Langmuir 1994,lO,2462-2465
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A Study of Heterogeneous Nucleation in Aqueous Solutions C. B. Richardson* and Tamara D. Snyder Physics Department, University of Arkansas, Fayetteville, Arkansas 72701 Received January 18, 1994. In Final Form: April 19, 1994@ Single,microscopic, aqueous solutiondropletsofNaC1, CsC1, KF, and NaN03 are levitated in a quadrupole trap filled with water vapor at room temperature. The solutions become supersaturated as the pressure of the vapor is slowly reduced until solidificationoccurs. Both homogeneous droplets and those consisting of a solution jacket surrounding a solid core of a similar salt, KC1 for the first three, NaaSO4 for the last, are studied. Except for KF, the solid catalyzes the nucleation, reducing the maximum supersaturation to 48, 78, and 64% of its value in the absence of the solid for the other three, respectively. Classical nucleation theory yields the critical size of the nucleus, its surface energy density, and, assuming it is a spherical cap on the surface of the solid core, the wetting angle.
I. Introduction Solids in contact with metastable liquids may catalyze the liquid to solid transiti0n.l It is generally believed that the transition is opposed by the free energy increase which accompanies the formation of the surface of the embryo solid within the liquid.2 Contact between that surface and a catalyst reduces the energy and the limit of metastability. To obtain valid results when studying the transitions, i t is necessary that the liquid be pure and the surface clean. Cleaving a solid may produce such a ~ u r f a c eIn .~ this paper we report the results of experiments in which the metastable liquid is a supersaturated solution and the clean surface is produced by precipitation of a solute. A second solute remains completely dissolved in a solution which is slowlymade more supersaturated until nucleation occurs. The sample is a microscopic droplet, charged and then levitated in a quadrupole trap at room temperature. The droplet is in thermodynamic equilibrium with water vapor which fills the trap and whose pressure is varied to control meta~tability.~ In section I1 we describe the technique, and in section I11 we present the classical nucleation theory of VolmeP and of Turnbull and Vonnegut.6 In section N we present our results, and in section V we conclude the paper.
C
Figure 1. Spherical cap model of the nucleus: C = catalyst, S = solid, L = liquid. dissolving one salt and then the second, then precipitatingthe second, and finally nucleating the solidification of the first. Though the particle is microscopic with a high surface-tovolume ratio and thus is quick to respond to changing pressure of the water vapor, the system has a surface area about 12orders of magnitude greater and thus is slow to respond. To maintain equilibrium, the cycle time is typically 1h or more. To reduce the labor of data collection, the experiment is partially automated.8 A feedback loop usinga CCD camera to view the particle is used to continuously match its changingweight with a vertical electric force. The value of the potential needed to produce this force and the temperature of the water source comprise the data. The levitation technique is an example of "containerless processing"which is advantageousfor nucleation studies. Since the sample is microscopic, undissolved impuritiesare eliminated from most particles. They are untouched except by vapor and thus physically unperturbed, and chemically uncontaminated above the levels achieved by high-vacuum practice.
III. Heterogeneous Nucleation Theory 11. The Experiment The solutions to be studied are prepared by mixing measured volumes of saturated solutionsof two salts and then dilutingthe mixture about 50-fold. Reagent grade salts without further purification and HPLC grade water are used. Charged droplets of the mixed solution, roughly 10 pm in diameter, are injected into a quadrupole trap, whose design and operation have been described previously.' A single particle is trapped. The system housing the trap is evacuated,dryingthe particle which becomes a solid. The system is then sealed and held at 25 f 0.05 "C. Water vapor is admitted by opening a valve to a nearby pool of water. The temperature of the pool is slowly cycled, first ~
~~~
Abstract published in Advance ACS Abstracts, June 1,1994. (1)Vonnegut, B. J. Colloid Sei. 1948,3, 563. (2)For a kinetic theory not using embryo free energy, see: Chiang, P. P.; Donohue, M. D.; Katz, J. L. J. Colloid Interface Sci. 1986,122, @
251. (3)Dunning, W.J.; Fox, P. G.; Parker, D. W. In Crystal Growth, Peiser, H. S., Ed.; Pergamon Press: Oxford, 1967. (4)Snyder, T.D.;Richardson, C. B. Langmuir 1995,9, 343. (5)Sigsbee, R. A. In Nucleation, Zettlemoyer, A. C., Ed.; Marcel Dekker, Inc.: New York, 1969. (6)Turnbull, D.;Vonnegut, B. I d . Eng. Chem. 1952,44,1292. (7)Richardson, C. B.;Kurtz, C. A. J. Am. Chem. Soc. 1984,106, 6615.
Since our experiment is macroscopic and thermodynamic, we will discuss only classical nucleation theory here, which is similarly limited. In this theory bulk matter properties such as density, surface tension, and free energy of condensation are assumed for the embryo solid, which, as we shall see, contains fewer than 200 molecules. VolmeP considered a model in which the embryo sits on a flat surface of a solid, the potential catalyst. The top surface of the embryo, in contact with the solution, is spherical, with radius r. See Figure 1. We denote the catalyst, solid, and liquid as C, S, and L. The contact angle 0 which minimizes free energy is given by COS
e = %L - Gcs -m as,
where the ds are the interface energy densities. The change in free energy with the production of the embryo (8)Richardson, C. B. Rev. Sci. Instrum. 1990,61, 1334.
0743-7463/94/2410-2462$04.50/0 .. . 0 1994 American Chemical Society T
.
~
(1)
Langmuir, Vol. 10, No. 7, 1994 2463
Heterogeneous Nucleation in Aqueous Solutions is given by AG =
GROWTH AND EVAPORATION OF A MIXED KCI ( 6 6 % ) N a C l (34%) PARTICLE
-
-4nr'flm)kT In s
3v
I
7.0 -
+ 2nr2(1- m)usL -
1
I
1
I
I
I
I
6.0 -
where v is the specific volume in the solid and s = ala" is the supersaturation of the solution, the solute activity relative to that in the saturated solution.
F
95.0
-
d
W (3
z a
m3-3m+2 Am) = 4
(3)
I V
v) v)
a
is the ratio of the embryo volume to that of a sphere of the same radius. When
4.0
I
-
I W
A
0 c
3.0 -
(4) the critical radius, AG reaches a maximum: AG* =
2.0
-
16nas2v2flm)
3(kT In s*I2
Turnbullg has derived a n expression for the rate of formation of critical embryos per unit area of catalyst:
I = I, exp(-AG*/kT)
(6)
with
"3f16(a)
-
exp( -Ag/kT)
+ a(6 -
E)
' 70' I 75'
80 1
85 I
90 I
RELATIVE H U M I D I T Y , %
Figure2. Water cycle for mixed NaC1-KC1 particle: (a)NaCl dissolves;(b)saturated mixed solution; (c)KC1 precipitates;(e) NaCl solidifies. Reprinted with permission from ref 11. Copyright 1993 Pergamon Press. s* through the Gibbs Duhem equation:
(8)
where 6 is the disregistry between the unstrained solids, E is the strain of the embryo due to interaction with the catalyst, and y and a are constants. If 6 - E = 0, the embryo and catalyst are coherent. The coherence lowers the surface energy contribution to AG while it raises the volume contribution an amount proportional to a n appropriate elastic constant. The homogeneous nucleation equations equivalent to eqs 1-5 are obtained by setting m = -1. The rate of formation of critical embryos per unit volume islo J = J, exp(-AG*/kT)
(9)
J, SZ (vlv) exp(-Aglkr)
(10)
with
Our measurements yield the critical supersaturation (9)Turnbull,D.J. Chem. Phys. 1952,20,411. (10)Turnbull,D.;Fisher, J. C. J. Chem. Phys. 1949,17,71.
' I65
(7)
where n* is the number of molecules in the upper surface of the embryo, U L is the specific volume of the molecules in the liquid, kTlh = v is the jump frequency of the molecules from liquid to embryo, and Ag is a free energy barrier to the jump. In their crystallographic theory6 Turnbull and Vonnegut relate the surface energy density ucs to the mismatch between the structures of the catalyst and embryo: a,, = y
L O 60 L A
where 'a is the water activity a t saturated solution, a* that a t the transition, and N the ratio of water molecules to solute ions in the salt solutions studied.
Iv. Results and Analyses We have studied both homogeneous and heterogeneous nucleation of sodium chloride, cesium chloride, potassium fluoride, and sodium nitrate from aqueous solutions. Potassium chloride is the catalyst for the first three and sodium sulfate for the last. These pairings yield critical solutions which contain little or no dissolved catalyst. An example of a water cycle for a levitated mixed salt paticle is shown in Figure 2, which is taken from a recent paper by Tang and Munkelwitz.ll When dry, the particle is 34% by mass NaCl and 66%KC1. The relative weight of the particle is shown as the relative humidity of the surrounding water vapor is cycled from about 60 to 93% and back. The weight increase around 73%,point a, occurs as all of the NaCl and some of the KC1 dissolve. Between a and b, a t 81%,the remainder of the KC1 dissolves. Above b the solution becomes dilute. When the humidity is reduced below 81%, the solution is supersaturated. At 64%, point c, most of the KC1 solidifies, forming a pure core in the particle which is surrounded by a solution saturated with KC1 and supersaturated with NaC1. At 62%, point e, the NaCl solidifies. Tang and Munkelwitz studied the dissolution at a, while we have studied the solidification at e. (11)Tang, I. N.; Munkelwitz, H.R.Atmos. Enuiron. 1993,27a,467.
Richardson and Snyder
2464 Langmuir, Vol. 10,No. 7,1994
0
, I
1
\f
m
0.4 -0.500
40
PotassiumChloride (Mass %)
Figure 3. Phase diagram of the mixed NaC1-KC1-water system. Points a-e show the composition of special states indicated in Figure 2. Points f and g show the composition of saturated KCI and NaCl solutions, respectively. Points a', d', and e' show the composition of the solution surrounding the KC1 solid core.
Figure 3 is a phase diagram of the system. The compositions of the special states of the particle of Figure 2 are indicated by points a-e on the diagram. The line ga'bf connects states of equilibrium coexistence of the solution and solid. Between points g and a' the solution is saturated with NaC1, between points a' and f with KCl. At points a, d, and e the particle consists of a solid KC1 core surrounded by a solution jacket with the composition ofthe solution denoted by points a', d', and e', respectively. The three tie lines, aa', dd', and ee' converge a t 100%KC1, the common state of the core. As the humidity increases from 73 to 81%, the state point moves from point a to point b and the solution point from point a' to point b. As the humidity decreases from 81 to 64%, the state point moves through the metastable states between points b and c. Since pure supersaturated NaCl solution has a water activity of 0.64 a t 32.9%salt, we have superimposed a straight line between this point and point c to approximate the isobar a t 64% humidity and a second, parallel to it, to approximate the 62%isobar. When the particle state jumps from point c to point d, the solution state jumps from point c to point d'. As the particle state moves from point d to point e, the solution state moves from point d to point e' a t 62%humidity, from which the NaCl transition is nucleated. This construct yields a point e' solution composed of roughly lo2 Naf ion&+ ion. It is important to note that any mix yielding state b between points a' and f will produce a final solution near point e'. Our measurements used mixes having roughly equal masses of NaCl and KC1, meeting the requirement. For the mix KF and KCl, the eutonic point a' is at 0.92% KC1 by mass and the precipitate is KC1 KF*~HZO.'~ For NaNO3 and NazS04 the eutonic point is at 3.04%NazSO1. We have no'information on the CsCl-KCl system solubility. An example of data collected in this study is shown in Figure 4 for which the sample is a pure NaCl particle. The potential needed to balance the particle weight is plotted versus a manometer output voltage which varies linearly with the water vapor pressure. The solution-to-solid transition which gives the sudden decrease in weight is equivalent to that at point e in Figure 2. The random nature of nucleation is illustrated by the eight transitions shown. An example of the determination of the critical supersaturation s* is shown in Figure 5. We have plotted the composition of the NaN03 supersaturated solution as the
+
(12)Seidell, A.; Linke, W. F. Solubilities of Inorganic and MetalOrganic Compounds; van Nostrand: New York, 1940.
I'
,
-0.496
-0.492 ManometerReadinp I Volts
I
-0.488
Figure4. Eight solution-to-solid transitionsin a NaCl particle, equivalent to point e in Figure 2. Balance potential is proportionalto particleweight and manometerreadingto water activity.
0
0.0
1.6 In a
-
2.4
3.2
Figure 5. Composition versus water activity of a supersaturated NaN03 solution. The area under the curveis ins*, where s* is the supersaturation at the transition. Cross-hatching indicates transition in the presence of solid NazS04. Table 1. Summary of Measured Supersaturations system
NaCl NaC1-KCI CsCl
CsCI-KCl KF KF-KCl Nd03
NaNOs-NazS04
' a
0.753 0.728 0.665 0.66 0.177 0.17 0.743 0.738
a*
0.455 f 0.006 0.612 f 0.005 0.323 f 0.003 0.428 f 0.002 0.090f 0.001 0.090f 0.001 0 0.16 f 0.02
S*
4.64 2.21 2.72 2.12 2.58 2.58 6 3.86
number of water molecules per ion versus the negative logarithm of the water activity. The area under this curve is In s*. In the absence of the NazSO4 catalyst NaN03 does not crystallize as the water content is reduced to zero. (This behavior was also found for "03 in a n earlier study.13) For water activity below 0.046 we extrapolate the curve to N = 0. When solid NazS04 is present, theNaN03 crystallizes at a* = 0.16 f0.02, which is shown as cross-hatches. Here, as with NaCl above, a small amount of catalyst may be dissolved, but this has a negligible effect on sodium nitrate activity. In Table 1we summarize the nucleation results for the four salts, pure and mixed. There we list the system, the saturated solution water activity for the pure salt, the eutonic point water activity for the mixed systems, and the water activity a* and solute supersaturations*when nucleation occurs. KC1 catalyzes the nucleation of NaCl and CsCl but not KF02H20. NazS04catalyzes the nucleation of NaN03. We use classical nucleation theory to analyze these results, beginning with homogeneous nucleation. To (13) Richardson, C. B.; Hightower,R.L.Atnos. Enuiron. 1987,21, 971.
Heterogeneous Nucleation in Aqueous Solutions
Langmuir, Vol.10,No. 7,1994 2465
Table 2. Classical Nucleation Theory Analysis' salt r* (nm) USL (erg/cmZ) re* (nm) N* N,* 0 (deg) NaCl CsCl
KF NaN03 a
0.91 1.24 1.02 1.00
64 36 51 59
1.76 1.65 1.33
70 112 114 67
123 138 114 75
69 92 (180) 88
The subscript c indicates catalysed.
estimate Jo,we set v = kT/h = 6.2 x 10l2Hz. The specific volume ofthe supersaturated liquid, VL, is estimated using tabulated saturated solution density and assuming constant molar volumes. The transport barrier Ag is assumed to be the work required to remove the waters of hydration from the ions. For lithium halide solutions Richardson and Kurtz7 found hydration energies of 6-8 kT. From this we estimate exp(-Ag/kT) = 2 x 10-3 for all salts. Together these estimates yield JO= 7 x 1031 s-l for NaCl and comparable values for the others. To estimate J , we assume that when supersaturation s* is reached, nucleation occurs within 100 s. Since a typical volume for a trapped particle is 10-lo cm3,J R lo8 s-l. Thus, for NaC1, CsC1, and KF, AG*IkT = 55, and from eq 4, USL = 64,36, and 51 erg/cmz, respectively. For NaN03 we increase our estimated induction time to 10 000 s, reducing J to lo6 s-l, and yielding USL = 59 erg/cmz. For heterogeneous nucleation we apply the VonnegutTurnbull theory a s follows. Again using 10-lo cm3 as a typical particle volume, we get 7 x cm2 as the area of the KC1 and Na2SO4catalyst cores so that I % 2 x lo4 cm-2 s-l, To estimate IO, we keep u , USL, v, and Ag as above and modify U L for the reduced supersaturation. The critical radius of curvature r* is known from eq 4, so n* and f are known when 8 is determined. Equation 5 is solved by trial and error. The results of the Volmer-Turnbull analysis are shown in Table 2, where N* is the number of molecules in the critical nucleus and the subscript c means catalyzed. Since U C L - U C ~ = musL, we see from Table 2 that the energy a t the interface between solid KC1 and CsC1, or between NaN03 and Na2S04, is almost constant as the size of the embryo fluctuates. For NaCl and KC1there is a reduction of 23 erg/cm2for solid on solid relative to solution on solid. Only NaCl and KC1 among the four pairs studied have the same crystal structure, cubic close packed. CsCl is body-centered cubic, KF2H20 is orthorhombic, NaN03 is rhombohedral, and NazS04 is orthorhombic. Though their structures are the same, there is a large disregistry 6 between NaCl and KC1. In the (111)plane containing like ions, for example, the nearest neighbor distances are 3.98 and 4.47 A, respectively. Turnbull and Vonnegut estimate that such disregistry may be the source of energy density as large as 30 erg/cm2. Still KClis a potent catalyst for NaCl solidification. Three early studies of nucleation in ionic solutions are related to the present one. Newkirk and Turnbull14 dispersed small droplets of ammonium iodide saturated solution in silicone oil a t 35 "C to study homogeneous nucleation. The dispersion was placed under a microscope, heated to 55 "C, returned quickly to 35 "C, and then slowly cooled to 4 "C, supersaturating the solution. Crystallization was observed over the whole range, presumably due to "dirt particles which promoted nucleation". Even so the authors estimated USL = 15.4 erg/cm2 from the results. To study catalyzed nucleation, the authors (14)Newkirk, J. E.; Turnbull, D. J. Appl. Phys. 1966,26, 579. (15)Upreti, M. C.; Walton, A. G. J. Chem. Phys. 1966, 44, 1936. (16)Hightower, R. L.; Richardson, C. E.; Lin, H.-E.; Eversole, J. D.; Campillo, A. J. Opt. Lett. 1988, 13, 346.
immersed freshly cleaved micas whose (100) surfaces contain a hexagonal array of K+ ions, matching in form the (111)planar array in NH4I. Supersaturation defined a s the concentration ratio, rather than activity ratio, was less than 1.01 a t nucleation in the presence of the mica, or supercooling was less than 2.5". These authors did not use the Volmer theory, but their u values yield a wetting angle 6 near zero. Upreti and Walton15repeated the study but with six salts forming cubic close packed solids, KC1, KBr, RbC1, KI, RbBr, and NH41, and a single mica, muscovite. The first three have disregistry similar to that of NaCl on KC1 in the present study. Critical supersaturations, again defined as concentration ratios, increased with 6 but were less than 1.125,far below that seen here. Dunning, Fox, and Parkel.3 repeated the NH4I mica experiment but with magnification 20 times greater than in the preceding studies. They observed a pattern of growth on the surface: "On restoring the undercooling the history is repeated in remarkable detail." Since this is contrary to the view that nucleation is a random process, the hexagonal array on the mica surface appears to be irrelevant to its function as a catalyst. We do not know ofmore recent studies ofheterogeneous nucleation in solutions.
V. Conclusions The reproducibility of our nucleation results supports the claim that clean catalyst surfaces may be produced by precipitating one salt from a binary mixture. Maximum supersaturations in the presence ofthe solid surface range from 47.6 to 100% of the values without the surface, the former for NaCl on solid KC1, the latter for KF on KCl. The potency of the catalyst is loosely correlated with the mismatch of solid structures, though no information on the face of the effective surface is obtained. Classical nucleation theory applied to our results yields the size of the critical embryo, the energy density a t the embryosolution interface, and the wetting angle at the embryocatalyst interface. Prior studies on the nucleation of similar solutions on mica show it to be a much more potent catalyst than the two ionic solids used here. At the nanometer scale at which nucleation is complete, however, it is problematical that mica is adequately described by crystallography. It would be possible to levitate solution droplets containing insoluble cores, for example, amorphous solids such as glass16 or polystyrene, or even some immiscible liquid to add to our understanding of heterogeneous nucleation. Repetition of the experiments of Turnbull and others using the advances in surface science would be useful. Still, observation of the formation of the nucleus, the ultimate goal, remains the formidable challenge. Acknowledgment. We are grateful to I. N. Tang and H. Munkelwitz for permission to use Figure 2. This work was supported by Grant ATM 8909233 from the National Science Foundation. Appendix Crystal structures and cell dimensions of the six salts used are as follows: salt NaCl KCl csc1 KF2Hz0 Nd03 NaZS04
structure fcc fcc bCC
orthorhombic rhombohedral orthorhombic
cell dimensions a = 5.63 8, a = 6.29 A a = 4.11 A a = 5.15 A c = 8.87 A, c = 4.06 A a2 = 6.32 a2 = 47.25" a = 5.85 A, b = 12.29 A, c = 9.75
A,
