J. Phys. Chem. 1992,96, 993-1000
993
Thresholds for Nucleation of Bubbles of N, In Varlous Solventst Mordecai B. Rubin*+*and Richard M. Noyes* Department of Chemistry, University of Oregon, Eugene, Oregon 97403 (Received: June 1 1 , 1990; In Final Form: October 21, 1991)
We have used procedures developed previously to measure maximum attainable concentrationsof N2in various supersaturated solutions. We are convinced that these concentrations are identical with the thresholds for nucleation of bubbles in the same solutions. The threshold in water is virtually constant between 15 and 35 OC,implying that the entropy of activation for forming an unstable nuclear bubble is quite negative or else that such a bubble contains more gas molecules at 35 than at 15 OC. Increase of ionic strength reduces the threshold for nucleation in water. Surfactants greatly reduce surface tensions of aqueous solutions but have rather little effect on thresholds for homogeneous nucleation in bulk solution. Nucleation thresholds in various solvents show little correlation with either surface tensions or viscosities. Addition of glycerol or ethylene glycol to water decreases the concentrations at which bubbles of N2are nucleated. However, nucleation thresholds in many organic solvents are 4-6 times greater than those in water and indicate that nucleation is more difficult in these nonaqueous solvents. Nucleation thresholds in aqueous solutions are about 100 times solubilities at 1 atm, while in many organic solvents and in aqueous glycerol thresholds are only about 30-50 times solubilities. We believe that techniques other than chemical reactions could be developed to measure nucleation thresholds in important systems which could not be studied by procedures employed in this paper.
I. Introduction If a bubble of radius r exists in a medium of surface tension u a t a depth where total hydrostatic pressure is P,, the pressure P, inside that bubble is given by P, = P, 2 u / r (1)
+
A derivation of eq 1 can be found in any textbook of physical chemistry. Because the pressure in a bubble increases indefinitely as its radius approaches zero, a bubble of finite size cannot be created by a continuous process passing through infinitesimal bubble size in a truly homogeneous medium. The nucleation of such a bubble must be caused by a local fluctuation in the composition and/or energy from the average values that would exist in a truly uniform homogeneous phase. At the time of such a fluctuation, the liquid phase must be thermodynamically unstable with respect to some system containing noninfinitesimal amounts of both liquid and gaseous phases. Such an instability of the liquid phase may arise either from superheating or from supersaturation. Nucleation of bubbles by superheating may occur in any pure liquid whose temperature has been raised sufficiently above its boiling point at the existing pressure. It may also occur in solutions of volatile solutes whose partial pressures a t equilibrium are comparable to that of the solvent.' Such nucleation may initiate almost explosive evolution of vapor and has been of great concem to engineers investigating processes such as distillation. The present paper is not concerned with such systems in which nucleation is caused by superheating. Nucleation may also occur in supersaturated solutions of a solute gas at temperatures far below the boiling point of the solvent itself. The bubbles in such a system consist almost entirely of molecules of the solute with only negligible fractions of molecules of solvent. Nucleation in supersaturated solutions has been studied much less than in superheated ones. It is obviously impossible to prepare a supersaturated solution by equilibrating the solvent with gas at constant pressure. Most attempts such as those of Hemmingsen2 to study nucleation in supersaturated solutions have equilibrated at pressures which may be hundreds of atmospheres and have then suddenly lowered the pressure. Such studies are difficult and employ rather cumbersome equipment. The results are also sensitive to heterogeneous nuclei such as dust particles which are 'This paper is No. 94 in the series "Chemical Oscillations and Instabilities". No. 93: Guslander, J.; Noyes, R. M.;Colussi, A. J. J. Phys. Chem. 1991,95, 4387-4393. 'Permanent address: Department of Chemistry, Technion-Israel Institute of Technology, Haifa, Israel.
difficult to remove completely with certainty. During our studies of chemical oscillators, we discovered many different examples of repetitive bursts of gas evolution during reactions which produced gaseous products molecule by molecule in homogeneous Such a burst occurs when the solution becomes so supersaturated that bubble nuclei are formed spontaneously a t a specific threshold. Although the first few such bursts may be influenced by nucleation on heterogeneous surfaces such as dust particles, such particles will almost certainly be swept out of solution by the bubbles they nucleate. Subsequent bubble formation in the bulk solution must result from homogeneous nucleation. Because of the regularity with which pulses of gas evolution occur, there appears to be a critical threshold of supersaturation a t which spontaneous homogeneous nucleation suddenly becomes possible. The effect is general for solutions supersaturated by the homogeneous production of several different dissolved gases.s The concentration of dissolved gas in a supersaturated solution can be calculated from the pressure change in a closed system after sudden initiation of rapid stirring or of s ~ n i c a t i o n . ~Fur,~ thermore, we have found that the maximum supersaturation attainable for a particular gas in a particular solvent is a constant independent of the reaction producing the gas or the method by which it is released.s We therefore believe that the threshold for nucleation of bubbles of a dissolved gas is the same as the maximum concentration of that gas which can be attained in a supersaturated solution. In the rest of this paper, we shall use "supersaturation limit" for the experimentally measured maximum concentration and treat it as equivalent to the theoretical "threshold for homogeneous nucleation . This procedure for measuring nucleation thresholds is much simpler than any other of which we are aware and usually gives satisfactorily reproducible results. The major objective of the present paper is to initiate a study of how the limit of supersaturation of N2depends upon various parameters such as solvent type, temperature, ionic strength, viscosity, and surface tension and also to validate the method by examining whether the results depend upon the size, shape, and surface composition of the retaining vessel. We have not studied a complete matrix of the effects of all of these variables for all solvents, but we believe that (1) Forest, T. W.; Ward, C. A. J. Chem. Phys. 1977, 66, 2322-2330. (2) Hemmingscn, E. A. Z . Naturforsch. 1978, 3 3 4 164-171. (3) Bowers, P. G.; Noyes, R. M. J. Am. Chem. Soc. 1983,105,2572-2574. (4) Rubin, M. 9.; Noyes, R. M.; Smith, IC. W. J . Phys. Chem. 1987, 91, 1618-1622. ( 5 ) Rubin, M. 9.; Noyes, R. M. J. Phys. Chem. 1987, 92, 4193-4198.
0022-365419212096-993$03.00/00 1992 American Chemical Society
994
The Journal of Physical Chemistry, Vol. 96, No. 2, 1992
the results reported here will provide increased understanding of the effects being studied. The procedure is described in section 11, and the measured supersaturation limits are presented in section 111. In section IV, we compare some of our supersaturation limits with equilibrium solubilities of N2 under similar conditions. In section V, we discuss possible dynamic effects and their importance to some of our measurements. This section specifically omits our measurements of rates of transport of molecules between liquid and gaseous phases; those measurements are described in a separate publication.6 Finally, section VI is devoted to a discussion of what has been accomplished and what further work is indicated. 11. Experimental Procedures A. General Considerations. The experimental procedure has been described p r e v i o u ~ l y . Nitrogen ~~~ is produced by chemical reaction in a closed system containing known volumes of solution and gas and connected to a pressure transducer. At various intervals, the supersaturation of the solution is released suddenly either by initiation of very rapid stirring or by sonication, and the increase of pressure is measured. The quantity in which we are interested is C,, the number of moles of gas which the supersaturated solution contained per unit volume of solution in excess of the concentration in a solution saturated at ambient conditions. If An moles of gas are evolved after rapid stirring or sonication of a solution of volume Vsoln,C, is given by eq 2.
cs = An/ Vsoln (2) Our pressures were never more than about 1 atm. If V, is the volume of gas in the apparatus in which the pressure rise hp was measured, eq 3 is valid to within a very few tenths of a percent. An = V,,,AP/RT (3) Then eq 4 shows how the supersaturation of any solution can be measured accurately. cs = V,,S~/RTVSOI" (4) The largest value of Cs which we could consistently obtain for a particular composition is called C,(max) in the tables and is presumed to be equivalent to the threshold for homogeneous nucleation. B. P"sfor Meawing Nucleation Thresholds in Aqt" Sohrtionn In these solutions, we used the decomposition of aqueous ammonium nitrite to produce supersaturated solutions. This reaction is particularly straightforward and reproducible, and the mechanism is well understood." Three stock solutions were prepared and mixed to make most of the desired reaction mixtures. Standard solution A was prepared by dissolving 13.2 g of ammonium sulfate in 50 cm3of 0.1 M sulfuric acid. It had a density of 1.134 g cm-3 and was 1.78 M in (NH4)2S04and 0.07 M in H2S04. Standard solution B was prepared by dissolving 13.8 g of sodium nitrite and 24.5 g of sodium perchlorate in 50 cm3 of water. It had a density of 1.351 g and was 3.06 M in NO2- and 3.06 M in C104-. Perchlorate-free solution B' was prepared by dissolving 13.8 g of sodium nitrite in 50 cm3of water. This solution had a density and was 3.57 M in NaN02. of 1.14 g of C. Modificatioas for Meamniog llwshdds in Organic Solvents. The sodium nitrite and ammonium sulfate salts which we used in studies with purely aqueous solutions were not sufficiently soluble in organic solvents to use them at the concentrations which were necessary, and we had to use a different reaction in order to produce nitrogen chemically. We selected the reaction of a primary amine with isoamyl nitrite (commercially available) according to the overall stoichiometry of (P). RNH2 i-AmONO ROH + i-AmOH N2 (P)
+
+
+
(6) Noyes, R. M.; Rubin, M. B.;Bowers, P.G.J . Phys. Chem., following paper in this issue.
Rubin and Noyes TABLE I: Suwrsahurrtion Limits at Different Temwmtures temp, O C 15 25 35 lO'C,(max), mol cm-' 2.42 2.42 2.29
The mechanism presumably involves the three steps (Sl)-(S3). At least (S2) and (S3) might be expected to be catalyzed by acid. RNH2 + i-AmONO RNH-NO + i-AmOH (Sl) RNH-NO RN=N-OH
--
RN=N-OH R+
(S2)
+ N2 + OH-
(S3) This mechanistic interpretation was supported by tests with rert-butylamine and isoamyl nitrite in acetonitrile and in dimethyl sulfoxide (DMSO).Those systems did indeed evolve nitrogen, but the reaction was too slow to attain the desired supersaturation. Addition of acetic acid in about 2-fold excess over the amine accelerated the reaction but presumably complicated the kinetics by formation of the alkylammonium acetate salt RNH30Ac. We were also concerned that a small R+ ion in the medium with acetic acid might form ROAc or undergo elimination to an alkene either of which might be sufficiently volatile to obfuscate the pressure change due to nitrogen evolution. We finally resolved these problems by using n-hexylamine but obtained comparable results with amines of lower molecular weight. Therefore, our concerns about volatile products from R+ were apparently unfounded. The procedure for measuring supersaturation limits was to add 2 mL of n-hexylamine to 5 mL of the organic solvent. Then 2 mL of glacial acetic followed by 0.15 mL of water were added while cooling in an ice bath to reduce the effects of exothermicity. A 2-mL portion of this solution was placed in the reaction flask, and 0.5 mL of isoamyl nitrite was added. This addition was camed out in a hood because of the toxicity of the nitrite. The flask was then connected to the transducer and sonicated at intervals. In each such run,the largest amount of gas evolved by any sonication was considered to be an estimate of the limit of supersaturation. D. procedures for Measwing E
