Dissolution Rates of Amorphous Silica in Highly Alkaline Solution

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Dissolution Rates of Amorphous Silica in Highly Alkaline Solution Yuichi NIIBORI, Masahisa KUNITA, Osamu TOCHIYAMA & Tadashi CHIDA To cite this article: Yuichi NIIBORI, Masahisa KUNITA, Osamu TOCHIYAMA & Tadashi CHIDA (2000) Dissolution Rates of Amorphous Silica in Highly Alkaline Solution, Journal of Nuclear Science and Technology, 37:4, , DOI: / To link to this article: Published online: 07 Feb Submit your article to this journal Article views: 3415 View related articles Citing articles: 18 View citing articles Full Terms & Conditions of access and use can be found at

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 37, No. 4, p (April 2000) Dissolution Rates of Amorphous Silica in Highly Alkaline Solution Yuichi NIIBORI*,t, Masahisa KUNITA**, Osamu TOCHIYAMA* and Tadashi CHIDA** * Department of Quantum Science and Energy Engineering, Graduate School of Engineering, Tohoku University ** Department of Geoscience and Technology, Graduate School of Engineering, Tohoku University (Received February 18, 1999) Cement is an essential materials to construct the subsurface radioactive waste disposal system. However, cementitious materials alter the groundwater ph to highly alkaline condition about 13. To comprehend the effect of such a hyperalkaline condition on the repository surroundings, this study focused on the dissolution rates of amorphous silica at [NaOH]=l0-1 mol dm- 3. The used samples were three kinds of pure commercial silica and a natural silica scale which was obtained from inside wall of the hot-water pipe of a geothermal power plant. The observed dissolution rates were interpreted with using the model, which assumed that the particle sizes decrease with the progress of dissolution. Moreover, due to the particle size distribution anticipated in the natural silica scale, this analysis assumed it contained particles with various initial diameters. In the results, (1) all pure silica samples and at least 60 wt% of the silica scale showed good agreement of the activation energy of the dissolution in the range of 77 through 88 kj-mol- 1 in the highly alkaline solution, (2) these rate constants were of the order of 10-s_ 10-7 mol m- 2 -s- 1 at around 310 K and were definitely larger than those already reported for quartz, (3) the specific surface area based on BET method was revealed to be an important factor to give the main difference in the dissolution rates between the synthetic silica and the natural silica. KEYWORDS: amorphous silica, dissolution rate, highly alkaline solution, radioactive wastes, repository system, alternation, kinetics, silica scale, silica gel, activation energy, ph value, solidification, waste processing, temperature dependence, radioactive waste disposal I. Introduction A main concern about the use of cement in the radioactive waste disposal system is that groundwater contacting with cement may attain ph values as high as 13( 1)( 2). The hyperalkaline plume would cause continuous alterations in the physical and chemical properties of the fractured layer or of the host rock surrounding the repository. Among various materials affected by such a change in ph, silica is one of the most important because of its abundant and ubiquitous existence and of its dominant role in the static and dynamic hydrogeochemical phenomena. Thus far, the dissolution rates of silica have been discussed particularly about the crystalline silicac 3)-C12l. These results have been applied to the feasibility study of placing the radioactive waste in man-made repositories situated in natural rock formation C1). However, as for the amorphous silica, the dissolution rates have not been discussed sufficientlyc 13)-C 15) in spite of its importance in the understanding of the radionuclide migration, particularly, through fractured layers accompanied by groundwater. In basic solution, the important factor governing the *,** Ammaki, Aoba-ku, Sendai t Corresponding author, Tel. & Fax , niibori@qse.tohoku.ac.jp dissolution rate of silica is considered to be the drastic increase in the concentration of the negatively charged surface species, [=Si-o-J. When the silica is in contact with water, the surface interaction can be described by =Si-0-S=+H (=Si-OH), where =Si-0-Si= represents a part of Si0 2 frameworkc 4 )C 5). In basic solution, =Si-OH changes into =Si-O-, depending on [OH-J. Brady and WaltherC 16) found from the dissolution rates of quartz that the rates are nearly proportional to [=Si-O-J. This fact suggested that the surface deprotonation (i.e., the formation of =Si-0-) leads to highly polarized interatomic Si-0 bonds and thus facilitates the detachment of Si into the solution. This dependency of the dissolution rate on [=Si-O-J has been also confirmed for amorphous silica by Niibori et al. C17), where the dissolution rates of two types of amorphous silica were shown to be almost proportional to [OH-jD- 5 in the range of ph from 10 through 13. However, the study was not sufficient to evalua_te the rate constants, particularly, with regard to the fraction of [=Si-0-J on the surface and the difference of specific surface area. Allen et al. C18) conducted the ph titration of suspended amorphous silica, and confirmed that above ph 12, almost all surface sites are present as =Si-o- sites. Thus in highly alkaline plume with ph 13, the dissolution rate strongly reflects on the surface concentration of =Si-O-. 349

3 350 Y. NIIBORI et al. Although the natural sample of amorphous silica produced in underground are not easily available, it is crucial to examine the dissolution rates of natural silica besides the man-made samples to estimate the role of silica in underground transport-phenomena. This paper discusses the dissolution rates of amorphous silica in high ph (13) solutions, using three kinds of commercial silica gel and a silica scale, where the latter is collected from Onuma geothermal field as a natural sample of amorphous silica. While highly alkaline plume mainly results from the dissolution of Ca(OH)2 in cement, this study used 10-1 mol-dm- 3 NaOH solution to avoid side reactions caused by Ca 2 + and to keep [=Si-O-J constant at the surface. In this solution, [OH-J was considered to be constant, since sufficiently small amounts of the samples were used in the experiments so that the amount of proton released by the dissolution could be neglected as compared with that of OH- in the solution. On the other hand, we could not ignore the change of the surface area accompanying the dissolution process. In order to consider its dependency in the course of time, the shrinking spherical particle model was applied to the rate estimation in this study. II. Experimental 1. Samples Table 1 gives three kinds of pure amorphous silica used in this study, as well as some of their physical/ chemical properties. They were obtained from Wako Pure Chemical Industries, Ltd., and from Mallinckrodt Co., and which will be respectively referred to as Wakogel C-200, Wako-gel LC-50H and Mallinckrodt silica in this paper. All of their X-ray diffraction patterns showed amorphous feature. Since Mallinckrodt silica was purchased as powder of 100 mesh under and contained small granules or coherent aggregates of submicron particlesc19l, a size fraction of µm particle diameters was separated by sieving. While, the particle sizes of the Wako-gel C-200 and LC-50H are in the given diameter ranges without sieving. Specific surface areas were estimated through BET method using N 2 gas. Photograph 1 shows the photomicrograph of Wakogel C-200 before dissolution. The Wako-gel C-200 grains exhibit surface morphology characteristic of angular grains with conchoidal mechanical fracturing pat- Photo. 1 The photomicrograph of pure silica sample (Wako-gel C-200) The similar morphology was observed also for Wako-gel LC-50H and Mallinckrodt silica. terns. The similar morphology was observed also for Wako-gel LC-50H and Mallinckrodt silica. As an amorphous natural silica, this study examined the silica scale collected from the inside wall of the hotwater pipe at Onuma geothermal power plant located in Akita prefecture, Japan. Ito et al.c 20l have reported its chemical composition, which indicated that Si02 was rich, and the weight ratios of Ab0 3/Si02 and CaO /Si02 were in the ranges from 0.03 to 0.15 and from 0.01 to 0.05, respectively. The X-ray diffraction pattern showed only the amorphous feature. This natural sample is referred to as Onuma silica scale. Onuma silica scale was crushed in agate mortar. Since the crushed silica contained very fine particles sticking to relatively larger ones, it was impossible to sieve the crushed sample. Photograph 2 shows the scanning electromicrographs (SEM) of Onuma silica scale before (f=o) and after (!=0.7) dissolution, where f denotes the fraction dissolved, that is,!=(amount of soluble silica)/ ( amount of silica sample introduced into the alkaline solution). As shown in Photo. 2(a), they clearly indicate that the diameters of the particles are smaller than 100 µm and not uniform. As for the specific surface area, BET method by N 2 gas and the air permeability method indicated l.2m 2 g- 1 and 0.95m 2 g-1, respectively, for Onuma silica scale. The latter method is based on Table 1 Pure amorphous silica samples examined in this study Samples Wako-gel C-200 Wako-gel LC-50H Mallinckrodt silica Particle diameter (µm) Specific surface area (m2/g) Apparent specific gravity (g/cm 3 ) H20 (TG, up to 378K) Si H20 Si H20 Si H20 +H20 (TG, from 378 to 1,073K) Si H20 Si02 0. l8h20 Si H20 -H20 and +H20 indicate the water contents obtained by thermogravimetry (TG), where -H20 refers to the molar amount of H20 per Si02 lost by heating from room temperature to 378K (sorbed water), while +H20 by heating from 378 to 1,073K (essential water). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

4 Dissolution Rates of Amorphous Silica in Highly Alkaline Solution 351 Ribbon heater ~ Polypropylene stirrer Flow me--;-e; - - f ~ N2gas Overflow Fig. 1 Thermostat Illustration of experimental apparatus Photo. 2 The SEM micrographs of the Onuma silica scale ((a) the fraction dissolved, f=o, i.e., the state before dissolution and (b) f =0. 7, temperature: 330 K, stirring rate: 8.3 s- 1 ) Kozeny-Carman equation relating the surface area with the residence of air-flow through the bed packed with the particles. These estimated values around 1 m 2 -g- 1 are very small as compared with the other pure samples shown in Table 1. The agreement of the specific surface area by the BET method with that by the air permeability method suggests that Onuma silica scale has little inner pores in the particle. For the water contents, TG showed that -H20 was 6.3wt% and +H20 was 8.6wt%, where wt% was adopted because the sample was not pure. (If pure, 8.6 wt% corresponds to Si H20 for +H 20. This value is almost similar to those for the other pure samples.) The specific gravity was 2.lg cm Procedure Figure 1 illustrates the apparatus used for the dissolution experiment. Purified nitrogen was continuously passed through the vessel to avoid contact with air. The gas had been saturated beforehand by water vapor at each temperature. The polyethylene vessel with the cover has a fluid volume of 500 cm 3. The alkaline so- lutions were prepared by dissolving analytical reagentgrade sodium hydroxide in distilled water. The concentration, i.e., the initial [NaOH], was always set at 10-1 mol-dm-3 in each experiment. This alkaline solution was put into the vessel and mechanically stirred with a polypropylene stirrer. The vessel was submerged into the thermostat. The temperature was kept constant within ±0.5 K of sufficient precision. Weighed amount of the pure silica gel (100 mg) or the crushed silica scale (200 mg) was then introduced into the vessel, and aliquots (less than 9 cm 3 ) were periodically taken for analysis. After the samples had been filtered through the membrane filter of pore size 0.45 µm, the amount of soluble silica was determined photometrically by the yellow silicomolybdate method. The values of initial and final ph were measured to confirm its constancy. To estimate the dissolution rates, the dissolution experiment should be carried out under such condition that the concentrations of dissolved silica are always well below the solubility limit. Since the solubility of the amorphous silica at ph>9 could not be determined with sufficient precision due to its strong dependence on [OH-J ( e.g., Ref. (19)), the rates of dissolution into the solutions containing various initial concentrations of soluble silica were compared. Figure 2 shows an example of the fraction dissolved, f, against time. The results agree with each other within the experimental error, indicating that the dissolution rate, df / dt, does not depend on the initial concentration of soluble silica. This means that the experiments were carried out under the condition sufficiently lower than the solubility limit. Also, we can recognize that the amount of proton liberated through the dissolution of Si02 does not give any appreciable change in the dissolution rate. This can be confirmed from the estimation that, e.g., 100mg of Si02 -l.24h20 (for Mallinckrodt silica in Table 1) in 500 cm 3 corresponds to [Si02]=2.4x 10-3 mol dm- 3, which will consume less than 5x 10-3 mol-dm-3 of [OH-] when converted into H 3Si04 and/ or H 2Si0~-c21 Jc22J. The stirring rate 8.3 s- 1 (500 rpm) was selected by judging from the preliminary experiments. As shown in Fig. 3, the dissolution is not affected by increased stirring from 1. 7 s- 1 (100 rpm) to s- 1 (1,000 rpm) over the whole range of the fraction dissolved. This means VOL. 37, NO. 4, APRIL 2000

5 352 Y. NIIBORI et al. 0.5 /...,/ p " /' Initial [SiOz]Jmol dm- 3., " ii -o-o_.../lo xl c xl.0- 'Pl 3... o K K...,!! K Fig Effects of initial [Si02] on the dissolution rate The initial solutions were prepared by dissolving Mallinckrodt silica (0 mol dm- 3, 0.6x 10-3 mol dm- 3 and l.8x 10-3 mol dm- 3 in [Si02], respectively) into [NaOH]=l0-1 mol dm- 3 at 293 K. After filtering the each solution through the membrane filter of pore size 0.45 µm, 100 mg of the Mallinckrodt silica was added to the solution (stirring rate: 8.3s- 1 )...._, ~ '+-< "O~ CL).e 0 ~ 0.5 ;,a. u,a... a s-1 -o- 8.3 s A s Wako-gel C ~~~-..-{':1-T-,R--~~ : l...-~~~-,./;!';"'... +"...A... Ls "(b).... i./ f r l,/! / 0.5 O.i ,.=i.f. i,...-is.,i.(,.t{ 303K... i K,./...,!! K Wako-gel LC (c) Fig Effect of the stirring rate on the dissolution rate (sample: the Mallinckrodt silica, sample amount: 100 mg, and temperature: 293 K) that in the range of from l.7s- 1 to 16.7s- 1 the dissolution rate is not limited by the rate at which dissolved silica or orr- is transported through the film existing between bulk and solid surface under these conditions. The importance of diffusion processes through such a film is frequently pointed out in some water-rock interactions. However in this case, since the reaction at the surface silica is slow in comparison with the diffusion, the whole dissolution process is controlled by the reaction at the surface. Under such a condition, the concentrations of solutes adjacent to the surface can be considered to be the same as the bulk solution. Fig. 4 -~ "'"',::J CL) ~ 0 rjl :.a d u e: '1; o K K...,!! K... IJ K Mallinckrodt Experimental results of dissolution behaviors for the pure silica gels ((a) the Wako-gel C-200, (b) the Wako-gel LC-50H and (c) the Mallinckrodt silica, (stirring rate:. 8.3s- 1 and sample amount: 100 mg)) JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

6 Dissolution Rates of Amorphous Silica in Highly Alkaline Solution 353 Ill. Results Figure 4 shows the relation of fraction dissolved, f, to time for the pure samples, i.e., Wako-gel C-200 (Fig. 4(a)), Waka-gel LC-50H (Fig. 4(b)) and Mallinckrodt silica (Fig. 4( c)). In all cases, the dissolution rates, df / dt, increase as the temperature of solution is set to higher value. However, the dependency on temperature is different between the samples. That is, Wakogel C-200 and LC-50H have the similar tendency against temperature, even if these geometric particle sizes are different. On the contrary, Mallinckrodt silica indicated relatively larger dissolution rates than that for Waka-gel C-200 or LC-50H. Photograph 3 shows the SEM micrographs of Mallinckrodt silica at (a) f=o and (b) /=0.7. It clearly indicates that the conchoidal fracturing patterns such as those indicated by the arrows in Photo. 3(b) are retained through the dissolution process. If the rate determining step is the diffusion process through the film, the shape of the grains would become round, because the film thickness between the surface and bulk depends on the irreg- ularities of particle-surface. Namely, the thickness will be relatively thick on the concave surface and thin, in reverse, on the convex surface. If the dissolution rate of particle is controlled by diffusion through the film, the concave surface lags behind in dissolution, as compared with the convex surface. Such a local gap in dissolution rate will make the particle surface round gradually. Figure 5 shows the dissolution behaviors of Onuma silica scale. While the initial dissolution rate at each temperature was relatively larger than the pure silica gels, the fraction dissolved at 400 min was smaller than those of the pure silica gels even if the temperature was set to 323K. IV. Discussion Considering the tendencies shown in Chap. III. Results, we have tried to interprets the observed dissolution rates with using the shrinking spherical modelc23l, which assumed that the particle is sphere with the initial radius r 0 and its sizes decrease with the progress of dissolution. Moreover, this analysis assumed that the silica scale contained particles with various initial diameters due to its particle size distribution. To estimate the dissolution rate, first, we assume dc Vai = aks, (1) where V is the bulk volume (dm 3 ), C the concentration of the soluble silica (mol dm-3), k the rate constant (mol m-2-s-1 ), S the total surface area of silica particles (m2), t the time (s) and a the fraction defined by [===Sio-1 a = ---'----'--- at the surface, (2) [= SiOH] + [= SiO-] ' where the introduction of a to the rate equation is based on the approach by Brady and WaltherC16l. In this work, we will assume a=l because [OH-J»(H4Si04]t 0 ta1, Photo. 3 The SEM micrographs of the Mallinckrodt silica ((a) f=o and (b) f=0.7, temperature: 293 K, stirring rate: 8.3 s- 1 and arrows in (b) examples of the surface of the conchoidal fracturing patterns) VOL. 37, NO. 4, APRIL 2000 Fig time(min) Experimental results of dissolution rate for Onuma silica scale (stirring rate: 8.3 s- 1 and sample amount: 200mg)

7 354 Y. NIIBORI et al. where [H4Si04]t 0 tal is the total concentration of the soluble silica. Applying the shrinking spherical particle model to the dissolution processes, the relation of C to f is where n is the number of particles, r 0 the initial radius (m) of particles, M the gram-molecular amount of Si02-xH20 (kg mol- 1 ), where x indicates the molar amount of the essential water per one mole of Si02, and Ps is the particle density (kg m-3). Also, the relation of Sand f is S = n47fr5(l -!) (4) Since silica particles are not spherical in geometry, the actual surface area is not equal to S. Moreover, BET data suggest the existence of inner surface, to which not only nitrogen gas but also solution may be accessiblec24). However, if the particles and their inner pores at various dissolution stage retain their initial morphology and are similar in shape as shown in Photo. 3, the effective surface area is considered to be proportional to S. Therefore, kin Eq. (1) is the apparent rate constant including the proportionality constant of the true surface area to s. Substituting Eqs. (3) and (4) into Eq. (1), we obtain dt = k* (1 -!)2/3' (5) where k* is 3Mk/(rop 8 ). Further, Eq. (5) yields 1 - (1 - f)l/3 =!k*t 3. (6) Figure 6 shows the application of Eq. (6) to the experimental results for the pure silica gels, shown in Fig. 4. Each line in Fig. 6 was drawn by selecting the data so that they would give the correlation coefficient of 1-(l-!) 1 13 against t larger than In all cases, Eq. (6) cannot describe the initial dissolution stage behavior at 1-(1-1) 1 13<0.1 (or f<0.27). The deviation from Eq. (6) is more remarkable at lower temperature. Probably, this delay in dissolution is caused by the extra time that is necessary for the solution to diffuse into the inner pores of the sample. In general, silica gel is produced in a liquid medium, in which case the pores are filled with the liquid. In the case of commercial (synthesized) silica gels, the liquid is removed by heating the wet gel in an autoclave to the temperature above the boiling point of the liquidc 18l. These processes may give the inner pores that require a kind of induction period before the continuous dissolution stage described by Eq. (6). As shown in Fig. 6, Mallinckrodt silica indicated the induction period shorter than Wako-gel C-200 and LC-50H. This seems to correspond with the fact that Mallinckrodt silica has smaller specific surface area (less inner pores) than Wako-gel C-200 and LC-50H, as shown in Table 1. After such a period, the dissolution behavior (3) Fig : ~0.5 I y,-< \o.s,-< y,-< 8 6: ~0.5 I C 1,-< Wako-gel C Wako-gel LC-SOH 01( '----''--.J...--'--'---'-'---...,.,_~ Application of the shrinking particle model to the experiment data for (a) the Wako-gel C-200, (b) the Wako-gel LC-50H and (c) the Mallinckrodt silica JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

8 Dissolution Rates of Amorphous Silica in Highly Alkaline Solution 355 follows Eq. (6). In this study, the rate constants are evaluated from the linear part, as shown in Fig. 6. On the other hand, for Onuma silica scale, the distribution of particle-size should be taken into consideration for the analysis, as shown in Photo. 2. We divided the sample into several groups according to their particle size, and introduced each initial value of particle radius of i-th group as Toi, and its fraction dissolved as fi. When the initial weight fraction of particle with Toi is described by Woi, the over-all fraction dissolved, f m, is In the same way as in Eq. (6), fi can be expressed in terms of the rate constant of i-th group, k7, as r fi = 1 _ ( 1 _ ~k;t (8) Substituting Eq. (8) into Eq. (7), we finally obtain fm=l-l(l-~k;t) 3 woi (9) i The curves in Fig. 7 show the result of fitting of the experiment data for silica scale to Eq. (9). In applying Eq. (9) to the data, this study assumed three kinds of particle sizes, i.e., small (i=l), medium (i=2) and large (i=3), having different k7 (i=l, 2, 3), respectively. Least-squares fitting of the data to Eq. (9) was done by the simplex method. If we divide the sample into the fractions of w01 =0.05, w 02=0.60, and w 03=0.35, the calculated curve agrees fairly well with the experimental data for each temperature, as shown in Fig. 7. All three curves intercept f-axis at 0.05, indicating that the small sized particles dissolve immediately after the contact (i.e., ki is very large). Table 2 shows the rate 1,----,--, ,-~-, (7) Table 2 Temperature (K) Apparent rate constants evaluated for Onuma silica scale Apparent rate constant, kl, defined by Eq. (8) (s- 1 ) Small sized Intermediate Large sized particles sized particles particles i=l i=2 i= x x xl x x xl0-7 constants estimated for each-sized particles. In contrast to the case of the commercial silica gels, Onuma silica scale does not show any induction period in its dissolution behavior. Probably this is because the silica scale has not experienced such heating treatment as done for commercial silica gel or powder to remove pore-waters. Since the over-all dissolution rates of the silica scale were found to be small compared with those of the pure samples, the temperatures examined for the silica scale were set at relatively higher values than those for the pure silica samples. In Fig. 7, the rates remarkably decrease as f exceeds 0.65, and it takes 400 min until f reaches 0.8 even at 343 K. Figure 8 shows that the contribution of large-sized particles to each!-curve shown in Fig. 7 is very small. In Fig. 8, the solid line indicates!-curves in Fig. 7 at each temperature, and the dotted line indicates the contribution of the particles other than large-sized ones. As shown in Fig. 8, the rate constants of large particles were negligibly small as compared to those for the mediumsized particles. Thus, Fig. 7 mainly reflects the dissolution behavior of the medium-sized particles, whose weight fraction is 0.6. Figure 9 shows the dependencies of k* on the temperature for all samples, where for Onuma silica scale, the I :.a "' 0.5 j Fig. 7 o~_....,, _ Dissolution behavior of Onuma silica scale Curves indicate the result of fitting by the shrinking particle model considering the particle size distribution. Fig. 8 'O.., _ time(min) Contribution of large-sized particles to each f-curve shown in Fig. 7 VOL. 37, NO. 4, APRIL 2000

9 356 Y. NIIBORI et al , a Onuma 0 Wako C Wako LC-50H A Mallinckrodt 10-S.... _...,... _ l03(f (K1) Fig. 9 Arrhenius plots for Wako-gel C-200, Wako-gel LC-50H, Mallinckrodt silica and Onuma silica scale rate constants for the medium-sized particles are plotted. From the slopes, the activation energies were obtained to be 85 kj mo1-1 for Mallinckrodt silica, 88 kj mo1-1 and 77kJ mo1-1 for Wako-gel C-200 and LC-50H, respectively, and 84 kj mo1-1 for the medium-sized particle of the Onuma silica scale. This rough agreement in the activation energy suggests the same dissolution mechanism. Further, Wako-gel C-200 and LC-50H agreed in rate constants, even if the particle diameters were different. This suggests that Wako-gel C-200 and LC-50H have the similar value of inner surface area per unit weight. (The inner surface is a kind of the effective surface directly contributes to the dissolution.) As for Onuma silica scale in Fig. 9, the apparent rate constant for the temperature range from 300 to 310 K is predicted around at 10-5 s-1. This value is two orders of magnitude smaller than the rate constants for the pure silica samples, and is at least one order larger than the rate constant for quartz already evaluated in the solution of [NaOH]=l0-1 mol dm-3 (6). We can translate k* into k through the relation of k*=3mk/(rops), if the effective surface area, 3/(rops), for each sample is reliably estimated. Onuma silica scale showed no induction period for the dissolution, indicating negligible contribution of inner pores. By using the surface area obtained by the BET and the air-permeability methods (i.e., 3/(r0p 8 )=1m2 g-1), the rate constants for the medium-sized particles of Onuma silica scale can be estimated to be of the order of 10-7 mol m- 2 s-1 at 310K. On the other hand, as mentioned above, synthesized silica gels are considered to have inner pores. The BET surface areas were estimated to be in the range of from 350 to 450rn 2 g-1, as shown in Table 1, which are two orders larger than that of Onuma silica scale (1 m2 g-1 ). While, the apparent rate constant, k*, for the pure samples were two orders larger than that of Onuma silica scale. At 310 K, the each rate-constant, k, was computed to be 9.4x 10-8 mol m-2 s-1 for Mallinckrodt silica, 3.5x 10-8 mol m-2 s-1 for Wako-gel C-200 and 2.8x10-s mol m-2 s-1 for Wako-gel LC-50H. These values of k are in roughly same order of Onuma silica scale. If the rate-constant is exactly equal to each other, it can be inferred that the synthesized pure silica gels have the effective surface area slightly smaller than those estimated from their BET data. V. Conclusions This paper discussed the dissolution rates of the amorphous silica in 10-1 mol dm-3 NaOH solution. As the pure samples, we took up some commercially available pure silica gels, i.e., Wako-gel C-200, Wako-gel LC-50H and Mallinckrodt silica. Applying the shrinking spherical particle model to the experiment data of each silica sample, these dissolution behaviors were compared with Onuma silica scale as one of natural amorphous silica sample. The moderate size of Onuma silica scale and the pure silica samples showed good agreements in the activation energy ranging from 77 to 88 kj mo1-1. This suggests the same dissolution mechanism for the pure silica gels and Onuma silica scale. Moreover, the rate constants were definitely larger than those already reported for quartz. While the pure silica gels required a kind of induction period before the continuous dissolution stage described by the shrinking spherical particle model, Onuma silica scale did not need such induced time. In addition to this result, the BET method and the air-permeability method showed that Onuma silica scale has little inner pores. When such inner pores are ignored, the effective surface area for dissolution is equivalent to that obtained from the BET or the air-permeability method. By using the data, the net rate constant for the medium-sized particle of Onuma silica scale was estimated to be of the order of 10-7 mol m-2 s-1 at around 310 K. Further, by applying the BET data to the apparent rate constant for the pure silica gels, the net rate constants were found to be of the order of mol m- 2-s-1, as well as Onuma silica scale. This suggests that the specific surface area is an important parameter giving the difference in the rate constants between the pure silica gels and the silica scale. In this study, it was showed that we need not only the initial dissolution processes, but also the whole behaviors, in order to estimate the dissolution rate with higher accuracy. Further, this study indicated the importance of the distribution of geometric particle diameter in determining the whole dissolution rates, when the inner pores can be ignored. To predict the effect of the hyperalkaline plume ( caused by cement) on the repository surroundings, as a subject for the future study, we need to link this understanding for the dissolution rates of amorphous silica to various bulk conditions, which are locally changing. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

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