The reaction equation for the reaction between water and silica reads 
						≡Si-O-Si≡ +H$_2$O ↔ [2 SiOH] 
					For this reaction the equilibrium constant, k, is affected by internal swelling stresses. We investigated the behaviour of erfc-shaped distributions of the total water amount in earlier Reports. The present report is intended to evaluate more complicated water profiles. Water concentrations at silica surfaces were measured by Zouine et al. Some of their data showed deviations from the expected erfc-shape. The associated datasets were used to demonstrate the procedure of determining the local equilibrium constant and the distributions of the hydroxyl and molecular water species on irregular water distributions. In an Appendix we discuss what could be the reason for the deviations in the distribution of the total water C$_w$ from the erfc-shape. The occurrence of back-diffusion after aging is assumed

Bucharsky, Claudia

Fett, Theo

Schell, Günter

English

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  KIT SCIENTIFIC WORKING PAPERS Evaluation of water profiles at silica surfaces at 23°C, 100°C and 200°C by Zouine et al.   Günter Schell, Claudia Bucharsky, Theo Fett    Institute for Applied Materials  Impressum Karlsruher Institut für Technologie (KIT) www.kit.edu    This document is licensed under the Creative Commons Attribution – Share Alike 4.0 International License (CC BY-SA 4.0): https://creativecommons.org/licenses/by-sa/4.0/deed.en  2023  ISSN: 2194-1629  III      Abstract The reaction equation for the reaction between water and silica reads  ≡Si-O-Si≡ +H2O ↔  [2 SiOH]  For this reaction the equilibrium constant, k, is affected by internal swelling stresses. We investigated the behaviour of erfc-shaped distri-butions of the total water amount in earlier Reports. The present report is intended to evaluate more complicated water profiles. Water con-centrations at silica surfaces were measured by Zouine et al. Some of their data showed deviations from the expected erfc-shape. The asso-ciated datasets were used to demonstrate the procedure of determining the local equilibrium constant and the distributions of the hydroxyl and molecular water species on irregular water distributions.  In an Appendix we discuss what could be the reason for the deviations in the distribution of the total water Cw from the erfc-shape. The occurrence of back-diffusion after aging is assumed.    IV                                             V          Contents   1 Basic equations  1 2 Evaluation of profiles with irregular behaviour at the surface 2   2.1  Evaluation at 200°C 2   2.2  Evaluation at 100°C  3   2.3  Evaluation at 23°C  4    Remarks  4    Appendix:     A probable reason for the occurrence of irregular profiles  5     References  7                 VI           1 1 Basic equations Water penetrated into silica reacts with the silica network. In our Reports [1] and [2] we dealt with the shape of the water profiles at silica surfaces. We found that the equi-librium between hydroxyl S = [≡SiOH] and molecular water C = [H2O] of the reaction   ≡Si-O-Si≡ +H2O ↔ ≡SiOH+HOSi≡ (1) must change with the distance from the glass surface due to the compressive swelling stresses. Expressed in terms of the equilibrium constant k,   CSk =   (2) the equilibrium also becomes dependent on concentration and location.  Then the equilibrium constant reads according to [3]      ∆−=RTVSkk λexp0  (3) with λ=18.8 GPa. The hydrostatic swelling stress is expressed by    Shsw λs −=,  . (4) Only erfc-shaped distributions Cw(z) of the total water    SCCw 21+=  (5) were prescribed in [2]     =bzCC ww 2erfc)0(  (6) The present report is intended to evaluate more complicated water profiles. Water con-centrations at silica surfaces under saturation pressure are available from an investiga-tion by Zouine et al. [4]. For our computations we used an activation volume of ∆V≅58 cm3/mol as was obtained in [2] by a fitting procedure. Some results in [4] deviate from the simple erfc-description as can be seen for meas-urements compiled in Fig. 1a. Figure 1b represents the same results in a normalized representation where C(0) are the surface concentrations from Table 1 in [4] and addi-tionally the concentrations are divided by the diffusion depth b at which the erfc func-tion has the value of ≅½.  2   Fig. 1 Some irregular profiles a) total water content Cw(z) measured by Zouine et al. [4], b) same data in normalized representation, Cw(0), Cw(z=0). The equilibrium constant as a function of the measured Cw finally results from (3) in the implicit equation    +∆−=kwCRTVkk1210exp λ  (7) since k is present on the left-hand side as well as on the right-hand side in the denomi-nator of the exponential function. From the measured values of Cw the two water spe-cies S and C can be computed via   kCC w211+= ,    (8)    +=kCS w1211817 (9) 2. Evaluation of profiles with irregular behaviour at the surface 2.1 Evaluation at 200°C The water profiles S, C were computed via eqs.(8) and (9) and plotted in Fig. 2 to-gether with the total water concentrations Cw as measured in [4]. The shortest distance below the surface is about z=40-50 nm. 2.0 0.005 0.004 0.003 0.002 0.001 1.0 z   (µm) Cw 23°C 100°C 200°C a) 1.0 2.0 0.8 1.0 0.6 0.4 0.2 z/b Cw/Cw(0) b)  3   Fig. 2 Water species S and C, derived from the measurements of total water, Cw, for soaking at 200°C. 2.2 Evaluation at 100°C The profiles obtained after a soaking time of 1319h are shown in Fig. 3. Unfortunately, there are no data available for z<170nm.      Fig. 3 Water species S and C, derived from the measurements of total water, Cw, for soaking at 100°C. 1 0.005 0.004 0.003 0.002 0.001 2 Cw S C C,S,Cw z   (µm) 0.5 0.002 0.0015 0.001 0.0005 1 1.5 2 z   (µm) S C Cw C,S,Cw  4 2.3 Evaluation at 23°C Finally, Fig. 4 shows the profiles at room temperature hydrated for about 15000h in humid air. At distances of 0<z<170nm, the water concentrations are significantly lower than expected from eq.(6). In this range, the distribution no longer follows eq.(6). Re-garding the low concentration near the surface, the authors of [4] note: “In the 23°C/air profile the near surface data points lie lower than to be expected. The reason for this is not clear. However, it seemed justified to omit these data points in fitting the profile.”   Fig. 4 Water species S and C, derived from the measurements of total water, Cw, for soaking at room temperature 23°C.  Remarks:  • In [1] we found that the hydroxyl water profile S(z) for small depth z must decrease with respect to the shape of the total water concentration as obtained by the nuclear reaction analysis (NRA). This was concluded for a Cw-distribution of type eq.(6). From Figs. 2-4, we can see that the same effect occurs also for different types of Cw(z). This makes it understandable that the concentration curves of the two water species S and C deviate from the curve of the total water concentration Cw, but does not explain why Cw itself shows the really unexpected distributions. • It is obvious that the equilibrium constant varies in a water diffusion zone where Cw varies with depth and an average value k  over the depth profile 0.0004 S C 0.0003 0.0002 0.0001 0.0005 0.2 0.4 0.6 0.8 C,S,Cw Cw z   (µm)  5   ∫∫==dzzCdzzSCSk)()( (10) according to [1], determined by measurements of Wiederhorn et al. [5]. Figure 5 shows the local distribution of the equilibrium constant k(z) as the circles. The dash-dotted lines indicate the average values according to eq.(10). • In the Appendix, we want to investigate whether back-diffusion may occur during the storage until the measurement, which is not defined in the article.     Fig. 5 Varying equilibrium constant k as a function of depth, horizontal lines: averages over the whole water zone, according to [1]. Appendix:  A probable reason for the occurrence of irregular profiles The irregular distributions of the measurement data from Zouine et al. [4], especially those at room temperature, can be understood by back-diffusion after water or air stor-age, respectively.  Unfortunately, no detailed information on storage after the end of the experiment is given in [4]. It therefore remains unclear in which medium and for how long the sam-ples were in until the subsequent NRA measurement.  Due to this circumstance, only the possibility of the effect should be addressed here, but no quantitative information should be given. This may be illustrated here by superimposing two erfc distributions of the type 1.0 200°C k=2.1 k=1.2 k=0.41 100°C 23°C 0.5 1.5 2.0 0.5 1.0 1.5 2.0 z   (µm) k  6   ][erfc][erfc 3210 zaazaaCw +=  (11) the first describing diffusion during aging in the wet medium and the second de-scribing diffusion towards the surface after aging. Zouine et al. [4] fitted the data far from the surface and thereby obtained the parameters a0 and a1 (introduced as curves in the original plots). Table 1 compiles these coefficients in the columns 2 and 3.  We fitted the whole data by eq.(11) and obtained the two parameters a2 and a3, given in columns 4 and 5. The negative parameter a1 can be taken as an indication of a rever-sal of diffusion. Finally, the best fitting curves are plotted in Figs. 6a-6c.         Fig. 6 Total water profiles Cw(z), fitted by two superimposed erfc-functions according to eq.(11) using the parameters of Table 1. 0.0005 0.0010 0.001 0.5 1 1.5 2 Cw 100°C z   (µm) b) 0.006 0.004 0.002 2 1 z   (µm) Cw 200°C a) 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.4 0.6 0.8 z   (µm) Cw 23°C c)  7 Temperature a0 a1 (µm.1) a2 a3 (µm.1) 200°C 0.0052 0.2421 -0.00143 4.53 100°C 0.00177 0.377 -0.000254 5.73 23°C 0.00063 2.218 -0.00041 15.6 Table 1 Parameters for eq.(11) obtained by curve fitting to data of Figs. 6a-6c.  References                                                  1 T. Fett, K.G. Schell, C.E. Bucharsky, Distribution of equilibrium constant k and hydroxyl S in silica surface layers, SWP 195, 2022, ISSN: 2194-1629, Karlsruhe, KIT. 2 T. Fett, K.G. Schell, C.E. Bucharsky, Interpretation of silica-disk-tests including the effect of limited mass transfer at the surface, SWP 196, 2022, ISSN: 2194-1629, Karlsruhe, KIT. 3 T. Fett, G. Rizzi, K.G. Schell, C.E. Bucharsky, P. Hettich, S. Wagner, M. J. Hoffmann, Consequences of hydroxyl generation by the silica/water reaction, Part I: Diffusion and Swell-ing, KIT Scientific Publishing, 101(2022), Karlsruhe.  4 A. Zouine, O. Dersch, G. Walter and F. Rauch, “Diffusivity and solubility of water in silica glass in the temperature range 23-200°C,” Phys. Chem. Glass: Eur. J. Glass Sci and Tech. Pt. B, 48 [2] 85-91 (2007). 5 S. M. Wiederhorn, F. Yi, D. LaVan, T. Fett, M.J. Hoffmann, Volume Expansion caused by Water Penetration into Silica Glass, J. Am. Ceram. Soc. 98 (2015), 78-87.  KIT Scientific Working Papers ISSN 2194-1629www.kit.eduKIT – The Research University in the Helmholtz Association

Evaluation of water profiles at silica surfaces at 23°C, 100°C and 200°C by Zouine et al

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Evaluation of water profiles at silica surfaces at 23°C, 100°C and 200°C by Zouine et al

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