated by hydrochloric acid or calcination. Adsorption and diffusion of water vapor on bare and modified silica were investigated. It can be seen from the analyses of FTIR, TG, and PSD that SiO2-H has less hydroxyl groups and micropore volumes, which is unfavorable for the adsorption of water vapor, thus it has better water resistance. After the grafting of ILs on silica, the sorbents form a hydrophobic film on the surface to block the entry of water molecules and retain partial pore characteristics of the support. Therefore, Si-P8TFSI/SiO2-H(II), with relatively higher IL loading and lower micropore, increases the water-resistance performance. Fitting the model with experimental data is beneficial and suggests that the effective diffusion coefficients of bare silica are at a level of 10 -7 , while SiO2-H, with relatively rapid diffusion, as lower content of water vapor is benefit for diffusivity. The diffusion of immobilized ionic liquids on silica did not change much and most of the values under different water vapor pressure were also at a level of 10 -7 , while a slight reduction of the diffusivity was observed due to the partial impairing of the pore structure and the forming of a hydrophobic ionic liquid film on the surface. Furthermore, with the increase of water vapor loading, effective diffusion coefficients give a decreasing trend.

Conclusions
Phosphonium-based ILs were successfully immobilized on bare silica pretreated by hydrochloric acid or calcination. Adsorption and diffusion of water vapor on bare and modified silica were investigated. It can be seen from the analyses of FTIR, TG, and PSD that SiO 2 -H has less hydroxyl groups and micropore volumes, which is unfavorable for the adsorption of water vapor, thus it has better water resistance. After the grafting of ILs on silica, the sorbents form a hydrophobic film on the surface to block the entry of water molecules and retain partial pore characteristics of the support. Therefore, Si-P 8 TFSI/SiO 2 -H(II), with relatively higher IL loading and lower micropore, increases the water-resistance performance. Fitting the model with experimental data is beneficial and suggests that the effective diffusion coefficients of bare silica are at a level of 10 −7 , while SiO 2 -H, with relatively rapid diffusion, as lower content of water vapor is benefit for diffusivity. The diffusion of immobilized ionic liquids on silica did not change much and most of the values under different water vapor pressure were also at a level of 10 −7 , while a slight reduction of the diffusivity was observed due to the partial impairing of the pore structure and the forming of a hydrophobic ionic liquid film on the surface. Furthermore, with the increase of water vapor loading, effective diffusion coefficients give a decreasing trend.
Author Contributions: C.L. and J.Z. conceived the research topic and wrote the manuscript. C.L. and X.H. designed and carried out the experiments. M.Z. and S.Z. participated to discuss and analyze the data.