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Heterogeneous and homogeneous nucleation of barium sulphate
T&ma, 1964,vol. 11,pp. 1231to 1237.
Pergamon
Press
Ltd. Printed in Northern Ireland
HETEROGENEOUS AND HOMOGENEOUS OF BARIUM SULPHATE DAVID
H.
KLJZIN*
and
NUCLEATION
BERNARDO FONTAL?
Department of Chemistry, Los Angeles State College, Los Angeles 32, California, U.S.A. (Received 14 February 1964. Accepted 23 April 1964) Summary-Nucleation of barium sulphate has been studied, using a homogeneous precipitation technique with solutions purified by preprecipitation of a portion of the barium sulphate. Three different nucleation processes have been observed. Two are heterogeneous and involve eight and eighteen ions. The third is homogeneous, and involves six ions. WALTON~ has recently discussed the nucleation of sparingly soluble salts, and has considered the relationships between heterogeneous (foreign particle) and homogeneous nucleation. Walton points out that the “critical” supersaturation observed in precipitation from homogeneous solution does not correspond to the critical supersaturation treated in nucleation theory, but is simply the minimum supersaturation required for experimentally observable precipitation on foreign particles present in the solution. He also suggests that in most precipitations from homogeneous solution, the supersaturation never reaches a level high enough to initiate homogeneous nucleation, so that only foreign particle nucleation is obtained. Nielsen2 has studied barium sulphate nucleation by a direct mixing method. Two different nucleation processes were observed. Heterogeneous nucleation is the predominant process for barium sulphate concentrations up to 10-2M. At concentrations higher than 10P2M a different process, presumably homogeneous nucleation, becomes predominant. Klein and Swift3 have also observed two different nucleation processes in the thioacetamide precipitation of zinc sulphide from ammonia buffers. Attempts to observe homogeneous nucleation are hindered by the occurrence of heterogeneous nucleation and its subsequent crystal growth, but removal of the foreign particles which act as heterogeneous nuclei is quite difficult, because no one knows how many of these ubiquitous particles are likely to be present in a solution, nor how they got there, nor what they consist of, nor how big they are. Their only known property is their ability to act as nuclei. This property may be employed to remove the foreign particles from the system, by precipitating a small fraction of the solute at relatively low supersaturation. Foreign particles will act as nuclei for this initial precipitation, and will grow to a size more readily removed by filtration. The resulting filtered, saturated solution should contain relatively few foreign particles. The rate of homogeneous nucleation of barium sulphate can be written:4
dN - = k(P)“, dt * Present address: Department of Chemistry, Hope College, Holland, Michigan, U.S.A. i Participant in the National Science Foundation Undergraduate Research Participation Programme (G-21893), Summers 1962 and 1963. 1231
1232
DAVIJI H. KLEIN and BERNAIUXIFONTAL
where N = number of nuclei formed, t = time, IP = ion product = [Ba2+] [S042-], and II = number of BaSO, units in the nucleus. The rate of heterogeneous nucleation may be written:
$ = k(N" -
N)(IP)",
where N” = number of foreign particles originally present, so that (N” - N) is the number of foreign particles available to act as nuclei. If the nucleation process is homogeneous, n represents the number of BaSO, units in the homogeneous nucleus, and if the nucleation is heterogeneous, IZis the number of these units which adsorb on the foreign particle to form a surface nucleus. In a general case, the value of n may be obtained as the slope of a plot of log dN/dt against log IP. In the special case where precipitant is generated at a constant rate, and before an appreciable amount of precipitation takes place, the ion product is directly proportional to time and the above equation becomes diV/dt = k’t”. The slope of a plot of log N against log t will have the value (n + 1). The information required for an experimental determination of the value or values of n is, therefore, the number of particles as a function of time, and the solution concentration as a function of time. Particle numbers may be obtained simply and directly by (light) microscopic counting of the precipitate suspension, but because particles cannot be observed microscopically until they have grown to an appreciable extent, a particle will not be detected until some time after it is formed; therefore the relationship between dN/dt and the ion product cannot be measured unequivocally. Turbidity measurements can detect much smaller particles,5 but the interpretation of such results for a polydisperse system in which both the number and sizes of the particles are changing is not feasible. In the present study of barium sulphate nucleation the two methods were employed to reinforce each other. Turbidity measurements were used to observe the nucleation process, and to aid in the interpretation of microscopic particle counts. EXPERIMENTAL Sulphate was generated in a solution of barium perchlorate by the quasi-homogeneous method of electrolvtic oxidation of thiocvanate to sulnhate. 6 A tvoical solution was O.OlM in barium perchlorate, 0.05M in sodium thiocyanate, O.fOM in sodium hydrogen diglycolate to buffer the solution to pH 3.35, and had a volume of 200 ml. This solution was electrolysed as previously described6 until a definite turbidity developed, at which time the electrodes were removed and the beaker was covered and left to stand overnight to allow the solution supersaturation to be relieved. Approximately 5% of the barium was pre-precipitated in this way. The resulting suspension was filtered through a membrane filter, of pore size 100 rnp, directly into the nucleation apparatus, which consisted of an electrolysis cell and an absorbance cell. The electrolysis cell contained a platinum gauze anode, a fritted-glass disc to isolate the cathode, and a sampling port fitted with a vaccine bottle stopper. Two lengths of flexible plastic tubing connected the electrolysis cell to the closed absorbance cell, so that the solution in which sulphate was being generated could be circulated through the absorbance cell in the sample compartment of a spectrophotometer. Between runs the apparatus was cleaned with ammoniacal EDTA solution, and then steamed. The first 100 ml of filtered reaction solution were circulated through the cells and out, and served as a rinse. The final 90 ml of solution were left in the cell, and the cell was sealed. The initial barium concentration was determined by EDTA titration of the rinse solution. The filled absorbance cell was placed in the sample compartment of a Cary Model 14 Spectrophotometer, which was then set to a wavelength of 300 mp, and was adjusted to read zero absorbance.
Nucleation
of barium sulphate
1233
The electrical leads were connected to a constant current source of 4.8 mA, circulation of the solution between the electrolysis cell and the absorbance cell was begun, and the current was turned on. The spectrophotometer produced a record of turbidity at 300 rnp. as a function of time. At appropriate intervals, samples for particle counting and for concentration determination were removed with a syringe. When many particles were present, particle numbers were determined using conventional blood-cell counting technique. When few particles were present, the relative counting technique of Fischer’ was employed, with cross-shaped barium sulphate crystals as the internal standard. The ion product of the solution was obtained by an X-ray fluorescence determination of the amount of barium sulphate precipitated. Samples of 0.50-ml volume were filtered through a membrane filter of 50 rnp pore size. The filters were washed with 1.0 ml of water and dried. The suspension at the conclusion of the run was analysed for unprecipitated barium by EDTA titration, and the precipitate from this suspension served as the standard for the X-ray determination. The filters were placed in the sample compartment of a Norelco X-ray fluorescence apparatus equipped with a lithium fluoride crystal and a scintillation detector, and were counted at the Ba Ka angle. Appropriate background corrections were made. The small size of the samples limited the accuracy of this method; runs with known suspensions indicated that the method was reliable to within 15-20%. The concentration of sulphate in solution was taken as the difference between the sulphate produced as calculated from current and time, and the amount of barium sulphate precipitated. The concentration of barium was taken as the difference between initial barium and barium sulphate precipitated. RESULTS
AND
DISCUSSION
The turbidity, ion product, and number of particles, as functions of time, for an experiment in which the solution was purified by pre-precipitation, are presented in Fig. 1. The turbidity of the solution can be seen to increase in two stages. Turbidity is detected within less than 1 min after the beginning of the run, increases relatively rapidly for a few minutes, and then increases only slowly. After about 1 hr, the turbidity begins to increase rapidly again. In an experiment with a solution not purified by pre-precipitation, the turbidity initially increases more rapidly, and levels off at a higher value. The second increase in turbidity is delayed and much less marked. Thus it appears that two types of nucleation occur. One of these, at low supersaturation, produces only a few particles in a purified solution, and corresponds to the initial turbidity increase. The second, at high supersaturation, produces many more particles, and corresponds to the second turbidity increase. These processes will be discussed separately. Nucleation at low supersaturation
A heterogeneous nucleation process requires the presence of foreign particles, and cannot continue after all the foreign particles have been used, regardless of the supersaturation of the solution. A homogeneous process depends only on the solution supersaturation, and its rate will increase as the supersaturation increases. Fig. 1 shows that after an initial rise the turbidity of the solution remains essentially constant, indicating the cessation of nucleation, even although the supersaturation is increasing. Thus the low-supersaturation nucleation must be heterogeneous. The results with an unpurified solution support this view. It appears that a single preprecipitation is not completely effective in purifying the solution; however, the technique is capable of reducing the number of foreign particles to a relatively low level. The ion product over the period of heterogeneous nucleation and growth is not measurably different from that calculated, assuming that no precipitation has taken place; i.e., growth of the heterogeneous nuclei removes only a negligible amount of barium sulphate from the supersaturated solution. The conditions discussed 11
1234
DAVID H. KLEIN and BERNARM FONTAL
FIG. I.-Turbidity,
ion product and number of particles during an experiment with solution purified by pre-precipitation.
previously are therefore fulfilled, so that dN/dt = ZC’(N’- N) (ZP)n, and a plot of log N against log t will be a straight line of slope (n + 1) over the period when N is small with respect to N”. A series of experiments was performed in which N was measured as a function oft over the period of heterogeneous nucleation. Samples were taken at 1-min intervals, and were permitted to stand for several hours in order for the nuclei to grow. Plots of the log of the number of particles against the log of the time at which the sample was taken gave good straight lines over a 6- to 7-min period. In the first two experiments the slopes of the log N VS.log t plots were 10-Oand 9.3, from which n = 9, corresponding to a barium sulphate nucleus of eighteen ions adsorbed on a foreign particle. In four subsequent experiments the slopes ranged from 4.9 to 52, corresponding to a nucleus of eight adsorbed ions.
Nucleation
of barium sulphate
1235
Various cell-cleaning methods were employed in an effort to repeat the experiments leading to a slope of 10, but these were unsuccessful. It is possible that the first results arose from some experimental mistake; however, we have not been able to find one. Therefore it appears most likely that the first experiments left behind some impurity which could not be removed by the techniques employed, and which permitted a heterogeneous nucleation of lower kinetic order to take place. Nucleation at high supersaturation Because turbidity is a function of both the number and the size of the particles, both nucleation and growth will increase turbidity. The maximum rate of increase
1.2 -
1.0 :: zos-
4 0.6-
a4
0
t 0.2 F
t.~~~~‘.~.‘.“‘.~.~.~.,
0
.04
.06
.I2
16
.20
LOG ION FIG. 2.-Rate
.24
26
32
36
.40
.44
PRODUCT
of nucleation as a function of ion product for the experiment of Fig. 1.
of turbidity does not therefore correspond to the maximum rate of nucleus formation, but rather to the maximum of some function of both nucleation and growth. In Fig. 1 the maximum rate of appearance of detectable particles comes later than the maximum rate of increase of turbidity, and both these maxima come appreciably later than the maximum ion product. This set of observations is not consistent with precipitation theory, according to which the maximum rate of nucleation must correspond to the maximum ion product, and the maximum rate of increase of turbidity must correspond to the maximum rate of removal of material from solution, which will not occur until after most nuclei have been formed. This inconsistency is attributable to the differing sensitivities of the methods used in making the observations. The method of determining the ion product will detect precipitate as soon as the particles reach a filterable size (somewhat less than the 50 rnp nominal pore size of the filter). Microscopic counting, however, cannot detect the particles until they are appreciably larger. Therefore the number-time curve will lag behind the ion product-time curve by the amount of time required for the particles to grow from filterable size to microscopically observable size. The kinetic order of the high-supersaturation nucleation process can be obtained from the values of Fig. 1 by assuming that over the period of interest the number
1236
DAVID
H. KLEIN and BERNARMIFONTAL
values lag behind the concentration values by a constant amount, i.e., that it requires a fixed amount of time for a particle to grow from filterable size to microscopically observable size, whether the particle was formed at 40 min or 50 min. This assumption is quite valid if we consider nucleation over a short enough time period, and becomes progressively worse as the time period considered is increased. The maximum rate of appearance of particles occurs at 117 min, and the maximum ion product occurs at 73 min. We assume that the difference, 44 min, is the time required for the particles to grow to observable size, so that the ion product at time I corresponds to the nucleation rate at (t + 44). The adjusted values may then be employed to obtain n from the equation dN/dt = k(P)“. Fig. 2 is a plot of log dN/dt against log (ZP). The points were taken from Fig. 1 at 5-min intervals from t = 25 to t = 110. The points from both the ascending and decending portions of the (P&time curve fit the same straight line except at ion products below about l-6 x 10P6, indicating that the assumption of a constant 44 min time for growth to observable size is valid over a fairly wide time interval. Further, the fit of the results to an equation describing homogeneous nucleation indicates that the process is a homogeneous one. The slope of the straight line of Fig. 2 is 2.8. In a repeat experiment a slope of 3.3 was obtained. The average value of n for this nucleation process is 3, corresponding to a homogeneous nucleus of six ions. ANALYTICAL
CONSIDERATIONS
the present study three kinetically different nucleation processes have been observed; two of these occur at relatively low supersaturation and are heterogeneous, and the third occurs at higher supersaturation and is homogeneous. Nielsen2 has reported another barium sulphate nucleation process which also appears to be homogeneous. This process takes place at ion products above 1O4, and corresponds to a nucleus of eighteen ions formed when the concentrations of barium and sulphate are equivalent. The homogeneous nucleation described in the present paper takes place at ion products about one-fortieth of that value, and corresponds to a much smaller nucleus, formed when the barium concentration is greatly in excess of the sulphate concentration. Thus it appears that many of the conflicting results obtained in nucleation studies result from the observation of different nucleation processes by various investigators. The results also show that homogeneous nucleation may be obtained in cases of precipitation from homogeneous solution, even when no particular pains are taken to purify the solutions, and that when homogeneous nucleation occurs it results in the formation of a large number of particles. In order to obtain a precipitate useful for analysis, homogeneous nucleation should be avoided. The accepted methods of precipitation from homogeneous solution succeed in avoiding homogeneous nucleation because a sufficient number of suitable nucleating particles are available and because the rate of generation of precipitant is low. Where these conditions are not met, precipitation from homogeneous solution does not offer significant advantages over direct mixing procedures. In the development of new methods of precipitation from homogeneous solution, seeding the solution with a known amount of the substance to be precipitated may be an aid in obtaining a suitable precipitate. In
Acknowledgement-This
G22610.
work was
supported by the National Science Foundation
under grant
Nucleation of barium sulphate Zusammenfassung-Die Keimbildung bei Bariumsulfat wurde mit einer homogenen Flllungsmethode untersucht. Die Lbsungen wurden durch vorherige Ausftillung eines Teils Bariumsulfat gereinigt. Es wurder drei verschiedene Keimbildungsvorgiinge beobachtet. Zwei davon sind heterogener Art, an ihnen sind acht beziehungsweise achtzehn Ionen beteiligt. Der dritte ist homogener Natur, hier handelt es sich urn sechs Ionen. RCsume-On a etudie l’amorcage du sulfate de baryum, en utilisant une technique de precipitation en milieu homogene avec des solutions purifiees par pre-precipitation d’une fraction du sulfate de baryum. On a observe trois processus differents d’amorcage. Deux sont heterogenes et mettent en jeu huit et dix-huit ions. Le troisieme est homogene, et met en jeu six ions. REFERENCES r A. a A. 8 D. 4 D. ’ A. 6 D. ’ R.
G. Walton, Analyt. Chim. Acta, 1963, 29,434. E. Nielsen, Acta Chem. Scand., 1961, 15, 441. H. Klein and E. H. Swift, results to be published. H. Klein, L. Gordon and T. H. Walnut, Talanta, 1959,3, 187. G. Walton and T. Hlabse. ibid.. 1963. 10.601. H. Klein and B. Fontal, ibid., i963, iO,8b8. B. Fischer, Analyt. Chem., 1960, 32, 1127.
1237
Pergamon
Press
Ltd. Printed in Northern Ireland
HETEROGENEOUS AND HOMOGENEOUS OF BARIUM SULPHATE DAVID
H.
KLJZIN*
and
NUCLEATION
BERNARDO FONTAL?
Department of Chemistry, Los Angeles State College, Los Angeles 32, California, U.S.A. (Received 14 February 1964. Accepted 23 April 1964) Summary-Nucleation of barium sulphate has been studied, using a homogeneous precipitation technique with solutions purified by preprecipitation of a portion of the barium sulphate. Three different nucleation processes have been observed. Two are heterogeneous and involve eight and eighteen ions. The third is homogeneous, and involves six ions. WALTON~ has recently discussed the nucleation of sparingly soluble salts, and has considered the relationships between heterogeneous (foreign particle) and homogeneous nucleation. Walton points out that the “critical” supersaturation observed in precipitation from homogeneous solution does not correspond to the critical supersaturation treated in nucleation theory, but is simply the minimum supersaturation required for experimentally observable precipitation on foreign particles present in the solution. He also suggests that in most precipitations from homogeneous solution, the supersaturation never reaches a level high enough to initiate homogeneous nucleation, so that only foreign particle nucleation is obtained. Nielsen2 has studied barium sulphate nucleation by a direct mixing method. Two different nucleation processes were observed. Heterogeneous nucleation is the predominant process for barium sulphate concentrations up to 10-2M. At concentrations higher than 10P2M a different process, presumably homogeneous nucleation, becomes predominant. Klein and Swift3 have also observed two different nucleation processes in the thioacetamide precipitation of zinc sulphide from ammonia buffers. Attempts to observe homogeneous nucleation are hindered by the occurrence of heterogeneous nucleation and its subsequent crystal growth, but removal of the foreign particles which act as heterogeneous nuclei is quite difficult, because no one knows how many of these ubiquitous particles are likely to be present in a solution, nor how they got there, nor what they consist of, nor how big they are. Their only known property is their ability to act as nuclei. This property may be employed to remove the foreign particles from the system, by precipitating a small fraction of the solute at relatively low supersaturation. Foreign particles will act as nuclei for this initial precipitation, and will grow to a size more readily removed by filtration. The resulting filtered, saturated solution should contain relatively few foreign particles. The rate of homogeneous nucleation of barium sulphate can be written:4
dN - = k(P)“, dt * Present address: Department of Chemistry, Hope College, Holland, Michigan, U.S.A. i Participant in the National Science Foundation Undergraduate Research Participation Programme (G-21893), Summers 1962 and 1963. 1231
1232
DAVIJI H. KLEIN and BERNAIUXIFONTAL
where N = number of nuclei formed, t = time, IP = ion product = [Ba2+] [S042-], and II = number of BaSO, units in the nucleus. The rate of heterogeneous nucleation may be written:
$ = k(N" -
N)(IP)",
where N” = number of foreign particles originally present, so that (N” - N) is the number of foreign particles available to act as nuclei. If the nucleation process is homogeneous, n represents the number of BaSO, units in the homogeneous nucleus, and if the nucleation is heterogeneous, IZis the number of these units which adsorb on the foreign particle to form a surface nucleus. In a general case, the value of n may be obtained as the slope of a plot of log dN/dt against log IP. In the special case where precipitant is generated at a constant rate, and before an appreciable amount of precipitation takes place, the ion product is directly proportional to time and the above equation becomes diV/dt = k’t”. The slope of a plot of log N against log t will have the value (n + 1). The information required for an experimental determination of the value or values of n is, therefore, the number of particles as a function of time, and the solution concentration as a function of time. Particle numbers may be obtained simply and directly by (light) microscopic counting of the precipitate suspension, but because particles cannot be observed microscopically until they have grown to an appreciable extent, a particle will not be detected until some time after it is formed; therefore the relationship between dN/dt and the ion product cannot be measured unequivocally. Turbidity measurements can detect much smaller particles,5 but the interpretation of such results for a polydisperse system in which both the number and sizes of the particles are changing is not feasible. In the present study of barium sulphate nucleation the two methods were employed to reinforce each other. Turbidity measurements were used to observe the nucleation process, and to aid in the interpretation of microscopic particle counts. EXPERIMENTAL Sulphate was generated in a solution of barium perchlorate by the quasi-homogeneous method of electrolvtic oxidation of thiocvanate to sulnhate. 6 A tvoical solution was O.OlM in barium perchlorate, 0.05M in sodium thiocyanate, O.fOM in sodium hydrogen diglycolate to buffer the solution to pH 3.35, and had a volume of 200 ml. This solution was electrolysed as previously described6 until a definite turbidity developed, at which time the electrodes were removed and the beaker was covered and left to stand overnight to allow the solution supersaturation to be relieved. Approximately 5% of the barium was pre-precipitated in this way. The resulting suspension was filtered through a membrane filter, of pore size 100 rnp, directly into the nucleation apparatus, which consisted of an electrolysis cell and an absorbance cell. The electrolysis cell contained a platinum gauze anode, a fritted-glass disc to isolate the cathode, and a sampling port fitted with a vaccine bottle stopper. Two lengths of flexible plastic tubing connected the electrolysis cell to the closed absorbance cell, so that the solution in which sulphate was being generated could be circulated through the absorbance cell in the sample compartment of a spectrophotometer. Between runs the apparatus was cleaned with ammoniacal EDTA solution, and then steamed. The first 100 ml of filtered reaction solution were circulated through the cells and out, and served as a rinse. The final 90 ml of solution were left in the cell, and the cell was sealed. The initial barium concentration was determined by EDTA titration of the rinse solution. The filled absorbance cell was placed in the sample compartment of a Cary Model 14 Spectrophotometer, which was then set to a wavelength of 300 mp, and was adjusted to read zero absorbance.
Nucleation
of barium sulphate
1233
The electrical leads were connected to a constant current source of 4.8 mA, circulation of the solution between the electrolysis cell and the absorbance cell was begun, and the current was turned on. The spectrophotometer produced a record of turbidity at 300 rnp. as a function of time. At appropriate intervals, samples for particle counting and for concentration determination were removed with a syringe. When many particles were present, particle numbers were determined using conventional blood-cell counting technique. When few particles were present, the relative counting technique of Fischer’ was employed, with cross-shaped barium sulphate crystals as the internal standard. The ion product of the solution was obtained by an X-ray fluorescence determination of the amount of barium sulphate precipitated. Samples of 0.50-ml volume were filtered through a membrane filter of 50 rnp pore size. The filters were washed with 1.0 ml of water and dried. The suspension at the conclusion of the run was analysed for unprecipitated barium by EDTA titration, and the precipitate from this suspension served as the standard for the X-ray determination. The filters were placed in the sample compartment of a Norelco X-ray fluorescence apparatus equipped with a lithium fluoride crystal and a scintillation detector, and were counted at the Ba Ka angle. Appropriate background corrections were made. The small size of the samples limited the accuracy of this method; runs with known suspensions indicated that the method was reliable to within 15-20%. The concentration of sulphate in solution was taken as the difference between the sulphate produced as calculated from current and time, and the amount of barium sulphate precipitated. The concentration of barium was taken as the difference between initial barium and barium sulphate precipitated. RESULTS
AND
DISCUSSION
The turbidity, ion product, and number of particles, as functions of time, for an experiment in which the solution was purified by pre-precipitation, are presented in Fig. 1. The turbidity of the solution can be seen to increase in two stages. Turbidity is detected within less than 1 min after the beginning of the run, increases relatively rapidly for a few minutes, and then increases only slowly. After about 1 hr, the turbidity begins to increase rapidly again. In an experiment with a solution not purified by pre-precipitation, the turbidity initially increases more rapidly, and levels off at a higher value. The second increase in turbidity is delayed and much less marked. Thus it appears that two types of nucleation occur. One of these, at low supersaturation, produces only a few particles in a purified solution, and corresponds to the initial turbidity increase. The second, at high supersaturation, produces many more particles, and corresponds to the second turbidity increase. These processes will be discussed separately. Nucleation at low supersaturation
A heterogeneous nucleation process requires the presence of foreign particles, and cannot continue after all the foreign particles have been used, regardless of the supersaturation of the solution. A homogeneous process depends only on the solution supersaturation, and its rate will increase as the supersaturation increases. Fig. 1 shows that after an initial rise the turbidity of the solution remains essentially constant, indicating the cessation of nucleation, even although the supersaturation is increasing. Thus the low-supersaturation nucleation must be heterogeneous. The results with an unpurified solution support this view. It appears that a single preprecipitation is not completely effective in purifying the solution; however, the technique is capable of reducing the number of foreign particles to a relatively low level. The ion product over the period of heterogeneous nucleation and growth is not measurably different from that calculated, assuming that no precipitation has taken place; i.e., growth of the heterogeneous nuclei removes only a negligible amount of barium sulphate from the supersaturated solution. The conditions discussed 11
1234
DAVID H. KLEIN and BERNARM FONTAL
FIG. I.-Turbidity,
ion product and number of particles during an experiment with solution purified by pre-precipitation.
previously are therefore fulfilled, so that dN/dt = ZC’(N’- N) (ZP)n, and a plot of log N against log t will be a straight line of slope (n + 1) over the period when N is small with respect to N”. A series of experiments was performed in which N was measured as a function oft over the period of heterogeneous nucleation. Samples were taken at 1-min intervals, and were permitted to stand for several hours in order for the nuclei to grow. Plots of the log of the number of particles against the log of the time at which the sample was taken gave good straight lines over a 6- to 7-min period. In the first two experiments the slopes of the log N VS.log t plots were 10-Oand 9.3, from which n = 9, corresponding to a barium sulphate nucleus of eighteen ions adsorbed on a foreign particle. In four subsequent experiments the slopes ranged from 4.9 to 52, corresponding to a nucleus of eight adsorbed ions.
Nucleation
of barium sulphate
1235
Various cell-cleaning methods were employed in an effort to repeat the experiments leading to a slope of 10, but these were unsuccessful. It is possible that the first results arose from some experimental mistake; however, we have not been able to find one. Therefore it appears most likely that the first experiments left behind some impurity which could not be removed by the techniques employed, and which permitted a heterogeneous nucleation of lower kinetic order to take place. Nucleation at high supersaturation Because turbidity is a function of both the number and the size of the particles, both nucleation and growth will increase turbidity. The maximum rate of increase
1.2 -
1.0 :: zos-
4 0.6-
a4
0
t 0.2 F
t.~~~~‘.~.‘.“‘.~.~.~.,
0
.04
.06
.I2
16
.20
LOG ION FIG. 2.-Rate
.24
26
32
36
.40
.44
PRODUCT
of nucleation as a function of ion product for the experiment of Fig. 1.
of turbidity does not therefore correspond to the maximum rate of nucleus formation, but rather to the maximum of some function of both nucleation and growth. In Fig. 1 the maximum rate of appearance of detectable particles comes later than the maximum rate of increase of turbidity, and both these maxima come appreciably later than the maximum ion product. This set of observations is not consistent with precipitation theory, according to which the maximum rate of nucleation must correspond to the maximum ion product, and the maximum rate of increase of turbidity must correspond to the maximum rate of removal of material from solution, which will not occur until after most nuclei have been formed. This inconsistency is attributable to the differing sensitivities of the methods used in making the observations. The method of determining the ion product will detect precipitate as soon as the particles reach a filterable size (somewhat less than the 50 rnp nominal pore size of the filter). Microscopic counting, however, cannot detect the particles until they are appreciably larger. Therefore the number-time curve will lag behind the ion product-time curve by the amount of time required for the particles to grow from filterable size to microscopically observable size. The kinetic order of the high-supersaturation nucleation process can be obtained from the values of Fig. 1 by assuming that over the period of interest the number
1236
DAVID
H. KLEIN and BERNARMIFONTAL
values lag behind the concentration values by a constant amount, i.e., that it requires a fixed amount of time for a particle to grow from filterable size to microscopically observable size, whether the particle was formed at 40 min or 50 min. This assumption is quite valid if we consider nucleation over a short enough time period, and becomes progressively worse as the time period considered is increased. The maximum rate of appearance of particles occurs at 117 min, and the maximum ion product occurs at 73 min. We assume that the difference, 44 min, is the time required for the particles to grow to observable size, so that the ion product at time I corresponds to the nucleation rate at (t + 44). The adjusted values may then be employed to obtain n from the equation dN/dt = k(P)“. Fig. 2 is a plot of log dN/dt against log (ZP). The points were taken from Fig. 1 at 5-min intervals from t = 25 to t = 110. The points from both the ascending and decending portions of the (P&time curve fit the same straight line except at ion products below about l-6 x 10P6, indicating that the assumption of a constant 44 min time for growth to observable size is valid over a fairly wide time interval. Further, the fit of the results to an equation describing homogeneous nucleation indicates that the process is a homogeneous one. The slope of the straight line of Fig. 2 is 2.8. In a repeat experiment a slope of 3.3 was obtained. The average value of n for this nucleation process is 3, corresponding to a homogeneous nucleus of six ions. ANALYTICAL
CONSIDERATIONS
the present study three kinetically different nucleation processes have been observed; two of these occur at relatively low supersaturation and are heterogeneous, and the third occurs at higher supersaturation and is homogeneous. Nielsen2 has reported another barium sulphate nucleation process which also appears to be homogeneous. This process takes place at ion products above 1O4, and corresponds to a nucleus of eighteen ions formed when the concentrations of barium and sulphate are equivalent. The homogeneous nucleation described in the present paper takes place at ion products about one-fortieth of that value, and corresponds to a much smaller nucleus, formed when the barium concentration is greatly in excess of the sulphate concentration. Thus it appears that many of the conflicting results obtained in nucleation studies result from the observation of different nucleation processes by various investigators. The results also show that homogeneous nucleation may be obtained in cases of precipitation from homogeneous solution, even when no particular pains are taken to purify the solutions, and that when homogeneous nucleation occurs it results in the formation of a large number of particles. In order to obtain a precipitate useful for analysis, homogeneous nucleation should be avoided. The accepted methods of precipitation from homogeneous solution succeed in avoiding homogeneous nucleation because a sufficient number of suitable nucleating particles are available and because the rate of generation of precipitant is low. Where these conditions are not met, precipitation from homogeneous solution does not offer significant advantages over direct mixing procedures. In the development of new methods of precipitation from homogeneous solution, seeding the solution with a known amount of the substance to be precipitated may be an aid in obtaining a suitable precipitate. In
Acknowledgement-This
G22610.
work was
supported by the National Science Foundation
under grant
Nucleation of barium sulphate Zusammenfassung-Die Keimbildung bei Bariumsulfat wurde mit einer homogenen Flllungsmethode untersucht. Die Lbsungen wurden durch vorherige Ausftillung eines Teils Bariumsulfat gereinigt. Es wurder drei verschiedene Keimbildungsvorgiinge beobachtet. Zwei davon sind heterogener Art, an ihnen sind acht beziehungsweise achtzehn Ionen beteiligt. Der dritte ist homogener Natur, hier handelt es sich urn sechs Ionen. RCsume-On a etudie l’amorcage du sulfate de baryum, en utilisant une technique de precipitation en milieu homogene avec des solutions purifiees par pre-precipitation d’une fraction du sulfate de baryum. On a observe trois processus differents d’amorcage. Deux sont heterogenes et mettent en jeu huit et dix-huit ions. Le troisieme est homogene, et met en jeu six ions. REFERENCES r A. a A. 8 D. 4 D. ’ A. 6 D. ’ R.
G. Walton, Analyt. Chim. Acta, 1963, 29,434. E. Nielsen, Acta Chem. Scand., 1961, 15, 441. H. Klein and E. H. Swift, results to be published. H. Klein, L. Gordon and T. H. Walnut, Talanta, 1959,3, 187. G. Walton and T. Hlabse. ibid.. 1963. 10.601. H. Klein and B. Fontal, ibid., i963, iO,8b8. B. Fischer, Analyt. Chem., 1960, 32, 1127.
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