u s a m Adsorption of water on porous Vycor glass studied by ellipsometry Alberto Álvarez-Herrero, Raquel L. Heredero, Eusebio Bernabeu, and David Levy The variation of the optical properties of porous Vycor glass ~Corning, Model 7930! under different relative-humidity conditions was studied. The adsorption of water into the glass pores was investigated with spectroscopic ellipsometry. The change of the refractive index was Dn ; 0.04 between 5% and 90% relative humidity. A linear relation between the ellipsometer parameter tan C, the amount of water adsorbed in the glass pores, and information about the pore-size distributions was established. The results are in accord with the values obtained from N2 isotherms, transmission electron microscope micrographs, and the manufacturer’s specifications ~radius of ;20 Å!. The possibility of using this material as a transducer for implementation in a fiber-optic sensor to measure humidity was evaluated. © 2001 Optical Society of America OCIS codes: 160.4760, 120.2130, 160.6030, 010.7340. o b i s a t t s s 1. Introduction Porous materials have been studied for several de- cades. They have been used for multiple applica- tions: desiccants, membranes, and host matrices for different dopants. In particular, surface and inter- facial effects that occur on silica glasses have been investigated because of their great potential for ap- plication in many technologies. In this sense the commercially available porous Vycor glass ~PVG!, Corning, Model 7930, is a 96%- silica glass that has been used in many studies. The porosity and the fractal structure of this material have been widely analyzed.1,2 PVG has also been sed as a template in the growth of metals, in emiconductor–insulator composite fabrication, and s a host dielectric matrix for organic or inorganic aterials.3,4 The behaviors of vapors and fluids con- A. Álvarez-Herrero ~alvarez@inta.es!, R. L. Heredero, and D. Levy are with the Laboratorio de Instrumentación Espacial ~LINES!, Área de Cargas Útiles e Instrumentación, División de Ciencias de Espacio, Instituto Nacional de Técnica Aeroespacial ~INTA!, 28850 Torrejón de Ardoz, Madrid, Spain. E. Bernabeu is with the Departamento de Óptica, Facultad de Ciencias Fı́sicas, Universidad Complutense de Madrid, 28040 Madrid, Spain. D. Levy is also with the Instituto de Ciencia de Materiales de Madrid, Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientificas, 28049 Cantoblanco, Madrid, Spain. Received 22 June 2000; revised manuscript received 30 October 2000. 0003-6935y01y040527-06$15.00y0 © 2001 Optical Society of America fined in small pores of PVG have been of great re- search interest5–7 because of their perturbation effects. These factors have important implications in many areas, such as molecular diffusion in mem- branes, solvation forces, or colloid interactions. Be- cause of the important role of water in most chemical and biological systems, its behavior in porous sys- tems such as PVG has been investigated extensive- ly.8,9 The behavior of the complex refractive index of porous materials with respect to the relative humid- ity ~RH! is an attractive topic for different areas in ptics: system design and manufacturing, the sta- ility of interference filters and antireflectance coat- ngs, and the development of new transducers for ensing. In this paper the optical properties of PVG re studied under different RH environments. In his sense the possibility of using this material as a ransducer that is implemented in a fiber-optic sen- or to measure RH is investigated through spectro- copic ellipsometry.10 Ellipsometry permits the measurement of the optical properties of materials with high accuracy and precision, and this technique is useful for studying changes in the refractive index with the RH. From the variation of ellipsometric parameters information about the pore size can be also extracted. The ellipsometric results of pore-size distributions were compared with data obtained from the adsorption and the desorption of N2 adsorbed in the PVG and from transmission electron microscope ~TEM! micrographs. 1 February 2001 y Vol. 40, No. 4 y APPLIED OPTICS 527 c p T 5 2. Experimental Details The PVG samples ~Corning, Model 7930! that were used were first cleaned with ultrasound waves inside a glass vial filled with acetone. After this process the samples were dried at 150 °C for 1 h. A. Optical Characterization: Spectroscopic Ellipsometry The sample for the ellipsometry measurements con- sisted of a disk with a 15-mm diameter and a 3-mm thickness. Only one face of the sample was polished to achieve adequate reflectivity for the ellipsometry measurements and to avoid backreflection from the opposite face. A rotating-polarizer spectroscopic ellipsometer11 ~SOPRA, Model ES-4G! was used to measure the re- fractive index of the PVG under different conditions of the RH. The ellipsometer’s nominal repeatability is 0.005 for the ellipsometric parameters tan C and os D, and its spectral range was 400–835 nm. A climatic chamber specially designed to be cou- led to the ellipsometer was used to perform in situ measurements of the change in optical properties with the RH. The stability of the chamber is 61% RH, and the working range is from 7% to 90% RH. Temperature and humidity inside the chamber were measured with VAISALA sensors: Model PHM 233 with probe Model HMP46 ~accuracies of 0.2 °C and 1% RH!. The ellipsometric measurements were performed at two different angles. Position A corresponds to an incident angle of 55.09° 6 0.01° ~similar to the Brew- ster angle of silica!, which is the optimum angle for transparent samples. For angle A the estimated systematic error was dn # 0.002. The RH and the temperature were 32% and 24.0 °C, respectively, for the measurements at position A. Position B corre- sponds to an incident angle equal to 70.11° 6 0.01°. All measurements with the climatic chamber were performed at this angle because at position A the errors introduced by changes in the polarization when light passes through the windows cannot be neglected. The total systematic error estimated for measurements at position B and with the climatic chamber coupled was dn # 0.01. The measurement repeatability was better than 0.001. We are inter- ested in relative changes in the optical properties of the PVG with the RH, so the systematic errors are not important for our purpose. B. Characterization by Use of a Surface-Area Analyzer and a Transmission Electron Microscope To compare the ellipsometric results, we used a Model ASAP 2010 accelerated surface-area analyzer from Micromeritics12 for measurements of the surface area and the porosity. The pore-size distribution was obtained from N2 adsorption–desorption iso- therms at 77 K. The PVG samples were outgassed at 150 °C for 24 h. Microstructural observations of the Vycor samples were performed in a Philips Model CM20 ~200-kV! EM. The samples were crushed in a dilute meth- 28 APPLIED OPTICS y Vol. 40, No. 4 y 1 February 2001 anol solution that eventually evaporates. The re- sulting particles were dispersed onto a nickel microscope carbon-holed grid. 3. Experimental Results and Discussion A. Ellipsometric Characterization Accurate measurements of the PVG optical proper- ties were obtained by ellipsometry at position A with- out the climate chamber. A rigorous model for calculating the refractive index from the ellipsomet- ric angles C and D should consider some degree of surface roughness and a certain inhomonegity be- cause the amount of water adsorbed near the exter- nal surface is greater than that adsorbed inside the sample.13 However, all the values for refractive in- dices in this study were obtained under the assump- tions that the PVG is an isotropic and a bulk material and that its surface is not rough to simplify all the calculations. Figure 1 shows the result of the refractive-index measurement at position A. The changes in the refractive index with the RH are shown in Fig. 2. These measurements were car- ried out at position B. Adsorption of the water mol- ecules on the walls of the pores and capillary condensation occur when the RH of the environment Fig. 1. Refractive index n of the Vycor sample measured at an incident angle of 55.09° for wavelengths from 400 to 835 nm with a RH of 32% and a temperature of 24 °C. Fig. 2. Change in the value of the refractive index n with the RH. The plots show values for a wavelength range of 400–835 nm. The reference was taken at a RH of 6.4%. t w e i p s a t t a T c a s c w b a d increases. The pores of the PVG fill with water, and therefore the effective refractive index increases too. The change in the refractive index is as high as Dn 5 0.04 in a range between 6% and 92% RH ~Fig. 2!. These high variations in the optical constants could be used to develop an optical sensor head. The possibility of using PVG for sensing purposes was examined by means of carrying out a more de- tailed study of the behavior of this material. One adsorption and desorption cycle of water vapor at position B was analyzed by ellipsometry at 835 nm. This wavelength was selected because it lies in the first window for sensor systems that are based on fiber optics. Figures 3~a! and 3~b! show the adsorp- ion and the desorption isotherms, respectively, that ere obtained at 23.1 °C 6 0.8 °C. In Fig. 3~a! the llipsometric parameter tan C plotted versus the RH s represented; Fig. 3~b! shows the refractive index lotted versus the RH. The shapes of both plots are imilar because both of the magnitudes represented re approximately proportional to the amount of wa- er adsorbed, as is shown below. The curves shown in Fig. 3 present a hysteresis Fig. 3. Adsorption ~Œ! and desorption ~h! isotherms of ellipso- metric measurements. The temperature inside the climatic chamber was 23.1 °C: ~a! The value of tan C versus the RH. The plot was smoothed ~solid curve! to permit the calculation of the pore-size distribution shown in Fig. 5. ~b! The value of the refrac- tive index n plotted versus the RH. loop. This is a typical behavior of mesoporous ma- terials ~i.e., materials with pore widths between 2 and 50 nm! that corresponds to isotherm types IV and V, according to the Brenauer–Deming–Deming– Teller classification.14 The type V isotherm is char- acterized by convexity starting at the origin toward the relative pressure axis because of the weak gas– solid interactions in which the adsorbate–adsorbate forces predominate. Otherwise, the type IV iso- therm is concave for low pressures and has a point of inflection because the strongest interactions are adsorbent–adsorbate. The Brunauer–Emmett– Teller model15 introduces the parameter c, which is related to the net heat of adsorption. The isotherms have an inflection point when c . 2 ~type IV iso- herm!, which is close to the point at which the mount adsorbed is equal to the Brunauer–Emmett– eller monolayer capacity. When 0 , c , 2, the urve does not have a inflection point, and the plot is type V isotherm. For more details see Ref. 16. The curves shown in Figs. 3~a! and 3~b! have the hape of a type V isotherm because these curves are onvex for low pressures. Besides, the fact that the ater molecules are polar—and therefore the forces etween them may be stronger than the adsorbent– dsorbate forces—supports the conclusion that the ata of Figs. 3~a! and 3~b! belong to the class of type V isotherms. Nevertheless, the procedure that we used only permits knowing a magnitude that is pro- portional to the amount of water adsorbed on the material ~refractive index or C! with an unknown proportional factor; hence the parameter c cannot be calculated, and the classification of the curves shown in Figs. 3~a! and 3~b! is ambiguous. Three parts can be distinguished in Figs. 3: Part 1 is located from 0% RH to the point at which the adsorption and the desorption points coincide ~to ap- proximately 20% RH!. At 20% RH the physical ad- sorption of water occurs on the walls of the PVG pores. Part 2 corresponds to the hysteresis of the plot. In this area adsorption and capillary conden- sation of the water take place. Part 3 starts at ap- proximately 90% RH when the pores are completely filled with water and bulk condensation begins over the external surface of the solid. The saturation of the amount of water adsorbed in the desorption branch for high RH indicates this behavior. Verifi- cation of the growth of this film of water was not carried out by ellipsometry because an achromatic compensator is required as a result of the low con- trast of this layer over PVG. The refractive-index behavior of PVG versus the RH precludes the possibility of using this material for sensing because of hysteresis. Any optical sensor that is based on changes in the refractive index of this material would generate an ambiguous value for the RH. Although we are mainly interested in the changes in the optical properties versus the humidity, it is also interesting to show that, from only the ellipso- metric data, remarkable information about the struc- tural features of PVG can be extracted. 1 February 2001 y Vol. 40, No. 4 y APPLIED OPTICS 529 n t o o D a d c n f m w c l l T a e d e 5 It was mentioned above that a linear relation exists between tan C and the amount of water adsorbed inside PVG pores. The Drude approximation17 is ot suitable for this case because it applies to only hin films that are adsorbed over the external surface f the solid, and for PVG water is adsorbed not only n the external surface but also inside the pores. espite this fact, this linear relation can be verified s follows: Our adsorbent–adsorbate system can be escribed in a simple way as a mixture of three main omponents: SiO2, pores, and water. The volume fraction of SiO2 ~ f1! is a constant, and the volume fractions of the pores and the water ~ f2 and f3, re- spectively! change as the pores become filled. The effective refractive index ne of the material is higher ~lower! when f3 increases ~decreases! and f2 decreases ~increases! in the adsorption process, producing vari- ations in the ellipsometer parameters tan C and cos D. PVG is transparent in the visible region, so only the variations of tan C are relevant because cos D equals 11 or 21. This behavior can be approxi- mated by a first-order Taylor series: tan C 5 tan C0 1 ] tan C ]ne ]ne ]f3 Df3. (1) The ellipsometric parameter tan C for bulk mate- rials18 has the well-known expression of tan C~ne, u! 5 2 cos u~ne 2 2 sin2 u!1y2 2 sin2 u cos u~ne 2 2 sin2 u!1y2 1 sin2 u , (2) where u is the incident angle. Differentiating over e yields ] tan C ]ne 5 2 sin2 u cos une ~ne 2 2 sin2 u!1y2@cos u~ne 2 2 sin2 u!1y2 1 sin2 u#2 , (3) On the other hand, the Bruggeman approximation or the effective refractive index of a three-component aterial15 is f1 n1 2 2 ne 2 n1 2 1 2ne 2 1 f2 n2 2 2 ne 2 n2 2 1 2ne 2 1 f3 n3 2 2 ne 2 n3 2 1 2ne 2 5 0, (4) here n1, n2, and n3 are the refractive indices of SiO2, the pores, and the water, respectively. Equation ~4! an be also written as a3 x3 1 a2 x2 1 a1 x 1 a0 5 0, (5) where a0 5 n1 2n2 2n3 2, a1 5 n1 2n2 2~2 2 3f3! 1 n1 2n3 2~2 2 3f2! 1 n2 2n3 2~2 2 3f1!, a2 5 2@n1 2~3f1 2 1! 1 n2 2~3f2 2 1! 1 n3 2~3f3 2 1!#, a3 5 24. (6) 30 APPLIED OPTICS y Vol. 40, No. 4 y 1 February 2001 If one takes into account that f1 is a constant, f2 5 1 2 f1 2 f3, and differentiating Eq. ~5! over f3, results in ]ne ]f3 5 3ne~n3 2 2 n2 2!~2ne 2 1 n1 2! 2~12ne 4 2 2a2 ne 2 2 a1! . (7) Substituting Eqs. ~7! and ~3! into Eq. ~1! yields the inear relation between tan C and f3. To verify the accuracy of this approximation, we compared the val- ues of tan C versus f3 from the exact expression with the values calculated from the linear approximation for the PVG. The SiO2 volume fraction f1 was cho- sen to be 0.70, according to manufacturer specifica- tions. Because of the water adsorption in the PVG pores, f3 varies from 0 to 0.30, and, consequently, f2 varies from 0.30 to 0. The incident angle was 70.11°, and the refractive indices n1, n2, and n3 at 800 nm were 1.453, 1, and 1.329, respectively. The results are shown in Fig. 4. The deviation between the plots is less than 0.002, which is lower than the repeatabil- ity of the ellipsometer ~0.005!. Hence it is demon- strated that the ellipsometer parameter tan C is inearly related to the amount of water adsorbed. his fact is useful in the following calculations. If one considers that tan C is proportional to the mount of water adsorbed the Pierce method14 can be used to calculate the pore-size distribution by use of the points obtained at a RH higher than 20% ~when capillary condensation takes place!. This method uses the increments of the amount of water that is adsorbed when the RH increases to calculate the pore-size distribution. To avoid negative incre- ments that are due to experimental errors required that the isotherm be smoothed beforehand by the application of a fast Fourier transform filter to ad- sorption points and by the averaging of adjacent de- sorption points. It is important to note that this procedure provides only an estimate of the pore size because some factors are not taken into account. First, the experiment was carried out without an outgassing process because we are interested in the material’s behavior under normal conditions. Hence Fig. 4. Plot of tan C versus the water volume fraction. Both the xact values and a linear approximation are shown. Note that the eviation between the plots is less than the repeatability of the llipsometer ~0.005!. t s s p l the walls of the pores had a layer of uncontrolled im- purities. Second, the strong intermolecular forces be- tween water molecules facilitate the growth of a multilayer during the adsorption process even though the monolayer is still incomplete on others parts of the surface. Finally, it is necessary to introduce a correc- tion in the thickness of the growing monolayer because of the physical adsorption on the pores walls before capillary condensation takes place. The t curve for he water–Vycor glass system is not known, i.e., the tatistical thickness t of the adsorbed film plotted ver- us the partial pressure ~RH in this study!. To solve this problem, we used the t curve of the N2–Vycor system and assumed that both curves were similar. If we consider that the molecular size of N2 and H2O is ;0.1 nm, the difference between the t curves would be of the same order, and therefore the error introduced in the pore-size calculation for this mesoporous mate- rial will be minor at 5%. Figure 5 shows the pore-size distributions that were calculated for the adsorption and the desorption branches, respectively. The distribution calculated from the desorption points is narrower than the one from the adsorption points because of the pores’ in- terconnectivity.16 The most probable pore radius obtained from the adsorption branch was 21 Å, and it was 15 Å from the desorption branch. As we show below in Subsection 3.B, the values obtained from more rigorous methods yield the same orders of mag- nitude for the pores. These values also agree with the specifications given by the manufacturer ~;20 Å!. B. Characterization by N2 Adsorption An alternative method was used to compare the pore- size results obtained from the ellipsometric measure- ments. One adsorption–desorption cycle of N2 was carried out with the Model ASAP 2010 analyzer. The isotherm that was obtained is shown in Fig. 6. The curve indicates a type IV isotherm, correspond- ing to a mesoporous material and in agreement with the ellipsometric results. A change of adsorptive ~N2 instead of water vapor! causes a change in the isotherm from type V to type IV. The adsorbent– adsorbate forces dominate the process compared with Fig. 5. Pore-size distribution calculated from the ellipsometric data @Fig. 3~a!#. the adsorptive–adsorptive forces. The software of the Model ASAP 2010 was used to analyze the data. The algorithm utilized is an implementation of the Barrett–Johner–Halenda method.12 It can be ob- served from Fig. 7 that a narrower shape of the de- sorption pore distribution was obtained, in accord with the distribution obtained from the ellipsometric data. The most probable pore radii obtained were 58 and 34 Å for the adsorption and the desorption branches, respectively. Pore sizes calculated from the ellipsometric mea- surements are smaller than those calculated from the N2-adsorption data. This result was expected be- cause, in the first case, the measurements were per- formed under room conditions. Therefore an indeterminate amount of impurities is placed on the pores’ walls, and when water adsorption occurs the effective radius of the pores is reduced. It is also necessary to note that the adsorbate–adsorbent sys- tem was different for both sets of measurements. C. Transmission Electron Microscope Micrographs Figure 8 shows the microstructural appearance of the Vycor samples. From the TEM micrographs, we can estimate that the radius of the pores is 50 Å, which is in accord with the Model ASAP 2010 analyzer re- sults. Again, this value is higher than the one ob- Fig. 6. Adsorption ~Œ! and desorption ~h! isotherms of N2 for orous Vycor glass as measured with the Model ASAP 2010 ana- yzer. Fig. 7. Pore-size distribution calculated from the data of the N2 isotherms. 1 February 2001 y Vol. 40, No. 4 y APPLIED OPTICS 531 p m c g f 1 1 1 1 1 5 tained by ellipsometry for the same reasons mentioned in Subsection 3.B. 4. Conclusions The behavior of the optical properties of the Model 7930 Vycor glass with the RH has been studied by ellipsometric techniques. An adsorption–desorption cycle with a hysteresis profile has been obtained, and the refractive-index changes were as high as 0.04 be- tween 5% and 90% RH. These great variations in the refractive index could be used when considering this material as a candidate for a transducer to be inte- grated in a fiber-optic sensor head, but the existence of a hysteresis loop advises against this possibility. In addition, information about the pore-size distri- bution has been extracted from the ellipsometric data and compared with N2 adsorption results. The ex- erimental curve is a typical isotherm of mesoporous aterials. The mean process in these solids is the apillary condensation of adsorbate in the pores of the lass. The estimation of pore-size distributions rom these data is in accord with the N2 isotherms and the TEM micrograph results. The values ob- tained by ellipsometry are the lowest because of the conditions under which all the ellipsometric mea- surements were performed: room conditions and therefore without outgassing. We conclude that the ellipsometric technique is a useful tool for estimating the porosity of thin films when traditional methods of measuring the amount of gas adsorbed ~gravimetric or volumetric methods! cannot be used. The authors gratefully acknowledge the contribu- tion of S. Martı́n Barbero for the adsorption measure- ments of N2 and P. Valles González for the TEM micrographs. We are much indebted to A. Pérez Masia and A. Ruiz Paniego for enlightening discus- sions about adsorption in porous materials. We are Fig. 8. TEM micrograph of the Vycor sample. 32 APPLIED OPTICS y Vol. 40, No. 4 y 1 February 2001 grateful to H. Guerrero for his support of this study. This research has been partially supported by the Comisión Interministerial de Ciencia y Tecnologı́a ~CICYT!, project ESP98-1332-C04-04. References 1. A. Hohr, H. B. Neumann, P. W. Schmidt, P. Pfeifer, and D. 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