1. Nonlinear Chemistry Nonlinear Chemistry 双语课程课件（ Courseware) 双语课程课件（ Courseware) 主讲教师：高庆宇 主讲教师：高庆宇

2. Chapter 1 Introduction to basic concepts Chapter 1 Introduction to basic concepts 1. Phenomena, Mechanism and Theory and Control 1. Phenomena, Mechanism and Theory and Control Phenomena: Phenomena: Batch: Clock ， oligooscillations, oscillations, transient complex oscillations and chaos Batch: Clock ， oligooscillations, oscillations, transient complex oscillations and chaos Chemical waves: front, pulse, spiral, target, twist, scroll Chemical waves: front, pulse, spiral, target, twist, scroll Open system: multistability, oscillations, chaos, spatiotemporal pattern. Open system: multistability, oscillations, chaos, spatiotemporal pattern. Example: 1. Iodate-Sulfite landolt reaction red iodine appear clock reaction Example: 1. Iodate-Sulfite landolt reaction red iodine appear clock reaction

3. 2 oscillation reaction 2 oscillation reaction 1 clock reaction +negative regent +Open =oscillation Iodate-sulfite-Thiosulfate (TU, Ferricyanide Ion) Iodate-sulfite-Thiosulfate (TU, Ferricyanide Ion) JPC 1988,92,2804-2807 JPC 1988,92,2804-2807 not only simple oscillations not only simple oscillations But also complex oscillations and chaos

4. 1 closed system The link reactions between postive and negative feedback =oscillator in closed system The link reactions between postive and negative feedback =oscillator in closed system BZ: Bromate-Malonic acid +Catalyst BZ: Bromate-Malonic acid +Catalyst Orban: hydrogen peroxide-Thiocyanate-Copper(2+) +OH - Orban: hydrogen peroxide-Thiocyanate-Copper(2+) +OH - Jensen: Oxygen+sulfide+sulfite+catalyst Jensen: Oxygen+sulfide+sulfite+catalyst CIMA: chlorite+malonic acid+iodide CIMA: chlorite+malonic acid+iodide The oxidation of organicals by oxygen with CoCl 3 The oxidation of organicals by oxygen with CoCl 3 Simple oscillations, complex oscillations and Chaos Simple oscillations, complex oscillations and Chaos

5. J. Phys. Chem. 1995,99, 5379-5384 Iodate-sulfite

6. 3 spatiotemporal phenomena Reaction +Diffusion + … = Pattern Front, pulses, Targets and spiral Stable pattern Similar in nature

7. Mechanism: Mechanism: Intermediates, rate equation, ratio constants, differential equations, comparing the experiments with solution of equation. Intermediates, rate equation, ratio constants, differential equations, comparing the experiments with solution of equation. Control: Control: Changing conditions to control the path of reaction ， Feedback, Nonfeedback Changing conditions to control the path of reaction ， Feedback, Nonfeedback

8. Book and references Book and references A. An introduction to nonlinear Chemical dynamics I R Epstein; J A Pojman Oxford University press 1998 A. An introduction to nonlinear Chemical dynamics I R Epstein; J A Pojman Oxford University press 1998 B.Oscillations, Waves and Chaos in Chemical kinetics B.Oscillations, Waves and Chaos in Chemical kinetics Stephen K Scott Oxford University Press 1994 Stephen K Scott Oxford University Press 1994 C. The Geometry of Biological Time, Arthur T Winfree, 2000 Springer-Verlag C. The Geometry of Biological Time, Arthur T Winfree, 2000 Springer-Verlag D. I R Epstein, K Showalter Nonlinear Chemical Dynamics, JPC, 1996, 100, 13132 D. I R Epstein, K Showalter Nonlinear Chemical Dynamics, JPC, 1996, 100, 13132 E. 辛厚文， 非线性化学， 中国科大出版社， 1998 ，合肥 E. 辛厚文， 非线性化学， 中国科大出版社， 1998 ，合肥 F. Homepage: http://scet.cumt.edu.cn/fxx1/kejian57.htm F. Homepage: http://scet.cumt.edu.cn/fxx1/kejian57.htmhttp://scet.cumt.edu.cn/fxx1/kejian57.htm G. P Atkins, J D Paula, Physical Chemistry, W H Freeman and Company, New G. P Atkins, J D Paula, Physical Chemistry, W H Freeman and Company, New York, 2002 York, 2002 H. 欧阳颀， 反应扩散系统中的斑图动力学， 上海科技教育出版社， 2000 H. 欧阳颀， 反应扩散系统中的斑图动力学， 上海科技教育出版社， 2000 I. JPC(A,B,C), PCCP, JACS, PRL, PRE, Chaos, Nature, Scince I. JPC(A,B,C), PCCP, JACS, PRL, PRE, Chaos, Nature, Scince www.acs.org www.aps.org www.rsc.org www.aip.org www.acs.org www.aps.org www.rsc.org www.aip.orgwww.acs.orgwww.aps.orgwww.rsc.orgwww.aip.orgwww.acs.orgwww.aps.orgwww.rsc.orgwww.aip.org www.nature.org www.scimag.org www.nature.org www.scimag.orgwww.nature.orgwww.scimag.orgwww.nature.orgwww.scimag.org J. 内容更新辅助教材：高庆宇编， “ 非线性化学 ” ，中国矿业大学化工学 J. 内容更新辅助教材：高庆宇编， “ 非线性化学 ” ，中国矿业大学化工学 院， 2006. 院， 2006. K. R C Desai and R Kapral, “Dynamics of Self-Organized and Self- Assembled K. R C Desai and R Kapral, “Dynamics of Self-Organized and Self- Assembled Structures,” Cambridge University Press, 2009. Structures,” Cambridge University Press, 2009.

9. 1.2 History of nonlinear chemistry 1800---1960 ， Discovering occasionally, BR, BZ, Landolt Reaction, Oscillatory P ignition, Liesegang rings Theoretical chemist do ’ not believe the oscillations because of the Second law of thermodynamics 1800---1960 ， Discovering occasionally, BR, BZ, Landolt Reaction, Oscillatory P ignition, Liesegang rings Theoretical chemist do ’ not believe the oscillations because of the Second law of thermodynamics Nonequilibrium to equilibrium irreversibility Nonequilibrium to equilibrium irreversibility

10. 1960s Dissipation structure ( Necessary condition: nonequilibrium, nonlinearity) 1960s Dissipation structure ( Necessary condition: nonequilibrium, nonlinearity) 1970s FKN mechanism to explain BZ oscillations 1970s FKN mechanism to explain BZ oscillations R ． J ． Field ， E ． Koros and R ． M ． Noyes ． J ． Am ． Chem ． Soc ， 1972 ， 94, 8649 (1) – (3) Bromide comsuption (5)-(6) dynamics of catalysis autaocatalyzation autaocatalyzation (7)-(10) Bromide production (4) deletion of autocatalysis

11. Oregon model : Oregon model : X=[HBrO2] ， Y=[Br-] ， Z=2[Fe3+] X=[HBrO2] ， Y=[Br-] ， Z=2[Fe3+] Field R. J., Noyes.R J. Chem. Phys., 1974, 60, 1877 Field R. J., Noyes.R J. Chem. Phys., 1974, 60, 1877

12. 1980s Chemical Chaos : 1.sensitivity of initial value, 2. nonorder in local but order in whole dynamics 1980s Chemical Chaos : 1.sensitivity of initial value, 2. nonorder in local but order in whole dynamics BZ chaos quasiperiod chaos, period-doubling chaos, homoclinic Chaos. BZ chaos quasiperiod chaos, period-doubling chaos, homoclinic Chaos. Current = 0.335 mA Current = 0.335 mA

13. 0.325 mA

14. Designing oscillations in a CSTR Designing oscillations in a CSTR Positive feedback and negative feedback Positive feedback and negative feedback A+HX+H ﹥ nH X+H ﹥﹤ HX B+H ﹥ Q Bromate-Sulfite-Ferrocyanide system

15. 1990s Turing pattern, spirals and spatiotemporal pattern. 1990s Turing pattern, spirals and spatiotemporal pattern. Space order appears spontaneously from Homogenous system – Turing pattern like zebra Space order appears spontaneously from Homogenous system – Turing pattern like zebra (De kepper, I R Epstein, Swinney) (De kepper, I R Epstein, Swinney) Instability of spiral wave(Ouyang,Bar,Kappral) Instability of spiral wave(Ouyang,Bar,Kappral) Noise stochastic resonance (showalter et al.) Noise stochastic resonance (showalter et al.) Nonlinear reaction +diffusion=spatiotemporal pattern Linear reaction +diffusion+ supersaturation =liesegang ring

16. 2000s- spatiotemporal chaos, soft matter, cell signal, material pattern http://chaos.aip.org/ Control Control Nonlinear science in life Nonlinear science in life Pattern in three dimension Pattern in three dimension Importance in application by examples A Analytical chemistry (metal ion perturbation with amplitude and period, Yangmirskii, ) A Analytical chemistry (metal ion perturbation with amplitude and period, Yangmirskii, Strizhak) B Explaining nature and biology phenomena B Explaining nature and biology phenomena C Drug delivery (coupling with soft polymer) C Drug delivery (coupling with soft polymer) D Performance of fuel cell D Performance of fuel cell low temperature fuel cell: poisons H 2 S CO impurities in H low temperature fuel cell: poisons H 2 S CO impurities in H 2, But in oscillation state higher outputs are yielded.

17. CO electrooxidation on Pt (1) Deibert, M. C.; Williams, D. L. J. Electrochem. Soc. 1969, 116, 1290. (2) Szpak, S. J. Electrochem. Soc. 1970, 117, 1056. (3) Yamazaki, T.; Kodera, T. Electrochim. Acta 1990, 36, 639. (4) Zhang, J.; Datta, R. J. Electrochem. Soc. 2002, 149, A1423. (5) Zhang, J.; Datta, R. Electrochem. Solid State Lett. 2004, 7, A37. (6) Zhang, J.; Datta, R. J. Electrochem. Soc. 2005, 152, A1180. (7) Zhang, J. X.; Fehribach, J. D.; Datta, R. J. Electrochem. Soc. 2004, 151, A689. (8) Kiss, I. Z.; Bracket, A. W.; Hudson, J. L. J. Phys. Chem. A 2004, 108, 14599. (9) Bonnefont, A.; Varela, H.; Krischer, K. J. Phys. Chem. B 2005, 109, 3408. (10) Gasteiger, H. A.; Markovic, N. M.; Ross, P. N. J. Phys. Chem. B 1999, 103, 9616. (11) Gasteiger, H. A.; Markovic, N. M.; Ross, P. N. J. Phys. Chem. 1995, 99, 16757 (12) Jan Siegmeier, Nilfer Baba, and Katharina Krischer J. Phys. Chem. C, 2007, 111 (36), 13481-13489 (13) Richard Morschl, Johannes Bolten, Antoine Bonnefont, and Katharina Krischer. J. Phys. Chem. C, 2008, 112 (26), 9548-9551

18. Sulfide electro-oxidation on Pt (1) Chen A, Miller B. Potential oscillations during the electrocatalytic oxidation of sulfide on a microstructured Ti/Ta2O5-IrO2 electrode. J Phys Chem B, 2004, 108: 2245 － 2251 (2) Helms H, Kunz H, Jansen W. Current-potential oscillations on pyrite electrodes in alkaline sulfide solution. Monatsh Chem, 1998, 129: 1275 － 1284 (3) Helms H, Schlomer E, Jansen W. Oscillation phenomena during the electrolysis of alkaline sulfide solution on platinum electrodes. Monatsh Chem, 1998, 129: 617 － 623 (4) Feng J, Gao Q, Xu L, Wang J. Nonlinear phenomena in the electrochemical oxidationof sulfide. Electrochem Commun, 2005, 7:1471 － 1476 (5) Miller B, Chen A. Oscillatory instabilities during the electrochemical oxidation of sulfide on a Pt electrode. J Electroanal Chem, 2006, 588: 314 － 323 (6) FENG JiaMin, GAO QingYu †, LI Jun, LIU Li & MAO ShanCheng, Current oscillations during the electrochemical oxidation of sulfide in the presence of an external resistor, Sci China Ser B-Chem Apr. 2008 vol. 51 no. 4 333-340 (7) S. Choi, J. H.Wang, Z. Cheng, and M. Liu "Surface modification of Ni-YSZ using niobium oxide for sulfur tolerant anodes in solid oxide fuel cells," Journal of the Electrochemical Society, Volume 155, Issue 5, B449- B454 (2008). (8) H. T. Chen, Y. M. Choi, M. Liu, and M. C. Lin, "A first-principles analysis for sulfur tolerance of CeO2 in solid oxide fuel cells," Journal of Physical Chemistry C, 111, 11117-11122, 2007.

19. (9) Z. Cheng and M. Liu, "Characterization of Sulfur Poisoning of Ni-YSZ Anodes for Solid Oxide Fuel Cells Using in situ Raman Microspectroscopy " Solid State Ionics, 178, 925-935, 2007. (9) Z. Cheng and M. Liu, "Characterization of Sulfur Poisoning of Ni-YSZ Anodes for Solid Oxide Fuel Cells Using in situ Raman Microspectroscopy " Solid State Ionics, 178, 925-935, 2007. (10) Z. Cheng, S. Zha, and M. Liu, "Influence of cell voltage and current on sulfur poisoning behavior of solid oxide fuel cells" Journal of Power Sources, 172, 688-693, 2007. (10) Z. Cheng, S. Zha, and M. Liu, "Influence of cell voltage and current on sulfur poisoning behavior of solid oxide fuel cells" Journal of Power Sources, 172, 688-693, 2007. (11) Z. Cheng, S. Zha, L. Aguilar, D. Wang, J. Winnick, and M. Liu, "A Solid Oxide Fuel Cell Running on H2S/CH4 Fuel Mixtures," Electrochemical and Solid-State Letters, 9, A31-A33, 2006. (12) Z. Cheng, S. Zha, and M. Liu, "Stability of materials as candidates for sulfur-resistant anodes of solid oxide fuel cells," Journal of the Electrochemical Society, 153, A1302-A1309, 2006. (13) Y. M. Choi, H. Abernathy, H.-T. Chen, M. C. Lin, and M. Liu, "Characterization of O2-CeO2 interactions using in situ Raman spectroscopy and first-principle calculations," ChemPhysChem, 7, 1957-1963, 2006. (14) Y. M. Choi, C. Compson, M. C. Lin, and M. Liu, "A mechanistic study of H2S decomposition on Ni- and Cu-based anode surfaces in a solid oxide fuel cell," Chemical Physics Letters, 421, 179-183, 2006. (11) Z. Cheng, S. Zha, L. Aguilar, D. Wang, J. Winnick, and M. Liu, "A Solid Oxide Fuel Cell Running on H2S/CH4 Fuel Mixtures," Electrochemical and Solid-State Letters, 9, A31-A33, 2006. (12) Z. Cheng, S. Zha, and M. Liu, "Stability of materials as candidates for sulfur-resistant anodes of solid oxide fuel cells," Journal of the Electrochemical Society, 153, A1302-A1309, 2006. (13) Y. M. Choi, H. Abernathy, H.-T. Chen, M. C. Lin, and M. Liu, "Characterization of O2-CeO2 interactions using in situ Raman spectroscopy and first-principle calculations," ChemPhysChem, 7, 1957-1963, 2006. (14) Y. M. Choi, C. Compson, M. C. Lin, and M. Liu, "A mechanistic study of H2S decomposition on Ni- and Cu-based anode surfaces in a solid oxide fuel cell," Chemical Physics Letters, 421, 179-183, 2006.

20. 01 复杂化学反应体系的物质分离与分析 01 复杂化学反应体系的物质分离与分析 02 硫化学基础与应用 02 硫化学基础与应用 03 模拟与实验研究：新奇化学波，软物质 的波 03 模拟与实验研究：新奇化学波，软物质 的波 基金 Fund: NSFC 、博士点基金、新世纪人才项目、 创新团队, 江苏省自然科学基金。 基金 Fund: NSFC 、博士点基金、新世纪人才项目、 创新团队, 江苏省自然科学基金。 Work at CUMT Work at CUMT

21. 1.2 Mechanism and Rate laws 1.2 Mechanism and Rate laws Procedure: Procedure: Experiment: spectroscopy, electrochemistry, magnetism; -- -- the variation of reactants, the intermediates → rate → main reactions (or elementary reactions) → rate equations → Simulation compare with experiment and fit → Model Experiment: spectroscopy, electrochemistry, magnetism; -- -- the variation of reactants, the intermediates → rate → main reactions (or elementary reactions) → rate equations → Simulation compare with experiment and fit → Model * Online and Coupling of detection * Online and Coupling of detection A elementary steps A elementary steps Ascertain: experiment computation Ascertain: experiment computation One step to products One step to products H+O2----OH+O H+O2----OH+O Law of mass action Law of mass action V=k[H][O2] V=k[H][O2] First order Second order Third order First order Second order Third order K(T)=Aexp(-E/RT) K(T)=Aexp(-E/RT) R=8.31 J K-1 mol-1 universal Gas constant A: preexponential factor E: The activation Energy R=8.31 J K-1 mol-1 universal Gas constant A: preexponential factor E: The activation Energy

22. B Rate equations B Rate equations Overall reaction decomposes the elementary reactions Overall reaction decomposes the elementary reactions H 2 +O 2 → 2H 2 O H 2 +O 2 → 2H 2 O Elementary reactions (chain reactions) Elementary reactions (chain reactions) 0. H 2 +O 2 → 2OH V0=k0[H 2 ][O 2 ] 0. H 2 +O 2 → 2OH V0=k0[H 2 ][O 2 ] 1. OH+H 2 - → H 2 O+H V1=k1[OH][H 2 ] 1. OH+H 2 - → H 2 O+H V1=k1[OH][H 2 ] 2. H+O 2 → OH+O V2=k2[H][O 2 ] 2. H+O 2 → OH+O V2=k2[H][O 2 ] 3. O+H 2 → OH+H V3=k3[O][H 2 ] 3. O+H 2 → OH+H V3=k3[O][H 2 ] 4. H → 0.5H 2 V4=k4[H] 4. H → 0.5H 2 V4=k4[H] The number of species The number of species H 2 O 2 OH H O H 2 O H 2 O 2 OH H O H 2 O Rate of species concentrations: Rate of species concentrations: d[species]/dt= rates of prodution - rates of cosumption - rates of cosumption

23. number of Independent species number of Independent species Number of independent species= number of species-number of conservations 6-2=4 independent species 6-2=4 independent species species: H O H 2 OH species: H O H 2 OH

24. C Rate equations of nonelementary processes (1)One system decomposes many reactions which are not elementary reactions (2)determining emprirical rate laws for every reaction (3) rate equations of all species (4) rate equations of independent speciesBZ system V5=-d[bromate]/dt=-d[bromide]/dt= 0.5d[H + ]/dt =d[HBrO2]/dt=d[HOBr] =k5[Bromate][Bromide][H + ] 2 =k5[Bromate][Bromide][H + ] 2

25. 1.3 What brings about the spatiotemporal order in chmical reaction A Nonequilibrium is source of spatiotemporal order A Nonequilibrium is source of spatiotemporal order Equilibrium V i =V -i Only one state Nonequilibrium: Vpositive>Vnegative dxi/dt> <0 New phenomena appear, driving force How can we keep the state of nonequilibrium How can we keep the state of nonequilibrium Open system CSTR CFUR continuous 流出液 玻璃板凝胶 电极探头 流入液 微孔玻璃板 Fig 12 CFUR 示意图 Fig 13 Couette 反应器示意 图 溢出液 由蠕动泵泵入反应 液 探针 循环水入口 循环水出口 Fig 11 CSTR 示意图

26. B. Nonlinearity B. Nonlinearity Af(x+y)≠f(ax)+f(ay) f=kx linear Af(x+y)≠f(ax)+f(ay) f=kx linear f=kx 2 nonlinear f=kx 2 nonlinear For chemical reaction For chemical reaction A+BC=AB+C A+BC=AB+C -dA/dt=k[A][BC]=K[A][BC0-(A0-A)] Nonlinear -dA/dt=k[A][BC]=K[A][BC0-(A0-A)] Nonlinear when [BC]>>[A] K[BC]=constant Ks (at specific Tempreture) when [BC]>>[A] K[BC]=constant Ks (at specific Tempreture) -dA/dt=Ks[A] linear -dA/dt=Ks[A] linear Even for first order reaction A  B ΔH Even for first order reaction A  B ΔH dT/dt=ΔH Ks[A]/(σCp) – χS(T-T0)/ （ V σCp ） dT/dt=ΔH Ks[A]/(σCp) – χS(T-T0)/ （ V σCp ） Ks=Iexp(-E/RT) Ks=Iexp(-E/RT) dT/dt=ΔH exp(-E/RT) [A]/(σCp) – χS(T-T0)/ （ V σCp ） Nonlinear dT/dt=ΔH exp(-E/RT) [A]/(σCp) – χS(T-T0)/ （ V σCp ） Nonlinear dA/dt= -Iexp(-E/RT) A dA/dt= -Iexp(-E/RT) A

27. The extent of reaction ξ=(A0-A)/A0 The extent of reaction ξ=(A0-A)/A0 dξ/dt=-A 0 -1 dA/dt dξ/dt=-A 0 -1 dA/dt for first order dA/dt=-kA for first order dA/dt=-kA dξ/dt= A 0 -1 kA=k{1-(A0-A)/A0}=k(1- ξ) linear dξ/dt= A 0 -1 kA=k{1-(A0-A)/A0}=k(1- ξ) linear for second order for second order dξ/dt=k(1-ξ) 2 nonlinear dξ/dt=k(1-ξ) 2 nonlinear For fraction order For fraction order dξ/dt=k(1-ξ) 1/n Nonlinear dξ/dt=k(1-ξ) 1/n Nonlinear

28. Feedback Feedback Feedback is the inspiring sources of spatiotemporal pattern Feedback: Products(result) of later steps in the mechanism influence the rate of some of early reactions, hence, also the rate of their own production Positive feedback : self-acceleration Positive feedback : self-acceleration A+B=2B V=k A B A+B=2B V=k A B Negative feedback : self-inhibition Negative feedback : self-inhibition ClO 2 +4I - +4H + → 2I+Cl - +2H2O I +I - I 3 - ClO 2 +4I - +4H + → 2I 2 +Cl - +2H2O I 2 +I - I 3 - Rate with extent A+B=2B dξ/dt= ξ(1-ξ) A+B=2B dξ/dt= ξ(1-ξ) A+2B=3B dξ/dt= ξ 2 (1-ξ) A=B+heat dξ/dt= (1-ξ)exp(Bξ) Feature: In Batch, reaction rate attains it maximum at ξ≠0

29. Specific example of chemical feedback The core source of nonlinear chemistry would be feedback. As important examples, the feedback of BZ, ignition of hydrogen and the iodate-reductant reaction have the impact on the understand for the course. A Belozov Zhabotinsky reaction A Belozov Zhabotinsky reaction BrO 3 -+HBrO 2 +H + ↔ 2BrO 2 ∙+H 2 O RX BrO 3 -+HBrO 2 +H + ↔ 2BrO 2 ∙+H 2 O RX BrO 2 ∙ +M red + H+ → HBrO 2 +M ox RY BrO 2 ∙ +M red + H+ → HBrO 2 +M ox RY Overall reaction Overall reaction RX+2*RY RX+2*RY BrO 3 - +HBrO 2 +3H + +2M red → 2HBrO 2 +2M ox +H 2 O BrO 3 - +HBrO 2 +3H + +2M red → 2HBrO 2 +2M ox +H 2 O V=d[HBrO 2 ]/dt= V=d[HBrO 2 ]/dt= -k Rx [Bromate][bromite][H + ]+k Rx [BrO 2 ∙]2+k Ry [BrO 2 ∙][ M red ][ H + ] -k Rx [Bromate][bromite][H + ]+k Rx [BrO 2 ∙]2+k Ry [BrO 2 ∙][ M red ][ H + ]

30. If Mox/red is Ce4+/Ce3+ RY is slow R X would tend to equilibrium, The dynamics can be treated by quasi-equilibrium If Mox/red is Ce4+/Ce3+ RY is slow R X would tend to equilibrium, The dynamics can be treated by quasi-equilibrium V RX =V -RX V RX =V -RX [BrO 2 ∙]={k RX [Bromate][bromite][H+]/k -RX } 0.5 [BrO 2 ∙]={k RX [Bromate][bromite][H+]/k -RX } 0.5 d[HBrO2]/dt=V=k RY {(k RX /k -RX )[Bromate] [HBrO 2 ] } 0.5 [M red ] [H+] 1.5 d[HBrO2]/dt=V=k RY {(k RX /k -RX )[Bromate] [HBrO 2 ] } 0.5 [M red ] [H+] 1.5 Indicating the parameter stoichiometry 0.5 to 1, Overall reaction represent is 0.5BrO 3 - +0.5HBrO 2 +3/2H + + M red → HBrO 2 +M ox +1/2H 2 O 0.5BrO 3 - +0.5HBrO 2 +3/2H + + M red → HBrO 2 +M ox +1/2H 2 O If M ox /M red is Fe(III)/Fe(II) RY is fast than -RX, [BrO 2 ∙] tend to unchangeable, The dynamics can be treated by steady state of BrO 2 ∙ If M ox /M red is Fe(III)/Fe(II) RY is fast than -RX, [BrO 2 ∙] tend to unchangeable, The dynamics can be treated by steady state of BrO 2 ∙ d[BrO 2 ∙]/dt=0 d[BrO 2 ∙]/dt=0 [BrO 2 ∙]ss=(2k RX /k RY ) [Bromate][bromite]/[M red ] [BrO 2 ∙]ss=(2k RX /k RY ) [Bromate][bromite]/[M red ] V =d[HBrO 2 ] V =d[HBrO 2 ] =-k8[Bromate][bromite][H+]+k-8[BrO2∙]2+k9[BrO2∙][ Mred][ H+] =-k8[Bromate][bromite][H+]+k-8[BrO2∙]2+k9[BrO2∙][ Mred][ H+] =k RX [Bromate][ HBrO 2 ][H + ] =k RX [Bromate][ HBrO 2 ][H + ] quadratic autocatalysis quadratic autocatalysis BrO 3 - +HBrO 2 +3H + + 2M red → 2HBrO 2 +2M ox +H2O BrO 3 - +HBrO 2 +3H + + 2M red → 2HBrO 2 +2M ox +H2O

31. B the H 2 +O 2 reaction B the H 2 +O 2 reaction 0. H 2 +O 2 → 2OH V0=k0[H2][O2] 1. OH+H2- → H2O+H V1=k1[OH][H2] 2. H+O2 → OH+O V2=k2[H][O2] 3. O+H2 → OH+H V3=k3[O][H2] 4. H → 0.5H2 V4=k4[H] 0 chain initiation 1-3 chain branch 4 chain termination one H in R2 produce three H R1*2+R2+R3 H+O2+3H2 → 3H+2H2O R2 slow as determination process R2 slow as determination process d[O]/dt=0, d[OH]/dt=0 d[O]/dt=0, d[OH]/dt=0 d[O]/dt= k2[H][O2]- k3[O][H2]=0 d[O]/dt= k2[H][O2]- k3[O][H2]=0 [O]ss= k2[H][O2]/ k3[H2] [O]ss= k2[H][O2]/ k3[H2] d[OH]/dt=2 k0[H2][O2]- k1[OH][H2]+ k2[H][O2]+ k3[O][H2]=0 d[OH]/dt=2 k0[H2][O2]- k1[OH][H2]+ k2[H][O2]+ k3[O][H2]=0 [OH]ss=(2 k0[H2][O2]+ k2[H][O2]+ k3[O][H2]/ k1[H2] [OH]ss=(2 k0[H2][O2]+ k2[H][O2]+ k3[O][H2]/ k1[H2] d[H]/dt=V1-V2+V3-V4= k1[OH][H2]- k2[H][O2]+ k3[O][H2]- k4[H] d[H]/dt=V1-V2+V3-V4= k1[OH][H2]- k2[H][O2]+ k3[O][H2]- k4[H] =2k0[H2][O2]+(2k2[O2]-k4)[H] =2k0[H2][O2]+(2k2[O2]-k4)[H] when 2k2[O2]-k4>0 H autocatalysis ignition when 2k2[O2]-k4>0 H autocatalysis ignition increase T k2 rises high P make 2k2[O2]-k4>0 easy increase T k2 rises high P make 2k2[O2]-k4>0 easy When 2k2[O2]-k4<0 chain terminates When 2k2[O2]-k4<0 chain terminates

32. C Iodate-iodide-reductant reaction C Iodate-iodide-reductant reaction Reductant AsO 3 3-, SO 3 2- Reductant AsO 3 3-, SO 3 2- 1 dushman reaction 1 dushman reaction IO3-+5I-+6H+ → 3I2+3H2O 10 IO3-+5I-+6H+ → 3I2+3H2O 10 Rα=(k α1 +k α2 [I - ])[I - ][IO 3 - ][H+] 2 Rα=(k α1 +k α2 [I - ])[I - ][IO 3 - ][H+] 2 k α1 =4.5×10 3 M -3 s -1, k α2 =1.0×10 8 M -4 s -1 k α1 =4.5×10 3 M -3 s -1, k α2 =1.0×10 8 M -4 s -1 2 Roeback reaction 2 Roeback reaction H 3 AsO 3 +I 2 +H 2 O → H 3 AsO 3 +2I - +2H + 11 H 3 AsO 3 +I 2 +H 2 O → H 3 AsO 3 +2I - +2H + 11 Rβ=kβ[I2][ H3AsO3]/[I-][H+] Rβ=kβ[I2][ H3AsO3]/[I-][H+] Kβ=3.2×10 -2 M s -1 Kβ=3.2×10 -2 M s -1 Overall stoichiometry Overall stoichiometry R10+3R11 R10+3R11 IO3-+5I-+3H3AsO3 → 6 I-+3 H3AsO4 IO3-+5I-+3H3AsO3 → 6 I-+3 H3AsO4 Net production of iodide Net production of iodide Controlled by slow reaction R10 Controlled by slow reaction R10 D[I]/dt= (kα1+kα2[I - ])[I - ][IO 3 - ][H + ] 2 D[I]/dt= (kα1+kα2[I - ])[I - ][IO 3 - ][H + ] 2 Mixed autocatalysis (quadratic and cubic ) Mixed autocatalysis (quadratic and cubic ) Reductant SO 3 2- in addition to R10, R11, There also a direct reaction between Iodate and sulfite Reductant SO 3 2- in addition to R10, R11, There also a direct reaction between Iodate and sulfite The reaction between Iodate and sulfite is called as landolt clock reaction

33. Closed and open systems Closed systems Closed systems Definition: No exchange between environment and system Definition: No exchange between environment and system Direction from nonequilibrium to equilibrium: exclusive Direction from nonequilibrium to equilibrium: exclusive The number of equilibrium: =1 when reaction conditions such pressure and temperature are fixed The number of equilibrium: =1 when reaction conditions such pressure and temperature are fixed Feature of equilibrium state: Feature of equilibrium state: Dxi/dt=production terms-removal terms=0 Vi=V-i Dxi/dt=production terms-removal terms=0 Vi=V-i Oscillations and Chaos may obtain and be transient for long time Oscillations and Chaos may obtain and be transient for long time Wang. J, Sorense P G, Hynne F J Phys Chem. 1994, 98,725 Wang. J, Sorense P G, Hynne F J Phys Chem. 1994, 98,725