J . Phys. Chem. 1989, 93, 7755-1756 between the molar volumes of C12E6and water (approximately equal to 25), is the total volume fraction of surfactant, and C is a phenomenological interaction parameter. Utilizing results from ref 6. we have computed A,(X.T) and deduced that y C / k = 14.3T - 4220. Using this information in eq IO,we have been able to predict aV,,,/RT as a function of surfactant concentration, X.at the three temperatures 25, 30, and 36 "C; see Figure 1. The favorable comparison with the original data of ref 4 adds further support to the central claim of this Letter, that, in general, osmotic prcssure measurements of micellar solutions, performed and analyzed a b described above, do not yield the number-aoerage micellar molecular weight.
+
7755
Acknowledgment. We are grateful to Professor J. Th. G. Overbeek for many illuminating discussions on membrane osmometry. This research was supported in part by the National Science Foundation under Grant DMR-87-19217 administered by the Center for Materials Science and Engineering at MIT. Daniel Blankschtein acknowledges the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of his research and is grateful for the support by the Texaco-Mangelsdorf Career Development Professorship at MIT. Registry No. CI2E6.3055-96-7.
Oscillatory Coupling of Chemical Oscillators and Other Reactive Systems Mihily T. Beck* and Istvin P. Nagy Department of Physical Chemistry, Kossuth Lajos University, Debrecen IO, Hungary 401 0 (Receiued: June 13, 1989)
The effect of periodic mass transfer between two reactive systems can be achieved by applying the principle of the hydrodynamic oscillator. The oscillatory coupling of chemical oscillators and the periodic perturbation of a reactive system by a suitable agent results in novel oscillatory responses.
Introduction The coupling of oscillatory chemical systems is basically important both from a chemical point of view and as modeling of regulation in biochemical systems.' So far, all these studies dealt with the coupling of two or more CSTRs (continuous-flow stirred tank reactors). Martin's discovery* that rhythmic downward and upward flows occur when two aqueous salt solutions of different density are connected by a vertical capillary indicated to us that it is possible to make a periodic mass transfer between two reactive systems. From among the many obvious possibilities the following appeared to us the most interesting. First is the coupling of two different chemical oscillators, and second, the periodic perturbation of an oscillatory system by a substance which either initiates or inhibits the oscillatory kinetics. The periodic mixing of the ingredients of an oscillatory system by the hydrodynamic oscillator also offers a deeper insight to the nature of such systems. Experimental Section The experimental setup is shown in Figure 1. The frequency and the amplitude of the hydrodynamic oscillator depend on the density difference of the solutions in the two compartments and on the length and the diameter of the capillary and the heights of the liquid columns in the compartments. In our experiments the frequency was about 0.238 m i d , while the volume of the dm3 per period. This means transferred solution was 7.68 X that about 5% of the full volume of each compartment was exchanged in 2 h. The solutions in both compartments were stirred (80 rpm). (A higher stirring rate would interfere with the hydrodynamic oscillator.) The volumes of the solutions in compartments A and B were always 31.5 and 45 cm3, respectively. In all cases, the hydrodynamic oscillation started by a downward stream. The potentials in one or both compartments were measured by a Radelkis OP-208/ 1 precision potentiometer using bright Pt electrodes and SCE reference electrodes and KN03-KCI double salt bridges. Reagent grade chemical were used without further purification. ( I ) Rehmus, P.;Ross, J. In Oscillarions and Traveling Wawes in Chemical Systems; Field, R . J., Burger, M., Eds.; Wiley: New York, 1985; pp 287-332. (2) Martin, S. Geophys. Fluid Dyn. 1970, I , 143.
0022-3654/89/2093-7755~01S O / O
All the experiments were performed at room temperature (22 f 2 "C).
Results and Discussion The mutual effects of two BZ systems containing two different catalysts depend to a large extent on the state of the two reactions at the moment of coupling, but the effect of the ferroin-catalyzed system on the manganese(I1)-catalyzed one is always much greater than vice versa. As appears from the curves of Figure 2 the length of the oscillatory stage of the Mn2+-catalyzed system can be increased or decreased by the coupling, while only rather small, but definite, changes in the amplitude and frequency of the oscillations in the potential of the ferroin-catalyzed system were found. Bromide ions play a crucial role in the BZ reactions3 A relatively small concentration of bromide inhibits the oscillatory character. When bromide ion is periodically introduced by the hydrodynamic oscillator into the BZ system, the response greatly depends on the concentration of the bromide solutions, as illustrated by curves of Figure 3. At smaller concentrations, first irregular changes occurred, and then a rather stahle oscillatory behavior is observed. At higher bromide concentrations mixedmode oscillation is observed for more than an hour. Later the period time increases and at even higher bromide concentrations the oscillatory character is totally suppressed. A most interesting phenomenon occurs when the reactants of the BZ system are mixed by the hydrodynamic oscillator (Figure 4). While the periodic mixing leads to an oscillatory change of the potential, the continuous addition of the same amount of bromate to the other reactants leads to a monotonous change of the potential. Note that the frequency of the potential change is much larger than that of the hydrodynamic oscillation! When the total amount of the bromate is added to the other reactants in a single dose, also oscillatory change of the potential occurs, but the shape of the curve and the characteristics of the oscillatory reaction are different. It has been found that while the oxidation of oxalic acid by bromate in the presence of a catalyst is not an oscillatory reaction, (3) Field, R. J.; Kijros, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649.
0 1989 American Chemical Society
7756 The Journal of Physical Chemistry, Voi. 93, No. 23, 1989 35
LO
A
Letters
T
B 0 1 1
t_i
5 O @ k ----~
L
5
9 0,s” The length of the capillary :
3.0 mm
Figure 1. The reactor used in the experiments. The reactor is made from Plexiglas. The numbers are millimeters. I
mv
0
5
10
t Imml
5
10
t lminl
L_
t (mini
-
1100r
I
~~~~
20
Figure 4. The effect of the mode of mixing of the reactants on the change of potential in the BZ reaction. (a) Mixing of the reactants by the hydrodynamic oscillator. Initial concentrations: compartment A: NaBr03 0.28 M, H2S04 0.45 M, Na2S04 0.81 M; compartment B: malonic acid 0.90 M, ferroin 0.00044 M, H2S040.45 M. Potential was measured in compartment B. The horizontal line shows the length of the period of the hydrodynamic oscillation. (b) Continuous mixing of the reactants. The initial concentrations were the same as in the former case in compartment B. A solution of the composition as in compartment A was introduced with a constant flow rate, corresponding to the average rate in the case of oscillatory mixing. (c) Immediate mixing. The initial composition of the reaction mixture corresponds to the former experiments after 1 h reaction time. mv,
1301
,
10
,
mV
1
1300
0
Figure 2. The effect of the hydrodynamic coupling of ferroin- and Mn2+-catalyzed BZ reactions on the potential measured in compartment B. Initial compositions of the solutions: compartment A: Na2S04 1 M, malonic acid 0.266 M, N a B r 0 3 0.07 M, H2S040.45 M, ferroin 4.4 X IO4 M; compartment B: malonic acid 0.266 M; NaBrO, 0.07 M; H2S04 0.45 M; MnSO, 4.4 X M. mv 1000 t
850 5
mV
20
25
I(min)
95
100
t
I
IOOO-
90
(mnl
Figure 3. The effect of bromide ion on the BZ reaction. Initial composition of the solutions: compartment A: N a 2 S 0 40.73 M, NaBr 0.13 M (dotted line), 0.325 M (full line); compartment B: NaBr03 0.07 M, malonic acid 0.266 M, ferroin 0.00044 M, H2S040.45 M. Potential was measured in compartment B. The horizontal line shows the length of the period of the hydrodynamic oscillation.
periodic changes of the redox potential occur when acetone is added to the reaction m i ~ t u r e . ~We found that the periodic self-regulatory introduction of acetone t o the bromate-oxalic acid-cerium( 1V)-sulfuric acid mixture results in a remarkable response. In the first 55 min the potential of the bright Pt electrode is almost constant, except for two short (between 5 and I O and ( 4 ) Noszticzius, Z. Magy. KPm. Foly. 1979, 85, 330.
BO
90
100
tlmlni
Figure 5. Emergence of oscillatory character of the potential change in the bromate-oxalic acid-cerium(1V) system on the effect of the introduction of acetone cosubstrate by the hydrodynamic oscillator. Initial concentrations: compartment A: acetone 2.05 M, Na2S04 0.675 M, H2S04 3.0 M; compartment B: NaBr03 0.02 M, Ce(S04) 0.0005 M, H2S043.0 M. The potential of the Pt electrode was measured in compartment B. The horizontal line shows the length of the period of the hydrodynamic oscillation.
then between 30 and 35 min, respectively) rather irregular oscillatory stages. As is shown by Figure 5 , this stage is followed by a long oscillatory phase characterized by a constant amplitude and continuously increasing time of period. If the solutions in the two compartments are not stirred, spatial structures may form. This is illustrated by the Briggs-Rauscher5 reaction. The following solutions were placed into the compartments: (A) H 2 0 2 (2.9 M), H2SO4 (0.35 M), Na2S04(0.75 M); (B) KIO, (0.067 M), malonic acid (0.05 M), MnS04 (0.0067 M), starch (0.1 wt 7%). After 6-10 min a double layer structure is formed at the bottom of the compartment B. The lower part of the structure is yellow, and the upper part is blue indicating that the lower part contains only iodine, while in the upper layer both iodine and iodide are present. The size of the structure increases with time but this difference in the colors is retained. Later the evolution of oxygen destroys the structure. These experiments prove that the oscillatory coupling of reactive systems provides a rich field of the study of exotic kinetic phenomena. Acknowledgment. The technical help by Mrs. B. A.Vet6si and Mr. L. Magl6czki as well as the financial support by the Hungarian Academy of Sciences is gratefully acknowledged. ( 5 ) Briggs, T. S.; Rauscher, W. C. J . Chem. Educ. 1973, 50, 496.
