J . Phys. Chem. 1990, 94, 1516-1519
1516
side of (A.6) is idependent of V. Equations A.4 and A.6 provide a parametric representation of the equilibrium sorption isotherm
with parameter (q,X). Note that, by virtue of (A.l), this parameter is the same in both phases at equilibrium. In the limit of very low pressures (Henry's law region), the above formalism simplifies substantially. Sorbate-sorbate interactions become unimportant in both phases in this limit. Equations A.5 and A.6 reduce to their ideal gas counterparts: ZIG(n,T,V) = ( ~ T ' V ) ~lexp(-@@'"'"(+)) [ d+]"
(A.8) (A.9)
-
-
As seen from (A.9), the limit P 0 necessarily implies X 0. From eq A.4 one obtains, with NA Avogadro's number, pz the density of the zeolite crystal, Ma the molecular weight of the sorbate molecule, and Kh Henry's constant in weight sorbate per weight zeolite per pressure
lexp{-@[@z(ro,9.+)+
P
dro d* d+
8?r2Vslexp{-b@int"a(+)) d+
where f,,S(rOi.Wi&) represents the integrand appearing in the definition of P(n,,T,Vs) (see eq A.2). In the Henry's law region (X-+O), under conditions of equilibrium between gas and solid, eq A. 11 reduces to
The probability density appearing in the integral is thus fsl(ro,~,B)/zs(l,T,Vs). It is this function that is used in the Metropolis Monte Carlo calculation of molecular conformation and siting within the zeolite pore system. The isosteric heat of sorption is defined as a difference in partial molar enthalpies: Qst = -E (A.13) If the pressure is sufficiently low to warrant using the ideal gas equation of state in the gas phase, and if the partial molar volume of sorbate in the solid phase is considered negligible in comparison to the gaseous molar volume, one is led, by straightforward thermodynamic arguments, from eq A.13 to the Clausius-Clapeyron relation?
(A.lO)
For a solid phase of macroscopic dimensions, and in the absence of lattice imperfections and surface anisotropies, the ratio p (1,T, Vs)/ Vs remains the same if the integration over ro contained in the configurational integral is confined to the asymmetric unit of the zeolite unit cell. For the orthorhombic phase of silicalite, the three applicable symmetry operators are a mirror plane, a screw axis, and a point of inversion. By taking advantage of these symmetry operators, the relevant integration volume, Vs, is reduced to one-eighth of the unit cell. Equilibrium properties, such as sorbate conformation, are computed by averaging over the property in the distribution of the ensemble of interest. Let g(ro,*,+) be any function of the configuration of a molecule. The average value of the quantity g within the solid phase under given (p,T,V,) is, by definition
(A.14) By combining our grand canonical formulation eq A.4 and A.9 with eq A.14, it is possible to derive the following relation in the limit of very low sorbate coverages: (A. 15) In view of eq A.10, eq A.15 can readily be proved consistent with the following well-known thermodynamic relation, obtained from A.14 in the limit P 0:
-
(A.16) Registry No. SO2, 7631-86-9;methane, 74-82-8; butane, 106-97-8; hexane, 110-54-3; 2-methylpentane, 107-83-5;3-methylpentane,96-14-0.
Oscillatory Behavior of a Beiousov-Zhabotinskii Reverse Micelle System I. Gonda* and G . A. Rodley Department of Pharmacy, University of Sydney, Sydney, NSW 2006, Australia (Received: April 19, 1989; In Final Form: August 29, 1989) A previously reported reverse micelle system, formed by the incorporation of the components of the Belousov-Zhabotinskii (B-Z) chemical oscillator into a bis(2-ethylhexyl) sodium sulfosuccinate (A0T)-isooctane solution, has been studied in greater detail. It has been established that the AOT does not enter into chemical reaction with the B-Z components. This has enabled variations in features of the batch oscillation patterns to be directly interpreted in terms of perturbing influences. Studies have been made of the effects of varying the composition, diluting the aqueous or micelle components, and adding chloride to the system. The results show that the chemical integrity of the B-Z aqueous oscillator is retained on encapsulation into the reverse micelle system but with differences that may be attributed to sequestering of the B-Z reactants and products. Introduction We recently reported the preparation and properties of a reverse micelle-chemical oscillator system.I This displays a range of ( I ) Balasubramanian, D.; Rodley, G. A. J . Phys. Chem. 1988,92,5995.
0022-3654/90/2094-1516$02.50/0
interesting properties that may be related to the effect of combining spatial chemical ordering (micellar structure) with ordering of the temporal type (a chemical oscillator). The system consisted of the surfactant bis(2-ethylhexyl) sodium sulfosuccinate (AOT) in bulk isooctane combined with an aqueous mixture of Belou0 1990 American Chemical Society
Oscillatory Behavior of a B-Z Reverse Micelle System sov-Zhabotinskii (B-Z) components to give a clear reverse micelle product (to be referred to as B-Z(RM)). This report contains the results of further studies of this system which clarify certain features. Most notably it has now been established that the AOT surfactant does not enter into chemical reaction with any of the B-Z reagents. This enables features of the overall oscillatory behavior to be analyzed directly in terms of the physical effects of containing a chemical oscillator within defined water regions. Conductivity studies show that the B-Z(RM) system exists within a conducting region of the reverse micelle phase diagram.2 Different models have been proposed for reverse micelle regionsM Eicke et aL3v4have described the conductivity of AOT-waterisooctane microemulsions in terms of charge fluctuation of defined water pool structures. Ninham and co-workerssy6 have developed a model, based on geometrical considerations, of an extended network of interconnected water cylinders, which also explains the conductivity feature. A recent ESR study of the AOTwater-isooctane system’ could not distinguish “closed water droplet” and “network of channels” models from each other. For the purpose of interpreting the results presented here a generalized “linked water pool” description is used. The B-Z(RM) oscillator-micelle system is considered as an extended array of microoscillators confined to water pool regions but directly linked to each other. The linking may be regarded to occur either through fluctuations or more specifically via connecting water channels. Synchronization of the microoscillators may occur, due to the linking effect, to give bulk oscillations, as observed. As the overall qualitative reaction features of the B-Z micelle-containing oscillator appear to be the same as those for the bulk water system, it is of interest to identify what new features containment produces. The latter have been probed by perturbing the B-Z(RM) system in a variety of ways such as dilution and the addition of chloride. Of particular interest is the way in which “pseudoopen” characteristics may be achieved, akin to those exhibited by the naturally occurring glycolytic oscillator.* Experimental Section The reverse micelle Belousov-Zhabotinskii oscillators were prepared by adding a small quantity of an aqueous B-Z mixture to a solution of AOT in isooctane, as described previously.’ Oscillations in electrical potential were monitored via a pair of platinum electrodes. Unlike the earlier study’ a small quantity of benzene was added to the initial AOT/isooctane mixture as this increases water pool size.9 The solutions were stirred with a magnetic stirrer. The basic B-Z composition used throughout the study (which corresponds closely to that used for the study of spatial patterns;’O hence the use of the term “spatial” mixture) was equal quantities of (i) a 0.01 M HzS04/0.02 M MnS04.H20 solution, (ii) 0.35 M KBr03, (iii) 0.7 M malonic acid, and (iv) 1.5 M H2SO4 together with a few drops of a ferroin solution, except that on one occasion (curve a, Figure 2) a normal, aqueous oscillatory B-Z composition was used (0.1 M KBrO,, 0.2 M malonic acid, 0.8 M H2S04,and 0.005 M MnS04.H20). Clear B-Z(RM) systems were prepared by dissolving in each case 1.2 g (except that for curve e, Figure 2, the quantity was 1.3 g) of AOT in 60 mL of isooctane (containing 0.5 mL of benzene) and adding 0.75 mL of an aqueous B-Z mixture, initially with rapid stirring using a magnetic stirrer. This was then followed with a slow constant stirring rate always at the same setting to achieve (2) Chen, S.J.; Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1984,88, 1631. (3) Eicke, H.-F.; Denns, A. In Solution Chemisfryof Surfucrums; Mittal, K. L., Ed.; Plennum: New York, 1979. (4) Eicke, H.-F.; Borkovec, M.; Das-Gupta, B. J . Phys. Chem. 1989, 93, 314. (5) Chen, S.J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S.J . Phys. Chem. 1986, 90, 842. (6) Hyde, S.T.; Ninham, B.W.; Zemb, T.J . Phys. Chem. 1989,93, 1464. (7) Haering, G.; Luisi, P. L.; Hauser, H. J . Phys. Chem. 1988, 92, 3574. (8) Hess, B.; Brand, K.; Pye, K. Biochem. Biophys. Res. Commun. 1966, 23, 102. (9) Verrall, R. E.; Milioto, S.;Zana, R. J . Phys. Chem. 1988, 92, 3939. (10) Welsh, B. J.; Gomatam, J.; Burgess, A. E. Nufure (London) 1983, 304, 611.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1517 TABLE I: Concentrations of Components of B-Z Mixtures’ Used in Forming the B-Z(RM) Systems run [H,SO,] [KBrO,] [MA] [Cl-] a
0.80
0.10
0.20
b
0.37 0.30 0.33
0.09 0.07 0.08
0.17
0.29
0.07
0.37 0.30
0.09 0.14
0.14 0.17 0.14
C
d e
f g
Additionally the
0.28 0.15
0.005 0.002
B-Z mixtures contained Mn2+ and ferroin.
good reproducibility. In the case of Figure 2c, the aqueous spatial mixture used contained two aliquots of malonic acid ((iii) above) rather than one as for the basic mixture, while for curve g a double quantity of bromate (ii) was used. These are referred to as “high malonic acid” and “high bromate” systems. In the case of curve d 0.675 mL of the basic spatial B-Z mixture was used together with 0.075 mL of a chloride solution to give an overall [Cl-] = 0.005 M. For curve e 0.6 mL of the basic B-Z mixture was used and 0.15 mL of a chloride solution to give [Cl-] = 0.002 M. The overall compositions for the different systems are given in Table I. Two methods of diluting the B-Z(RM) systems, during oscillations, were used. For curves b, c, and e dilution at the points indicated (Figure 2) was carried out by removing 20 mL of the original mixture and adding 20 mL of isooctane only. For curve f the aqueous B-Z component was diluted at f (Figure 2) by the addition of 20 mL of isooctane, 0.4 g of AOT, and 0.25 mL of H 2 0 (in order to maintain the same relative concentrations of isooctane, AOT, and water). Conductivity studies were carried out by measuring the electrical resistivity of the B-Z(RM) mixtures using a high-impedance Thurlby Electronics Ltd. (Cambridge, England) Model 1905a digital multimeter. In the first study of the effect of the B-Z components on AOT, the latter was extracted after oscillations had finished, using chloroform. A second study was made in order to determine whether the AOT was hydrolyzed by the acid present in the B-Z component. A reverse micelle system was prepared with sulfuric acid alone. The molar quantity used was three times that of the normal B-Z aqueous mixture used for the B-Z(RM) systems. After the mixture was stirred for 8 h isooctane was removed by evaporation, the acid neutralized with NaOH, and the AOT extracted with chloroform. Mass spectra of the extracts and the starting material were obtained with a Finnegan 3200 series GC/MS using methane chemical ionization and direct insertion of a nickel-tipped solid probe. ‘H NMR spectra of the samples from the first study were recorded with a Bruker W M 400 MHz spectrometer. Results Two studies were made of the possible reaction of B-Z components with AOT. In the first (which was primarily a test of whether AOT became brominated) AOT was extracted and studied after B-Z(RM) oscillation. The ‘H N M R spectra for the starting AOT and extracted AOT samples were found to be the same except for diminished resolution for the latter (probably due to the paramagnetic effect of a small amount of residual MnZ+ or Fe2+/Fe3+from the B-Z reaction) and the disappearance of a broad band in the starting AOT (probably from some water associated with the original sample). The mass spectra for the corresponding samples were virtually identical with each other (Figure 1). The N M R and mass spectral results gave no indication that AOT has been brominated during the oscillations. In the second study, the mass spectrum of the product, quantitatively recovered at a level of 95%, was also indistinguishable from that of starting AOT, indicating that no degradation by acid had occurred. The conductivity study showed that the oscillations of the binary system occur within the conducting region of the reverse micelles.2 Specific conductance values obtained were of the order of f2-I as observed by Chen et aL2 Oscillations of conductivity values were also observed to occur at the times of color or electrical
1518 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
Gonda and Rodley
55
1
100
0' 0
1
2
3
4
5
6
7
8
9
TlV,E ( h i )
1
100
150
250
200
3w
MIZ (b)
Figure I . Mass spectra for starting AOT (a) and the AOT extracted with chloroform after oscillation of a B-Z(RM) system (b).
potential change. These were relatively small in magnitude, indicating that the oscillations were not associated with phase changes. The observed changes probably reflect the changes in overall ionic composition that occur during the B-Z oscillations. In a range of studies of the B-Z(RM) system different compositions were prepared and the effects of dilution and addition of chloride also investigated. Representative results are given in Figure 2. The plots are of the changes in period of oscillation with time. The results are presented in three categories. ( I ) The Effect of Composition on the Periods of Oscillation. In the initial study' a B-Z composition close to that used for nonoscillatory spatial systems'O was used for the micelle system. This gave relatively long periods (several minutes) and long-lasting oscillations (up to 14 h). By contrast it has been found here that a B-Z composition corresponding to the normal oscillatory domain gives a shorter periodshorter lived system (Figure 2a). The other plots in Figure 2 have the basic spatial B-Z composition (except that for curves c and g the compositions were modified by the addition of extra volumes of malonic acid and bromate to the initial B-Z mixture, while curves d and e represent the effect of added chloride). All of these gave relatively long periods which is consistent with the description of the bulk water spatial system as a long period oscillator." Certain details of the oscillations seem to be critically dependent on the manner in which the systems are prepared as indicated by a comparison of the unperturbed regions of the equivalent (b) and (0 systems (Figure 2). It appears that the character of the stirring (rate and duration at given speeds) has a major influence on what is obtained.I2 Induction times vary quite considerably (for curves b and f, these were just under 2 h and about 3/4 h, respectively), which also reflects the sensitivity of these systems to precise conditions of preparation. Variations for repeated preparations of the same overall B-Z (RM) composition were not investigated in detail for any of the other systems [apart from the (b)/(f) one]. ( 2 ) The Eflect of Dilution on Oscillatory Behavior. The arrows on plots in Figure 2 represent positions at which systems were diluted by removing 20 mL of the binary system and adding 20 mL of isooctane, thereby reducing the water (B-Z) plus surfactant (1 I ) Symposium of the Faraday Society. Phys. Chem. Oscillatory Phenom. 1974, No. 9 , 85. ( 1 2 ) Sevcik, B.;AdamEikovi, L . Chem. Phys. L e f f .1988, 146, 419.
Figure 2. Plots of change in period with time for various B-Z(RM) oscillators: (see Experimental Section and Table I for details). (a) Composition of B-Z components corresponding to that for normal bulk aqueous B-Z oscillator (the remaining plots have the "spatial" B-Z composition). (b) "Spatial" B-Z composition system with 2-h induction time and interrupted by dilution at b (20 mL of mixture removed and 20 mL of isooctane added). (c) 'High malonic acid", same as (b) except for addition of extra aliquot of malonic acid; same isooctane dilution at c. (d) Same as (b) except for addition of chloride at a concentration of 0.005 M. (e) Same as (b) except for addition of chloride at a concentration of 0.002 M; system diluted, as above, at e. (f) Same as (b); induction time of 0.75 h and disruption of oscillation at f by dilution of the aqueous B-2 component (see Experimental Section). (g) "High bromate", same as (b) except for addition of extra aliquot of bromate; isooctane dilution at g.
concentration. As can be seen, this had virtually no initial effect on the oscillations except that the amplitude of the electrical potential changes decreased (as expected for a reduction in the concentrations of the B-Z components). By contrast, alteration of the B-Z/water ratio immediately eliminated oscillations (curve 0. In this case a sample of AOT/isooctane/water was added so that the effect was to keep the AOT, isooctane, and water concentrations the same but to dilute the B-Z components. An additional study showed that dilution of a normal aqueous B-Z oscillator produces the same inhibiting effect, with oscillations recommencing (after a delay of about 5 min) at longer periods. In the case of the B-Z(RM) system the delay was longer at about 2 h and a longer period was observed in the same way. The most notable observation for the dilution studies was the effect of overall initial composition on the subsequent values of the oscillation periods after dilution. This is exemplified by plots c, e, and g. In the first case (high malonic) the period decreases with time in the same manner that is always observed for unperturbed oscillators in the reverse micelle system. By contrast, plot g which was high bromate showed the opposite effect, with the period increasing with time after dilution. Plot e represents a system where chloride was added (see next section) and in this case the period remained constant after dilution. ( 3 ) The Effect of Added Chloride on Oscillations. The other results shown in Figure 2 are for systems where chloride, which inhibits oscillation for the bulk water B-2 oscillator, had been added. It is generally considered that for the aqueous system no oscillations can be obtained for mixtures containing relatively small amounts of ch10ride.I~ But as with dilution, it was found that oscillations do arise after a certain delay or induction time. In the case of B-Z(RM) systems containing chloride, oscillations were observed after very long induction times. The higher the chloride concentration the longer the induction time. Induction times greater than 6 h were observed. One example, where the induction time was 4 h, subsequently gave a particularly good pattern of oscillations (Figure 3). (13) Field, R. J.; Koros, E.; Noyes, R. M. J . Am. Chem. SOC.1972, 94, 8649.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1519
Oscillatory Behavior of a B-Z Reverse Micelle System
4
5
6
7
0
9
10
11
12
13
TIME (hr)
Figure 3. Electrical potential change trace for system d.
Discussion The observation of sustained oscillations for an aqueous B-Z mixture contained within reverse micelles shows that the water pool oscillating system is maintained over an extended period of time. The direct observation of changes in electrical potential (using a pair of platinum electrodes), together with the complementary conductivity evidence, indicates that the oscillations are associated with the conducting region of the phase diagram for reverse micelles.2 Furthermore, as the N M R and mass spectrometry studies establish that the AOT remains unaffected by the B-Z chemicals, the AOT surfactant component can be regarded as a chemically inert matrix for the B-Z oscillator. Thus observed differences between the bulk aqueous B-Z oscillator and the B-Z(RM) one may be attributable to the physical effects of containment within the reverse micelle system. The most obvious overall difference that has been observed is an opposite change in period with time. Bulk aqueous oscillators show an increase in period with time which is generally associated with the gradual depletion of reactants as the overall reaction progres~es.’~By contrast, the reverse micelle, B-Z systems consistently show a decrease in period with time (as shown by the downward slopes of the Figure 2 curves). Reaction in the micelle water pools should be subject to the same depletion-of-reactants effect. Consequently another factor, not operating in the bulk aqueous system, must be responsible for the opposite change in period effect. It is proposed that the micelle system segregates reagents to some extent, something that the bulk aqueous one cannot produce at any time under continuously stirred conditions. Because of the particular properties of micelles, selective compartmentalizations of ions and molecules can occur and may directly influence chemical oscillation, as already reported.14 It is of interest to note, in this connection, the relationship between the B-Z(RM) oscillators and the spatial properties of the bulk aqueous, unstirred B-Z system. The B-Z composition giving the longest lasting B-Z(RM) system corresponds to that which produces nonuniform spatial patterns for unstirred bulk aqueous conditions.1° The B-Z(RM) system may be interpreted in terms of the water pools, in effect, producing an environment for the B-Z components that is similar to the “static” bulk aqueous one.1° This means the two situations can be considered to be comparable to each other. The aqueous one demonstrably involves a nonuniform arrangement due to the formation of spatial patterns of the colored component, ferroin.1° The B-Z(RM) system can therefore be regarded, by analogy, to be nonuniform at the micro level (although being dynamic and the total micelle-aqueous system being constantly moved by stirring). Consequently the observed effect for the reverse micelle systems of the period decreasing with time may be due to compartmentalization which facilitates the transport of the components of the reaction in a way different from the ordinary stirred aqueous B-Z system. In the case of the high bromate example (Figure 2, curve g) the period shows a unique behavior in that after dilution the period increases with time. In this case it is suggested that the excess bromate extends the network of reactions involved in the oscillations by incorporating to a greater extent the bromomalonic acid (initially formed) into a further step of bromination. In terms (14) Maritato, M.; Nikles, J.; Romsted, L. Chem. 1985.89, 1341.
S.;Tramontin, M. J . Phys.
of the description presented here the bromomalonic acid would tend to be initially removed from the main reaction center. Dilution would have the effect of further dispersing this substrate. Thus as the overall oscillating reaction scheme moves from the initial malonic acid substrate to the bromomalonic acid one, a critical stage could be reached where a key reactant becomes significantly less acessible. At such a stage the period would suddenly start to increase, as observed (curve g, Figure 2). The dilution-with-isooctane studies shows that the basic B-Z water network is retained intact during the dilution processes. Calculation of wo, the water pool size, using the formula wo = [H,O]/[AOT], shows that dilution, of the type used, causes no change in the micelle-water stoichiometry. This mode of dilution demonstrates that the B-Z aqueous component is fully encapsulated into the AOT reverse micelle system. Dilution of the B-Z, aqueous components stops oscillation ((0, Figure 2), as also occurs for the bulk water system (Results section). In both cases there is a delay of some considerable time before longer period oscillation recommences. These results confirm that basic, overall properties of the B-Z oscillator are retained on encapsulation into the AOT micelle system. The study of the addition of chloride was carried out in order to ascertain to what extent foreign chemicals could be sequestered into regions of the water network where they would not interfere with the B-Z oscillator units. It has been stated that trace amounts of chloride completely inhibit B-Z oscillation^.'^ However, it was found here that oscillations can be obtained for aqueous B-Z, after a delay, for reasonable amounts of chloride. For example [CI-] = 0.005 M gave oscillations after 20 min. It is probable that there are reactions available for the consumption of chloride so that once the latter has been reduced to an appropriate level oscillation can commence. It is also possible that chloride becomes incorporated into the network of reactions producing oscillations. Nonetheless the chloride study produced some results of interest. Curves d and e (Figure 2) represent B-Z(RM) systems having initial chloride concentrations of 0.005 and 0.002 M, respectively. These gave marked differences in initial behavior. System d had an induction time of 4.2 h while that for curve e was 1.5 h. However, curve e commenced at a significanty higher period and changed much more rapidly with time. This indicates that chloride ion becomes incorporated into the scheme of oscillation reactions, because of the large differences arising from a change in chloride concentration only. The attainment of a near-constant period for chloride-containing system (curve e), after dilution (Figure 2), shows that synthetic “closed” systems can also achieve “pseudoopen” characteristics, as exhibited by the naturally occurring glycolytic oscillator^.^ Presumably this arises from a delicate balance of factors favoring a decrease in period with time (as exemplified by most of the reverse micelle systems studied there) and the opposite trend (as observed for the high bromate reverse micelle example). Consequently, additional features, such as preferential sequestering of reactants or products which a micelle system provides, may be seen to significantly enhance the range of behavior of chemical oscillators. Acknowledgment. We thank B. W. Ninham and D. Balasubramanian for helpful discussions, Warren Lazer and Bruce Tattam for recording N M R and mass spectrometry data, and Rosemary Makos, Sandy Butler, and Herbert Schade for assistance in preparing the manuscript.
