J. Phys. Chem. 1996, 100, 10615-10619
10615
pH Oscillations in the Bromate-Sulfite-Marble Semibatch and Flow Systems1 Gyula Ra´ bai Institute of Physical Chemistry, Kossuth Lajos UniVersity, H-4010 Debrecen, Hungary
Ichiro Hanazaki* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan ReceiVed: February 12, 1996; In Final Form: April 23, 1996X
A self-accelerating oxidation of an unbuffered aqueous sodium sulfite-hydrogen sulfite solution by sodium bromate and a selective removal of the hydrogen ion by solid marble chips from the reaction mixture have been used to construct an oscillatory system. The system exhibits large-amplitude oscillations between pH 3.5 and 7.5 at 25.0 °C in a continuous-flow stirred tank reactor and in a semibatch configuration. The shape, the periodic time (from 10 min to 2 h), and the region of oscillations can be controlled by using different amounts and grade size of marble. A simple reaction scheme, consisting of the protonation equilibria of SO32- and HSO3-, the oxidation of HSO3- and H2SO3 by BrO3-, and a removal of H+ by the CaCO3 in marble in the form of HCO3- has successfully been used to simulate the observed dynamical behavior.
Introduction In the past ten years a great number of inorganic chemical reaction systems were found to be accompanied by largeamplitude periodic temporal changes in hydrogen ion concentration in a homogeneous aqueous solution. In these systems the [H+] change is usually an important kinetic regulating force rather than merely a consequence or an indicator of chemical oscillations. These phenomena have been observed both in a closed and, more frequently, in an open reactor.2 In addition to the theoretical interest, such a reaction has recently been suggested for the control of rhythmically pulsatile mechanical motion of polymer hydrogel systems. This self-oscillating swelling and deswelling of polymer hydrogels was considered to be similar to the periodic motion of some muscular tissue and it may contribute to further understanding of certain periodic biological phenomena.3 Furthermore, an interesting idea has recently emerged that pH oscillators might be of interest in the efficient fabrication of temporally controlled drug delivery systems.4,5 This approach seems to be promising because the uncharged form of certain drugs can permeate across lipophilic membranes much faster than their charged forms. By changing the pH of a drug solution, the ratio of the two forms can be varied on a large scale through the acid dissociation equilibrium of the drug. This results in a pH-dependent rate of the diffusion through the membrane. A periodic delivery profile may be obtained by oscillating the pH of the drug solution.5 A significant progress in this application is, however, hampered because very few of the known oscillator systems have long enough periodic time and the low-pH state within a cycle is usually short. The slow diffusion through the membrane is not competitive with the fast oscillations. Furthermore, certain chemicals like ferrocyanide, which are widely used in the oscillators, are not welcomed by drug delivery applications. It is, therefore, desired to design new systems which have long periods and avoid harmful chemicals. The principles of designing pH oscillators are known.2 In general, two main composite processes are needed, one of which produces H+ in a self-accelerating manner (positive feedback pathway), while the other consumes it (negative feedback). The X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00428-5 CCC: $12.00
oxidation of a mixture of SO32-/HSO3- by different oxidizing agents such as H2O2, IO3-, and BrO3- has often been used as the self-accelerating part. On the other hand, the oxidation of thiourea, thiosulfate, or ferrocyanide6 with the same oxidizing agents was applied as the hydrogen ion removing composite reaction. These reactions are obviously very complex ones consisting of many steps. From a practical point of view, however, the simpler a chemical oscillator the better it is for any use. Model calculations clearly show that a simple selective removal of H+ can replace the complex redox reactions for the negative feedback. Here our aim was to find a replacement of the complex negative feedback in an experimental system. In this paper, we present a pH oscillator, in which solid granular or lumpy marble is used for removal of H+ from an aqueous reaction mixture of sulfur(IV)-bromate ion. The CaCO3 content of marble reacts with H+ when the pH is low. Oscillations are measured both in a continuously fed stirred tank reactor (CSTR) and in a semibatch configuration if marble is placed in the reactor at the start. CaCO3-containing powders are not appropriate because their reactions with the hydrogen ion are apparently too rapid. Experimental Section Materials. Reagent-grade H2SO4 (Merck), NaBrO3, and Na2SO3 (Reanal) were used without purification. Granular marble (Reanal; size 1-2 mm, 4-5 mg each, irregular shape) was soaked with distilled water overnight before use. In other experiments coarse marble was smashed to pieces, riddled, washed, and soaked with water before use. We found that it was informative to characterize marble used in our experiments by the average weight of the chips. Stock solutions of sulfite containing some sulfuric acid were prepared fresh daily with deionized, distilled water and were kept from air to avoid autoxidation. S(IV) content was determined by iodimetric titration in the presence of starch. Procedure. We studied the system in three different reactor configurations. First, a few experiments were performed in a thermostated cylindrical-shaped glass reactor (4 cm in diameter) in a batch configuration. The reaction was started by injection of a stock solution containing sodium sulfite and the desired amount of sulfuric acid into the reactor containing marble and © 1996 American Chemical Society
10616 J. Phys. Chem., Vol. 100, No. 25, 1996 a prethermostated NaBrO3 solution. The final volume of the mixture was 40 mL. It was continuously stirred with a 2 cm magnetic stirrer bar at around 500 rpm. Since a component process takes place on a solid-liquid surface, the efficiency of stirring is obviously very important. The stirring rate was, therefore, kept constant in all the experiments. In order to monitor pH changes, the reactor was equipped with a pH electrode (Horiba Model S8721) that was connected to a Horiba D-13 pH meter. The pH-time curves were recorded. Second, some marble was placed into a well-stirred glass reactor with a water jacket (40 mL volume) that was continuously fed with a solution containing Na2SO3 and H2SO4, and another solution containing NaBrO3, through two inlet tubes by means of a peristaltic pump (Desaga) at a constant flow rate. The excess of liquid was removed continuously by the same pump using four of its channels in the reverse mode. The level of the reaction mixture could be controlled by the vertical position of the outlets. The reactor was open to the air. The pH change was monitored. This configuration is very similar to the well-known CSTR. The only difference is that marble is not refreshed continuously. However, its amount did not change significantly: During a 5-h CSTR experiment, the mass loss of solid marble did not exceed 10%. Third, we applied a semibatch configuration. Here we placed the bromate solution and some marble into the reaction vessel (300 mL Erlenmeyer flask immersed in a thermostated water bath). A solution of sodium sulfite containing some sulfuric acid flowed at a constant very slow rate into the reactor by means of a syringe pump (Perfusor7). No outflow was applied. The reaction mixture was stirred continuously by a magnetic stirrer. Results and Discussion Batch Experiments. The reaction between excess bromate and a mixture of sulfite-hydrogen sulfite is accompanied by large, characteristic pH changes. If no additional acid-base buffer is used, the pH drops from the initial value of about 8 to about 3 with increasing rate as the S(IV) is depleted. A sharp break appears at the point when all the S(IV) is exhausted. Then the pH remains almost steady because of the lack of significant reactions.6,8 This reaction provides the necessary positive feedback pathway for pH oscillations in our system because its rate increases with increasing H+ concentration.9 Note that the measured acceleration in the change of pH is the result of two factors: (i) decrease of the buffering effect of S(IV) with decreasing [S(IV)]; (ii) the acceleration of the depletion of S(IV) with increasing [H+]. We made a few kinetic runs in the presence of different amounts of marble. The first part of the pH vs time traces was hardly affected. However, as was expected, we found that the pH rose in the second part. The shape of the rising part of the curves was dependent on the amount and the grade size of marble particles. As seen in Figure 1, the pH rose more rapidly if more marble of the same grade size was used. Above a critical amount, the sharp drop in pH was prevented; only a shallow minimum could be observed (Figure 1, curve d). Furthermore, particles of smaller size caused a faster pH increase, indicating that the surface of the marble strongly affects the rate of the H+-removing process. From these experiments we can conclude that marble opens a good regulatable negative feedback pathway as it neutralizes H+ in the mixture when the pH is low. The rate of H+ removal can be varied very conveniently as desired by the amount and the size of marble particles. Experiments in a CSTR. Dynamical behavior of the bromate-sulfite-hydrogen ion-marble reaction system is
Ra´bai and Hanazaki
Figure 1. pH vs. time curves measured in a batch reactor in the bromate-sulfite reaction in the presence of different amounts of marble (grade size 1-2 mm): [Na2SO3]0 ) 0.0097 M, [H2SO4]0 ) 7.50 × 10-4 M, [NaBrO3]0 ) 0.090 M; volume of the reaction mixture is 40 mL; and the amount of marble is 0.10 (a), 0.20 (b), 1.0 (c), and 2.0 g (d). T ) 25.0 °C.
rather complex in an open reactor. At least, three different steady states develop depending on the flow rates at fixed input concentrations: first, a high-pH steady state (pH 7-8) at high flow rates when only a small fraction of sulfite is oxidized because of the short residence time (SSI); second, a low-pH steady state (pH 3.5-4) at intermediate flow rates when most of the sulfite is oxidized (SSII), but the residence time is not long enough for removing H+ by marble. There is a wide range of bistability between SSI and SSII. Finally, another high pHsteady state exists at low flow rates when there is enough time for marble to remove most of the hydrogen ion (SSIII) (Figure 2). As it was expected, large-scale pH oscillations could be measured in a narrow range of input flow rates at certain initial concentrations. The oscillatory behavior is robust and readily reproducible. As it appears from the curve shown in Figure 3, the amplitude of oscillations can be as high as more than three pH units in the optimum case. The length of the periods can be varied on a large scale by varying the input concentrations, flow rate, and the amount of marble. We found oscillations at 25.0 °C with about 10-min periodic time when the input concentrations calculated for the total feed were [NaBrO3]0 ) 0.100 M, [Na2SO3]0 ) 0.097 M, and [H2SO4]0 ) 0.011 M. These would be the concentrations in the reactor if no chemical reaction took place. The normalized flow rate was k0 ) 2.5 × 10-4 s-1 (k0 ) F/V, where F is the total flow rate (mL/s) and V is the cell volume (40 mL)). The cell contained 6.0 g of granular marble (size 1-2 mm). On the other hand, the periodic time can be as long as 1 h when a more diluted solution of bromate and less marble is used (Figure 3). The length of the low-pH state relative to that of the high-pH state can also be varied on a large scale by changing, for example, the amount of marble. A longer low-pH state is favored within an oscillatory period when the amount of marble is relatively small. Oscillations can last for many hours or even days, but they cannot be sustained for an unlimited time. Since marble is not refreshed during a single run, the shape and the time of periods are changing as marble is slowly being dissolved. Finally, oscillations cease. We performed several experiments with CaCO3 powder instead of granular or lumpy marble. However, sustained
pH Oscillators with Marble
Figure 2. pH values characteristic for steady states (points) and oscillatory state (region marked with dashed line) at different flow rates in a CSTR. Observe the bistability between SSI and SSII. Input concentrations calculated for the total input feed: [NaBrO3]0 ) 0.050 M, [Na2SO3]0 ) 0.096 M, [H2SO4]0 ) 0.010 M; 2.0 g of granular marble (grade size 1-2 mm) is placed in the reactor. T ) 25.0 °C.
J. Phys. Chem., Vol. 100, No. 25, 1996 10617
Figure 4. Oscillatory curve measured in a semibatch reactor. A solution of 1.0 M Na2SO3 containing 0.085 M H2SO4 flowed, at 2.0 mL/h by means of a syringe pump, into 200 mL of a 0.050 M NaBrO3 solution containing 6.0 g of marble chips (size 6-8 mm, 0.3-0.4 g/piece). T ) 25.0 °C.
TABLE 1: The Simplest Model of the Oscillatory Oxidation of Sulfite by Bromate in the Presence of Marble rate constants at 25.0 °C no.
reactions
1
3HSO3- + BrO3 f 3SO42- + Br- + 3H+ 3H2SO3 + BrO3- f 3SO42- + Br- + 6H+ H+ + SO32- T HSO3H+ + HSO3- T H2SO3 H+ + CaCO3 f Ca2+ + HCO3-
2 3 4 5
Figure 3. Typical measured oscillatory curve in a CSTR mode. Experimental conditions are given in Figure 2. k0 ) 2.51 × 10-4 s-1.
oscillations could not be maintained with the powder. The reason could be that the powder reacts with H+ more rapidly than required because of its large surface. The fast removal of H+ prevents the H+-producing component process from accelerating. Experiments in a Semibatch Reactor. A semibatch reactor requires simpler equipment and it is obviously more convenient to use than a CSTR for studying new applications of chemical oscillators. Its major advance is that, in contrast to a CSTR, no outflow is necessary to be maintained during experiments. Such a configuration has been applied by Giannos et al.5 for studying the possibility of temporal drug delivery controlled by a pH oscillator. Since just a few of the known CSTR systems can keep an oscillatory nature in a semibatch configuration, an important question is whether the present system can oscillate under these conditions. Our systematic search has revealed that
-
M-1 s-1 k1 ) 2.71 ×
s-1 10-2
k2 ) 6.0 k3 ) 5 × 1010 k4 ) 2 × 108
k-3 ) 5 × 103 k-4 ) 3.6 × 106 k5 ) 7.0 × 10-3
oscillations could be maintained not only in a CSTR but also in a semibatch configuration. Shown in Figure 4 are typical curves obtained when a solution containing Na2SO3 and some H2SO4 is introduced, at a constant very slow flow rate, into a solution of NaBrO3 containing marble. The initial pH of the NaBrO3 solution with marble is between 8 and 9. The pH of the incoming solution is around 7.5 because the sulfite ion is in excess over the hydrogen ion. The pH starts to decrease immediately as the sulfite solution starts to flow in. No induction period precedes the oscillations. The number of periods strongly depends on the experimental constraints and it can be as many as 100 under favorable conditions. Here we note that, in a semibatch reactor, oscillatory behavior may be a long-lived response, but it is necessarily a transient phenomenon. The periodic time ranges from about 10 min to 2 h, depending mostly on the concentration of NaBrO3 and the amount and grade size of marble. Model of Oscillations. After showing experimentally that this system is capable of oscillating under both open and semibatch conditions, we try to simulate this dynamical behavior. Here we propose a simple model as summarized in Table 1. According to Williamson and King,9 reactions 1 and 2 have simple second-order rate laws R1 and R2, respectively.
V1 ) -d[BrO3-]/dt ) k1[BrO3-][HSO3-]
(R1)
V2 ) -d[BrO3-]/dt ) k2[BrO3-][H2SO3]
(R2)
10618 J. Phys. Chem., Vol. 100, No. 25, 1996
Ra´bai and Hanazaki
Figure 5. Calculated oscillations in a CSTR mode. Input concentrations and the flow rate are as in Figures 2 and 3, respectively. Rate constant values used in the calculations are shown in Table 1.
The values of k1 ) 0.0271 M-1 s-1 and k2 ) 6.0 M-1 s-1 were calculated from the batch experiments carried out at 25.0 °C. Simple mass action kinetics equations of the forward and reverse reactions of the fast protonation equilibria 3 and 4 were used in the calculations. The rate constant values were measured10 for equilibrium 4, and reasonable values were suggested11 for equilibrium 3: k3 ) 5 × 1010 M-1 s-1, k-3 ) 5 × 103 s-1, k4 ) 2 × 108 M-1 s-1, and k-4 ) 3.4 × 106 s-1. These rate constants are consistent with the values of the corresponding equilibrium constants. Reactions 1-4 compose the positive feedback pathway. Reaction 5 represents the simplest possible negative feedback for a pH oscillator. Since the amount of CaCO3 can be taken as constant during a single run, we consider the following equation as the rate law of the H+ removal.
V5 ) -d[H+]/dt ) k5[H+]
(R5)
where k5 is regarded as an empirical pseudo reaction rate constant. Its numerical value is a dependent on the grade size and the amount of marble used in the experiments. Naturally, the rate of stirring, the volume of the reaction mixture, and the geometry of the reactor also affect the value of k5. Therefore, k5 can only be regarded as constant during a single run. Its numerical value was determined by measuring the change in the pH of a diluted sulfuric acid solution which is in contact with marble chips under the same conditions as the CSTR and semibatch experiments were conducted. The value was found to be k5 ) 0.007 s-1 for both 2.0 g of smaller grade size (1-2 mm) marble under the CSTR conditions and for 6.0 g of 6-8 mm grade size marble under the semibatch conditions. The model in Table 1 consists of three irreversible reactions and two fast protonation equilibria and involves, for variable concentrations, [BrO3-], [SO32-], [HSO3-], and [H+]. The differential equations for the variable species were augmented with inflow and outflow terms for the CSTR mode. Only inflow terms for SO32- and H+ were considered in the semibatch mode. A semi-implicit Runge-Kutta method was applied to solve the differential equation system numerically. We found that both the CSTR and the semibatch oscillations could be simulated by the model. A typical oscillatory curve calculated for CSTR mode is shown in Figure 5. The periodic time and the shape of the calculated curve are rather similar to that of the measured
Figure 6. Calculated oscillations in the semibatch mode. The simulations were carried out by augmenting the rate law model with inflow terms for the sulfite and hydrogen ion. The inflow terms were obtained by multiplying the input concentrations with the inflow rate constant, which is defined by kr ) r/V, where V is the volume of reaction mixture (in mL) and r is the incoming flow rate of the sulfite solution (in mL s-1). The increase of the volume of the reaction mixture during the experiments was neglected: [BrO3-]0 ) 0.050 M, [SO32-]0 ) 1.0 M, [H+]0 ) 0.170 M; kr ) 2.78 × 10-6 s-1. Rate constant values are shown in Table 1.
one. However, the calculated amplitude is bigger than its measured counterpart mostly because the pH minimum on the calculated curve is lower. SO42- formed during oxidation of SO32- acts as a buffer at low pH values and prevents the pH from falling below 3. Our model does not take into account this buffering effect, which may cause the disagreement between the calculated and the measured pH minimum. The dynamical behavior seen in Figure 2 can also be simulated at least qualitatively. Shown in Figure 6 is a calculated oscillatory curve in a semibatch reactor. Again the minima are lower on the calculated curves than on the measured ones (Figure 4), and the calculated periodic time is smaller by a factor of 2. We do not think, however, that it would be a fruitful effort to try to reach better agreement between the model and the experiments because this simple model can only be a core of the mechanism of the system. The core is responsible for the oscillatory kinetics but it cannot reflect most of the side effects influencing the details of the dynamical behavior. Conclusion The importance of this oscillator is, at least, twofold. First, a simple negative feedback process is connected to the selfaccelerating bromate-sulfite reaction. In this way any “crosstalk” between the two main component reactions can be avoided, which is an advantage in understanding the mechanism. In the closely related bromate-sulfite-ferrocyanide system, the two component reactions interfere with each other, because they have many common intermediates (BrO2-, HOBr, Br2). We believe that this complication led to a misunderstanding of the mechanism of that system.6 Here we offer a more reasonable explanation: The nonlinearity of the bromate sulfite reaction arises from the difference in the reactivity of differently protonated S(IV) species rather than from simproportionations and disproportionations of bromine species. Giannos et al. called for new systems because “discovery of new oscillators should increase the adaptability of the technol-
pH Oscillators with Marble ogy” of the pH-controlled periodic drug delivery.5 A good oscillator with long period and large amplitude is offered here. In this context the advantage of the present system is that the length of the low-pH state relative to that of the high-pH state within a cycle can be varied by using different amounts of marble. More similar oscillators are expected to be designed by combining such removal of H+ with an autocatalytic H+producing chemical reaction. Whether the latter should be, in any case, a redox process or nonredox reactions are also appropriate, remains to be seen.
Acknowledgment. This work was supported by the Hungarian Science Foundation (Grant OTKA T14440) and the Japan Society for Promotion of Science through a grant to G.R.
J. Phys. Chem., Vol. 100, No. 25, 1996 10619 References and Notes (1) Part 1 in the series pH Oscillators with Marble. (2) Ra´bai, Gy.; Orba´n, M.; Epstein, I. R. Acc. Chem. Res. 1990, 23, 258. (3) Yoshida, R.; Ichijo, H.; Hakuta, T.; Yamaguchi, T. Macromol. Rapid Commun. 1995, 16, 305. (4) Giannos, S. A.; Dinh, S. M.; Berner, B. Macromol. Rapid Commun. 1995, 16, 527. (5) Giannos, S. A.; Dinh, S. M.; Berner, B. J. Pharm. Sci. 1995, 84, 539. (6) Edblom, E. C.; Luo, Y.; Orba´n, M.; Kustin, K.; Epstein, I. R. J. Phys. Chem. 1989, 93, 2722. (7) The syringe pump was kindly donated to us by Ursula Kummer. (8) Sorum, C. H.; Charlton, F. S.; Neptune, J. A.; Edwards, J. O. J. Am. Chem. Soc. 1952, 74, 219. (9) Williamson, F. S.; King, E. L. J. Am. Chem. Soc. 1957, 79, 5393. (10) Eigen, M.; Kustin, K.; Maass, G. Z. Phys. Chem. N.F. 1961, 30, 130. (11) Ga´spa´r, V.; Showalter, K. J. Am. Chem. Soc. 1987, 109, 4869.
JP960428D
