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Chapter 3 Chemical Oscillations

Chapter 3 Chemical Oscillations. Definition: Resetting of clock reactions 3.1 BZ oscillator reactants and catalysis Bromate malonic acid metal ion or ligand compounds Batch phenomena analysis: Br- electrode : Br- Pt electrode: mostly metal ion Feature: Relaxation oscillations

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Chapter 3 Chemical Oscillations

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  1. Chapter 3 Chemical Oscillations • Definition: Resetting of clock reactions • 3.1 BZ oscillator reactants and catalysis Bromate malonic acid metal ion or ligand compounds • Batch phenomena analysis: Br- electrode : Br- Pt electrode: mostly metal ion • Feature: Relaxation oscillations AB Br- consume slowly slow Metalox increase BC: bromide sharp drop quick Metal(ox at state) rise CD: Bromide rise slowly , Mred rise slowly DA: Bromide rise suddenly Mred rise rapidly • Bacth: induction→oscillations → steady state →equilibrium • Bromate and malinic acid decrease stepwise

  2. 3.2 Mechanism for BZ reaction A Field- Koros -Noyes mechanism FKN(mechanism) J. Am. Chem. Soc. 1972 94, 8649-64 B Chemical Oscillatlons, Chaos, and Fluctuations in Flow Reactors(Classification of phenomena) F. W. Schneider' and A. F. Miinster Institute of Physical Chemistry, University of Wiirzburg, Marcusstrasse 911 1, 0-8700 Wiirzburg, FRG J. Phys. Chem. 1991, 95, 2130-2138 C Deterministic chaos in the Belousov-Zhabotinskii reaction: experiments and simulations (mechanism for complex oscillations) Zhang, Dongmei; Gyorgyi, Laszlo; Peltier, William R. Department of Physics, University of Toronto, Toronto, ON, Can. Chaos (1993), 3(4), 723-45.

  3. Process A Bromide consumption FKN3 BrO3-+Br-+2H+→ HBrO2+HBrO Rate=k3[BrO3-][Br-][H+]2 FKN2 HBrO2+Br-  2HOBr Rate=k2[HBrO2][Br-][H+] Process A sum reaction BrO3-+2Br-+3H+->3HBrO • Process B HBrO2 autocatalysis (FKN5) BrO3-+ HBrO2+H+ <->2BrO2·+2H+ • Rate=k5[BrO3-][HBrO2][H+]-k-5[BrO2·] (FKN6) BrO2· +Mred+H+→ HBrO2+Mox • Rate=k6[BrO2·][Mred][H+] • Process B sum reaction • BrO3- +HBrO2+2Mred+3H+→2HBrO2+2Mox+H2O Process B is limited by the self-disproportionation reaction of HBrO2 • FKN4 2HBrO2 → BrO3- +HOBr+H+ Rate=k4[HBrO2]2 Switch from A to B when consumption of HBrO2 by Bromide to HBrO2 autocatalysis Rate 2=Rate 5 k2[HBrO2][Br-][H+]= k5[BrO3-][ HBrO2][H+] [Br-]cr=(k5/k2)[BrO3-]≈1.4×10-5[BrO3-] Bromide ion as inhibitor consume autocatalyst HBrO2 • Process C Br- reproduction The catalyst return low oxidation state resetting the clock 1Br-→HBrO2+HOBR→2HBrO2+BrMA+2Mox→HOBr+ BrMA+2Mox→2BrMA+2Mox HOBr+MA→BrMA+H2O 2Mox+MA+BrMA→fBr-+2Mred+other products Rate=kc[Org][Mox] • Special points: 1 EMn+1 / Mn=0.9～1.5 Mn3+, Ferroin, Ce4+, Ru(bipy)3 2+ • 2. MA may be replace by other organic compound • which may be brominated by HOBr • 3. f is a adjusted parameter f>2/3, [Br-] increases after the cycle

  4. 3.3 From mechanism to oregonator model • A oregonator • J Chem Phys. 1974, 60, 1877-84 • O3 A+Y=X+P V3=k3AY • O2 X+Y=2P V2=K2XY • O5 A+X=2X+2Z V5=K5AX • O4 2X=A+P V4=K4X2 • OC Z+B=0.5fY VC=KcBZ • A: Bromate, Y: Bromide, P: HBrO hypobramate, X: subbromate HBrO2, Z: Mox, B: organic compound • DX/dt=v3-V2+V5-2V4 • DY/dt=-V3-V2+0.5fVc • DZ/dt=2V5-Vc

  5. 3.4 BZ Complex oscillations and Chaos A Phenomena In Batch transient complex oscillations

  6. In CSTR Hudson Mixed-mode oscillations at High flowrate

  7. Swinney Period-doubling oscillations and Chaos and mixed-mode oscillations at low flowrate

  8. Roux Quansiperiodic Oscillations and Chaos 3325-3338

  9. Hourai symmetric diagram around P1 mixed-mode oscillations at low flowrate JPC 1985,89,1760-1764 LS SS→0n →1n → 12 → chaos → 11 →chaos → 21 → 31→ 10

  10. B Mechnism and model L Gyorgyi and R J Field Two cycle coupling • Oregonator HBrO2 autocatalysis and consumption and production of Br- • BrMA cycle production by bromination of MA consumed by oxidation of Catalylyst • 11 variable JPC 1991, 95, 3159-3165 and 6594-6602 9 variables [MA] as constant deleting Br· bromine radical by rate sensitivity analysis

  11. 7 variable removing diffusion-controlled reactions (B1 B9), HOBr replaced by BrMA Brmine deleted 4 variable model delete the Ce(III) by conservation rule remove the MA radical by QSSA Quasi Steady State Assumption remove the BrO2 radical by QSSA or EQA Equilibrium Assumption

  12. 3 variable model remove the bromide by QSSA Modify the 4 variable model D4 according to mass action law delete D8 N model Nature 1992, 355, 808-810

  13. Questions: (1)When and how can we get PD Mixed-mode and QP dynamics by two cycle coupling ? (2)What is Experimental whole sequence of BZR in a CSTR? ….31 PD 21 PD 10 PD 11 PD 12 PD 13 PD…… (3)Can we use the model to simulate the spatiotemporal patterns in the medium of complex and Chaos?

  14. 3.5 Dimensionless equation of Oregonator • Definition: to make the variable dimensionless • Why: ①variable reduction ② for relaxation oscillations and ③f oscillatory range • ④slow and fast variable • x=2k4X/k5A y=k2Y/k5A z=kck4BZ/(k5A)2 τ=kcBt • ε=kcB/k5A=1×10-2 • ε’=2kck4B/k2k5A=2.5×10-5 • q=2k3k4/k2k5=9×10-5 • A=0.06M B=0.02M • X(1-X) quadratic autocatalysis

  15. C Steady-state approximation for bromide ε’ is so small , dy/dt change quickly comparing to dx/dt and dz/dt, Relative to x, z, y change quickly to steady state, for whole dynamics, dy/dt≈0 • y=yss=fz/(q+x) εdx/dt=x(1-x)-(x-q)fz/(q+x) • dz/dt=x-z • ε<<1 x fast variable z slow variable D. Simulation of kinetics of equation f=1/4 high x z stable state f=1 oscillations f=3 low x z stable state steady state dx/dt=0 dz/dt=0 xss=zss=0.5{1-(f+q)+[(f+q-1)2+4q(1+f)]0.5} yss=fzss/(q+xss) solid line stable state dash line unstable state 1/2<f<1+20.5

  16. 3.6 Pictorial explanation of dynamics Feature: dx/dt=0 dz/dt=0 1 f=0.25 intersection at right stable point high x f=1 intersection at the middle branch of nullcline oscillations f=3 intersection at left branch of nullcline stable state at low x 2. dx/dt is much bigger than dz/dt x: quick variable z: slow variable 3. nullcline dx/dt=0 dz/dt=0 above the lines dx/dt<0 dz/dt<0 belov the lines dx/dt>0 dz/dt>0 4. x nullcline S type Bistable middle line is nonstable 5 State at x nullcline slow movement State at other position x quick movement go to x nullcline then slow movement Explain the relaxation oscillations The intersection lies at the middle branch of x nullcline , from any point, horizontal movement and movement along the A ,B branch are quick and slow, respectively, never reach the intersection. The amplitude and period depend on the tempreture and concentrations, not the initial point. .

  17. 3.7Conditions for oscillations intersection at middle branch, and at nullclines between minimum and maximum of x dx/dt=0 εdx/dt=x(1-x)-(x-q)fz/(q+x) dz/dx=0 minimum point : Maximum point: • X=Z • Minimum f=1+1.414 • Maximum: f=0.5 • Oscillations : 0.5< f<1+1.414 • Precondition: ε<<1 • When ε rise, the range of f can be decreased. • ε<<1 ε=kcB/k5A A=[BrO3-]0 B=[MA]0 • [BrO3-]>>(kc/k5)[Org]=0.03[MA]

  18. 3.8 Amplitude and period of oscillations Amplitude EBr amplitue∞log(yA/yC) = 6.4 400mv Ept amplitude∞log(zA/zC) = 2.7 180mv Period: AB slowest period≈move time of AB dz/dt=x-z x is almost constant dz/dt=q-z intergrating the equation from A to B f=1

  19. 3.9 Excitability For stable steady state small perturbation system return quickly large perturbation system does not return back immediately. First a single excursion, develop a single oscillation this is excitability There is a critical value or threshold of perturbation from small perturbation to excitability For BZ reaction Small perturbation: from xss to X1 ---return xss straightforward Larger perturbation: ---from xss to x2 single oscillation When system is moving along the x-nullcline , it is virtually insensitive tofurther perturbation. This phenomena is call refractory.

  20. 3. 10 Other oscillatory systems • A Liquid phase oscillations 1. Bray-Liebhafsky oscillations • Iodate-catalysed disproportionation of hydrogen peroxide • 2H2O2=2H2O+O2 • JACS 1931, 53,38 2. Briggs-Rauscher oscillations • BR + Malonic acid • Gold to blue to colourless • J Chem. Edu 1973, 50,496 3. CIMA oscillations • Chlorite-iodide-malonic acid oscillations • B. Noszticzius Z., Ouyang Q., McCormick W.D., Swinney, H.L.:"Long-lived oscillations in the chlorite-iodide-malonic acid reaction in batch"J. Am. Chem. Soc. 114, 4290-4295 (1992) • Lengyel, I. & Epstein, I. R. [1990] "Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system," Science251, 650-652. Lengyel, I., Rábai, I. & Epstein, I. R. [1990a] "Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid," J. Am. Chem. Soc.112, 4606-4607. Lengyel, I., Rábai, I. & Epstein, I. R. [1990b] "Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction," J. Am. Chem. Soc.112, 9104-9110. Lengyel, I. & Epstein, I. R. [1992] "A chemical approach to designing Turing patterns in reaction-diffusion systems," Proc. Nat. Acad. Sci. (USA)89, 3977-3979. Lengyel, I. & Epstein, I. R. [1995] "The chemistry behind the first experimental chemical example of Turing patterns," in Chemical Waves and Patterns, eds.Kapral, R. & Showalter, K. (Kluwer, Dordrecht), pp.297-322. • Lengyel, I., Li, J., Kustin, K. & Epstein, I. R. [1996] "Rate constants for reactions between iodine and chlorine species: A detailed mechanism of the chlorine dioxide-chlorite-iodide reaction," J. Am. Chem. Soc.118, 3708-3719 • De Kepper, P., Epstein, I. R., Orbán, M. & Kustin, K. [1982] "Batch oscillations and spatial wave patterns in chlorite oscillating systems," J. Phys. Chem.86, 170-171. De Kepper, P., Boissonade, J. & Epstein, I. R. [1990] "Chlorite-iodide reaction: A versatile system for the study of nonlinear dynamical behavior," J. Phys. Chem.94, 6525-6536. De Kepper, P., Perraud, J. J., Rudovics, B. & Dulos, E. [1994] "Experimental study of stationary Turing patterns and their interaction with traveling waves in a chemical system," Int. J. Bifurcation and Chaos4, 1215-1231

  21. B Gas phase oscillations • CO oxidation at Pt single-crystal (110) most studied by ertl group in Max-plank institute • Hydrocarbon oxidation : cool frames • J. F. Griffiths Adv. Chem. Phys. 1986, 64, 203-303 C Gas evolution oscillations • Decomposition of formic acid by sulphuric acid the morgan reaction • HCOOH=H2O+CO supersaturation to nucleation then supersaturation again • The decomposition of aqueous ammonium nitrite • NH4NO2=N2+H2O • D. Chemical oscillations by transport of reactants • Benzaldehyde oxidation by oxygen • Oxidation of p-xylene to terephthalic acid E. Biochemical oscillations • Glycolysis oscillations ( to alcohol)( in vivi or vitro) • Michaelis-Menten kinetics • Activation inhibition • Allosteric effects • PO oscillations nicotinamide adenine dinucleotide Hydride NADH oxidation by oxygen catalyzed by peroxidase • Benno Hess, Quarterly Reviews of Biophysics 30, 2 (1997), pp. 121±176.

  22. 3.9 Oscillations in closed system • Feature of batch: A.easily set up and operated B. for every oscillations, small reactants are consumed, So each oscillations occurs against different from background concentration of reactants. Each oscillations is slightly different from its predecessor and subsequent excursion C. when composition move out from range of oscillations, then to steady state, to equilibrium

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