Kinetics of Cluster-Mediated Filling of Water Molecules into Carbon

(3) Thus, site adsorption of water molecules occurs at the edge of the slit-shaped ..... carbon, it is necessary to apply models that are associated w...
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Kinetics of Cluster-Mediated Filling of Water Molecules into Carbon Micropores Hiromitsu Ito,† Taku Iiyama,*,‡,§ and Sumio Ozeki‡ †

Interdisciplinary Graduate School of Science and Technology, Department of Material Science and Engineering and ‡Department of Chemistry, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan § Center for Energy and Environmental Science, Shinshu University, 4-17-1 Wakasato, Nagano, Nagano 380-8553, Japan S Supporting Information *

ABSTRACT: Understanding the kinetics of water adsorption/ desorption on activated carbon is significant for chemical applications in which competitive adsorption of water occurs. In this study, we investigated the water adsorption process by determining the adsorption rate constant using the novel pressure feedback method (PFM), which measures the rate of adsorption directly with high precision (∼10 nmol s−1) by controlling the introducing and outgassing flow rates. The PFM was used to investigate water vapor adsorption kinetics on activated carbon fibers (ACFs) of different pore sizes and to obtain a correlation of rate constant with pore size. The systems show good agreement with the stretched exponential model. The adsorption rate constants were found to be lower for ACFs with a larger pore width (average pore width; w = 1.03 nm) as compared with those for smaller pore systems (w = 0.57, 0.72 nm).

1. INTRODUCTION Microporous activated carbon is a very powerful adsorbent for gas storage, gas separation, electric double-layer capacitors,1 and so on. In chemical applications of activated carbon, such as gas separation, adsorption of the target is frequently obstructed by multicomponent adsorption of water. This significant problem must be resolved when applying microporous activated carbon for gas separation and removal of volatile organic compounds (VOCs). In-depth understanding of water vapor adsorption on carbon micropores, from both equilibrium and kinetics aspects, is required to improve the efficiency of such applications. Moreover, water vapor adsorption on microporous activated carbon is of great interest from a scientific viewpoint, with relevance to the nature of water in hydrophobic small spaces due to the formation of cluster-like water molecular assemblies and hydrogen-bonding networks. Water vapor adsorption processes on activated carbon can be broadly divided into two stages: the initial adsorption on activated sites including surface functional groups and structural defects, followed by micropore filling through intermolecular interactions. The site adsorption process occurs at P/P0 < 0.4 and has its origin in the electrostatic interactions between the dipole moments of water molecules and surface functional groups. Most of the functional groups exist on the edges of the basal planes of the graphitic units,2 and various oxygen- and nitrogen-containing functional groups are distributed.3 Thus, site adsorption of water molecules occurs at the edge of the slitshaped pores, and the adsorbed water molecules have various © XXXX American Chemical Society

energy states depending on the surface sites. Contributions of several investigators2,4−7 have led to the conclusion that pore filling is associated with the formation of cluster-like water molecular assemblies. The cluster formation mechanism was proposed by Dubinin and Serpinsky to explain the steep uptakes of water in the adsorption isotherm.8 Cluster formation has been investigated by Iiyama and Kaneko through smallangle X-ray scattering (SAXS) and semiempirical determination (reverse Monte Carlo; RMC) of the water intermolecular structure using large-angle X-ray diffractometry.5−7 These results revealed that the size of the water assembly is dependent on the amount adsorbed and the average pore size of activated carbon. Through grand canonical Monte Carlo (GCMC) simulations, Gubbins et al. concluded that the primary process is the adsorption of water molecules on activated sites and that additional adsorption occurs on the initially adsorbed water molecules, which act as nucleation sites with the formation of 3D clusters.4 The unique nature of adsorption of water molecules on activated carbon would likely affect the kinetics of water vapor adsorption as well. The kinetics of adsorption of water on porous carbon is unique, as opposed to the case of other adsorbates such as supercritical fluids. The adsorption kinetics of supercritical gases (such as nitrogen, oxygen, and argon) on porous carbon Received: November 26, 2014 Revised: January 29, 2015

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low flow rate (1 to 2 mL min−1), and the water vapor pressure in the sample cell is measured by a pressure gauge. The signal from the pressure gauge is passed to a high-speed feedback circuit, and the open degree of CV is determined in the downstream so that the pressure of the system remains constant. Thus, the introducing and outgassing water vapor flow rates are controlled with MFC, CV, and MFM to attain a constant system pressure. Time integration of the subtraction of upstream and downstream flow rates was performed, corresponding to the mass change of water in the sample cell. Therefore, along with the blank data, it was possible to calculate the amount adsorbed at each equilibrium pressure. A comparison of water adsorption isotherms by PFM and volumetric method is shown in Figure S1 in the Supporting Information. In this experiment, the ACFs were pretreated at 398 K and P < 1.0 × 10−3 Pa for 3 h; then, the changes in upstream and downstream flow rates were measured in the range 0.599−3.13 kPa at 298 K. The saturated vapor pressure was calculated by the Antoine equation20

follow the linear driving force (LDF) model.3,9−16 This model has a single rate-determining step, with a distribution of relaxation time that is associated with the passing-through process of the molecule at the pore entrance.17 However, the adsorption kinetics of water vapor can be better explained by the stretched exponential (SE) model or the double exponential (DE) model.3 The primary process of site adsorption is expected to be of significance in the elucidation of water vapor adsorption kinetics. Thomas et al. have investigated the effect of surface functional groups on the kinetics of water vapor adsorption and indicated that site−site hopping of water molecules is the rate-determining step in the primary adsorption region.3 They have also suggested that associative adsorption (adsorption of additional water molecules onto the initially adsorbed molecules) probably occurs at surface functional groups in the pore-filling process. Do et al. have proposed an alternative mechanism and established the water vapor adsorption isotherm equation for the pore filling process. In this model, initial adsorption of water molecules occurs around surface functional groups located at the edge of the basal planes of graphitic units. These form clusters around the functional groups; the clusters are partially withdrawn into slit-shaped pores.2 Molecular dynamics (MD) simulations carried out by Bhatia et al. also indicated that the adsorbed water diffuses into carbon micropores not only as single molecules but also as molecular clusters.18 Thus, it is evident that understanding the formation of water molecular clusters is necessary for elucidating the kinetics of water vapor adsorption. In this study, we investigate the water adsorption process by determining the adsorption rate constant through a novel technique, the pressure feedback method (PFM). In this method, the rate of adsorption is directly measured by an electrical feedback circuit and two different flow rate controllers. Hence, precise determination of the dependence of adsorption rate constant on the amount adsorbed becomes possible. The obtained rate constant changes with water adsorption can be compared with the changes in size of the water molecular assembly determined by SAXS measurements in previous reports. The adsorption kinetics of water vapor on activated carbon fibers (ACFs) with different pore sizes were investigated to obtain a correlation between the rate constant and the pore size and to correlate the size of water molecular assemblies and the ACF pore size.

log P0 = A −

B T+C

(1)

where P0 is the saturated vapor pressure (bar) and T is the measurement temperature (K). A, B, and C are constants for water vapor, where A = 5.40221, B = 1838.675, and C = −31.737 in the range 273−303 K.21 2.1. Theory and Method. In PFM analysis, the method of determination of the adsorption rate and the amount adsorbed is considerably different from volumetric analysis, gravimetric analysis, and other flow methods. In gravimetric analysis, the adsorption rate is determined by the differential of time dependence of amount adsorbed, measured by a microbalance. While this method yields high accuracy in measurement of amount adsorbed, the resolution is low (∼0.1 μg), which is a disadvantage for the determination of adsorption rate. Furthermore, the porous sample must be separated from the heat capacitor for the measurement of mass change, causing an increase in sample temperature due to adsorption heat. In the volumetric method, while the resolution is dependent on the volume of the sample chamber, it is high (∼nmol) compared with the gravimetric method, and the thermal contact of the sample with the heat capacitor is good. However, the volumetric method cannot measure the change of amount adsorbed at constant pressure because the pressure change due to the adsorption in the hermetically closed sample chamber must be measured. The change of system pressure becomes large when a small volume sample chamber is used for highresolution measurement. In the PFM, the adsorption rate can be directly measured with high precision from the introducing and outgassing flow rates, while the sample maintains thermal contact with the heat capacitor. Furthermore, the target adsorptive flows through the introducing and outgassing flow controller without a carrier gas. Figure 1 shows an example of change in introducing and outgassing flow rates and pressure as a function of time for water vapor adsorption on ACF. In Figure 1 the profile of measurement of adsorption rate at pressure changing from 1.20 to 1.34 kPa at 298 K is shown. Time 0 in the horizontal axis indicates the starting point of the change in settle pressure. The introducing flow rate is kept constant by the MFC, and outgassing flow rate is controlled by the CV so that the system pressure is constant at the settle value (in this case, P = 1.34 kPa.). In this case, the system pressure increased to the settle

2. EXPERIMENTAL SECTION Pitch-based ACFs A7, A10, and A20 (Ad’all) were used as adsorbents for nitrogen and water vapor in all experiments. Nitrogen adsorption measurements were carried out on a BELLSORP-MAX (BEL Japan), equipped with rotary and turbomolecular vacuum pumps. Pure nitrogen (99.9998 vol %) and helium (99.9995 vol %) (Taiyo Nippon Sanso) gases were used as adsorbate and for excluded volume measurements, respectively. Following pretreatment at 398 K and 60s. Therefore, the adsorption rate can be obtained simply and directly from the relation Figure 1. Example of measurement of rate of water adsorption on A10 at 298 K, 1.34 kPa. (a) Water vapor pressure in the sample chamber. (b) Introducing and outgassing flow rates. (c) Time differential amount of water in the sample chamber.

dnads P° intro = (f − f iout ) dt RT ° i

Thus, the PFM can directly measure the adsorption rate at constant temperature and gas pressure, with significantly low noise. Additionally, this technique employs a metal sample cell and does not require a microbalance, making the application of PFM feasible for in situ adsorption measurements such as FTIR, UV−vis, and X-ray analysis. This is a major improvement over conventional kinetics measurement techniques, and PFM can provide the correlation between time change in adsorption rate and molecular dimension information such as the size of water clusters, the number of hydrogen bonds around the adsorbed molecules, and so on.

pressure, showed a little overshoot, and then reached settle pressure again within 30 s. The outgassing rate was lower than the introducing rate at 30 s because the water vapor was adsorbed by the sample. After 30 s past, outgassing flow rate changed gradually over a few thousand seconds. This change is associated with water vapor adsorption on ACF. As seen in Figure 2, when the system achieves adsorption equilibrium, the introducing and outgassing flow rates are equal.

3. RESULTS AND DISCUSSION 3.1. Characterization of ACF. For the characterization of ACF samples, nitrogen adsorption isotherms were measured (Figure 3). The isotherms belonged to Type I of the IUPAC classification, and from their shape, it was concluded that A7 and A10 had similar pore character, while A20 showed large pore volume and wide pore size distribution (PSD). The PSD of these samples was determined by the Horvath− Kawazoe (HK) method22 (Figure 4). A7 and A10 showed similar PSD, although the pore volume of A10 in the region 0.5 to 1 nm is slightly higher. The A20 sample showed a significantly larger pore volume in the region of 1 to 2 nm. The results of characterization of the ACFs including atotal (αs23 total specific surface area), apore (pore specific surface area, atotal − aexternal), aexternal (external specific surface area determined by αs plot), ναs(micropore volume determined by αs plot), and νDR (micropore volume determined by Dubinin−Radushkevich (DR)24 plot) are shown in Table 1. The average pore width, w̅ , which was calculated from the apore and ναs, is also shown.

Figure 2. Measurement data of introducing flow rate and outgassing flow rate on A10 at 298 K, 1.34 kPa as a function of time with PFM.

The change of total amount of water Δni in a measurement point can be determined by the time integration of the subtraction between introducing and outgassing flow rates, f intro i and f out i . Δni =

P° RT °

∫t

ti + 1 i

(f iintro − f iout ) dt

(7)

(2) C

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dM t = Me{k1A exp[− k1t ] + k 2(1 − A) exp[− k 2t ]} dt (8)

ads

where r is the rate of adsorption as a function of time, Mt is the amount adsorbed at time t, Me is the equilibrium amount adsorbed in a measurement point, A is the fractional contribution, and k1 and k2 are the rate constants. The DE model represents the relaxation process with two ratedetermining steps corresponding to the rate constants k1 and k2. The time differentiated SE model is described by following equation r ads(t ) = Figure 3. Nitrogen adsorption isotherms of A7, A10, and A20 at liquid nitrogen temperature.

Table 1. Results of Pore and Surface Characterization atotal/ m2 g−1

apore/ m2 g−1

aexternal/ m2 g−1

ναs/ cm3 g−1

A7 A10 A20

1020 1210 1770

1006 1190 1750

14 20 20

0.28 0.43 0.90

w̅ /nm 0.57 0.72 1.03

(9)

where β is the exponential factor. In the SE model, β corresponds to a distribution of the relaxation time due to the Fickian diffusion of PSD structure, surface transient, and pore through diffusions. From the results of fitting with DE and SE models (Figure 5a,b), it is seen that both of the models exactly reproduced the rate of adsorption as a function of time. According to Thomas et al., it is difficult to distinguish the most suitable kinetics model for water vapor adsorption on activated carbon.3 However, taking into account the distribution of relaxation time and applying the criteria of least fitting parameter, the SE model is more suitable than the DE model from the physical and mathematical point of view. 3.3. Water Vapor Adsorption on ACF. Adsorption and desorption isotherms of water vapor on A7, A10, and A20 at 298 K are shown in Figure 6. All isotherms belonged to Type V in the IUPAC classification. The desorption branches (A7 and A20) are almost agreeing with adsorption branches at low relative pressure, but in the A20 case it is slightly smaller than adsorption branches by accumulated error. At low amounts of adsorbed water vapor the isotherms were proportional to pressure, and this association with Henry’s law suggests that the adsorbed water molecules can move freely along the surface of the ACF.3 The adsorption isotherms of A7 and A10 were similar in the region of 0 to 0.5 of relative pressure; however, the saturated amount adsorbed by A10 was higher than that of A7 due to the difference in the total pore volume. The pressure corresponding to the end of steep water uptake and the saturated amount adsorbed increased from A7 to A20. From the results of Iiyama et al. and Do et al., it is evident that the formation of cluster-like water molecular assemblies occurs in the steep water uptake region.2,27 Do’s results also indicate that the pressure of steep water uptake increases with the size of the water molecular assemblies.2 3.4. Rate Constants and Other Kinetic Parameters. Figure 7 shows the rate constants and the amount adsorbed at 298 K as a function of pressure. In all cases, the rate constants initially decreased with increasing water vapor pressure, reached a minimum at the region where steep water uptake occurred, and then increased with increasing pressure. The rate constants corresponding to the steep water uptake region were lower than those of the other regions by an order of magnitude of 1, 2, and 3 for A7, A10, and A20, respectively. This significant decrease in the rate constant suggests that the rate-determining steps corresponding to steep water uptake are associated with a different kinetic process than that of the initial and saturated water uptake region.

Figure 4. Pore-size distributions of A7, A10, and A20 calculated by HK method from nitrogen adsorption isotherms.

ACF

dM t = Mek ββt β − 1 exp[−(kt )β ] dt

νDR/ cm3 g−1 0.28 0.41 0.63

3.2. Determination of Adsorption Rate Constant. For the investigation of water vapor adsorption on ACFs, it is necessary to ensure the validity of the adsorption kinetics models. The LDF model3 is the most commonly used adsorption kinetics model for the determination of rate constants. However, for the investigation of adsorption of gas or vapor on activated carbon, it is necessary to apply models that are associated with Fickian diffusion (such as the nested LDF model) due to PSD and pore surface heterogeneity, including surface functional groups of activated carbon. Three nested LDF models, the double stretched exponential model (DSE), the double exponential model (DE), and the SE model,3,17,25,26 have been proposed. We applied the DE and SE models for water vapor−carbon adsorption system due to the reproducibility of the change in adsorption rate as a function of time, and their time differentiated forms were applied to the fitting. The time-differentiated DE model is described by following equation D

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Figure 5. Fitting results of the rate of water vapor adsorption on A10 at 298 K, 1.34 kPa: (a) SE model and (b) DE model.

pores.17 Intermediate cases are described by the SE model or the combined barrier resistance/Fickian diffusion model. In Figure 8, the variation of exponential factor β as a function of fractional fillings ϕ is shown. The state of water in the region of ϕ < 0.15 corresponds to the adsorption on the activated sites such as functional groups and defects in the activated carbon. In this region, β increased from 0.5 to 0.7 with increasing fractional filling, except in the initial stage of A20. The variation of β value corresponds to the result of Thomas;3 therefore, the rate-determining step is associated with the site−site hopping of water molecules. In the region of 0.15 < ϕ < 0.85, β was almost constant in the range 0.7 ∓ 0.07, and this corresponds to the formation of cluster like assemblies of water molecules. Finally, in the region of 0.85 < ϕ, β showed a decrease and then increased up to ∼1, which corresponds to the filling up of the micropores and adsorption on the external surface. Thomas et al. suggested that β = 0.5 implies the occurrence of 1D relaxation, and β = 1 (LDF) indicates diffusion through the 3D pore structure. Therefore, the value β = 0.7 indicated an approximately 2D pore structure, with a distribution of relaxation time. The fact that β remains fairly constant in the steep uptake region suggests that the rate-determining step is the same during filling of the micropores by water. From these considerations, it appears that the rate-determining step is associated with a 2D process such as diffusion of water molecules in the molecular assemblies or diffusion of the molecular assemblies themselves. For confirmation, it is necessary to investigate the relationship between water molecular assemblies and kinetic parameters. 3.5. Dependence of Rate Constants on Pore Size. Figure 9 shows rate constants of A7, A10, and A20 as a function of fractional fillings ϕ at 298 K. At low fractional fillings the rate constants decreased and reached a minimum in the region of 0.3 0.9 the rate constants increased rapidly. While the variation of rate constants in the case of A7 was similar to that of A10, the A20 samples showed significantly lower rate constants at all regions of fractional fillings. The PSD

Figure 6. Water vapor adsorption isotherms at 298 K on A7, A10, and A20 obtained by the PFM.

Thomas et al.3 have proposed that a water molecule hopping among functional groups is the rate-determining step in the initial adsorption stage and showed that the rate constant displays a negative linear correlation with the concentration of oxygen functional groups and total acidity. They also suggested that the decrease in rate constants with increase in relative pressure in steep uptake region is related to the associative adsorption of water molecules on adsorbed water with the formation of hydrogen bonds, as there is no negative linear correlation with the concentration of oxygen functional groups and total acidity. Many adsorption processes are considered candidates for the rate-determining step: for example, surface transition diffusion, site−site hopping, and passing through pore entrance. Furthermore, in the case of water vapor adsorption system, a diffusion of cluster like molecular assemblies18 and their passing through the pore entrance2 are also considered. The LDF model can describe the relaxation of amount adsorbed when the diffusion through the barriers at pore entrances is the rate-determining step, and Fickian diffusion occurs when kinetics are controlled by diffusion along the E

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Figure 9. Rate constants of A7, A10, and A20 as a function of fractional fillings at 298 K.

This suggests that the rate constants for water vapor adsorption on ACF decreased with increase in pore size of the ACF. This also indicates a correlation between the rate constants and size of the water molecular assemblies. Previous results5 indicate that the size of the cluster-like water molecular assemblies depends on the pore size and fractional fillings. Molecular assemblies become larger in ACF with wider pores, and increase in fractional fillings also results in an increase in the size of molecular assemblies. This variation of the molecular assembly size corresponds well to the observed rate constants. Most of the kinetic processes in porous materials can be divided into two stages: gas diffusion processes and processes to form the adsorbed phase. If the rate-determining step of water vapor adsorption on ACF is associated with gas diffusion, the relaxation of adsorption rate follows a diffusion equation such as Fickian diffusion including molecular diffusion and Knudsen diffusion. The contribution of molecular (Dm) or Knudsen (DK) diffusivity to Fickian diffusivity (D) is associated with the mean free path of water vapor and ACF pore size. The mean free path of water vapor, employing ideal gas approximation, is as follows Figure 7. Rate constants (closed circle) and amount adsorbed (open triangle) at 298 K as a function of pressure, obtained by PFM from isothermal measurements on (a) A7, (b) A10, and (c) A20.

l=

RT 2 NAσP 1/2

(10)

Here l is the mean free path, NA is Avogadro’s number, σ is the collision cross section (0.234 nm2), and P is the vapor pressure. At the pressure range of 0.6−2.9 kPa in this experiment, the mean free path of water vapor is 2.07 × 104 to 4.24 × 103 nm, which is considerably larger than the pore size of the ACF samples (0.57 to 1.03 nm). In this case, Knudsen diffusion becomes the dominant transport mechanism and total diffusivity is nearly equal to Knudsen diffusivity. Knudsen diffusivity is proportional to the mean pore radius and hence becomes large in the case of larger pores. However, in our results, this tendency is not observed in the rate constant in the range of fractional fillings 0.1 to 0.9. The rate constants in the range of fractional fillings 0 to 0.1, which are kinetically associated with site−site water molecular hopping, are almost of the same order in three samples, implying that the small pore size cannot be the rate-determining step. Hence, the ratedetermining step in the range of fractional filling 0.1 to 0.9 is expected to be associated with the formation of the adsorbed phase.

Figure 8. Exponential factor β for A7, A10, and A20 as a function of fractional fillings at 298 K.

of A7 was similar to that of A10, while A20 had a wider distribution up to ∼2.5 nm (Figure 4). F

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ACKNOWLEDGMENTS This research was supported by JSPS Grants-in-Aid for Scientific Research Number 24550017 and the Cooperative Research Program of “Network Joint Research Center for Materials and Devices”

The rate-determining step in the formation of adsorbed phase can be considered as the formation of cluster like water molecular assemblies. Our previous results have shown that the number of small size clusters (five to six water molecules) increases with increasing pressure for smaller pore ACF such as A7 and A10 and that larger clusters grow with increasing pressure for larger pore ACF such as A20. This results in a significant difference in the adsorption kinetics. Analysis of the results of our kinetics experiments reveal that the rate constants for A7 and A10 (which have comparable PSD), which are dominated by the increase in number of small clusters, are higher than those for A20, which is dominated by the growth of the cluster. Therefore, the large difference in rate constants of the three samples is associated with the difference in mode of adsorption of water vapor on ACF. With regard to detailing the rate-determining step in region 0.1 < ϕ < 0.9, it is difficult to distinguish whether the ratedetermining step is associated with the diffusive process or adsorption phase growth. However, our results strongly suggest that the rate constants depend on pore size and that the ratedetermining steps are associated with the process corresponding to the formation of water molecular assemblies.

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ASSOCIATED CONTENT

S Supporting Information *

Comparison of water adsorption isotherms by PFM and volumetric method of A7 at 298 K. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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4. CONCLUSIONS We investigated the kinetics of water adsorption on ACF by a newly developed adsorption apparatus (PFM). PFM can measure the amount adsorbed by time integration of the difference between the introducing and outgassing flow rates and can also determine the adsorption rate constant directly. Therefore, this method can be a considerably useful tool in adsorption kinetics investigations. The accuracy of the measurement of rate of adsorption was confirmed by the good fit with the SE model. In the investigation of water−ACF systems, the variation of rate constants with fractional fillings revealed a dependence on the pore size. ACFs with wider pores display a significantly slower adsorption process than narrower pore systems. This indicated that the rate constants vary with the size of molecular assemblies formed in ACF pores. Although it remains difficult to distinguish whether rate-determining step is associated with diffusive process or adsorption phase growth, our results strongly suggest that the rate constants depend on pore size and that the rate-determining steps is associated with the process corresponding to the formation of water molecular assemblies. Efforts are in progress to achieve the simultaneous measurement of adsorbed rate constant and structure of adsorbed molecular assemblies.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. G

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