1. INTRODUCTION

Imbibition and drainage of wetting fluid in porous materials is of very wide interest from both fundamental and practical perspectives. For instance, there is fundamental interest in the effect of finite size constraints on bulk properties of fluids [1]. From the practical perspective, the behavior of wetting fluids in small pores has vast importance in a wide range of technologies, such as catalyst supports and ultrafiltration membranes, for which the adsorption and desorption of fluids are critical to their performance [2]. While the transport properties of saturated porous media have been extensively studied, recent attention is focused on those of partially saturated porous media [3–5]. Traditionally, the behavior of the imbibed wetting fluid in porous material has been analyzed by using probes with penetrating power, such as small-angle x-ray scattering [6,7] or neutron scattering [8–10]. Therefore, these approaches require radiologic protection equipment to study the behavior of the imbibed wetting fluid in porous materials.

Fortunately, porous Vycor glass is transparent in the visible region because nanosized pores are transparent for visible light. Furthermore, its large specific surface of about $200{\mathrm{m}}^2/\mathrm{g}$ allows it to easily adsorb ambient fluids. In other words, nanoporous Vycor glass is transparent in the wide ultraviolet-visible-near-infrared (UV-Vis-NIR) region. Consequently, we can easily observe the behavior of imbibed fluid inside the pore space using a spectrophotometer; i.e., the imbibition and drainage of water in nanoporous Vycor glass are optically observable.

In a previous paper [11], we reported that the imbibed water within nanoporous Vycor glass exhibits two optical hysteretic features. One is an absorbance peak in the NIR region (more specifically at around the wavelength of 1900 nm), which is caused by the water adsorbed by pore walls [11–13]. This absorbance peak responding to increasing and decreasing humidity at a constant rate of change exhibits a hysteretic characteristic quite similar to sorption isotherms of water in porous glass [11]. Sorption isotherms are traditionally used to characterize porous materials [2,14]. The other feature is the transient white turbidity phenomenon, which is observed in the visible region strongly when porous Vycor glass desorbs wetting fluid or weakly when the glass adsorbs wetting fluid [11]. This white turbidity phenomenon is attributed to Rayleigh scattering caused by the spatial fluctuation (inhomogeneity) of constituent materials within the glass, i.e., the distribution of wetting fluid in the pore space [12]. The strongest scattering was explained in terms of the adjacent pore clusters interconnected by imbibed water. Water- or air-filled pore clusters, whose dimensions are almost the same order of magnitude as light wavelengths, are expected to be highly light scattering.

On the basis of the Rayleigh scattering model [11,12] of the white turbidity phenomenon, we introduced the effective radius of Rayleigh scatterers as a measure of the extent of inhomogeneities that cause the scattering and estimated it to be at most 10 nm. In general, the problem of light scattering can also be approached from Einstein’s fluctuation viewpoint [15,16], apart from the above particle-scattering viewpoint. In the fluctuation approach, the inhomogeneity present in a nanoporous composite (consisting of Vycor and wetting fluid) is generally characterized by introducing pore-space correlation length. On the basis of the theory of dielectric constant fluctuation, we have reported that the correlation length of the interconnected network of drained pores is about twice the above radius, i.e., 20 nm [17]. These findings imply that the optical inhomogeneity due to the inhomogeneous distribution of water in the pore space can be explained by bridging structures between several water-filled pores and air-filled ones, whose size is characterized by the correlation length. Therefore, by reversing the logical deduction, we can obtain a direct measure of the extent of the inhomogeneous distribution of wetting fluid in pore space by observing the white turbidity phenomenon of nanoporous glass.

We are interested in understanding imbibition and drainage of wetting fluid in porous media as a function of partial saturation. In this work, we analyzed the effect of increasing and decreasing humidity in ambient air on the transparency of Vycor glass with emphasis on its response to the humidity change with or without holding at the maximum constant humidity and its response to the humidity change at various values of maximum humidity.

This paper is organized as follows. The next section briefly describes the transmission measurement system, sample preparation, and procedure in the humidity change experiments. In Section 3.A, we show the effect of the maximum humidity duration on the absorption in the NIR region (or the filling fraction) and the turbidity phenomenon in the Vis region as an example of the data analysis procedure. In Section 3.B, we report the effect of the maximum attained humidity on hysteretic responses of the filling fraction and turbidity phenomenon. In the subsequent subsections, on the basis of these presented experimental data, we offer a possible explanation of the optical hystereses of the transparency change and filling fraction during the humidity change. Finally, Section 4 concludes the paper.

2. EXPERIMENTS

A. Transmission Measurement System

The instrument used in this study was a UV-Vis-NIR spectrophotometer (Shimadzu U-3150) coupled through fiber optics with a remote measurement unit that is embedded in a humidity-controlled thermostatic chamber (TABAI ESPEC Corp. Model PR-2K). The remote measurement unit is optically coupled to the spectrophotometer by silica optical fibers. The humidity-controlled thermostatic chamber is used to precisely and separately control the temperature and humidity of ambient air around the sample according to a program installed beforehand. For the Model PR-2K, the nominal controllable temperature and humidity ranges are $-20–100°\mathrm{C}$ and 20 to 98% relative humidity (RH), respectively, and the corresponding nominal accuracies of controlling temperature and humidity are $\pm 0.3°\mathrm{C}$ and $\pm 2.5\%$ RH, respectively. The temperature and humidity of the air near the sample are monitored by a temperature and humidity sensor that is embedded in the remote measurement unit. The actual accuracy of the temperature monitored around the sample by the embedded sensor is about $\pm 1.1°\mathrm{C}$. Mechanical and operational details of the remote measurement unit during the transmission measurement and details of the transmission measurement system are described in our previous paper (see Fig. 1 in Ref. [11]).

To investigate the effect of the humidity change in the ambient air on the transmission of nanoporous Vycor glass, we use a UV-Vis-NIR spectrophotometer to measure the transmission responses of the nanoporous Vycor glass to the humidity change. With this system, we can easily change the span and rate of the humidity change at a constant temperature and the scan speed of the transmission measurement. In this paper, we report mainly the data for a constant rate of humidity change of $(80–20)/600(=0.1)$ % RH/min.

The humidity inside the chamber was kept as low as 20% RH for more than 4 h before a porous glass sample was inserted into the sample holder of the remote measurement unit, and it was kept there for two more hours after insertion to dry the porous glass sufficiently before the humidity change experiment started.

B. Sample Preparation

We used 1-mm-thick Vycor 7930 porous glass slabs cut into 8-mm square pieces. The average diameter of pores in the glass was nominally reported to be 4.2 nm, with a vacancy ratio of 28% and a specific area of about $200{\mathrm{m}}^2/\mathrm{g}$. These values of pore diameter and specific area were verified by measuring low-temperature ${\mathrm{N}}_2$ sorption isotherms, as previously reported in Ref. [12]. All porous glasses tend to yellow over time when exposed to free air because they absorb organic contaminants in their pores. To remove the influence of these organic contaminants on the light transmission experiments, all of our porous glass samples were chemically cleaned with acetone (99.8%), ethanol (99.5%), 1% hydrofluoric acid (HF) solution, and ultrapure water (18 MΩ⋅cm). After the cleaning, they were dried for 6 h in a desiccator with flowing dry nitrogen gas. Details of the cleaning procedures are described in Refs [11,12].

After these preparations, a glass chip was set into the sample holder in the remote measurement unit within the humidity-controlled and thermostatic chamber.

C. Procedure of Humidity Change Experiments

In this work, we investigated systematically the optical responses of Vycor glass to the humidity change with or without holding at the maximum constant humidity and to the humidity change up to various values of maximum humidity.

As a basic outline for the controlled-humidity-change experiments, Fig. 1 shows the measured change of relative humidity with or without holding at the maximum constant humidity near the sample in the chamber and the pore-filling fraction, which is converted from the absorbance response at around the wavelength of 1900 nm. The pore-filling fraction will be explained in the next subsection. Before sample insertion into the holder of the remote measurement unit inside the chamber, the chamber’s temperature was always set to a constant value of 25°C (298 K) and its relative humidity was initially set to a constant value of 20% RH. After the sample had been inserted into the holder (time 0 in Fig. 1), the controller’s timer started. The sample inside the chamber was exposed to ambient air with relative humidity of 20% RH for 2 h (from time 0–120 min) to drain the water within the porous glass sample sufficiently. Then (2 h later at 120 min), the humidity inside the chamber was gradually increased at the rate of $(80–20)/600(=0.1)$ % RH/min up to the maximum of 80% RH (from 120 to 720 min, in Fig. 1). Here, two humidity changing patterns are presented. Solid diamonds with a solid line show the “Hm duration” (with maximum humidity duration) pattern in which the humidity inside the chamber was kept at 80% RH for an hour (from 720 to 780 min) and then decreased to 20% RH at the same rate of $-(80–20)/600(=-0.1)$ % RH/min (for 10 h, from 780 to 1380 min in Fig. 1). On the other hand, solid triangles with a solid line show the “Hm nonhold” (without holding the maximum humidity) pattern in which the humidity inside the chamber was immediately decreased to 20% RH at the same rate of $-0.1\%$ RH/min (for 10 h, from 720 to 1320 min in Fig. 1).

 

Fig. 1. Changes in the ambient relative humidity with or without the maximum humidity duration around a porous Vycor glass chip and the corresponding responses of the pore-filling fraction as a function of exposure time in minutes. The pore-filling fraction is estimated from the absorbance peak (${\alpha }_{1900}$) at around a wavelength of 1900 nm, normalized by the initial maximum value measured immediately after the removal from the immersion container [12]. The ambient temperature was set to 25°C (298 K), and its measured value remained constant within $\pm 2°\mathrm{C}$ while the humidity was changed.

Download Full Size | PDF

The ambient humidity and temperature within the chamber were monitored by the built-in humidity and temperature sensors embedded in the chamber to control their values. In addition to these embedded sensors, the humidity and temperature near the porous glass sample were also monitored simultaneously by a humidity and temperature sensor (Vaisala’s HMP233 transmitter), and their measured values were recorded by the controller. Only the humidity values are shown in Fig. 1 by the solid diamonds (Hm duration) and triangles (Hm nonhold). As shown in Fig. 1, the relative humidity of the chamber was kept at 20% RH for the first 2 h. According to the humidity-control program, the relative humidity inside the chamber was precisely controlled to be a value in the range of (20–80) % RH. The maximum humidity in the program was set to 80% RH, but the humidity measured by the HMP233 transmitter deviated a little from 80% RH. This deviation is considered to be due to the holder of the remote measurement unit, which has a structure for enclosing the porous glass sample to avoid stray light from disturbing the transmission measurement.

The corresponding transparency change of the porous Vycor glass was monitored by the spectrophotometer. The transmission and absorption spectra of the sample from 2000 to 300 nm were measured every 15 min immediately after the sample was set into the holder and the controller’s timer started. In the following analysis of these experimental data, we focus on two parts of the spectra: the peak at around 1900 nm and the transmission in the range from 350 to 800 nm.

3. RESULTS AND DISCUSSION

A. Effect of the Maximum Humidity Duration (as Example of Data Analysis Procedure)

The transmission spectrum $T(\lambda )$ of a porous glass chip at a wavelength $\lambda$ in the UV-Vis-NIR region (300–2000 nm) was measured every 15 min during the humidity-change experiments. In our previous studies [11,12], we showed that the transient white turbidity phenomenon can be well-characterized by the following two optical responses: a near-infrared absorption peak and a transparency response in the visible region (350–800 nm).

The absorbance peak at around 1900 nm (which is defined as ${\alpha }_{1900}={\log }_{10}[1/T(\lambda =1900\mathrm{nm})]$) is related to the amount of water inside the porous glass [13], and it exhibits a pronounced hysteresis that seems to be the same as the hysteresis in sorption isotherms for water vapor (see Fig. 6 in Ref. [11]). We consider the absorbance peak at around 1900 nm to be approximately proportional to the amount of water adsorbed on the pore walls in the porous glass [11,12]. The maximum ${\alpha }_{1900}$ is known to be equal to 2.5 [12], which corresponds to the state where all pores are considered to be filled completely with water. The pore-filling fraction (which varies in the range between 0 to 1), starting with unity for the state where all pores are completely filled with water, should be less than unity for the state where the number of partially filled and empty pores increases. On the basis of these observations, the pore-filling fraction ($f$) can be estimated from the absorbance peak as the ratio of ${\alpha }_{1900}$ to ${[{\alpha }_{1900}]}_{\max }$, i.e., $f\equiv {\alpha }_{1900}/{[{\alpha }_{1900}]}_{\max }$.

As shown in Fig. 1, both filling fractions for two humidity changing patterns increase with increasing humidity (from 120 to 720 min). The fraction with the maximum humidity duration (Hm duration) still continues to increase even when the humidity is kept constant (from 720 to 780 min). The fraction without the maximum humidity duration (Hm nohold) also still continues to increase even when the humidity starts to decrease (from 720 to 765 min). Nevertheless, both filling fractions, after temporarily increasing for about 30–45 min, start to decrease when the humidity decreases (from 810 to 1380 min for Hm duration; from 765 to 1320 min for Hm nonhold).

Figure 2 shows the change in the filling fractions as a function of the relative humidity in percent. In Fig. 2, the bottom curves are the filling fraction responses to the increasing humidity and the top curves are those to the decreasing one. The data show typical hysteretic responses of the filling fractions to the humidity change at a constant rate. At a constant humidity of 81% RH, the filling fraction (Hm duration) is observed to increase vertically and gradually. This gradual increase in the filling fraction can be explained by the delayed imbibition of water vapor into pores from the surrounding highly moist air. The delayed imbibition continues until an equilibrium state is achieved at the interface between the ambient air and sample surface. This is because at a constant high humidity the filling fraction approaches its saturated value, which corresponds to the filling fraction equilibrated with that humidity. In this sense, the duration of 1 h at a humidity of 80% RH is considered to be insufficient to equilibrate with that humidity. Furthermore, both initial slight increases (Hm duration and Hm nonhold) in the filling fractions with decreasing humidity imply that the imbibition of water vapor into pores still occurs for about 30–45 min because of the high humidity, in spite of the negative changing rate of humidity. However, thereafter, with decreasing humidity, the water is drained from the bulk of the porous glass through pores directly connected to the surface. The water-air interfaces initially located at the surface gradually move deep inside the porous glass as the drainage proceeds.

 

Fig. 2. Responses of the pore-filling fraction of a porous Vycor glass chip to the relative humidity change between 18 and 81%RH around a Vycor glass chip with and without the maximum humidity duration. The duration makes it possible to imbibe more water vapor into the pores of porous glass, which can be observed as a vertical increase in the filling fraction as compared to that without the duration.

Download Full Size | PDF

The second feature of the transient white turbidity phenomenon is the temporal change in the turbidity in the visible region (350–800).

In general, in terms of the turbidity, at normal incidence, the transmission $T$through a porous glass parallel plate with sample thickness $d$ (in units of μm) is expressed as [18]

In our previous study [11], we analyzed the wavelength dependence of the transitory white turbidity of nanoporous Vycor on the filling and draining of water vapor and showed that the turbidity response to the humidity change is dependent on the inverse fourth power of the wavelength ($1/{\lambda }^4$). From this dependence, the phenomenon can be consistently interpreted and quantitatively analyzed by a simple Rayleigh-type scattering model.

In the particle-scattering approach [19], where we assume that the scatterers are isolated spherical voids of uniform effective radius $r_{\text{sca}}$ embedded in a continuous matrix composed of ${\mathrm{SiO}}_2$, the turbidity $\tau$ is given as the product of the number density $N$ of incoherent Rayleigh scatterers with the scattering cross section $C_{\text{sca}}$ [19] as

On the basis of the above Rayleigh scattering model, the transmission spectrum between 350 and 800 nm is analyzed as a linear function of $1/{\lambda }^4$ and its slope $\beta$ of the turbidity ($\tau$) versus $1/{\lambda }^4$ is obtained as a function of the exposure time.

Figure 3 shows time evolutions of slope $\beta$ and the filling fraction for the humidity change with/without the maximum humidity 1 h duration (Hm duration/Hm nonhold).

 

Fig. 3. Time evolution of slope $\beta$ of turbidity ($\tau$) versus $1/{\lambda }^4$ plots and of the filling fraction estimated from the absorbance peak (${\alpha }_{1900}$) at a wavelength of around 1900 nm for the humidity change with or without the maximum humidity 1-h duration. The maximum humidity duration strongly affects slope $\beta$, which characterizes the turbidity responses with decreasing humidity. With the maximum humidity duration, slope $\beta$ increases remarkably to its maximum with decreasing humidity, while without the maximum humidity duration it increases to a slightly larger value with decreasing humidity. However, the duration of the maximum humidity makes slope $\beta$ relax or decrease, while the immediate change from increasing to decreasing humidity makes it further gradually increase to a rather lower peak.

Download Full Size | PDF

The filling fractions for both humidity changing patterns increase with increasing humidity (between 120 and 720 min). The filling fraction with the maximum humidity duration still continues to increase even when the humidity is kept constant (from 720 to 780 min). The filling fraction without the maximum humidity duration (Hm nonhold) also still continues to increase even when the humidity starts to decrease (from 720 to 765 min). However, both filling fractions, after temporarily increasing for about 30–45 min, start to decrease when the humidity decreases (from 810 to 1380 min for Hm duration; from 765 to 1320 min for Hm nonhold).

For the Hm duration pattern, slope $\beta$ increases with increasing humidity in a way similar to the filling fraction. However, it starts to decrease when the humidity is kept constant, as shown in Fig. 3 (see solid diamonds with a line in the interval between 720 and 780 min). This implies that the inhomogeneous distribution of the imbibed water in the pore space is redistributed uniformly to relax the optical inhomogeneity during constant humidity. With this understanding of slope $\beta$, its initial increase with decreasing humidity until 990 min implies that this humidity change causes the inhomogeneous distribution of drained water in the pore space. After 990 min, there no longer remains sufficient imbibed water to make optical inhomogeneity so that slope $\beta$ starts to decrease rapidly thereafter and then stays constant at a low value.

For the Hm nonhold pattern, the humidity always changes without a constant humidity duration. This implies that there exists no term during which imbibed water can redistribute to relax the spatial inhomogeneity in the pore space. Therefore, slope $\beta$ should increase with increasing humidity because the increasing humidity creates the optical inhomogeneity in the pore space. Furthermore, the gradual increase in slope $\beta$, even with decreasing humidity until 900 min, is a natural conclusion of the evolving inhomogeneous distribution of drained water in the pore space.

The different responses of slope $\beta$ with and without the maximum humidity duration imply that the redistribution of the imbibed water in the pore space and the increasing amount of the imbibed water during the maximum humidity duration strongly affect the subsequent turbidity response.

The direct correlation between slope $\beta$ and the filling fraction $f$ for two different humidity changing patterns is depicted in Fig. 4, which shows explicitly the different responses of slope $\beta$ for these patterns. As previously discussed in Refs. [11,12], the transient white turbidity is caused by the inhomogeneous distribution of the imbibed water within the pore space of porous Vycor glasses, which subsequently causes the Rayleigh scattering of the light emerging from the sample. On the basis of this understanding of the white turbidity phenomenon, the different responses of slope $\beta$ are considered to be due to the different amounts of water within the porous glass. Obviously, the amount of water imbibed into the glass with the maximum humidity duration is much larger than that without it. This is clearly shown in Fig. 3 by the maximum values of the filling fraction, i.e., 0.78 and 0.67 with and without duration, respectively.

 

Fig. 4. Responses of slope $\beta$ in the 350–800 nm range to the humidity change with or without the duration of the maximum constant humidity as a function of the pore-filling fraction $f$. The duration makes the filling fraction exceed a threshold value of 0.6, so that its corresponding slope has the peak value of about $6\times {10}^{-6}[{\mathrm{\mu m}}^3]$. This causes the strong white turbidity with decreasing humidity, as compared to that with the immediate humidity change from increasing to decreasing.

Download Full Size | PDF

On the basis of our Rayleigh scatterer model [11], we can estimate the effective radius $r_{\text{sca}}$ of a Rayleigh scatterer, which is regarded as a measure of the extent of inhomogeneities that cause the scattering. The estimation procedure is as follows: from expression (3), we can plot the turbidity as a linear function of $1/{\lambda }^4$ and, from its proportional constant $\beta$, we obtain the effective radius $r_{\text{sca}}$ with appropriate values of the refractive indices of the scatterer and surrounding medium, i.e., $n_1$ and $n_2$. Here, we need to consider the change in the refractive index of scatterers when the imbibition or drainage of water occurs. Since the refractive indices for water-filled and air-filled pore clusters are considered to be equal to those of water and air, respectively, the refractive index of a Rayleigh scatterer can be estimated by using effective-medium models in which a pore is regarded as a superposition of its components. The most frequently used model is that of Bruggeman [20]. It is assumed in this model that the following formula is valid for pore clusters whose pores are cavities of spherical shape with an effective radius of $r_{\text{sca}}$ that connect with each other,

Figure 5 shows responses of the effective radius to the change in the pore-filling fraction for two humidity changing patterns. The effective radius $r_{\text{sca}}$ naturally exhibits a pronounced hysteretic characteristic similar to slope $\beta$ depicted in Fig. 4 because the radius $r_{\text{sca}}$ is estimated from slope $\beta$ through Eqs. (3) and (4). Both the maximum effective radii (7.59 nm with the maximum humidity duration; 5.68 nm without duration) are observed at around the filling fraction near 0.6. The difference between these radii is obviously caused by the amount of water imbibed into the pore space of porous Vycor glass during the maximum humidity duration.

 

Fig. 5. Scatterer’s effective radii ($r_{\text{sca}}$) as a function of the pore-filling fraction $f$ for increasing and decreasing humidity with and without the duration of the maximum constant humidity. For imbibition, the effective radius of the Rayleigh scatterer changes along almost the same line up to $f=0.65$. The radius, as a measure of the extent of the optical inhomogeneity that causes the scattering, becomes large when the humidity change pattern has the duration of the maximum constant humidity.

Download Full Size | PDF

In a previous study [17], we showed that the effective radius in the particle-scattering picture is about one-half of the correlation length of the pore space correlation, which characterized the optical inhomogeneity of the turbid medium in the fluctuation picture. In other words, the diameter of the Rayleigh scatterer is almost equal to the correlation length that characterizes the optical inhomogeneity of the turbid medium.

In the following, we will repeat the same procedure to show the effect of an experimental parameter to optical responses of the white turbidity phenomenon, i.e., the absorption in the NIR region and the scattering in the Vis region. First, we will show the changing pattern of the experimental parameter, such as Fig. 1; the filling fraction response versus the humidity change (Fig. 2); the corresponding slope responses versus the filling fraction (Fig. 4); and the effective radius responses versus the filling fraction to the experimental parameter (Fig. 5). The parameter is the maximum humidity up to the value that the humidity inside the chamber was controlled to reach.

B. Maximum Humidity Effect on the White Turbidity

In a series of experiments, we studied the effect of maximum attained humidity on the optical responses of the white turbidity phenomenon to increasing and decreasing humidity. In this study, the parameter was the maximum attained humidity, which varied from 20% to 90% RH, while the temperature and the rate of change in humidity were set to constant values of 25°C and $\pm 0.09\%\mathrm{RH}/\min$ (the “+” sign for increasing and “−” for decreasing), respectively.

Figure 6 shows typical measured patterns of changing humidity with various values of maximum attained humidity as the experimental parameter. The starting and ending values of humidity were set to the same value of 20% RH, but the maximum attained humidity was set to 60, 65, 70, 75, 80, 85, and 90% RH. The respective actual values of attained maximum humidity near the sample were measured to be 63.1, 68.7, 72.8, 76.9, 81.5, 86.1, and 88.8% RH by the humidity sensor embedded in the remote measurement unit.

 

Fig. 6. Patterns of increasing, holding, and decreasing humidity around a porous Vycor glass sample with various values of maximum attained humidity (60, 65, 70, 75, 80, 85, and 90) at the same constant rate of $\pm 0.09\%\mathrm{RH}/\min$ in the humidity-controlled thermostatic chamber as a function of exposure time in minutes. The ambient temperature was set to 25°C (298 K), and its measured value remained constant within $\pm 2°\mathrm{C}$ while the humidity was changed.

Download Full Size | PDF

The sample inside the chamber was initially exposed to ambient air of the starting humidity for 2 h to drain the water within the porous glass sample sufficiently. Then, the humidity was gradually increased at the specified rate to arrive at the programmed value of maximum humidity. Thereafter, the humidity was kept to that attained value for 1 h. Finally, the humidity was controlled so that it decreased with the same rate to the ending value of humidity.

With the same rate of humidity change of 0.09% RH/min, it takes a longer time to arrive at the larger values of maximum humidity. In this series of experiments, the ambient temperature was set to a constant value of 25°C (298 K), and its measured value almost remained constant within $\pm 2°\mathrm{C}$ while the humidity was changed, as shown in Fig. 6.

The optical absorption analysis in the NIR region reveals the partially saturated response of the filling fraction of the nanoporous Vycor glass to the humidity change.

Figure 7 shows the change in the filling fractions estimated from the absorbance peaks at around 1900 nm as a function of the relative humidity at various values of the maximum attained humidity. The bottom curves are the filling fraction responses to the increasing humidity and the top curves are those to the decreasing one.

 

Fig. 7. Responses of the pore-filling fraction to the relative humidity change between 18% RH and various values of maximum attained humidity of 60%, 65%, 70%, 75%, 80%, 85%, and 90% RH with the 1-h duration of the corresponding constant maximum humidity. Adsorption branches of the filling fraction response change along almost the same line. The dashed line represents a calculation based on the FHH equation, Eq. (7), for $B_{\mathrm{FHH}}=0.2796$ and $\nu =0.4423$.

Download Full Size | PDF

The data show typical hysteretic responses of the filling fraction to the humidity change at a constant rate. For each of the durations of the constant maximum attained humidity, the filling fraction increases vertically and gradually. These gradual increases in the filling fraction are due to the delayed imbibition of water vapor into the pores from the surrounding highly moist air, which continues until an equilibrium state is achieved at the interface between the ambient air and sample surface. For each of the durations of the constant high humidity, the respective filling fractions approach their saturated values, each of which corresponds to the filling fraction equilibrated with the corresponding constant maximum attained humidity.

As shown in Fig. 7, the greater the value of maximum attained humidity, the more the hysteresis area between the top and bottom curves increases. The optical hysteresis of absorbed water for partially saturated nanoporous Vycor glass exhibits different hysteresis area. This feature is quite different from that of the saturated hysteresis that characterizes sorption isotherms for water vapor in Vycor glass (see Fig. 6 in Ref. [11]). The optical hysteresis area between the top and bottom curves increases exponentially with increasing values of the maximum attained humidity. The pore-filling fraction has been assumed to be proportional to the amount of water adsorbed on pore walls of the porous glass [11,12], the optical hysteresis areas of the filling and draining curves seem to represent a kind of thermodynamic work, since each area is a product of volume ($V$) of adsorbed water and the relative pressure ($P$) of water vapor.

Figure 7 also shows the existence of the threshold value of humidity of about 60% RH below which the filling fraction becomes a simple function of the relative humidity, but above which the fraction exhibits a hysteretic characteristic; i.e., it bifurcates into two branches, an adsorbing branch and a desorbing one.

Note that the bottom curves of the filling fraction are almost the same for all values of the maximum attained humidity at a constant temperature of 298 K and that a universal curve is obtained by fitting the experimental data with the following Frenkel–Halsey–Hill (FHH) isotherm function [23]:

When adsorption isotherm data are expressed as a function of the adsorption potential $A$, the result is roughly humidity-independent for filling fractions below the hysteresis loop, as shown in Fig. 8. Capillary condensation in mesopores necessarily restricts the range of linearity of the FHH plot and tends to reduce the value of the exponent $\nu$. As shown in Fig. 8, the characteristic adsorption curve concept does not work for filling fractions at which hysteresis sets in, that is, in the region of capillary condensation. Fig. 8 shows that the best fits of the FHH equation [Eq. (7)] are obtained for $B_{\mathrm{FHH}}=8.8927$ and $\nu =0.4423$ for water vapor.

 

Fig. 8. Characteristic adsorption and desorption branches of the filling fraction of water on a porous Vycor glass as a function of the adsorption potential defined as $A=RT\ln (100/H)$. The solid line represents a calculation based on the FHH equation for $B_{\mathrm{FHH}}^{\prime }=8.8927$ and $\nu =0.4423$. The value of $B_{\mathrm{FHH}}^{\prime }$ is different from that of $B_{\mathrm{FHH}}$ because the abscissa represents the adsorption potential including the factor $RT$, whereas the abscissa of Fig. 7 lacks that factor.

Download Full Size | PDF

According to Refs. [23,24], the fractal form of the FHH equation [Eq. (7)] can be obtained with $\nu =3-d$: $f_{\text{adsorption}}(A)=B_{\mathrm{FHH}}·A^{-(3-d)}$, where $d$ is the fractal dimension. From the fit of Eq. (7) to our intermediate filling fraction data, an average value of $\nu =0.4423\pm 0.004$ is obtained for water vapor. From the value of the exponent, we found that the fractal dimension of the pore distribution of porous Vycor glass is $d=2.5577\pm 0.004$. In investigations of $d$ by other methods, such as laser light scattering, almost the same value of the fractal dimension of 2.6 has been observed [15,16].

The light scattering analysis in the Vis region reveals another feature of the partially saturated response of the white turbidity, i.e., slope $\beta$ versus the filling fraction of the nanoporous Vycor glass to the humidity change with various values of maximum attained humidity.

Figure 9 shows the effect of the maximum attained humidity on the turbidity response to the humidity change, i.e., slope $\beta$ versus the filling fraction curves. If the maximum humidity exceeds a threshold value of about 60% RH in the adsorption branch, the larger the maximum humidity is, the higher the peak value of slope $\beta$ is observed at about $f=0.6$ with a decreasing fraction. If the humidity varies in the range of less than 60% RH in both adsorption and desorption, the white turbidity becomes negligibly small. This implies that the optical hysteresis of the transient turbidity in the visible region is strongly affected by the maximum attained humidity above the threshold of the absorption branch. As shown in Fig. 7, along the absorption branch the humidity of 60% RH corresponds to the filling fraction of about 0.4. In terms of the filling fraction, correspondingly, there exists the threshold of about 0.4 in addition to another threshold of about 0.6. In this $f$ range between 0.4 and 0.6, capillary condensation takes place, which is just a crossover state between the entire filling ($f=1$) and adsorbed layer film ($f\le 0.4$) regime. In the adsorbed layer film range, which corresponds to a maximum humidity less than the threshold of 60% RH in the adsorption branch, slope β does not bifurcate into two branches. This result is quite reasonable because the white turbidity phenomenon is caused by the optical inhomogeneity of water distribution within the pore space of Vycor glass in the state of capillary condensation. The inhomogeneity becomes large with an increasing maximum amount of water within the pore space.

 

Fig. 9. Responses of slope $\beta$ in the 350–800 nm range as a function of the pore-filling fraction $f$ to the humidity change with various values of maximum attained humidity. The maximum attained humidity changes the corresponding values of the maximum fractional filling $f$ of water in Vycor, which subsequently determines the corresponding slope $\beta$ as another optical hysteresis of the transient white turbidity. The larger the maximum filling fraction, the higher the peak value of slope $\beta$ at about $f=0.6$ with decreasing filling fraction. Maximum filling fractions between 0.5 and 0.6 can create only weak white turbidity.

Download Full Size | PDF

Correspondingly, Fig. 10 shows the effective radius of Rayleigh scatterers in the pore space as a function of the pore-filling fraction. In this figure, the radius should be interpreted as a measure of the extent of optical inhomogeneity caused by nonuniform and nonequilibrium distribution of the imbibed water in the pores. In the adsorbed layer film regime ($f\le 0.4$), the radius seems to be a simple linear function of the filling fraction. However, in the capillary condensation regime ($f\ge 0.6$), the higher the maximum humidity is, the larger the effective radius becomes. This means that during the drainage of water, the long-range capillary bridges inside the pores extend over at most 10 nm (or in terms of the correlation length, over about 20 nm), which subsequently constructs large-scale spatial inhomogeneities comparable to the wavelength of the incident light and then causes the strong light scattering during the drainage of wetting fluid.

 

Fig. 10. Responses of the scatterer’s effective radius ($r_{\text{sca}}$) as a function of the pore-filling fraction $f$ to the humidity change with various values of maximum attained humidity. For all adsorptions, all effective radii of Rayleigh scatterers trace on the same universal line up to $f=0.65$, whereas the effective radii exhibit the larger peak at about $f=0.6$, the more the attained filling fraction exceeds the threshold at about $f=0.6$. The maximum filling fraction is determined by the corresponding maximum attained humidity. There exists another threshold at about $f=0.4$ below which the radii are converged to a simple function of fraction $f$.

Download Full Size | PDF

4. CONCLUSION

In this paper, we optically studied the imbibition and drainage of water in nanoporous Vycor glass by using a spectrophotometer. The light scattering and absorption of monolithic nanoporous Vycor glass during periods of increasing and decreasing humidity, or during water imbibition and drainage, exhibit the following two optical hysteretic characteristics: a hysteretic response of the absorbance peak in the NIR region and transient white turbidity in the visible region. The former is caused by adsorbed water on pore walls and is quite similar to sorption isotherms of water in porous glass. The latter is another type of hysteretic response of the transmission in the visible region observed in nanoporous Vycor glass that is caused by the optical inhomogeneities due to the nonuniform distribution of the imbibed wetting fluid in the pore space.

An analysis of hysteresis loops that appear in the absorbance (or filling fraction) responses to the humidity change reveals that the maximum humidity duration and the maximum values of the attained humidity strongly affect the imbibition and drainage of water in pores of porous glass. This is because the duration of the maximum constant humidity and the maximum values of the attained humidity determine the amount of the imbibed water in the pore space, which subsequently determines the hysteresis area of the filling fraction. This is quite different from the sorption isotherms of water adsorbed on porous Vycor glass since the hysteresis area of sorption isotherms seems to be invariable.

The white turbidity responses in the visible region to the humidity change are also strongly affected by the duration of the maximum constant humidity and the maximum values of the attained humidity. This implies that the amount of the imbibed water and its inhomogeneous distribution in the pore space of porous glass determines the transmission responses to the humidity change. An effective radius analysis reveals that as the maximum humidity becomes higher, the greater the radius, but there exists a threshold value of the pore-filling fraction, i.e., $f\approx 0.4$. Below this threshold, the effective radius slightly increases with the response to the filling-fraction increase. The maximum of the effective radius is observed at the filling fraction of about 0.6 along each of desorption curves. In this $f$ range capillary condensation approximately takes place, which is just a crossover state between the entire filling ($f=1$) and adsorbed layer film ($f\le 0.4$) regime.

It should be noted that the white turbidity is caused by the optical inhomogeneity due to the nonuniform distribution of the imbibed water in the pore space and that during the constant humidity period, the imbibed water is redistributed to relax the nonuniformity so that the turbidity is reduced during this period. In this sense, the turbidity analysis can be used to characterize the uniformity of distribution of wetting fluid in the pore space of porous glass.

Finally, it is worth mentioning the difference between our experiments and those by Soprunyuk and co-workers [25–27]. They observed that quite similar scattering phenomena also occur during capillary sublimation, upon freezing and melting or, generally speaking, during phase transitions of molecular liquids and solids in nanoporous Vycor. Notably, they reported almost the same optical transmission as a function of the filling fraction as in our Figs. 4 and 9 (cf. Fig. 2 in [25]; Figs. 4 and 5 in [26]), although they measured the optical transmission at a single wavelength of a He-Ne laser beam (${\lambda }_0=623.8\mathrm{nm}$) and the filling fraction extracted from isothermal sorption curves at various temperatures.

In our experiments, the parameters to control were the presence of the duration of the maximum constant humidity and the maximum values of the attained humidity, both of which determine the amount of water in the pore space of porous material. The amount of water determines the range of inhomogeneous distribution of the imbibed water and subsequently affects decisively the optical responses in the visible region. Whole measurements were performed isothermally. In other words, imbibition and drainage of a wetting fluid at its controlled amount determine the subsequent optical response to the humidity change.

On the other hand, the experimental parameter in the study by Soprunyuk and co-workers was temperature. In that meaning, strictly speaking, their hysteretic curves are not isotherms. They used the thermal cycle to control the filling fraction; i.e., they had to change the temperature to control the vapor pressure of adsorbents in the pore space of porous materials. This makes their obtained data more difficult to analyze on the basis of sorption isotherms. However, it also makes it easier to focus on the phase change of adsorbents inside the pore space.

On the basis of this understanding, the difference can be summarized as follows. They observed a kind of white turbidity phenomena as an inhomogeneous distribution of vaporized adsorbents caused by the effect of temperature, while we observed the same phenomena as an inhomogeneous distribution of the imbibed water continuously disturbed by changing the humidity, i.e., the effect of the unequilibrated amount of the imbibed water.