Porous Vycor glass with nanopores is transparent in the visible region and is often used in colorimetric chemical sensing when impregnated with selectively reacting reagents. However, it has some disadvantages in sensing, since changes in the humidity of ambient air strongly affect its transmission. In this work, by combining a humidity-controlled thermostatic chamber and an ultraviolet–visible and near-infrared spectrophotometer through fiber optics, we analyzed the effect of increasing and decreasing humidity in the ambient air on the transparency change of the nanoporous glass. The transparency response in the visible region to changes in humidity is analyzed to correlate the turbidity response of the glass with the amount of water in it. The turbidity is found to be dependent on the inverse fourth power of the wavelength (), which implies that Rayleigh-type scattering takes place for both adsorption and desorption of water. We show that measures of the extent of the optical inhomogeneity that causes the scattering, such as the effective radius of scatterers and their number density, exhibit a pronounced hysteretic characteristic for the imbibition and drainage of water, while the absorption inherent to imbibed water also shows another type of hysteresis that is quite similar to the sorption isotherms of water. On the basis of the above observations, we show that the transitory white turbidity of nanoporous glasses during changes in humidity can be consistently interpreted and quantitatively analyzed by a simple Rayleigh scattering mechanism.
© 2013 Optical Society of America
Porous Vycor glass with nanopores is used as the base material for irreversible chemical sensors, such as nitrogen dioxide () sensor elements [1,2], ozone () sensor elements , and formaldehyde sensor elements [4,5], acting as the stage for gas sensitive reagents. Porous glasses with pore size of less than 20 nm are transparent to visible light and have a relatively large specific surface area of about . These properties of porous glass make it possible to apply them for sensing. Optical methods  have an advantage over conventional ones in that they can distinguish gas species by chemically detecting the inherent optical absorption.
Unfortunately, porous Vycor glasses also absorb ambient water vapor in high-humidity environments, and rapid changes in humidity cause severe changes in their transparency. This transparency change in porous glasses with nanopores decreases the accuracy of the sensed concentration of the gases from humid ambient air, i.e., it strongly affects the photodetection application to gas sensing [7,8]. The transparency change is mostly observed during the evaporation process from a high-humidity state to a low-humidity state in ambient air and is marked by the appearance of transitory white turbidity in porous glass slabs. The glass seems to adsorb and desorb water vapor differently, and this difference in adsorption and desorption processes has been empirically found to cause a hysteresis in an estimated concentration of the detected gas . This nonlinear response of the transparency to the change in the humidity of ambient air makes it difficult to estimate the gas concentration from its inherent optical absorption.
In a previous paper , we analyzed the wavelength dependence of the transitory white turbidity during the drying process and found that the turbidity obeys the inverse of the fourth power of wavelength (). This dependence implies that the transitory white turbidity phenomenon observed during the drying process can be well explained by Rayleigh scattering due to the inhomogeneity of the distribution of a wetting fluid (such as water) within the pore space of porous Vycor glass. The previous paper reported only the effect of evaporating water from the surface of Vycor glass with nanopores on the transmission in a drying-after-dipping experiment. To clarify the effect of wetting the pores of porous glass on its optical transmission characteristics, the optical transmission has to be measured when the ambient humidity is increased.
In this work, we analyzed the effect of increasing and decreasing humidity in ambient air on the transparency of Vycor glass by combining a humidity-controlled thermostatic chamber with an ultraviolet–visible–near-infrared (UV–Vis–NIR) spectrophotometer through a fiber optics system. In the humidity-controlled thermostatic chamber, the amount of water vapor is precisely controlled by changing the ambient-air humidity at a constant temperature. Correspondingly, the transparency change of porous Vycor glass is simultaneously monitored by the spectrophotometer.
This paper is organized as follows: the next section describes the transmission measurement system and sample preparation. In Section 3.A, we show the measured transmission changes of porous Vycor glass in response to changes in humidity to determine the wavelength dependence of the transmission. In Section 3.B, we describe the relationship between the absorbance peak and water filling fraction and compare the optical absorption response to the humidity change with the water vapor sorption curves. In Section 3.C, we analyze the time dependence of the amount of water and the turbidity change during adsorption and desorption of water vapor to assess the correlation between the turbidity and the amount of water in the pores. In the subsequent several subsections, on the basis of these presented experimental data, we offer a possible explanation of the optical hysteresis of the transparency change during the humidity change. Finally, Section 4 concludes the paper.
A. Transmission Measurement System
To investigate the effect of the humidity change in the ambient air on the transmission of porous Vycor glass, we combined an UV–Vis–NIR spectrophotometer with a humidity-controlled thermostatic chamber, in which the temperature and humidity of ambient air are precisely controlled according to a program installed beforehand. The transmission measurement system is shown in Fig. 1. It comprises the UV–Vis–NIR spectrophotometer (Shimadzu U-3500) with a remote measurement unit embedded in a temperature and humidity chamber (TABAI ESPEC Corp. Model PR-2KP).
The remote measurement unit consists of a sliding sample holder connected to a stepping motor, fiber optics, such as collimators and optical fiber connectors, and a temperature and humidity sensor. As illustrated in Fig. 1, the sliding sample holder can be set in two positions, one for measuring the reference light beam and the other for measuring the light beam transmitted from the sample. There are two small apertures in the holder, and a porous glass sample is set in front of one of them. A piston-crank mechanism driven by the stepping motor shuttles the holder along the linear guide-rail through. In the mode for measuring the reference light beam, the light beam travels through the aperture as shown in Fig. 1(a), and the reference light intensity is measured by the spectrophotometer. In the mode for measuring the transmitted light beam, the light beam emitted from the incident collimator travels through the sample porous glass as shown in Fig. 1(b), and the intensity of the beam emerging from the sample, , is measured. The transmission spectrum of the sample at a wavelength can be computed numerically according to . Thus, we have to scan twice across the wavelength range for each spectroscopic measurement, while the holder is set at the position in Fig. 1(a) and then at the position in Fig. 1(b). The temperature and humidity of the air near the sample are monitored by the temperature and humidity sensor, which is embedded in the remote measurement unit. A connecting silica fiber transparent in the UV–Vis light range (from 100 to 1200 nm) and NIR range around 1900 nm, except for the intense overtone absorption of the light around the wavelength of around 1380 nm, was chosen because of the intrinsic hydroxyl ion concentration within the fiber glass .
The humidity-controlled thermostatic chamber is used to adjust the temperature at constant and humidity as a variable. The chamber contains a fan (not shown in Fig. 1) to agitate the air, and the air temperature in the chamber is controlled to be constant at 25°C within . Humidity in the chamber is controlled by an adjustable heater element on an evaporator coil. The chamber atmosphere is stirred constantly by the fan, which enables the relative humidity to be maintained within about 2 %RH for the range from 20 to 90 %RH. The rate of the humidity change is set to about 0.1 %RH/min in the range from 20 to 80 %RH to keep the humidity change quite small during the transmission measurement. While the sample holder is in the chamber, the response of the optical transmission of the Vycor glass to the humidity change is monitored by the UV–Vis–NIR spectrophotometer, which is coupled to the holder by optical fibers.
With this system, we can easily change the span and rate of the humidity change, the temperature to be controlled, and the scan speed of the transmission measurement. In this paper, we report mainly the data for a constant temperature of 25°C, a humidity range of (20–80) %RH and a humidity change rate of .
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 and kept there for two more hours 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, with an average nominal pore-diameter of 4.2 nm, cut into chips.
All porous glasses tend to yellow over time when exposed to free air because they absorb organic contaminants into 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%), and ultrapure water (). The procedure was as follows: all samples were first immersed in acetone for 10 min in a test tube, which was then immersed in the water-filled container of a supersonic cleaner. This step was repeated three times in fresh acetone after each cleaning. The samples were then rinsed with ultrapure water and immersed in ethanol in another test tube for 10 min in the supersonic cleaner. This step was also repeated three times. The samples were again rinsed with ultrapure water and immersed in ultrapure water for 10 min three times to eliminate all traces of ethanol.
Next, all samples were immersed in 1% hydrofluoric acid (HF) solution for 1 min in a Teflon container for chemical etching. (This step yields optically transparent porous glass even after heating in a vacuum at about 450°C.) They were then rinsed and immersed in flowing ultrapure water for 20 min to eliminate all traces of HF. They were dried for 6 h in a desiccator with flowing dry nitrogen gas.
The specific surface and the mean size of the porous glass pores were experimentally determined by using an automatic gas adsorption apparatus (BELSORP-mx, BEL Japan, Inc.), which measures the adsorption of nitrogen into the porous glass. Then, from the adsorption curve, the pore size distribution was analyzed by using the Dollimore and Heal method . The adsorption isotherm was measured on porous glass chips that had been vacuum-heated at about 450°C for 6 h prior to the measurements. The sorption isotherms of water vapor into the porous glass were also measured with the same gas adsorption apparatus.
After these preparations, a glass chip was set into the sliding holder within the humidity-controlled and thermostatic chamber.
As a basic outline for the controlled-humidity-change experiment, Fig. 2 shows the measured change of relative humidity near the sample in the chamber and the absorbance response at around the wavelength of 1900 nm. The latter (absorbance change) will be explained in detail later. Before sample insertion into the holder inside the chamber, the chamber’s temperature was always set to a constant value of 25°C 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. 2), 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 to 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 up to the maximum of 80 %RH (from 120 to 720 min, in Fig. 2) and kept at 80 %RH for an hour (from 720 to 780 min). Subsequently, it was decreased to 20 %RH at the same rate of (for 10 h, from 780 to 1380 min in Fig. 2).
The ambient humidity and temperature within the chamber were monitored by the built-in humidity and temperature sensors (not shown in Fig. 1) embedded in the chamber to control their values. In addition to these embedded sensors, the humidity and temperature near a porous glass sample were also monitored simultaneously by the humidity and temperature sensor mentioned earlier (Vaisala’s HMP233 transmitter), and their measured values were recorded by the control PC. Only humidity values of these are shown in Fig. 2 by solid diamonds with a solid line. The sensor was installed close to the sample inside the holder (see Fig. 1). As shown in Fig. 2, 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 equal the value in the range of (20–80) %RH. The maximum humidity in the program was set to 80 %RH, but the measured humidity by the HMP233 transmitter shows that its value deviated a little from 80 %RH. This deviation is considered to be due to the holder, which has a structure for enclosing the porous glass sample to avoid the 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 300 to 800 nm.
3. RESULTS AND DISCUSSION
A. Transmission Spectra and Their Wavelength Dependence
The time-dependent changes in the transmission spectrum of a porous glass chip in the UV–Vis–NIR region (300–2000 nm) with increasing and decreasing humidity are shown in Figs. 3(a) and 3(b), respectively. The transmission curves were measured every 15 min during the humidity-change experiments. However, in Fig. 3(a), only six selected curves with increasing humidity (curves 1 to 6, every 120 min) and two curves (curves 7 and 8) at the constant high-humidity stage are depicted. In a similar manner, in Fig. 3(b), only the curves with pronounced changes in the visible transmission spectrum are selectively depicted, i.e., curves 10 and 11 as the starting curves, 12 at 150 min, and 13 at 225 min from the starting time to decrease the humidity. The transmission spectra around the wavelength of 1400 nm are not shown in either Fig. 3(a) or Fig. 3(b) because of the strong attenuation due to the fiber optics  connecting the spectrophotometer and sample holder set inside the humidity chamber.
With increasing humidity, the transmission in the visible region between 300 and 800 nm, as well as the transmission at about 1900 nm, is gradually decreased. The absorption peak near 1900 nm is attributed to the absorption of water or the presence of an outer hydroxyl group in the pores . The monotonic increase in the absorption peak at 1900 nm implies the amount of water inside the porous glass also increases as time passes to increase humidity [see Fig. 3(a)].
Even when the humidity reached its maximum value at 720 min and thereafter stopped changing, the transmission at around 1900 nm still continued to decrease (curves 7 and 8), while the transmission in the visible range began to increase.
On the other hand, with decreasing humidity, as shown in Fig. 3(b), the transmission at around 1900 nm increases with time (see curves 10 to 18), while the transmission in the visible region from 300 to 800 nm is initially large (i.e., curves 10 and 11), then becomes small (curves 12 and 13), and finally recovers gradually toward the original transmission (curves 13 to 16) and even more than the original one (curves 17 and 18). This transmission change corresponds exactly to the phenomenological appearance of the sample during the drying process: the sample is initially transparent, becomes opaque, and gradually recovers its transparency sufficiently with decreasing humidity.
We then examined the wavelength dependence of the transmission change in the visible region (350–800 nm). In general, at normal incidence, the transmission through a porous glass parallel plate with sample thickness (in units of ) is expressed as1), is the reflectance of a single interface between air and porous glass and is given for normal incidence by
According to our previous study , the transparency change in the visible region (350–800 nm) can be consistently interpreted and quantitatively analyzed by a simple Rayleigh scattering mechanism through the turbidity . The nominal pore diameter is known to be about 4.2 nm, which is so small compared to the wavelength of the incident light (ranging from 350 to 800 nm) that we may assume that these pores act as Rayleigh scatterers [9,13] and their shape has no effect on the light scattering . Since these pores are considered to be randomly distributed in porous glasses, the scattering is incoherent so that the scattering intensity per unit volume of the medium is the sum of the effect from each individual scattering center. Let the number of scatterers per unit volume be and the scattering cross section of a single scatterer be . Turbidity can then be expressed as · . For a Rayleigh scatterer, the scattering cross section is given as 4) for , which satisfies the condition , we obtain the reflectance of a single interface as
On the basis of the above consideration, the transmission profile between 350 and 800 nm is replotted as a linear function of in Fig. 4(a) for increasing humidity and Fig. 4(b) for decreasing humidity, which show the common logarithm of the transmission as a function of the inverse fourth power of the wavelength in the medium. The linear range covered from 350 to 800 nm. The linearity in both Figs. 4(a) and 4(b) implies that the opalescence of the porous glass during the humidity change can be well explained by the Rayleigh scatterer model [9,13,14]. At present, the slight deviation from linearity cannot be explained exactly by this simple scattering model only. This slight deviation may be due to multiple scatterings, which are no doubt occurring. In Figs. 4(a) and 4(b), each line has a label that contains information about not only the imbibition or drainage time but also about the filling fraction (described in detail later) as extracted from the absorbance peak at around 1900 nm. Thus, Figs. 4(a) and 4(b) also indicate how the wavelength scaling depends on the filling fraction.
B. Absorbance Peak at around 1900 nm and Water Filling Fraction
The transmission peak at around 1900 nm can be converted to the absorbance peak, which is defined as . As shown in Fig. 2, the absorbance peak changes with changes in humidity, except for the increase in the peak during constant humidity. This indicates the peak is related to the amount of water inside the porous glass , i.e., a reasonable explanation of this change in is the change in the amount of water in pore space within the porous glass, which is responding to the ambient humidity change. Assuming that the Beer–Lambert law still holds quantitatively for a system of a wetting fluid such as water in a porous glass, 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. The maximum is known to be equal to 2.5 , which corresponds to the state where all pores are considered to be occupied completely with water. The pore filling fraction (which varies in the range between 0 and 1) should be less than unity for the state where the number of partially filled and empty pores increases, starting with unity for the state where all pores are completely filled with water. On the basis of these observations, the pore filling fraction () can be estimated from the absorbance peak as the ratio of to , i.e., .
Figure 5 shows the change in the absorbance peak at around 1900 nm or the filling fraction as a function of the relative humidity in percent. In Fig. 5, the bottom curve is the absorbance response to the increasing humidity and the top curve is that to the decreasing one. The data show a typical hysteretic response of the absorbance peak at around 1900 nm to the humidity change at a constant rate. At a constant humidity of 81 %RH, the absorbance peak is observed to increase vertically and gradually. This gradual increase in the peak can be explained by the delayed imbibition of water vapor into 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. This is because at a constant high humidity the absorbance peak approaches its saturated value, which corresponds to the absorbance value equilibrated with that humidity. In this sense, the duration of 1 h at a humidity of 80 %RH is considered to be not sufficient to equilibrate with that humidity. The initial slight increase in the peak with decreasing humidity implies that the imbibition of water vapor into pores still occurs for about 30 min due to the high humidity, in spite of the negative changing rate of humidity. However, thereafter, with decreasing humidity, the water is drained from the surface into the bulk of the porous glass through some pores directly connected to the surface.
To see whether there is a correlation between the absorbance peak at around 1900 nm and the water in the porous glass, we determined the sorption isotherms volumetrically using an automatic gas adsorption manometry  apparatus (BELSORP) with the same sample used in the light-scattering measurements. Figure 6 shows the volumetric sorption isotherms for water vapor at 298 K, the solid diamonds are obtained for filling, while the open squares are obtained for drainage. The horizontal axis shows the ratio of the pressure to the saturated pressure of the gas at 298 K. This sorption isotherm exhibits a pronounced hysteresis, which seems to be the same as the hysteresis in the absorbance peak shown in Fig. 5. In our previous paper , we presented the volumetric sorption isotherms of the same Vycor glass for nitrogen gas at 77 K, which showed the typical hysteretic characteristic of mesoporous materials (i.e., adsorbents having effective pore diameters in the approximate range of 2–50 nm ).
C. Data Analysis Based on Rayleigh Scattering Model
1. Time-Dependent Behavior of
On the basis of the aforementioned Rayleigh scattering model [9,14], the data depicted in Figs. 3 and 4 are reconstructed in terms of slope and filling fraction estimated from the absorbance peak () at around 1900 nm, and they are plotted as a function of time passed in Fig. 7.
The filling fraction increases with increasing humidity (between 120 and 720 min), and it still continues to increase even when the humidity is kept constant (from 720 to 780 min). However, the filling fraction, after a slight increase, starts to decrease when the humidity decreases (from 780 to 1380 min).
Slope 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. 7 (see the interval between 720 and 780 min). Furthermore, as the humidity decreases, it initially increases until 990 min and then starts to decrease rapidly thereafter, and stays to be constant. This time dependence of the slope change with decreasing humidity exactly corresponds to the time sequence of the phenomenological appearance of the Vycor sample during the drying process, i.e., initially transparent, then transitory whitish when it scatters light, and finally transparent again.
2. Humidity-Dependent Behavior of
Figure 8 shows direct responses of slope to the humidity change at a constant rate. Although the slope also shows a marked hysteretic characteristic, its hysteresis is quite different from that of the filling fraction (see Fig. 5). During the humidity increase up to 81 %RH, slope remains almost constant until the humidity reaches 55 %RH, and after the humidity exceeds 55 %RH, it increases a little gradually up to the second largest peak of . In contrast to the gradual increase in the filling fraction at the constant humidity of about 81 %RH, the slope decreases gradually to the value of . Furthermore, with decreasing humidity, the responding slope initially increases up to the maximum value and then decreases steeply to almost its initial value for the humidity of less than 45 %RH. The slight increase in slope means that the transparency hardly changes with increasing humidity. In contrast, with decreasing humidity, the transparency of the porous glass slab changes markedly, i.e., initially it is transparent, and then becomes opaque and white turbid and finally recovers its original transparency rapidly. This change in the slope is directly related to the phenomenological change in the transitory turbidity of the porous glass with decreasing humidity. This nonlinear response of slope to the humidity change causes the severe interference problem in the sensory application of Vycor glass to the optical detection.
3. Correlation between and
The direct correlation between slope and filling fraction is shown in Fig. 9. In this figure, for the sake of comparison, the previous result for the drying-after-dipping experiment  is also shown. In the previous experiment , the amount of water inside the porous glass was considered to be maximum because all pores were filled by immersing the glass chip into water. On the other hand, in this experiment the amount water within the glass was not sufficient to completely fill all of the pores because it was supplied from the water vapor of the humidity of 81 %RH at most in the humidity-controlled thermostatic chamber. Figure 9 directly shows the hysteretic response of slope to the filling fraction change. The slope change with increasing filling fraction is limited to the range from to , while that with decreasing humidity spans in the range from to .
A comparison of the present data to the previous data indicates that the span of the slope change is narrower than the previous one. This can be reasonably explained by the difference in the maximum amount of water imbibed in the pores, i.e., the amount of water in this experiment was not sufficient to fill all pores in the porous glass. The maximum of the absorbance peak at around 1900 nm in this experiment was about 1.96 (see Fig. 2), which is smaller than the previous value (i.e., 2.43 ). In addition, notice that slope has such a small value of even though the filling fraction is about 0.78, which means that about 80% of all pores are filled with water but the remaining 20% are empty. The comparison also shows that the maxima of both slopes on desorption are observed at almost the same filling fraction value of about 0.6. Furthermore, both slopes tend to approach almost the same curve for the filling fraction of less than 0.45. At present, however, we have not verified that the curve is universal for all desorption branches with the filling fraction of less than 0.45.
D. Optical Inhomogeneity and Transmission Changes
In the previous study on light scattering during the drying process , we attributed the transitory white turbidity phenomenon of nanoporous glass to Rayleigh scattering caused by the spatial fluctuation (inhomogeneity) of constituent materials within the glass, i.e., the water distribution in the pore space [16,17]. The strongest scattering was explained in terms of the adjacent interconnected pore cluster model [18–20] based on a simple percolation theory . The important element of this model is the presence of water- or air-filled pore clusters, whose dimensions are the same order of magnitude as light and therefore expected to be highly light scattering.
In general, optically nonabsorbing glasses in the visible region are transparent when they are structurally homogeneous and compositionally uniform at least up to the same order of magnitude of the visible light scale . This is because inhomogeneity on a sale of much smaller than the wavelength of visible light leads to insignificant light scattering. In contrast, structures comparable to the visible light scale lead to intense scattering of light.
According to the above understanding, for desorption, it is natural that the strongest scattering occurs when the filling fraction is approximately 0.6. In this state, the system is in the capillary evaporation regime, and large empty and filled pore clusters are present in the pore space. On the other hand, for the completely filled state (corresponding to ) and completely empty state (corresponding to ), there are no such large-scale structures present. Therefore, the scattering caused by this kind of inhomogeneity is quite small. Nonetheless, the existence of the small even at forces us to take into account the intermediate state where all pores are partially filled (for example, in the form of water film on the pore walls) and uniformly distributed on a scale comparable to the visible light, or there is a uniformly distributed (or homogeneous) mixture of empty and filled pores with a specified filling fraction on a scale comparable to the wavelength of visible light. Without such spatial homogeneity or uniformity, we can not explain the small at a partial filling fraction much less than unity.
On the basis of the above understanding, for desorption, it is clear that all pores are initially in the aforementioned intermediate state (or film-condensed state) and they constitute a single interconnected network of partially filled pores. However, the distribution of water film in the linked pore space is uniform and the scattering due to inhomogeneity is therefore quite small. Since water evaporates from the sample surface, only some of the pores, those directly connected to the surface, are fully emptied and thus the number of connections of drained pores increases with time, causing large-scale spatial inhomogeneities. These emptied pockets can cause scattering, making a drying Vycor glass appear translucent or even white and opaque, even though individual pores are much too small to cause scattering. In the process, the water is drained from the bulk of the porous glass to its surface where evaporation occurs. As a result, the drying-front surface moves toward the inside of the bulk along linked pores, which are connected to the surface [19,20]. Inhomogeneity occurring at such a drying-front causes the intense scattering of light. Finally, the filled pores disappear, leaving only a network of uniformly distributed empty pores that exhibits insignificant light scattering.
For adsorption, it is considered that the water vapor fills the pore space uniformly until capillary condensation occurs [16,17]. As shown in Fig. 8, slope gradually increases with increasing humidity at a constant rate. However it begins to decrease when the humidity stops changing and holds constant at a high humidity. Furthermore, Fig. 7 shows that the filling fraction continues to increase (from 0.62 to 0.74) during constant humidity (from 720 to 780 min). There are two possible explanations of the slope change during adsorption. One is that there exists a maximum slope at around the filling fraction of 0.6, which implies that the adsorption branch shown in Fig. 9 is universal for all the imbibition of water into nanoporous Vycor glass. The other is that the slope increases as long as the humidity continues to increase, and the slope starts to decrease when the humidity stops increasing and becomes constant, which implies that the water imbibition is driven by the nonequilibrium transport of water molecules from the high-humidity surrounding air into surface-linked pores. The water imbibition induced by the enhanced humidity difference with increasing humidity causes inhomogeneous water distribution in the pore space inside the porous glass, resulting in intense scattering of light. In contrast, after the humidity stops increasing and stays constant at a high value, the water imbibition into the pore space still continues to relax the inhomogeneity of the water distribution in the pore space and continues not to create more inhomogeneity. As a result, the light scattering caused by this kind of inhomogeneity will weaken .
Which explanation would be correct? Several runs of humidity-change experiments with different maximum humidity showed the former explanation is correct. There does exist a maximum slope at around the filling fraction of 0.65, which would coincide with the starting point of capillary condensation of the adsorption branch (see Fig. 6).
What would cause such a pronounced hysteretic response of slope to the filling fraction change between filling and draining, as shown in Fig. 9? The reason for the difference between the adsorption and desorption branches in slope is considered to be the inhomogeneity of the water distribution itself in the pore space. During adsorption, the pores are imbibed by a wetting liquid (such as water) homogeneously, and the imbibed liquid seems to be distributed almost homogeneously in the pore space so that the light scattering due to the inhomogeneity is not strong. On the other hand, during desorption, the liquid at only the surface can evaporate, and the liquid imbibed deeply inside the pores needs to move through the pore linkage toward the surface before evaporation. The random nature of pore linkage in porous glass causes the inhomogeneous distribution of the imbibed liquid in the pores. This inhomogeneity causes strong light scattering for the drainage of water.
On the basis of the above understanding on the transmission change during the humidity change, let us examine the turbidity data quantitatively using the Rayleigh scattering model [9,14], assuming the scatterers to be isolated spherical voids of uniform radius embedded in a continuous matrix composed of . From the measured slope , which is proportional to the product , we can estimate the radius . Since the product of the number density of scatterers () in units of and the volume of a single scatterer () in units of should be equal to the porosity (, dimensionless) of the porous glass, is given by .
In order to adapt the model to the aforementioned understanding, the effective radius of a scatterer should be regarded as a measure of the extent of inhomogeneities that cause the scattering. In addition to light scattering by inhomogeneities such as pore linked clusters, we also need to consider the change in the mean refractive index of the scattering unit, i.e., , 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 on the basis of the simplest effective-medium expression 24]) in Eqs. (3) and (4), we calculate the effective radius as a function of the filling fraction.
Figure 10 shows responses of the effective radius to the pore filling fraction change. The effective radius naturally exhibits a pronounced hysteretic characteristic similar to slope depicted in Fig. 9 because the radius is estimated from the slope through Eqs. (3) and (4). Along the adsorption curve, the effective radius increases gradually from 2.94 to 4.96 nm (expanded to 1.69 times) with increasing filling fraction up to 0.6. During constant humidity, the filling fraction increases from 0.62 to 0.74 at most, and correspondingly, the effective radius also increases a little from 4.96 to 5.32 nm (expanded to only 1.07 times). This saturated increase in the effective radius contributes to the reduction of slope during constant humidity in Fig. 9. In contrast, along the desorption curve, the effective radius increases markedly from 4.96 to 7.48 nm (expanded 1.5 times with respect to the starting radius) with decreasing filling fraction down to about 0.6, while it decreases steeply from 7.48 to 2.94 nm (reduced to 0.39 times) with decreasing filling fraction to less than about 0.6.
Figure 11 shows that the number density of the scatterers is on the order of , which implies that this system of scatterers is so condensed that multiple scatterings are no doubt occurring. The figure shows the inverted hysteretic response of the number density to the filling fraction change. As the water imbibes into pores, water-filmed pores are linked with one another, forming water-filled clusters, which act as effective scatterers and whose effective radius grows gradually. Correspondingly, the number of effective scatterers per unit volume decreases monotonically for the imbibition of water into pores. In contrast, for the drainage of water, air-filled clusters initially act as effective scatterers, whose effective radius grows rapidly until the filling fraction reaches about 0.6, where the corresponding number density becomes the minimum. As the filling fraction becomes smaller than 0.6, the remaining water-filled pores are linked with one another, forming smaller fragments of filled pore clusters in a large network of uniformly distributed emptied pores. These smaller fragments of filled pores act as effective scatters, whose effective radius becomes smaller and smaller as the filling fraction decreases. Correspondingly, the number density of effective scatterers evolves rapidly with decreasing filling fraction and finally reaches the initial maximum value of completely emptied pores.
E. Evaluation of the Rayleigh Scattering Model
Finally, as a test of our Rayleigh scatterer model, let us examine the refractive index of the porous glass, , which can be estimated in two different ways. Previously, we have used the method of linear least squares to fit data depicted in Figs. 4(a) and 4(b) to a linear function of according to Eq. (4), from which slope and the ordinate intercept were obtained. From the calculated value of , we can obtain the refractive index of porous glass as5) and is the aforementioned refractive index of air. Alternatively, by using effective-medium models in which the medium is regarded as a homogeneous (and uniform) superposition of its components , such as pores and the silica skeleton, the expression of the refractive index of the porous glass is given as 6), the porosity , and the refractive index of the silica skeleton .
Indices estimated by Eq. (7) as a function of the pore filling fraction are shown in Fig. 12 by solid diamonds for adsorption and by open squares for desorption. To check the validity of this estimation, the refractive index based on an effective-medium model, , calculated by Eq. (8), is depicted by a solid line in the figure.
Estimated indices represented by solid diamonds and open squares exhibit a pronounced hysteretic characteristic to the filling fraction change. These scattered data represent the deviation from the average value given by the solid line. These data deviations are considered to be due to the inhomogeneous distribution of water in pore space, which is caused by the nonequilibrium transport of water along linked pores during the filling and draining of water. On the other hand, the average line is based on the effective-medium model, in which the medium is regarded as a homogeneous superposition of its constituent water-filled pores, emptied pores, and the silica skeleton, causing in principle no deviation due to nonequilibrium inhomogeneous distribution of water in pore space.
Two results for the small filling fraction (i.e., ) and for the saturated fraction (around ) are in good agreement with the corresponding values of the effective-medium model, which confirms the validity of applying Rayleigh scattering as the underlying scattering mechanism to this transitory white turbidity phenomenon.
In this paper, we studied the light scattering of a monolithic nanoporous glass (Vycor) during periods of increasing and decreasing humidity, or in other words, during water adsorption and desorption. We combined an UV–Vis–NIR spectrophotometer with a humidity-controlled thermostatic chamber through fiber optics to investigate the wavelength dependence of the transparency change during changes in humidity. We measured the amount of water adsorbed into the pore space using either volumetric sorption isotherm or inherent optical absorption measurements. The combination of these data enables us to develop a consistent picture for the transitory white turbidity of nanoporous glasses during humidity change.
A wavelength analysis reveals that the transparency of the porous matrix varies with the inverse of the fourth power of the wavelength, typical of Rayleigh-type scattering for both adsorption and desorption. We show that a measure of the extent of the optical inhomogeneity that cause the scattering, such as the effective radius of scatterers and their number density, exhibits a pronounced hysteretic characteristic for the imbibition and drainage of water, while the absorption inherent to imbibed water also shows another type of hysteresis that is quite similar to the sorption isotherms of water. From the above observations, it is shown that the transitory white turbidity of nanoporous glasses during humidity changes can be consistently interpreted and quantitatively analyzed by a simple Rayleigh scattering mechanism.
Soprunyuk and co-workers [25–27] observed that quite similar scattering phenomena also occur during capillary sublimation, upon freezing and melting or generally spoken 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 our Fig. 9 (cf. Fig. 2 in ; Figs. 4 and 5 in ), although they measured the optical transmission at a single wavelength of a He–Ne laser beam () and the filling fraction extracted from isothermal sorption curves at various temperatures.
Finally, we demonstrated that the spectrophotometric measurements of the transparency change can be used to obtain the mean pore radius (i.e., the effective radius of scatterers), which is usually estimated from the nitrogen desorption isotherm. The main advantage of this method is that only the wavelength analysis of the transmission, combined with an appropriate effective medium model, can provide a plausible value of pore radius, although there remains a lot of room for improvement. The main limitation of the method is its restriction to sample thickness, which makes it impossible to obtain the measurable transmission when the turbidity becomes large. In practice, this implies that samples should be thin enough to measure their transmission accurately in the visible range.
It would be quite interesting to apply the method presented here to those aforementioned phenomenologies [25–27] in order to gain information on typical length scales of phase nucleation and rearrangement centers.
The authors are indebted to Mr. Tylor Richard Long, who performed the experiments during his stay at NTT as the first participant in the NTT-University of Wisconsin-Platteville Student Fellowship Program. The authors are indebted to Dr. Duane Ford, the Dean of UWP, Dr. Hiroki Tanaka, former director of NTT Energy and Environment Systems Laboratories, and Mr. Tatsuya Kunioka, former supervisor of our research program, for their continuous efforts in starting the fellowship program. We are sincerely grateful to Dr. Yuko Ueno for permitting us to use the nitrogen and water vapor sorption measurement apparatus and to Dr. Yasuko Yamada Maruo for her kind and thoughtful suggestions.
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