J . Phys. Chem. 1987, 91, 1553-1557 as KDL/KLL, K being the electronic transmission coefficient.46 While at the present it is difficult to quantify such effects, a rough estimate of KDL/KLL from the foregoing values gives 1.4 f 0.5 for both substrates. Semiempirical calculations are in progress to verify this point.47 Concluding Remarks We have constructed by conformational energy calculations theoretical models of diastereomeric noncovalent electron-transfer complexes between L-dopa or L-adrenaline and [Fe(tetpy)(OH),]+ ions anchored to enantiomeric ordered polypeptides. In agreement with experimental evidence, the computed conformations show (46) In the framework of a semiclassical treatment of electron-transfer processes4’ and under the foregoing assumptions, i.e. AG”LL(R’L.L) = AG‘ ‘DL(R’DL)and AC*~,LL= AG’i?DL (AG*i, being temperature dependent if nuclear tunneling occurs), kinetic stereoselectivity may be expressed as (ktDL/kctLL) = (V,DL/V,LL)(KDL/KLL) exp[(AG*LL- AG*DL)oUt/RT] where Y, is the effective frequency for nuclear motion and K the electronic transmission coefficient. Since ui >> u0 and AGli, >> AG*,,,, vi being the mean frequencies of molecular vibrations (around 1350 cm-’ for catecholic moietyL9)and uo those of solvent orientations, to a first approximation u, may be written v,
= ui[AG*in/(AG*in + AG*o,,t)]i/2
Then (unDL/vnLL) is very close to unity because uiDL uiLL As a result, kinetic stereoselectivity is expected to depend on exp[(AGILL- AG*DL),,/RT] as well as on the preexponential term (KDLIKLL),as compared to a dependence on exp[(G*F.L- G*DL),/RT] when transition-state theory is considered, GILL and G*DL being the standard free energies of the diastereomeric transition states of the electron-transfer step.9a (47) Cave, R. J.; Siders, P.; Marcus, R. A. J . Phys. Chem. 1986, 90, 1436.
1553
that the polymeric matrices play a basic role in controlling the stereochemical features of diastereomeric adducts undergoing stereoselective electron transfer. At variance with previous simpler analysis, we now find that such control involves no dominant steric interaction that discriminates between DL and LL pairs. Instead, binding stereoselectivity results from a delicate balance between ionic and nonbonding forces that ultimately leads to a modest difference in the stability of the diastereomers. The same forces, however, enable the redox centers in the diastereomeric pairs to experience a different mutual orientation and separation distance that account for the remarkable kinetic discrimination observed in the elementary charge-transfer process. Using the ellipsoidal cavity model for short-range electron-transfer reactions we were able to evaluate the variation in outer-sphere reorganization energy associated with the change in solvent polarization about the diasteromeric complexes upon charge transfer. Such variation may already explain the observed kinetic stereoselectivity, but differences in electronic coupling strength between the reactants in the diastereomeric pairs may also contribute to the phenomenon.
Acknowledgment. We thank Professor P. De Santis for helpful discussions, Professor G. Nemethy for a critical reading of the manuscript, and Professor F. Sgarlata for Mossbauer spectra. Collaboration of Dr. G. Villani in calculating partial atomic charges and of Dr. S . Chiavarini in making ready the program for computer graphics is also acknowledged. This work was supported by M.P.I. (Rome) and the Italian Research Council (C.N.R.). Registry No. L-Dopa, 59-92-7; [Fe(tetpy)(OH),]+, 61412-01-9; Ladrenaline, 51-43-4; sodium poly(L-glutamate), 26247-79-0; sodium pOly(D-ghtamate), 3081 1-79-1.
Phase Behavior of Quinary Systems: Tracing the Three-phase Body M. Kahlweit* and R. Strey Max-Planck-Institut fuer biophysikalische Chemie, 0-3400 Goettingen, West Germany (Received: August 28, 1986; In Final Form: November 1 1 , 1986)
The phase behavior of quinary systems H20-oil-nonionic amphiphile-ionic amphiphile-electrolyte is represented in T-7-6 space at constant brine concentrtation, y being the weight percentage of both amphiphiles in the system, and 6 that of the ionic amphiphile in the mixture of the two amphiphiles. This representation permits a trace to be made of the three-phase body as it changes its position and extensions from the purely nonionic (6 = 0 wt 5%) to the purely ionic (6 = 100 wt %) amphiphile. As an example, the method is applied to the system H20-n-decane-C4E,-AOT-NaCI. If, upon application, the temperature, the oil, and the brine concentration are given, a systematic study of the trajectorieswith different combinations of nonionic and ionic amphiphiles should help to find the “optimum detergent” for a given problem. The significance of these trajectories for studying the properties of microemulsions and for tracing the tricritical line is noted.
Introduction Ternary mixtures of H 2 0 (A), an oil (B), and a nonionic amphiphile (C) may separate into three fluid phases within a well-defined temperature interval AT, the mean temperature of which depends sensitively but systematically on the chemical nature of both the oil and the amphiphile.’ At the point at which the three-phase body touches the homogeneous ternary solution, one finds the highest mutual solubility between H 2 0 and the oil, combined with the lowest interfacial tensions. These properties, in particular, are of major interest in both theory and application. Upon application, in general, the temperature (range) the oil (mixture), and the composition of the aqueous solutions (the “brine”) are given. The problem is to find the “optimum (1) For a review see: Kahlweit, M.; Strey, R. Angew. Chem., In?.Ed. Engl. 1985, 24, 654.
0022-3654/87/2091-1553$01.50/0
detergent”, Le., that detergent that enforces the formation of a three-phase body under these conditions with the lowest concentration. In most cases in practice, one applies for this purpose mixtures of nonionic and ionic amphiphiles, for which reason the phase behavior of quinary systems H 2 0 (A)-oil (B)-nonionic amphiphile (C)-ionic amphiphile (D)-inorganic electrolyte (E) has become the subject of a rapidly increasing number of publications (see, e.g., ref 2-5 and papers cited therein). In most of (2) Bourell, M.; Salagar, J. L.; Schechter, R.; Wade, W. H. J . Colloid Interface Sci. 1980, 75,451. (3) Bellocq, A. M.; Biais, J.; Bothorel, P.; Clin, B.; Fourche, G.; Lalanne, P.; Lemaire, B.; Lemanceaux, B.; Roux, D. Adu. Colloid Interface Sci. 1984, 20, 167. (4) Kunieda, H.; Hanno, K.; Tamaguchi, S.; Shinoda, K. J . Colloid Interface Sci. 1985, 107,129. (5) van Niewkoop, J.; de Boer, R. B.; Snoei, G . J . Colloid Interface Sci. 1986, 109, 350.
0 1987 American Chemical Society
Kahlweit and Strey
nonionicKI +
ionic (D)
amphiphile 6 =D/IC+DI
T
I I *@
5
1
/
/
I
I
L+U
H20( A I
+salt(E)
. .
E 3 E/(A+E) Figure 1. Pseudoternary phase prism for representing the temperature dependence of the phase behavior of quinary systems at constant 6 and e.
a = constant
these investigations the temperature was kept constant. Since, however, studies on ternary systems with nonionic amphiphiles have demonstrated that the phase behavior depends very sensitively on temperature, we shall, in this paper, suggest an experimental procedure how to systematically study the phase behavior of quinary systems with mixtures of nonionic and ionic amphiphiles, as it depends on the temperature and on the chemical nature of both C and D, as well as on the ratio between the two.
Representation of the Phase Behavior At constant pressure, a quinary system has five independent variables, namely the temperature and four composition variables. As such we have found it convenient to introduce the weight percentage of the oil in the mixture of oil and brine, a 5 B/(A B E), that of the nonionic and the ionic amphiphile in the system, y (C + D)/(A + B C + D + E), that of the ionic in the mixture of the two amphiphiles, 6 D/(C + D), and that of the salt in the mixture of H 2 0 and salt, e E/(A + E). If the components B, C, D, and E are given, and the pressure is kept constant, each point in the five-dimensional space is then defined by a certain set of T, a,y, 6, and t. In order to represent the phase behavior in three-dimensional space one has to dispense with two of these variables by, e.g., keeping them constant. If T i s kept constant, one may represent the phase behavior in a pseudoquaternary phase tetrahedron, keeping, in addition, one of the four composition variables constant. If one wishes to retain T as a variable, it is convenient to represent the phase behavior in an upright pseudoternary phase prism with T as ordinate and the triangle (A + E)-B-(C D) as base, with constant 6 and t, as shown on Figure 1. The phase behavior may then be studied by determining the phase diagrams along either horizontal (isothermal) or vertical (e.g., at constant a or y) sections through the phase prism. In order to obtain an overview over the dependence of the phase behavior on 6 (at constant e ) , one may cut vertical sections through the prism at constant a and then arrange these sections in a rectangular coordinate system with T as ordinate and y and 6 as abcissas, as shown schematically in Figure 2. Since the phase boundaries at that point at which the three-phase body touches the homogeneous solution resemble the shape of an XLwe shall denote it by X and characterize it by its temperature T and the mass fraction 7 of the amphiphile mixture in the system. Both T and 7 depend on the fraction a between brine and oil, as well as on the pressure. Isothermal sections through this T-7-13 space will then yield the positions and extensions of the (isothermal) three-phase regions as well as the location of point X at the considered temperature and that particular value of E . At constant e , the T-7-6 space is bound by the two quaternary systems AB-C-E at 6 = 0 and A-B-D-E at 6 = 100 wt %. The essential properties of the three-phase bodies in the system A-B-C-E can be considered as being clarified.’ If one characterizes the oils (within a homologues series) by their carbon number k and chooses as nonionic amphiphiles n-alkylpolyglycol ethers C,E,, one finds the following qualitative rules: (1) For a given CiE, both T and 7 increase with increasing k .
+ +
+
+
E
= constant
Figure 2. T y - 6 space for representing the dependence of the phase behavior of quinary systems on 6 at constant c (schematical). a is the weight percentage of oil in the mixture of oil and brine, y the weight percentage of both amphiphiles in the system, 8 the weight percentage of the ionic amphiphile in the mixture of the two amphiphiles and t the
brine concentration.
(2) For a given B, both and 9 decrease with increasing i (at constant j ) but increase with incretsing j (at constant i ) . (3) For given B and given CiE,. T rises, whereas 7 decreases when adding small amounts of D. (4) For given B and given C,E,, drops when adding small amounts of E. 7,on the other hand, increases with short-chain C,EJ but decreases with long-chain CiEJ. (5) The effect of the pre_sure is opposite to that of E, Le., increasing pressure makes T rise. The phase behavior of mixtures of oils or amphiphiles appears to be determined essentially by the behavior of the major component, so that the above rules may also be applied to simple multicomponent systems. With respect to the quaternary system A-B-D-E further research is required, although studies by Kunieda and Shincda’ as well as by us8 on systems with anionic detergents with branched alkyl chains (like AOT) permit some preliminary predictions with respect to the properties of their three-phase bodies, namely that they appear to be antagonistic to those of systems with nonionic amphiphiles. (1) In the system A-B-D-E, the three-phase bodies drop temperaturewise with increasing carbon number k of the oil. (2) For a given B, the three-phase bodies rise temperaturewise with increasing length of the alkyl chains of D. (3) For a given B and D, the three-phase bodies rise and widen with increasing t. (4) With respect to the sequence of phases with rising temperature, the system A-B-C-E shows the sequence 2-3-2 (the bar denoting in which of the two phases the amphiphile is mainly dissolved6) whereas the system A-B-D-E shows the sequence 2-3-2. (5) Like in A-B-C-E systems, the effect of pressure is opposite to that of E, Le., increasing the pressure makes the three-phase bodies drop temperaturewise. Now let us assume that (at fixed E ) system A-B-C-E (6 = 0 wt %) shows a three-phase body at some mean temperature To between the melting and boiling point of the mixture, and that > system A-B-D-E (6 = 100 wt %) shows such a body at Tlo0 To. If one adds some D to system A-B-C-E, that is, if one increases 6 from 0 wt %, the position and shape of the three-phase body will change. The same will happen if one adds some C to system A-B-D-E, that is, decreases 6 from 100 wt %. Experience ( 6 ) Knickerbocker, B. M.; Pesheck, C. V.;Scriven, L. E.; Davis, H. T. J . Phys. Chem. 1979,83, 1984. ( 7 ) Kunieda, H.; Shinoda, K. J . Colloid Interface Sci. 1979, 70, 577. 1980, 75., 601. . .
~
(8) Kahlweit, M.; Strey, R. J . Phys. Chem. 1986, 90, 5239.
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 1555
Phase Behavior of Quinary Systems
100
80 6
I
T
t
@@fw 6o
40
00
2
\
Y
\
Ii
0
700
/
20
a =constant E = constant
0
0
20
60
40
Figure 3. Isothermal sections through T-7-6 space for representing the
positions and extensions of the three-phase regions as well as the % points for a quinary system at constant E (schematic). shows that these bodies may either rise or drop temperaturewise, depending on the nature of the components and, in particular, on the brine concentration e. If one chooses low brine concentrations, the A-B-C-E body rises rather steeply with increasing 6, whereas the A-B-D-E body drops steeply with decreasing 6. In that case the two bodies do not meet but pass each other at some intermediate value of 6. An isothermal section through TT-6 space at some temperature between To and Tlo0 then shows two three-phase regions, one a t low 6 evolving from the A-B-C-E system, the other one a t high 6 evolving from the A-B-D-E system. Such a section is shown schematically in Figure 3. The vertical plane in front shows the section (at constant a)through the phase prism of system A-B-C-E, that in the rear that through the phase prism of system A-B-D-E. The horizontal plane shows the isothermal sec_tionthrough the two three-phase bodies, each of them with an X point. Also shown is the sequence of phases as one proceeds from the two-phase region 2 below the three-phase body of system A-B-C-E to the 5 region above that body, into TT-6 space where it changes to 2 behind the first three-phase region, to change again to 2 behind the second three-phase region , to, finally, end as 2 above the three-phase body of system A-BD-E. Since the phase behavior of the quinary system depends on the nature of all components as well as on the particular value of E at which it is studied, one may find various types of such sections with various phase sequences. In order to demonstrate that one can actually find such a section as shown schematically on Figure 3 we present in Figure 4 a section at 30 OC through the T-7-6 space of the system H20n-decane-C4El-AOT-NaC1, determined at E = 1 from 15 vertical sections through the corresponding phase prisms at a = 50 wt %, varying 6 between 0 and 100 wt %. The vertical section through the A-B-C-E system (6 = 0 wt %) looks similar to that shown on top of Figure 3 in ref 9, with a somewhat lower temperature a t 30 "C due to the addition of NaCl (we emphasize that is not identical with T, since the latterjs defined9 as T 1 (Tu T1)/2being independent of cy, whereas T rises from TIto Tuwith increasing a). The vertical section through the A-B-?E system, on the other hand, is s h o y on Figure 4 in ref 8 with T = 62 OC. At 30 OC, one is thus a t T of the 6 = 0 wt % body, but still well below the 6 = 100 wt % body. Accordingly, the three-phase region at low 6 is still connected to the 6 = 0 wt % side, whereas the region a t high 6 has disconnected from the 6 = 100 wt % side. Upon application, the positions and extensions of the isothermal three-phase regions are presumably of less interest than the lo-
+
( 9 ) Kahlweit, M.;
Strey, R.; Firman, P. J. Phys. Chem. 1986, 90, 671.
80
100
-Y Figure 4. Isothermal section through T-4
space for the system HzOn-decane-C4E,-AOT-NaC1 at 30 OC, a = 50 wt %, and E = 1 wt %.
, 1
60
I
1
-A
f
nonionic branch
[ionic
t
2o 0' 0
branch I
I
20
40
I
I
60
80
I
I
1 I
100
- 6 I
ionic branch
6
t
80 60
20 0
0
20
40
--v
60
80
100
(top) and of 7 (bottom) vs. 6 for the system H20-n-decane-C4EI-AOT-NaCl at a = 50 wt 3'6 and c = 1 wt %. Figure 5. Trajectories of
cations of the points where one finds the highest mutual solubility between H 2 0 and oil combined with the lowest interfacial tensions. Since each vertical section through a phase prism_yields, in principle, such a point (see Figure 2), one may tracejhe X points in TT-6 space. On top of Figure 5 we have plotted T (projected onto the T-6 plane at y = 0 wt %) and on bottom ;F. (projected onto the base of the T-y-6 space) vs. 6 for this particular system
1556 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
\
f
6~301
30
0
10
30
20
LO
50
- Y
r
80 7
1
I
6=70
1
[“CI . : 0 1
t 20 I-
-1
I
O L
0
10
20
30
LO
50
Figure 6. Vertical sections through the phase prism at 6 = 30 wt % (top) and 6 = 70 wt % (bottom) of the system H,0-n-decane-C4E,-AOTNaCl at 01 = 50 wt % and c = 1 wt %.
(at a = 50 wt % and t = 1 wt %). The “nonionic branch” evolving from the A-B-C-E system at 6 = 0 wt % ascends temperaturewise to rise above the boiling point at about 6 5 60 wt %, whereas the “ionic branch” evolving from the A-B-D-E system at 6 = 100 wt % descends to drop below the melting point at about 6 k 60 wt %. 4, on the other hand, decreases monotonically fEom 6 = 0 to 6 = 100 wt %. As a consequence, one finds two X points at 30 “C, as can also be seen on Figure 4. In order demonstrate the existence of the two branches, we have, in Figure 6, reproduced as examples two of the vertical sections through the phase prism, the upper one at 6 = 30 wt %, the lower one at 6 = 70 wt %. The lower boundary of the three-phase body of the nonionic branch at 6 = 30 wt % lies above 30 “ C so that it does not show up on the isothermal section in Figure 4. At very low y, however, one observes the steepjy rising “head” of the three-phase body of the ionic branch, the X point of which appears to lie below the melting point. Accordingly, one finds in Figure 4 a rather narrow three-phase region at low y with a wide twophase region behind. The three-phase body at 6 = 70_ wt %, on the other hand, belongs to the ionic branch, with its X point at = 50.5 O C , whereas the three-phase body of the nonionic branch has apparently disappeared above the boiling point. Close to 6 = 60 wt %, the vertical sections through the phase prism show rather complex phase diagrams. One finds two three-phase bodies. One-belonging to the nonionic brancha t high temperatures with point X apparently above the boiling point, and a second one-belonging to the ionic branch- at low temperatures with the point X apparently below the melting point. These phase diagrams depend very sensitively on t. If one increases t from 1 to 1.5 wt %, the two boiies seem to merge without, however, showing either one of the X points. It is at this fraction 6 where one finds at a y a little higher than 7 a practically temperature-independent narrow homogeneous region that can be visualized as an almost vertical channel on top of Figure 5 at 6 60 wt % and 7 = 20 wt 5%. We presume this to be the
Kahlweit and Strey explanation for the phase diagram presented by Kunieda et al. on Figure 11 in ref 4 for the system H,O-isooctane-ClzE,AOT-NaCl at a = 50 wt %, y = 7 wt %, 6 i= 68 wt %, and t = 1 wt %. A detailed study of these phase diagrams is in progress and will be published in a forthcoming paper. This particular system thus -bows a “broken” trajectory at a = 50 wt % and t = 1 wt %. Whether or not connected trajectories (at constant t) do exist in view of the antagonistic phase behavior of nonionic and ionic amphiphiles (see Figure 3) remains to be studied. As important, however, is the dependence of the trajectories on the nature of the two amphiphiles C and D. If, for example, one chooses C more hydrophobic than C4El,e.g., C4E, (1-butanol), the three-phase body at 6 = 0 wt %, with decane as oil, lies below the melting point as can be seen on top of Figure 4 in ref 9, to rise above the melting point only after addition of a sufficient amount of D. Consequently, the X trajectory of the nonionic branch will enter the T-y-6 space from below the melting point at 6 > 0 wt %. If, on the other hand, one chooses C more hydrophilic than C4E1,e.g., C4E3,the entire nonionic branch will lie above the boiling point, so that, with AOT as D, one will find the ionic branch only. We have, therefore, started a systematic study of the phase behavior of such quinary systems with various combinations of C and D. Upon application one uses, in general, single-chain amphiphiles. With single-chain ionic amphiphiles, however, it appears difficult to find a three-phase body at 6 = 100 wt %, since these amphiphiles are, in general, rather hydrophilic so that one expects the three-phase bodies with (standard) single-chain ionic amphiphiles to appear above the melting point-if at all-only at high brine concentrations.
Microemulsions and Tricritical Line Once a trajectory has been determined for a certain system, one may choose a value of y a little higher than 4 to find a narrow channel of an isotropic homogeneous solution just behind the trajectory in T-7-6 space that permits a study of the properties of the microemulsion as they change with 6 at constant t. Since the experimental determination of the entire vertical section through the phase prism may be rather time consuming, in particular, with systems with slowly separatkg phases, one may restrict oneself to the determination of point X. This can be done by preparing a mixture of brine and oil at a certain value of a and t and then adding a mixture of the nonionic and the ionic amphiphile at a certain 6. If y is appropriately chosen, one finds with rising temperatureJhe phase sequence 2-1-2 which yields a pair of points behind X (see Figure 2). By stepwise addition of corresponding masses of brine and oil, the homogeneous interval narrows until one finds the sequence 2-3-2 which yields the first pair of points ahetd of X. The determination of a few such pairs of ppints close to X permits in sufficient precision the evaluation of Tan$ 4. The X tracjectoeies may, furthermore, be used as guides to the trajectory of the tricritical line in T-6-t space. As we have suggested in a recently published paper,’ the phase behavior of a quinary system appears to evolve from a tricritical line that spans across T - 6 t space as shown schematically in Figure 7, taken from ref 8. Each point on this tricritical line is defined by a certain set of T, a, y,6, and t. If represented in T-6-t space, it is assumed that a and y vary continuously as one proceeds along that line_. To trace its trajectory one may, accordingly, determine the X trajectories a function of E and then represent them in T-6-6 space assuming 3 to vary continuously along them. In this representation the X trajectories will shape a surface with the tricritical line as its edge at low t. When this edge is approached by gradually decreasing t, the shrinking three-phase bodies will eventually move out of the a = 50 wt % sections so that close to the tricritical line one has, in addition, to adjust a . One can, however, not exclude the possibility that the projection of the tricriiical line onto the T-d plane at t = 0 shows a shape similar to the X trajectory shown on top of Figure 5, except that it may not start at 6 = 0 but enters the 1-bar space at tcp (2) on Figure 7 . In other words, it may very well be that the nonionic branch of the tricritical line rises above the boiling point at some intermediate value of 6, whereas
J. Phys. Chem. 1987, 91, 1557-1561
1557
three-phase bodies in quinary systems by arranging vertical sections through the pseudoternary phase prism at constant oil/brine ratio and constant brine concentration in T-y-6 space, where y is the weight percentage of the nonionic and the ionic detergent in the system, and 6 is that of the ionic amphiphile in the mixture of the two amphiphiles. These trajectories vary strongly with the chemical nature of both amphiphiles as well as with the brine concentration. In the particular system chosen as a representative example, one finds a nonionic and an ionic branch of the trajectory which pass each other at an intermediate value of 6, thus dividing the phase behavior of the system into one part that is dominated by the nonionic, and one that is dominated by the ionic detergent. If, for a given oil, the temperature and the brine concentration are given, one may cut an isothermal section through the corresponding T-7-6 space a t that temperature in order to find the optimum ratio 6 for this particular combination of detergents which yields the highest mutual solubility between brine and oil combined with the lowest interfacial tensions. Once a trajectory has been determined, it, furthermore, permits a study of the properties of the microemulsion as they change with 6. Last but not least, the trajectories may be used as guides for tracing the tricritical line. Figure 7. Trajectory of the tricritical line in a quinary system in T-6-E space, taken from ref 8 (schematic).
the ionic branch enters the l-bar space from below the melting point at some higher value of 6.
Acknowledgment. We are indebted to Mrs. H. Frahm for measuring the vertical sections through the phase prisms and to the German Federal Ministry for Research and Technology (BMFT) for financial support.
Conclusion A representation is suggested for the trajectories of the
n-decane, 124-18-5.
Registry No. AOT, 577-1 1-7; C4E1,11 1-76-2; NaCl, 7647-14-5;
Experimental Observations of Complex Dynamics in a New Bromate Oscillator: The Bromate-Thiocyanate Reaction in a CSTR Reuben H. Simoyi* Department of Chemistry, University of Zimbabwe, Mount Pleasant, Zimbabwe (Received: February 28, 1986)
In a continuously stirred tank reactor (CSTR) the reaction between bromate and thiocyanate in acidic medium (HC104) exhibits sustained oscillations in the potential of a platinum redox over a wide range of flow rates and input concentrations. In closed system environments and in excess bromate concentrations the stoichiometry of the reaction is 6Br03- + 5SCN+ 2H20 3Br2 + 5 s 0 d 2 - + 5CN- + 4H'. The production of bromine is preceded by a finite induction period. On varying the dynamical variable of the flow rate of reactants into the CSTR at fixed input concentrations, one observes various oscillatory states. The bifurcation sequence is highlighted by persistent quasi-periodic behavior.
-
Introduction The number of chemical oscillators discovered in the past 5 years far outstrips the number of all the oscillators known before 1980.' This came directly on the heels of the discovery of a plausible algorithm for the systematic design of chemical oscillators2 The most significant discovery of this algorithm is the subset of chlorite-based oscillators? Among the chlorite oscillators were two-component, uncatalyzed oscillators such as the chloriteiodide4 and chlorite-thiosulfate system^.^ Despite the apparent simplicity of the two-component oscillators,the chloritethiosulfate system displays a rich and varied dynamical behavior by altering only the dynamical variable of flow rate of reactants into the (1) Epstein, I. R. J. Phys. Chem. 1984, 88, 187-198. (2) Epstein, I. R. In Chemical Instabilities; Nicolis, G., Baras, F., Eds.; D. Reidel: Dordrecht, Holland, 1984; pp 3-18. (3) Orbfin, M.; Dateo, C.; De Kepper, P.; Epstein, I. R. J. Am. Chem. SOC. 1982,104, 5911-5918.
(4) Dateo, C.; Orbfin, M.; De Kepper, P.; Epstein, I. R. J. Am. Chem. SOC.
1982, 104, 504-509.
(5) Orbfin, M.; De Kepper, P.; Epstein, I. R. J . Phys. Chem. 1982, 86, 43 1-433.
0022-3654/87/2091-1557$01.50/0
reactor. Other interesting dynamical behavior has been observed in the chlorite-thiourea reaction in both batch and continuously stirred tank reactor (CSTR) conditions.6 Bromate-driven oscillators are by far the most thoroughly studied of all known oscillator^,^ especially the Belousov-Zhabotinskii reaction and its variations.* Until recently, however, uncatalyzed two-component bromate oscillators were unknown. A few two-component bromate oscillators have now been discovered, and they resemble chlorite-based oscillators more than Using the the prototype Belousov-Z ha bo tins kii systems .9 chlorite-iodide reactionlo and the bromate-iodide reaction9 as typical examples of these subclasses of chemical oscillators, one notices that in both cases (a) oscillations are only possible when the oxidant is in stoichiometric excess,ll (b) more than one (6) Alamgir, M.; Epstein, I. R. Znt. J. Chem. Kinet. 1985, 17, 429-439. ( 7 ) Noyes, R. M. J. Am. Chem. SOC.1980, 102,4644-4649. !8) (a) Belousov, B. P. Sb. Ref. Radiat. Med. 1958 1959, 145. (b) Zhabotmskii, A. M. Dokl. Akad. Nauk SSSR 1959, 157, 392. (9) Alamgir, M.; De Kepper, P.; Orbfin, M.; Epstein, I. R. J. Am. Chem. SOC.1983, 105, 2641-2643. (10) Kern, D. M.; Kim, C-H. J . Am. Chem. SOC.1965,87, 5309-5313.
0 1987 American Chemical Society
