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Water diffusion into a silica glass optical fiber
Journal of Non-Crystalline Solids 324 (2003) 256–263 www.elsevier.com/locate/jnoncrysol
Water diffusion into a silica glass optical fiber Stephanie Berger a, Minoru Tomozawa b
b,*
a Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110, 8th Street, Troy, NY 12180-3590, USA
Received 30 July 2002
Abstract The diffusion coefficient and solubility of water in silica glass optical fiber cladding were measured in the temperature range of 600–800 °C and were compared with the corresponding values of bulk silica glasses. It was found that the diffusion coefficient was slightly lower and the solubility was appreciably higher in optical fiber, especially at low temperatures, compared with those in bulk silica glasses. The observed trend was consistent with the expected effect of fictive temperature. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Optical fibers are part of the important new technology currently being used in the telecommunications industry. These fibers are composed of pure silica glass cladding and a germaniumdoped silica glass core. Since the fibers are drawn from high temperatures 2000 °C and are quenched rapidly, the structure and properties of fiber cladding glasses are expected to be different from those of annealed silica glasses even though the composition is same. Among various glass characteristics, water diffusion is of particular concern since water in glasses has a disproportionately large influence on many glass properties. For example, water in glass reduces both mechanical
*
Corresponding author. Tel.: +1-518 276 6659; fax: +1-518 276 8554. E-mail address: [email protected] (M. Tomozawa).
strength and chemical durability, and increases the optical absorbance. Since the optical fibers can be exposed to water vapor for an extended period during their usage, the water diffusion into the fibers may become an important concern. Previous studies on water diffusion of silica glasses [1] have found that the diffusion constant of water in silica glass varies with fictive temperature, or cooling rate from the melt. The fictive temperature is the temperature at which the supercooled liquid changes to its glassy state [2]. In general, glasses prepared using a faster cooling rate acquire a higher fictive temperature. Due to their fast cooling rate silica glass optical fibers have a much higher fictive temperature, e.g. 1650 °C [3] compared to 1100–1200 °C of normal annealed silica glasses. Silica glasses cooled at a faster rate have a lower volume and therefore a higher density and a higher index of refraction compared with silica glasses cooled at a slower rate [4,5]. Roberts and Roberts [1] found that silica glass
0022-3093/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00247-3
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263
2. Experimental procedure A commercial single mode silica glass optical fiber with the diameter of 125 lm made by Furukawa Electric Co. was used. The fibers were exposed to water vapor of constant water vapor pressure, 335 Torr, for varied times at selected temperatures. The water uptake was monitored using Fourier transform infrared spectroscopy (FTIR). From the water (hydroxyl) uptake data, both the water diffusion coefficient and water solubility were obtained. First, the fibers were cut into pieces several centimeters in length and the plastic coating was removed from the fibers by placing them for 30 s in a mixture of sulfuric acid and nitric acid (98% H2 SO4 –2% HNO3 ), which was heated to 200 °C. This process was followed by ethanol and water washing. The obtained bare fibers were then heattreated in an electric furnace for various lengths of time up to 24 h at temperatures of 600, 700, and 800 °C. The constant water vapor pressure, 355 Torr, generated by a water bath kept at 80 °C, was flown into the furnace where the fiber samples were heat-treated. The fiber samples were placed in a wire holder and then into a silica glass tube that was placed in the electric furnace. The wire holder allowed most of the surface area of the fiber to be exposed to water vapor. After heat-treatment for a prescribed period of time, the fiber was quickly taken out of the furnace and kept in a glass vial until the FTIR measurement could be taken. The temperature range of the heat-treatment was chosen because of the relaxation kinetics. If a high temperature such as 1200 °C had been used
the glass would quickly relax and lose memory of its original structure. Even at lower temperature, surface structural relaxation can take place [6]. In the temperature range below 850 °C, however, the rate of the surface relaxation is slower than the rate of water diffusion [6] and water is expected diffuse into the unrelaxed fiber. The IR absorption spectrum of each fiber was obtained using a Nicolet Magna 560 FT-IR with Spectra-Tech IR-Plan Advantage microscope attachment. The beam size was fixed by an aperture of 20 lm 160 lm with the longer dimension parallel to the fiber axis. An absorbance spectrum across the fiber diameter was taken with 256 scans for each reading. It is known that the absorption band near 3670 cm1 is due to the vibration of the hydroxyl and that peaks at this wavenumber indicate the presence of hydroxyl water [6]. An example of the absorbance data is shown in Fig. 1. The sample before heat-treatment showed no absorbance at the hydroxyl band. The absorbance of the heat-treated samples were obtained as the heights of the peaks at 3570 cm1 above the value for the un-heat-treated sample. The obtained absorbance is proportional to the amount of the absorbing species, hydroxyl in the present case. The water uptake was measured as a function of heat-treatment time and temperature. Water diffusion into silica glass at the heat-treated temperature is expected to exhibit the Fickian diffusion
0.12 23hr
0.10
16hr 0hr
Absorbance
with higher fictive temperatures had lower water diffusion constants and higher water solubility at a constant temperature of 750 °C in the fictive temperature range of 1100–1300 °C. However, no water diffusion data are available for a silica glass with fictive temperature as high as those of optical fibers silica glasses. This study attempts to provide the water diffusion constant and water solubility data for silica glass optical fibers. The data are useful for estimating the long-range stability of optical fibers.
257
0.08 0.06 0.04 0.02 0.00 3000
3200
3400
3600
3800
4000
-1
Wavenumber (cm ) Fig. 1. Absorbance due to hydroxyl in silica glass fiber after heat-treatment times indicated at 800 °C.
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263
p p [4], following the relation Q ¼ Cs ð4= pÞ Dt, where Q is the hydroxyl uptake, Cs is the surface concentration, D is the diffusion constant, and t is the heat-treatment time. This is the expression for the uptake of a thick plate, water entering from both surfaces [7]. The uptake was plotted against the square root of the heat-treatment time and the resulting slope was evaluated. In order to obtain the diffusion coefficient from the slope, it is necessary to know the surface concentration or solubility, Cs , of hydroxyl in the glass. The surface concentration was determined by measuring the hydroxyl content in the surface layer of the heattreated samples. For this purpose, the samples were successively etched with a hydrofluoric acid, 25% HF–15% H2 SO4 mixture and the corresponding change in IR absorbance was monitored. After each acid etching, the fibers were washed with ethanol, followed by water. The depth removed was measured using a Unitron optical microscope. The negative slope of the residual absorbance vs. etch depth near the specimen surface provides the surface concentration. The observed surface concentration was also considered to be the solubility of water under the water vapor pressure and temperature employed.
3. Results The water uptake data expressed in terms of IR absorbance values are plotted against the square root of the heat-treatment time in Fig. 2 for all three different heat-treatment temperatures. Error bars are shown where they are larger than the symbols. Data were least-square fitted with the expected straight lines [7] at each heat-treatment temperature. The slopes of the linear relationships between the absorbance and the square root of the heating time obtained at various temperatures are shown in Table 1. The slopes show a slight increase with increasing temperature indicating that at higher temperatures water is absorbed at a faster rate. Fig. 3 shows the etched depth vs. etching time for the glass fiber samples heat-treated at various temperatures. Within the experimental error, all the samples had the same etching rate of 1.6 lm/min.
0.12
0.1
Absorbance
258
0.08
0.06
0.04
800C 700C
0.02
600C
0 0
2
4
6 1/2
Square Root Time (hr ) Fig. 2. Absorbance of the hydroxyl peak as a function of square root of the heat-treatment time at three different temperatures.
Table 1 Slopes of absorbance vs. square root time Temperature (°C)
p Slope (absorbance/ h)
800 700 600
0.021 0.0183 0.0168
To increase accuracy of the depth measurement, the least-square fit line of the etching data was taken as seen in Fig. 3, and was used to estimate the thickness removed from the etching time employed. As the fibers were etched, their remaining water content decreased. This decrease in water content was reflected in the decrease in height of the water peak as shown in Fig. 4. Fibers heated at higher temperatures had a slower rate of water decrease than those heated at lower temperatures. The rate of water decrease in relation to thickness reduction allows the surface concentration, Cs , to be calculated. For finding Cs the slope of the data in Fig. 4 near the surface was used for samples treated at 600 and 700 °C. However, for the sample treated at 800 °C, the slope to the last (or deepest) point was used because the change in water content was
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 Table 2 Surface hydroxyl concentrations
Total Thickness Etched (um)
10 9 8
Temperature (°C)
Cs (cm1 )
7
800 700 600
14.3 25.8 44.1
6 5 4
800C
3
700C
2
600C
1 0 0
1
2
3
4
5
6
Time (min) Fig. 3. Thickness of fibers etched vs. etching time for silica fiber after heat-treatment at indicated temperatures.
0.12
0.1
Absorbance
259
0.08
silica glass with increasing temperature, especially at lower temperature. Using the slope of water uptake shown in Table 1 and the surface concentration for each temperature the diffusion constant was calculated. The obtained diffusion coefficients are shown in Table 3. The diffusion data are also plotted as logðDÞ vs. the inverse of the absolute temperature in Fig. 6. The diffusion coefficients obtained here are compared with the diffusion coefficients for bulk silica glasses obtained earlier by Davis and Tomozawa [6]. The water diffusion coefficients of the silica optical glass fiber were slightly smaller and had a steeper slope than those of the bulk silica glass. The activation energy for the diffusion of water
0.06
50 0.04
0.02
Davis and Tomozawa [6] Present Data
45
800C 700C 600C
40 35
0
2
4
6
8
Depth (um) Fig. 4. Decrease in absorbance due to hydroxyl with thickness etched for fibers heat-treated at indicated temperature for 24 h.
Cs (cm-1 )
0
30 25 20 15
so small at early etching times that it was difficult to determine the slope accurately. The values for the surface hydroxyl concentration, Cs , expressed in terms of absorbance per unit sample thickness, are shown in Table 2. The fibers heated at lower temperatures had higher Cs values. Fig. 5 shows the surface concentration data for the fibers, compared to data previously taken by Davis and Tomozawa for bulk silica glass [6]. The surface concentrations for the fibers are much higher and decrease at faster rate than in bulk
10 5 0 800
1000
1200
1400
1600
Temperature (K) Fig. 5. Surface concentration data for silica glass fibers compared to previous data for bulk silica glass with fictive temperature of 1075 °C as a function of heat-treatment temperature in 355 Torr water vapor.
260
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263
Table 3 Effective water diffusion constants Temperature (°C)
D (cm2 /s)
800 700 600
1.2 1010 2.8 1011 7.9 1012
-8 -8.5
Davis and Tomozawa [6]
-9
Present Data -9.5 -10 -10.5 -11 -11.5 -12 0.5
0.7
0.9
1.1
1.3
1.5
1000/T (K)
Fig. 6. Log D (cm2 /s) plotted against 1000/temperature (Kelvin) for both silica glass fibers and bulk silica glass samples by Davis and Tomozawa [6].
into silica fibers was evaluated assuming the temperature dependence of diffusion coefficient of D ¼ D0 expðE=RT Þ; where D0 and E are pre-exponential factor and activation energy, respectively. The obtained value of the activation energy for silica glass fiber, 104 kJ/mol, is larger than 83 kJ/mol obtained by Davis and Tomozawa [6] for bulk silica glass. 4. Discussion The present sample was glass fiber with a circular cross-section while a model for a thick plate was used for the data analysis. Error associated with this assumption will be evaluated first. According to Crank [7], the uptake of diffusing species, Mt , at small time, t, by a fiber with radius, a, is given by p p p Mt =M1 ¼ ð4= pÞ Dt=a2 Dt=a2 ½1=ð3 pÞ
ðDt=a2 Þ3=2 þ ;
where M1 is the uptake at time 1, and is given by pa2 Cs . When the second and higher order terms can be ignored, the uptake p per p unit surface area is given by Mt =2pa ¼ Cs ð2= pÞ Dt, which is equivalent to the quantity Q for a semi-infinite plate employed in the present analysis. (The factor of 2 difference comes from the uptake from one side vs. both sides.) Therefore, the error caused by ignoring the higher order terms in the above equation will be evaluated. Taking the worst case scenario of the highest diffusion coefficient of 1.17 1010 cm2 /s at 800 °C and the longest heat-treatment time of 24 h, the diffusion distance becomes p Dt ¼ 31:8 lm. Using the radius of the optical fiber, 62.5 lm, the error in water uptake by approximating the fiber by a thick plate is at most 25%. At lower temperatures and shorter times, the error is smaller. Furthermore, the observed nearly linear relationship between the uptake and square root of time suggests that the higher order terms are not playing an important role. With the microscope attachment to the FT-IR used in the present experiment, the IR beam during the absorbance measurement is diverged and converged instead of passing through the sample vertically. The extent of the divergence is proportional to the specimen thickness and the angle, a, of the diverging beam schematically shown in Fig. 7. In the Spectra-Tech IR-Plan Advantage microscope employed, the average angle of incidence is 28°. If the refractive index of silica glass at 3500 cm1 is assumed to be 1.42, the average value of the diverging angle, a, is estimated to be 19.3°. Under these conditions, the beam passes through the fiber off-center across 118 lm distance as shown in the figure. This distance is smaller than the fiber diameter of 125 lm but is sufficiently larger than the maximum water diffusion distance, 32 lm, and the water uptake equation employed would still be valid. The general trends of the temperature dependence of water diffusion into the silica glass fiber were consistent with what was expected from previous research. For example, the observed higher solubility of water at lower temperatures in the measured temperature range is consistent with previous research by Davis and Tomozawa [6]. The water uptake data shown in Fig. 2 at three different
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 IR beam
20µ m
α
Fig. 7. Schematic IR ray diagram of the absorbance measurement of the fiber using FT-IR with a microscope attachment.
temperatures were very close. This is because, while the water diffusion coefficient is greater at higher temperature, the surface hydroxyl concentration, or hydroxyl solubility, is lower at higher temperature. The FT-IR absorbance measures the total amount of water in the sample and the opposite temperature dependence of diffusion coefficient and surface concentration makes the uptake rates at different temperature very close. The main cause of the different diffusion behavior between the fiber and the bulk silica glasses is the different fictive temperature. Roberts and Roberts [1] showed that a silica glass with higher fictive temperature has a lower water diffusion coefficient and higher hydroxyl solubility. Since the fibers have a higher fictive temperature they should have lower diffusion constants and higher surface concentration compared with the bulk silica glasses.
261
In Fig. 8, water diffusion data at 750 °C, obtained by interpolation in the present case, are collected as a function of fictive temperature. Since the solubility data by Roberts and Roberts [1] are expressed in a different unit from that of the present study, the value was normalized using the data by Davis and Tomozawa [6] who used the silica glass with the fictive temperature 1060 °C. The general trend is consistent but the diffusion coefficients obtained by Roberts and Roberts [1] are different from other data. The silica glass used by Roberts and Roberts was type I [1,4] made by fusion of crystalline quartz, while the glass used by Davis and Tomozawa [6] as well as the glass fiber used here were made by a CVD method. Different types of silica glasses may be a cause of some discrepancy. Another source of difference is the water vapor pressure employed in the measurement. While 335 Torr was used by the present authors as well as by Davis and Tomozawa [6], 700 Torr was used by Robert and Roberts [1]. Diffusion of water in silica glass is believed to involve the motion of molecular water and the following reaction between water and the glass network [8] H2 O þ BSiAOASiB $ BSiAOH þ HOASiB; where B represents three chemical bonds to the neighboring oxygen. It is believed that the reaction is fast at high temperature and the local equilibrium is maintained during the water diffusion, with the equilibrium constant 2
K ¼ ½OH =½H2 O ; where [OH] and [H2 O] represent the activity or concentration of hydroxyl and molecular water, respectively and the activity of silica network is considered to be unity. When the water concentration is low, the major part of water in silica glass exists as hydroxyl. The measured water diffusion coefficient under such condition is an effective diffusion coefficient, Deff , given by Deff ¼ 4D½OH =K; where D is the diffusion coefficient of molecular water. Silica glasses with higher fictive temperature are expected to contain greater concentration of defects such as vacancy and strained bonds. These
262
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 25
Cs (cm-1)
20
15
10 Roberts and Roberts [1] Davis and Tomozawa [6] Present Data
5
0 800
1000
1200
1400
1600
1800
Fictive Temperature (oC)
(a) 2.50E-10
Roberts and Roberts [1] Davis and Tomozawa [6] Present Data
Diffusion Coefficient (cm2/s)
2.00E-10
defects are expected to increase the reactivity of silica glass with water. Furthermore, silica glasses with higher fictive temperatures have a structure in which Si–O–Si bond angles are smaller. It was reported [9] that silica structures with smaller Si– O–Si bond angles have a greater reactivity with water. This structural feature would also increase the hydroxyl concentration. Thus, the solubility of water, which exists predominantly in the form of hydroxyl, is expected to increase with increasing fictive temperature. On the other hand, the concentration of molecular water in a silica glass, [H2 O], would change only slightly with fictive temperature. This would make the resulting value of K greater for a glass with higher fictive temperature at a constant temperature. The effective water diffusion coefficient, Deff , is expected, then, to decrease with increasing fictive temperature due to a larger value of K. Thus, the observed trend of water diffusion in silica glasses, both bulk and fibers, appears to be consistent with the trend expected for glasses with different fictive temperatures. 5. Conclusion Silica glass optical fibers were found to have higher surface hydroxyl concentrations (or solubility) and lower effective water diffusion constants than bulk silica glass. The observed features are attributed to the higher fictive temperature of the silica glass optical fibers.
1.50E-10
1.00E-10
Acknowledgements 5.00E-11
0.00E+00 1000
(b)
1200
1400
1600
1800
Fictive Temperature (oC)
Fig. 8. Fictive temperature dependence of (a) water solubility and (b) diffusion coefficient at 750 °C, under 355 Torr water vapor pressure. N: present data, r: Roberts and Roberts [1], j: Davis and Tomozawa [6]. (Roberts and RobertsÕ data [1] were obtained under 700 Torr water vapor pressure. Their solubility data were shifted to match that by Davis and Tomozawa data [6].)
This research was performed as a part of the NSF sponsored Research Experience for Undergraduates (REU) program at Rensselaer Polytechnic Institute under grant number DMR-97589. Careful reading of the manuscript by Mr Michael Magyar of Rensselaer is greatly appreciated. References [1] G.J. Roberts, J.P. Roberts, Phys. Chem. Glasses 5 (1964) 26. [2] A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240.
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 [3] D.-L. Kim, M. Tomozawa, J. Non-Cryst. Solids 286 (2001) 132. [4] R. Bruckner, J. Non-Cryst. Solids 5 (1970) 123. [5] J. Murach, R. Bruckner, J. Non-Cryst. Solids 211 (1997) 250. [6] K.M. Davis, M. Tomozawa, J. Non-Cryst. Solids 185 (1997) 203.
263
[7] J. Crank, Mathematics of Diffusion, 2nd Ed., Clarendon, Oxford, 1975, p. 32 and p. 74. [8] R.H. Doremus, in: J.W. Mitchell, R.C. DeVries, R.W. Roberts, P. Cannon (Eds.), Reactivity of Solids, Wiley, NY, 1969, p. 667. [9] T.A. Michalske, B.C. Banker, J. Am. Ceram. Soc. 76 (1993) 2613.
Water diffusion into a silica glass optical fiber Stephanie Berger a, Minoru Tomozawa b
b,*
a Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110, 8th Street, Troy, NY 12180-3590, USA
Received 30 July 2002
Abstract The diffusion coefficient and solubility of water in silica glass optical fiber cladding were measured in the temperature range of 600–800 °C and were compared with the corresponding values of bulk silica glasses. It was found that the diffusion coefficient was slightly lower and the solubility was appreciably higher in optical fiber, especially at low temperatures, compared with those in bulk silica glasses. The observed trend was consistent with the expected effect of fictive temperature. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Optical fibers are part of the important new technology currently being used in the telecommunications industry. These fibers are composed of pure silica glass cladding and a germaniumdoped silica glass core. Since the fibers are drawn from high temperatures 2000 °C and are quenched rapidly, the structure and properties of fiber cladding glasses are expected to be different from those of annealed silica glasses even though the composition is same. Among various glass characteristics, water diffusion is of particular concern since water in glasses has a disproportionately large influence on many glass properties. For example, water in glass reduces both mechanical
*
Corresponding author. Tel.: +1-518 276 6659; fax: +1-518 276 8554. E-mail address: [email protected] (M. Tomozawa).
strength and chemical durability, and increases the optical absorbance. Since the optical fibers can be exposed to water vapor for an extended period during their usage, the water diffusion into the fibers may become an important concern. Previous studies on water diffusion of silica glasses [1] have found that the diffusion constant of water in silica glass varies with fictive temperature, or cooling rate from the melt. The fictive temperature is the temperature at which the supercooled liquid changes to its glassy state [2]. In general, glasses prepared using a faster cooling rate acquire a higher fictive temperature. Due to their fast cooling rate silica glass optical fibers have a much higher fictive temperature, e.g. 1650 °C [3] compared to 1100–1200 °C of normal annealed silica glasses. Silica glasses cooled at a faster rate have a lower volume and therefore a higher density and a higher index of refraction compared with silica glasses cooled at a slower rate [4,5]. Roberts and Roberts [1] found that silica glass
0022-3093/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00247-3
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263
2. Experimental procedure A commercial single mode silica glass optical fiber with the diameter of 125 lm made by Furukawa Electric Co. was used. The fibers were exposed to water vapor of constant water vapor pressure, 335 Torr, for varied times at selected temperatures. The water uptake was monitored using Fourier transform infrared spectroscopy (FTIR). From the water (hydroxyl) uptake data, both the water diffusion coefficient and water solubility were obtained. First, the fibers were cut into pieces several centimeters in length and the plastic coating was removed from the fibers by placing them for 30 s in a mixture of sulfuric acid and nitric acid (98% H2 SO4 –2% HNO3 ), which was heated to 200 °C. This process was followed by ethanol and water washing. The obtained bare fibers were then heattreated in an electric furnace for various lengths of time up to 24 h at temperatures of 600, 700, and 800 °C. The constant water vapor pressure, 355 Torr, generated by a water bath kept at 80 °C, was flown into the furnace where the fiber samples were heat-treated. The fiber samples were placed in a wire holder and then into a silica glass tube that was placed in the electric furnace. The wire holder allowed most of the surface area of the fiber to be exposed to water vapor. After heat-treatment for a prescribed period of time, the fiber was quickly taken out of the furnace and kept in a glass vial until the FTIR measurement could be taken. The temperature range of the heat-treatment was chosen because of the relaxation kinetics. If a high temperature such as 1200 °C had been used
the glass would quickly relax and lose memory of its original structure. Even at lower temperature, surface structural relaxation can take place [6]. In the temperature range below 850 °C, however, the rate of the surface relaxation is slower than the rate of water diffusion [6] and water is expected diffuse into the unrelaxed fiber. The IR absorption spectrum of each fiber was obtained using a Nicolet Magna 560 FT-IR with Spectra-Tech IR-Plan Advantage microscope attachment. The beam size was fixed by an aperture of 20 lm 160 lm with the longer dimension parallel to the fiber axis. An absorbance spectrum across the fiber diameter was taken with 256 scans for each reading. It is known that the absorption band near 3670 cm1 is due to the vibration of the hydroxyl and that peaks at this wavenumber indicate the presence of hydroxyl water [6]. An example of the absorbance data is shown in Fig. 1. The sample before heat-treatment showed no absorbance at the hydroxyl band. The absorbance of the heat-treated samples were obtained as the heights of the peaks at 3570 cm1 above the value for the un-heat-treated sample. The obtained absorbance is proportional to the amount of the absorbing species, hydroxyl in the present case. The water uptake was measured as a function of heat-treatment time and temperature. Water diffusion into silica glass at the heat-treated temperature is expected to exhibit the Fickian diffusion
0.12 23hr
0.10
16hr 0hr
Absorbance
with higher fictive temperatures had lower water diffusion constants and higher water solubility at a constant temperature of 750 °C in the fictive temperature range of 1100–1300 °C. However, no water diffusion data are available for a silica glass with fictive temperature as high as those of optical fibers silica glasses. This study attempts to provide the water diffusion constant and water solubility data for silica glass optical fibers. The data are useful for estimating the long-range stability of optical fibers.
257
0.08 0.06 0.04 0.02 0.00 3000
3200
3400
3600
3800
4000
-1
Wavenumber (cm ) Fig. 1. Absorbance due to hydroxyl in silica glass fiber after heat-treatment times indicated at 800 °C.
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263
p p [4], following the relation Q ¼ Cs ð4= pÞ Dt, where Q is the hydroxyl uptake, Cs is the surface concentration, D is the diffusion constant, and t is the heat-treatment time. This is the expression for the uptake of a thick plate, water entering from both surfaces [7]. The uptake was plotted against the square root of the heat-treatment time and the resulting slope was evaluated. In order to obtain the diffusion coefficient from the slope, it is necessary to know the surface concentration or solubility, Cs , of hydroxyl in the glass. The surface concentration was determined by measuring the hydroxyl content in the surface layer of the heattreated samples. For this purpose, the samples were successively etched with a hydrofluoric acid, 25% HF–15% H2 SO4 mixture and the corresponding change in IR absorbance was monitored. After each acid etching, the fibers were washed with ethanol, followed by water. The depth removed was measured using a Unitron optical microscope. The negative slope of the residual absorbance vs. etch depth near the specimen surface provides the surface concentration. The observed surface concentration was also considered to be the solubility of water under the water vapor pressure and temperature employed.
3. Results The water uptake data expressed in terms of IR absorbance values are plotted against the square root of the heat-treatment time in Fig. 2 for all three different heat-treatment temperatures. Error bars are shown where they are larger than the symbols. Data were least-square fitted with the expected straight lines [7] at each heat-treatment temperature. The slopes of the linear relationships between the absorbance and the square root of the heating time obtained at various temperatures are shown in Table 1. The slopes show a slight increase with increasing temperature indicating that at higher temperatures water is absorbed at a faster rate. Fig. 3 shows the etched depth vs. etching time for the glass fiber samples heat-treated at various temperatures. Within the experimental error, all the samples had the same etching rate of 1.6 lm/min.
0.12
0.1
Absorbance
258
0.08
0.06
0.04
800C 700C
0.02
600C
0 0
2
4
6 1/2
Square Root Time (hr ) Fig. 2. Absorbance of the hydroxyl peak as a function of square root of the heat-treatment time at three different temperatures.
Table 1 Slopes of absorbance vs. square root time Temperature (°C)
p Slope (absorbance/ h)
800 700 600
0.021 0.0183 0.0168
To increase accuracy of the depth measurement, the least-square fit line of the etching data was taken as seen in Fig. 3, and was used to estimate the thickness removed from the etching time employed. As the fibers were etched, their remaining water content decreased. This decrease in water content was reflected in the decrease in height of the water peak as shown in Fig. 4. Fibers heated at higher temperatures had a slower rate of water decrease than those heated at lower temperatures. The rate of water decrease in relation to thickness reduction allows the surface concentration, Cs , to be calculated. For finding Cs the slope of the data in Fig. 4 near the surface was used for samples treated at 600 and 700 °C. However, for the sample treated at 800 °C, the slope to the last (or deepest) point was used because the change in water content was
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 Table 2 Surface hydroxyl concentrations
Total Thickness Etched (um)
10 9 8
Temperature (°C)
Cs (cm1 )
7
800 700 600
14.3 25.8 44.1
6 5 4
800C
3
700C
2
600C
1 0 0
1
2
3
4
5
6
Time (min) Fig. 3. Thickness of fibers etched vs. etching time for silica fiber after heat-treatment at indicated temperatures.
0.12
0.1
Absorbance
259
0.08
silica glass with increasing temperature, especially at lower temperature. Using the slope of water uptake shown in Table 1 and the surface concentration for each temperature the diffusion constant was calculated. The obtained diffusion coefficients are shown in Table 3. The diffusion data are also plotted as logðDÞ vs. the inverse of the absolute temperature in Fig. 6. The diffusion coefficients obtained here are compared with the diffusion coefficients for bulk silica glasses obtained earlier by Davis and Tomozawa [6]. The water diffusion coefficients of the silica optical glass fiber were slightly smaller and had a steeper slope than those of the bulk silica glass. The activation energy for the diffusion of water
0.06
50 0.04
0.02
Davis and Tomozawa [6] Present Data
45
800C 700C 600C
40 35
0
2
4
6
8
Depth (um) Fig. 4. Decrease in absorbance due to hydroxyl with thickness etched for fibers heat-treated at indicated temperature for 24 h.
Cs (cm-1 )
0
30 25 20 15
so small at early etching times that it was difficult to determine the slope accurately. The values for the surface hydroxyl concentration, Cs , expressed in terms of absorbance per unit sample thickness, are shown in Table 2. The fibers heated at lower temperatures had higher Cs values. Fig. 5 shows the surface concentration data for the fibers, compared to data previously taken by Davis and Tomozawa for bulk silica glass [6]. The surface concentrations for the fibers are much higher and decrease at faster rate than in bulk
10 5 0 800
1000
1200
1400
1600
Temperature (K) Fig. 5. Surface concentration data for silica glass fibers compared to previous data for bulk silica glass with fictive temperature of 1075 °C as a function of heat-treatment temperature in 355 Torr water vapor.
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Table 3 Effective water diffusion constants Temperature (°C)
D (cm2 /s)
800 700 600
1.2 1010 2.8 1011 7.9 1012
-8 -8.5
Davis and Tomozawa [6]
-9
Present Data -9.5 -10 -10.5 -11 -11.5 -12 0.5
0.7
0.9
1.1
1.3
1.5
1000/T (K)
Fig. 6. Log D (cm2 /s) plotted against 1000/temperature (Kelvin) for both silica glass fibers and bulk silica glass samples by Davis and Tomozawa [6].
into silica fibers was evaluated assuming the temperature dependence of diffusion coefficient of D ¼ D0 expðE=RT Þ; where D0 and E are pre-exponential factor and activation energy, respectively. The obtained value of the activation energy for silica glass fiber, 104 kJ/mol, is larger than 83 kJ/mol obtained by Davis and Tomozawa [6] for bulk silica glass. 4. Discussion The present sample was glass fiber with a circular cross-section while a model for a thick plate was used for the data analysis. Error associated with this assumption will be evaluated first. According to Crank [7], the uptake of diffusing species, Mt , at small time, t, by a fiber with radius, a, is given by p p p Mt =M1 ¼ ð4= pÞ Dt=a2 Dt=a2 ½1=ð3 pÞ
ðDt=a2 Þ3=2 þ ;
where M1 is the uptake at time 1, and is given by pa2 Cs . When the second and higher order terms can be ignored, the uptake p per p unit surface area is given by Mt =2pa ¼ Cs ð2= pÞ Dt, which is equivalent to the quantity Q for a semi-infinite plate employed in the present analysis. (The factor of 2 difference comes from the uptake from one side vs. both sides.) Therefore, the error caused by ignoring the higher order terms in the above equation will be evaluated. Taking the worst case scenario of the highest diffusion coefficient of 1.17 1010 cm2 /s at 800 °C and the longest heat-treatment time of 24 h, the diffusion distance becomes p Dt ¼ 31:8 lm. Using the radius of the optical fiber, 62.5 lm, the error in water uptake by approximating the fiber by a thick plate is at most 25%. At lower temperatures and shorter times, the error is smaller. Furthermore, the observed nearly linear relationship between the uptake and square root of time suggests that the higher order terms are not playing an important role. With the microscope attachment to the FT-IR used in the present experiment, the IR beam during the absorbance measurement is diverged and converged instead of passing through the sample vertically. The extent of the divergence is proportional to the specimen thickness and the angle, a, of the diverging beam schematically shown in Fig. 7. In the Spectra-Tech IR-Plan Advantage microscope employed, the average angle of incidence is 28°. If the refractive index of silica glass at 3500 cm1 is assumed to be 1.42, the average value of the diverging angle, a, is estimated to be 19.3°. Under these conditions, the beam passes through the fiber off-center across 118 lm distance as shown in the figure. This distance is smaller than the fiber diameter of 125 lm but is sufficiently larger than the maximum water diffusion distance, 32 lm, and the water uptake equation employed would still be valid. The general trends of the temperature dependence of water diffusion into the silica glass fiber were consistent with what was expected from previous research. For example, the observed higher solubility of water at lower temperatures in the measured temperature range is consistent with previous research by Davis and Tomozawa [6]. The water uptake data shown in Fig. 2 at three different
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 IR beam
20µ m
α
Fig. 7. Schematic IR ray diagram of the absorbance measurement of the fiber using FT-IR with a microscope attachment.
temperatures were very close. This is because, while the water diffusion coefficient is greater at higher temperature, the surface hydroxyl concentration, or hydroxyl solubility, is lower at higher temperature. The FT-IR absorbance measures the total amount of water in the sample and the opposite temperature dependence of diffusion coefficient and surface concentration makes the uptake rates at different temperature very close. The main cause of the different diffusion behavior between the fiber and the bulk silica glasses is the different fictive temperature. Roberts and Roberts [1] showed that a silica glass with higher fictive temperature has a lower water diffusion coefficient and higher hydroxyl solubility. Since the fibers have a higher fictive temperature they should have lower diffusion constants and higher surface concentration compared with the bulk silica glasses.
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In Fig. 8, water diffusion data at 750 °C, obtained by interpolation in the present case, are collected as a function of fictive temperature. Since the solubility data by Roberts and Roberts [1] are expressed in a different unit from that of the present study, the value was normalized using the data by Davis and Tomozawa [6] who used the silica glass with the fictive temperature 1060 °C. The general trend is consistent but the diffusion coefficients obtained by Roberts and Roberts [1] are different from other data. The silica glass used by Roberts and Roberts was type I [1,4] made by fusion of crystalline quartz, while the glass used by Davis and Tomozawa [6] as well as the glass fiber used here were made by a CVD method. Different types of silica glasses may be a cause of some discrepancy. Another source of difference is the water vapor pressure employed in the measurement. While 335 Torr was used by the present authors as well as by Davis and Tomozawa [6], 700 Torr was used by Robert and Roberts [1]. Diffusion of water in silica glass is believed to involve the motion of molecular water and the following reaction between water and the glass network [8] H2 O þ BSiAOASiB $ BSiAOH þ HOASiB; where B represents three chemical bonds to the neighboring oxygen. It is believed that the reaction is fast at high temperature and the local equilibrium is maintained during the water diffusion, with the equilibrium constant 2
K ¼ ½OH =½H2 O ; where [OH] and [H2 O] represent the activity or concentration of hydroxyl and molecular water, respectively and the activity of silica network is considered to be unity. When the water concentration is low, the major part of water in silica glass exists as hydroxyl. The measured water diffusion coefficient under such condition is an effective diffusion coefficient, Deff , given by Deff ¼ 4D½OH =K; where D is the diffusion coefficient of molecular water. Silica glasses with higher fictive temperature are expected to contain greater concentration of defects such as vacancy and strained bonds. These
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S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 25
Cs (cm-1)
20
15
10 Roberts and Roberts [1] Davis and Tomozawa [6] Present Data
5
0 800
1000
1200
1400
1600
1800
Fictive Temperature (oC)
(a) 2.50E-10
Roberts and Roberts [1] Davis and Tomozawa [6] Present Data
Diffusion Coefficient (cm2/s)
2.00E-10
defects are expected to increase the reactivity of silica glass with water. Furthermore, silica glasses with higher fictive temperatures have a structure in which Si–O–Si bond angles are smaller. It was reported [9] that silica structures with smaller Si– O–Si bond angles have a greater reactivity with water. This structural feature would also increase the hydroxyl concentration. Thus, the solubility of water, which exists predominantly in the form of hydroxyl, is expected to increase with increasing fictive temperature. On the other hand, the concentration of molecular water in a silica glass, [H2 O], would change only slightly with fictive temperature. This would make the resulting value of K greater for a glass with higher fictive temperature at a constant temperature. The effective water diffusion coefficient, Deff , is expected, then, to decrease with increasing fictive temperature due to a larger value of K. Thus, the observed trend of water diffusion in silica glasses, both bulk and fibers, appears to be consistent with the trend expected for glasses with different fictive temperatures. 5. Conclusion Silica glass optical fibers were found to have higher surface hydroxyl concentrations (or solubility) and lower effective water diffusion constants than bulk silica glass. The observed features are attributed to the higher fictive temperature of the silica glass optical fibers.
1.50E-10
1.00E-10
Acknowledgements 5.00E-11
0.00E+00 1000
(b)
1200
1400
1600
1800
Fictive Temperature (oC)
Fig. 8. Fictive temperature dependence of (a) water solubility and (b) diffusion coefficient at 750 °C, under 355 Torr water vapor pressure. N: present data, r: Roberts and Roberts [1], j: Davis and Tomozawa [6]. (Roberts and RobertsÕ data [1] were obtained under 700 Torr water vapor pressure. Their solubility data were shifted to match that by Davis and Tomozawa data [6].)
This research was performed as a part of the NSF sponsored Research Experience for Undergraduates (REU) program at Rensselaer Polytechnic Institute under grant number DMR-97589. Careful reading of the manuscript by Mr Michael Magyar of Rensselaer is greatly appreciated. References [1] G.J. Roberts, J.P. Roberts, Phys. Chem. Glasses 5 (1964) 26. [2] A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240.
S. Berger, M. Tomozawa / Journal of Non-Crystalline Solids 324 (2003) 256–263 [3] D.-L. Kim, M. Tomozawa, J. Non-Cryst. Solids 286 (2001) 132. [4] R. Bruckner, J. Non-Cryst. Solids 5 (1970) 123. [5] J. Murach, R. Bruckner, J. Non-Cryst. Solids 211 (1997) 250. [6] K.M. Davis, M. Tomozawa, J. Non-Cryst. Solids 185 (1997) 203.
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[7] J. Crank, Mathematics of Diffusion, 2nd Ed., Clarendon, Oxford, 1975, p. 32 and p. 74. [8] R.H. Doremus, in: J.W. Mitchell, R.C. DeVries, R.W. Roberts, P. Cannon (Eds.), Reactivity of Solids, Wiley, NY, 1969, p. 667. [9] T.A. Michalske, B.C. Banker, J. Am. Ceram. Soc. 76 (1993) 2613.