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Temperature Dependence of Bubble Nucleation Limits for Aqueous Solutions of Carbon Dioxide, Hydrogen, and Oxygen
Journal of Colloid and Interface Science 215, 441– 442 (1999) Article ID jcis.1999.6261, available online at http://www.idealibrary.com on
NOTE Temperature Dependence of Bubble Nucleation Limits for Aqueous Solutions of Carbon Dioxide, Hydrogen, and Oxygen We report the temperature variation of critical supersaturation for carbon dioxide, hydrogen, and oxygen in water at 1 atm pressure. The measurements were made by generating solutions of the gases chemically. Between 273 and 323 K, the bubble nucleation limit for carbon dioxide decreases from 0.4 to 0.2 M. For oxygen the limit decreases from 0.15 to 0.10 M in the range 283–298 K. The limit for hydrogen increases from 0.03 M at 290 K to 0.08 M at 308 K. The trends correlate with the Lennard–Jones interaction energies of the molecules, in agreement with recently published bubble nucleation models based on density functional calculations. © 1999 Academic Press Key Words: bubbles; supersaturation; nucleation theory.
Theories of homogeneous nucleation of solute gas bubbles in liquids can in principle be tested against two experimental measurable quantities, the nucleation rate ( J) and the maximum attainable supersaturation concentration (c crit). Although it is quite difficult to measure J, critical concentrations can be measured with a fair degree of reproducibility, either by decompressing a solution saturated at high pressure or by generating a supersaturated solution chemically (1, 2). Classical nucleation theory generally gives bad predictions of c crit, almost certainly because the calculation employs macroscopic surface tension to calculate the free energy of an extremely small critical nucleus. A new theoretical treatment of nucleation has recently been described by Oxtoby et al. (3, 4), using density functional methods to calculate this free energy without making assumptions about the surface tension. A major finding of the theory is that at the point of bubble formation, the gas/solvent interface is diffuse, covering several molecular diameters, rather than sharp as in a planar situation. Although the density functional theory is not yet able to make quantitative comparisons with measured critical concentrations, it does address the temperature dependence, dc crit/dT. For a given solvent, this quantity is predicted to vary with the Lennard–Jones interaction energy e of the solute, decreasing as e decreases. In support of the expectation, Oxtoby et al. cite a brief report by Rubin and Noyes (5) that the temperature coefficient for hydrogen in water is positive. This note reports more extensive measurements of the temperature behavior of critical supersaturation for CO 2, H 2, and O 2 in water, and their bearing on density functional nucleation theory. Our experiments used chemical reaction to generate critically supersaturated solutions of the gases. The critical concentration of dissolved gas in an unstirred solution was measured by sonicating the solution and collecting the released gas in a conventional gas buret at atmospheric pressure. The general experimental arrangement and procedures have been described previously (1, 5). Oxygen was prepared by the iodide-catalyzed decomposition of hydrogen peroxide (1.8 M) and presented no particular difficulty when a preflamed reaction vessel was employed to prevent surface decomposition of the peroxide. Hydrogen was prepared by decomposing sodium borohydride solution (1.2 M) in a pH 9 buffer. Both the O 2 and the H 2 reactions were relatively slow, with maximum supersaturation attained only after several minutes. Carbon
dioxide solutions were formed by the vigorous action of 1.0 M NaHCO 3 with excess 2.0 M HCl. When the effervescence due to evolved CO 2 had subsided (;30 s), the remaining supersaturated solution was sonicated. The results are shown in Fig. 1, together with earlier data for nitrogen (6). Between 273 and 323 K, the bubble nucleation limit for carbon dioxide decreases from 0.4 to 0.2 M. For oxygen the limit decreases from 0.15 to 0.10 M in the range 283–298 K. The limit for hydrogen increases from 0.03 M at 290 K to 0.08 M at 308 K. The values for nitrogen are almost temperature independent. The temperature range over which c crit could be determined reliably varied for each gas: at low temperatures, especially for oxygen and hydrogen, the reactions became slow compared to the rate of gas loss by diffusion, while at high temperatures, for these gases, the reactions were too vigorous to allow reproducible supersaturation. The reaction producing carbon dioxide is vigorous at all temperatures, and we were surprised that reasonably reproducible supersaturation concentrations shown in Fig. 1 remained when the reaction died down. Evidently supersaturation builds up during the final slower part of the reaction. Heterogeneous effects are undoubtedly present with carbon dioxide, although these seem to be less important when the supersaturation is generated chemically than when it is generated by decompression (7). Nevertheless, the true homogeneous limit for carbon dioxide may be higher than that shown in Fig. 1. Rubin and Noyes (6) demonstrated that c crit (like the thermodynamic solu-
441
FIG. 1. Critical concentration for homogeneous nucleation of bubbles in aqueous solution. The values for nitrogen are taken from Ref. (5). 0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
442
NOTE dependence is due to the fact that at nucleation, a liquid–liquid, rather than a liquid– gas, phase separation initially occurs when the solute and solvent intermolecular energies are very different. The liquid-like nucleus rapidly becomes gaseous as it grows. This is the exact opposite of what we would expect with the gases studied here. Hydrogen is well above its critical temperature, making a true liquid nucleus impossible, although as with other supercritical fluids, a liquid-like density might be appoached. On the other hand carbon dioxide (critical temperature 31°C) might easily form a true liquid nucleus if the cavity pressure is sufficiently high. Clarification of these difficulties must await further refinement of the theory, and perhaps experiments designed to measure nucleation rates directly.
REFERENCES
FIG. 2. Relationship between the Lennard–Jones potential for the solute and the temperature coefficient for critical supersaturation, taken from Fig. 1.
bility) decreased substantially with increasing ionic strength for nitrogen. For the data shown in Fig. 1, the final ionic strengths are approximately 0.6 (CO 2), 1.7 (H 2), 3.0 (N 2), and 0.025 (O 2). Thus oxygen is the only gas for which the measured value is close to the true homogeneous limit in pure water. Ionic strength due to spectator ions is a major disadvantage of generating supersaturation by chemical reaction. Despite these uncertainties, we believe that the temperature effects we found are valid for comparison with density functional theory. In Fig. 1, although there is no reason to suppose exact linearity, we have shown the best linear fit to the data for each gas, and used this to calculate dc crit/dT. Given all the experimental difficulties, the temperature coefficients correlate surprisingly well with the Lennard–Jones interaction energies e for the gases (8). The comparison is shown in Fig. 2. Density functional theory predicts what is observed: that is, that the temperature variation will be negative when the ratio e solute/e solvent is relatively large (as for carbon dioxide in water) and may invert if this ratio is sufficiently small (as for hydrogen in water). According to the density functional treatment, reversal of the temperature
1. Bowers, P. G., Hofstetter, C., Letter, C. R., and Toomey, R. T., J. Phys. Chem. 99, 9632 (1995); Bowers, P. G., Bar-Eli, K., and Noyes, R. M., J. Chem. Soc. Faraday Trans. 92, 2843 (1996). 2. Finkelstein, Y., and Tamir, A., AIChEJ 31, 1409 (1985). 3. Talanquer, V., and Oxtoby, D. W., J. Chem. Phys. 102, 2156 (1995). 4. Oxtoby, D. W., Acc. Chem. Res. 31, 91 (1998). 5. Rubin, M. B., and Noyes, R. M., J. Phys. Chem. 91, 4193 (1987). 6. Rubin, M. B., and Noyes, R. M., J. Phys. Chem. 96, 993 (1992). 7. Carr, M. W., Hillman, A. R., and Lubetkin, S. D., J. Colloid Interface Sci. 169, 135 (1995). 8. Atkins, P. W., “Physical Chemistry,” 5th ed., p. C25. Freeman, New York, 1994. Peter G. Bowers 1 Christine Hofstetter 2 Helen Le Ngo 3 Richard T. Toomey 4 Department of Chemistry Simmons College Boston, Massachusetts 02115 Received January 22, 1999 1
To whom correspondence should be addressed. Fax: 617-521-3086. Email: [email protected]. 2 Present address: Chemistry Department, Brandeis University, Waltham, MA 02158. 3 Present address: Covalent Associates, Inc., Woburn, MA 01810. 4 Present address: Chemistry Department, Brandeis University, Waltham, MA 02158.
NOTE Temperature Dependence of Bubble Nucleation Limits for Aqueous Solutions of Carbon Dioxide, Hydrogen, and Oxygen We report the temperature variation of critical supersaturation for carbon dioxide, hydrogen, and oxygen in water at 1 atm pressure. The measurements were made by generating solutions of the gases chemically. Between 273 and 323 K, the bubble nucleation limit for carbon dioxide decreases from 0.4 to 0.2 M. For oxygen the limit decreases from 0.15 to 0.10 M in the range 283–298 K. The limit for hydrogen increases from 0.03 M at 290 K to 0.08 M at 308 K. The trends correlate with the Lennard–Jones interaction energies of the molecules, in agreement with recently published bubble nucleation models based on density functional calculations. © 1999 Academic Press Key Words: bubbles; supersaturation; nucleation theory.
Theories of homogeneous nucleation of solute gas bubbles in liquids can in principle be tested against two experimental measurable quantities, the nucleation rate ( J) and the maximum attainable supersaturation concentration (c crit). Although it is quite difficult to measure J, critical concentrations can be measured with a fair degree of reproducibility, either by decompressing a solution saturated at high pressure or by generating a supersaturated solution chemically (1, 2). Classical nucleation theory generally gives bad predictions of c crit, almost certainly because the calculation employs macroscopic surface tension to calculate the free energy of an extremely small critical nucleus. A new theoretical treatment of nucleation has recently been described by Oxtoby et al. (3, 4), using density functional methods to calculate this free energy without making assumptions about the surface tension. A major finding of the theory is that at the point of bubble formation, the gas/solvent interface is diffuse, covering several molecular diameters, rather than sharp as in a planar situation. Although the density functional theory is not yet able to make quantitative comparisons with measured critical concentrations, it does address the temperature dependence, dc crit/dT. For a given solvent, this quantity is predicted to vary with the Lennard–Jones interaction energy e of the solute, decreasing as e decreases. In support of the expectation, Oxtoby et al. cite a brief report by Rubin and Noyes (5) that the temperature coefficient for hydrogen in water is positive. This note reports more extensive measurements of the temperature behavior of critical supersaturation for CO 2, H 2, and O 2 in water, and their bearing on density functional nucleation theory. Our experiments used chemical reaction to generate critically supersaturated solutions of the gases. The critical concentration of dissolved gas in an unstirred solution was measured by sonicating the solution and collecting the released gas in a conventional gas buret at atmospheric pressure. The general experimental arrangement and procedures have been described previously (1, 5). Oxygen was prepared by the iodide-catalyzed decomposition of hydrogen peroxide (1.8 M) and presented no particular difficulty when a preflamed reaction vessel was employed to prevent surface decomposition of the peroxide. Hydrogen was prepared by decomposing sodium borohydride solution (1.2 M) in a pH 9 buffer. Both the O 2 and the H 2 reactions were relatively slow, with maximum supersaturation attained only after several minutes. Carbon
dioxide solutions were formed by the vigorous action of 1.0 M NaHCO 3 with excess 2.0 M HCl. When the effervescence due to evolved CO 2 had subsided (;30 s), the remaining supersaturated solution was sonicated. The results are shown in Fig. 1, together with earlier data for nitrogen (6). Between 273 and 323 K, the bubble nucleation limit for carbon dioxide decreases from 0.4 to 0.2 M. For oxygen the limit decreases from 0.15 to 0.10 M in the range 283–298 K. The limit for hydrogen increases from 0.03 M at 290 K to 0.08 M at 308 K. The values for nitrogen are almost temperature independent. The temperature range over which c crit could be determined reliably varied for each gas: at low temperatures, especially for oxygen and hydrogen, the reactions became slow compared to the rate of gas loss by diffusion, while at high temperatures, for these gases, the reactions were too vigorous to allow reproducible supersaturation. The reaction producing carbon dioxide is vigorous at all temperatures, and we were surprised that reasonably reproducible supersaturation concentrations shown in Fig. 1 remained when the reaction died down. Evidently supersaturation builds up during the final slower part of the reaction. Heterogeneous effects are undoubtedly present with carbon dioxide, although these seem to be less important when the supersaturation is generated chemically than when it is generated by decompression (7). Nevertheless, the true homogeneous limit for carbon dioxide may be higher than that shown in Fig. 1. Rubin and Noyes (6) demonstrated that c crit (like the thermodynamic solu-
441
FIG. 1. Critical concentration for homogeneous nucleation of bubbles in aqueous solution. The values for nitrogen are taken from Ref. (5). 0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
442
NOTE dependence is due to the fact that at nucleation, a liquid–liquid, rather than a liquid– gas, phase separation initially occurs when the solute and solvent intermolecular energies are very different. The liquid-like nucleus rapidly becomes gaseous as it grows. This is the exact opposite of what we would expect with the gases studied here. Hydrogen is well above its critical temperature, making a true liquid nucleus impossible, although as with other supercritical fluids, a liquid-like density might be appoached. On the other hand carbon dioxide (critical temperature 31°C) might easily form a true liquid nucleus if the cavity pressure is sufficiently high. Clarification of these difficulties must await further refinement of the theory, and perhaps experiments designed to measure nucleation rates directly.
REFERENCES
FIG. 2. Relationship between the Lennard–Jones potential for the solute and the temperature coefficient for critical supersaturation, taken from Fig. 1.
bility) decreased substantially with increasing ionic strength for nitrogen. For the data shown in Fig. 1, the final ionic strengths are approximately 0.6 (CO 2), 1.7 (H 2), 3.0 (N 2), and 0.025 (O 2). Thus oxygen is the only gas for which the measured value is close to the true homogeneous limit in pure water. Ionic strength due to spectator ions is a major disadvantage of generating supersaturation by chemical reaction. Despite these uncertainties, we believe that the temperature effects we found are valid for comparison with density functional theory. In Fig. 1, although there is no reason to suppose exact linearity, we have shown the best linear fit to the data for each gas, and used this to calculate dc crit/dT. Given all the experimental difficulties, the temperature coefficients correlate surprisingly well with the Lennard–Jones interaction energies e for the gases (8). The comparison is shown in Fig. 2. Density functional theory predicts what is observed: that is, that the temperature variation will be negative when the ratio e solute/e solvent is relatively large (as for carbon dioxide in water) and may invert if this ratio is sufficiently small (as for hydrogen in water). According to the density functional treatment, reversal of the temperature
1. Bowers, P. G., Hofstetter, C., Letter, C. R., and Toomey, R. T., J. Phys. Chem. 99, 9632 (1995); Bowers, P. G., Bar-Eli, K., and Noyes, R. M., J. Chem. Soc. Faraday Trans. 92, 2843 (1996). 2. Finkelstein, Y., and Tamir, A., AIChEJ 31, 1409 (1985). 3. Talanquer, V., and Oxtoby, D. W., J. Chem. Phys. 102, 2156 (1995). 4. Oxtoby, D. W., Acc. Chem. Res. 31, 91 (1998). 5. Rubin, M. B., and Noyes, R. M., J. Phys. Chem. 91, 4193 (1987). 6. Rubin, M. B., and Noyes, R. M., J. Phys. Chem. 96, 993 (1992). 7. Carr, M. W., Hillman, A. R., and Lubetkin, S. D., J. Colloid Interface Sci. 169, 135 (1995). 8. Atkins, P. W., “Physical Chemistry,” 5th ed., p. C25. Freeman, New York, 1994. Peter G. Bowers 1 Christine Hofstetter 2 Helen Le Ngo 3 Richard T. Toomey 4 Department of Chemistry Simmons College Boston, Massachusetts 02115 Received January 22, 1999 1
To whom correspondence should be addressed. Fax: 617-521-3086. Email: [email protected]. 2 Present address: Chemistry Department, Brandeis University, Waltham, MA 02158. 3 Present address: Covalent Associates, Inc., Woburn, MA 01810. 4 Present address: Chemistry Department, Brandeis University, Waltham, MA 02158.