1. INTRODUCTION

Porous Vycor glass is used in environmental sensor applications [1–3], acting as the stage for environmental-gas-sensitive reagents, because its huge specific surface area is very attractive for gas sensing by adsorption. In addition, the transparency of porous silica glass with nanopores in the visible region allows optical methods to be used [4]. Optical methods have an advantage over conventional ones in that they can distinguish gas species by chemically detecting the inherent optical absorption. For example, an irreversible nitrogen dioxide (${\mathrm{NO}}_2$) sensor element consists of porous glass as a substrate impregnated with diazo-coupling reagents; ${\mathrm{NO}}_2$ concentration is determined from the light transmission of the irreversible sensor [1,2].

Unfortunately, the estimated concentration of detected ${\mathrm{NO}}_2$ is strongly affected by the humidity in the ambient air, i.e., the ambient humidity interferes with the sensing operation [5]. The transparency change in porous glasses with nanopores strongly affects the photodetection application to gas sensing. This transparency change is observed mainly during the drying process from a high-humidity state to a low-humidity state of the ambient air and is marked by the appearance of white turbidity of the porous glass slabs.

In this work, we measured the transmission change of porous Vycor glass in a water-dipping experiment, in which the glass was removed from the water immersion to determine the wavelength dependence of the transmission and assess the correlation between the turbidity and the amount of water in the pores. The time dependence of the amount of water and the turbidity change during the drying process were analyzed, and pore size was analyzed by using the low-temperature nitrogen sorption curves. On the basis of the presented experimental data, we offer a possible explanation of the white turbidity during the drying process.

2. EXPERIMENT

We used 1 mm thick Vycor 7930 porous glass slabs, with an average nominal pore diameter of 4.2 nm, cut into $8\mathrm{mm}\times 8\mathrm{mm}$ chips.

All porous glasses tend to yellow over time when exposed to free air, since they absorb organic contaminants in their pores. To remove the influence of these organic contaminants on the light transmission experiments, all porous glass samples were initially subjected to chemical cleaning with acetone (99.8%), ethanol (99.5%), and ultrapure water ($18\mathrm{M\Omega }\mathrm{cm}$). 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, with 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 one minute 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 desiccators 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 based on the Dollimore–Heal method [6]. 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.

After these preparations, a glass chip was immersed in a container filled with the ultrapure water for 2 h and then set in the sample holder of the Shimadzu UV-3150 UV-visible-near-IR spectrophotometer (Japan), which was set up in a room where the temperature and humidity were controlled to be 25°C and $45\%\pm 5\%$ relative humidity. The transmission and absorption spectra of the sample from 2500 to 300 nm were measured every 15 min for the duration of the drying process, which took place immediately after the sample removal from the water immersion container.

3. RESULTS AND DISCUSSION

The time-dependent change in the transmission spectrum of a porous glass chip in the UV-visible-near-IR region (300–2500 nm) during the drying process is shown in Fig. 1. The transmission curves were measured every 15 min immediately after the sample removal from the immersion from time 0–165 min. In the figure, only the first seven (0–90 min) curves are depicted.

 

Fig. 1. Change in UV-visible-near-IR light transmission spectra of a porous Vycor glass chip after drying for 0, 15, 30, 45, 60, 75, and 90 min, immediately after removal from ultrapure water immersion for 2 h at room temperature.

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As shown in Fig. 1, two absorption peaks near 1400 and 1900 nm decrease with time. On the other hand, in the visible region from 350 to 800 nm, the transmission is initially large (curve 1) immediately after the removal but becomes small (curves 2, 3, and 4) after about 45 min. It finally recovers gradually to the original transmission (curves 6 and 7) after about 75 min. This transmission change corresponds exactly to the phenomenological appearance of the sample: the sample is initially transparent immediately after the removal from the immersion water, becomes opaque after about 45 min, and gradually recovers its transparency sufficiently long after the removal.

Important here is that the porous glass chip was transparent over the whole visible-near-IR region (350–1300 nm) except for the two absorption peaks at about 1400 and 1900 nm after it had sufficiently dried out, and even long after the immersion, and that the scattering caused by the innumerable pores amounts to only between 5% and 10% of the incident light, depending on wavelength. Hereafter, we focus on the transmission changes in the visible region (350–800 nm) and the absorption around the wavelength of 1900 nm.

The two absorption peaks near 1400 and 1900 nm are attributed to the adsorption of water or the presence of an outer hydroxyl group in the pores [7]. The monotonic decrease in the absorption peaks at 1900 nm implies the amount of water inside the porous glass decreases as time passes.

We then examined the wavelength dependence of the transmission change in the visible region (350–800 nm). 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 as a working hypothesis that these pores act as Rayleigh scatterers [8] and their shape has no effect on the light scattering [8,9]. Since these pores are considered to be randomly distributed in the porous glass, 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 $N$ and the intensity of light be $I$. The attenuation due to scattering is then expressed as $-dI/dx=N·C_{\text{sca}}·I$, where $C_{\text{sca}}$ is the scattering cross section of a scatterer. By solving the differential equation, the transmission $T$ is expressed as

On the basis of the above consideration, the transmission profile between 350 and 800 nm is replotted as a function of $1/{\lambda }^4$ in Fig. 2, which shows the common logarithm of the transmission as a function of the inverse 4th power of the wavelength in the medium. The linear range is covered from 350 to 800 nm. This linearity implies that the opalescence of the porous glass during the drying process can be well explained by the Rayleigh scatterer model [8,9]. At present, the slight deviation from the linearity cannot be explained exactly by this simple scattering model only. This slight deviation may be due to multiple scattering, which is no doubt occurring. In this figure, each line has a label that contains information on not only the drainage time but also the filling fraction, which will be described in detail later, as extracted from the absorbance peak at around 1900 nm. Thus, Fig. 2 also indicates how the wavelength scaling depends on the filling fraction.

 

Fig. 2. Changes in the common logarithm of the transmission (which is proportional to the turbidity $\tau$) as a function of the inverse 4th power of wavelength ($1/{\lambda }^4$). The slope initially decreases gradually, then becomes steeper, and recovers again gradually. The pore filling fraction ($f$) with 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 immersion.

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Since the thickness $d$ of the sample is constant during the drying process, the slope $\beta$ of the natural logarithm of the inverse of the transmission between 350 and 800 nm is proportional to the square of the scatterer’s volume $V_1$, or to the number $N$ of scatterers per unit volume in the porous glass slab. Here, the slope $\beta$ can be regarded as representative of all data in that region. In this meaning, the value of the slope is more accurate than one data point measured at, for example, $\lambda =514.5\mathrm{nm}$ (${\mathrm{Ar}}^{+}$ laser).

On the other hand, the peak at around 1900 nm decreased monotonically with time. The absorbance peak, which is defined as ${\alpha }_{1900}={\log }_{10}(1/T)$ at the wavelength of 1900 nm, may be related to the amount of water inside the porous glass [7]. A reasonable explanation of this monotonic decrease in ${\alpha }_{1900}$ is the decrease in the amount of water from the glass pores by evaporation. Assuming that the Beer–Lambert law still holds quantitatively for a system of a wetting fluid such as water in a porous glass, the absorbance peak at around 1900 nm is considered to be approximately proportional to the amount of water adsorbed in the porous glass. The initial ${\alpha }_{1900}$ of almost 2.5, which was the maximum value measured immediately after the removal from the immersion, corresponds to the state where all pores were considered to be occupied completely with water. When capillary evaporation occurs in the pores, 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 ($f$) can be estimated from the absorbance peak as the ratio of ${\alpha }_{1900}$ to ${[{\alpha }_{1900}]}_{\max }$, i.e., $f\equiv {\alpha }_{1900}/{[{\alpha }_{1900}]}_{\max }$.

As shown in Fig. 1, the experimental accuracy of ${\alpha }_{1900}$ is very poor, since the transmission $T$ varies from 0.0001 to 0.1. The absorbance value of 1 implies that the output light intensity is $1/10$ as weak as the incident one. Furthermore, the absorbance value of 3 means the output intensity is $1/1000$ of that of the incident beam. Immediately after the removal from the immersion water, the peak transmission at around 1900 nm is close to zero, which implies the corresponding absorbance is larger than 3. Experimentally, it becomes very difficult to measure weaker light intensity with high accuracy with high-speed wavelength scanning. Thus, the accuracy of one data point value, ${\alpha }_{1900}$, for an absorbance of more than 3 is very poor. To improve the accuracy of ${\alpha }_{1900}$ obtained experimentally, we tried to fit the spectrum data between $\lambda =1850$ and 1950 nm by the 5th order algebraic interpolation curve. From this interpolated curve, we obtained a more accurate representative value of the peak absorbance at around 1900 nm.

In this way, the data depicted in Fig. 1 were reconstructed in terms of slope $\beta$ and the filling fraction $f$. The reconstructed data are plotted as a function of time in Fig. 3, which indicates explicitly the transitory nature of the white turbidity that occurred during the drying process.

 

Fig. 3. Time dependence of the slope $\beta$ of turbidity ($\tau$) versus $1/{\lambda }^4$ plots and of the absorbance peak (${\alpha }_{1900}$) at around a wavelength of 1900 nm. The slope changes remarkably as the time passes. Initially a small value of $1.01\times {10}^{-6}{\mathrm{\mu m}}^3$, it then increases to the maximum value of $8.81\times {10}^{-6}{\mathrm{\mu m}}^3$, and then decreases and saturates to the value of $8.11\times {10}^{-7}{\mathrm{\mu m}}^3$, which is a little smaller than the starting value.

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As expected, the filling fraction decreases monotonically and approaches its saturated value, which corresponds to the absorbance value equilibrated with the humidity in the measurement instrument room. On the other hand, slope $\beta$, which was initially small, rapidly increases to its maximum value and then decreases and approaches the saturated value, which is slightly smaller than its initial value. This time dependence of the slope exactly corresponds to the time sequence of the phenomenological appearance of the sample, i.e., initially transparent, then transitory whitish when its scatters light, and finally transparent again.

To obtain the direct correlation between the slope and the filling fraction extracted from the absorbance peak at around 1900 nm, we have eliminated the time parameter from Fig. 3. Figure 4 shows the change in the slope $\beta$ as a function of filling fraction. From these results, it turns out that the maximum of the slope is observed when the filling fraction is at about 0.6. Several runs of drying-after-dipping experiments under the same conditions showed almost the same curve as in Fig. 4. However, at present, we did not verify that the curve is universal for all drying processes with different drying speeds.

 

Fig. 4. Slope $\beta$ in the 350–800 nm range as a function of the pore filling fraction $f$ extracted from the peak absorbance at around 1900 nm. The slope reaches its peak value of about $8.81\times {10}^{-6}{\mathrm{\mu m}}^3$ at about $f=0.6$.

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In general, the 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 the phenomenon of light scattering caused by inhomogeneities is minimized. On the other hand, dry porous glasses are structurally inhomogeneous due to the presence of the innumerable air-filled pores and surrounding silica skeleton, but they predominantly exhibit insignificant light attenuation, determined by the relatively low level of scattering by inhomogeneities. This implies that the inhomogeneities are almost uniform within the porous glasses with nano-sized pores and much smaller than the wavelength of the visible light scale.

Let us examine this reasoning on the basis of our data in Figs. 3 and 4 and the simple Rayleigh scatterer model [8,9], assuming the scatterers to be isolated spherical voids of uniform radius $r_{\text{sca}}$ embedded in a continuous matrix composed of ${\mathrm{SiO}}_2$. From the measured slope $\beta$, which is proportional to the product $N·V_1^2$, we can estimate the radius ($r_{\text{sca}}$) of the scattering unit. Since the product of the number of scatterers in a unit volume of sample ($N$) in units of ${\mathrm{\mu m}}^{-3}$ and the volume of a single scatterer ($V_1$) in units of ${\mathrm{\mu m}}^3$ should be equal to the porosity ($\phi$, dimensionless) of the porous glass, $N$ is given by $N=\phi /V_1$. Inserting numerical values for the sample used ($n_1=1.0003$ for air-filled pores, $n_2=1.45$ for the silica skeleton, $d=1\mathrm{mm}$, $\phi =0.3$) in Eqs. (2) and (3), we calculate $r_{\text{sca}}$ to be 3.2 nm.

To verify the pore size distribution of the porous Vycor glass, we measured nitrogen sorption isotherms for the glass at liquid nitrogen temperature. The sorption isotherms were determined volumetrically by using an automatic gas adsorption manometry [10] apparatus (BELSORP) with the same sample used in the light scattering measurements. In Fig. 5, the adsorption data are plotted as solid points, while the desorption data are plotted as open points. The sorption isotherm exhibits a pronounced hysteresis, which is characteristic of mesoporous materials (i.e., adsorbents having effective pore widths in the approximate range of 2–50 nm) [10].

 

Fig. 5. Volumetric adsorption isotherm for nitrogen on porous Vycor glass. The horizontal axis shows the ratio of the pressure to the saturated pressure of the nitrogen gas at 77 K. The specific surface area as measured from the BET plot from 0.02 to $0.5P/P_0$ is $207{\mathrm{m}}^2/\mathrm{g}$, which coincides with the specifications for the glass [11].

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The isotherms in Fig. 5 were analyzed on the basis of the Brunauer, Emmett, and Teller (BET) model for multilayer adsorption to obtain the specific surface area. An excellent straight line in the BET plot of $P/v(P_0-P)$ versus $P/P_0$ fit is obtained, giving a specific surface area of $207{\mathrm{m}}^2/\mathrm{g}$, which is almost the same as the nominal value in the specifications of Vycor glass [11]. From the sorption curves, especially from the desorption branch, the corresponding mesopore size distribution was analyzed by using the Dollimore–Heal method [6], which assumes a cylindrical pore geometry, and the peak radius was found to be about 2.89 nm, as shown in Fig. 6. This radius value is slightly larger than the nominal average pore diameter (4.2 nm), but this is not unexpected considering that the sample was subjected to HF etching before the pore size measurement.

 

Fig. 6. Pore size distribution of porous Vycor glass obtained from the Dollimore–Heal analysis [6] of the nitrogen desorption isotherm.

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The difference between these estimated pore radii (3.2 and 2.89 nm) can be attributed to the underlying assumption associated with pore geometry. Rather, such agreement between the two radii, although based on a crude model, confirms broadly that the observed weak scattering by the dry porous glass is of approximately the expected magnitude. This explains why the dry porous Vycor glass itself is so transparent in the visible region. Since the pores with a radius between 1.0 and 6.0 nm, mostly 2.89 nm, in the glass are very small compared to the wavelength of the incident visible light, even for the shortest wavelength of 350 nm, they exhibit insignificant light scattering and the glass is transparent. In other words, the porous glass is optically homogeneous on length scales comparable to the wavelength of light. In the same reasoning, when all pores are completely filled with water, the completely wet porous glass should therefore also be transparent, because the original pore distribution within the porous glass is optically homogeneous as compared to the visible light scale. From this point of view, the small values of the slope $\beta$ observed at the initial and final stages during the drying process are quite reasonable.

Furthermore, when the pores are completely filled with water, or close to saturation, the turbidity should be much smaller than that of the dry porous glass. This is one of the predictions of the Rayleigh theory, since it can be accounted for entirely by the reduction of the factor involving powers of $m$. For fully water-filled pores, for example, $n_1=1.3333$, $m=0.92$, and ${[(m^2-1)/(m^2+1)]}^2=0.0029$, leading to a reduction in the turbidity by an order of magnitude. However, this is not the case, as shown in Figs. 3 and 4. At the beginning of the drying process, the porous glass remains transparent and the corresponding $1/{\lambda }^4$ light scattering is very weak but still exists. In Fig. 1, the initial transmission (curve 1 around 500 nm), where all pores are considered to be filled with water, is slightly smaller than that 90 min later (curve 7), where most of the pores are filled with air instead of water. In other words, the dry porous glass is more transparent than that filled with water.

How should we interpret this discrepancy between our experimental results and the prediction? One possible answer is that the immersion of samples in water for two hours was insufficient to fill all pores completely with water, and that there remain microbubbles within the porous glass. Page et al. [12,13] observed that upon filling, when capillary condensation of a wetting fluid in Vycor occurs, vapor-filled voids or microbubbles are formed in the pore space and persist until the sample is completely full. To verify this possibility, let us examine the effective radius of a Rayleigh scatterer, by using the data obtained for the sample immediately after the removal from the immersion. Inserting numerical values for the sample used ($n_1=1.3334$ for the water-filled pores, $n_2=1.45$ for the silica skeleton, $d=1\mathrm{mm}$, $\phi =0.3$), $r_{\text{sca}}$ is calculated to be 6.9 nm, which is two or three times larger than that for air-filled pores. This suggests the existence of additional inhomogeneities, such as microbubbles remaining inside the initial sample.

At intermediate saturations the turbidity considerably exceeds that of the dry or completely wet porous glass by one order of magnitude during the drying process. As the evaporation proceeds, as shown in Fig. 3, the porous glass becomes very opaque, which implies that the $1/{\lambda }^4$ scattering of the incident light becomes dominant. In this situation, one can expect a state to in which half of the pores are filled with water and the remaining are empty, which causes large optical scattering. Figure 4 shows that the maximum of the slope is observed when the filling fraction is about 0.6.

What would explain the change? One simple explanation of this phenomenon is that the scattering itself is caused by the spatial fluctuation (inhomogeneity) of constituent materials within the porous glass, i.e., the water distribution in the pore space. The adjacent inter-connected pore cluster model [14–16] based on a simple percolation theory [17] is one possible answer. 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 are therefore expected to be highly light scattering. In our drying experiment, initially all pores are filled with water, and they constitute a single interconnected network of filled pores. But the distribution of water in the linked pore space is uniform, as previously discussed, and therefore the scattering caused by this kind of inhomogeneity is quite small. Since water evaporates from the sample surface, only some of the pores, those directly connected to the surface, are emptied, and thus the porous glass drains in from the surface into the bulk, causing large-scale inhomogenieties. As time passes, one would see the number of empty pores increasing and an increasingly fragmented network of empty pores. The number of connections of empty pores increases with time, creating smaller and smaller clusters of filled pores. Finally, the filled pores disappear, leaving only a network of uniformly distributed empty pores. During this evaporation process, the drying front (i.e., the water/vapor interface) is fractally rough on the scale of the pores, but stable on a much larger scale [16,17]. Because of variations in pore cluster size, regions containing thousands of pores can empty while the surrounding pores remain full. These dried 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. These empty pores can form structures with much larger range correlations; the size of the structures can be comparable to the wavelength of the incident light, which will result in strong light scattering, much stronger than that of either the empty or the filled Vycor. Page et al. [12,13] observed that the empty pores, on draining, exhibit spatial correlations with a fractal dimension of 2.6, which they derived from the wave vector dependence of the scattered light intensity.

On the basis of the above understanding of the transitory white turbidity, let us examine the turbidity data quantitatively by using the Rayleigh scattering model [8,9]. To adapt the model to the above understanding, the effective radius $r_{\text{sca}}$ of a scattering unit should be regarded as a measure of the extent of the inhomogeneities that cause the scattering. In addition to the considerations of light scattering by inhomogeneities such as pore linked clusters, one also needs to consider the change of mean refractive index of the scattering unit, i.e., $n_1$, when the drainage 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 the scattering unit can be estimated on the basis of effective medium expression, i.e., $n_1(f)=f·n_w+(1-f)·n_a$, where $f$ is the filling fraction and $n_a=1.0003$ and $n_w=1.3334$ are the refractive indices for air and water, respectively.

Figure 7 shows the effective radius and the corresponding number density as a function of the pore filling fraction. As shown in the figure, the filled pore clusters are bigger in size and fewer in number, which is consistent with the physical picture based on the above understanding. The effective radius of Rayleigh scatterers never reaches the same order of magnitude as the wavelength of visible light, since the radius extends to about 10 nm at most. This means that the size parameter, which is defined as $2\pi r_{\text{sca}}/\lambda$ with the wavelength $\lambda$ in the medium, does not exceed a value of 0.5 [9], which confirms the validity of adapting the Rayleigh scattering as the underlying scattering mechanism to this transitory white turbidity phenomenon. Furthermore, an interpretation of the transitory white turbidity in terms of a single Mie scattering event is no longer meaningful.

 

Fig. 7. Scatterer’s effective radius ($r_{\text{sca}}$) and number density ($N$) as a function of the pore filling fraction. The effective radius of Rayleigh scatterers is initially about 6.9 nm, then becomes the maximum at about 9.4 nm, and finally reduces to its minimum of about 3.2 nm. Correspondingly, the number density of scatterers starts with a value of $2.20\times {10}^{17}{\mathrm{cm}}^{-3}$, then becomes the minimum of $8.67\times {10}^{16}{\mathrm{cm}}^{-3}$, and finally approaches the maximum of $2.16\times {10}^{18}{\mathrm{cm}}^{-3}$.

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On the other hand, Fig. 7 shows also that the number density of the Rayleigh scattering units is of the order of ${10}^{18}{\mathrm{cm}}^{-3}$, which implies that our system is extremely concentrated with respect to the normal standards in the light scattering literature. Thus, multiple scattering is no doubt occurring.

In conclusion, the transitory white turbidity phenomena of porous glasses with nano-sized pores, which occurs during the drying process, can be interpreted consistently and quantitatively analyzed by a simple Rayleigh scattering mechanism.