T H E JOURNAL OF
PHYSICAL CHEMISTRY Registered in U . 8. Patent Ofice
@ Copyright, 1970, by the American Chemical Societu
VOLUME 74, NUMBER 7 APRIL 2 , 1970
Crystallization of Slightly Soluble Salts from Solution by R. H. Doremus Genera! Electric Research and Development Center, Schenectady, New York (Receized October 20, 1068)
The rate of crystallization of barium sulfate from aqueous solution was studied simultaneously with two methods, electrical conductivity of the solution and light scattering from the particles. From these measurements the particle size was estimated and the interface growth coefficient was calculated. The results indicated that the particles coagulated in the later stages of precipitation. Results of several authors on crystallization of salts from solution are compared. The order of the crystallization process depends upon the stoichiometry of the salt and its supersaturation. The effect of supersaturation may result from different growth processes on different crystal faces. The interface growth coefficients for different salts, orders of crystallization, and supersaturation are compared. These coefficients are usually not a function of order or supersaturation, but do depend upon the type of salt crystallizing.
Introduction Crystals of ionic salts are nearly always prepared and purified by precipitation from solution. Although this process has often been studied, the sequence of events from the mixing of solutions to the final crystals is still debated. The steps of the precipitation process are nucleation of the crystals, their growth by accretion of material from the solution, and possible coagulation and competitive growth (Ostwald ripening). I n the present work the precipitation of barium sulfate from aqueous solution mas followed with two techniques simultaneously, electrical conductivity of the solution and light scattering from the crystals. The combination of these two techniques allowed a rough calculation of the particle size and therefore of the interface growth coefficient. Furthermore, these experiments indicated that the particles coagulate in the later stages of precipitation, showing that measurements of nucleation rates from counts of particles are questionable. The growth of crystals from solution can be studied in several ways. For larger crystals the rate of growth becomes influenced by diffusion of the precipitating ions or molecules in the liquid near the Thus
to measure the rate of the interface growth process it is necessary to study small crystals, often submicroscopic. Two methods can be used to measure this growth process. I n one, seed crystals are added to a slightly supersaturated solution in which no nucleation can occur. Then growth takes place only on the seed crystals, whose size can be measured in the light or electron microscope. The rate of growth is calculated from the rate a t which material disappears from the solution, usually followed with the solution conductance, and the crystal size. I n the other method the rate of precipitation of crystals is followed in two different ways so that both the rate of removal of material from solution and the crystal size can be calculated, as was done in the present work. In the precipitation method the supersaturation must be high enough for crystals to nucleate, so that the two methods measure the growth rate a t different supersaturations. I n this paper, measurements of growth rates a t different supersaturations (1) D. Turnbull, Acta Met., 1 , 764 (1953). (2) A. E. Nielsen, “Kinetics of Precipitation,’’Macmillan Co., New York, N.Y., 1964. This book has an extensive bibliography.
(3) R. H. Doremus, J . Phgs. Chem., 62, 1068 (1958).
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1406
R. H, DOREMCS
and for different salts are compared and discussed in terms of various theories.
Growth Equations In the present work it is assumed that all particles are nucleated at the time of mixing, so that the number of growing particles N is constant and they are all of the same size. Furthermore it is assumed that the growth rate is controlled by a process at the particle surface (interface control). Turnbull has shown that these conditions are valid for the precipitation of barium sulfate at the concentrations used here.' Then the flux of material J per unit area and time that is deposited on the particles is G(C, - Co)"(l - W)"
dR dt
J = p - =
CO"
(1)
In this equation p is the density of the particles in concentration units, R is their radius, G is an interface growth coefficient, n is the order of the growth process, C, and Co are the initial and equilibrium concentration of barium sulfate in the solution, respectively, and W is the fraction of precipitation and is given by
W =
4aNR3p 3 ( C m - Cd
Detailed discussions and deviations of these equations are given in a number of publication^.'-^ The factor of (1 - W ) in eq 1 accounts for competition between particles for the solute. Nielsen2gives a table of values of integrals of eq 1 for different n values, using eq 2 to express dR/dt in terms of W . If W , the extent of precipitation, is small, G can be calculated from an integration of eq 1 with W constant and assuming the crystal has negligible radius at the time of mixing. Then
G =
RP
tsy1 - W)"
(3)
where the particle has radius R after growth time t. The supersaturation S is
S = cln
~
LO
co
(4)
and is the best parameter to use to compare results at different concentrations, with different crystals, and with different n values.
Experimental Section Solutions of barium nitrate and potassium sulfate were mixed together with vigorous stirring to give the same final concentration of the two salts. One portion of the mixture was poured into a conductivity cell and the other in a light scattering cell. The resistance and light scattering of the solution was then measured as a function of time. Neither solution was stirred or moved during precipitation. The Journal of Physical Chemistry
0.7
11
0.6 I
o'21 0.1
0
4
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I
I
I
I
I
I
I
I
8
I2
16
20
24
28
32
36
40
44
48
TIME. MIN.
Figure 1. Fraction of barium sulfate precipitation a6 a function of time. Curve drawn from eq 1 with n = 3, points measured from the electrical conductivity of the solution.
The conductivity cell was of standard design and held about 25 ml of solution. The electrodes were shiny platinum, so that they did not nucleate crystals. The resistance of the cell was measured with a Wheatstone bridge of Luder's designU4 The temperature of the cell was held constant at 25.00 A 0.02"with a water bath. The light scattering was measured in an apparatus built by P. D. Zemany and H. T. Hall in this laboratory and having an optical system similar to that of Zimm.6 The measurements were made at 90" from the incident beam with plane polarized light of 0,546-p wavelength. The solutions were filtered through millipore filters just before mixing to ensure that no spurious scattering centers were present. The output of the photomultiplier was recorded continuously.
Experimental Results The results of measurements for a solution containing 1.6 X lo-' mol/cm3 of potassium sulfate and barium nitrate are shown in Figures 1 and 2. The fraction of precipitation W was calculated from the conductivity of the solution and the known equivalent conductances of barium, potassium, sulfate, and nitrate ions. No corrections were made for changes in activity coefficients, ion pairing, or equivalenl conductances as a function of time, since the solutions were very dilute and the total concentration changed only about 30% in the region of interest. The line in Figure 1 was calculated from eq 1 with n = 3. The fit is good up to about 20 min, after which the experimental results drop below the curve. This same deviation was found for other experiments of barium sulfate and strontium sulfate. The line in Figure 2 is the same as in Figure 1. The raw scattering data were normalized t o the line at W = 0.1. Since they fit the line fairly well, the scattering (4) W. F. Luder, J . Amer. Chem. SOC.,6 2 , 89 (1940). (5) B. H. Zimm, J . Chem. Phys., 16, 1099 (1948).
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CRYSTALLIZATION OF SLIGHTLY SOLUBLE SALTSFROM SOLUTION
05 -
sO4-
t
g-
i
o
E03c 0
Y Eo2-
01
-
0
2
4
6
I 8
1
I
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IO
12
14
I 16
I I8
I 20
22
TIME. MIN
Figure 2. Fraction of barium sulfate precipitation as a function of time. Curve same as for Figure 1; points are intensity of scattered light, normalized with the curve a t W = 0.1.
tu O
00110
is apparently about proportional to the volume of the particles during the growth studied here. The scattering decreased sharply at about 18 min after the start of precipitation, and continued to decrease until it reached nearly background level after about 30 min. Occasional dips, such as the one at 21 min, were observed shortly after the break, and peaks were observed during later stages of the decrease of the scattering. An estimate of the size of the precipitating particles can be derived from the comparison between scattering and the growth curve in Figure 2. The intensity of 90" scattering calculated for spherical particles for refractive index 1.25 (that of barium sulfate is about 1.22) is plotted against particle size in Figure 3. It is seen that the scattering is proportional to the volume of the particles only over a narrow size range. The scattering results in Figure 2 seem to be slightly less than proportional to the volume of the particles over a size range in which the radius is doubled. If these two size ranges are equated, the radius of the particles is found to be about 1000 at W = 0.05. Then from eq 4, G = 2.6 X mol/cm2 sec, and the number density of particles is about los per cm3. The following parameters for barium sulfate at 25" were used in this calculation: p = 0.0192 mol/cm3, Co = 1.06 X mol/ cm3. Discussion and Comparison with Previous Results In an earlier study the deviations from the growth curve shown in Figure 1 were attributed to a change in the mode of g r ~ w t h . I~n the earlier stages the rate of growth increased proportional to the surface area of the crystals, but after the deviations the rate data behaved as if the area for deposition of material were constant. The light scattering results shown in Figure 2 suggest that coagulation of the crystals formed first is the reason for this change. After about 20 min of growth the crystals begin to coagulate together to form larger crystals
5
3
I
'
i
05
a
Figure 3. Intensity of light scattered a t 90" from incident beam from spherical particles of refractive index 1.26 as a function of 01 = 2T(particle radius)/(wavelength of light in solution). Incident light perpendicularly plane polarized. Points are calculated from tables of W. J. Pangonis, W. Heller, and A. Jacobsen, "Light Scattering Functions," Wayne State University Press, Detroit, Mich., 1957, and H. Blumer, 2. Phys. 32, 119 (1925); 38, 304 (1926); line is drawn with slope 3.
which subsequently sediment to the bottom of the vessel containing them. The larger crystals have a lower scattering cross section per unit volume than do the smaller particles, as shown in Figure 3, so that as coagulation proceeds the scattering actually decreases, as shown in Figure 2. As the particles sediment the scattering also decreases until there are few particles in the scattering volume. After precipitation of slightly soluble salts a deposit often is found in the reaction vessel, consistent with this view. The coagulation of smaller particles into larger ones gives a somewhat smaller eff ective area for deposition. The area of these larger particles is increased only very slightly with further deposition of material, giving the appearance in the kinetics of a constant growth area. Therefore, the experimental results are consistent with coagulation of the precipitating crystals. Meehan and Miller also concluded that coagulation mas occurring in their study of rapid precipitation of silver bromide.6 Because of the possibility of coagulation, any study of nucleation rates and crystal sizes in precipitation from counts or observation of crystals after a certain time of crystallization is questionable. For example, the original precipitation laws of von Weimarn were deduced from observations of this sort; it seems likely that results were often affected by coagulation. Various authors have found different values for the (6) E. J.
Meehan and J. K. Miller, J. Phys. Chem., 72,
2168 (1968).
Volume 74, Number 7 April 2 , 1970
R. H. DORENUS Table I : Order of Growth Laws for the Precipitation of Ionic Crystals
Table I1 : Interface Growth Coefficient for Various Crystals G,
Salt
Reference
-Supersatn-Low High
Silver chloride Barium sulfate Strontium sulfate Lead sulfate Magnesium oxalate Siiver chromate
2 2 2 2 2 3
Barium sulfate 3 (4?) 3
c, d e , f, 8, i j k, 1
4
5 C. W. Davies and G. H. Nancollas, Trans. Faraday Soc., 53, 1449 (1957). M. J. Insley and G. D. Parfitt, ibid., 64, 1945 (1968). See ref 1-3. G. H. Nancollas and N. Purdie, Trans. J. Salomon, Faraday SOC., 59, 735 (1963). See ref 3. Thesis, Kew York University, 1964. J. R. Campbell and G. H . Xancollas, J . Phys. Chem., 73, 1736 (1969). S. Oden and D. Werner, A r k . K e m i Mineral., Geol., 9, No. 23 and 32 (1926). G. H. Nancollas and N. Purdie, Quart. Rev., 18, 1 (1964). G. H. Nancollas and N. Purdie, Trans. Faraday SOC.,57, 2272 (1961). A. Van Hook, J . Phys. Chem., 44, 751 (1940). J. R. Howard and G. H. Nmcollas, Trans. Faraday Soc., 53, 1449 (1957).
'
'
order n of the precipitation process. A summary is given in Table I. From the table one can deduce that n depends on at least two factors, the stoichiometry of the crystallizing salt and its supersaturation, as deduced p r e v i ~ u s l y . ~The results of Salomon' are particularly interesting in this regard, since he studied the growth rate of strontium sulfate crystals over a wide range of supersaturation and observed their morphology under the microscope as well. Salomon found that the morphology of the crystals was quite different a t high and low supersaturation and that these differences correspond to the change in order from 2 to 3. It seems likely, therefore, that the change of order results from the nucleation of crystals with different crystallographic faces and that the growth mechanism on different faces is different. Further Fvork to clarify and confirm this relation between growth mechanism and morphology should give attractive results. To calculate the interface growth coefficient G' of eq 1 from the rate of precipitation of a suspension of crystals it is necessary to known the size of the crystals. I n the seed crystal experiments of Davies and Nancollas and their collaboraters the crystals were large enough to observe in the microscope, I n the present case the simultaneous measurement of conductivity and light scattering provided information to estimate the particle size and therefore to calculate G, as shown in the last section. Calculations of G for various crystal growth experiments are given in Table 11. The agreement
The Journal of Physical Chemistry
Salt
Silver chloride PIIagnesium oxalate
Supersatn
Order
mol/cma
AT
seo
2 14 Low Low 0.36 1.3
2 3 2 2 2 2
3 x 10-13 3 X 10-13 3 x 10-11 3 x 10-11 4 X 10-ls 10-11
Ref
a b c Cl e c
a G. H. Nancollas and K. Purdie, Trans. Faraday SOC.,59, 735 (1963). b Present work. C. W.Davies and G. H. Nancollas, Trans. Faraday SOC.,53, 1449 (1937). d 11. J. Insley and G. D. Parfitt, ibid., 64, 1943 (1968). e G. H. Kancollar and N. Purdie, ibid., 57, 2272 (1961).
between G measured for barium sulfate in the present experiments and those of Nancollas and Purdie on seed crystals, notwithstanding the difference in reaction order, is noteworthy. The agreement between two different sets of experiments on silver chloride, done in quite different ways, also shows the usefulness of comparing G values. The value of G mas not a function of supersaturated except in magnesium oxalate. The higher rate at higher supersaturation possibly resulted from the nucleation of new crystals. It would be interesting to obtain more accurate results for G on R wide variety of salts to see if it is related to such factors as ion size, ion polarizability, hydration, and other factors. I n any event it appears that G', the rate of growth at unit supersaturation, is the correct parameter to compare for diff erent conditions of precipitation. A number of different theories have been proposed for interface controlled growth from s o l ~ t i o n . 2 ~ ~Fea~*-~~ tures such as surface diffusion, surface reactions including dehydration, surface defects such as energent dislocations, surface steps and kinks in the steps, step spacing, surface roughness, impurity adsorption, and others are involved in these theories. To test most of these ideas more detailed study of the crystal surface itself during growth is required. The present results show the importance of stoichiometry of the crystallizing salt, of the orientation of crystal faces, and the possibility of coagulation of crystals during grorvth from solution. (7) J. Salomon, Thesis, New York
University, 1964.
(8) W. R. Burton, N. Cabrera, and F. C. Frank, Phil. Trans. Roy. Soc. London, 243, 299 (1951). (9) G. W.Sears, J. Chem. Phys., 2 9 , 979, 1045 (1958). (10) J. W.Cahn, Acta Met., 8, 554 (1960).
