1756
J. Phys. Chem. 1985,89, 1756-1760
Interactions of Positronium with Co2+ In Water: Mechanlsms and Temperature Effects G. Duplatre,* A. Haessler, and J. Ch. Abbe Centre de Recherches Nucliaires et UniversitC Louis Pasteur, Laboratoire de Chimie NuclCaire, B.P. 20 67037 Strasbourg Cedex, France (Received: June 11, 1984)
The interactions of positronium (Ps) with the paramagnetic Co2+ion are investigated in water at various temperatures by both lifetime spectroscopy and the Doppler broadening of annihilation radiation line shape technique. They are shown to arise essentially from spin conversion reactions. However, the consistent fitting of the various data indicates the presence of an additional process, ascribed to Ps complex formation. The relative contribution of the latter increases importantly with temperature while the spin conversion is almost temperature independent. This peculiar behavior is tentatively explained on the basis of weak spin interactions.
Introduction The exotic positronium (Ps) and muonium (Mu) atoms, respectively the bound states of a positron and of a muon with an electron, can undergo most of the usual chemical reactions, such as oxidation or complex formation, and several papers have been concerned with these possibilitie~.~-~ An additional type of interaction is the so-called spin conversion which has been treated theoretically to some extent for Ps.~,' However, experimental studies have remained sparse until now and have not allowed a precise knowledge of the spin conversion mechanism. Two major techniques have been used for these studies: lifetime spectroscopy (LS) which delivers information mainly on the long-lived triplet state of Ps, orthopositronium (0-Ps), and the angular correlation (AC) technique which is very sensitive to the presence of the narrow singlet parapositronium (p-Ps) component in the two quantum annihilation momentum distribution spectra. Although the existence of spin conversion has been demonstrated unambiguously in some instances, particularly using AC in the case of paramagnetic gasess or in the presence of a magnetic field,g the results obtained from L S for paramagnetic ions in solution have not always been convincing and have sometimes been conflicting with those from AC measurements." Recently, results have been reported on the reactions of Mu with a variety of dia- and paramagnetic ions in water." Although only the disappearance of the Mu triplet-state component can be followed with the muonium spin rotation technique used, and not its increase from the singlet state upon conversion, the authors' conclusion pointed to the existence of spin conversion in the presence of the paramagnetic ions. Owing to the situation in Ps chemistry and in view of these results on Mu spin conversion, it seemed interesting to investigate in some detail the Ps behavior in aqueous solutions of paramagnetic ions. For better accuracy of the results, both the LS and the Doppler broadening of the annihilation radiation line shape (DBARL)'z.13techniques have been used. Although not displaying ( I ) As general reference. see, e& "Positronium and Muonium Chemistry", H. J . Ache. Ed.. American Chemical Society, Washington, DC, 1979, Adv. Chem. Ser., No. 175. (2) V. 1. Goldanskii, 0. V. Koldawa, and V. P. Shantarovich. High Energy Chem., 9, 5 5 (1975). (3) H . J. Ache, Angew. Chem.. Inr. Edir. Engl.. 11, 179 (1972). (4) Y. C. Jean, J . H. Brewer, D. G.Fleming, D. M. Gamer, R. J. Mikula, L. C. Vaz, and D. C. Walker, Chem. Phys. Lerr., 57, 293 (1978). (5) V. I. Goldanskii and V. P. Shantarovich, Appl. Phys., 3, 335 (1974). (6) W. R. Dixon and L. E. H. Trainor, Phys. Rec., 97, 733 (1955). (7) R . A. Ferrell, Phys. Rec., 110, 1355 (1958). (8) A. D. Mokrushin and V. I . Goldanskii, Sou. Phys. JETP, 26. 314 ( 1968). (9) M. Heinberg and L. A. Page, Phys. Rec., 107, 1589 (1957). (IO) G. Trumpy, Phys, Ret.* 118, 668 (1960). ( 1 I ) Y . C. Jean, J . H. Brewer, D. G.Fleming, and D. C. Walker, Chem. Phys. Leu., 60,125 (1978). (12) G. Duplltre, J . Ch. AbbC. A. G.Maddock, and A. Haessler. J . Chem. Php.i., 72, 89 (1980).
TABLE I:
LS and DBARL Parameters for Pure Water" 72O,
73O,
1307
T, K
ns
ns
% '
275 294 313 333 363
0.38 0.39 0.41 0.42 0.41
1.87 1.78 1.73 1.74 1.69
27.9 28.0 28.1 28.9 30.8
"fwhm2 = 3.12 f 0.01 keV and * f 0 . 0 2 keV. c f 0 . 0 3 keV.
rl,b rp,c keV 1.01 1.01 0.90 0.89 0.89
keV
fwhmO, keV
2.44 2.40 2.35 2.33 2.30
2.82 2.80 2.77 2.77 2.72
r2 = 2.67 f 0.02 keV
at all T .
such good resolution as AC, DBARL can deliver valuable complementary information, which has k n lacking in most previous studies, to that given by LS.123'3 In this paper, results are reported on the Co2+ion at various temperatures in aqueous solutions. Experimental Section The LS apparatus has been described previo~sly.'~The time resolution, for the 6oCo prompt curve, was 0.27 ns. The same ampoules, sealed after the usual freeze-thaw operation, served for the LS and DBARL measurements. The LS data were analyzed with the extended positron fit programl5 in terms of three components with lifetimes T~ (or decay rate constant Xi = l/~,) and relative intensities liLs. Subscripts 1, 2, and 3 will refer to the short-, medium-, and longlifetime components respectively, viz. to p-Ps, e,,+, and 0-Ps in pure water. Values for pure water will be denoted by a superscript 0. As the measured i3values were not lower than 0.7 ns, no significant difference was found for T~ whether T~ was fixed at T; = 0.4 ns or not. The error on 7 3 was within 0.025 ns. The characteristics of the DBARL device and the data analysis procedure have been described p r e v i o ~ s l y . ~The ~ ~ energy '~ resolution, from the full-width at half-maximum (fwhm) of the 85Sr photopeak, was 1.45keV. The DBARL results will be presented in terms of the fwhm of the positron annihilation radiation line. Correcting the experimental spectra for the resolution and resolving the deconvoluted spectra into a sum of Gaussians delivers the intrinsic fwhm's related to each positron containing species in the solution, ri,and the associated intensities, l?. The error on fwhm was within 0.01 keV. To avoid possible ion association and any extraneous effect in either the LS or DBARL measurements, the anion was C104-, known to have little influence in LS.I6 Several of the previous (13) G. DuplPtre, J. Ch. AbW, J. Talamoni, J. C. Machado, and A. Haessler, Chem. Phys., 57, 175 (1981). (14) A. G . Maddock, J. Ch. AbbC, and A. Haessler, Chem. Phys., 17, 343 (1976). (15) P. Kirkegaard and M. Eldrup, Computer Phys. Commun., 3, 240 (1972). (16) L. J. Bartal, J. B. Nicholas, and H . J. Ache, J. Phys. Chem., 76, 1124 (1972).
0022-3654/85/2089-1756$01.50/00 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 1757
Interactions of Positronium with Co2+ in Water
~
m
n
e
o
3 x
I
I 2.;
2
2s
2.!
2.8
-
2.1.2.
0.57
I
I
0.1 Figure 1. Variations of
0
0.2
I
0.3
I
1
0.4 C(M)
(ns-I) with concentration C (M) of Co-
(C104)2at various temperatures.
studies on transition-metal ions have been concerned with the chloride ~ a l t s . ~ ~ J However, ’-~~ C1- would have blurred the LS and DBARL results because of the formation of a bound state with the C10, has been reinvestigated for a better definition of the pure cation effects. The temperature, T, ranged from 275 to 363 K and was controlled to within 1 K. The pH of the solution was 2.30 f 0.02. Results The L S and DBARL parameters for pure water at various temperatures are given in Table I. The intrinsic r2parameters related to e,+ have been determined separately, using concentrated solutions of a very efficient Ps inhibitor and oxidizer,12-22 Na2Cr207; fwhm2 for these solutions and, consequently, r2are temperature independent, in contrast to rl and rs which decrease with increasing T , in agreement with previous results in various polar As previously,I2*l3a broad component (I’ = 5.8 keV) appeared in the deconvoluted spectra at all T, with a small intensity (3%) which has been systematically corrected for. In the presence of NaC104, T~ remains constant while IsLs decreases with the concentration C.The variations are very smooth up to 4 M and therefore not reported.I6 The inhibition constant, derived on the basis of the empirical expression (1) is k = 0.08 1, = 130/(1
+ kC)
(1)
f 0.02 M-’ a t all T . With eq 1, the r i from Table I and the resolution function of the detector allow us to calculate the predicted fwhm vs. Cvariati~ns.’z~~ These are in excellent agreement with the experimental DBARL data which show a very smooth increase of fwhm with C. (17) (18) (19) (20)
R. E. Green and R. E. Bell, Can. J. Phys., 36, 1684 (1958). H. Horstman, J. Inorg. Nucl. Chem., 27, 1191 (1965). R. L. DeZafra, Phys. Rev., 113, 1547 (1959). V. I. Goldanskii, B.V.Sobolw, and V.P. Shantarovich, Dokl. Phys.
Chem., 194,662 (1970). (21) J. Talamoni, J. Ch. Abbb, G. Duplstre, and A. Haessler, Radiat. Phys. Chem., 20, 275 (1982). (22) 0.E . Mogensen and V.P. Shantarovich, Chem. Phys., 6, 100 (1974). (23) J. Talamoni, J. Ch. AbM, G. DuplPtre, and A. Haessler, Chem. Phys., 58, 13 (1981). (24) J. Talamoni, J. Ch. AbM, G. Duplitre, and A. Haessler, Radiat. Phys. Chem., 21, 431 (1983).
0 a5 Figure 2. Variations of fwhm (keV) with (C104)2at various temperatures.
10
IS
UM)
concentration C (M) of Co-
Figure 1 shows the variations of l / with ~ C O ( C ~ Ocon~)~ centration at various T . Quite noticeably, the slope of the curves increases with T, although less markedly as T rises. The variations of Z3Ls with C are very smooth and hence not reported. Figure 2 shows the variations of fwhm with C at the same temperatures. These go through a minimum which is more marked, but relatively less deep, the higher the temperature. Data Analysis The large variations of T~ show that Co2+reacts effectively with Ps. The possible reactions can be described as follows: kh oxidation Ps S eaq+ S(1)
- + + -
+
complex formation Ps spin conversion
0-Ps
S
+S
k’rmp
(PSS)
ktm
p-Ps
+S
(11) (111)
These reactions are to compete with the various positron annihilation reactions with decay rate constants XIo, X20, X30, and A, for p-Ps, eaq+,0-Ps, and (PsS), respectively. Solving the relevant differential equations leads to the expressions giving the LS and DBARL parameters (lifetimes, intensities) as a function of concentration C of solute S. These expressions have been reported previously2s and are used to fit the experimental data. Before proceeding to the data analysis in detail some preliminary remarks seem necessary: (i) the apparent slope of the experimental l / ~ ~ vs. Cvariations, k’,,,, can be a combination of the reaction rate constants k’mv, k&, and Pqp;(ii) besides the quenching reactions which relate to the thermalized Ps, processes occurring at very short times in the presence of S can affect the formation yields Zloand Z30 as measured in the pure solvent. In the case of inhibition of Ps formation by S the effective yields (corrected for the effects of the quenching reactions), ZIMr and Z3Mr, can be related to Zlo and Zso through eq 1.12,13,25 Qualitatively, the remarkable decrease of fwhm a t low Co2+ concentration (Figure 2) can arise from either spin conversion (reaction 111), by which the broad 0-Ps component (r3in Table (25) J. Ch. Abbe, G. DuplPtre, A’. Haessler, A. Marques Netto, and D. Pilo Veloso, J . Phys. Chem., 88, 2071 (1984).
Duplatre et al.
1758 The Journal of Physical Chemistry, Vol. 89, No. 9, 1985
t ? ? !
15. 10
20.
15. 10
15. 10.
10.
I
I
I
0
J
I l0l 0
0.5
10
1.5
C(H)
Figure 3. Variations of ZID(%), the p-Ps narrow component intensity, with concentration C (M) of CO(CIO~)~ at various temperatures. ZID is the same when supposing the presence of three or four components in the deconvoluted DBARL spectra. I) is essentially converted into the narrow p-Ps (I?,) component, or from Ps complex formation (reaction 11) by which both p-Ps and 0-Ps are converted into a Ps bound state having a narrow rC value. However, the minimum in fwhm shows that necessarily more than one single process is occurring. In the most general case, the parameters involved would include the various rate constants k', an inhibition constant k, due at least to the Clod- anion, plus A, and rcrelated to the hypothesized Ps ~ o m p l e x . ' In ~ view of these numerous parameters, we found it more convenient to proceed stepwise in the analysis of the data. Three-Component Analysis of the DBARL Spectra. The simplest approach relates to a combination of spin conversion with oxidation and/or inhibition reactions. In this case, the DBARL spectra should not include any other components than p-Ps, e, +, and 0-Ps. Therefore, ZID and Z3D (ZzD is the complement to 100%) can be directly derived from the deconvoluted ~ p e c t r a ' ~using *'~ the r i from Table I. As shown in Figure 3, the increase with C of the ZID values is quite noticeable at all T and definitely shows that the dominant process involved is spin conversion. Various fitting procedures have been attempted using combinations of the experimental data T3, ZID, and Z3D. In all cases the fitting gave kLnvin turn of 1.8 ns-' M-I associated with lower values for k;, (from 0.2 to 1.6 ns-' M-'between 275 and 363 K) and a very small inhibition constant ( k = 0.06 M-I). However, none of these fitting procedures allowed the recovery of the totality of the experimental curves. This is illustrated in Figure 4 which shows the large discrepancy between the experimental plots of (crosses) and of fwhm and the calculated variations of Z3D (solid lines) and of fwhm (broken lines) at 333 and 363 K, respectively, when using only IIDand T~ as fitting data,in spite of the good fit of these latter data (solid lines in Figures 1 and 3). Four-Component Analysis of the DBARL Spectra. It is thus shown that the major process is spin conversion but that the addition of oxidation or of inhibition reactions alone or combined cannot account for the results. One is then left with complex formation as the subsidiary process. Resolving the deconvoluted DBARL spectra in terms of four components unfortunately does not give a clear picture. Very significantly though, ZID remains the same as previously, but the values of rcderived at a given T and various concentrations are rather spread. The reason is values are necessarily small as complex that the associated ICD formation can only be a secondary process. It is only at high T or C that a relatively constant value stems for r,: 2.4 0.15 keV. Considering the very good reproducibility of IIDwhatever the
*
05
10
15
0
io
a5
is c
Figure 4. (Upper) Experimentalvariations of fwhm (keV) with C (M) at 333 and 363 K (full symbols)and curves calculated on the basis of three (broken lines) or four (solid lines) components in the deconvoluted DBARL spectra. (Lower) Variations with C (M) of Z3D(%) derived on the basis of three (crosses) or four (full symbols) components. The calculated curve is the same in either case (solid lines).
TABLE II: Experimental (kE,k'-J Reaction Rate Constants'
275 294 313 333 363
6.0 6.9 7.8 7.1 5.8
0.17 0.43 0.64 1.1 1.6
and Calculated (k, kw)
3.75 6.83 10.9 16.2 26.2
5.70 7.45 1.78 7.24 6.11
a k = 0.06 M-'at all T. * kE = 4k',,v.C From eq 2 with rh = 0.053 nm and rco = 0.074 nm. dFrom eq 3 with B = 1.4 c F 2and either F = 1 and rCa = 0.3 nm or F = 1.9 and rc0 = 0.074 nm.
treatment used, the following procedure was then adopted. The data on ZID and on 7 3 were used to determine khnV, kiomprand k at each T. This is equivalent to the previous three-component treatment since k6, and kLmpcan be interchanged in the relevant equations.25 The derived values are given in Table I1 with the conversion process expressed in terms of the encounter rate constant,25kE = 4k',,,. The corresponding calculated curves are shown as solid lines in Figures 1 and 3. The intensity of the complex, ICD, was then calculated and the DBARL spectra were resolved into four components with I',, rz,and r3known (Table I) and ICD fixed to the calculated values. As expected, IID was again the same as previously, and a concentration- and temperature-independent value arose for rc: 2.36 0.02 keV. With this procedure, the derived Z3D values (full symbols in Figure 4) are in excellent agreement with the calculated variations, which are drawn as solid lines in Figure 4. With the parameters in Table 11, the rifrom Table I, and rc= 2.36 keV at all T, the fwhm vs. C curves have been all back-calculated. The results are shown as solid lines in Figures 2 and 4. The agreement with the experimental points confirms the consistency of the method.
*
Discussion The experimental data definitely point to an abnormal behavior of the overall Co2+/Ps reaction rate constant with T, as may be seen from the changes of kip, with T (Figure 1). Similarly, the lowering of Afwhm, the maximum amplitude variation of fwhm, between 275 and 363 K (Figure 2) is not consistent with the increase of k i p on the basis of a single process. These observations are confirmed at the quantitative level. A pure spin conversion process, with only a small contribution from inhibition, can account for the results at 275 K, not at higher T. The presence of spin conversion has been concluded in previous studies at room tem-
The Journal of Physical Chemistry, Vol. 89, No. 9, 1985 1759
Interactions of Positronium with Co2+ in Water
I
k’comp
amined successively. Regarding the kinetics, several trials have been made using different equations than those implied in the competition scheme, reactions 1-111. For the sake of length, only two of these treatments will be discussed. Goldanskii and co-workers have proposed a general scheme for Ps reactions, in which the formation of an intermediate complex (PsS) would be the initial step, as30 oxidation annihilation
I
~
0.2
.
-
(h;,
A);
Ps t
S
kl
(PsSl
l
conversion
I O
2.8
3.2 3.4 1 O’IT I K - I ) Figure 5. Arrhenius plots of kE = 4k‘,,, and k’mp (ns-’ M-I). For the solid lines, see text.
10
p e r a t ~ r e , ’ ~ *but ’ ~ most - ~ ~ of these have been of a rather qualitative nature. In AC experiments, a quantitative treatment very similar to ours has been made by Goldanskii et alSBThese authors found a monotonous increase of ZID, the narrow component intensity, and their data are consistent with those in Figure 3 at 294 K. However, the method to derive ZID was not uniqueB and the errors indicated do not preclude the existence of some small secondary process besides the spin conversion reaction. In lifetime experiments, spin conversion reactions could be characterized from 1 / vs.~ C~variations in two ways: (i) these should not be linear, in contrast to what is expected with pure oxidation or complex formation reactions. Unfortunately, the parameters involved for aqueous solutions are such that the expected curvature is rather small. For this reason too, the implication of more than one process cannot be inferred from these data alone; (ii) 73 should tend to a limiting value such that l/qim = ‘/4(X10 h30). With XIo = 8 ns-’ and X30 = 0.56 ns-’ at 294 K, this gives qim= 0.47 ns. This value is close to that for the eaq+lifetime, 72’ = 0.39 ns, which is the limiting value in case of oxidation and, presumably too, in most cases of complex formation. Therefore, the observation of limiting lifetimes in turn of 0.4 ns with various solutes may have been misleading in the past. 17*26 Combining the LS and DBARL results indicates that the conversion process is competing with the formation of a Co2+/Ps bound state, with an increasing relative importance of the latter when T increases. Several arguments speak in favor of this scheme: (i) Ps oxidation by Coz+ is chemically very unlikely, as confirmed by thermodynamical consideration^;^^ (ii) the inhibition constant value is small and is consistent with that due to C10,alone, pointing to a negligible effect of Co2+on Ps formation, as previously found;2s (iii) the Arrhenius plot for kLmpis linear (Figure 5 ) giving an activation energy, E = 0.17 f 0.02 eV, close to that for the viscosity, E,, = 0.16 eV, and suggests a diffusion-controlled mechanism. However, the anomalous behavior of kip, with Tis reflected in the kL,, values which are hardly affected by T. For comparison, the values expected for a purely diffusion-controlled reaction with Ps are given in Table 11, calculated on the basis o f 9
+
where N is Avogadro’s number; Tis the absolute temperature; k is the Boltzmann constant; rpsand rco are the effective radii of the reactants. It is striking to note that kE is higher than kD at low T. Comparing kLmpto kDshows that complex formation would occur with a probability factorz9 of about 1/17. The peculiar changes of k b , with T can arise from either kinetic or mechanistic factors and these possibilities will be ex(26) A. Bisi, L. Bcsi, E. Lazzarini, and L. Zappa, J . Chem. Phys., 63,5087 (1975). (27) V. M. Byakov, V. I. Goldanskii, and V. P. Shantarovich, Elektrokhimiya, 13, 681 (1977). (28) S . J. Tao, Appl. Phys., 10.67 (1976). (29) S. J. Tao, J . Chem. Phys., 52, 752 (1970).
The corresponding kinetic equations have been unsuccessful to fit the data, and the following remarks may be made: (i) preservation of the nearly linear variations of with C demands rather high values of either kz, k3, or A,. It is hardly conceivable that X,would exceed Xlo = 8 ns-I. However, much higher values are obtained in the fitting procedure; (ii) Supposing A, is nearly constant and kl changes with T according to the diffusion laws, the relative importance of X, will be higher the lower the temperature. Fixing X, to values between 2.5 (A?) and 8 ns-’ (Xlo) at 275 K leads to very low k2 and k3, which is contrary to the experimental evidence. An alternative explanation to the anomalous behavior of k LnV with T has been sought in terms of an equilibrium3’ conversion annihilation
.; (A
rp,
k2
Ps t S
k1
Sr
(PsS)
/
/ .
The occurrence of spin conversion reactions alone has been tested first. If kz is very large and k, is diffusion controlled, conditions can be found to fit the 1 / 7 3 vs. C variations. However, kz must be about constant with T while k3 should increase very markedly with T, with an activation energy well above 0.3 eV. More importantly, the ZID and Z3D values derived are the same as when using reaction I11 so that, again, the calculated Z3D values are inconsistent with the experimental ones. When adding X into the problem, the inconsistencies are not removed. Turning finally to the mechanistic aspects, we see that there are two possibilities for spin exchange interaction^.^^ In “strong” interactions, the exchange rate constant is diffusion controlled and should increase with T with the activation energy E,,. This is contrary to the data (Figure 5) and therefore the existence of weak interactions may be suspected as was the case for Ps reaction with free radicals.25 On this basis, the rate constant is expressed as32 kw = FkDPT2/ (1
+ J%’)
(3)
where J and r are the spin overlap integral and collision time, respectively, and F is a factor taking into account steric and attractive (repulsive) effect^.^^^^^ If we combine eq 2 and 3 and set J%2 = Bq2, there are two possibilities to fit the kE vs. T variations with two parameters (solid line in Figure 5 ) . If we take the effective Coz+ radius as rc0 = 0.074 nm, the solid-state radius, the fitting parameters are F = 1.9 and B = 1.4 c y z ; with F fixed to F = 1, the parameters are rco = 0.3 nm and B = 1.39 c y 2 . The calculated kw are given in Table 11. The physical implications of the two possibilities are similar: factors other than just diffusion could be involved in the reaction of Ps with Co2+,as was the case for the reaction with iodine in various solvents.29 Note that rco = 0.3 nm is compatible with the radius of the hydrated Coa:+ ion but then the spin density should expand significantly out to (30) V. I. Goldanskii, V. P. Shantarovich, A. V. Shishkin, and 0.Tatur, Dokl. Phys. Chem., 229, 750 (1976). (31) W. S . Madia, A. L. Nichols, and H. J. Ache, J . A m . Chem. Soc., 97, 5041 (1975). (32) Yu. N. Molin, K. M. Salikhov, and K. I. Zamaraev, “Spin Exchange”, Springer Series in Chemical Physics, Vol. 8, Springer-Verlag, Berlin, 1980.
1760
J. Phys. Chem. 1985, 89, 1760-1764
the limit of the first hydration shell of Co2+to explain the effectiveness of the reaction with Ps.
Conclusion This work demonstrates again the importance of using both the LS and DBARL techniques for thorough information in Ps chemistry. As Ps is becoming a common probe for the study of the physicochemical properties of solid and liquid media, it is essential to have a precise knowledge of its behavior with impurities. The possibility of spin interactions is one of the attractive sides of Ps chemistry in view of applications. The reactions with Co2+in aqueous solutions are shown to be of a complex nature. They arise primarily from spin interactions, as is probably the
case for muonium too, but the detailed analysis of the data indicates that an additional process is involved, ascribed to Ps complex formation. The variations with temperature of the overall reaction rate constant, reflected in the behavior of the spin conversion rate constant, are peculiar, betraying a nonpurely diffusion-controlled process. Possibilities are discussed on the basis of weak spin interactions but the theoretical studies would be welcome to unravel their relative importances, Acknowledgment. The authors thank P. E. Cade from the University of Massachusetts, for valuable discussions. Registry NO. Ps,12585-87-4;CO", 22541-53-3;CO(C10,)2, 1345531-7.
Blfurcatlon Structure of the Belousov-Zhabotimrkll Reactlon In a Stirred Flow Reactor Masataka Hourai, Yashige Kotake, and Keiji Kuwata* Department of Chemistry, Faculty of Science, Osaka University, Toyonaka Osaka 560, Japan (Received: June 5, 1984)
The bifurcation structure of the oscillation modes in the Belousov-Zhabotinskii reaction in a continuous-flow stirred tank reactor was investigated in detail. By fine control of the flow rate of reactants, a novel structure was found at residence time region longer than that of the single-peak oscillation. By the addition of new modes the bifurcation structure was proven to be symmetric about the single-peak oscillation with respect to the alignment of modes. The experimental results were described phenomenologicallyby use of a one-dimensionalmap. The whole bifurcation structure was reproduced by vertically sliding a map of the same shape. The shape of the map strongly suggests the presence of two stationary states in the Belousov-Zhabotinskii reaction.
Introduction The Belousov-Zhabotinskii (BZ) reaction is known as an oscillatory reaction. Numerous investigations have been carried out to analyze its reaction kinetics which are responsible for the Since Hudson et al. observeds5 that there is a transition between various regular oscillatory states under stirred flow conditions, the BZ reaction has been realized to be a typical nonequilibrium open system.69 Also, a chemical turbulent state was observed for the first time in chemical reaction.4~~ Tomita and Tsuda camed out theoretical studies that include one-dimensional (1-D) map analysis based on Hudson's experiment.'+l2 Many experimental and theoretical investigations on the bifurcation structure in nonequilibrium systems have been concentrated on hydrodynamic systems. In chemical systems, even the BZ reaction has been investigated on the basis of rather diverse (1) See,for example: Field, R. J.; KBrijs, E.; Noyes, R. M. J . Am. Chem. Soc. 1972,94,8649. Noyes, R. M.; Field, R. J. Annu. Rev. Phys. Chem. 1974, 25, 95. Nicolis, G.; Portnow, J. Chem. Rev. 1973, 73, 365. Tyson, J. J. J . Chem. Phys. 1977,66,905. Noyes, R. M.; Field, R. J. Acc. Chem. Res. 1977, 10, 273. Noszticzius, 2.;Farkas, H.; Schelly, Z. A. J . Chem. Phys. 1984.80, 6062. ( 2 ) Gray, B. F. 'Kinetics of Oscillatory Reactions" in "Reaction Kinetics"; The Chemical Society: London, 1975; Vol. 1. (3) Graziani, K. R.; Hudson, J. L.; Schmitz, R. A. Chem. Eng. J . 1976, 12, 9. (4) Hudson, J. L.; Hart, M.; Marinko, D. J . Chem. Phys. 1979,67, 160. (5) Schmitz, R. A.; Graziani, K. R.; Hudson, J. L. J. Chem. Phys. 1977, 67, 3040. (6) Reichl, L. E.; Schieve, W. C. 'Instabilities, Bifurcations, and Fluctu-
ations in Chemical Systems"; University of Texas Press: 1982. ( 7 ) Gurel, 0. Top. Curr. Chem. 1983, 118. ( 8 ) Rossler, 0. E.; Wegman, K. Nature (London) 1978, 271, 89. (9) Hudson, J. L.; Mankin, J. C. J. Chem. Phys. 1981, 74, 6171. (10) Tomita, K.; Tsuda, I. Phys. Lett. 1979, 71A, 489. (11) Tomita, K.; Tsuda, I. Prog. Theor. Phys. 1980, 64, 1138. (12) Tomita, K.; Tsuda, I. Prog. Theor. Phys. 1980, 69, suppl., 185.
0022-3654185 12089- 1760%01S o,l 0 I
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interest. The bifurcation structure of the BZ reaction has not been established yet. The present work aims to completely describe the bifurcation structure from an experimental viewpoint. By use of a continuous flow stirred tank reactor (CSTR) Hudson et al. many periodic oscillation modes and chaotic modes in the residence-time region of the reactants shorter than that of single-peak oscillation. Recently Turner et al. rep0rtedl3 the presence of a bifurcation in the residence time longer than that of a single-peak oscillation. The structure is very similar with respect to the formation of oscillation pattern to that of the shorter residence time but appears to be in reverse order with respect to residence time. By combining these experimental results, one may construct the whole bifurcation structure. However, it is difficult to find a rule governing the generation of the whole structure. The possible reason for this difficulty is that some structures still are unobserved. In this study, bifurcation in the longer residence time region was experimentally examined by the fine control of the flow rate. Novel bifurcation was found in the residence time region close to that of a single-peak oscillation. The whole structure of the bifurcation including chaotic modes can be reproduced according to a simple rule when this new bifurcation is added. In addition, the presence of intermittence was confirmed experimentally. The analysis of the bifurcation structure based on the reaction mechanism is not an easy task, because even a model which can generate chaotic state is very difficult to con~truct.~"" In this report a one-dimensional map was used for the phenomenological (13) Turner, J. S.; Roux, J.-C.; McCormick, W. D.; Swinney, H. L. Phys. Lett. 1981, 85A, 9. (14) Tyson, J. L. J . Math. Biol. 1978, 5, 351. (15) Wegman, K.; Rossler, 0. E. Z . Naturforsch. A 1978, 33, 1179. (16) Iwamoto, K.; Seno, M. J . Chem. Phys. 1979, 70, 5851. (17) Sakanoue, S.;Murase, C.; Endo, M. Bull. Chem. SOC.Jpn. 1983,56, 2380.
0 1985 American Chemical Society
