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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 10 — Oct. 1, 2013
  • pp: 2079–2089
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Hysteretic characteristics of 1/λ4 scattering of light during adsorption and desorption of water in porous Vycor glass with nanopores

Shigeo Ogawa and Jiro Nakamura  »View Author Affiliations


JOSA A, Vol. 30, Issue 10, pp. 2079-2089 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002079


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Abstract

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 (1/λ4), 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

1. INTRODUCTION

Porous Vycor glass with nanopores is used as the base material for irreversible chemical sensors, such as nitrogen dioxide (NO2) sensor elements [1

1. T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998). [CrossRef]

,2

2. T. Tanaka, A. Guilleux, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “A ppb-level NO2 gas sensor using coloration reactions in porous glass,” Sens. Actuators B 56, 247–253 (1999). [CrossRef]

], ozone (O3) sensor elements [3

3. Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007). [CrossRef]

], and formaldehyde sensor elements [4

4. Y. Y. Maruo, J. Nakamura, and M. Uchiyama, “Development of formaldehyde sensing element using porous glass impregnated with β-diketone,” Talanta 74, 1141–1147 (2008). [CrossRef]

,5

5. Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s reagent,” Sens. Actuators B 129, 544–550 (2008). [CrossRef]

], 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 200m2/g. These properties of porous glass make it possible to apply them for sensing. Optical methods [6

6. A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995). [CrossRef]

] 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

7. T. Ohyama, Y. Y. Maruo, T. Tanaka, and T. Hayashi, “A ppb-level NO2 detecting system using coloration reactions in porous glass and its humidity dependence,” Sens. Actuators B 64, 142–146 (2000). [CrossRef]

,8

8. K. Izumi, M. Utiyama, and Y. Y. Maruo, “Evaluation of air quality with simple and easy chemical sensors: development of porous glass-based elements,” in International Conference on Control, Automation and Systems (IEEE, 2008), pp. 2756–2760.

]. 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 [8

8. K. Izumi, M. Utiyama, and Y. Y. Maruo, “Evaluation of air quality with simple and easy chemical sensors: development of porous glass-based elements,” in International Conference on Control, Automation and Systems (IEEE, 2008), pp. 2756–2760.

]. 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 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.

2. EXPERIMENTS

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).

Fig. 1. Schematic diagram of the measurement system for the transmission of a porous Vycor glass chip in the artificial environment.

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 Iref 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, Imeas, is measured. The transmission spectrum T(λ) of the sample at a wavelength λ can be computed numerically according to Imeas(λ)/Iref(λ). 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 [10

10. M. E. Lines and P. Klocek, “Optical transmission theory,” in Infrared Fiber Optics, J. S. Sanghera and I. D. Aggarwal, eds. (CRC Press, 1998), p. 19.

].

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 ±0.2°C. 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 (8020)/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 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 8mm×8mm 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 (18·cm). 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 [11

11. D. Dollimore and G. R. Heal, “An improved method for the calculation of pore size distribution from adsorption data,” J. Appl. Chem. 14, 109–114 (1964). [CrossRef]

]. 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 (8020)/600(=0.1)%RH/min 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 (8020)/600(=0.1)%RH/min (for 10 h, from 780 to 1380 min in Fig. 2).

Fig. 2. Change in the ambient relative humidity around a porous Vycor glass chip and the corresponding response of the peak absorbance (α1900) at around the wavelength of 1900 nm as a function of exposure time in minutes. Temperature remains constant while the humidity is changed.

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 [10

10. M. E. Lines and P. Klocek, “Optical transmission theory,” in Infrared Fiber Optics, J. S. Sanghera and I. D. Aggarwal, eds. (CRC Press, 1998), p. 19.

] connecting the spectrophotometer and sample holder set inside the humidity chamber.

Fig. 3. Change in UV–Vis–NIR light transmission spectra of a porous Vycor glass chip after (a) increasing the humidity from 20 to 80 %RH at a constant rate of 0.1 %RH/min for 0, 120, 240, 360, 480, and 600 min (which correspond to the cumulative exposure times of 120, 240, 360, 480, 600, and 720 min) and keeping it constant for 30 and 45 min (exposure times of 750 and 765 min), and after (b) decreasing the humidity from 80 to 20 %RH at the same rate of 0.1 %RH/min for 0, 60, 150, 225, 255, 270, 300, 360, and 600 min (which correspond to the cumulative exposure times of 760, 820, 910, 985, 1015, 1030, 1060, 1120, and 1360 min). The label of each line in the figures shows the cumulative exposure time inside the humidity-controlled thermostatic chamber and the filling fraction.

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 [12

12. D. L. Wood and E. M. Rabinovich, “Infrared studies of alkoxide gels,” J. Non-Cryst. Solids 82, 171–176 (1986). [CrossRef]

]. 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 T through a porous glass parallel plate with sample thickness d (in units of μm) is expressed as
T(λ)=Iout/Iin=(1r)2·exp(τ·d),
(1)
where Iin is the incident light intensity, Iout the intensity of the light beam from the sample, and τ the turbidity in units of μm1. In Eq. (1), r is the reflectance of a single interface between air and porous glass and is given for normal incidence by
r=(nanpna+np)2,
(2)
where na and np are the refractive indices of air and porous glass, respectively.

On the basis of the above consideration, the transmission profile between 350 and 800 nm is replotted as a linear function of 1/λ4 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

9. S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013). [CrossRef]

,13

13. A. A. Evstrapov and N. A. Esikova, “Study of porous glasses by the methods of optical spectroscopy,” J. Opt. Technol. 75, 266–270 (2008). [CrossRef]

,14

14. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 31–39.

]. 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.

Fig. 4. (a) Changes in the common logarithm of the transmission (which is proportional to the turbidity τ) during imbibition of water vapor as a function of the inverse fourth power of wavelength (1/λ4). The slope decreases gradually only within a limited range with increasing humidity. After the ambient humidity is set to be constant at about 80 %RH, the slope recovers gradually. The pore filling fraction (f) with imbibing water is estimated from the absorbance peak at around a wavelength of 1900 nm, normalized by the initial maximum value measured immediately after the removal from the immersion container [9]. (b) Changes in the common logarithm of the transmission (which is proportional to the turbidity τ) during drainage of water vapor as a function of the inverse fourth power of wavelength (1/λ4). The slope decreases gradually, becomes steeper, and then recovers again gradually with decreasing humidity. The range of the slope change during drainage is wider than that during imbibition.

B. Absorbance Peak at around 1900 nm and Water Filling Fraction

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.

Fig. 5. Responses of the absorbance of a porous Vycor glass chip at around the wavelength of 1900 nm to the relative humidity change between 18 and 80 %RH inside the humidity-controlled thermostatic chamber. Pore filling fraction f with imbibing water is estimated from the absorbance peak at around a wavelength of 1900 nm, normalized by the initial maximum value measured immediately after the removal from the immersion container [9].

Fig. 6. Volumetric sorption isotherm for water vapor in the Vycor glass sample used in the light scattering experiments. The horizontal axis shows the ratio of the pressure to the saturated pressure of the H2O gas at 298 K.

C. Data Analysis Based on Rayleigh Scattering Model

1. Time-Dependent Behavior of β

On the basis of the aforementioned Rayleigh scattering model [9

9. S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013). [CrossRef]

,14

14. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 31–39.

], the data depicted in Figs. 3 and 4 are reconstructed in terms of slope β and filling fraction f estimated from the absorbance peak (α1900) at around 1900 nm, and they are plotted as a function of time passed in Fig. 7.

Fig. 7. Time evolution of slope β of turbidity (τ) versus 1/λ4 plots and of the filling fraction estimated from the absorbance peak (α1900) at around a wavelength of 1900 nm. Although slope β increases gradually with increasing humidity, it starts to decrease at constant humidity. Furthermore, slope β initially increases remarkably to the maximum and then decreases and saturates to the minimum with decreasing humidity as the cumulative exposure time passes. On the other hand, as the time passes, the filling fraction increases with increasing humidity, and it decreases with decreasing humidity, while it still increases at constant humidity.

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 β 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 β

Fig. 8. Slope β in the 350–800 nm range as a function of the relative humidity. For the adsorption branch, the slope increases monotonically a little with increasing humidity, but decreases at constant humidity. For the desorption branch, initially the slope takes a small value of 0.984×106μm3, then increases to the maximum value of 5.63×106μm3, and finally decreases and saturates to the minimum of 0.741×106μm3.

3. Correlation between β and f

Fig. 9. Slope β in the 350–800 nm range as a function of pore filling fraction f extracted from the peak absorbance at around 1900 nm. For comparison with the fully water-filled case, the previous result for a drying-after-dipping experiment (Fig. 4 in [9]) is included in the figure. Both slopes reach their peak value at about f=0.6.

D. Optical Inhomogeneity and Transmission Changes

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 [22

22. J. Schroeder, “Light scattering in glass,” in Treatise on Materials Science and Technology, M. Tomozawa and R. H. Doremus, eds. (Academic, 1977), Vol. 12, pp. 157–222.

]. 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 f1) and completely empty state (corresponding to f0.3), 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 β even at f0.78 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 β 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

19. T. M. Shaw, “Movement of a drying front in a porous material,” in Material Research Society Symposium Proceedings, C. J. Brinker, D. E. Clark, and D. R. Ulrich, eds., Better Ceramics Through Chemistry II (Material Research Society, 1986), Vol. 73, pp. 215–223.

,20

20. T. M. Shaw, “Drying as an immiscible displacement process with fluid counterflow,” Phys. Rev. Lett. 59, 1671–1674 (1987). [CrossRef]

]. 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

16. J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993). [CrossRef]

,17

17. J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995). [CrossRef]

]. As shown in Fig. 8, slope β 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 [23

23. S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Eglehaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. U.S.A. 109, 10245–10250 (2012). [CrossRef]

].

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 β 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 β 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

9. S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013). [CrossRef]

,14

14. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 31–39.

], assuming the scatterers to be isolated spherical voids of uniform radius rsca embedded in a continuous matrix composed of SiO2. From the measured slope β, which is proportional to the product N·V12, we can estimate the radius rsca. Since the product of the number density of scatterers (N) in units of μm3 and the volume of a single scatterer (V1) in units of μm3 should be equal to the porosity (φ, dimensionless) of the porous glass, N is given by N=φ/V1.

In order to adapt the model to the aforementioned understanding, the effective radius rsca 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., n1, 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 [13

13. A. A. Evstrapov and N. A. Esikova, “Study of porous glasses by the methods of optical spectroscopy,” J. Opt. Technol. 75, 266–270 (2008). [CrossRef]

]
n1(f)=f·nw+(1f)·na,
(6)
where na=1.0003 and nw=1.3334 are the refractive indices for air and water, respectively. Inserting numerical values for the sample used (n2=1.45 for the silica skeleton, d=1mm, and φ=0.3 [24

24. P. R. Wakeling, “What is Vycor glass?” Appl. Opt. 18, 3208–3210 (1979).

]) 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 rsca naturally exhibits a pronounced hysteretic characteristic similar to slope β depicted in Fig. 9 because the radius rsca is estimated from the slope β 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 β 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.

Fig. 10. Scatterer’s effective radius (rsca) as a function of pore filling fraction f for adsorption and desorption of water vapor. For adsorption, the effective radius of Rayleigh scatterers is initially about 2.94 nm and then gradually increases up to 4.96 nm with the change in the filling fraction from 0.22 to 0.62, which corresponds to the humidity increase. The radius reaches the second maximum of 5.32 nm at f=0.71 during the period of constant humidity. In contrast, for desorption, the radius starts with the value of about 4.98 nm, then becomes the maximum of 7.48 nm at about f=0.58, and finally approaches its initial value of about 2.94 nm.

Figure 11 shows that the number density of the scatterers is on the order of 1018cm3, 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.

Fig. 11. Scatterer’s number density N as a function of pore filling fraction f for adsorption and desorption of water vapor. For adsorption, the number density starts with an initial maximum value of 2.81×1018cm3 and then decreases monotonically to 5.85×1017cm3 with increasing filling fraction from 0.22 to 0.62. During the period of constant humidity, the fraction still increases up to 0.73 with an almost saturated number density of about 4.98×1017cm3. In contrast, for desorption, the number density starts with the value of about 5.04×1017cm3, then decreases steeply and saturates to the minimum of 1.71×1017cm3 at about f=0.58, and finally steeply recovers to its initial density of 2.81×1018cm3.

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, np, 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 1/λ4 according to Eq. (4), from which slope β and the ordinate intercept C were obtained. From the calculated value of C, we can obtain the refractive index of porous glass npC as
npC=1+r1r·na,
(7)
where r is already given in Eq. (5) and na 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 [13

13. A. A. Evstrapov and N. A. Esikova, “Study of porous glasses by the methods of optical spectroscopy,” J. Opt. Technol. 75, 266–270 (2008). [CrossRef]

], such as pores and the silica skeleton, the expression of the refractive index of the porous glass is given as
npeff(f)=φ·n1(f)+(1φ)·n2,
(8)
where n1(f) is the effective-medium expression for the refractive index of a Rayleigh scatterer in Eq. (6), the porosity φ=0.3 [24

24. P. R. Wakeling, “What is Vycor glass?” Appl. Opt. 18, 3208–3210 (1979).

], and the refractive index of the silica skeleton n2=1.45.

Indices npC 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, npeff(f), calculated by Eq. (8), is depicted by a solid line in the figure.

Fig. 12. Experimentally obtained values of refractive indices of nanoporous glass as a function of the pore filling fraction for adsorption (solid diamonds) and desorption (open squares). The solid line is estimated by using an effective-medium model [13].

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., f0.4) and for the saturated fraction (around f0.7) 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.

4. CONCLUSION

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

25. V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 144105 (2003). [CrossRef]

27

27. D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005). [CrossRef]

] 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 [25

25. V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 144105 (2003). [CrossRef]

]; Figs. 4 and 5 in [26

26. V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements on phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004). [CrossRef]

]), although they measured the optical transmission at a single wavelength of a He–Ne laser beam (λ0=623.8nm) 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

25. V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 144105 (2003). [CrossRef]

27

27. D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005). [CrossRef]

] in order to gain information on typical length scales of phase nucleation and rearrangement centers.

ACKNOWLEDGMENTS

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.

REFERENCES

1.

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998). [CrossRef]

2.

T. Tanaka, A. Guilleux, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “A ppb-level NO2 gas sensor using coloration reactions in porous glass,” Sens. Actuators B 56, 247–253 (1999). [CrossRef]

3.

Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007). [CrossRef]

4.

Y. Y. Maruo, J. Nakamura, and M. Uchiyama, “Development of formaldehyde sensing element using porous glass impregnated with β-diketone,” Talanta 74, 1141–1147 (2008). [CrossRef]

5.

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s reagent,” Sens. Actuators B 129, 544–550 (2008). [CrossRef]

6.

A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995). [CrossRef]

7.

T. Ohyama, Y. Y. Maruo, T. Tanaka, and T. Hayashi, “A ppb-level NO2 detecting system using coloration reactions in porous glass and its humidity dependence,” Sens. Actuators B 64, 142–146 (2000). [CrossRef]

8.

K. Izumi, M. Utiyama, and Y. Y. Maruo, “Evaluation of air quality with simple and easy chemical sensors: development of porous glass-based elements,” in International Conference on Control, Automation and Systems (IEEE, 2008), pp. 2756–2760.

9.

S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013). [CrossRef]

10.

M. E. Lines and P. Klocek, “Optical transmission theory,” in Infrared Fiber Optics, J. S. Sanghera and I. D. Aggarwal, eds. (CRC Press, 1998), p. 19.

11.

D. Dollimore and G. R. Heal, “An improved method for the calculation of pore size distribution from adsorption data,” J. Appl. Chem. 14, 109–114 (1964). [CrossRef]

12.

D. L. Wood and E. M. Rabinovich, “Infrared studies of alkoxide gels,” J. Non-Cryst. Solids 82, 171–176 (1986). [CrossRef]

13.

A. A. Evstrapov and N. A. Esikova, “Study of porous glasses by the methods of optical spectroscopy,” J. Opt. Technol. 75, 266–270 (2008). [CrossRef]

14.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 31–39.

15.

F. Rouquerol, J. Rouquerol, and K. Sing, Adsorption by Powders & Porous Solids (Academic, 1999).

16.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993). [CrossRef]

17.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995). [CrossRef]

18.

G. W. Scherer, “Theory of drying,” J. Ceram. Am. Soc. 73, 3–14 (1990). [CrossRef]

19.

T. M. Shaw, “Movement of a drying front in a porous material,” in Material Research Society Symposium Proceedings, C. J. Brinker, D. E. Clark, and D. R. Ulrich, eds., Better Ceramics Through Chemistry II (Material Research Society, 1986), Vol. 73, pp. 215–223.

20.

T. M. Shaw, “Drying as an immiscible displacement process with fluid counterflow,” Phys. Rev. Lett. 59, 1671–1674 (1987). [CrossRef]

21.

D. Wilkinson and J. F. Willemsen, “Invasion percolation: a new form of percolation theory,” J. Phys. A 16, 3365–3376 (1983). [CrossRef]

22.

J. Schroeder, “Light scattering in glass,” in Treatise on Materials Science and Technology, M. Tomozawa and R. H. Doremus, eds. (Academic, 1977), Vol. 12, pp. 157–222.

23.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Eglehaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. U.S.A. 109, 10245–10250 (2012). [CrossRef]

24.

P. R. Wakeling, “What is Vycor glass?” Appl. Opt. 18, 3208–3210 (1979).

25.

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 144105 (2003). [CrossRef]

26.

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements on phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004). [CrossRef]

27.

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005). [CrossRef]

OCIS Codes
(290.4210) Scattering : Multiple scattering
(290.5870) Scattering : Scattering, Rayleigh
(160.2710) Materials : Inhomogeneous optical media

ToC Category:
Materials

History
Original Manuscript: July 24, 2013
Manuscript Accepted: August 12, 2013
Published: September 23, 2013

Citation
Shigeo Ogawa and Jiro Nakamura, "Hysteretic characteristics of 1/λ4 scattering of light during adsorption and desorption of water in porous Vycor glass with nanopores," J. Opt. Soc. Am. A 30, 2079-2089 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-10-2079


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References

  1. T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998). [CrossRef]
  2. T. Tanaka, A. Guilleux, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “A ppb-level NO2 gas sensor using coloration reactions in porous glass,” Sens. Actuators B 56, 247–253 (1999). [CrossRef]
  3. Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007). [CrossRef]
  4. Y. Y. Maruo, J. Nakamura, and M. Uchiyama, “Development of formaldehyde sensing element using porous glass impregnated with β-diketone,” Talanta 74, 1141–1147 (2008). [CrossRef]
  5. Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s reagent,” Sens. Actuators B 129, 544–550 (2008). [CrossRef]
  6. A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995). [CrossRef]
  7. T. Ohyama, Y. Y. Maruo, T. Tanaka, and T. Hayashi, “A ppb-level NO2 detecting system using coloration reactions in porous glass and its humidity dependence,” Sens. Actuators B 64, 142–146 (2000). [CrossRef]
  8. K. Izumi, M. Utiyama, and Y. Y. Maruo, “Evaluation of air quality with simple and easy chemical sensors: development of porous glass-based elements,” in International Conference on Control, Automation and Systems (IEEE, 2008), pp. 2756–2760.
  9. S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013). [CrossRef]
  10. M. E. Lines and P. Klocek, “Optical transmission theory,” in Infrared Fiber Optics, J. S. Sanghera and I. D. Aggarwal, eds. (CRC Press, 1998), p. 19.
  11. D. Dollimore and G. R. Heal, “An improved method for the calculation of pore size distribution from adsorption data,” J. Appl. Chem. 14, 109–114 (1964). [CrossRef]
  12. D. L. Wood and E. M. Rabinovich, “Infrared studies of alkoxide gels,” J. Non-Cryst. Solids 82, 171–176 (1986). [CrossRef]
  13. A. A. Evstrapov and N. A. Esikova, “Study of porous glasses by the methods of optical spectroscopy,” J. Opt. Technol. 75, 266–270 (2008). [CrossRef]
  14. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 31–39.
  15. F. Rouquerol, J. Rouquerol, and K. Sing, Adsorption by Powders & Porous Solids (Academic, 1999).
  16. J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993). [CrossRef]
  17. J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995). [CrossRef]
  18. G. W. Scherer, “Theory of drying,” J. Ceram. Am. Soc. 73, 3–14 (1990). [CrossRef]
  19. T. M. Shaw, “Movement of a drying front in a porous material,” in Material Research Society Symposium Proceedings, C. J. Brinker, D. E. Clark, and D. R. Ulrich, eds., Better Ceramics Through Chemistry II (Material Research Society, 1986), Vol. 73, pp. 215–223.
  20. T. M. Shaw, “Drying as an immiscible displacement process with fluid counterflow,” Phys. Rev. Lett. 59, 1671–1674 (1987). [CrossRef]
  21. D. Wilkinson and J. F. Willemsen, “Invasion percolation: a new form of percolation theory,” J. Phys. A 16, 3365–3376 (1983). [CrossRef]
  22. J. Schroeder, “Light scattering in glass,” in Treatise on Materials Science and Technology, M. Tomozawa and R. H. Doremus, eds. (Academic, 1977), Vol. 12, pp. 157–222.
  23. S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Eglehaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. U.S.A. 109, 10245–10250 (2012). [CrossRef]
  24. P. R. Wakeling, “What is Vycor glass?” Appl. Opt. 18, 3208–3210 (1979).
  25. V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 144105 (2003). [CrossRef]
  26. V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements on phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004). [CrossRef]
  27. D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005). [CrossRef]

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