NUCLEATION-From
Liquids
LITERATURE CITED
(1) Becker, R., and Doring, W., Ann. Phusiic, 24, 719 (1935).
(2) Buckley, H. E., “Crystal Growth,” New York, John Wiley & Sons, 1951. (3) Camel, H., and Landt, E., Z. V e r . deut. Zuckerind., 77, 483 (1927). (4) Davies, J. G., and Yearwood, R. D. F., Trop. A g r . ( T r i n i d a d ) , 21, 43 (1944). ( 5 ) Hudson, C. S., Division of Sugar Chemistry, Symposium on Fundamental Reactions in Carbohydrate Chemistry. 117th Meeting AM. CHEM.SOC., Detroit, hlich. (6) International Committee on Uniform Methods of Sugar Analysis, Intern. S u g a r J . , 52,236,263 (July 1950);Subjects l2and 19. (7) Kucharenko, I. A., Planter Sugar Mfr., 75, 361 (May-June 9, 1928); Katl. Bur. Standards, CZN.440 (1942). (8) hIcGinnis, R. -4.,Moore, S., and Alston, P. W,,IND.E m . CHEY.,34, 171 (1942). (9) Meade, G. P., Division of Sugar Chemistry, Symposium on Sugar Technology, 120th Meeting AM.CHEY.SOC., New York, N. Y . 10) O’Connor, J. J., h1.S. thesis, College of the Holy Cross, 1950. 11) Powers, H. E. C., I n t e r n . Sugar J . , 50, 149 (1948). 1 2 ) Roginskii, S. Z., and Todes, 0. M., Bull. A c a d . Sci. (U.R.S.S.), 1940, 331; 1942, 106; C o m p t . rend. acad. sci. U.R.S.S., 27,
677-80 (1940).
(13) Schweizer, A., Intern. S u g a r J . , 35, 385 (1933). (14) Shearon, W. H., Louviere, W. H., and Laperouse, R. M., IKD. ENG.CHEM.,43, 553 (1951). ( 1 5 ) Tipson, R. S.,in Teissberger’s “Technique of Organic Chemistry,” Vol. 111, Chap. 6, New York, Interscience Publishers, 1950. (16) Turnbull, D., J . A p p l i e d Phus., 20, 817 (1949). (17) Turner, C. F., Galkowski, T. T., Radle, W.F., and VanHook, h., Intern. Sugar J . , 52, 298 (1950). (18) Turner, C. F., and VanHook, -4., J . Colloid Sci., 5, 315 (1950). (19) VanHook, A., IND.ENG.CHEW,36, 1042 (1944). (20) Ibid.,40, 85 (1948). (21) VanHook, A,, Proc. Am. Soc. Sugar Beet Technol., 6 , 570 (1950). (22) VanHook, 8 . , and Biggins, W. F., I n t e r n . Sugar J., 54, 7 (1952). (23) VanHook, A., and Bruno, A. J., Discussions Faraday SOC.,Yo. 5, 112 (1949). (24) Volmer, PI.,“Kinetik der Phasenbildung,” Dresden, T. Steinkopff, 1939. ( 2 5 ) Webre, A. L., in Spencer-Meade’s “Cane Sugar Handbook,” S e w York, John Wiley & Sons, 1945. (26) Khelan, W.P., Jr., Galkowski, T. T., and VanHook. 4..Proc. Am. SOC.Sugar Beet Teehnol., 5, 552 (1948). RECEIVED for review December 21, 1951.
Nucleation of Supersaturated Salt -Solutions
ACCEPTED March 10, 1952
-
MARIA T E L K E S MASSACHUSETTS INSTITUTE
OF
to 6.55 A. within a range of 15%. Manganese sulfide (5.21 A.) was active within t h e half range t o 5.63 A, with a full range of 16%. Using the 15% fit-limitation, it can be predicted that lead selenide should catalyze the nucleation of the salts within the
TECHNOLOGY, CAMBRIDGE, MASS.
Llci
E$r g;$l
N ~ B
5 14 5 33 49
1; ~5 94 6 00
M n ~ 21
MnSe 5 45
t
Liquids
NUCLEATION-From proximate weight of 10-18 gram corresponds t o nearly 10-'8 cc., or a cube of 10-6 cm. or 100 A. on edge. From supersaturated solutions Na&O4.lOH20 crystals form a t a transition temperature of 32.383' C. This transition or melting point is very sharply defined, to the extent that it can be used for the standardization of thermometers (6, 17). The transition, on heating, occurs with the incongruent formation of anhydrous ealt and its saturated solution. The heptahydrate, NazS04.7Hz0, i s less stable than the decahydrate and has a transition temperature of 24.2' C. The limits of supersaturation have been determined by Hartley ( 4 ) ; the limit of labile supersaturation is 15"C. Undercooled supersaturated solutions contain 53 grams of sodium sulfate per 100 grams of water, and they crystallize spontaneously a t 18'C. The undercooling (At) is therefore never less than about At = 14"C., although higher values have been observed. The specific heat and the heat of transition have been determined repeatedly (1, 7 , 10, 16, 16). The heat of transition of NazS04.10Hz0is 58 calories per gram or 85 calories per cc. Owing to its relatively high heat of transition and its convenient transition temperature (around 90" F.),the use of Na#Od.lOHnO has been suggested by the writer (BB, 23) for solar heat storage for the heating of houses. I n regions where sufficient solar energy is available during the winter, the energy can be collected by suitable heat traps or solar heat collectors, and the collected heat can be stored as the heat of fusion or transition. The low cost and availability of sodium sulfate are in favor of this method. The salt is placed into sealed containers, and the surfaces of the containers serve as heat exchangers. The rate of heat exchange and the prevention of undercooling are some of the determining factors in the use of Na2S0,.10H20 for heat storage purposes. The rate of crystal growth in the vicinity of the transition temperature will determine the amount of heat t h a t can maximally be abstracted from the surroundings or delivered t o them. The crystallization velocity and its temperature dependence have been studied by Tamman (91). Near the transition point the rate of crystal growth (C) per degree of temperature difference between the solid crystals and the melt will be: C = k,". Here H i s the heat of fusion per unit volume (cal. cmeVa);IC is the specific heat conductivity (cal. cm.-' deg.-l set.-'). I n the case of NazSOa.IOHZO,H = 85 and t = 0.0013, hence the crystallization velocity within one degree of the melting point will be 1.52 x 10-6 cm. per second or 0.055 om. per hour, following Tamman's calculation. The actual crystallization velocity may be derived from experimental data ($, If?), which are in the range 0.03 t o 0.07 cm. per hour, in reasonable agreement with the theoretical calculation. NUCLEATION OF HYDRATED SODIUM SULFATE
For the purpose of using the heat of transition of Na2S04.10H20 for heat storage in sealed containers, nucleation had t o occur invariably and with the minimum of undercooling. Na2S04.10H20is isomorphous with several salt hydrates, forming mixed crystals with them. Most of these salt hydrates are very soluble in water, and the mixed crystals show a considerably lower transition temperature. Therefore, they cannot be used for heating purposes in houses where a transition temperature around 90"F. is desirable. Some of these salt hydrates are listed in Table 11, giving the known (3, 9, 20),crystallographic data, which are in close agreement, considerably within the 15% sizefactor rule. Double salt formation occurs with Na2S04.10Hz0and several salts of the general type MeSO+sHnO, where Me can be iron, nickel, cobalt, zinc, cadmium, etc., but these salts do not catalyze the nucleation of Na2S04.10H20because their crystallographic data are not within the 15% size-factor fit (8). It was necessary to find a nucleation catalyst, which was only slightly soluble in supersaturated solutions of sodium sulfate to avoid depression of the transition temperature. It was preferable June 1952
Table II.
A. 1.116
Salt NaaSOclOHeO NanSeOd.1OHpO NazQOj.1OHg0-
a,
1.106 1.113
... ...
NaaMoV4.lOHzV
PjaaW04.10HzO
3.0
Monoclinic Salts, CEhGroup Crystallographic Data b , A. c , A. 1 1.238 1 1.238 1 1 213
.. ..
... ...
8 (angle) 107"45' 107'54' 107'43'
..
..
1
I
, 10
00
20
30
9
P
40
50
so,
Figure 1.
Solubility of Sodium Sulfate-Sodium Tetraborate in Water Grams anhydrous salt/100 grams of water
to find a catalyst that increased in solubility a t higher temperatures, dissolving as the sodium sulfate was heated above its transition temperature and crystallizing again as the supersaturated solution was cooled, forming a large number of nuclei for the Na2SOd.lOHzO crystals. It was equally essential that such a nucleation catalyst should not diminish the heat of transition of NazS04.10H20. According to the literature, the only known nucleation catalysts were those listed in Table 11. The crystallographic tables (3, 9, BO) were therefore examined for possible materials with crystallographic data within the 15% size-factor rule. Two materials were found; Table I11 gives the data and the deviations of these data in per cent as compared to those of Na2S04.10H20. The deviations were well within the 15% limits for sodium tetraborate but not for lead tungstate. Experiments were carried out in sealed glass tubes with solutions of these salts: NazBcOl.10H20 catalyzed the nucleation of Na$301. 10HzO, but PbWO, did not. The nucleation could be performed repeatedly in closed containers. The equilibrium of the system sodium sulfate-sodium tetraborate and water has been investigated by Sborgi (I@, and part of this is shown in Figure 1. The relatively slight solubility of sodium tetraborate in water (at the temperatures shown) is further decreased by the presence of sodium sulfate in solution. The
INDUSTRIAL AND ENGINEERING CHEMISTRY
1309
NUCLEATION-From
Liquids ~~
Table II I.
Materials w i t h Crystallographic Data w i t h i n t h e 1570 Rule
Salt NazS04.10H~O NazB~07.10HzO PbWOi (as rsspite) NrtzB401.10HzO PbW04
a, A.
b, A.
1.116 1.114 1.344
1 1 1
-
0.2 20.5
Crystallographic D a t a E , A. p (angle)
1.238 1.159 1.114 Deviations -6.3 10.0
107O45’ 106O35’ 107O33’
Group C%
q*
...
% -1.1
size-factor rule. Such salts are highly soluble and depress the transition temperature of Na2S04.10HzO. I n a closed system, supersaturated solutions of sodium sulfatc can be nucleated if the solution contains a relatively small amount of sodium tetraborate. The undercooling At is less than 2 ” C. when the solution is saturated with both sodium sulfate and sodium tetraborate a t the transition temperature. The crystslIographic data of the two salt hydrates are in sufficient agreement to account for the nucleation catalytic effect.
-0.2 BIBLIOGRAPHY
transition temperature of the equilibrium mixture is decreased slightly, to 31.9 from 32.383’ C. At the transition temperature, 100 grams of water dissolve 48.91 grams of sodium sulfate and only 2.12 grams of sodium tetraborate; without the presence of sodium tetraborate the solubility of sodium sulfate is 50 grams which may increase to 53 grams in the supersaturated, undercooled state. Solutions were prepared, being saturated R ith sodium sulfat,e and sodium tetraborate a t the transition temperature, and the nucleation was observed in sealed glass tubes. Crystallization started invariably when the tubes were cooled to 30.0” t o 30.5O C. -that is, the maximum undercooling At was only 1.4” to 1.9” C. Control tubes, without the addition of sodium tetraborate never crystallized, except if cooled below the temperature of labile supersaturation (15 C. or lower). Tubes were filled with solutions of sodium sulfate saturated a t the transition temperature, with decreasing amounts of sodium tetraborate added to these tubes. If the amount of nucleation catalyst was more than 1%, the solution invariably crystallized above 27 O C.-that is, the undercooling A2 was not greater than 5 ” C. Alternate heating and cooling cycles could be carried out with such sealed tubes or containers without any appreciable undercooling, except as stated. CONCLUSIONS
Kucleation in supersaturated salt solutions may occur only if the crystallographic data of the nucleation catalyst and the salt to be crystallized show agreement within less than 15%. Nucleation of supersaturated sodium sulfate solutions is feasible with certain isomorphous salts in accordance with the 15%
d
(1) d’Ans, J., and
Tollert, H., 2. Elektrochem., 43, 81 (1937). ( 2 ) Coberly, C. W., thesis Mass. Inst. Technol. (1936) (3) “Handbook of Chemistry and Physics,” 30th ed., Cleveland, Chemical Rubbei Pub. Co.. 1948. Hartley, H., Jones, B. iM.,and Hutchinson, G. A., J . Chem. SOC., 93, 825 (1908).
Hole, J., Chem. & M e t . Eng., 52, KO.6, 115 (1946). I-Iume-Rothery, Is’., “Atomic Theory,” Institute of Metale, 1946.
Kobe, K. A,, and Anderson, C. H., J . Phys. Chem., 40, 429 (193 6).
Koppel, J., 2. Phgs. Chem., 52, 385 (1905). “Kristallographische Strukturberichte,” Vol. 1-7, Leiyzig, Akademische Verlagsgeselluchaft, 1931-39. Leenhart, C., and Boutaric, A , Bull. SOC.Chem., 13, 651 (1913). McIntosh, D., T r a n s . Roy. SOC.Can., 13, No. 3, 265 (1919). Montillon, G. H., and Badger, W. L., IND. ENG.CHEM.,19, SOB (1927).
iieuhaua, A., 2. Krist., 105, 161 (1943). Ostwald, W..“Lehrbuoh der allnemeinen Chemie.” 2nd ed.. Vol. 11, Part 2, pp. 719-84, Leipeig, Engelmann, 1896. Perman, E. O., and Urry, W,D., T r a n s . Faraday Soc., 24, 337 (1928).
Pitzer, K. S., and Coiilter, L. V., J . Am. Chem. Soc., 60, 1310 (1938).
Richards, T. S., 2. Phys. Chem., 43, 471 (1903). Royer, L., Bull. SOC. franc. mineral., 51, 1-156 (1928). Sborgi, U., Bovaline, E., and Capeline, L., Gazz. chim. ital., 54, 298 (1924).
Strune, H., “Mineralogische Tabellen,” Leipzig, Becker & Erler, 1941. Tamman, G., “The States of Aggregation,” New York, D. Van Nostrand Co., 1925. Telkes, M., Heating and Ventilating, 46, 68 (September 1949). Ibid., 46, 79 (November 1949). Violette, R., Compt. rend., 60, 831 (1865). RECEIVEDfor review December 21, 1951. ACCEPTEDApril 22, i9.52“ Publication No. 31, 1I.I.T.Solar Energy Conversion Project.
ation in Liquids
U
LOUIS BERNATH E. 1. DU PONT
D E N E M O U R S & CO., INC.,S C H E N E C T A D Y , N . Y .
T h e nucleation theory of Volmer, Becker, and Doring, as applied t o t h e formation of vapor bubbles i n pure liquids, is reviewed. An application of t h e theory t o t h e calculat i o n of t h e fracture pressures of pure liquids i s presented. Recent experimental data are compared w i t h fracture pressures calculated f r o m t h e Volmer theory and w i t h values calculated using t h e Eyring reaction rate process theory as applied by Fisher.
A
BUBBLE is formed in the body of a liquid by the vaporization of molecules of the liquid into a cavity, which may be considered as any space within the liquid phase unoccupied by liquid molecules, either empty or occupied by vapor. When this process occurs a t normal pressures because the boiling temperature of the liquid is exceeded, the process is called superheating; when it occurs a t negative pressures (hydrostatic tensile stresses) and a critical bubble size is exceeded, cavitation results. THEORETICAL CONSIDERATIONS. An elementary cavity (the space vacated by a liquid molecule removed from its equilibrium 1310
position) is formed under the influence of localized thermal fluctuations and requires a single molecular heat of vaporization for‘ its production. The following illustration will demonstrate the connection between the heat of vaporization and the energy required to produce a cavity. Suppose an amount of energy, X , is required to tear a liquid molecule from its surroundings. Then, X N is the amount of energy per mole required to remove each liquid molecule in turn from its surrounding molecules, where AT is -4vogadro’fi number. Since the energy is expended in the breaking of molecular bonde, each bond will be broken twice by X N and so the molar latent heat of vaporization, L , is actually X N / 2 . Rut, L = NX, where
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 6
