J. Phys. Chem. B 1999, 103, 9841-9845
9841
Effect of Cooling Rate on Pore Distribution in Quenched Sodium Borosilicate Glasses Tetsuo Yazawa,*,† Koji Kuraoka,† and Wei-Fang Du‡,§ Optical Materials Department, Osaka National Research Institute, Midorigaoka 1-8-31, Ikeda City, Osaka 563-8577, Japan, and New Energy and Industrial Technology DeVelopment Organization, Midorigaoka 1-8-31, Ikeda City, Osaka 563-8577, Japan ReceiVed: July 12, 1999; In Final Form: September 2, 1999
The distribution of pores, based on spinodal phase separation in sodium borosilicate glasses that were rapidly quenched at different cooling rates, was investigated. The N2 adsorption-desorption behavior of samples shows that the pore is of the micropore type with pore size (8π Dθ )/(λ T) 2
2
2
(4)
then the phase separation will be avoided. Equation 4 can be written as follows:
τ > ΦD
(5)
where Φ ) (8π2θ2)/(λ2T). For the sodium borosilicate glass used in this experiment, T ≈ 900 K, θ ≈ 90 K, and λ ) (3-10) × 10-9 m. The constant Φ ) (8π2θ2)/(λ2T) = 7.10 × 1018-7.89 × 1019. The parameter D is usually >10-12 m2/s and can be as large as 10-9 m2/s in fluid melts of sodium borosilicate glass.17 In such melts, cooling rate should be >7.10 × 106-7.89 × 1010 K/s to completely avoid spinodal phase separation on quenching. The theoretical analysis shows that the cooling rate approaching 106 K/s by the twin-roller method in the present experiments can still not prevent spinodal decomposition, which further supports our experimental results. The amount of N2 adsorption varies with quenching methods, as shown in Figures 2 and 3. The amount of N2 adsorption in the air-quenched samples is apparently larger than that in the roller-quenched samples, which indicates that the pore volume of the air-quenched samples is larger than that of the samples quenched by other methods. The analysis of the surface area and the pore volume with different quenching methods is shown in Table 2. The results indicate that the surface area and the pore volume increase with decreasing cooling rate. When the cooling rate decreases from 106 to 10 K/s, the pore volume and surface area increase from 6.60 × 10-5 m3/kg and 1.409 × 105 m2/kg to 1.06 × 10-4 m3/kg and 2.301 × 105 m2/kg, respectively. The samples quenched by roller 1 and brass have nearly the same values of pore volume and surface area due to their approximate rates of cooling. Similar behavior is unexpectedly observed between the samples quenched by air and liquid nitrogen. Theoretical calculation predicts that the cooling rate by liquid nitrogen is higher than the rate by air cooling, as shown in Table 1. However, the effect of the liquid nitrogen on cooling may occur only on the surface of the glass in the present experiment because the shape of the samples after quenched by liquid nitrogen is spherical, with diameters as large as 6-10 mm. It is possible that the cooling rate inside such large-size samples is still as low as in the air-quenched samples. Thus, it is reasonable to see that the liquid-nitrogen-quenched samples have nearly the same values for the pore volume and the surface area as the air-quenched samples. The order of the pore volume and surface area of the samples by different quenching methods is: roller-quenching 2 < roller-quenching 1 ≈ brass-quenching < liquid-nitrogen-quenching ≈ air-quenching. The effect of cooling rate on pore volume and surface area is thought to be mainly caused by the difference in the spinodal decomposition amplitude at different cooling rates. In the initial stage of spinodal decomposition, the continuous changes of temperature below the spinodal temperature result in a series of fluctuation waves of spinodal decomposition under cooling. The dependence of amplitude on wave number at different cooling rates is illustrated in Figure 4. The maximum value of the amplitude, Am, corresponds to the wave λm formed at the point that is ∼10% below the spinodal temperature (i.e., the λm represents the wave with the most rapid decomposition under cooling). The parameter A corresponds to a wave λ, the wave number of which is around λm. According to eq 2, the time that
J. Phys. Chem. B, Vol. 103, No. 45, 1999 9843 TABLE 2: Measurement Results of the Surface Area and Pore Volume of the Samples Quenched at Different Cooling Rates cooling condition roller-quenching 2 roller-quenching 1 brass-quenching liquid-nitrogenquenchinga air-quenching a
cooling rate (K/s)
pore volume (10-5 m3/kg)
surface area (105 m2/kg)
∼106 ∼103 ∼2.5 × 102 ∼1.5 × 102
6.60 8.00 8.10 10.4
1.409 1.671 1.760 2.167
10.6
2.301
∼10
Sample shape is spherical, with diameter as large as 6-10 mm.
Figure 4. The dependence of amplitude on wave number at different cooling rates.
Figure 5. The effect of the amplitude of the decomposition wavelength on pore distribution.
is required to cool past the point below ∼10% of the spinodal temperature will increase with decreasing cooling rate. Therefore, with decreasing cooling rate, the amplitudes of a series of waves whose wave numbers are around λm increase rapidly. Figure 5 illustrates the schematic evaluation of the concentration profiles for spinodal decomposition at different cooling rates with an acid-leaching model. In the initial stage of spinodal decomposition, there exists a spinodal pore line that divides the boron-rich phase into two parts. The model suggests that only the part above the spinodal pore line can neglect the disturbance of silica network and lead to connective pores. This suggestion can be confirmed by the experimental data of the leaching process. As shown in Figure 6, the measurement result of the elution of boron indicates that all the borate oxide in the glass
9844 J. Phys. Chem. B, Vol. 103, No. 45, 1999
Figure 6. The dependence of the elution of boron and silicon on leaching time at 371 K.
Figure 7. Illustration of the increase of surface area and pore volume with decreasing cooling rate.
is completely leached out during acid leaching. According to the composition of the glass and the density of B2O3, it is easy to calculate the volume percent occupied by the leached borate oxide, which is 1.60 × 10-4 m3/kg. However, the calculation result does not coincide with the experimental measurement result of the pore volume shown in Table 2. The volume of the spinodal pore is actually much smaller than the volume of the elution borate oxide. This result confirms that only part of the leached boron contributes to the formation of the spinodal pore. In general, the amplitude of the wave formed at the point that is ∼10% below the spinodal temperature, λm, grows most rapidly under cooling. Therefore, the amplitude of the wave, λm, will exceed the spinodal pore line firstly. Under high cooling rate, because the amplitude of spinodal decomposition waves is very small, few waves, except for λm, can exceed the spinodal pore line, as shown in Figure 5a. With decreasing cooling rate, more waves whose wave numbers are around λm, develop and exceed the spinodal pore line, as shown in Figure 5b. Thus, after acid leaching, the amount of spinodal pores in the samples quenched at a relatively low cooling rate should be more than that in samples quenched at a high cooling rate, as shown in Figure 7. As a result, both the surface area and pore volume increase with decreasing cooling rate. The model of the relation between spinodal pore and spinodal decomposition wave, as shown in Figures 5 and 7, suggests that the size of the spinodal pore is far less than the wavelength of spinodal decomposition in the initial stage of the phase separation under cooling. Theoretical calculation of the wavelength at the initial stage of the phase separation has been investigated by Cahn and Charles.17 The results show that the wavelength is typically in the range 3-10 nm. Figures 8 and 9 show the results of the experimental measurement of pore size distribution of the leached samples quenched by different methods. The pore size diameter of roller-quenched samples is ∼0.7 nm. The domain size of the spinodal pore increases to ∼0.9 nm for the air-quenched samples. The pore sizes in both the air-quenched and the roller-quenched samples are
