J. Phys. Chem. 1994,98, 1449-1453
1449
Behavior of the Belousov-Zhabotinskii Oscillator in Reverse Micelles of AOT in Octane Vladimir K. Vanag' and Dmitrii V. Boulanov Department of Photochemistry, N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 11 7421, Novatorov Str., 7A, Moscow, Russia Received: August 25, 1993; In Final Form: November 2, 1993"
Ferroin-catalyzed Belousov-Zhabotinskii (BZ) oscillations proceeding in water-in-oil microemulsions made of anionic surfactant have been studied under batch conditions. It was found experimentally that in the o-C, plane, where w = [HzO]/[surfactant] and C, is the concentration of the droplets of a reverse microemulsion, there exists a limited oscillatory region a t the constant chemical composition of the oscillatory BZ system. This phenomenon is theoretically conceptualized.
Introduction A novel promising trend in the field of chemical nonlinear dynamic systems is an investigation of oscillatory chemical reactions proceeding in interacting microvolumes (MV) such as droplets of reverse microemulsionsl-4 or vesicles. In nature, a suspension of living cells is a prototype of such a system. The behavior of such a complex, spatially and temporally organized dynamic system must be notably dependent on the MV linear size. This is caused by the effect of the MV size on the rate of matter exchange between MVs,536 on the choice of the reaction p a t h ~ a yand , ~ on the magnitude of substance concentration fluctuations.' The Belousov-Zhabotinskii (BZ) reaction839 is a convenient model reaction for studying dynamic systems in interacting MVs, while reverse micelles of the surfactant bis(2-ethylhexyl) sodium sulfosuccinate (AOT) in saturated hydrocarbons are the most widely-known system of MVs offering variation in droplet size.I0 Balasubramanian and Rodleyl were the first to observe the oscillations of the BZ reaction in reverse micelles of AOT in isooctane. The reaction was catalyzed by Mn2+ ions in the presence of a small amount of tris( 1,lo-phenanthroline)iron(II), called ferroin, Fe(~hen)3~+. The BZ system in AOT reverse micelles (which will be hereafter referred to as BZ(RM) following Gonda and Rodley2) is convenient for two reasons: (i) its mechanism is well-known" and (ii) its components do not interact with AOT molecules. At least no bromination and destruction of AOT molecules were observed.2 At prsent there exist no works studying the effects of the linear size of a MV and the rate of matter exchange between MVs on the behavior of dynamical systems incorporated in these MVs. Gonda and Rodley have been studying only the effect of microemulsion droplet concentration on the period of the BZ (RM) reaction oscillations.2 They have discovered that a dilution 1.5 times the emulsion with the size of the droplets remaining constant does not lead to any noticeable changes, provided the chemical composition of the mixture remains unchanged. In the given work we pay special attention to the dependence of the BZ(RM) system behavior on the linear size and concentration of droplets a t the constant chemical composition of the reaction mixture, the concentration of the droplets being varied within the broad range, from 2 X 10-5 M to 5 X l e 3 M, and the radius of a droplet water core bing varied from 8 to 43 A. In the present work we use ferroin as a catalyst and follow the reaction spectrophotometrically. Experimental Section The chemicals, namely, H N 0 3(Reachim), KBr03 (Reachim), malonic acid (MA) (Sojuzchimexport), FeSOc7H2O (Reachim), 0
Abstract published in Advance ACS Abstracts, January 1 , 1994.
1,lO-pheanthroline (Chemapol), H2SO4 (Reachim), AOT (Serva), and octane (Reachim) were of analytical grade, and all except octane were used without further purification. Before using, octane was purified by intensive stirring with concentrated sulfuric acid for 2-3 h. Ferroin was obtained by mixing the solutions of 1,lO-phenanthrolineand FeS04 in a 3:l molar ratio. The BZ(RM) system was prepared by adding a small volume V, (V, zz 0.1-0.3 mL) of an aqueous oscillating BZ mixture to a volume Veil of solution of AOT in octane (Veil zz 20 mL) as soon as the oscillations started in water (1-2 min after mixing). The following BZ composition was used throughout all the experiments: 0.8 M H N 0 3 , 0.6 M KBr03, 0.12 M MA, 2.67 X 10-3 M Fe(~hen)3~+. The employment of nitric acid instead of the usual H2SO4 or HC104 is explained by the fact that in this case reverse micelles of AOT in octane can be more easily obtained. The ratio r V,/Vo, where V, = Veil + V, is the total volume of the system, was varied from 2 X lo-' to 2 X 1t2, o = [ H20] / [AOT] from 4.6 to 30.0. The radius of the micellar water core R , and the micelle concentration C, were calculated by the following formula~:~96+12
where V H ~=O29.0 A3 is the molecular volume of water, VN,zz 40 A3is the apparent molecular volume of the sodium ion, VHNO, = 69.15 A3 is the molecular volume of HNO3, WHNO~= [HN03] / [AOT], A, is the cross-section area of the AOT molecule (equal to 67.8 A2)13 and V, = 47rRW3/3is the volume of the micellar water core. Equation 2 follows from the fact that V,/V,,, and C,VdV, are the total number of micelles in the volume V,. The reaction was run in a 20-mL cylindrical Teflon cell with flat silica windows pressed in on four sides, the optical path length, 1, of the cell being 3 cm. Upon adding the BZ mixture to AOT reverse micelles, the system was thoroughly mixed with a Tefloncoated magnetic stir bar at 5-10 Hz and bubbled through with Ar for 5-10 min ( ~ 1 0 0mL/min). Then it was hermetically sealed with a Teflon plug. The stirring with a reduced rate was continued during the experiments. After about 30-60 min of stirring, the system was completely clarified, which was followed spectrophotometrically. The reaction was monitored at the wavelength X = 5 10 nm by ferroin concentration using a spectrophotometrical device described in detail in ref 14, the extinction coefficient value being taken as €510 = 11 700 M-1 cm-l.I5 Reference aqueous oscillations were monitored at X = 630 nm by ferriin concentration, [Fe(~hen)~3+], €630 being 620 M-I cm-I. In this case the reaction was run in a
0022-365419412098- 1449%04.50/0 0 1994 American Chemical Society
Vanag and Boulanov
1450 The Journal of Physical Chemistry, Vol. 98, No. 5, 1994
hD 1
I
1
2
3
4 5 Time (hr)
6
7
Figure 1. Kinetics of the BZ reaction in AOT reverse micelles in octane at w = 10 for (a) C, = 2.4 X 10-4 M, r = 2.25 X l e 3 ; (b) C, = 3.76 X lo4 M, r = 3.53 X lP3; and (c) C, = 4.2 X 10-4 M, r = 3.94 X l P 3 , The reagent concentrations are given in the text. The insert shows a fragment of oscillations in the reference aqueous BZ system.
1
2
3
4 5 Time ( h r )
6
7
Figure 2. Kinetics of the BZ reaction in AOT reverse micelles in octane at w = 15.07 for (a) C, = 0.93 X 10-4 M, r = 2.63 X l P 3 ; (b) C, = 2.4 X 10-4 M, r = 6.7 X l P 3 ; (c) C, = 4.3 X 10-4 M, r = 12.2 X le3. The reagent concentrations are given in the text.
standard spectrophotometrical cell with 1 = 1 cm. The reactions were carried out at 22 f 1 OC. Results and Discussion The most typical kinetic curves of the BZ(RM) reaction observed in 1 h after the reaction onset are presented in Figures 1 and 2 for w = 10 and 15, respectively. The existence of an oscillatory region in the w-C, plane can be seen in Figure 3. As soon as the aqueous BZ mixture was added to the solution of AOT in octane, the catalyst in all the experiments was transformed into the reduced form. Then, over the course of 1-2 h an autocatalytic ferroin ferriin transition occurred, which in some cases can be clearly recorded (see curves a and c in Figure 1). In special experiments we recorded the autocatalytic transition and found that the exponent y of the ferriin exponential growth at w = constant was independent of micelle concentration ranging from 2 X 10-3 to 10-4 M and roughly equal to 0.1 s-1 for w = 10-15. At a relatively small concentration of micelles at r d 2.7 X 10-3, no oscillations appear for 6-8 h (see, for example, curve a in Figures 1 and 2). At higher C, a t r > 3 X l P 3 , 1-3 h after the ferroin ferriin transition, oscillations can be observed for the w values ranging from 10 to 17. At w < 8.5 and w 2 20, no oscillations occur either at high or at low C,. Thecurves recorded in these cases are analogous to the curve a in Figures 1 or 2. Figure 2 shows that as C, increases, the oscillation amplitude grows nonlinearly: the ratio AAmax/Aozz 13% for C, = 2.4 X loA M (curve b), while for C, = 4.3 X 10-4 M (curvec) it equals
-
-
0
d
Figure 3. Experimentallyobtained phasediagramfor the BZ(RM) system in the w-C, plane at the constant chemical composition of the oscillatory Dashed aqueous BZ reaction: damped oscillations (*),steady state (0). line corresponds to the condition r = 6.7 X l t 3 ; inclined solid line, r = 2.7 X l t 3 , vertical solid lines, w = 9 and w = 19. The reagent concentrations are given in the text.
39% (AAmax is the maximum oscillation amplitude, A , = [Z]&,,l, [Z],” is the initial concentration of Fe(phen)++ in the total volume Vo). That is, with increasing C ,, a portion of the catalyst which turns in one oscillation cycle from the reduced form to the oxidized one and vice versa, AAi/Ao,grows, while for the reference oscillations in water (see the insert in Figure 1) AAJA, = 3.7%, where AAi is the amplitude of the i-th oscillation. The smaller the ratio AAJA,, the shorter the oscillation period (curve c in Figure 2). The number of oscillation cycles n in the BZ(RM) system varies from 10 to 25, and the period T , on the average, from 8 to 15 min, while in the reference aqueous BZ system n 60 and T z 60-62.5 s. Most likely, the number of cycles n, both in the B Z ( R M ) and in the reference aqueous B Z system, is determined by bromate depletion, since the value of the [BrO> 1 becomes valid, instead of the notion of the concentration of droplets containing a single molecule A, [M(A)], the notion of concentration of A molecules in the aqueous phase,
+
M ( @ - 1)AYXZ’)
+ 2M(*) F? M(n’AY) + M(m’AX) + km
=
-
M(Z’AZ’) (1 IC) Symbol M@AXZ) means that a micelle containsp molecules of A, one molecule of X, and one molecule of Z, etc. (n,m, p, 1, 1’, n’, and m’are integers: n m = p 1. M(*) is an arbitrary micelle. If we drop, for the sake of simplicity, symbol A (keeping in mind that each micelle contains large enough amount of bromate molecules), pathway 11 in shorthand form can be represented as follows:
+
+
+
-
+
+
M(X) M ( Z ) M ( Y ) M ( X ) M(Z’) (12) Canceling M(X) both in the left and in the right side of eq 12, we see that eq 12 is equivalent to eq 10. This route can be regarded as the transformation of micelles M(Z) intomicelles M(Y) and M(Z’) catalyzed by micelles M(X). Asaconsequence, theratesof [M(Y)] and [M(Z)] concentration changes prove to be dependent on the product [M(Z)] [M(X)], which is not met in the rate equations derived from the classical Field-Koros-Noyes (FKN) mechanism.llJ8 For example, for d[M(Y)]/dt we get the following rate equation: d[M(Y)]/dt = 2Wl- 2W-l+ L
+ ...
(13) where L = ky[A],(2@/(2kF k:))[M(Z)][M(X)]/C, is the rate of reaction 11 or 12. According to estimations,4 at w > 20-30, when the ratio L / W l 3 1, where L/W1 = V”A[Z]~F(~), and F(r) = ((k_m,+ kexr)/kexr)(2kF/(2~+ k:)), the member L may be a determining factor in the equations for d[M(Y)]/dt andd[M(Z)]/dt. Togetherwiththedependenceof theelementary constants k y on V, and consequently on w , the reported mechanism explains why, following the line r = constant, e.g., r = 6.67 X (dashed line in Figure 3), we can observe the
+
1452 The Journal of Physical Chemistry, Vol. 98, No. 5, 1994
transition between oscillatory and stationary states of the system twice: at w = 9 and w = 19. It is noteworthy that the probability of reaction 11 depends not only on the possible occurrence of all three molecules A, X, and Z in one micelle at a time but also on the relationship between the rate of intramicellar reaction M(YYZ) M(YXZ') and the rate of intermicellar matter exchange in the course of which molecules Y and Z move apart to different micelles. If
-
2k?l( VmNA) > k,xCm (14) then reaction 11 is highly probable. For k: z 109-107 M-1 s-1, k,, z 10' M-' s-l and r V,NAC, z 0.01, relation 14 should hold true. The validity of relation 14 proves to be strongly dependent on the high value of the constant k y , which is typical of the reaction with ferroin. When Ce(II1) is used as a catalyst, relation 14 may not assert and pathway 11 will be hardly probable. It is interesting to follow the modification of the reaction mechanism under the further growth of micelles. If w is increased to 55-70, which corresponds to R , g 80-110 A, then for the value [Z], = 2.67 X 10-3 M used the inequality nZ 3 1 becomes true. In this case the probability P (32) of finding not less then 2 molecules of a catalyst in one micelle becomes high enough. Thus, for example, for nz = 2 we have P (32) = 1 - P ( 0 ) - P( 1) 0.6, where P ( k ) = nk exp(-nz)/k! is the Poisson distribution equation. P(k) is the probability that a droplet contains k species whose average occupancy is nz. In this case we should take into account the reaction mechanism involving micelles with one molecule of X and at least two molecules of Z. Omitting for brevity the symbols for molecules A and Z', we get the following reaction scheme:
P is HOBr. According to this pathway, the autocatalytic multiplication of molecules X occurs in one micelle. However, the probability of the formation of micelles M(X) from micelles M(XX) depends on t h e relationship between t h r e e constants: k,,C,, ky/(V,NA), and k;"[A],. If the rate of intramicellar disproportion of molecules X dominates over t h e other two rates, that is, k,,C,
