Adsorption and Desorption of Water in Two-Dimensional Hexagonal

Article pubs.acs.org/JPCC

Adsorption and Desorption of Water in Two-Dimensional Hexagonal Mesoporous Silica with Different Pore Dimensions Junho Hwang,*,†,‡ Sho Kataoka,‡,§ Akira Endo,‡,§ and Hirofumi Daiguji†,‡ †

Department of Mechanical Engineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ‡ CREST, Japan Science and Technology Agency (JST), 7 Gobancho, Chiyoda-ku, Tokyo 102-0076, Japan § National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5-2, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan S Supporting Information *

ABSTRACT: We have investigated the adsorption and desorption of water in twodimensional hexagonal mesoporous silica (MPS) with three different pore dimensions. All the adsorption−desorption isotherms exhibited type V behavior with significant hysteresis. Hysteresis was observed in the transient region between the layer adsorption state and the pore filling state, where capillary condensation and evaporation occurred. When the relative humidity is changed in steps from the onset point of capillary condensation and capillary evaporation, the relaxation curves of water uptake and release were measured at 298 K using a gravimetric method. For all MPSs, the relaxation rates of water uptake and release increased as the magnitude of the stepwise change in relative humidity increased. The relaxation curves of some MPSs could be well fitted by the exact solution of the Fickian diffusion equation at a small stepwise change in relative humidity. On the other hand, the adsorbed mass is proportional to the square root of time at large stepwise changes in relative humidity. The relationship between the mass flux of water uptake or release and the difference in chemical potential between the initial and final states of moist gases depends on the structural properties of the mesopores. Our earlier experimental21 and theoretical22 studies of water uptake and release in mesoporous silica (MPS) showed that when the relative humidity is changed in small steps from the onset of capillary condensation, the relaxation curve can be fitted by an exponential function. This relaxation curve suggests that water transport is diffusive. In contrast, when the relative humidity is changed in large steps from the onset of capillary condensation, the relaxation curve can be fitted by a square root function, suggesting that water transport is advective. However, the kinetics of water uptake and release in nanopores is not yet fully understood. The relaxation curves of water adsorption and desorption in porous materials depend on the structural properties of porous materials and the kinetic properties of water in nanopores. In order to understand the kinetics of water uptake and release in nanopores, porous materials with a well-ordered pore structure must be synthesized and characterized. For porous materials with a 2D hexagonal pore structure, the pore diameter, pore length, and interpore distance must be determined. Even if the pore structures are well characterized, the kinetics of water uptake and release must still be determined.

1. INTRODUCTION Understanding and controlling liquid transport in the nanoscale environment of permeable porous materials play a crucial role in state-of-the-art technologies such as adsorption, nanofiltration, and nanofluidics.1−3 The liquid transport mechanism in nanosized porous materials has been extensively investigated through theoretical4−12 and experimental13−17 studies. These studies have shown that the macroscopic concept of capillaryinduced liquid transport is still valid on the nanometer-length scale. Hence, liquid uptake in nanopores can be spontaneously driven by capillary action on the surface of nanopores. Capillarity-induced liquid transport can be described by the classical Lucas−Washburn law, in which capillary forces and the viscous drag force work on advancing the liquid simultaneously. Thus, mass uptake is proportional to the square root of time, provided the stationary water layers form on the inner surface of pores.18 The spontaneous imbibition of liquid into nanopores has been thoroughly investigated for the system in which one end of the porous material is in contact with a liquid bath. If porous materials are exposed to a vapor phase, vapor molecules will adsorb on the inner surface of the pores at low relative humidity. At high relative humidity, vapor molecules will condense at the entrance of the pores, and then the condensed liquid will migrate into the pores. This process is known as capillary condensation and leads to a large uptake of liquid.19,20 © 2015 American Chemical Society

Received: September 2, 2015 Revised: October 27, 2015 Published: October 28, 2015 26171

DOI: 10.1021/acs.jpcc.5b08564 J. Phys. Chem. C 2015, 119, 26171−26182

Article

The Journal of Physical Chemistry C

Merck Millipore, Germany), hydrochloric acid (HCl) (Wako Pure Chemistry Industries, Ltd., Japan), and DMF were stirred at 333 K for 1 h in a capped vial. After stirring, the PS-P4VP and TEOS solutions were mixed and then stirred at room temperature for 0.5 h. The final TEOS/DMF/H2O/HCl/PSP4VP molar ratio of the resulting solution was 1.2:63:22:0.0010:0.0054. The resulting solution was then precipitated at room temperature for a couple of days. Precipitates (siloxane/polymer complexes) were collected using filtration processes. The precipitates were calcined at 823 K for 5 h in air at a slow ramping rate (∼2 K min−1) to remove the polymers. MPS 2, which is well-known as SBA-15, was produced by the simple synthesis route proposed by Sayari et al.31 The triblock copolymer, poly(ethylene glycol)-poly(propylene glycol)-poly(ethylene glycol) (Pluronic P123) (BASF, Germany), was used as a template for the mesopore. P123, DI water, and HCl were mixed in a capped vial, and the mixture was stirred at 308 K for 3.5 h. TEOS was added to the mixture, and it was stirred for 5 min. The final molar ratio of the mixture was TEOS/P123/ HCl/H2O = 1.00:0.017:40.9:40.3. The resulting solution was placed in an autoclave at 308 K for 20 h. The solution was then aged at 403 K for 24 h. The solid products were collected by filtration. The collected solid was rinsed with DI water, dried at room temperature, and calcined to remove the polymers at 773 K for 5 h in air at a slow ramping rate (∼1 K min−1). MPS 3 was Zr-doped mesoporous silica synthesized by a vacuum-assisted solvent evaporation method.32 Trimethylstearylammonium chloride (C18TAC) was used as a template for this mesopore. TEOS, C18TAC, HCl, DI water, ethanol (EtOH) (Wako Pure Chemistry Industries, Ltd., Japan), and a metal source (ZrO(NO3)2·2H2O) were mixed in a capped vial and stirred at room temperature for 1 h. The final molar ratio of the resulting solution was TEOS/Zr/C18TAC/EtOH/HCl/ H2O = 0.99:0.01:0.2:10:(1.8 × 10−4):10. The solution was evaporated using a vacuum rotary evaporator to generate a micelle-templated nanocomposite that was then calcined at 873 K for 5 h to remove the polymers. The Si/Zr molar ratio in the resulting solid was expected to be the same as that of the starting solution (Si/Zr = 99). 2.2. Characterization of MPSs. The highly ordered hexagonal pore array of the MPSs was confirmed by SEM (S4800, Hitachi High-Technologies, Japan), STEM (SU9000, Hitachi High-Technologies, Japan), and small-angle X-ray diffraction spectroscopy (D8 Advance, Bruker AXS, Germany) operated at 40 kV and 40 mA employing Cu Kα radiation (λ = 0.154 nm). The pore structure of the MPSs was characterized by measuring the adsorption−desorption isotherms of nitrogen at 77 K using an automatic adsorption measurement apparatus (BELSORP-max, MicrotracBEL Corp., Japan). The sample was degassed at 573 K for 8 h below 8 × 10−3 Pa before adsorption measurements. Details of the characterization of MPSs using XRD and nitrogen adsorption measurements were described in our previous studies (ref 30 for MPS 1 and ref 33 for MPSs 2 and 3). The structural properties of MPSs employed in this study are summarized in Table 1. Figures 1a−1c show the SEM and TEM images for the three different MPSs. All the synthesized MPSs had two-dimensional hexagonal pore structures. The average pore lengths, Lp, of MPSs 1, 2, and 3 were about 500, 570, and 650 nm, respectively. The shape of MPS 1 and 3 particles was a polygonal prism, but that of MPS 2 was a polygonal prism and a pyramid. The average pore length of MPS 2 was calculated by

In a previous report, the measured relaxation rate of water uptake and release in a well-ordered MPS was much lower than that predicted by the Lucas−Washburn law for capillarityinduced liquid transport.21 This low water uptake and release could be caused by a capillary force working in the opposite direction to the water front because the pores were not in contact with liquid water. This result could also be caused by nonstraight pore geometry, which is considered a geometry factor for porous materials in the Lucas−Washburn law. The actual cause has not yet been determined. In addition, the measured relaxation rate depends on the magnitude of the stepwise change in relative humidity when the relative humidity is changed in steps from the onset point of capillary condensation and capillary evaporation. That is, the relaxation rates depend on the difference in chemical potentials between the initial and final relative humidities, Δμ = μinitial − μfinal.21 However, the relative humidity at the onset point for capillary condensation and capillary evaporation depends on the pore diameter and pore surface state.23,24 That is, μinitial depends on the pore diameter and pore surface state. The relaxation rate might depend not only on Δμ but also on μinitial and μfinal. Therefore, it is more difficult to evaluate the kinetics of water uptake and release in nanopores with different pore dimensions and pore surface states. In this study, when the relative humidity was changed in steps from the onset point of capillary condensation and capillary evaporation, the relaxation curves of water uptake and release in three different MPSs were measured by a gravimetric method at 101.3 kPa and 298 K. Recent advances in methods for synthesizing nanostructured materials allow for controlling pore size and structure. Among these nanostructured materials, MPS has great potential as an absorbent because of its highly ordered pore structure, uniform pore size, high specific surface area, high porosity, and in particular, reliable adsorption− desorption performance.25,26 Furthermore, the pore structure of MPS can be controlled by adjusting its synthesis conditions and template molecules.27−29 Therefore, studies of well-ordered MPSs can be useful for a deeper understanding of the fundamental mechanism of liquid transport in nanopores. The three MPSs employed in this study had a two-dimensional hexagonal pore structure (p6mm), but different pore dimensions. These MPSs, which were synthesized using three different surfactants, were named MPS 1, 2, and 3, respectively. MPS 1 was 10.5 nm in diameter and ca. 500 nm in length, MPS 2 was 9.1 nm in diameter and ca. 570 nm in length, and MPS 3 was 3.8 nm in diameter and ca. 650 nm in length. All adsorption−desorption isotherms exhibited type V behavior with significant hysteresis. The objective of this study is to evaluate the kinetics of water uptake and release in well-ordered MPSs with a two-dimensional hexagonal pore structure, but different pore dimensions.

2. EXPERIMENTAL METHODS 2.1. Synthesis of MPS. Three different MPSs were synthesized using the following methods. MPS 1 was synthesized by controlling the microphase separation of block copolymers.30 Polystyrene-block-poly(4-vinylpyridine) (PSP4VP) (Polymer Source Inc., Canada) was used as the block copolymer. PS-P4VP was dissolved in N,N-dimethylformamide (DMF) (Kishida Chemical Co., Japan). Tetraethyl orthosilicate (TEOS) (Tokyo Chemical Industry Co., Japan), deionized (DI) water with resistivity greater than 18.3 MΩ cm produced from a water purification system (Milli-Q Advantage A10, 26172


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3. RESULTS AND DISCUSSION 3.1. Adsorption−Desorption Isotherms and Relaxation Kinetics. Figures 3a−3c show the time course of the amount of adsorbed water, m, and the relative humidity, p/p0, for MPSs 1, 2, and 3, respectively. Here, p is the actual pressure and p0 is the saturation pressure of water vapor. In the adsorption process data shown in Figure 3, when p/p0 was changed in a stepwise manner, the adsorbed mass, m, quickly reached the equilibrium value at (a) p/p0 = 0−0.78 and 0.90−0.95, (b) p/p0 = 0−0.77 and 0.87−0.95, and (c) p/p0 = 0−0.50 and 0.60−0.90. In contrast, the adsorbed water more slowly reached the equilibrium value at (a) p/p0 = 0.78−0.90, (b) p/p0 = 0.77−0.87, and (c) p/p0 = 0.50−0.60. In addition, despite a small change in p/p0 in this last data set, a large uptake of water occurred. This process is known as capillary condensation. In the desorption process, a similar trend is observed. The adsorbed mass, m, quickly reaches the equilibrium value at low and high relative humidity, whereas it reached the equilibrium value more slowly at an intermediate relative humidity ((a) p/p0 = 0.80−0.74, (b) p/p0 = 0.76−0.72, and (c) p/p0 = 0.50−0.30). In addition, a small change in p/p0 led to a large release of water. This process is known as capillary evaporation. To better understand the adsorption and desorption processes on MPSs, the mass uptake at equilibrium and the relaxation rate of the three MPSs were plotted at each relative humidity, as shown in Figures 4a−4c. The mass uptake at equilibrium and the relaxation rates at each stepwise change in the relative humidity can be calculated by fitting the relaxation curves of water uptake and release to a linear driving force model (LDF). Assuming that the time when the relative humidity begins to change in a stepwise manner is zero (t = 0) and the adsorbed mass is zero (m = 0) at t = 0, the LDF model is given by eq 1,34

Table 1. Pore Structural Properties of Three Different 2D Hexagonal MPS Particles sample (template molecule)

dpa (nm)

d100b (nm)

wc (nm)

ABETd (m2 g−1)

Vpe (cm3 g−1)

MPS 1 (PS−P4VP) MPS 2 (P123) MPS 3 (C18TAC)

10.5 9.1 3.8

14.7 9.6 3.71

6.47 1.97 0.48

451 637 1086

0.648 1.16 0.81

a

Pore diameter calculated using nonlocal density functional theory (NLDFT). b(100) interplanar spacing. cPore wall thickness obtained by subtracting pore diameter, dp, from unit cell dimension, a, which represents calculated d100 using the following formula: a = d100 × (2/ √3). dBrunauer−Emmett−Teller (BET) specific surface area. ePore volume calculated from αs-plot.

Lp = hprism + 2hpyramid/3, where hprism is the height of the prism and hpyramid is the height of the pyramid. The normal distribution for the pore length of MPS 2 can be described as X ∼ N(570,51.22). 2.3. Experimental Apparatus and Water Uptake and Release Measurements. In this study, a low-temperature vapor adsorption measurement system (MSB-Flow-SPT, MicrotracBEL Corp., Japan) integrated with a magnetic suspension balance (IsoSORP E10, Rubotherm, Germany) was employed. The accuracy of the measured mass was ±10 μg. A schematic diagram of this system is shown in Figure 2. This apparatus allows us to measure the time evolution of the adsorbed mass of water in a MPS by a gravimetric method in a flow system at atmospheric pressure. Helium (He) was used as the carrier gas. The flow rate and absolute humidity of He were controlled by two mass flow controllers (accuracy of ±1% at 200 sccm (gas flow rate at 273 K and 101.3 kPa)) in the branching tubes shown in Figure 2. The upper tube supplies dry He gas through a desiccant dryer. The lower tube supplies water-saturated He gas through a vaporizer and a condenser. Wet He gas at a fixed absolute humidity was supplied at 200 sccm into a test section where an electrolytically polished stainless steel basket containing sample particles (∼3.2 mg) was suspended by a balance. The temperature of the test section was controlled at 298 K by a temperature-controlled oil bath. Before entering the test section, the supplied gas passed through a channel at the same temperature as the test section. Thus, the temperature and relative humidity of the supplied gas were controlled at the setting values. The relative humidity of He was changed in a stepwise manner, and the transient response of water uptake and release was measured with time. Prior to adsorption, all samples were evacuated by a rotary vacuum pump at 573 K for 8 h below 8 × 10−3 Pa to remove any moisture and adsorbed gases on the samples.

m = 1 − exp( −kt ) meq

(1)

where meq is the mass uptake at equilibrium and k is the relaxation rate constant. All the adsorption−desorption isotherms were of type V and exhibited significant hysteresis. The amount of adsorbed water in the pore filling state was 0.56, 1.12, and 0.72 g g−1 for MPSs 1, 2, and 3, respectively. These values are related to the specific pore volumes of the corresponding MPSs shown in Table 1. The amount of adsorbed water in the pore filling state increases as the specific pore volume increases. The adsorption− desorption isotherms also show that the relative humidity, where capillary condensation or evaporation occurs, is different depending on the pore diameter. The capillary condensation and evaporation of MPS 3, which has the smallest pore

Figure 1. SEM and STEM images of synthesized MPSs: (a) MPS 1, (b) MPS 2, and (c) MPS 3. 26173


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Figure 2. Schematic diagram of a low-temperature vapor adsorption measurement system.

than that of MPS 2 (9.05 × 10−5 s−1 at 0.84 relative humidity) or MPS 3 (1.52 × 10−4 s−1 at 0.56 relative humidity). It should be noted that capillary condensation occurred at a similar relative humidity, p/p0 = 0.80−0.81, in MPSs 1 and 2, but the relaxation rates were considerably different. This could be caused by differences in pore structural properties. This subject is discussed in detail in section 3.4. The relaxation rates in the capillary evaporation process showed a similar trend. The lowest relaxation rate of MPS 1 was 3.36 × 10−4 s−1 at 0.78 relative humidity, which was higher than that of MPS 2 (1.86 × 10−4 s−1 at 0.73 relative humidity) and MPS 3 (2.98 × 10−4 s−1 at 0.4 relative humidity). 3.2. Evaluation of the Thickness of Water Films Where Capillary Condensation or Evaporation Occurs. The combined Kelvin and Gibbs−Tolman−Koenig−Buff (GTKB) equations for the modification of the interfacial tension due to interfacial curvature was employed to evaluate the thickness of water, t, at the relative humidity where capillary condensation and capillary evaporation occur.35−38 The curvature radius, ρ, for capillary condensation or evaporation within the pores at a given relative humidity is given by the Kelvin eq (eq 2).

ρ=

2γ∞Vm −RT ln(p /p0 )

(2)

where Vm is the molar volume of water, which is assumed to be 1.8 × 10−5 m3 mol−1, R is the gas constant, T is the absolute temperature, and γ∞ is the interfacial tension. γ∞ is defined as a function of temperature according to the Vargaftik equation (eq 3).39

Figure 3. Time course of the amount of water adsorbed on (a) MPS 1, (b) MPS 2, and (c) MPS 3, and relative humidity in adsorption (left) and desorption (right) processes.

⎡ Tc − T ⎤ μ⎡ ⎛ T − T ⎞⎤ γ∞(T ) = B⎢ ⎥ ⎢1 + b ⎜ c ⎟⎥ ⎣ Tc ⎦ ⎢⎣ ⎝ Tc ⎠⎥⎦

diameter, occurred at the lowest relative humidity. In MPSs 1 and 2, which have larger diameter pores, the capillary condensation and evaporation occurred at around 0.8 relative humidity. Regarding relaxation kinetics, the rates of adsorption and desorption were slow at large uptake and release, respectively. Fast adsorption−desorption processes occurred in the layeradsorption state at low relative humidity, and in the pore-filling state at high relative humidity. The relaxation rate of MPS 1 was higher than that of MPS 2 or 3 during the capillary condensation process. The lowest relaxation rate for MPS 1 was 5.28 × 10−4 s−1 at 0.85 relative humidity, which is much higher

(3)

In eq 3, it is assumed that B = 0.2358 N m−1, Tc = 647.15 K, μ = 1.256, and b = −0.625. The effect of the curvature radius on the interfacial tension is obtained from the GTKB equation according to eq 4,

⎛ nδ ⎞ γ(ρ) = γ∞⎜1 − ⎟ ρ⎠ ⎝

(4)

where n is the geometrical factor (n = 1 for a cylindrical interface, and n = 2 for a spherical interface) and δ is the displacement of the surface of the zero mass density relative to the surface tension and assumed to be −0.3 nm.40 By replacing 26174


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Figure 4. Adsorption−desorption isotherms (top) of water adsorbed on (a) MPS 1, (b) MPS 2, and (c) MPS 3, and the relaxation rate with respect to p/p0 (bottom) at 298 K.

Table 2. Curvature Radii, Water Film Thickness, and Inner Radii at Which Capillary Condensation (n = 1) and Capillary Evaporation (n = 2) Occur sample (template molecule)

interface factor

MPS 1 (PS-P4VP) MPS 2 (P123) MPS 3 (C18TAC)

n n n n n n

= = = = = =

1 2 1 2 1 2

p/p0

m (g g−1)

ρ (nm)

t (nm)

ri (nm)

0.845 0.775 0.835 0.74 0.545 0.380

0.341 0.355 0.655 0.693 0.380 0.375

6.50 4.63 6.09 4.00 1.98 1.51

2.00 0.62 1.51 0.56 0.91 0.39

3.25 4.63 3.04 4.00 0.99 1.51

the interfacial tension, γ∞, in eq 2 with γ(ρ) in eq 4, the GTKB−Kelvin equation for the curvature radius results is shown in eq 5. ρ=

γ∞Vm +

3.3. Kinetics of Capillary Condensation and Evaporation. Figures 5a-I, 5b-I, 5c-I, 5a-II, 5b-II, and 5c-II show the relaxation curves of (I) water adsorption and (II) water desorption for the three MPSs, (a) MPS 1, (b) MPS 2, and (c) MPS 3, obtained for several different stepwise changes in relative humidity, from the onset points of capillary condensation (p/p0 = 0.81, 0.80, and 0.50 for MPSs 1, 2, and 3, respectively) and capillary evaporation (p/p0 = 0.80, 0.76, and 0.45 for MPSs 1, 2, and 3, respectively). For all MPSs, both in adsorption and desorption, the relaxation rates increased as the relative humidity increased in step changes. In particular, the relaxation rate significantly increased as the relative humidity increased above a critical point, at which point water transport could be divided into two major types: Fickian diffusion and capillarity-induced liquid flow.21,22 Figures 6a-I, 6b-I, 6c-I, 6a-II, 6b-II, and 6c-II show the curve fitting of the corresponding relaxation curves of water adsorption and water desorption for the three MPSs shown in Figures 5a-I, 5b-I, 5c-I, 5a-II, 5b-II, and 5c-II, respectively. The adsorbed mass, m, was normalized by the equilibrium value, meq. Two fitting functions were employed, shown in eqs 6 and 7,

(γ∞Vm)2 + 2nδγ∞VmRT ln(p /p0 ) −RT ln(p /p0 )

(5)

If the diameter of an MPS is perfectly uniform, the adsorbed and desorbed mass will change at a specific relative humidity during capillary condensation and evaporation. However, the mass gradually changed as the relative humidity changed, as shown in Figure 4, even though the corresponding relative humidity was confined within narrow limits. This finding indicates that the diameter was not completely uniform. Therefore, in this study, the relative humidity at the midpoint of capillary condensation and evaporation was used to evaluate the curvature radius at pores with a mean diameter. That is, p/ p0 = 0.845, 0.835, and 0.545 during capillary condensation and p/p0 = 0.775, 0.74, and 0.38 during capillary evaporation for MPSs 1, 2, and 3, respectively. Furthermore, in capillary condensation, the geometrical factor for the cylindrical interface in the GTKB equation was used to evaluate the curvature radius, i.e., n = 1. In contrast, the geometrical factor for the spherical interface is used for capillary evaporation, i.e., n = 2, since a hemispherical meniscus interface is formed at the entrance of the pores. It has been reported that capillary condensation starts at the curvature radius ρ = 2ri, whereas capillary evaporation starts at ρ = ri.41,42 Here, ri = dp/2 − t, i.e., the inner radius, except for the water film. The thickness of the water film is given by t = dp/2 − ρ/2 for capillary condensation and t = dp/2 − ρ for capillary evaporation. The water film thickness, curvature radii, and inner radii calculated for MPSs 1, 2, and 3 are summarized in Table 2.

m = sgn(m /meq )[1 − meq

10

∑ (Cn sin ζn/ζn)exp(−ζn2k1t )] n=1

(6)

m = sgn(m /meq )(k 2t )1/2 − A meq

(7)

where ζn = (π/2)(2n − 1), Cn = (4 sin ζn)/(2ζn + sin(2ζn)), and k1, k2, and A are fitting parameters. Sgn(x) is the signum function of x, which is defined as sgn(x) = {−1 if x < 0; 0 if x = 0; 1 if x > 0}. Equation 6 is a function based on the exact solution of the Fickian diffusion equation, whereas eq 7 is the 26175


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Figure 5. Relaxation curves of (I) adsorption and (II) desorption of water for (a) MPS 1, (b) MPS 2, and (c) MPS 3 obtained upon several different stepwise changes of the relative humidity at 298 K. In the adsorption process, at t = 0, the relative humidity changed (a) from 0.81 to 0.85, 0.86, 0.87, 0.88, and 0.90, (b) from 0.80 to 0.84, 0.85, 0.87, and 0.90, and (c) from 0.50 to 0.54, 0.58, 0.60, 0.70, 0.80, and 0.90. In the desorption process, at t = 0, the relative humidity changed (a) from 0.80 to 0.77, 0.75, 0.70, 0.60, 0.30, and 0.10, (b) from 0.76 to 0.73, 0.70, 0.65, 0.60, 0.50, 0.30, and 0.10, and (c) from 0.45 to 0.40, 0.37, 0.34, 0.30, 0.20, and 0.10.

function based on advective liquid flow (the Lucas−Washburn equation) or diffusion-controlled flow where the diffusion coefficient increases with concentration increasing.43 In Figure 6, the fitting functions given by eqs 6 and 7 are denoted by f1 and f2, respectively. In the adsorption process, when the stepwise change in relative humidity is small, the relaxation curves are fitted well by eq 6. Examples of this good fit are from 0.81 to 0.85 and 0.86 for MPS 1, and from 0.50 to 0.54 for MPS 3. On the other hand, when the stepwise change in relative humidity is large, the relaxation curves are well fitted by eq 7. Examples of this good fit are from 0.81 to 0.90 for MPS 1, from 0.80 to 0.87 and 0.90 for MPS 2, and from 0.50 to 0.70, 0.80, and 0.90 for MPS 3. It should be noted that the relaxation curves for MPS 2 are not well fitted by eq 6 for all of the conditions we tested, including small stepwise changes. For MPS 2, when the stepwise change in relative humidity is small, from 0.80 to 0.84 or 0.85, it took more than 10,000 s to reach the equilibrium state (see Supporting Information S1). Similarly, in the desorption process, when the stepwise change in relative humidity is small, the relaxation curves are well fitted by eq 6. Examples of this good fit are from 0.80 to 0.77 for MPS 1 and from 0.45 to 0.40 for MPS 3. On the other hand, when the stepwise change in relative humidity is large, the relaxation curves are well fitted by eq 7. Examples of this good fit are from 0.80 to 0.70, 0.60, 0.30, and 0.01 for MPS 1,

from 0.76 to 0.70, 0.65, 0.60, 0.50, 0.30, and 0.10 for MPS 2, and from 0.45 to 0.30, 0.20, and 0.10 for MPS 3. The relaxation curve data for MPS 2 did not fit eq 6 well for all conditions including small step changes in relative humidity. The parameters that fit eqs 6 and 7 are summarized in Table 3. We see that the relaxation rate increases as the magnitude of the stepwise change in relative humidity increases. This trend occurs for all three MPSs. However, the transport mechanism of water in mesopores, especially the transition from the diffusive flow to the advective flow, depends on the type of MPS used. 3.4. Comparison of Water Kinetics in Different MPSs. Figures 7a-I, 7b-I, 7a-II, and 7b-II show representative relaxation curves for (I) water adsorption and (II) water desorption for comparison of the amount of water uptake and release, m, per (a) unit mass of MPS and (b) unit surface area on the pores for the three MPSs. All the curves in Figure 7 are well fitted by eq 7. The transport mechanism in pores is liquid water flow by capillary action. The maximum relaxation rate was obtained for each MPS under these conditions. The adsorbed mass was assumed to be zero (m = 0) when the adsorption and desorption processes occurred in a stepwise manner (t = 0). In the adsorption process, as shown in Figure 7a-I, the equilibrium mass per unit mass of MPS was the largest for MPS 2 because it had the largest specific pore volume (VP = 1.16 cm3 26176


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Figure 6. Curve fitting of the relaxation curves shown in Figure 5 for (I) water adsorption and (II) water desorption for (a) MPS 1, (b) MPS 2, and (c) MPS 3. The adsorbed mass, m, was normalized by the equilibrium value, meq. The fitting functions are given by eqs 6 and 7, denoted by f1 and f2, respectively. 26177


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Table 3. Fitted Parameters of Relaxation Curves of Water Adsorption and Desorption in Different Stepwise Changes in Relative Humidity, p/p0, for MPSs 1, 2, and 3a f1b p/p0

a

meq

[m/meq]

0.81 0.81 0.81 0.81 0.81

→ → → → →

0.85 0.86 0.87 0.88 0.90

0.209 0.270 0.360 0.380 0.383

[0, [0, [0, [0, [0,

1.00] 1.00] 1.00] 1.00] 1.00]

0.80 0.80 0.80 0.80 0.80 0.80

→ → → → → →

0.77 0.75 0.70 0.60 0.30 0.10

−0.184 −0.290 −0.358 −0.393 −0.437 −0.454

[0, [0, [0, [0, [0, [0,

−1.00] −1.00] −1.00] −1.00] −1.00] −1.00]

0.80 0.80 0.80 0.80

→ → → →

0.84 0.85 0.87 0.90

0.745 0.745 0.771 0.858

[0, [0, [0, [0,

1.00] 1.00] 1.00] 1.00]

0.76 0.76 0.76 0.76 0.76 0.76 0.76

→ → → → → → →

0.73 0.70 0.65 0.60 0.50 0.30 0.10

−0.780 −0.793 −0.769 −0.783 −0.804 −0.833 −0.866

[0, [0, [0, [0, [0, [0, [0,

−1.00] −1.00] −1.00] −1.00] −1.00] −1.00] −1.00]

0.50 0.50 0.50 0.50 0.50 0.50

→ → → → → →

0.54 0.58 0.60 0.70 0.80 0.90

0.153 0.460 0.548 0.563 0.574 0.598

[0, [0, [0, [0, [0, [0,

1.00] 1.00] 1.00] 1.00] 1.00] 1.00]

0.45 0.45 0.45 0.45 0.45 0.45

→ → → → → →

0.40 0.37 0.34 0.30 0.20 0.10

−0.240 −0.389 −0.456 −0.521 −0.528 −0.542

[0, [0, [0, [0, [0, [0,

−1.00] −1.00] −1.00] −1.00] −1.00] −1.00]

f2c k1/s

−1

k2/s−1

[m/meq]

(a) MPS 1 Adsorption 1.94 × 10−4 1.90 × 10−4 2.67 × 10−4 3.99 × 10−4 5.62 × 10−4 Desorption 2.15 × 10−4 3.20 × 10−4 8.39 × 10−4 1.61 × 10−3 3.00 × 10−3 4.38 × 10−3 (b) MPS 2 Adsorption 2.57 × 10−5 4.09 × 10−5 2.09 × 10−4 3.30 × 10−4 Desorption 1.05 × 10−4 2.42 × 10−4 5.70 × 10−4 7.90 × 10−4 1.12 × 10−3 1.49 × 10−3 2.14 × 10−3 (c) MPS 3 Adsorption 9.43 × 10−5 1.46 × 10−4 2.57 × 10−4 7.49 × 10−4 8.85 × 10−4 1.13 × 10−3 Desorption 1.51 × 10−4 2.61 × 10−4 3.74 × 10−4 6.68 × 10−3 1.08 × 10−3 1.48 × 10−3

A

[0, [0, [0, [0, [0,

0.60] 0.60] 0.70] 0.80] 0.95]

4.90 3.94 5.04 6.97 1.29

× × × × ×

10−4 10−4 10−4 10−4 10−3

1.81 1.37 1.74 1.58 3.12

[0, [0, [0, [0, [0, [0,

−0.65] −0.70] −0.90] −0.95] −0.95] −0.95]

4.71 6.86 1.91 4.82 7.05 1.60

× × × × × ×

10−4 10−4 10−3 10−3 10−3 10−2

−2.10 −2.45 −3.08 −4.38 −2.70 −4.49

[0, [0, [0, [0,

0.50] 0.50] 0.95] 0.95]

4.09 8.61 4.04 7.22

× × × ×

10−5 10−5 10−4 10−4

8.53 1.45 5.15 6.89

[0, [0, [0, [0, [0, [0, [0,

−0.70] −0.80] −0.90] −0.90] −0.95] −0.95] −0.95]

1.66 4.47 1.17 1.75 2.49 4.41 8.75

× × × × × × ×

10−4 10−4 10−3 10−3 10−3 10−3 10−3

−1.61 −2.37 −2.80 −3.05 −3.22 −4.78 −6.73

[0, [0, [0, [0, [0, [0,

0.65] 0.70] 0.80] 0.90] 0.95] 0.95]

1.44 × 10−4 2.34 × 10−4 4.48 × 10−4 1.52 × 10−3 2.0 × 10−3 2.69 × 10−3

[0, [0, [0, [0, [0, [0,

−0.65] −0.70] −0.75] −0.85] −0.90] −0.95]

2.65 4.77 7.08 1.28 2.32 3.28

× × × × × ×

10−4 10−4 10−4 10−3 10−3 10−3

5.44 1.24 1.70 2.57 3.01 3.32

× × × × ×

× × × ×

× × × × × ×

−1.26 −2.99 −1.85 −4.77 −4.86 −6.96

10−1 10−1 10−1 10−1 10−1 × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1

10−2 10−1 10−1 10−1 × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1

10−2 10−1 10−1 10−1 10−1 10−1 × × × × × ×

10−2 10−1 10−1 10−1 10−1 10−1

The fitting range for each fitting function is shown in the column of [m/meq]. bEquation 6. cEquation 7.

g−1). However, the uptake rate per unit mass for the MPSs was the highest in MPS 3, followed by MPS 2 and then MPS 1. While in the desorption processes, as shown in Figure 7a-II, the equilibrium mass per unit mass of MPS was the largest for MPS 2, but the release rate per unit mass of MPS was the smallest for MPS 3. The release rates for MPSs 1 and 2 were almost the same. The uptake and release rates per unit mass of MPS are useful for practical applications such as desiccant dehumidifiers, but it is difficult to evaluate the kinetics of water uptake and release in nanopores with different pore dimensions. In this study, a simple model for MPS is proposed to evaluate the kinetics of water uptake and release per unit surface area on the pores. We assume that the shape of the MPS particles is a

polygonal prism, and the cylindrical pores are aligned vertical to the parallel planes. The cross sectional area of the cylindrical pores on the polygonal plane per unit mass of MPS can be given by Ap = Vp/Lp, where VP is the specific pore volume (cm3 g−1) and Lp is the pore length (cm). In the case of MPS 2, the shape of the MPS particles is a polygonal prism and pyramids as shown in Figure 1b. If the cylindrical pores are aligned vertical to the parallel planes of the prism and the average pore length is given by Lp = hprism + 2hpyramid/3, Ap is also given by Vp/Lp. However, it should be noted that a liquid water film formed on the inner surface of the mesopores during capillary condensation or evaporation. The calculated thicknesses of this water film at the onset of capillary condensation and capillary 26178


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Figure 7. Relaxation curves of (I) water adsorption and (II) water desorption for comparison of the amount of water uptake and release, m, per (a) unit mass and (b) unit surface area on the pores for all three MPSs.

is the mass flux of pore water uptake. The mass flux of water uptake at t = 0 is 7.68 × 10−8, 6.34 × 10−8, and 3.69 × 10−7 g cm−2 s−1 for MPSs 1, 2, and 3, respectively. In the desorption process, the gradient of the relaxation curves in Figure 7b-II is the mass flux of water release from the pores. The mass flux of water release at t = 0 is −7.44 × 10−7, −3.65 × 10−7, and −3.68 × 10−7 g cm−2 s−1 for MPSs 1, 2, and 3, respectively. However, it is not appropriate to compare these values because a driving force was different. Assuming the ideal gas law for water vapor, the difference in chemical potential between the initial and final states is given by eq 8.

evaporation are summarized in Table 2. If a stable water film of these thicknesses is formed over the entire inner surface of the pores at the onset point of capillary condensation, the volume ratio of the water film to the entire pore was 0.62, 0.55, and 0.73 for MPSs 1, 2, and 3, respectively. However, the mass ratio of the adsorbed water at the onset point of capillary condensation to the adsorbed water in the pore filling state was 0.25, 0.23, and 0.19 for MPSs 1, 2, and 3, respectively, as shown in Figure 4. The calculated thickness for capillary condensation shown in Table 2 was overestimated. In this study, we assumed that two molecular layers of water were formed over the entire mesopore inner surface at the onset of capillary condensation. The thickness of the water layer was 0.5 nm.14,44 The calculated values shown in Table 2 were employed to determine the thickness of the water film at the onset of capillary evaporation. The calculated Ap and the effective Ap in adsorption and desorption processes, Ap,ads and Ap,des, are summarized in Table 4. The rate of water uptake per unit pore surface area, which is also the gradient of the relaxation curves shown in Figure 7b-I,

⎛ (p /p )final ⎞ 0 ⎟⎟ Δμ = RT ln⎜⎜ ⎝ (p /p0 )initial ⎠

The values for Δμ in the adsorption process for MPSs 1, 2, and 3 are 0.262, 0.292, and 1.459 kJ mol−1, respectively, while the values of Δμ in the desorption process for MPSs 1, 2, and 3 are 5.160, 5.034, and 3.733 kJ mol−1, respectively. Figure 8 shows the mass flux of water uptake and release at t = 0 as a function of the difference in chemical potential before and after stepwise changes in relative humidity. In the adsorption process, all the data could be plotted on a line, suggesting that J(0) is proportional to Δμ. This result indicates that the dominant factor for determining J(0) is Δμ. The larger the Δμ applied, the larger the resulting J(0). Assuming that the transport of water in mesopores is advective and the density of liquid water is ρw = 1 g cm−3, the velocity of liquid water in MPS 3 at J(0) = 3.69 × 10−7 g cm−2 s−1 is v = J(0)/ρw = (3.69 × 10−7 g cm−2 s−1)/(1 g cm−3) = 3.69 × 10−9

Table 4. Calculated Ap and the Effective Ap in Adsorption and Desorption Processes, Ap,ads and Ap,des, per Unit Mass of the Three MPSs sample (template molecules)

Ap (cm2 g−1)

Ap,ads (cm2 g−1)

Ap,des (cm2 g−1)

MPS 1 (PS-P4VP) MPS 2 (P123) MPS 3 (C18TAC)

12960 20351 12462

10627 16120 6770

10115 15686 7878

(8)

26179


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that the relative humidity adjacent to pore entrances was kept constant at the same value of a supplied moist gas but the transport of water in the vapor phase was still the rate controlling step. This is supported by the linear behavior in the curve of the mass flux of water uptake at t = 0 vs the difference in chemical potential before and after stepwise changes in relative humidity shown in Figure 8. However, as time progressed, the mass flux of water uptake decreased. The mass flux of water uptake during the capillary condensation was smaller than the initial value. This result suggests that the transport of liquid water in mesopores is the rate controlling step in overall water transport processes during the capillary condensation. Furthermore, because the experimental transport rate of liquid water in mesopores was much lower than that predicted by the Lucas−Washburn law, the liquid water in mesopores could move only intermittently. In the desorption process, when Δμ is less than 1 kJ mol−1, all data could be plotted on a line. However, as Δμ increased, the data moved away from the line, especially for MPSs 2 and 3. As Δμ increased, not only water molecules condensed inside mesopores but also water molecules adsorbed on the pore surface could release. Thus, the mechanism of transport and desorption of water inside mesopores became more complicated. The dependency of the type of MPS on J(0) and the nonlinear behavior in Figure 8 for water release could be attributed to the transport and desorption phenomena inside mesopores. The average pore diameter of MPS 3 was smaller that that of MPS 1, and the relative humidity at the onset point of capillary evaporation of MPS 3 was lower than that of MPS 1. At a fixed value of Δμ (= μinitial − μfinal), μfinal of MPS 3 was smaller than that of MPS 1 since μinitial of MPS 3 was smaller than that of MPS 1. Thus, water molecules adsorbed on pore surface more stably could affect J(0) in MPS 3. Therefore, J(0) of MPS 3 was smaller than that of MPS 1 especially at large Δμ. Regarding MPS 2, the desorption rate of water during capillary evaporation for small stepwise changes in relative humidity was much smaller than that of MPS 1, as shown in Figure 4. Furthermore, the relaxation curves were fitted by a square root of time function, as shown in Figure 6. These results suggest that water does not move diffusively but moves advectively, overcoming energy barriers. Therefore, J(0) of MPS 2 was smaller than that of MPS 1. Finally, it should be noted that J(0) in capillary condensation is approximately equal to that in capillary evaporation, when Δμ is less than 1 kJ mol−1.

Figure 8. Mass flux of water uptake and release at t = 0, J(0), as a function of the difference in chemical potential before and after stepwise changes in relative humidity, Δμ. Solid lines are the fitted lines for all data in water uptake, and data less than 1 kJ mol−1 in water release.

m s−1. The mass flow rate of supplied water vapor was ṁ all = 7.53 × 10−5 g s−1 at 298 K, p/p0 = 0.90, and 200 sccm. The rate of water adsorption was ṁ a0 = J(0)Ap,adsmMPS = (3.69 × 10−7 g cm−2 s−1) × (6770 cm2 g−1) × (3.2 mg) = 7.99 × 10−6 g s−1. Therefore, the mass ratio of ṁ a0 to ṁ all was 1.06 × 10−1. This result suggests that at least about 90% supplied water vapor passed through the test section without adsorbing in mesopores. If all supplied water vapor adsorbs in MPS 3 and the condensed liquid water transports advectively, the velocity of liquid water in MPS 3 is v = ṁ all/(ρwAp,adsmMPS) = 7.53 × 10−5 g s−1/((1 g cm−3) × (6770 cm2 g−1) × (3.2 mg)) = 3.48 × 10−8 m s−1. The rate of supplied water vapor to the test section was sufficiently high, and it was not the rate controlling step in the overall adsorption processes. Furthermore, the Lucas− Washburn law for the mass uptake is given by the following equation:18 ⎛ r ⎞1/2 σ eff m(t ) = Δm⎜⎜ t ⎟⎟ 2 ⎝ 2Lp η ⎠

(9)

where Δm is the total mass uptake during the capillary condensation, i.e., Δm = ρwAp,adsLpmMPS, Lp is the pore length, reff is the effective pore radius, i.e., the pore radius minus the thickness of the water layer, t is time, η is viscosity, and σ is the surface tension of liquid. For the capillary rise of liquid water in MPS 3, eq 9 was given by m(t) = 1.41(mg) × (1.34 × 105 × t(s))1/2. Here, the following parameters were employed: Ap,ads = 6770 cm2 g−1, Lp = 650 nm, mMPS = 3.2 mg, reff = 1.4 nm, η = 8.9 × 10−4 Pa s, σ = 7.2 × 10−2 N m−1, and ρw = 1 g cm−3. This result shows that MPS 3 is filled with water at t = 7.46 μs and the velocity of liquid water in MPS 3 is about v = Lp/t = 8.71 × 10−2 m s−1. The experimental transport rate of liquid water in mesopores was much lower than that predicted by the Lucas− Washburn law. This result suggests that the transport of water vapor approaching pore entrances was the rate controlling step in overall adsorption processes just after the relative humidity was changed in a stepwise manner. However, it does not mean that the rate of supplied water vapor to the test section was sufficiently low and the relative humidity adjacent to pore entrances was lower than that of a supplied moist gas. It means

4. CONCLUSIONS The time course of water uptake and release in twodimensional hexagonal MPSs with three different pore dimensions, (MPS 1) 10.5 nm in diameter and ca. 500 nm in length, (MPS 2) 9.1 nm in diameter and ca. 570 nm in length, and (MPS 3) 3.8 nm in diameter and ca. 650 nm in length, were measured at 298 K and atmospheric pressure using a gravimetric method. The adsorption−desorption isotherms and the relaxation curves of water uptake and release were obtained and analyzed. The following conclusions are drawn from this study. (1) All the adsorption−desorption isotherms exhibited type V behavior with significant hysteresis. The hysteresis was observed in the transient region between the layer adsorption state and the pore filling state, where capillary condensation and evaporation occurred. For all MPSs, the relaxation rates of water uptake and release in the 26180


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(10) Joly, L. Capillary Filling with Giant Liquid/Solid Slip: Dynamics of Water Uptake by Carbon Nanotubes. J. Chem. Phys. 2011, 135, 214705. (11) Stroberg, W.; Keten, S.; Liu, W. K. Hydrodynamics of Capillary Imbibition under Nanoconfinement. Langmuir 2012, 28, 14488− 14495. (12) Bakli, C.; Chakraborty, S. Capillary Filling Dynamics of Water in Nanopores. Appl. Phys. Lett. 2012, 101, 153112. (13) Ajayan, P. M.; Lijima, S. Capillarity-Induced Filling of Carbon Nanotubes. Nature 1993, 361, 333−334. (14) Gruener, S.; Hofmann, T.; Wallacher, D.; Kityk, A. V.; Huber, P. Capillary Rise of Water in Hydrophilic Nanopores. Phys. Rev. E 2009, 79, 067301. (15) Oh, J. M.; Faez, T.; de Beer, S.; Mugele, F. Capillarity-Driven Dynamics of Water−Alcohol Mixtures in Nanofluidic Channels. Microfluid. Nanofluid. 2010, 9, 123−129. (16) Acquaroli, L. N.; Urteaga, R.; Berli, C. L.; Koropecki, R. R. Capillary Filling in Nanostructured Porous Silicon. Langmuir 2011, 27, 2067−2072. (17) Chauvet, F.; Geoffroy, S.; Hamoumi, A.; Prat, M.; Joseph, P. Roles of Gas in Capillary Filling of Nanoslits. Soft Matter 2012, 8, 10738. (18) Washburn, E. W. The Dynamics of Capillary Flow. Phys. Rev. 1921, 17, 273−283. (19) Horikawa, T.; Do, D. D.; Nicholson, D. Capillary Condensation of Adsorbates in Porous Materials. Adv. Colloid Interface Sci. 2011, 169, 40−58. (20) Miyahara, M.; Kanda, H.; Yoshioka, T.; Okazaki, M. Modeling Capillary Condensation in Cylindrical Nanopores: A Molecular Dynamics Study. Langmuir 2000, 16, 4293−4299. (21) Yanagihara, H.; Yamashita, K.; Endo, A.; Daiguji, H. Adsorption/Desorption and Transport of Water in Two-Dimensional Hexagonal Mesoporous Silica. J. Phys. Chem. C 2013, 117, 21795− 21802. (22) Yamashita, K.; Daiguji, H. Molecular Dynamics Simulations of Water Uptake into a Silica Nanopore. J. Phys. Chem. C 2015, 119, 3012−3023. (23) Inagaki, S.; Fukushima, Y.; Kuroda, K.; Kuroda, K. Adsorption Isotherm of Water Vapor and Its Large Hysteresis on Highly Ordered Mesoporous Silica. J. Colloid Interface Sci. 1996, 180, 623−624. (24) Inagaki, S.; Fukushima, Y. Adsorption of Water Vapor and Hydrophobicity of Ordered Mesoporous Silica, FSM-16. Microporous Mesoporous Mater. 1998, 21, 667−672. (25) Kresge, C.; Leonowicz, M.; Roth, W.; Vartuli, J.; Beck, J. Ordered Mesoporous Molecular Sieves Synthesized by a LiquidCrystal Template Mechanism. Nature 1992, 359, 710−712. (26) Beck, J.; Vartuli, J.; Roth, J.; Leonowicz, M.; Kresge, C.; Schmitt, K.; Chu, C.; Sheppard, E.; McCullen, S.; Higgins, J.; et al. A New Family of Mesoporous Molecular Sieves Prepared with Liquid Crystal Templates. J. Am. Chem. Soc. 1992, 114, 10834−10843. (27) Vartuli, J.; Schmitt, K.; Kresge, C.; Roth, W.; Leonowicz, M.; McCullen, S.; Hellring, J.; Beck, J.; Schlenker, J.; Olson, D.; et al. Effect of Surfactant/Silica Molar Ratios on the Formation of Mesoporous Molecular sieves: Inorganic Mimicry of Surfactant Liquid-Crystal Phases and Mechanistic Implications. Chem. Mater. 1994, 6, 2317− 2326. (28) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G.; Chmelka, B.; Stucky, G. Triblock Copolymer Syntheses of Mesoporous Silica with Periodic 50 to 300 Angstrom Pores. Science 1998, 279, 548−552. (29) Hwang, J.; Shoji, N.; Endo, A.; Daiguji, H. Effect of Withdrawal Speed on Film Thickness and Hexagonal Pore-Array Dimensions of SBA-15 Mesoporous Silica Thin Film. Langmuir 2014, 30, 15550− 15559. (30) Kataoka, S.; Takeuchi, Y.; Kawai, A.; Yamada, M.; Kamimura, Y.; Endo, A. Controlled Formation of Silica Structures Using Siloxane/ Block Copolymer Complexes Prepared in Various Solvent Mixtures. Langmuir 2013, 29, 13562−13567.

transient region increased as the magnitude of the stepwise change in relative humidity increased. At large stepwise changes in relative humidity, the adsorbed mass is proportional to the square root of time. (2) In the adsorption processes, the mass flux of water uptake showed a linear relationship as a function of the difference in chemical potential between the initial and final states of moist He gas. In the desorption processes, when the difference in chemical potential is less than 1 kJ mol−1, the mass flux of water release and the difference in chemical potential also have a linear relationship. However, as the difference in chemical potential increased further, the gradient of mass flux of water release with respect to the difference in chemical potential gradually decreased, especially for MPSs 2 and 3. The energy barrier for transport and desorption in mesopores of MPSs 2 or 3 should be higher than that of MPS 1, resulting in the suppression of the mass flux of water release.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b08564. Experimental details (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +81 3 5841 8833. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by the JST−CREST program “Phase Interface Science for Highly Efficient Energy Utilization.” REFERENCES

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