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Influence of polyethylenimine on the precipitation process of lead sulfate crystals
ARTICLE IN PRESS
Journal of Crystal Growth 260 (2004) 500–506
Influence of polyethylenimine on the precipitation process of lead sulfate crystals Akio Katayama*, Takahiro Sakuma, Izumi Hirasawa Department of Applied Chemistry, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan Received 3 July 2003; accepted 25 August 2003 Communicated by M. Schieber
Abstract Crystals of lead sulfate were precipitated in a solution of polyethylenimine (PEI) using a double-jet crystallizer. PEI controlled both the nucleation rate and the growth rate, and enabled to produce fine monodispersed crystals. This effect is considered to be due to a complexation between PEI and lead ion. The on-line measurement of the variation in the lead ion concentration indicated PEI lost its effect when a certain amount of reactants was supplied. And the duration in which PEI could control the precipitation rate and the amount of PEI had a strong correlation. In addition, it was suggested that their relationship could be utilized in order to produce monodispersed particles. r 2003 Elsevier B.V. All rights reserved. PACS: 81.10.Dn Keywords: A1. Nucleation; A1. Growth models; A1. Impurities; A2. Growth from solutions; B1. Inorganic compounds; B1. Polyethylenimine
1. Introduction Precipitation process has been widely applied to various inorganic salts [1–9] in order to produce fine particles with high monodispersity, or the uniformity of the size and the morphology of product crystals. Especially for producing fine particles of sparingly soluble salts, double-jet precipitation technique is very suitable [10,11]. However, polydispersity of produced crystals due *Corresponding author. Tel.: +81352863215; fax: +81332086896. E-mail address: a [email protected] (A. Katayama).
to the continual nucleation and an overgrowth of crystals are often troublesome. Some organic additives, e.g. water-soluble polymers or amino acids, are known to modify the growth rate and/or the morphology of precipitated crystals [12–19]. For example, carboxylic polymers, such as poly(acrylic acid), are often used in precipitation systems of calcium carbonate in order to stabilize a particular crystalline form of calcium carbonate [13,20–24]. Acidic polyelectrolytes or amino acids are also utilized in order to prevent a scale formation of sparingly soluble salts [25,26]. As to silver halides, bone gelatins and amino acids have been used as an agglomeration
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2003.08.039
ARTICLE IN PRESS A. Katayama et al. / Journal of Crystal Growth 260 (2004) 500–506
restrainer and a growth controller [10,11,29–31]. However, although numerous studies have been reported about an application of organic additives in several precipitation systems of inorganic salts, these investigations mainly focus on the function of those additives (mostly acidic polyelectrolytes) that modifies the crystal morphology [27] or completely inhibits the scale formation. There are not so many researches about the control of growth rate by polyelectrolytes [28], especially by polyamides or polyamines, for the purpose of producing monodispersed fine particles. Thus the investigation about the growth control effect of polyelectrolyte and its practical application might give useful information, and this is the purpose of our studies. In the present paper, polyethylenimine (PEI) was used as a growth rate controller and an agglomeration inhibitor in the double-jet precipitation system. PEI is a basic polyelectrolyte and it is used in many industrial fields such as a dispersion agent [32,33]. The effect of PEI on the nucleation and growth phenomena of lead sulfate crystals was studied, and a method for precipitation of monodispersed fine crystals of lead sulfate using PEI was suggested.
2. Experimental procedure Precipitation of lead sulfate was performed in a solution of PEI using the double-jet crystallizer [10]. An aqueous PEI solution of 1 l was prepared in the baffled crystallization vessel of 2 l that was thermostated at 25 C. This solution of PEI is referred to as a ground solution in the following texts for the simplicity. Two aqueous solutions of lead nitrate and sodium sulfate were separately supplied from two inlet tubes that were inserted into the ground solution. Reactant solutions had an equal concentration and they were supplied at a constant rate in order to perform an equimolar reaction. The ground solution was stirred at a constant rate of 300 rpm, therefore supplied reactants were immediately mixed by the impeller, and lead sulfate crystals were produced. Concentration and feed rate of reactant solutions were ranged from 0.25 to 1.0 mol/l (as Pb2+ or SO2 4 ) and from 0.01 to 0.02 l/min, respectively.
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The ground solution contained 5–20 g/l of PEI. In all experiments, pH of this solution was adjusted by acetic acid at approximately 2.7. The reason of this is to prevent the co-precipitation of lead hydroxide, and to make PEI positively charged [32]. In addition, the ground solution also contained a small amount (0–0.03 mol) of lead nitrate that is supposed to stabilize the morphology of crystals [10]. The variation in the lead ion concentration during precipitation was observed by the online measurement with ThermoElectron ionplus 9682BN ISE electrode and SensorLinkt measurement system. ISE electrode was well rinsed and calibrated before each experiment, and it was directly inserted into the crystallization vessel. Concentration data were continually acquired every 10 s and recorded automatically. In several experiments, precipitated crystals of lead sulfate were directly observed in a following manner. Suspension of 10 ml was withdrawn at the selected operation time, and diluted with ionexchanged water. This sample was centrifuged at 3000 rpm, and then the supernatant was removed. This rinsing operation was repeated 3 times in order to remove PEI from the sample. Rinsed crystals were filtrated with a membrane filter (0.1 mm) and dried well at 40 C. Dried sample crystals were observed with Hitachi S-2500CX or Hitachi S-4500S scanning electron microscope. The size of crystals was measured with electronic vernier calipers on printed SEM photographs. All chemicals except PEI, i.e. lead nitrate, sodium sulfate and acetic acid, were analytical grade and purchased from Kanto Chemical Co., Inc. PEI (P-1000, average Mw E70; 000) was provided by Nippon Syokubai Co., Ltd. Ionexchanged water was used as a solvent throughout this research.
3. Results and discussion 3.1. Effect of PEI on the size and the morphology of crystals Lead sulfate crystals precipitated with and without PEI are shown in Figs. 1a and b,
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(a)
0.5 µm
(b)
5 µm
Fig. 1. SEM photographs of lead sulfate crystals precipitated in the presence of PEI of 10 g (a) and absence of PEI (b); concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min, excess lead ion=0.01 mol. Both samples were withdrawn 2 min after the visible nucleation was observed.
respectively. As clearly shown in these figures, PEI largely influenced on the size and the crystal habit of precipitated crystals. Crystals precipitated in a solution of PEI were much smaller and had a better monodispersity than crystals produced without PEI. The average size of those crystals was 0.4 mm, and the coefficient of variation of CSD was approximately 0.15. Therefore, PEI had an effect that greatly decreased the crystal size and stabilized the morphology of crystals. These effects of PEI might be particularly useful in order to produce monodispersed fine particles. 3.2. Investigation of the effect of PEI and its dependence on operation conditions A typical example of variation in the lead ion concentration during an experiment was shown in Fig. 2. At an early stage of a reaction, concentration of lead ion remained almost at a same value, in spite of the continuous supply of reactant ions. And during this period, a visible change was hardly observed in the crystallization vessel. Then the concentration value suddenly began to decrease at a certain operation time. This operation time when the lead ion concentration began to decrease is referred to as ‘‘bend point’’ in the following texts. After the bend point, a sharp reduction in concentration was observed, followed
Fig. 2. The variation of the lead ion concentration against the operation time; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min, PEI content in the ground solution=10 g, excess lead ion=0.01 mol.
by a gradual change of a slope. In addition, solution in the crystallizer became cloudy and very quickly (within 10 s or less) turned into complete white at the bend point or shortly (within 30 s) before that. This phenomenon is considered to indicate that a large number of crystals of lead sulfate rapidly nucleated. The sudden reduction of the lead ion concentration can be also explained by this rapid nucleation and growth of those nuclei, because that means the high consumption of reactant species.
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Fig. 3. The variation of the lead ion concentration when PEI was not used; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min., excess lead ion=0.01 mol.
It is a characteristic phenomenon that concentration of lead ion was almost constant at an early stage. In an ordinary precipitation process, concentration is expected to decrease immediately after reactants begin to be supplied because of the very low solubility of lead sulfate. Fig. 3 shows a concentration change in the experiment without PEI. This figure shows that actually the lead ion concentration rapidly decreased from the beginning when PEI was not used. In the presence of PEI, however, the lead ion concentration kept constant before the bend point. Thus PEI is considered to have an interesting function that controls the concentration level of lead ion during a precipitation and significantly decreases the reaction rate, while it does not inhibit a precipitation completely. Although the detailed mechanism is not fully understood, it is considered that this effect is due to the complexation between PEI and lead ion [32,34]. This peculiarity of PEI seems highly useful in order to produce monodispersed fine particles, since the restraint of both continual nucleation and excessive growth of crystals is essential to keep the monodispersity of crystals [11]. A rapid cloudiness and the concentration drop also give another interesting aspect. In most experiments, the variation in the lead ion concentration showed similar behavior (not shown in this paper) to that illustrated in Fig. 2. It is plausible
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there was a certain limitation on the effect of PEI that controlled the rate of both the nucleation and the growth, and the bend point was the time when the condition of the working solution reached that limit and PEI lost its influence on precipitation phenomena. The increase of the amount of supplied reactants and the decrease of the concentration of PEI in the working solution are probable factors that affected the limit of PEI’s effect. Therefore, the total amount of lead ion at the bend point was calculated in order to see the relationship between operation conditions and the value of the bend point. It was calculated from Ntot ¼ CR FR tb þ NG ;
ð1Þ
where Ntot was the total molar amount of lead ion at the bend point (mol), CR was concentration of reactant solution (mol/l), FR is feed rate (l/min), tb was the observed bend point (min) and NG was the amount of lead ion in the ground solution (mol). Operation conditions of a series of experiments and corresponding values of Ntot are summarized in Table 1. Each experiment was performed at least 3 times and averaged value (reproducibility was 3–5%) of Ntot is reported. As shown in this table, Ntot was approximately 4.8 102 mol when PEI dosage was 10 g, regardless of reactant concentration, feed rate and the amount of excess ion. Assuming that the complexation between PEI and lead ion is a key to decrease the reaction rate, it is thought at the bend point no more complexes can be formed or the complexation reaction reaches to equilibrium, and consequently PEI cannot control the lead ion concentration any longer. Concentration data (not shown in this paper) of an experiment where the amount of lead ion in the ground solution was 0.05 mol, which is larger than the value of Ntot ; also supported our assumption. The lead ion concentration began to decrease and the cloudiness was observed immediately after reactants began to be supplied. Above discussions about the bend point and Ntot only deal with the case where the amount of PEI dissolved in the around solution was 10 g. And the bend point, or Ntot is expected to have a close relationship with PEI dosage if the bend point is
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Table 1 Operation conditions and corresponding Ntot (PEI=10 g) Reactant concentration (mol/l)
Feed rate (l/min)
Molar feed rate (mmol/min)
Amount of excess ion (mol)
Average Ntot (mol)
0.25 0.25 0.5 0.5 0.5 0.5 0.75 0.5 1.0
0.01 0.02 0.01 0.01 0.01 0.015 0.01 0.02 0.01
2.5 5.0 5.0 5.0 5.0 7.5 7.5 10.0 10.0
0.01 0.01 0 0.01 0.03 0.01 0.01 0.01 0.01
4.9 102 5.0 102 4.5 102 4.9 102 5.3 102 4.6 102 4.9 102 4.7 102 4.7 102
0.07
0.06
0.04
N
tot
[mol]
0.05
0.03
0.02 0.01
0 0
5
10
15
20
25
Amou nt of PE I in the ground solution [g]
Fig. 4. Relationship between Ntot and the amount of PEI in the ground solution; molar feed rate=5.0 mmol/min, excess lead ion=0.01 mol.
the time when the ‘‘effective’’ complexation between lead ion and PEI comes to cease. The relationship between the amount of PEI and Ntot is shown in Fig. 4. The correlation equation was Ntot ¼ kW 0:49 ;
ð2Þ
where k was an experimental factor (mol/g) and kE1:4 102 in our results, W was the amount of PEI in the ground solution (g). They were strongly correlated (correlation coefficient=0.98), suggesting that PEI content in the ground solution determined Ntot ; and consequently the bend point. In other words, the bend point can be predicted from the operation conditions, i.e. the amount
(not the concentration) of PEI, molar feed rate and the amount of excess ion. It is noteworthy that the correlation is not firstorder with respect to the amount of PEI. This result seems to indicate that PEI became less effective at higher concentration. In an acidic solution, highly protonated PEI molecule is supposed to expand its branches and has a larger hydrodynamic diameter. Therefore, the intermolecular and intramolecular steric hindrance as well as the repulsive interaction between charged amino groups and lead ion prevent the complexation between PEI and lead ion especially at higher PEI concentration [32,33,35]. Consequently, the ratio of available amino groups to the total PEI mass decreases with the increase of PEI concentration. 3.3. Producing monodispersed fine particles in a solution of PEI As mentioned above, it was suggested that PEI could no longer control the precipitation rate and the rapid nucleation occurred at the bend point. This rapid nucleation is not a favorable phenomenon for producing monodispersed fine crystals, since the continual nucleation and the growth of those nuclei leads to the polydipersity of product crystals. Therefore it should be better that precipitation with PEI is ceased and produced crystals are collected before the cloudiness observed in order to produce monodispersed particles. And it is possible to do this operation because
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References
Fig. 5. SEM photograph of lead sulfate crystals precipitated in PEI solution. Crystals were sampled when 6 min were elapsed; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/ min, PEI content in the ground solution=10 g, excess lead ion=0.01 mol.
the bend point can be predicted. Fig. 5 is an SEM photograph of crystals that were sampled before (ca. 1 min.) the bend point estimated by Eq. (2). Although crystals were slightly damaged, probably because of the rinsing operation and the long centrifugation time, obtained crystals were smaller than those sampled after the bend point (see Fig. 1a). Average size of this sample was 0.2 mm, and the coefficient of variation of CSD was approximately 0.2. Thus our idea might be useful for the purpose of producing monodispersed fine crystals, since it tells appropriate operation duration and sampling time in the precipitation process using PEI as a growth modifier.
Acknowledgements This study was supported and subsidized by Mizuho Foundation for the Promotion of Sciences. And the authors truly acknowledge the assistance of Nippon Syokubai Co., Ltd. for the provision of the samples of PEI and their specification data. And also we wish to thank Mr. Yukio Ibe of Tahira Co., Ltd. for his advice on ISE electrode and its usage.
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[33] D.A. Tomalia, G.R. Killat, in: H.F. Mark, N. Bikales, C.G. Overberger, G. Menges, J.I. Kroschwitz (Eds.), Encyclopedia of Polymer Science and Technology, 2nd Edition, Wiley, Tronto, 1985, pp. 688–697. [34] B.F. Smith, T.W. Robinson, N.N. Sauer, D.S. Ehler, US Patent 5,928,517, 1999. [35] J.H. Hodgkin, in: H.F. Mark, N. Bikales, C.G. Overberger, G. Menges, J.I. Kroschwitz (Eds.), Encyclopedia of Polymer Science and Technology, 2nd Edition, Wiley, Tronto, 1985, pp. 363–378.
Journal of Crystal Growth 260 (2004) 500–506
Influence of polyethylenimine on the precipitation process of lead sulfate crystals Akio Katayama*, Takahiro Sakuma, Izumi Hirasawa Department of Applied Chemistry, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan Received 3 July 2003; accepted 25 August 2003 Communicated by M. Schieber
Abstract Crystals of lead sulfate were precipitated in a solution of polyethylenimine (PEI) using a double-jet crystallizer. PEI controlled both the nucleation rate and the growth rate, and enabled to produce fine monodispersed crystals. This effect is considered to be due to a complexation between PEI and lead ion. The on-line measurement of the variation in the lead ion concentration indicated PEI lost its effect when a certain amount of reactants was supplied. And the duration in which PEI could control the precipitation rate and the amount of PEI had a strong correlation. In addition, it was suggested that their relationship could be utilized in order to produce monodispersed particles. r 2003 Elsevier B.V. All rights reserved. PACS: 81.10.Dn Keywords: A1. Nucleation; A1. Growth models; A1. Impurities; A2. Growth from solutions; B1. Inorganic compounds; B1. Polyethylenimine
1. Introduction Precipitation process has been widely applied to various inorganic salts [1–9] in order to produce fine particles with high monodispersity, or the uniformity of the size and the morphology of product crystals. Especially for producing fine particles of sparingly soluble salts, double-jet precipitation technique is very suitable [10,11]. However, polydispersity of produced crystals due *Corresponding author. Tel.: +81352863215; fax: +81332086896. E-mail address: a [email protected] (A. Katayama).
to the continual nucleation and an overgrowth of crystals are often troublesome. Some organic additives, e.g. water-soluble polymers or amino acids, are known to modify the growth rate and/or the morphology of precipitated crystals [12–19]. For example, carboxylic polymers, such as poly(acrylic acid), are often used in precipitation systems of calcium carbonate in order to stabilize a particular crystalline form of calcium carbonate [13,20–24]. Acidic polyelectrolytes or amino acids are also utilized in order to prevent a scale formation of sparingly soluble salts [25,26]. As to silver halides, bone gelatins and amino acids have been used as an agglomeration
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2003.08.039
ARTICLE IN PRESS A. Katayama et al. / Journal of Crystal Growth 260 (2004) 500–506
restrainer and a growth controller [10,11,29–31]. However, although numerous studies have been reported about an application of organic additives in several precipitation systems of inorganic salts, these investigations mainly focus on the function of those additives (mostly acidic polyelectrolytes) that modifies the crystal morphology [27] or completely inhibits the scale formation. There are not so many researches about the control of growth rate by polyelectrolytes [28], especially by polyamides or polyamines, for the purpose of producing monodispersed fine particles. Thus the investigation about the growth control effect of polyelectrolyte and its practical application might give useful information, and this is the purpose of our studies. In the present paper, polyethylenimine (PEI) was used as a growth rate controller and an agglomeration inhibitor in the double-jet precipitation system. PEI is a basic polyelectrolyte and it is used in many industrial fields such as a dispersion agent [32,33]. The effect of PEI on the nucleation and growth phenomena of lead sulfate crystals was studied, and a method for precipitation of monodispersed fine crystals of lead sulfate using PEI was suggested.
2. Experimental procedure Precipitation of lead sulfate was performed in a solution of PEI using the double-jet crystallizer [10]. An aqueous PEI solution of 1 l was prepared in the baffled crystallization vessel of 2 l that was thermostated at 25 C. This solution of PEI is referred to as a ground solution in the following texts for the simplicity. Two aqueous solutions of lead nitrate and sodium sulfate were separately supplied from two inlet tubes that were inserted into the ground solution. Reactant solutions had an equal concentration and they were supplied at a constant rate in order to perform an equimolar reaction. The ground solution was stirred at a constant rate of 300 rpm, therefore supplied reactants were immediately mixed by the impeller, and lead sulfate crystals were produced. Concentration and feed rate of reactant solutions were ranged from 0.25 to 1.0 mol/l (as Pb2+ or SO2 4 ) and from 0.01 to 0.02 l/min, respectively.
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The ground solution contained 5–20 g/l of PEI. In all experiments, pH of this solution was adjusted by acetic acid at approximately 2.7. The reason of this is to prevent the co-precipitation of lead hydroxide, and to make PEI positively charged [32]. In addition, the ground solution also contained a small amount (0–0.03 mol) of lead nitrate that is supposed to stabilize the morphology of crystals [10]. The variation in the lead ion concentration during precipitation was observed by the online measurement with ThermoElectron ionplus 9682BN ISE electrode and SensorLinkt measurement system. ISE electrode was well rinsed and calibrated before each experiment, and it was directly inserted into the crystallization vessel. Concentration data were continually acquired every 10 s and recorded automatically. In several experiments, precipitated crystals of lead sulfate were directly observed in a following manner. Suspension of 10 ml was withdrawn at the selected operation time, and diluted with ionexchanged water. This sample was centrifuged at 3000 rpm, and then the supernatant was removed. This rinsing operation was repeated 3 times in order to remove PEI from the sample. Rinsed crystals were filtrated with a membrane filter (0.1 mm) and dried well at 40 C. Dried sample crystals were observed with Hitachi S-2500CX or Hitachi S-4500S scanning electron microscope. The size of crystals was measured with electronic vernier calipers on printed SEM photographs. All chemicals except PEI, i.e. lead nitrate, sodium sulfate and acetic acid, were analytical grade and purchased from Kanto Chemical Co., Inc. PEI (P-1000, average Mw E70; 000) was provided by Nippon Syokubai Co., Ltd. Ionexchanged water was used as a solvent throughout this research.
3. Results and discussion 3.1. Effect of PEI on the size and the morphology of crystals Lead sulfate crystals precipitated with and without PEI are shown in Figs. 1a and b,
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(a)
0.5 µm
(b)
5 µm
Fig. 1. SEM photographs of lead sulfate crystals precipitated in the presence of PEI of 10 g (a) and absence of PEI (b); concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min, excess lead ion=0.01 mol. Both samples were withdrawn 2 min after the visible nucleation was observed.
respectively. As clearly shown in these figures, PEI largely influenced on the size and the crystal habit of precipitated crystals. Crystals precipitated in a solution of PEI were much smaller and had a better monodispersity than crystals produced without PEI. The average size of those crystals was 0.4 mm, and the coefficient of variation of CSD was approximately 0.15. Therefore, PEI had an effect that greatly decreased the crystal size and stabilized the morphology of crystals. These effects of PEI might be particularly useful in order to produce monodispersed fine particles. 3.2. Investigation of the effect of PEI and its dependence on operation conditions A typical example of variation in the lead ion concentration during an experiment was shown in Fig. 2. At an early stage of a reaction, concentration of lead ion remained almost at a same value, in spite of the continuous supply of reactant ions. And during this period, a visible change was hardly observed in the crystallization vessel. Then the concentration value suddenly began to decrease at a certain operation time. This operation time when the lead ion concentration began to decrease is referred to as ‘‘bend point’’ in the following texts. After the bend point, a sharp reduction in concentration was observed, followed
Fig. 2. The variation of the lead ion concentration against the operation time; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min, PEI content in the ground solution=10 g, excess lead ion=0.01 mol.
by a gradual change of a slope. In addition, solution in the crystallizer became cloudy and very quickly (within 10 s or less) turned into complete white at the bend point or shortly (within 30 s) before that. This phenomenon is considered to indicate that a large number of crystals of lead sulfate rapidly nucleated. The sudden reduction of the lead ion concentration can be also explained by this rapid nucleation and growth of those nuclei, because that means the high consumption of reactant species.
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Fig. 3. The variation of the lead ion concentration when PEI was not used; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/min., excess lead ion=0.01 mol.
It is a characteristic phenomenon that concentration of lead ion was almost constant at an early stage. In an ordinary precipitation process, concentration is expected to decrease immediately after reactants begin to be supplied because of the very low solubility of lead sulfate. Fig. 3 shows a concentration change in the experiment without PEI. This figure shows that actually the lead ion concentration rapidly decreased from the beginning when PEI was not used. In the presence of PEI, however, the lead ion concentration kept constant before the bend point. Thus PEI is considered to have an interesting function that controls the concentration level of lead ion during a precipitation and significantly decreases the reaction rate, while it does not inhibit a precipitation completely. Although the detailed mechanism is not fully understood, it is considered that this effect is due to the complexation between PEI and lead ion [32,34]. This peculiarity of PEI seems highly useful in order to produce monodispersed fine particles, since the restraint of both continual nucleation and excessive growth of crystals is essential to keep the monodispersity of crystals [11]. A rapid cloudiness and the concentration drop also give another interesting aspect. In most experiments, the variation in the lead ion concentration showed similar behavior (not shown in this paper) to that illustrated in Fig. 2. It is plausible
503
there was a certain limitation on the effect of PEI that controlled the rate of both the nucleation and the growth, and the bend point was the time when the condition of the working solution reached that limit and PEI lost its influence on precipitation phenomena. The increase of the amount of supplied reactants and the decrease of the concentration of PEI in the working solution are probable factors that affected the limit of PEI’s effect. Therefore, the total amount of lead ion at the bend point was calculated in order to see the relationship between operation conditions and the value of the bend point. It was calculated from Ntot ¼ CR FR tb þ NG ;
ð1Þ
where Ntot was the total molar amount of lead ion at the bend point (mol), CR was concentration of reactant solution (mol/l), FR is feed rate (l/min), tb was the observed bend point (min) and NG was the amount of lead ion in the ground solution (mol). Operation conditions of a series of experiments and corresponding values of Ntot are summarized in Table 1. Each experiment was performed at least 3 times and averaged value (reproducibility was 3–5%) of Ntot is reported. As shown in this table, Ntot was approximately 4.8 102 mol when PEI dosage was 10 g, regardless of reactant concentration, feed rate and the amount of excess ion. Assuming that the complexation between PEI and lead ion is a key to decrease the reaction rate, it is thought at the bend point no more complexes can be formed or the complexation reaction reaches to equilibrium, and consequently PEI cannot control the lead ion concentration any longer. Concentration data (not shown in this paper) of an experiment where the amount of lead ion in the ground solution was 0.05 mol, which is larger than the value of Ntot ; also supported our assumption. The lead ion concentration began to decrease and the cloudiness was observed immediately after reactants began to be supplied. Above discussions about the bend point and Ntot only deal with the case where the amount of PEI dissolved in the around solution was 10 g. And the bend point, or Ntot is expected to have a close relationship with PEI dosage if the bend point is
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Table 1 Operation conditions and corresponding Ntot (PEI=10 g) Reactant concentration (mol/l)
Feed rate (l/min)
Molar feed rate (mmol/min)
Amount of excess ion (mol)
Average Ntot (mol)
0.25 0.25 0.5 0.5 0.5 0.5 0.75 0.5 1.0
0.01 0.02 0.01 0.01 0.01 0.015 0.01 0.02 0.01
2.5 5.0 5.0 5.0 5.0 7.5 7.5 10.0 10.0
0.01 0.01 0 0.01 0.03 0.01 0.01 0.01 0.01
4.9 102 5.0 102 4.5 102 4.9 102 5.3 102 4.6 102 4.9 102 4.7 102 4.7 102
0.07
0.06
0.04
N
tot
[mol]
0.05
0.03
0.02 0.01
0 0
5
10
15
20
25
Amou nt of PE I in the ground solution [g]
Fig. 4. Relationship between Ntot and the amount of PEI in the ground solution; molar feed rate=5.0 mmol/min, excess lead ion=0.01 mol.
the time when the ‘‘effective’’ complexation between lead ion and PEI comes to cease. The relationship between the amount of PEI and Ntot is shown in Fig. 4. The correlation equation was Ntot ¼ kW 0:49 ;
ð2Þ
where k was an experimental factor (mol/g) and kE1:4 102 in our results, W was the amount of PEI in the ground solution (g). They were strongly correlated (correlation coefficient=0.98), suggesting that PEI content in the ground solution determined Ntot ; and consequently the bend point. In other words, the bend point can be predicted from the operation conditions, i.e. the amount
(not the concentration) of PEI, molar feed rate and the amount of excess ion. It is noteworthy that the correlation is not firstorder with respect to the amount of PEI. This result seems to indicate that PEI became less effective at higher concentration. In an acidic solution, highly protonated PEI molecule is supposed to expand its branches and has a larger hydrodynamic diameter. Therefore, the intermolecular and intramolecular steric hindrance as well as the repulsive interaction between charged amino groups and lead ion prevent the complexation between PEI and lead ion especially at higher PEI concentration [32,33,35]. Consequently, the ratio of available amino groups to the total PEI mass decreases with the increase of PEI concentration. 3.3. Producing monodispersed fine particles in a solution of PEI As mentioned above, it was suggested that PEI could no longer control the precipitation rate and the rapid nucleation occurred at the bend point. This rapid nucleation is not a favorable phenomenon for producing monodispersed fine crystals, since the continual nucleation and the growth of those nuclei leads to the polydipersity of product crystals. Therefore it should be better that precipitation with PEI is ceased and produced crystals are collected before the cloudiness observed in order to produce monodispersed particles. And it is possible to do this operation because
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References
Fig. 5. SEM photograph of lead sulfate crystals precipitated in PEI solution. Crystals were sampled when 6 min were elapsed; concentration of reactant solution=0.5 mol/l, feed rate=0.01 l/ min, PEI content in the ground solution=10 g, excess lead ion=0.01 mol.
the bend point can be predicted. Fig. 5 is an SEM photograph of crystals that were sampled before (ca. 1 min.) the bend point estimated by Eq. (2). Although crystals were slightly damaged, probably because of the rinsing operation and the long centrifugation time, obtained crystals were smaller than those sampled after the bend point (see Fig. 1a). Average size of this sample was 0.2 mm, and the coefficient of variation of CSD was approximately 0.2. Thus our idea might be useful for the purpose of producing monodispersed fine crystals, since it tells appropriate operation duration and sampling time in the precipitation process using PEI as a growth modifier.
Acknowledgements This study was supported and subsidized by Mizuho Foundation for the Promotion of Sciences. And the authors truly acknowledge the assistance of Nippon Syokubai Co., Ltd. for the provision of the samples of PEI and their specification data. And also we wish to thank Mr. Yukio Ibe of Tahira Co., Ltd. for his advice on ISE electrode and its usage.
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