Diffusive Equilibrium Properties of O2 in Amorphous SiO2

Article pubs.acs.org/JPCC

Diffusive Equilibrium Properties of O2 in Amorphous SiO2 Nanoparticles Probed via Dependence of Concentration on Size and Pressure G. Iovino, S. Agnello,* F. M. Gelardi, and R. Boscaino Dipartimento di Fisica e Chimica, Università di Palermo, Via Archirafi 36, I-90123 Palermo, Italy ABSTRACT: An experimental study on the diffusive equilibrium value of interstitial O2 in silica nanoparticles was carried out on samples with average particles diameter 40, 14, and 7 nm. The investigation was performed by measuring the concentration of interstitial O2 by Raman and photoluminescence techniques. The dependence of diffusive equilibrium concentration on pressure and temperature was investigated in the pressure range from 0.2 to 76 bar and in the temperature range from 98 to 244 °C. The equilibrium concentration of interstitial O2 follows Henry’s law at pressures below 13 bar whereas a departure from this model is observed at higher pressures. In particular, O2 concentration saturates above about 60 bar, reaching a temperature-independent value for fixed particles size. The concentration of dissolved O2, under fixed thermodynamical conditions, is size dependent, being lower in smaller particles. These results evidence an effect of interaction among diffusing species in the dynamics of transport and give support to a shell-like model for the distribution of O2 in nanoparticles.

■

in the near infrared.15,16 The presence of interstitial oxygen can be achieved by means of thermal treatments of silica nanoparticles in oxygen atmosphere to induce the diffusion of the gas into and through the nanoparticles.15 In addition to the above technological reasons, the study of oxygen diffusion in silica nanoparticles makes possible to extend the range of temperature in which this process has been investigated until now. Indeed, whereas oxygen diffusion in silica is a well investigated topic at temperatures above 500 °C for external pressure of diffusing gas below 3 atm, no experimental data exist at lower temperatures due to small values of the diffusion coefficient below 500 °C that makes the diffusion process in bulk silica too slow to be investigated in laboratory times. On the other hand, in the case of silica nanoparticles, the small size reduces the diffusion time, making it possible to investigate the diffusion process at temperatures below 500 °C. Moreover, the study of the diffusion process in nanometer silica allows to investigate the role of the size in the diffusion process since the structural properties of silica nanoparticles are size dependent.17−23 In refs 24, 25, and 26, the kinetics aspects of the diffusion of O2 in silica nanoparticles were investigated. These previous studies showed a dependence of the diffusion coefficient on pressure and nanoparticles size apart from the temperature, but limited investigation has been dedicated to the analysis of the equilibrium values of

INTRODUCTION Amorphous silicon dioxide (a-SiO2), or silica, is a relevant, widely used material in current technology and biomedical research due to its physicochemical properties.1−9 The relevant properties of silica are related both to its intrinsic structural features and to the presence of defects.1 Indeed, defects related for example to impurities such as interstitial molecules could affect the material performances so the investigation of their physical behavior is fundamental for the material final use. In particular, due to the open structure of silica, small molecules can diffuse from environment into and through silica under working conditions, compromising the material featuresfor example, in the presence of ionizing radiation in the environment or at high temperature.10 The miniaturization on nanoscale of optical and electronic devices, in which silica plays an important role, as well as in the case of microscale,4,5 makes interesting the investigation of the physical properties of silica when one or more dimensions are reduced at the nanoscale, indeed, the properties of a solid can show a strong dependence on its size when it falls into nanometer scale. In particular, the diffusion process of oxygen in nanometer silica is important because oxygen is a common element in the atmosphere and silica often is the material composing the shell in core−shell systems whose core properties can be damaged by oxygen molecules.11 Diffusion of oxygen in silica is also relevant in the synthesis of materials as in the case of core−shell systems such as Si−SiO2 ones.12−14 Furthermore, interstitial oxygen molecules are optically active and this property can be used to obtain luminescence probes of nanometer size emitting © 2014 American Chemical Society

Received: December 27, 2013 Revised: July 7, 2014 Published: July 10, 2014 18044

dx.doi.org/10.1021/jp501796p | J. Phys. Chem. C 2014, 118, 18044−18050

The Journal of Physical Chemistry C

Article

concentration up to high external pressures, albeit of particular interest to determine the overall solubility of silica. In fact, for what concerns the equilibrium value of interstitial O2 in bulk silica at temperature above 500 °C for external pressure of diffusing gas below 3 atm, it was found that it follows Henry’s law, which is valid in general for dilute systems27,28

Table 1. Physicochemical Properties of Investigated Fumed Silica Types35,36 nickname

av dia (nm)

sp surface (m2/g)

Aerosil300 Aerosil150 AerosilOX50

AE300 AE150 AEOX50

7 14 40

300 150 50

(1)

C = SP

GPa. This procedure allows us to have handleable samples without losing the nanometer features of the material. Indeed, only points of contact among nanoparticles are established as a consequence of the applied pressure.37 In order to determine the dependence of equilibrium value of interstitial O2 on pressure and temperature, the tablets were thermally treated in a furnace (whose temperature was stabilized within ±1 °C) in O2 atmosphere for a time long enough to reach the diffusive equilibrium between the O2 inside the particles and that in the treatment atmosphere.24−26 The dependence of O2 concentration value at diffusive equilibrium in silica nanoparticles was investigated in the pressure range from 0.2 (partial pressure of O2 in air atmosphere) to 76 bar and at temperatures from 98 to 244 °C. The interstitial O2 concentration after each thermal treatment was determined by measurements carried out with a RAMII Bruker FT-Raman spectrometer equipped with a Nd:YAG laser source at 1064 nm that enabled the detection of both intrinsic vibrational modes of silica and the photoluminescence emission from singlet oxygen.38−40 In particular, the source power was fixed at 500 mW and the detection system spectral resolution at 15 cm−1. The interstitial O2 concentration was determined by the amplitude of the luminescence band of interstitial O2 present in the Raman spectra as described in refs 15 and 38−40. It is worth noting that in the explored pressure and temperature ranges no structural changes are induced in the nanoparticles as detected through Raman investigation.15,22 Furthermore, thermal treatments up to 600 °C have evidenced no morphological changes by atomic force microscopy.41

where C is the concentration of dissolved molecules, P is the external O2 pressure, and S is the solubility of the gas in the solid, depending only on the temperature. In ref 27 it was found that the solubility of O2 in bulk silica in the temperature range from 800 to 1000 °C follows the Arrhenius law ̃

S = S0e−Ea / KBT

(2)

where Ẽ a is the activation energy, KB the Boltzmann constant, T the absolute temperature, and S0 is the pre-exponential factor that is temperature independent. Values of the pre-exponential factor and activation energy found in ref 27 were 4.8 × 1015±0.2 cm −3/atm and −0.18 ± 0.03 eV, respectively. Henry’s law should not be valid at high concentration, that is, under high external pressure. In particular, under this condition, a saturation of interstitial O2 concentration is expected. No such investigation has been performed for O2 in silica but a study of solubility of helium in silica showed that the concentration of interstitial He follows the Langmuir model29−34 C(P) =

commercial name

SP 1+

S P Cmax

(3)

where C(P) and Cmax are the concentrations of dissolved molecules at external pressure P and its maximum value, respectively, and S is a constant depending on the temperature, corresponding to the solubility in Henry’s law. However, the applicability of this law also to oxygen has not been proved due to the limit in the experimental procedures for bulk silica. With the aim to extend the study of solubility in silica of O2 at high pressure and low temperature, in the present work, the equilibrium value of interstitial oxygen was investigated in the temperature range below 250 °C and at pressure from 0.2 bar up to 76 bar, basing on the experimental reliability of finding the equilibrium in the laboratory time scale using nanoparticles proven in previous works. The study was carried out on silica nanoparticles differing in size. The experiments show a dependence on nanoparticles size and a departure from Henry’s law, suggesting both features of solubility that could be related to diffusing molecules interaction and peculiarities due to inhomogeneous interstitial O2 spatial distribution in nanoparticles.

■

RESULTS Figure 1 shows the dependence of the equilibrium concentration of interstitial O2 in the AEOX50 sample on the external

■

EXPERIMENTAL PROCEDURE The equilibrium O2 concentration in silica nanoparticles was investigated on fumed silica of commercial origin produced by Evonik industries AG.35,36 Evonik fumed silica has a purity larger than 99.8% by weight, and the physicochemical properties of the investigated types are summarized in Table 1. These nanoparticles are not porous and with hydrophilic surfaces, and are characterized by a size distribution with the average diameter shown in the table. Experiments were carried out on tablets of volume 4 × 4 × 2 mm3, obtained by pressing the starting powder in an uniaxial press at pressure of about 0.3

Figure 1. Pressure dependence of the O2 equilibrium concentration at low pressure in the AEOX50 sample at various temperatures. Lines are the best fit straight lines. 18045



Article

concentration reaches a limit value almost independent of temperature. The study of the equilibrium concentration in particles of different average size has been carried out at 127 °C as a function of the pressure. As can be seen in Figure 4 for the

pressure below 13 bar for different temperatures as reported in the legend of the figure. At every temperature, the O2 concentration increases linearly with pressure whereas it decreases on increasing temperature at each pressure value. At higher pressure, a departure from the linear behavior is found, as can be seen in Figure 2 where the equilibrium

Figure 4. Equilibrium concentration of interstitial O2 as a function of pressure in the AEOX50, AE150 and AE300 samples at 127 °C.

Figure 2. Dependence of O2 equilibrium concentration on pressure in the AEOX50 sample at various temperatures.

AE300, AE150 and AEOX50 samples, the equilibrium concentration shows a dependence on pressure, in the low pressure range, and successively a tendency to a limit value that depends on the particles size. In particular, for a given pressure and temperature the smaller is the particles average diameter the smaller is the limit concentration.

concentration value as a function of the external pressure in a wider pressure range is shown. Experimental data show a saturation tendency for pressure above 60 bar and a saturation value of concentration independent of temperature. At intermediate pressure, the concentration is higher at lower temperature in agreement with the expectation from the negative activation energy of solubility. Equilibrium concentration values of interstitial O2 in AE300 at two different temperatures, 98 and 127 °C, in the pressure range from 6 to 76 bar are shown in Figure 3. As in the case of

■

DISCUSSION The linear dependence on pressure of the equilibrium O2 concentration determined for the AEOX50 sample (see Figure 1) shows that below 13 bar the system follows Henry’s law of eq 1 in the investigated temperature range.28 In this pressure range, the slope of each straight line is the O2 solubility. The determined slopes of the best fit lines drawn in Figure 1 are collected in Table 2. It is observed that the solubility increases Table 2. O2 Solubility in AEOX50 Sample at Various Temperatures for Pressure below 13 bara temp (°C) 127 143 157 177 194 244 a

Figure 3. Equilibrium concentration of interstitial O2 as a function of pressure in the AE300 sample at 98 and 127 °C.

solubility (1018 molecules cm−3/bar) 0.63 0.52 0.45 0.41 0.34 0.26

± ± ± ± ± ±

0.03 0.03 0.02 0.02 0.02 0.01

Solubility values are the slopes of best fit straight lines in Figure 1.

on decreasing the temperature as predicted by the law reported in eq 2. In order to analyze quantitatively this temperature dependence, the found values of solubility for pressure below 13 bar are reported in an Arrhenius plot in Figure 5. The solid line in the figure is the best fit line obtained by fitting the experimental data with the Arrhenius law of the solubility (eq 2), whereas the dashed lines are the extremal Arrhenius laws drawn by using the parameters of solubility of O2 in silica derived from literature data relative to experiments performed at temperatures above 500 °C and for pressure lower than 3 bar

AEOX50 sample, equilibrium concentration increases with external pressure at a given temperature and decreases on increasing temperature at a fixed pressure. Moreover, similarly to the AEOX50 case, equilibrium concentration does not increase linearly with pressure by following Henry’s law in the whole investigated pressure range and at high pressure the 18046



Article

Figure 6. Comparison between O2 equilibrium concentration values of AEOX50 sample shown in Figure 2 and Langmuir model (eq 3). Solid lines are the Langmuir isotherms with solubility values reported in Table 2 and saturation concentration 1.8 × 1019 molecules cm−3 (see Figure 2) whereas dashed lines are the Langmuir isotherms with the same solubility values as the solid lines but saturation concentration 5.5 × 1021 molecules cm−3.

Figure 5. Arrhenius plot of O2 solubility values reported in Table 2 and referring to pressure below 13 bar in AEOX50 sample. Straight line is the best fit curve obtained by fitting experimental values with the Arrhenius law (eq 2). Dashed lines are the extremal Arrhenius laws drawn by using the parameters from the literature relative to experiments performed at temperatures above 500 °C and pressure lower than 3 bar in bulk silica.27

reported as dashed lines in Figure 6. The maximum concentration value, which is about 3 orders of magnitude greater than that experimentally observed in the present work, is the concentration of interstices in which O2 could be trapped, as theoretically predicted for bulk silica.43 It is worth noting that this concentration is close to the value 1.9 × 1021 molecules cm−3 determined by fitting experimental data for He in bulk silica,42 based on the applicability of the Langmuir model to this molecule diffusion, and it is evidence that a small influence derives from the differences on the estimated van der Waals radius of He and oxygen.44 By inspection of Figure 6, it is observed that the dashed lines are straight lines with good approximation in the range from 0 to 76 bar predicting the validity of Henry’s law in the overall experimentally investigated pressure range. Comparison between the experimental data and dashed lines reveals that the observed concentration is lower than the expected one, not supporting the applicability of the Langmuir model to O2 equilibrium concentration in the investigated system. The differences between the values predicted by the Langmuir model and the experimental data for each temperature are reported in Figure 7. This analysis shows that the accuracy of the model increases with temperature. Some conjectures could be done to try to find an explanation of the not easy application of the Langmuir model to O2 diffusive equilibrium concentration in nanometer silica. One of the basic hypothesis under which the Langmuir isotherm was obtained is that all hosting sites are equivalent, but this could not be true for O2 in silica due to its amorphous nature and possible different interactions as compared to He due to the presence of nearby interacting oxygen, silicon, or hydroxyl groups.45 The other basic assumption is that there is no interaction between hosting sites. By means of simulative studies, a positive and sitedependent formation energy of an interstitial O2 in silica was found in ref 43. This energy value is referred to the unperturbed silica network and the isolated O2 molecule, and is related to interaction between the guest molecule and the host matrix, and its value depends on the volume of hosting interstice. This study showed that for about 50% of sites the formation energy is lower than 0.5 eV but no interaction between occupied sites was accounted for to determine these

in bulk samples.27 Parameters of the best fit Arrhenius law are S0 = 1015.9±0.3 molecules cm−3/bar and Ẽ a = −0.13 ± 0.03 eV. The negative value of Ẽ a means that, on average, the system constituted by silica and O2 lowers its energy during the dissolution process. The relative position between experimental data and dashed lines, as well as the comparison between best fit parameters and values of Arrhenius parameters reported in ref 27 and recalled in the Introduction section, suggests that O2 solubility in 20 nm radius silica particles follows the same law as that describing solubility in bulk silica at higher temperature. Equilibrium values of interstitial O2 concentration at the investigated temperature in a wider pressure range (see Figures 2−4) show a departure from the linear behavior predicted by Henry’s law and saturation above about 60 bar. From a qualitative point of view, this behavior is theoretically expected on the basis of the Langmuir model and was experimentally observed for dissolution of He in bulk silica.42 In this case, the departure of helium equilibrium concentration from Henry’s law was observed at pressure much higher than that explored in the present work and no saturation was observed up to 1300 atm (upper limit of the investigated pressure range).42 Moreover, in ref 42, experimental data were found to be in agreement with the Langmuir model. This latter model predicts that the equilibrium concentration at a given pressure is given by eq 3 and depends only on two parameters, the solubility S and the saturation concentration Cmax. In order to explain the experimental dependence of interstitial O2 concentration on pressure derived for silica nanoparticles here, we apply the Langmuir model whose validity for interstitial molecules dissolution should be general and so valid also for O2 and not only for He. By using this equation and inserting the values experimentally found in the present investigation for the solubility determined at pressure below 13 bar and for the maximum concentration at about 60 bar, the solid lines in Figure 6 are found. Comparison between curves and experimental data shows that the model does not agree with the observed behavior. To deepen this aspect, the Langmuir isotherms in which the solubility was put equal to that experimentally determined here and the value of Cmax was fixed at 5.5 × 1021 molecules cm−3 have been calculated and are 18047



Article

In order to explain this dependence, it is useful to consider the schematic grid drawn in Figure 8 in which the squares

Figure 7. Differences between expected O2 equilibrium concentration values predicted by Langmuir model (dashed lines in Figure 6) and experimental data (shown in Figure 6).

Figure 8. Grid schematically representing the silica network in a bulk solid. The lines are the walls of the interstices in which O2 molecules could be trapped. Dashed line schematically represents the surface of a spherical silica nanoparticle.

energy values. The absence of negative formation energy does not agree with experimental results that give a negative, even if small, value of Ẽ a for the solubility; however, the value of O2 concentration found by the authors is in agreement with that experimentally measured. To comment on these findings in connection with the results reported in the present work, it is relevant to note that since the authors of ref 43 were interested in equilibrium concentration at high temperature (1078 °C) and low concentration (1.94 × 1017 molecules cm−3), probably the presence of a small negative formation energy and of the interaction between occupied sites were not relevant due to the high thermal energy and low concentration of molecules with respect to potentially available sites. By contrast, in the present work, temperatures are about 1 order of magnitude lower and the concentrations are about 2 orders of magnitude higher than in ref 43. Under these experimental conditions, the interaction between occupied sites could be relevant; that is, the formation energy of an interstitial molecule could depend on the presence of other interstitial molecules nearby. In particular, the formation energy of two near-interstitial O2 could be higher than the sum of their separated formation energies. This aspect could qualitatively explain why the value of O2 concentration is lower than that predicted by the Langmuir model and could also explain why the discrepancy diminishes on increasing the temperature. Indeed, if temperature is raised, higher energy configurations could become probable. These considerations unveil limits of solubility of O2 in silica at low temperature and could be useful for theoretical deepening. Equilibrium concentration values of interstitial O2 in AE300 sample as a function of external pressure at two different temperatures, 98 and 127 °C, are shown in Figure 3. Like the case of the AEOX50 sample, the equilibrium concentration increases with pressure at a given temperature but not linearly in all the explored range. Furthermore, it decreases on increasing temperature at a fixed pressure according to findings relative to the AEOX50 for which a negative value of the activation energy in the Arrhenius law of solubility was found. Even if the qualitative behavior of the equilibrium concentration is equal for AE300 and AEOX50 samples, its value, under given thermodynamical conditions, is size dependent as can be seen in Figure 4 in which the equilibrium concentration values at 127 °C as a function of external pressure are shown for AE300, AE150, and AEOX50.

represent silica interstices in a bulk solid, and the dashed line schematizes the surface of a silica nanoparticle. As can be seen, the particle surface destroys a part of the interstices near the same surface, so the number of intact cages per unit volume inside the nanoparticle is lower than in the case of a bulk solid. This effect is size dependent, being negligible if the particle volume is much larger than the volume of a cage, but becoming relevant when the size of the particle is of comparable order of magnitude to the cage one, as could occur in the smaller nanoparticles investigated here. The above scheme can be used to clarify the dependence of the O2 equilibrium concentration on the specific surface, or particles’ average diameter. In the following, the effect sketched in Figure 8 is modeled by supposing that there is a shell on the particles surface in which O2 cannot be trapped.40,41 If C0 is the O2 concentration in the inner part of the particle (region without surface shell, see further) whose volume is V0, the number N of molecules dissolved in it is N = C0V0

(4)

By dividing both sides of eq 4 by the total volume V of the particle, eq 5 is obtained

⎛ V⎞ C = C 0 ⎜1 − s ⎟ ⎝ V⎠

(5)

where C is the concentration estimated by considering the total volume of the particle and Vs = V − V0 is the volume of the surface shell in which O2 cannot be trapped. By supposing, as a first approximation, Vs = δS,̅ where δ is the surface thickness and S̅ is the surface of particle, eq 5 can be put in the form of eq 6 C = C0(1 − ρδS)

(6)

where ρ = m/V is the density of the particle (m is its mass) and S = S̅/m is its specific surface. eq 6 predicts that the O2 concentration decreases linearly with the specific surface. By supposing as a first approximation that each investigated material is made by identical particles and that the surface shell thickness is independent of the sample type, the intercept of the linear dependence on S in eq 6 is the O2 concentration in bulk silica (S = 0) and the slope is −C0ρδ. Since the 18048



Article

interstices not able to trap O2 molecules near to the particles surface, but effects related to small size of particles could also be present. Indeed, particle volume is comparable to or less than the average volume occupied by a molecule in bulk silica.

concentration of interstitial O2 is proportional to the ratio between its PL amplitude and its PL lifetime, the law in eq 6 is also valid, apart for a factor, for this ratio. In refs 23, 40, and 41, it was found, by fitting the experimental data relative to this ratio as a function of the specific surface, that the thickness of the surface shell is about 1 nm. This value of the surface shell thickness essentially represents the region that comprises the broken and not filled interstices and its size could be compared with the one predicted on the basis of experimentally determined number of available cages for unit volume. Based on the already reported number of available sites estimated for He,42 about 1.9 × 1021 cm−3, the average volume associated with each cage is found to be about 0.5 nm3 and an average distance among sites of about 0.8 nm is expected, in agreement with the thickness estimated for the surface shell explaining that it could be constituted by broken interstices. Even if the above analysis suggests that a part of the dependence of O2 equilibrium concentration on the size is due to surface effects, other effects related to the small size of the host system could also be present. Indeed, the above reasoning was made by considering a single particle and could not be valid when the average number of O2 molecules per particle is less than one, that is when the average volume of the particles is lower than the average volume occupied by a molecule in the bulk material as occurs in the case of AE300 sample, where the maximum concentration of O2 is 5 × 1018 molecules/cm−3, suggesting an average distance of 6 nm comparable to the particles diameter. This point suggests another limit related to the nanosize and requests a deepening on the theoretical approach to be used at the nanometer scale.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +39 091 23891703. Fax: +39 091 6162461. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the people of the LAMP group (http:// www.fisica.unipa.it//amorphous) for useful discussions. Technical assistance by G. Napoli and G. Tricomi is acknowledged. Partial financial support by FAE-PO FESR SICILIA 2007/2013 4.1.1.1 and by FFR 2012/2013 of University of Palermo projects are acknowledged

■

REFERENCES

(1) Pacchioni, G., Skuja, L., Griscom, D. L., Eds. Defects in SiO2 and Related Dielectrics: Science and Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. (2) Nalwa, H. S., Ed. Silicon Based Materials and Devices; Academic Press: San Diego, CA, 2001. (3) Burns, A.; Ow, H.; Weisner, U. Chem. Soc. Rev. 2006, 35, 1028− 1042. (4) Watcharotone, S.; Dikin, D. A.; Stankovich, S.; Piner, R.; Jung, I.; Dommett, G. H. B.; Evmenenko, G.; Wu, S.-E.; Chen, S.-F.; Liu, C.-P.; Nguyen, S. T.; Ruoff, R. S. Nano Lett. 2007, 7, 1888−1892. (5) Noginov, M. A.; Zhu, G.; Belgrave, A. M.; Bakker, R.; Shalaev, V. M.; Narimanov, E. E.; Stout, S.; Herz, E.; Suteewong, T.; Wiesner, U. Nature 2009, 460, 1110−1113. (6) Lu, J.; Liong, M.; Zink, J. I.; Tamanoi, F. Small 2007, 3, 1341− 1346. (7) Hom, C.; Lu, J.; Tamamoi, F. J. Mater. Chem. 2009, 19, 6308− 6316. (8) Park, J.-H.; Gu, L.; von Maltzahn, G.; Ruoslahti, E.; Bhatia, S. N.; Sailor, M. J. Nat. Mater. 2009, 8, 331−336. (9) Iovino, G.; Malvindi, M. A.; Agnello, S.; Buscarino, G.; Alessi, A.; Pompa, P. P.; Gelardi, F. M. Mater. Chem. Phys. 2013, 142, 763−769. (10) Kajihara, K.; Miura, T.; Kamioka, H.; Aiba, A.; Uramoto, M.; Morimoto, Y.; Hirano, M.; Skuja, L.; Hosono, H. J. Non-Cryst. Solids 2008, 354, 224−232. (11) Santra, S.; Zhang, P.; Wang, K.; Tapec, R.; Tan, W. Anal. Chem. 2001, 73, 4988−4993. (12) Watanabe, T.; Tatsumura, K.; Ohdomari, I. Phys. Rev. Lett. 2006, 96 (196102), 1−4. (13) Ohta, H.; Watanabe, T.; Ohdomari, I. Phys. Rev. B 2008, 78 (155326), 1−7. (14) Deal, B. E.; Grove, A. S. J. Appl. Phys. 1965, 36, 3770−3776. (15) Agnello, S.; Cannas, M.; Vaccaro, L.; Vaccaro, G.; Gelardi, F. M.; Leone, M.; Militello, V.; Boscaino, R. J. Phys. Chem. C 2011, 115, 12831−12835. (16) Agnello, S.; Boscaino, R.; Cannas, M.; Gelardi, F. M.; Leone, M.; Militello, V. Patent no. 0001399551 WO 2011/128855 A1, 2013. (17) Stesmans, A.; Clemer, K.; Afanas’ev, V. V. Phys. Rev. B 2005, 72 (155335), 1−12. (18) Uchino, T.; Aboshi, A.; Yamada, T.; Inamura, Y.; Katayama, Y. Phys. Rev. B 2008, 77 (132201), 1−4. (19) Roder, A.; Kob, W.; Binder, K. J. Chem. Phys. 2001, 114, 7602− 7614. (20) Schweigert, I. V.; Lehtinen, K. E. J.; Carrier, M. J.; Zachariah, M. R. Phys. Rev. B 2002, 65 (235410), 1−9.

■

CONCLUSION In this work, the features of the diffusive equilibrium concentration of O2 in fumed silica made up by primary nanoparticles having average diameter from 40 down to 7 nm were investigated. The equilibrium O2 concentration values were found to increase with pressure and decrease on increasing temperature below about 60 bar, whereas they are temperature and pressure independent at higher pressure in the investigated temperature range (127−177 °C). The O2 concentration below 13 bar depends on pressure in accordance to Henry’s law in the temperature range from 127 to 244 °C, and the found values of solubility change with temperature according to Arrhenius law and with thermodynamic parameters in agreement with values extrapolated from bulk silica at higher temperatures and lower pressures. Departure from Henry’s law and saturation of equilibrium concentration with pressure cannot be explained by the Langmuir model. O2 concentration is less than predicted by this law and the difference decreases on increasing the temperature. This behavior suggests that occupation of near interstices could be dependent on their distance, and the energy of the configuration in which two or more near interstices are occupied, which corresponds to high density of interstitial O2, could be greater than that in which the same number of isolated interstices are occupied. For what concerns the dependence of equilibrium values of interstitial O2 on temperature and pressure in samples with diameter smaller than 40 mn, it is qualitatively equal to that observed in larger samples but absolute values are different. In particular, they depend on specific surface being smaller in samples with smaller size or higher specific surface. A part of this dependence was related to the presence of “broken” 18049



Article

(21) Vaccaro, G. “Structural Modification Processes in Bulk and Nano-sized Amorphous SiO2 Systems”; Ph.D. Thesis, Università di Palermo, 2011. (22) Vaccaro, G.; Agnello, S.; Buscarino, G.; Gelardi, F. M. J. Phys. Chem. C 2010, 114, 13991−13997. (23) Vaccaro, G.; Buscarino, G.; Agnello, S.; Sporea, A.; Oproiu, C.; Sporea, D. G.; Gelardi, F. M. J. Phys. Chem. C 2012, 116, 144−149. (24) Iovino, G.; Agnello, S.; Gelardi, F. M.; Boscaino, R. J. Phys. Chem. C 2012, 116, 11351−11356. (25) Iovino, G.; Agnello, S.; Gelardi, F. M.; Boscaino, R. J. Phys. Chem. C 2013, 117, 9456−9462. (26) Iovino, G.; Agnello, S.; Gelardi, F. M. J. Nanopart. Res. 2013, 15 (1876), 1−6. (27) Kajihara, K.; Kamioka, H.; Hirano, M.; Miura, T.; Skuja, L.; Hosono, H. J. Appl. Phys. 2005, 98 (013529), 1−7. (28) Dill, K. A.; Bromberg, S. Molecular Driving Forces; Garland Science: New York, 2003. (29) Hill, T. L. Introduction to Statistical Thermodymics; AddisonWesley: Reading, MA, 1960. (30) Fowler, R. H.; Guggenheim, E. A. Statistical Thermodynamics; Cambridge University Press: Cambridge, UK, 1939. (31) Barrer, R. M.; Waughn, D. E. W. Trans. Faraday Soc. 1967, 63, 2275−2290. (32) Shelby, J. E. J. Appl. Phys. 1976, 47, 135−139. (33) Shackelford, J. F.; Masaryk, J. S. J. Non-Cryst. Solids 1978, 30, 127−134. (34) Hartwig, C. M. J. Appl. Phys. 1976, 47, 956−959. (35) Basic Characteristics of Aerosil, 4th ed.; Degussa: Frankfurt, 2001. (36) http://www.aerosil.com/product/aerosil/en/products/ hydrophilic-fumed-silica/pages/default.aspx, 2013. (37) Buscarino, G.; Ardizzone, V.; Vaccaro, G.; Agnello, S.; Gelardi, F. M. J. Appl. Phys. 2010, 108 (074314), 1−9. (38) Skuja, L.; Guttler, B. Phys. Rev. Lett. 1996, 77, 2093−2096. (39) Skuja, L.; Guttler, B.; Schiel, D.; Silin, A. R. J. Appl. Phys. 1998, 83, 6106−6110. (40) Agnello, S.; Di Francesca, D.; Alessi, A.; Iovino, G.; Cannas, M.; Girard, S.; Boukenter, A.; Ouerdane, Y. J. Appl. Phys. 2013, 114 (104305), 1−6. (41) Alessi, A.; Iovino, G.; Buscarino, G.; Agnello, S.; Gelardi, F. M. J. Phys. Chem. C 2013, 117, 2616−2622. (42) Shelby, J. E.; Keeton, S.; Iannucci, J. J. J. Appl. Phys. 1976, 47, 3952−3955. (43) Bongiorno, A.; Pasquarello, A. Phys. Rev. B 2004, 70 (195312), 1−14. (44) Mantina, M.; Chamberlin, A. C.; Valero, R.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2009, 113, 5806−5812. (45) Sohn, S.; Kim, D. Chemosphere 2005, 58, 115−123.

18050


Diffusive Equilibrium Properties of O2 in Amorphous SiO2

Recommend Documents