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Scanning electron microscopic and kinetic studies of the crystallization and dissolution of barium sulfate crystals
Journal ofCrystal Growth 33 (1976) 11—20 © North-Holland Publishing Company
SCANNING ELECTRON MICROSCOPIC AND KINETIC STUDIES OF THE CRYSTALLIZATION AND DISSOLUTION OF BARIUM SULFATE CRYSTALS S.T. LIU and G.H. NANCOLLAS chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214, U.S.A. and
E.A. GASIECKI Caispan Corporation, Buffalo, New York. U.S.A. Received 14 February 1975; revised manuscript received 9 October 1975
The kinetics of crystallization and ofdissolution of well-characterized seed crystals ofbarium sulfate in stable supersaturated and undersaturated solutions, respectively, of this salt, have been studied at 25°Cusing a highly reproducible conductance technique. Seed crystals of three distinctly different morphologies have been used and the crystal growth has also been followed by parallel scanning electron microscopic experiments. Following an initial growth surge reflecting some secondary nucleation, the rate of crystallization is proportional to the square of the supersaturation indicating a surface controlled reaction. The rate of dissolution is also controlled by a surface reaction being proportional to the square of the undersaturation and independent of fluid dynamics. In spontaneous precipitation experiments crystals have been obtained of widely differing morphologies dependmg upon the nature and concentration of the reactants and the fluid dynamics of mixing. Different shaped crystals have different densities of active growth sites, monitored kinetically, on their surfaces. The rate of growth of all the crystals, however, varies linearly with the square of the barium sulfate supersaturation.
Doremus [7], after analyzing the experimental data of Turnbull [8], reached the conclusion that the reaction order was between 3 and 4. Using a light scattering technique to investigate the spontaneous precipitation, Walton [9, 10] reported a kinetic order close to 2 in agreement with the seeded crystal growth data [3]. A first order diffusion rate law was proposed by Collins and Leineweber [11] from studies of precipitation from homogeneous solution in which the sulfate ions are produced by the reaction between persulfate and thiosulfate. Recently, Gunn and Murphy [12] made a detailed study of the nucleation and crystal growth of barium sulfate and concluded that the rate of growth followed a third order dependence on barium sulfate concentration when the crystals were small. They also pointed out that a first order dependence on relative supersaturation was found for the growth of large barium sulfate crystals at low supersaturation. A number of microscopic investigations have been
1. Introduction The kinetics of nucleation and crystallization of bivalent metal sulfate salts have been extensively studied since they serve as model systems for the study of precipitation reactions of sparingly soluble salts in aqueous solutions. After an initial fast surge, the crystal growths of lead sulfate and strontium sulfate follow a rate law in which the rate of precipitation is proportional to the square of the relative supersaturations [1, 2]. Similar conclusions have been reached in the seeded growth study of barium sulfate [3] from a supersaturated solution but there is a considerable diversity in the reported reaction orders for the corresponding spontaneous precipitation reaction. Using a stopped flow technique, Nielsen [4, 5] reported a rate which was proportional to the third or fourth power of the relative supersaturation. From conductance measurements, O’Rourke and Johnson [6] found a similar fourth order dependence, while 11
12
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/ Crystallization and dissolution
of barium sulfate crystals
made of the precipitation of barium sulfate crystals [13 20]. Fisher found [15,16] that the morphology and size of precipitated barium sulfate particles is greatly influenced by such factors as the initial composition of the electrolyte solution, pH, temperature and the presence of foreign ions. Lieser and his coworkers [19, 20] also observed marked changes in morphology of precipitated barium sulfate crystals as a function of barium and sulfate ionic concentrations. In another study, Takiyama [17, 18] reported morphologies varying from a regular rectangular perfect crystal form at low initial supersaturation to an irregular dendritic form at relatively high concentrations. Recently Murthy [211used transmission electron microscopy to examine the surfaces of grown barium sulfate crystals and suggested that secondary nucleation accompanied the precipitation process. Unfortunately, most of these studies were concerned with only the shape and particle size of the precipitated crystals and were not able to show the detailed surface structure. Not only is the precipitation and dissolution of barium sulfate of considerable analytical importance, but the salt is a persistent scalant under down hole oil field conditions. The morphology of precipitated crystals can markedly influence the formation of hard adherent scale deposits under such conditions. In the present work, the scanning electron microscope has been used to examine precipitated barium sulfate crystals. Different types of seed crystals have also been used in kinetic crystal growth studies in order to relate the effect of the size, shape and surface area on the crystal growth and dissolution processes.
were centrifuged, washed several times with distilled water and either dried with acetone or freeze dried. Seed crystals for kinetic studies were preparedby mixing equivalent amounts of barium chloride with sulfuric acid. Suspension A was prepared by quickly adding 6.0 X iO~M barium chloride to a 6.OX 10 M sulfuric acid without agitation. Seed suspension B was prepared in a similar way using 0.01 M barium chloride and sulfuric acid. Seed suspension C was prepared under similar conditions to those of suspension B but with stirring. After preparation, the seed suspensions were washed several times until free from external salts, and aged for at least one month before use. Stable supersaturated solutions of barium sulfate were prepared by the careful mixing of barium chloride and sulfuric acid solutions in a HartleyBarrett type conductance cell maintained at 25 ±0.01°C;supersaturated solutions of concentration up to 7.5 X 10 ~ M in barium sulfate were stable for at least several hours. Crystal growth was initiated by adding known volumes of seed suspension and a Wayne—Kerr Transformer Ratio Arm conductance bridge was used to follow the resistance of the supersaturated solutions during the course of the crystallization and dissolution experiments. At the low concentrations of the crystallization and dissolution experiments, the equivalent conductivity value of barium sulfate was taken as effectively constant, 140.5 ohm 1 equiv~cm2 at 25°C.All experiments were made in a nitrogen atomosphere. The specific surface area of the crystals was determined by nitrogen adsorption using a Quantasorb single point BET apparatus.
2. Experimental
3. Results and discussion
Analytical reagent grade chemicals, triply distilled water and Grade A glassware were used throughout. Stock solutions were made by weight using triply distilled water. Potassium sulfate, sodium sulfate and barium chloride solutions were analyzed by passing aliquots through a column of Dowex 50 ion exchange resin in the hydrogen form and titrating the liberated acid. Barium sulfate crystals for scanning electron microscopic observations were made by mixing barium chloride with sulfuric acid, potassium sulfate or sodium sulfate. After certain time periods, the crystals
Three distinct types of seed crystals shown in fig. 1 were used in the crystal growth and dissolution experiments; the specific surface areas were 0.66, 1.25, and 1.31 m2 g1 for seed crystals A, B, and C respectively. Suspension B, although similar in size to the crystals of suspension A showed a surface roughness which resulted in the higher specific surface. Crystal growth experiments using equivalent eoncentrations of lattice ions are summarized in table 1, and a typical rate curve is shown in fig. 2. At an initial concentration of about 7.0 X l0~ M, the growth
‘~
-~
Fig. 1. Seed crystal A (a), seed crystal B (b), seed crystal C (c). Seed crystal A (d) and B (e) after 1 h growth from 2.1 X l0~ M barium sulfate solution.
14
S. 1’. Liu et al.
/ Crystallization and dissolution
of barium sulfate crystals
Table 1 Crystallization experiments of barium sulfate using equivalent concentrations of ions at 25°C; supersaturated solutions are prepared by mixing barium chloride with sulfuric acid Expt. No.
1 2 3 4
3
Surface area
Initial (BaSO
Seed
Initial fast
kcs X i0
4) (10 M)
suspension
period (mm)
. —i (lmole —1 mm )
7.02 7.02 7.02 7.02
A A B C
50 30 20
0.208 0.383 0.542
5
1.48
reaction from stable supersaturated solutions was characterized by an initial fast growth surge whose duration is given in table 1. Following this surge, the experimental kinetic data can be satisfactorily represented by eq. (1): 2 dm/dt = kcS (m m 0) (1) where m and m0 represent the concentration of barium sulfate at time t and at equilibrium respective-
6
of seed crystal per umt volume of cell solution 2fl) (m 0.064 0.138 0.248 0.430
ly. kc is the rate constant for crystallization. S represents the surface area of the added seed crystals which is proportional to the number of the active growth sites of the seed crystals added in unit volume of solution. Typical plots of the integrated form of eq. (1) are shown in fig. 3 in which the initial fast growth surges are clearly indicated. The second order rate constants kcs following the initial surge are calculated from the slopes of the linear parts of the curves in
B.
2 ~+
I
2
Time 1 hr 1
Fig. 2. Growth curves of barium sulfate at 25°C.Expt. 2(0); Expt. 4(+).
Time
(hr
Fig. 3. Integrated plots of equation 1 for the growth of barium sulfate: Expt. 1(S); Expt. 2(0); Expt. 3 (V);Expt. 4 (o).
I Crystallization and
S. T. Liu et al.
fig. 3. The duration of the initial surge decreases as the concentration of seed crystals is increased. It is interesting to note that eq. (1) satisfactorily explains the growth data for all three types of seed crystals for the ranges of(rn m0) values 3.0 X i0~ to 0.5 X l0~ —
M. The initial growth surges are influenced more by the subsequent reaction rate than by the type of crystal used, decreasing as the total available surface area for growth increases. During the surge the effective “order” of reaction [exponent in eq. (1)] is between 3 and 4 as might be expected for a nucleation process. Similar surge effects have been found in the seeded growth of strontium sulfate [2], lead sulfate [1] and calcium oxalate monohydrate [22]. The observed increase in the growth surge with increase of supersaturation or decrease of added seed led to the suggestion that additional surface nucleation occurred at the beginning of the reaction. For a given supersaturation, a sufficient number of growth sites have to be provided for the growth to proceed according to eq. (1) in order to eliminate the initial surge. The micrographs shown in fig. 1 clearly indicate that after one hour of growth in a supersaturated solution containing 2.1 X 1 ~ M barium sulfate, additional small partides on the surfaces of the crystals are induced by a surface nucleation process. The results presented here support the previous conclusion that the seeded crystal growth of barium sulfate at relatively low supersaturation follows a rate law second order in relative supersaturation. This evidence, together with an observed negligible stirring effect on the growth rate and relatively high activation energy [23], strongly suggests that the crystal growth process is controlled by a surface reaction rather than by a bulk diffusion process. The conflicting reaction orders reported in the literature probably result from the fact that the degree of supersaturation m the spontaneous precipitation studies is an important factor in determining the kinetics of precipitation. This will be discussed later. Unlike the dissolution of most sparingly soluble salts in which the transport of materials from the surface of crystals to the bulk of solution the rate determining step, the dissolution of bariumis sulfate crystals into a subsaturated solution follows eq. (2): -
d,n/dt
.
=
kds
(m
2 0
—
rn)
-
,
-
.
.
.
(2)
dissolution of barium sulfate crystals
15
where kd represents the dissolution rate constant. The validity of eq. (2) is clearly demonstrated by the plot of the integrated form shown in fig. 4. Changes in s during the dissolution experiments are less than a few percent of the total surface area and can be neglected. Eq. (2) satisfactorily represents the dissolution reaction for all three types of crystals to about 90% of the total reaction and a summary of the dissolution experiments is given in table 2. The rate of dissolution is independent of stirring rate and appears to be controlled by a surface reaction process. Similar results have been reported previously for the dissolution of barium sulfate [24], lead sulfate [25] and strontium sulfate [2]. Although s in eq. (2) usually represents either the total surface area of the number of active sites, marked differences in these quantities with different seed materials are clearly shown by the results of the experiments in table 2. It can be seen that for the different seed crystal morphologies, kds is not proportional to the total surface area of the added seed crystal in unit volume of solution. The surface area of added C crystals in expt. 7 is only about three times that of seed crystal A in expt. 5. However, the resulting overall rate constant, kds for expt. 7 is about twelve times that of expt. 5. This indicates that the different seed crystals may contain quite different numbers of active sites per unit area for growth or dissolution. A number of spontaneous precipitation experiments were made to study the effect of solution composition, fluid dynamics and the presence of external ions on the size and morphology of the precipitated barium sulfate crystals. The micrographs in fig. 5a show
Table 2 Dissolution of barium sulfate crystals at 25°C .
Expt. Initial Seed No. (BaSO4) suspension (1O~M)
5
6
0 0
~
0
A B -
C
kds X 10
—i
(I mole
0.887 2.67 10.8
.
mm
—i
Surface area of seed crystal per unit volume of cell2/l) solu— (m 0.069 0.124 0.215
16
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/ Crystallization and dissolution
Time
of barium sulfate crystals
(mm)
Fig. 4. Integrated plots of eq. (2) for the dissolution of barium sulfate: Expt. 5(s); Expt.
crystals prepared by adding, without stirring, 50 ml of 4.0 X 10—2 M sulfuric acid to 50 ml of 4.0 X 10—2 M barium chloride while the crystals in fig. Sb result from the nthing of 5 ml of 4.0 X 10—2 M sulfuric acid with 5 ml 4.0 X 10—2 M barium chloride solution in 90 ml of H20. Crystals prepared from the same reagents but at concentrations of 4.0 X 10~ M and 1.0 X 1 o—~M of barium sulfate are given in figs. Sc and Sd respectively. It can be seen that the dendritic crystals formed from solutions containing 2.0 X 10 ~M barium sulfate (fig. Sb) are much smoother than those formed at a higher concentration, 2.0 X 10 ~ M (fig. 5a). However, concentrations below 4.0 X 10 ‘l M result in well-formed retangular crystals (figs. Sc and Sd). Takiyama [17, 18] also reported spindle-shaped dendritic barium sulfate crystal having rugged edges which were produced in the range of concentration, 1.0 X 10—2 to 2.0 X 10—2 M. The barium sulfate crystals shown in fig. 6, obtained from supersaturated solution prepared by mixing barium chloride with sodium sulfate or potassium sulfate under unstirred conditions show the same marked morphological differences as was found in the absence of alkali metal ion. At a concentration of 2.0 X l0~ M, dendritic crystals are usually formed
6(V); Expt.
7(o).
but the crystallites derived from sodium sulfate solution have much more rugged edges than those prepared from potassium sulfate solution. At concentration lower than 4.0 X i0~ M in barium sulfate, the rectangular crystals are also obtained from sodium ion containing solutions. By comparing fig. 5 with fig. 6, it is interesting to note that the barium sulfate crystals precipitated from supersaturated solution containing potassium or sodium ions always show a surface roughness which is not observed in crystals prepared using sulfuric acid solution (fig. 5). It is possible that adsorbed sodium or potassium ions on the surface of the crystals may serve as active centers for surface nucleation during the crystallization process. After a certain period of growth, these ions are incorporated into the growing crystals resulting in the frequently observed coprecipitation [26] of these external ions in analytical precipitation of barium sulfate. Under conditions of stirring the morphologies of the crystals are quite different (fig. 7). In these experiments, the second reagent was added with vigorous stirring over a period of about two minutes. By comparison with fig. 5, it is seen that the crystals formed are very much smaller with the increased frequency of ion encounters increasing the rate of nuclea-
S. T~Liu et al.
/ Crystallization and dissolution
of barium sulfate crystals
17
—
4 Fig. 5. Barium sulfate crystals precipitated out under unstirred condition by mixing barium chloride with sulfuric acid at concentration 2.0 X 10_2 M (a), 2.0 X 10~ M (b), 4.0 X i0~ M (c), 1.0 X i0~ M (d).
tion [27] and resulting in a smaller crystal size, The kinetic study of seeded crystal growth and the scanning electron microscope observation of spontaneously precipitated barium sulfate in this study throws light on the conflicting results reported in the literature for which the effective reaction order for growth ranges from ito 4 [3—12].Thus the growth of dendritic crystals is usually believed to be a bulk diffusion controlled process [10, 28]. For barium sulfate,
it is found that dendritic crystals invariably form at higher than about 2.0 X iü~ M (figs. 5a, 6a), and similar observations were reported by Lieser and Wertenbach [19]. At such concentrations diffusion of the ions to the crystal surface would be expected to be the rate controlling step in the precipitation. As the concentration is decreased, a competition between diffusion and surface growth processes will result in an effec-
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& 7’. Liu etaL
/ Crystallization and dissolution
of barium sulfate crystals
7ig. 6. Harium sulfate crystals precipitated out under unstirred condition by mixing barium chloride with sodium sulfate at concenl tration 2.0 x i0~ M (a), 4.0 x i0~ M (b), and by mixing barium chloride with potassium sulfate at concentration 2.0 X i0~ M (c),6.OX 10 4M(d).
reaction order greater than one. Under concentration conditions where surface nucleation is important, the reaction wifi be expected to proceed with a rate law in which the rate of deposition may be proportional to the third, fourth or even higher power of the supersaturation. At low supersaturation, a screw dislocation growth mechanism would lead to reaction second order in relative supersaturation. The rectangultive
ar well-formed crystals at a concentration of about 4.0 X 10~M barium sulfate (fig. Sc). suggests a controlling step different from that for the formation of dendrites. Under such conditions the growth of seed crystals follows eq. (1). Previous studies of barium sulfate crystal growth have been made over a wide range of concentration and fluid dynamics both in the presence and absence
ST. Liu etal. /Crystallization and dissolution of barium sulfate crystals
19
~:
~
Fig. 7. Barium sulfate crystals precipitated out under vigorously stirred condition by mixing barium chloride with sulfuric acid at 3 (a) 4.0 X i0~M (b). concentration 2.0 X i0
of neutral electrolytes and added seed crystals. It is quite clear from the results of the present work that the morphology of the crystals formed is sensitive to these experimental factors. Moreover, the different shaped crystals have different densities of active growth sites on their surfaces. The number of such growth sites greatly influences the duration of the initial growth surge in the seeded crystallization experiments. In attempting to compare the results of different investigations, all these factors have to be taken into consideration, and it is not surprising that different workers have reported conflicting results.
Acknowledgements Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society for partial support of this work. We also thank the National Science Foundation for a supporting grant (ENG 74-15486). References [1] D.M.S. Little and G.H. Nancollas, Trans. Faraday Soc.
66 (1970) 3103.
[2] J.R. Campbell and G.H. Nancollas, J. Phys. Chem. 73
(1969) 1735. [3] G.H. Nancollas and N. Purdie, Trans. Faraday Soc. 59 [4] (1963)735. A.E. Nielsen, J. Colloid Scm. 10 (1955) 576. [5] A.E. Nielsen, Kinetics ofPrecipitation (Pergamon, 1964). [6] J.D. O’Rourke and R.A. Johnson, Anal. Chem. 27 (1955) 1699. ~ ~ 0 1068. [9] A.G. Walton and T. Hlabse, Anal. Chim. Acta 29 (1963) 249. [10] A.G. Walton, The Formation and Properties of Precipitation (Interscience, 1967).
[11] F.C. Collins and J.P. Leineweber, J. Phys. Chem. 60 (1956) 389. [12] D.F. Gunn and M.S. Murthy, Chem. Eng. Sci 27 (1972) 1293. [13] K.H. Lieser, Angew. Chem. Intern. Ed. 8 (1969) 188. [14] S. Popoff and E.W. Neuman, Ind. Eng. Chem., Anal. [15] R.B. Fisher, Anal. Chem. 23 (1951)1667. [16] R.B. Fisher and T. Rhinehammer, Bull. Anal. Chem. 25 (1958) 950. [17] K. Takiyama, Bull. Chem. Soc. Japan 32 (1959) 68. [18] E. Suito and K. Takiyama, Bull. Chem. Soc. Japan 27 (1954)121, 123; 20(1955) 305. [19] K.H. Lieser and H. Wertenbach, Z. Physik. Chem. NF 34 (1962) 1. [20] A. Fabrikanos and K.H. Lieser, Z. Physik. Chem. NF
34 (1962) 16, 29.
20
[21] M.5. Murthy, in:
S. 7’. Liu etaL
/ Crystallization and dissolution of barium sulfate crystals
Industrial Crystallization, Proc. Symp. Inst. of Chemical Engineers, London, 1969, 87. [22] G.H. Nancollas and G.L. Gardner, J. Crystal Growth 21(1974) 267. [23] D.M.S. Little, ph.D. Thesis, Univ. of Glasgow (1964). [24] C.H. Bovington and A.L. Jones, Trans. Faraday Soc. 66 (1970) 764.
[25] C.H. Bovington and A.L. Jones, Trans. Faraday Soc. 66 (1970) 2088. [26] G. Walton and G.H. Walden, Jr., J. Am. Chem. Soc. 68 (1946) 1742. [27] J.W. Mullin, Crystallization, 2nd ed. (Butterworths, London, 1972). [28] R.F. Strickland-Constable, Kinetics and Mechanism of Crystallization (Academic Press, New York, 1968).
SCANNING ELECTRON MICROSCOPIC AND KINETIC STUDIES OF THE CRYSTALLIZATION AND DISSOLUTION OF BARIUM SULFATE CRYSTALS S.T. LIU and G.H. NANCOLLAS chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214, U.S.A. and
E.A. GASIECKI Caispan Corporation, Buffalo, New York. U.S.A. Received 14 February 1975; revised manuscript received 9 October 1975
The kinetics of crystallization and ofdissolution of well-characterized seed crystals ofbarium sulfate in stable supersaturated and undersaturated solutions, respectively, of this salt, have been studied at 25°Cusing a highly reproducible conductance technique. Seed crystals of three distinctly different morphologies have been used and the crystal growth has also been followed by parallel scanning electron microscopic experiments. Following an initial growth surge reflecting some secondary nucleation, the rate of crystallization is proportional to the square of the supersaturation indicating a surface controlled reaction. The rate of dissolution is also controlled by a surface reaction being proportional to the square of the undersaturation and independent of fluid dynamics. In spontaneous precipitation experiments crystals have been obtained of widely differing morphologies dependmg upon the nature and concentration of the reactants and the fluid dynamics of mixing. Different shaped crystals have different densities of active growth sites, monitored kinetically, on their surfaces. The rate of growth of all the crystals, however, varies linearly with the square of the barium sulfate supersaturation.
Doremus [7], after analyzing the experimental data of Turnbull [8], reached the conclusion that the reaction order was between 3 and 4. Using a light scattering technique to investigate the spontaneous precipitation, Walton [9, 10] reported a kinetic order close to 2 in agreement with the seeded crystal growth data [3]. A first order diffusion rate law was proposed by Collins and Leineweber [11] from studies of precipitation from homogeneous solution in which the sulfate ions are produced by the reaction between persulfate and thiosulfate. Recently, Gunn and Murphy [12] made a detailed study of the nucleation and crystal growth of barium sulfate and concluded that the rate of growth followed a third order dependence on barium sulfate concentration when the crystals were small. They also pointed out that a first order dependence on relative supersaturation was found for the growth of large barium sulfate crystals at low supersaturation. A number of microscopic investigations have been
1. Introduction The kinetics of nucleation and crystallization of bivalent metal sulfate salts have been extensively studied since they serve as model systems for the study of precipitation reactions of sparingly soluble salts in aqueous solutions. After an initial fast surge, the crystal growths of lead sulfate and strontium sulfate follow a rate law in which the rate of precipitation is proportional to the square of the relative supersaturations [1, 2]. Similar conclusions have been reached in the seeded growth study of barium sulfate [3] from a supersaturated solution but there is a considerable diversity in the reported reaction orders for the corresponding spontaneous precipitation reaction. Using a stopped flow technique, Nielsen [4, 5] reported a rate which was proportional to the third or fourth power of the relative supersaturation. From conductance measurements, O’Rourke and Johnson [6] found a similar fourth order dependence, while 11
12
& T. Liu et al.
/ Crystallization and dissolution
of barium sulfate crystals
made of the precipitation of barium sulfate crystals [13 20]. Fisher found [15,16] that the morphology and size of precipitated barium sulfate particles is greatly influenced by such factors as the initial composition of the electrolyte solution, pH, temperature and the presence of foreign ions. Lieser and his coworkers [19, 20] also observed marked changes in morphology of precipitated barium sulfate crystals as a function of barium and sulfate ionic concentrations. In another study, Takiyama [17, 18] reported morphologies varying from a regular rectangular perfect crystal form at low initial supersaturation to an irregular dendritic form at relatively high concentrations. Recently Murthy [211used transmission electron microscopy to examine the surfaces of grown barium sulfate crystals and suggested that secondary nucleation accompanied the precipitation process. Unfortunately, most of these studies were concerned with only the shape and particle size of the precipitated crystals and were not able to show the detailed surface structure. Not only is the precipitation and dissolution of barium sulfate of considerable analytical importance, but the salt is a persistent scalant under down hole oil field conditions. The morphology of precipitated crystals can markedly influence the formation of hard adherent scale deposits under such conditions. In the present work, the scanning electron microscope has been used to examine precipitated barium sulfate crystals. Different types of seed crystals have also been used in kinetic crystal growth studies in order to relate the effect of the size, shape and surface area on the crystal growth and dissolution processes.
were centrifuged, washed several times with distilled water and either dried with acetone or freeze dried. Seed crystals for kinetic studies were preparedby mixing equivalent amounts of barium chloride with sulfuric acid. Suspension A was prepared by quickly adding 6.0 X iO~M barium chloride to a 6.OX 10 M sulfuric acid without agitation. Seed suspension B was prepared in a similar way using 0.01 M barium chloride and sulfuric acid. Seed suspension C was prepared under similar conditions to those of suspension B but with stirring. After preparation, the seed suspensions were washed several times until free from external salts, and aged for at least one month before use. Stable supersaturated solutions of barium sulfate were prepared by the careful mixing of barium chloride and sulfuric acid solutions in a HartleyBarrett type conductance cell maintained at 25 ±0.01°C;supersaturated solutions of concentration up to 7.5 X 10 ~ M in barium sulfate were stable for at least several hours. Crystal growth was initiated by adding known volumes of seed suspension and a Wayne—Kerr Transformer Ratio Arm conductance bridge was used to follow the resistance of the supersaturated solutions during the course of the crystallization and dissolution experiments. At the low concentrations of the crystallization and dissolution experiments, the equivalent conductivity value of barium sulfate was taken as effectively constant, 140.5 ohm 1 equiv~cm2 at 25°C.All experiments were made in a nitrogen atomosphere. The specific surface area of the crystals was determined by nitrogen adsorption using a Quantasorb single point BET apparatus.
2. Experimental
3. Results and discussion
Analytical reagent grade chemicals, triply distilled water and Grade A glassware were used throughout. Stock solutions were made by weight using triply distilled water. Potassium sulfate, sodium sulfate and barium chloride solutions were analyzed by passing aliquots through a column of Dowex 50 ion exchange resin in the hydrogen form and titrating the liberated acid. Barium sulfate crystals for scanning electron microscopic observations were made by mixing barium chloride with sulfuric acid, potassium sulfate or sodium sulfate. After certain time periods, the crystals
Three distinct types of seed crystals shown in fig. 1 were used in the crystal growth and dissolution experiments; the specific surface areas were 0.66, 1.25, and 1.31 m2 g1 for seed crystals A, B, and C respectively. Suspension B, although similar in size to the crystals of suspension A showed a surface roughness which resulted in the higher specific surface. Crystal growth experiments using equivalent eoncentrations of lattice ions are summarized in table 1, and a typical rate curve is shown in fig. 2. At an initial concentration of about 7.0 X l0~ M, the growth
‘~
-~
Fig. 1. Seed crystal A (a), seed crystal B (b), seed crystal C (c). Seed crystal A (d) and B (e) after 1 h growth from 2.1 X l0~ M barium sulfate solution.
14
S. 1’. Liu et al.
/ Crystallization and dissolution
of barium sulfate crystals
Table 1 Crystallization experiments of barium sulfate using equivalent concentrations of ions at 25°C; supersaturated solutions are prepared by mixing barium chloride with sulfuric acid Expt. No.
1 2 3 4
3
Surface area
Initial (BaSO
Seed
Initial fast
kcs X i0
4) (10 M)
suspension
period (mm)
. —i (lmole —1 mm )
7.02 7.02 7.02 7.02
A A B C
50 30 20
0.208 0.383 0.542
5
1.48
reaction from stable supersaturated solutions was characterized by an initial fast growth surge whose duration is given in table 1. Following this surge, the experimental kinetic data can be satisfactorily represented by eq. (1): 2 dm/dt = kcS (m m 0) (1) where m and m0 represent the concentration of barium sulfate at time t and at equilibrium respective-
6
of seed crystal per umt volume of cell solution 2fl) (m 0.064 0.138 0.248 0.430
ly. kc is the rate constant for crystallization. S represents the surface area of the added seed crystals which is proportional to the number of the active growth sites of the seed crystals added in unit volume of solution. Typical plots of the integrated form of eq. (1) are shown in fig. 3 in which the initial fast growth surges are clearly indicated. The second order rate constants kcs following the initial surge are calculated from the slopes of the linear parts of the curves in
B.
2 ~+
I
2
Time 1 hr 1
Fig. 2. Growth curves of barium sulfate at 25°C.Expt. 2(0); Expt. 4(+).
Time
(hr
Fig. 3. Integrated plots of equation 1 for the growth of barium sulfate: Expt. 1(S); Expt. 2(0); Expt. 3 (V);Expt. 4 (o).
I Crystallization and
S. T. Liu et al.
fig. 3. The duration of the initial surge decreases as the concentration of seed crystals is increased. It is interesting to note that eq. (1) satisfactorily explains the growth data for all three types of seed crystals for the ranges of(rn m0) values 3.0 X i0~ to 0.5 X l0~ —
M. The initial growth surges are influenced more by the subsequent reaction rate than by the type of crystal used, decreasing as the total available surface area for growth increases. During the surge the effective “order” of reaction [exponent in eq. (1)] is between 3 and 4 as might be expected for a nucleation process. Similar surge effects have been found in the seeded growth of strontium sulfate [2], lead sulfate [1] and calcium oxalate monohydrate [22]. The observed increase in the growth surge with increase of supersaturation or decrease of added seed led to the suggestion that additional surface nucleation occurred at the beginning of the reaction. For a given supersaturation, a sufficient number of growth sites have to be provided for the growth to proceed according to eq. (1) in order to eliminate the initial surge. The micrographs shown in fig. 1 clearly indicate that after one hour of growth in a supersaturated solution containing 2.1 X 1 ~ M barium sulfate, additional small partides on the surfaces of the crystals are induced by a surface nucleation process. The results presented here support the previous conclusion that the seeded crystal growth of barium sulfate at relatively low supersaturation follows a rate law second order in relative supersaturation. This evidence, together with an observed negligible stirring effect on the growth rate and relatively high activation energy [23], strongly suggests that the crystal growth process is controlled by a surface reaction rather than by a bulk diffusion process. The conflicting reaction orders reported in the literature probably result from the fact that the degree of supersaturation m the spontaneous precipitation studies is an important factor in determining the kinetics of precipitation. This will be discussed later. Unlike the dissolution of most sparingly soluble salts in which the transport of materials from the surface of crystals to the bulk of solution the rate determining step, the dissolution of bariumis sulfate crystals into a subsaturated solution follows eq. (2): -
d,n/dt
.
=
kds
(m
2 0
—
rn)
-
,
-
.
.
.
(2)
dissolution of barium sulfate crystals
15
where kd represents the dissolution rate constant. The validity of eq. (2) is clearly demonstrated by the plot of the integrated form shown in fig. 4. Changes in s during the dissolution experiments are less than a few percent of the total surface area and can be neglected. Eq. (2) satisfactorily represents the dissolution reaction for all three types of crystals to about 90% of the total reaction and a summary of the dissolution experiments is given in table 2. The rate of dissolution is independent of stirring rate and appears to be controlled by a surface reaction process. Similar results have been reported previously for the dissolution of barium sulfate [24], lead sulfate [25] and strontium sulfate [2]. Although s in eq. (2) usually represents either the total surface area of the number of active sites, marked differences in these quantities with different seed materials are clearly shown by the results of the experiments in table 2. It can be seen that for the different seed crystal morphologies, kds is not proportional to the total surface area of the added seed crystal in unit volume of solution. The surface area of added C crystals in expt. 7 is only about three times that of seed crystal A in expt. 5. However, the resulting overall rate constant, kds for expt. 7 is about twelve times that of expt. 5. This indicates that the different seed crystals may contain quite different numbers of active sites per unit area for growth or dissolution. A number of spontaneous precipitation experiments were made to study the effect of solution composition, fluid dynamics and the presence of external ions on the size and morphology of the precipitated barium sulfate crystals. The micrographs in fig. 5a show
Table 2 Dissolution of barium sulfate crystals at 25°C .
Expt. Initial Seed No. (BaSO4) suspension (1O~M)
5
6
0 0
~
0
A B -
C
kds X 10
—i
(I mole
0.887 2.67 10.8
.
mm
—i
Surface area of seed crystal per unit volume of cell2/l) solu— (m 0.069 0.124 0.215
16
& 7’. Liu et al.
/ Crystallization and dissolution
Time
of barium sulfate crystals
(mm)
Fig. 4. Integrated plots of eq. (2) for the dissolution of barium sulfate: Expt. 5(s); Expt.
crystals prepared by adding, without stirring, 50 ml of 4.0 X 10—2 M sulfuric acid to 50 ml of 4.0 X 10—2 M barium chloride while the crystals in fig. Sb result from the nthing of 5 ml of 4.0 X 10—2 M sulfuric acid with 5 ml 4.0 X 10—2 M barium chloride solution in 90 ml of H20. Crystals prepared from the same reagents but at concentrations of 4.0 X 10~ M and 1.0 X 1 o—~M of barium sulfate are given in figs. Sc and Sd respectively. It can be seen that the dendritic crystals formed from solutions containing 2.0 X 10 ~M barium sulfate (fig. Sb) are much smoother than those formed at a higher concentration, 2.0 X 10 ~ M (fig. 5a). However, concentrations below 4.0 X 10 ‘l M result in well-formed retangular crystals (figs. Sc and Sd). Takiyama [17, 18] also reported spindle-shaped dendritic barium sulfate crystal having rugged edges which were produced in the range of concentration, 1.0 X 10—2 to 2.0 X 10—2 M. The barium sulfate crystals shown in fig. 6, obtained from supersaturated solution prepared by mixing barium chloride with sodium sulfate or potassium sulfate under unstirred conditions show the same marked morphological differences as was found in the absence of alkali metal ion. At a concentration of 2.0 X l0~ M, dendritic crystals are usually formed
6(V); Expt.
7(o).
but the crystallites derived from sodium sulfate solution have much more rugged edges than those prepared from potassium sulfate solution. At concentration lower than 4.0 X i0~ M in barium sulfate, the rectangular crystals are also obtained from sodium ion containing solutions. By comparing fig. 5 with fig. 6, it is interesting to note that the barium sulfate crystals precipitated from supersaturated solution containing potassium or sodium ions always show a surface roughness which is not observed in crystals prepared using sulfuric acid solution (fig. 5). It is possible that adsorbed sodium or potassium ions on the surface of the crystals may serve as active centers for surface nucleation during the crystallization process. After a certain period of growth, these ions are incorporated into the growing crystals resulting in the frequently observed coprecipitation [26] of these external ions in analytical precipitation of barium sulfate. Under conditions of stirring the morphologies of the crystals are quite different (fig. 7). In these experiments, the second reagent was added with vigorous stirring over a period of about two minutes. By comparison with fig. 5, it is seen that the crystals formed are very much smaller with the increased frequency of ion encounters increasing the rate of nuclea-
S. T~Liu et al.
/ Crystallization and dissolution
of barium sulfate crystals
17
—
4 Fig. 5. Barium sulfate crystals precipitated out under unstirred condition by mixing barium chloride with sulfuric acid at concentration 2.0 X 10_2 M (a), 2.0 X 10~ M (b), 4.0 X i0~ M (c), 1.0 X i0~ M (d).
tion [27] and resulting in a smaller crystal size, The kinetic study of seeded crystal growth and the scanning electron microscope observation of spontaneously precipitated barium sulfate in this study throws light on the conflicting results reported in the literature for which the effective reaction order for growth ranges from ito 4 [3—12].Thus the growth of dendritic crystals is usually believed to be a bulk diffusion controlled process [10, 28]. For barium sulfate,
it is found that dendritic crystals invariably form at higher than about 2.0 X iü~ M (figs. 5a, 6a), and similar observations were reported by Lieser and Wertenbach [19]. At such concentrations diffusion of the ions to the crystal surface would be expected to be the rate controlling step in the precipitation. As the concentration is decreased, a competition between diffusion and surface growth processes will result in an effec-
18
& 7’. Liu etaL
/ Crystallization and dissolution
of barium sulfate crystals
7ig. 6. Harium sulfate crystals precipitated out under unstirred condition by mixing barium chloride with sodium sulfate at concenl tration 2.0 x i0~ M (a), 4.0 x i0~ M (b), and by mixing barium chloride with potassium sulfate at concentration 2.0 X i0~ M (c),6.OX 10 4M(d).
reaction order greater than one. Under concentration conditions where surface nucleation is important, the reaction wifi be expected to proceed with a rate law in which the rate of deposition may be proportional to the third, fourth or even higher power of the supersaturation. At low supersaturation, a screw dislocation growth mechanism would lead to reaction second order in relative supersaturation. The rectangultive
ar well-formed crystals at a concentration of about 4.0 X 10~M barium sulfate (fig. Sc). suggests a controlling step different from that for the formation of dendrites. Under such conditions the growth of seed crystals follows eq. (1). Previous studies of barium sulfate crystal growth have been made over a wide range of concentration and fluid dynamics both in the presence and absence
ST. Liu etal. /Crystallization and dissolution of barium sulfate crystals
19
~:
~
Fig. 7. Barium sulfate crystals precipitated out under vigorously stirred condition by mixing barium chloride with sulfuric acid at 3 (a) 4.0 X i0~M (b). concentration 2.0 X i0
of neutral electrolytes and added seed crystals. It is quite clear from the results of the present work that the morphology of the crystals formed is sensitive to these experimental factors. Moreover, the different shaped crystals have different densities of active growth sites on their surfaces. The number of such growth sites greatly influences the duration of the initial growth surge in the seeded crystallization experiments. In attempting to compare the results of different investigations, all these factors have to be taken into consideration, and it is not surprising that different workers have reported conflicting results.
Acknowledgements Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society for partial support of this work. We also thank the National Science Foundation for a supporting grant (ENG 74-15486). References [1] D.M.S. Little and G.H. Nancollas, Trans. Faraday Soc.
66 (1970) 3103.
[2] J.R. Campbell and G.H. Nancollas, J. Phys. Chem. 73
(1969) 1735. [3] G.H. Nancollas and N. Purdie, Trans. Faraday Soc. 59 [4] (1963)735. A.E. Nielsen, J. Colloid Scm. 10 (1955) 576. [5] A.E. Nielsen, Kinetics ofPrecipitation (Pergamon, 1964). [6] J.D. O’Rourke and R.A. Johnson, Anal. Chem. 27 (1955) 1699. ~ ~ 0 1068. [9] A.G. Walton and T. Hlabse, Anal. Chim. Acta 29 (1963) 249. [10] A.G. Walton, The Formation and Properties of Precipitation (Interscience, 1967).
[11] F.C. Collins and J.P. Leineweber, J. Phys. Chem. 60 (1956) 389. [12] D.F. Gunn and M.S. Murthy, Chem. Eng. Sci 27 (1972) 1293. [13] K.H. Lieser, Angew. Chem. Intern. Ed. 8 (1969) 188. [14] S. Popoff and E.W. Neuman, Ind. Eng. Chem., Anal. [15] R.B. Fisher, Anal. Chem. 23 (1951)1667. [16] R.B. Fisher and T. Rhinehammer, Bull. Anal. Chem. 25 (1958) 950. [17] K. Takiyama, Bull. Chem. Soc. Japan 32 (1959) 68. [18] E. Suito and K. Takiyama, Bull. Chem. Soc. Japan 27 (1954)121, 123; 20(1955) 305. [19] K.H. Lieser and H. Wertenbach, Z. Physik. Chem. NF 34 (1962) 1. [20] A. Fabrikanos and K.H. Lieser, Z. Physik. Chem. NF
34 (1962) 16, 29.
20
[21] M.5. Murthy, in:
S. 7’. Liu etaL
/ Crystallization and dissolution of barium sulfate crystals
Industrial Crystallization, Proc. Symp. Inst. of Chemical Engineers, London, 1969, 87. [22] G.H. Nancollas and G.L. Gardner, J. Crystal Growth 21(1974) 267. [23] D.M.S. Little, ph.D. Thesis, Univ. of Glasgow (1964). [24] C.H. Bovington and A.L. Jones, Trans. Faraday Soc. 66 (1970) 764.
[25] C.H. Bovington and A.L. Jones, Trans. Faraday Soc. 66 (1970) 2088. [26] G. Walton and G.H. Walden, Jr., J. Am. Chem. Soc. 68 (1946) 1742. [27] J.W. Mullin, Crystallization, 2nd ed. (Butterworths, London, 1972). [28] R.F. Strickland-Constable, Kinetics and Mechanism of Crystallization (Academic Press, New York, 1968).