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Novel oscillatory reactions involving double substrate
Chemical Physics Letters 369 (2003) 434–440 www.elsevier.com/locate/cplett
Novel oscillatory reactions involving double substrate R.P. Rastogi a
a,*,1
, Prem Chand
b
Chemistry Department, Lucknow University, UP Council of Science and Technology, Lucknow 226001, India b Food Toxicology Division, ITRC, Lucknow 226003, India Received 19 April 2002; in final form 28 November 2002
Abstract The oscillatory features of a novel type B–Z type oscillator, fructose [F] + oxalic acid ½OA þ Ce4þ þ BrO 3 þ H2 SO4 has been investigated. The induction time is found to be usually small or negligible. Both single frequency oscillations and two oscillatory states separated by a time-pause are observed. Oscillations occur between two critical limits of [F] and [OA]. A tentative mechanism has been suggested which involves both Br ion control and free radical control. Computer simulation correctly predicts some of the oscillatory features such as (i) time of initiation, (ii) critical limits of [OA] and (iii) stoppage of oscillations by higher ½Br , confirming the primary role of Br control mechanism. Ó 2003 Published by Elsevier Science B.V.
1. Introduction Coupling and switching of control mechanism is of potential importance for the study of complex oscillatory processes [1,2] and physiological systems [3–5]. In physiological systems, both transport processes and chemical reactions can exercise control. In chemical systems, B–Z reaction is a good example of such coupling in a multi-component reaction network. In the classical B–Z system at room temperature and at low malonic acid [MA], Br control prevails while at higher [MA], oscillations can be explained and modeled
*
Corresponding author. E-mail addresses: [email protected] (R.P. Rastogi), [email protected] (P. Chand). 1 Present address: 295/281 KA, Asherfabad, Lucknow 226003, (UP) India.
on the basis of free radical control [6]. Evidence is provided by the detection of MA radical which is experimentally shown to react with BrO2 [7]. The stirring effects are related to diffusion-controlled reaction. In both the situations of high and low [MA], the experimental results during stirring can be semi-quantitatively interpreted on the basis of diffusion-controlled free-radical reaction as shown by Noszticzius et al. [8], which is evidently the one involved in the Radicaltor. Recent studies 2þ by Gao and F€ orsterling on ½RuðdipyÞ3 þ bromomalonic acid ðBrMAÞ þ BrO3 system [9] suggest the occurrence of two negative feedback loops viz., the primary feedback loop is the reaction of Br with HBrO2 and the secondary loop involves reactions of organic radicals with BrO2 radicals. The new experimental results involving radical-controlled oscillating B–Z reaction further confirm the existence of the second loop. However, the primary loop cannot be ruled out.
0009-2614/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V. doi:10.1016/S0009-2614(02)01980-2
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
No oscillations are observed in oxalic acid ½OA þ Ce4þ þ BrO 3 þ H2 SO4 [10]. However, when acetone is added to the system, oscillations are observed due to removal of bromine and consequently lowering of ½Br to the level required for oscillations to occur. Further, in the former case, many features of the reaction can be simulated on the basis of bromine–hydrolysis–controlled model due to Field and Boyd [11]. When [F] is used as organic substrate, oscillations occur only within a very limited range of concentration of [F] where the possibility of dual control [12,13] of Br and BrO2 cannot be ruled out as the earlier detailed studies show. It has been reported that when tartaric acid + fructose are used as double substrate, oscillations are observed below the lower critical limit of [F] [14]. Anticipating that oxalic acid ½OA þ ½F as double substrate would behave in a similar fashion but with important difference in reaction mechanism, the detailed study of the latter oscillator was undertaken and the results are reported in the present communication.
435
at interval of 0.1 s. using Perkin–Elmer UV/Vis spectrophotometer Lambda BIO 20. Cuvette having cross-sectional area equal to 1 1 cm2 in which, the solution was continuously stirred with a magnetic stirrer. The results are recorded in Figs. 1–3. The computer simulation results following the procedure described earlier [13] are recorded in Figs. 3–5. The effect of (a) order of addition of organic substrates on oscillation characteristics and (b)
2. Experimental 2.1. Materials Fructose, oxalic acid, sulphuric acid and KCl (E. Merck), cerric ammonium sulphate (AR, Thomas Baker), potassium bromide (S.D. Fine Chem.), potassium bromate (AR, CDH) and acrylamide (LR, Koch-light) were used as such without purification. All solutions were prepared in 1.5 M sulphuric acids in double distilled water. 2.2. Procedure + results Experimental procedure for (i) monitoring of oscillations, (ii) estimation of ½Br during various stages of oscillations using Orion electrode and electronic recorder, (iii) the study of kinetics of Br2 evolution was the same as followed earlier [13,14]. [Br ] during oscillations is found to be 106 M. The exact magnitude cannot be estimated since the system is far away from equilibrium. The absorbance of reaction mixture was measured at 530 nm
Fig. 1. Oscillations in bromide ion potential (I) and redox potential (II), for the system: H2 SO4 ð1:5 MÞ þ BrO 3 ð0:06 MÞ þ Ce4þ ð1:45 103 MÞ þ F ð0:025 MÞ þ (a) OA (0.008 M), (b) OA (0.01 M), (c) OA (0.025 M), (d) OA (0.03 M), (e) OA (0.045 M), (f) OA (0.055 M), (g) (0.06M), (h) OA (0.1 M), (i) OA (0.25 M), (j) OA (0.3 M), respectively. Temp. 28 1 °C.
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Fig. 2. Oscillations in bromide ion potential (I) and redox potential (II), for the system: H2 SO4 ð1:5 MÞ þ BrO 3 ð0:06 MÞ þ Ce4þ ð1:45 103 MÞ þ OA ð0:05 MÞþ (a) F (0.005 M), (b) F (0.01 M), (c) F (0.03 M), (d) F (0.05 M), (e) F (0.06 M), (f) F (0.1 M), (g) F (0.2 M), (h) F (0.3 M), (i) F (0.35 M), (j) F (0.40 M), respectively. Temp. 28 1 °C.
addition of F and BrO 3 after stoppage of oscillations was investigated in the same manner as described earlier [13–15]. The experimental results are recorded in Figs. 1–3.
3. Discussion Results recorded in Figs. 1 and 2 show that: 1. Oscillations are initiated in F + OA or OA + F oscillators within definite concentration limits of [OA] and [F], respectively.
Fig. 3. Effect of addition of KBr/Fructose/ BrO 3 on Br ion 4þ potential for the systems: BrO ð0:06 MÞ þ Ce ð1:45 3 103 MÞ þ H2 SO4 (1.5 M) + F (0.025 M) + OA (0.05 M). Experimental results: effect of addition of [Br ] (a) and (b) 2:0 102 M, (c) effect of addition of [F] 0.025 M, (d) effect of addition of ½BrO 3 0.06 M. Computer simulation results: effect of addition of [Br ] (e) ð1:0 102 MÞ; ðfÞð1:0 103 MÞ. Arrow indicates the instant of addition of bromide ion/Fructose in the reaction mixture.
2. F [0.025M] constant and [OA] is variable. Following situations arise: (a) For [OA] ¼ 0.008 M, and below no oscillations were observed. (b) When [OA] ¼ 0.01–0.015 M, only one type of oscillation is observed as the induction period decreases, number of cycles increases, life time increases, as the [OA] increases; amplitude 135 mV.
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
437
Fig. 4. Computed results for Bromide ion oscillations for the 4þ systems: BrO ð1:45 103 Þ M þ H2 SO4 (1.5 3 ð0:06 MÞ þ Ce M) + F (0.025 M) constant and (a) OA (0.001 M), (b) OA (0.1 M), (c) OA (0.2 M), (d) OA (0.3 M), (e) OA (0.7 M).
(c) When [OA] ¼ 0.02–0.055 M, sequential oscillations are observed, induction period is maximum and life time and number of cycles remain unaltered, amplitude decreases with increase in concentration, time pause increases. In case of second type of oscillations the number of cycles, lifetime and amplitude decreases sharply.
Fig. 5. Computed results for Bromide ion oscillations for the 4þ systems: BrO (1:45 103 MÞ þ H2 SO4 (1.5 3 (0.06 M) + Ce M) + OA (0.05 M) constant and (a) F (0.005 M), (b) F (0.01 M), (c) F (0.025 M), (d) F (0.035 M), (e) F (0.05 M).
(d) Between [OA] ¼ 0.07–0.25 M, only one type of oscillations occur in which the induction period is same, number of cycles tend to
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R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
decrease with increasing [OA], amplitude remains constant. (e) Above [OA] ¼ 0.3 M, no oscillations were observed. 3. [OA] (0.05 M) constant and [F] is variable: (a) When [F] ¼ (0.005 M), no oscillations were observed. (b) When [F] ¼ (0.009 M), only one type oscillations with induction period 2.00 min. (c) When [F] ¼ 0.015–0.3 M, (sequential oscillations) induction period 1.25 min. (d) When [F] ¼ 0.03–0.3 M, no induction period was found and, (e) when [F] ¼ 0.40 M, no oscillations could be detected. 4. Induction period is negligible, sequential oscillations also occur in a definite range of [F] and [OA]. 5. The oscillations are Br ion controlled. Attempt was made to estimate [Br ] during oscillations. But these yield only a rough estimate. Br2 evolution results confirm that it is one of the major end product of both (a) F þ BrO 3 (b) F þ BrO þ OA reaction. Further both the rate of 3 evolution as well as the maximum ½Br2 102 M indicate that Br2 is mainly generated by reaction (a). This is in conformity with results reported in an earlier paper [13]. In case of fructose oscillator [13], where oscillations are free-radical controlled, the free radical P is generated from the reaction of Ce4þ with acid P which is produced by the reaction of F þ BrO 3. This free radical P reacts with BrO2 and the reaction acts as a negative feedback to counter the autocatalysis of HBrO2 . Hence, ultimately the oscillatory reaction is free-radical controlled. However in OA + F system, COOH free radicals produced from OA þ Ce4þ reaction react with BrO2 to produce HBrO2 and thus the possibility of autocatalysis of HBrO2 is restored. Hence, when the rates of autocatalytic reaction and inhibiting reaction are balanced, once again Br controlled oscillations occur as it happens in the present case. A tentative mechanism based on the above ideas and the mechanism for fructose and oxalic acid oscillator based on modified version [13] of FKN mechanism [16] can be postulated as follows:
Br þ HOBr þ Hþ Br2 þ H2 O
ð1Þ
Br þ HBrO2 þ Hþ 2HOBr
ð2Þ
þ Br þ BrO 3 þ 2H HOBr þ HBrO2
ð3Þ
þ 2HBrO2 HOBr þ BrO 3 þH
ð4Þ
þ HBrO2 þ BrO 3 þ H Br2 O4 þ H2 O
ð5Þ
Br2 O4 2BrO2
ð6Þ
Ce3þ þ BrO2 þ Hþ Ce4þ þ HBrO2
ð7Þ
P þ Ce4þ P þ Ce3þ þ Hþ
ð8Þ
þ F þ BrO 3 þ H ! P þ HOBr þ H2 O
ð9Þ
HOBr þ P ! Products þ Br þ Hþ
ð10Þ
2P ! Inert Products
ð11Þ
P þ BrO2 ! Products þ Br þ Hþ
ð12Þ
F þ Ce4þ ! P þ Other products
ð13Þ
Ce4þ þ OA ! Ce3þ þ COOH þ CO2 þ Hþ
ð14Þ
BrO2 þ COOH ! HBrO2 þ CO2
ð15Þ
þ OA þ BrO 3 þ H ! HBrO2 þ 2CO2 þ H2 O
ð16Þ F þ 2HOBr ! P þ 2Br þ H2 O þ 2Hþ
ð17Þ
Here P is 2-keto-L -gulonic acid produced by oxidation of one –CH2 OH group of fructose to COOH. Using the above model and using the rate constants and the initial values given in Tables 1 and 2, numerical modeling was attempted. The mechanism yields non-linear equations involving 13 variables. The mechanism has been tested by computer simulation for which the results are recorded in Figs. 4 and 5. The rate constants and initial conditions used in the computations are given in Tables 1 and 2. The experimental results are in agreement with respect to following points. Computer results show in agreement with experiments, that the
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440 Table 1 Rate constants Step 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Forward reaction 2
1
8:0E09 M s 2:5E06 M2 s1 1:6 M3 s1 3:0E03 M1 s1 33:0 M2 s1 7:5E04 s1 6:2E04 M1 s1 3 M1 s1 (assigned) 0:015 M2 s1 (assigned) 3 M1 s1 (assigned) 2:0E9 M1 s1 (assigned) 1:0E9 M1 s1 (assigned) 5:0E-3 M1 s1 (assigned) 0:01 M1 s1 (assigned) 1:0E09 M1 s1 (assigned) 1:0E-6 M2 s1 (assigned) 5:5E03 M2 s1 (assigned)
Backward reaction 80:0 s1 2:0E 05 M1 s1 3:2 M1 s1 1:0E 08 M1 s1 2:2E03 s1 1:4E09 M1 s1 8:4E03 M1 s1 2:2E04 M2 s1
Table 2 Initial values of reactants Reactant
Value
½Br [HOBr] ½Br2 ½HBrO2 ½BrO 3 ½Br2 O4 ½BrO2 ½Ce4þ [P] [P ] [F] [OA] ½ COOH
1.0E ) 20 M 1.0E ) 20 M 1.0E ) 20 M 7.0E ) 07 M 0.06 M 2.0E ) 07 M 1.0E ) 20 M 0.00145 M 1.0E ) 20 M 1.0E ) 20 M 0.005–0.05 M 0.001–0.7 M 1.0E ) 20
induction period is small and oscillation occurs below the critical limit of [F] when OA is present. Since both BrO2 and P are produced simultaneously, induction time is small and negligible. Another important aspect of F + OA mixed substrate oscillator is that addition of Br -ions in sufficient amount suppresses, oscillations (Fig. 3) and further, oscillations are revived by addition of [F]. This is also confirmed by computer simulation (Fig. 3). This is in sharp contrast with the behaviour of [F] oscillator, which is non-bromide ion controlled and where the oscillations are generated by radical control.
439
An important feature of oscillatory behaviour is that sequential oscillations are observed within a certain range of [F]. It can be understood qualitatively as follows. The first type of oscillations occurs due to free radical generated from P. During oscillations, P is oxidized to tartaric acid, which also generates the corresponding free radical. When sufficient amount of such free radicals have accumulated, second type of oscillations appear. The explanation is similar to the case of B–Z oscillator with ascorbic acid and acetone as organic substrate [17]. The important shortcoming of the model is that it is not able to predict sequential oscillation, for which further amplification of the model is needed. The mechanism is tentative justification of the assigned rate constant is needed. For simplification additional reaction of COOH have not been included. Further work is in progress and would be reported in due course. Thus fructose oscillator is a typical case where switching of one mechanism to another can take place on addition of oxalic acid since in the latter case oscillations are Br controlled in the absence of oxalic acid [13].
Acknowledgements Thanks are due to Department of Science and Technology and Indian National Science Academy for financial support. One of the authors (PC) also thanks the Council of Scientific and Industrial Research (New Delhi, India) for the award of a Senior Research Fellowship.
References [1] P. Gray, S.K. Scott, Chemical Oscillations and Instabilities, Clarendon Press, Oxford, 1990. [2] G. Nicolis, I. Prigogine, Self-organization in Non-equilibrium Systems, Wiley, New York, 1977. [3] C. Britton, E. Kendall Pye, A.K. Ghosh, B. Hess (Eds.), Biological and Biochemcal Oscillations, Academic Press, New York, 1973. [4] A.P. Peacock, An introduction to the Physical Chemistry of biological Organization, Clarendon Press, Oxford, 1983.
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[5] A. Goldbeter, Biochemical Oscillations and Cellular Rhythms, The molecular Basis of Periodic and Chaotic behaviour, Cambridge University Press, Oxford, 1996. [6] K.P. Zeyer, F.W. Schneider, J. Phys. Chem. A 102 (1998) 9702. [7] H.D. F€ orsterling, Sz. Muranyi, Z. Nosticzius, J. Phys. Chem. 94 (1990) 2915. [8] Z. Noszticzius, Z. Bondar, L. Garamszegi, M. Wittman, J. Phys. Chem. 95 (1991) 6575. [9] Y. Gao, H.D. F€ orsterling, J. Phys. Chem. 99 (1995) 8438. [10] R.P. Rastogi, G.P. Misra, Chem. Phys. Lett. 174 (1990) 617. [11] R.J. Field, P.M. Boyd, J. Phys. Chem. 89 (1985) 3707.
[12] L. Gy€ orgyi, T. Turanyi, R.J. Field, J. Phys. Chem. 94 (1990) 7162. [13] R.P. Rastogi, M.M. Husain, P. Chand, G.P. Misra, M. Das, Chem. Phys. Lett. 353 (2002) 40. [14] R.P. Rastogi, M.M. Husain, P. Chand, M. Das, Indian J. Chem. 39A (2000) 679. [15] R.P. Rastogi, R. Khare, G.P. Misra, S. Srivastava, Indian J. Chem. 36A (1997) 19. [16] R.J. Field, E. K€ or€ os, R.M. Noyes, J. Am. Chem. Soc. 94 (1972) 8649. [17] R.P. Rastogi, G.P. Misra, I. Das, A. Sharma, J. Phys. Chem. 97 (1993) 2571.
Novel oscillatory reactions involving double substrate R.P. Rastogi a
a,*,1
, Prem Chand
b
Chemistry Department, Lucknow University, UP Council of Science and Technology, Lucknow 226001, India b Food Toxicology Division, ITRC, Lucknow 226003, India Received 19 April 2002; in final form 28 November 2002
Abstract The oscillatory features of a novel type B–Z type oscillator, fructose [F] + oxalic acid ½OA þ Ce4þ þ BrO 3 þ H2 SO4 has been investigated. The induction time is found to be usually small or negligible. Both single frequency oscillations and two oscillatory states separated by a time-pause are observed. Oscillations occur between two critical limits of [F] and [OA]. A tentative mechanism has been suggested which involves both Br ion control and free radical control. Computer simulation correctly predicts some of the oscillatory features such as (i) time of initiation, (ii) critical limits of [OA] and (iii) stoppage of oscillations by higher ½Br , confirming the primary role of Br control mechanism. Ó 2003 Published by Elsevier Science B.V.
1. Introduction Coupling and switching of control mechanism is of potential importance for the study of complex oscillatory processes [1,2] and physiological systems [3–5]. In physiological systems, both transport processes and chemical reactions can exercise control. In chemical systems, B–Z reaction is a good example of such coupling in a multi-component reaction network. In the classical B–Z system at room temperature and at low malonic acid [MA], Br control prevails while at higher [MA], oscillations can be explained and modeled
*
Corresponding author. E-mail addresses: [email protected] (R.P. Rastogi), [email protected] (P. Chand). 1 Present address: 295/281 KA, Asherfabad, Lucknow 226003, (UP) India.
on the basis of free radical control [6]. Evidence is provided by the detection of MA radical which is experimentally shown to react with BrO2 [7]. The stirring effects are related to diffusion-controlled reaction. In both the situations of high and low [MA], the experimental results during stirring can be semi-quantitatively interpreted on the basis of diffusion-controlled free-radical reaction as shown by Noszticzius et al. [8], which is evidently the one involved in the Radicaltor. Recent studies 2þ by Gao and F€ orsterling on ½RuðdipyÞ3 þ bromomalonic acid ðBrMAÞ þ BrO3 system [9] suggest the occurrence of two negative feedback loops viz., the primary feedback loop is the reaction of Br with HBrO2 and the secondary loop involves reactions of organic radicals with BrO2 radicals. The new experimental results involving radical-controlled oscillating B–Z reaction further confirm the existence of the second loop. However, the primary loop cannot be ruled out.
0009-2614/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V. doi:10.1016/S0009-2614(02)01980-2
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
No oscillations are observed in oxalic acid ½OA þ Ce4þ þ BrO 3 þ H2 SO4 [10]. However, when acetone is added to the system, oscillations are observed due to removal of bromine and consequently lowering of ½Br to the level required for oscillations to occur. Further, in the former case, many features of the reaction can be simulated on the basis of bromine–hydrolysis–controlled model due to Field and Boyd [11]. When [F] is used as organic substrate, oscillations occur only within a very limited range of concentration of [F] where the possibility of dual control [12,13] of Br and BrO2 cannot be ruled out as the earlier detailed studies show. It has been reported that when tartaric acid + fructose are used as double substrate, oscillations are observed below the lower critical limit of [F] [14]. Anticipating that oxalic acid ½OA þ ½F as double substrate would behave in a similar fashion but with important difference in reaction mechanism, the detailed study of the latter oscillator was undertaken and the results are reported in the present communication.
435
at interval of 0.1 s. using Perkin–Elmer UV/Vis spectrophotometer Lambda BIO 20. Cuvette having cross-sectional area equal to 1 1 cm2 in which, the solution was continuously stirred with a magnetic stirrer. The results are recorded in Figs. 1–3. The computer simulation results following the procedure described earlier [13] are recorded in Figs. 3–5. The effect of (a) order of addition of organic substrates on oscillation characteristics and (b)
2. Experimental 2.1. Materials Fructose, oxalic acid, sulphuric acid and KCl (E. Merck), cerric ammonium sulphate (AR, Thomas Baker), potassium bromide (S.D. Fine Chem.), potassium bromate (AR, CDH) and acrylamide (LR, Koch-light) were used as such without purification. All solutions were prepared in 1.5 M sulphuric acids in double distilled water. 2.2. Procedure + results Experimental procedure for (i) monitoring of oscillations, (ii) estimation of ½Br during various stages of oscillations using Orion electrode and electronic recorder, (iii) the study of kinetics of Br2 evolution was the same as followed earlier [13,14]. [Br ] during oscillations is found to be 106 M. The exact magnitude cannot be estimated since the system is far away from equilibrium. The absorbance of reaction mixture was measured at 530 nm
Fig. 1. Oscillations in bromide ion potential (I) and redox potential (II), for the system: H2 SO4 ð1:5 MÞ þ BrO 3 ð0:06 MÞ þ Ce4þ ð1:45 103 MÞ þ F ð0:025 MÞ þ (a) OA (0.008 M), (b) OA (0.01 M), (c) OA (0.025 M), (d) OA (0.03 M), (e) OA (0.045 M), (f) OA (0.055 M), (g) (0.06M), (h) OA (0.1 M), (i) OA (0.25 M), (j) OA (0.3 M), respectively. Temp. 28 1 °C.
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Fig. 2. Oscillations in bromide ion potential (I) and redox potential (II), for the system: H2 SO4 ð1:5 MÞ þ BrO 3 ð0:06 MÞ þ Ce4þ ð1:45 103 MÞ þ OA ð0:05 MÞþ (a) F (0.005 M), (b) F (0.01 M), (c) F (0.03 M), (d) F (0.05 M), (e) F (0.06 M), (f) F (0.1 M), (g) F (0.2 M), (h) F (0.3 M), (i) F (0.35 M), (j) F (0.40 M), respectively. Temp. 28 1 °C.
addition of F and BrO 3 after stoppage of oscillations was investigated in the same manner as described earlier [13–15]. The experimental results are recorded in Figs. 1–3.
3. Discussion Results recorded in Figs. 1 and 2 show that: 1. Oscillations are initiated in F + OA or OA + F oscillators within definite concentration limits of [OA] and [F], respectively.
Fig. 3. Effect of addition of KBr/Fructose/ BrO 3 on Br ion 4þ potential for the systems: BrO ð0:06 MÞ þ Ce ð1:45 3 103 MÞ þ H2 SO4 (1.5 M) + F (0.025 M) + OA (0.05 M). Experimental results: effect of addition of [Br ] (a) and (b) 2:0 102 M, (c) effect of addition of [F] 0.025 M, (d) effect of addition of ½BrO 3 0.06 M. Computer simulation results: effect of addition of [Br ] (e) ð1:0 102 MÞ; ðfÞð1:0 103 MÞ. Arrow indicates the instant of addition of bromide ion/Fructose in the reaction mixture.
2. F [0.025M] constant and [OA] is variable. Following situations arise: (a) For [OA] ¼ 0.008 M, and below no oscillations were observed. (b) When [OA] ¼ 0.01–0.015 M, only one type of oscillation is observed as the induction period decreases, number of cycles increases, life time increases, as the [OA] increases; amplitude 135 mV.
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
437
Fig. 4. Computed results for Bromide ion oscillations for the 4þ systems: BrO ð1:45 103 Þ M þ H2 SO4 (1.5 3 ð0:06 MÞ þ Ce M) + F (0.025 M) constant and (a) OA (0.001 M), (b) OA (0.1 M), (c) OA (0.2 M), (d) OA (0.3 M), (e) OA (0.7 M).
(c) When [OA] ¼ 0.02–0.055 M, sequential oscillations are observed, induction period is maximum and life time and number of cycles remain unaltered, amplitude decreases with increase in concentration, time pause increases. In case of second type of oscillations the number of cycles, lifetime and amplitude decreases sharply.
Fig. 5. Computed results for Bromide ion oscillations for the 4þ systems: BrO (1:45 103 MÞ þ H2 SO4 (1.5 3 (0.06 M) + Ce M) + OA (0.05 M) constant and (a) F (0.005 M), (b) F (0.01 M), (c) F (0.025 M), (d) F (0.035 M), (e) F (0.05 M).
(d) Between [OA] ¼ 0.07–0.25 M, only one type of oscillations occur in which the induction period is same, number of cycles tend to
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decrease with increasing [OA], amplitude remains constant. (e) Above [OA] ¼ 0.3 M, no oscillations were observed. 3. [OA] (0.05 M) constant and [F] is variable: (a) When [F] ¼ (0.005 M), no oscillations were observed. (b) When [F] ¼ (0.009 M), only one type oscillations with induction period 2.00 min. (c) When [F] ¼ 0.015–0.3 M, (sequential oscillations) induction period 1.25 min. (d) When [F] ¼ 0.03–0.3 M, no induction period was found and, (e) when [F] ¼ 0.40 M, no oscillations could be detected. 4. Induction period is negligible, sequential oscillations also occur in a definite range of [F] and [OA]. 5. The oscillations are Br ion controlled. Attempt was made to estimate [Br ] during oscillations. But these yield only a rough estimate. Br2 evolution results confirm that it is one of the major end product of both (a) F þ BrO 3 (b) F þ BrO þ OA reaction. Further both the rate of 3 evolution as well as the maximum ½Br2 102 M indicate that Br2 is mainly generated by reaction (a). This is in conformity with results reported in an earlier paper [13]. In case of fructose oscillator [13], where oscillations are free-radical controlled, the free radical P is generated from the reaction of Ce4þ with acid P which is produced by the reaction of F þ BrO 3. This free radical P reacts with BrO2 and the reaction acts as a negative feedback to counter the autocatalysis of HBrO2 . Hence, ultimately the oscillatory reaction is free-radical controlled. However in OA + F system, COOH free radicals produced from OA þ Ce4þ reaction react with BrO2 to produce HBrO2 and thus the possibility of autocatalysis of HBrO2 is restored. Hence, when the rates of autocatalytic reaction and inhibiting reaction are balanced, once again Br controlled oscillations occur as it happens in the present case. A tentative mechanism based on the above ideas and the mechanism for fructose and oxalic acid oscillator based on modified version [13] of FKN mechanism [16] can be postulated as follows:
Br þ HOBr þ Hþ Br2 þ H2 O
ð1Þ
Br þ HBrO2 þ Hþ 2HOBr
ð2Þ
þ Br þ BrO 3 þ 2H HOBr þ HBrO2
ð3Þ
þ 2HBrO2 HOBr þ BrO 3 þH
ð4Þ
þ HBrO2 þ BrO 3 þ H Br2 O4 þ H2 O
ð5Þ
Br2 O4 2BrO2
ð6Þ
Ce3þ þ BrO2 þ Hþ Ce4þ þ HBrO2
ð7Þ
P þ Ce4þ P þ Ce3þ þ Hþ
ð8Þ
þ F þ BrO 3 þ H ! P þ HOBr þ H2 O
ð9Þ
HOBr þ P ! Products þ Br þ Hþ
ð10Þ
2P ! Inert Products
ð11Þ
P þ BrO2 ! Products þ Br þ Hþ
ð12Þ
F þ Ce4þ ! P þ Other products
ð13Þ
Ce4þ þ OA ! Ce3þ þ COOH þ CO2 þ Hþ
ð14Þ
BrO2 þ COOH ! HBrO2 þ CO2
ð15Þ
þ OA þ BrO 3 þ H ! HBrO2 þ 2CO2 þ H2 O
ð16Þ F þ 2HOBr ! P þ 2Br þ H2 O þ 2Hþ
ð17Þ
Here P is 2-keto-L -gulonic acid produced by oxidation of one –CH2 OH group of fructose to COOH. Using the above model and using the rate constants and the initial values given in Tables 1 and 2, numerical modeling was attempted. The mechanism yields non-linear equations involving 13 variables. The mechanism has been tested by computer simulation for which the results are recorded in Figs. 4 and 5. The rate constants and initial conditions used in the computations are given in Tables 1 and 2. The experimental results are in agreement with respect to following points. Computer results show in agreement with experiments, that the
R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440 Table 1 Rate constants Step 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Forward reaction 2
1
8:0E09 M s 2:5E06 M2 s1 1:6 M3 s1 3:0E03 M1 s1 33:0 M2 s1 7:5E04 s1 6:2E04 M1 s1 3 M1 s1 (assigned) 0:015 M2 s1 (assigned) 3 M1 s1 (assigned) 2:0E9 M1 s1 (assigned) 1:0E9 M1 s1 (assigned) 5:0E-3 M1 s1 (assigned) 0:01 M1 s1 (assigned) 1:0E09 M1 s1 (assigned) 1:0E-6 M2 s1 (assigned) 5:5E03 M2 s1 (assigned)
Backward reaction 80:0 s1 2:0E 05 M1 s1 3:2 M1 s1 1:0E 08 M1 s1 2:2E03 s1 1:4E09 M1 s1 8:4E03 M1 s1 2:2E04 M2 s1
Table 2 Initial values of reactants Reactant
Value
½Br [HOBr] ½Br2 ½HBrO2 ½BrO 3 ½Br2 O4 ½BrO2 ½Ce4þ [P] [P ] [F] [OA] ½ COOH
1.0E ) 20 M 1.0E ) 20 M 1.0E ) 20 M 7.0E ) 07 M 0.06 M 2.0E ) 07 M 1.0E ) 20 M 0.00145 M 1.0E ) 20 M 1.0E ) 20 M 0.005–0.05 M 0.001–0.7 M 1.0E ) 20
induction period is small and oscillation occurs below the critical limit of [F] when OA is present. Since both BrO2 and P are produced simultaneously, induction time is small and negligible. Another important aspect of F + OA mixed substrate oscillator is that addition of Br -ions in sufficient amount suppresses, oscillations (Fig. 3) and further, oscillations are revived by addition of [F]. This is also confirmed by computer simulation (Fig. 3). This is in sharp contrast with the behaviour of [F] oscillator, which is non-bromide ion controlled and where the oscillations are generated by radical control.
439
An important feature of oscillatory behaviour is that sequential oscillations are observed within a certain range of [F]. It can be understood qualitatively as follows. The first type of oscillations occurs due to free radical generated from P. During oscillations, P is oxidized to tartaric acid, which also generates the corresponding free radical. When sufficient amount of such free radicals have accumulated, second type of oscillations appear. The explanation is similar to the case of B–Z oscillator with ascorbic acid and acetone as organic substrate [17]. The important shortcoming of the model is that it is not able to predict sequential oscillation, for which further amplification of the model is needed. The mechanism is tentative justification of the assigned rate constant is needed. For simplification additional reaction of COOH have not been included. Further work is in progress and would be reported in due course. Thus fructose oscillator is a typical case where switching of one mechanism to another can take place on addition of oxalic acid since in the latter case oscillations are Br controlled in the absence of oxalic acid [13].
Acknowledgements Thanks are due to Department of Science and Technology and Indian National Science Academy for financial support. One of the authors (PC) also thanks the Council of Scientific and Industrial Research (New Delhi, India) for the award of a Senior Research Fellowship.
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R.P. Rastogi, P. Chand / Chemical Physics Letters 369 (2003) 434–440
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