chapter 2 clocks and fronts 2.1 clock reactions a clock reaction in iodate-iodide-reductant system...

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Chapter 2 clocks and Chapter 2 clocks and fronts fronts 2.1 2.1 clock reactions clock reactions A clock reaction in Iodate-iodide-reductant system A clock reaction in Iodate-iodide-reductant system discovery: 1866, Landolt Iodate-bisulfite system(s discovery: 1866, Landolt Iodate-bisulfite system(s tarch indicator) tarch indicator) iodate excess stoichiomistry (>1:3): noncolour -> re iodate excess stoichiomistry (>1:3): noncolour -> re d d Bisulfite excess stoichiomistry: noncolour-red-nonco Bisulfite excess stoichiomistry: noncolour-red-nonco lour lour Induction time tind (begin-red) Induction time tind (begin-red) t t ind ind =k/[IO =k/[IO 3 - ] ] 0 [HSO [HSO 3 - ] ] 0 k=4×10 k=4×10 -3 -3 M M 2 s s -1 -1 when [IO3 when [IO3 - ] ] 0 =[HSO =[HSO 3 -] -] 0 =0.01M, t =0.01M, t ind ind =1min, =1min, C decreases, t C decreases, t ind ind rises rises Works equally well with Arsenite Works equally well with Arsenite Fig. 1 excess bisulfite Fig. 1 excess bisulfite

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Chapter 2 clocks and frontsChapter 2 clocks and fronts

2.1 2.1 clock reactionsclock reactionsA clock reaction in Iodate-iodide-reductant systemA clock reaction in Iodate-iodide-reductant systemdiscovery: 1866, Landolt Iodate-bisulfite system(starch indicator)discovery: 1866, Landolt Iodate-bisulfite system(starch indicator)iodate excess stoichiomistry (>1:3): noncolour -> rediodate excess stoichiomistry (>1:3): noncolour -> redBisulfite excess stoichiomistry: noncolour-red-noncolourBisulfite excess stoichiomistry: noncolour-red-noncolourInduction time tind (begin-red)Induction time tind (begin-red)ttindind=k/[IO=k/[IO33

--]]00[HSO[HSO33--]]00

k=4×10k=4×10-3-3 M M22ss-1-1 when [IO3 when [IO3--]]00=[HSO=[HSO33-]-]00=0.01M, t=0.01M, tindind=1min,=1min,C decreases, tC decreases, tindind rises rises Works equally well with ArseniteWorks equally well with ArseniteFig. 1 excess bisulfiteFig. 1 excess bisulfite

Explaining by using autocatalysisExplaining by using autocatalysisξ=0, r=0 specificξ, rmaxξ=0, r=0 specificξ, rmaxSimulation: Mixed quadratic and cubic autocatalysisSimulation: Mixed quadratic and cubic autocatalysis when consider Main cubic autocatalysiswhen consider Main cubic autocatalysisda/dt=-kda/dt=-kccabab22=-k=-kcca(a0+b0-a)a(a0+b0-a)22

a=[iodate] b=[iodide] ka=[iodate] b=[iodide] kcc=k=ka2a2[H+][H+]22

ttindind, at [iodate]=0.5[iodate], at [iodate]=0.5[iodate]00 Generally b0<<a0 Generally b0<<a0 tind=(ktind=(kccaa00bb00))-1-1 =(k =(ka2a2[H[H++]]22[IO[IO33

--][I][I--])])-1-1

This equation is confirmed in above figure, but induction time is dependenThis equation is confirmed in above figure, but induction time is dependence on [I-]0 deviates from linearity at high initial iodide concentrations.ce on [I-]0 deviates from linearity at high initial iodide concentrations.

When [IOWhen [IO33--]=0.005 M, [I]=0.005 M, [I--]=2.5×10]=2.5×10-5-5 M, [H M, [H++]=7.1 ×10]=7.1 ×10-3 -3 MM

Calculated tin=27 minCalculated tin=27 minExperimentally tin=15 minExperimentally tin=15 minBecause quadratic autocatalysis is negiligibleBecause quadratic autocatalysis is negiligible

Compare empirical and theoretical equationCompare empirical and theoretical equation

Empirical equation: tEmpirical equation: tindind=k/([IO=k/([IO33--]]00[HSO[HSO33

--]]00))-1-1

HSOHSO33--=H=H+++SO+SO33

-- Ka=[H Ka=[H++][SO][SO33--]/[HSO]/[HSO33

--]=[H]=[H++]]22/[HSO/[HSO33--]]

ttindind=(k=(kccaa00bb00))-1-1 =(k =(ka2a2[H[H++]]22[IO[IO33--]]00[I[I--]]00))-1-1=(k=(ka2a2KKaa[HSO[HSO33

--]]00[IO[IO33--]]00[I-][I-]00))--11

When [IWhen [I--]]00=constant=constantttindind= k/([IO= k/([IO33

--]]00[HSO[HSO33--]]00))-1-1

k=(kk=(ka2a2KKaa[I[I--]]00))-1-1

II-- autocatalysis and Proton autocatalysis autocatalysis and Proton autocatalysisIOIO33

--+HSO+HSO33--+H+H++=2H=2H+++SO+SO44

--+ IO+ IO22- -

J. Phys. Chem. J. Phys. Chem. 1988, 1988, 92, 92, 2804-28072804-2807J. Phys. Chem. J. Phys. Chem. 1988, 1988, 92, 92, 4831-48354831-4835IOIO33

--+5I+5I--+6H+6H++→3I→3I22+3H+3H22OOII22+ H+ H22O+HSOO+HSO33

-- =3H =3H+++ SO+ SO442-2-+2I+2I--

质子自催化和碘离子自催化的反应条件有何不同? 质子自催化和碘离子自催化的反应条件有何不同? pH?pH? J. Boissonade, P. De Kepper, F. Gauffre, I. Szalai, Chaos, 2006, 16, 037110.

ChemPhysChemChemPhysChem What is RSS?What is RSS? Volume 9999, Issue 9999Volume 9999, Issue 9999 , Pages NA - , Pages NA - Published Online: Published Online: 24 Apr 200824 Apr 2008 Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimCopyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Save Title to My Profile Save Title to My Profile Set E-Mail Alert Set E-Mail Alert << Previous Abstract Previous Abstract | | Next Abstract Next Abstract >> AbstractAbstract | References | Full Text: PDF (315k) | Related Articles | Citation Tracking | References | Full Text: PDF (315k) | Related Articles | Citation Tracking ArticleArticle

The Transition from pH Waves to Iodine Waves in the Iodate/Sulfite/Thiosulfate Reaction-Diffusion SystemThe Transition from pH Waves to Iodine Waves in the Iodate/Sulfite/Thiosulfate Reaction-Diffusion System Qingyu Gao, Prof. *, Rongyong XieQingyu Gao, Prof. *, Rongyong Xie College of Chemical Engineering, China University of Mining and TecCollege of Chemical Engineering, China University of Mining and Tec

hnology, Xuzhou 221008, P.R.China, Fax:(+86)-516-83591088hnology, Xuzhou 221008, P.R.China, Fax:(+86)-516-83591088email: Qingyu Gao ([email protected])email: Qingyu Gao ([email protected])

*Correspondence to Qingyu Gao, College of Chemical Engineering, China University of Mining and Technology, Xuzhou 221008, P.R.China, Fax:(+*Correspondence to Qingyu Gao, College of Chemical Engineering, China University of Mining and Technology, Xuzhou 221008, P.R.China, Fax:(+86)-516-8359108886)-516-83591088

Funded by:Funded by: National Science Foundation of China; Grant Number: 20050290512 National Science Foundation of China; Grant Number: 20050290512 Ministry of Chinese Education Ministry of Chinese Education

Keywordschemical waves • diffusion • quadratic and cubic autocatalysis • reaction dynamicsKeywordschemical waves • diffusion • quadratic and cubic autocatalysis • reaction dynamics AbstractAbstractNonlinear spatial temporal behavior of the iodate/thiosulfate/sulfite reaction is investigated both in a stirred and spatially exteNonlinear spatial temporal behavior of the iodate/thiosulfate/sulfite reaction is investigated both in a stirred and spatially exte

nded media. In accord with the temporal dynamics in the homogeneous media, both propagating fronts and target patterns are achievended media. In accord with the temporal dynamics in the homogeneous media, both propagating fronts and target patterns are achieved in the spatially extended medium. On increasing the iodate concentration the system evolves from exhibiting propagating fronts to cird in the spatially extended medium. On increasing the iodate concentration the system evolves from exhibiting propagating fronts to circular waves and then shows target patterns and finally the iodine waves. Influences of concentrations of sulfite, thiosulfate and acid on tcular waves and then shows target patterns and finally the iodine waves. Influences of concentrations of sulfite, thiosulfate and acid on the reaction kinetics and pattern formation are also investigated systematically, and transitions from pH waves to iodine waves can be ache reaction kinetics and pattern formation are also investigated systematically, and transitions from pH waves to iodine waves can be achieved via adjusting the concentration of the three species. The propagation velocities of pH and iodine waves are understood with the qhieved via adjusting the concentration of the three species. The propagation velocities of pH and iodine waves are understood with the quadratic and cubic autocatalysis of proton and iodide respectively.uadratic and cubic autocatalysis of proton and iodide respectively.Received: 2 January 2008 Received: 2 January 2008

Digital Object Identifier (DOI)Digital Object Identifier (DOI)

B Other example of clock reactionsB Other example of clock reactionsFeature of clock reactionFeature of clock reaction during induction period: slowly reactionduring induction period: slowly reaction After explosion : reaction almost completed between reactantsAfter explosion : reaction almost completed between reactantsClassification of categoryClassification of category Liquid phase : dushman reactionLiquid phase : dushman reaction Gas phase : hydrogen and hydrocarbon oxidationGas phase : hydrogen and hydrocarbon oxidation Solid phase: haystack ignition Solid phase: haystack ignition Soft matter: polymerization of a mutant form of haemoglobin, to form a hiSoft matter: polymerization of a mutant form of haemoglobin, to form a hi

ghly viscous gel. ghly viscous gel. Thermal clockThermal clock When reaction heat transfer slowly to increase When reaction heat transfer slowly to increase system temperature, hence quick the reactionsystem temperature, hence quick the reactionrate to produce thermal runawayrate to produce thermal runawayHyperthesisHyperthesis

Fixed ambient temperature system is uniformFixed ambient temperature system is uniformThermal equationThermal equation

R(T) reaction heatR(T) reaction heat φφtransfer heattransfer heat Initial temperature TInitial temperature Ta1a1 T Tssss is stable is stable Initial temperature TInitial temperature Ta2a2 no intersection point no intersection point dT/dt is proportional to the difference between R(T) reaction heat and tdT/dt is proportional to the difference between R(T) reaction heat and t

ransfer heat. ransfer heat. During the difference is small, rate is slow, When the system crawled acroDuring the difference is small, rate is slow, When the system crawled acro

ss the narrow channel between R(T) and , ss the narrow channel between R(T) and , finial acceleration began.finial acceleration began.

C Supercatalysis:C Supercatalysis:Induction time of clock can’t repeatly buInduction time of clock can’t repeatly bu

t distributed statistically about a mean vt distributed statistically about a mean valuealue

Chlorite-thiosulfate systemChlorite-thiosulfate systemdHdH++/dt=k..[H/dt=k..[H++]]1010

1% error give rise to factor of (1.01)10, 1.1\1% error give rise to factor of (1.01)10, 1.1\Sickle cell haemoglobin clock shows such Sickle cell haemoglobin clock shows such

a distribution of clock time.a distribution of clock time.I R Epstein, Nature, 1995,374,321-327I R Epstein, Nature, 1995,374,321-327

2.2 Front2.2 FrontA. Reaction situation of clock reaction:A. Reaction situation of clock reaction:Control condition : Stirred Unstirred Control condition : Stirred Unstirred System state : Uniform nonunformSystem state : Uniform nonunformDynamics: Time Time and spaceDynamics: Time Time and spacePhenomena: clock frontPhenomena: clock frontB. B. How to get frontHow to get frontInitiate the aucatalysis in unstirred systemInitiate the aucatalysis in unstirred system①①add a drop of catalyst ② perturbation by light, heat,electrochemistry, magnetism, add a drop of catalyst ② perturbation by light, heat,electrochemistry, magnetism,

et al.et al.C C example: example: H2O2-sulfite systemH2O2-sulfite systemOX+HSOOX+HSO33

--=SO=SO442-2-+H+H++

dH/dt=(k1+k2[H])[OX][ HSOdH/dt=(k1+k2[H])[OX][ HSO33--] (] ( 甲基红甲基红 ))

IOIO33--+AsO+AsO33

--

IO3-+3H3AsO3+5I-=6I-+3H3AsO4IO3-+3H3AsO3+5I-=6I-+3H3AsO4D[I-]/dt=(kD[I-]/dt=(kαα11 +k +k αα22 [I[I--])[I])[I--][IO][IO33

--][H+]][H+]22≈k ≈k αα22 [I-][I-]22 [IO [IO33--][H+]][H+]22=k =k αα22 [I[I--]]22 [IO [IO33

--]]Kc=k Kc=k αα22 [H[H++]]22

D. Feature:D. Feature:Front: the place of autocatalysis reaction happening ( band, circulaFront: the place of autocatalysis reaction happening ( band, circula

r or ball shell )r or ball shell )Ahead of the front, unreacted fieldAhead of the front, unreacted fieldBehind the front: reacted fieldBehind the front: reacted fieldFront shape: line , curveFront shape: line , curveFront spead: steady, oscillation, chaos, immobility, increasing gradFront spead: steady, oscillation, chaos, immobility, increasing grad

ually in two dimensionually in two dimension E. simulation E. simulation ddXX/dt=F(/dt=F(XX)+D∂)+D∂22XX/ ∂r/ ∂r22

One dimension: initiate, top hat, propagation. One dimension: initiate, top hat, propagation. Two dimension: point, circularTwo dimension: point, circularThree dimension: point, sphereThree dimension: point, sphere diffusion couple of reaction and diffusiondiffusion couple of reaction and diffusionSpeed 400min/1cm 10min/1cmSpeed 400min/1cm 10min/1cmExplain reaction enhance diffusionExplain reaction enhance diffusion

F: F: Relationship between the wave speed and reaction kineticsRelationship between the wave speed and reaction kineticsOne dimension, cubic autocalysisOne dimension, cubic autocalysisa+2b=3ba+2b=3bequation:equation:initial condition:initial condition: t=0, a=a0, b=0, t=t a=a , b=a0-at=0, a=a0, b=0, t=t a=a , b=a0-aboundary condition:boundary condition:x-x--∞ a=0 b=a0-∞ a=0 b=a0x-x-+∞ a=a0 b=0+∞ a=a0 b=0DDaa=D=Dbb

c={0.5Dkc={0.5Dkccaa0022}}1/21/2

The thickness of the zoneThe thickness of the zoneId=(2D/kId=(2D/kcc a a00

22))1/21/2

For landolt reactionFor landolt reactionkc=kkc=ka2a2[H[H++]]22

c={0.5 D Kc={0.5 D Ka2a2[IO3-][IO3-]22[H+][H+]22}}0.50.5 K Ka2a2=1.0×108M=1.0×108M-4-4ss-1-1

If [IOIf [IO33--]=5×10]=5×10-3-3M, [H+]=7.1×10M, [H+]=7.1×10-3-3M D=2×10M D=2×10-5 -5 cmcm22/s/s

C=0.66mm/minC=0.66mm/min

for quadratic aucatalysisfor quadratic aucatalysisc=2{Dkc=2{Dkqqaa00}}1/21/2

BrOBrO33--+HBrO+HBrO22+3H+3H++ + 2M + 2Mredred→2HBrO→2HBrO22+2M+2Moxox+H+H22O R8O R8

d[HBrO2]=kd[HBrO2]=k88[Bromate][bromite][H[Bromate][bromite][H++] kq=k8[H] kq=k8[H++]] c=2{Dkc=2{Dk88[H[H++][Bromate]}][Bromate]}0.50.5

Other quafratic autocatalysisOther quafratic autocatalysisOxidation of bisulfite by bromate, iodate and hydrogen peroxideOxidation of bisulfite by bromate, iodate and hydrogen peroxideOxidation of Ferrion by bromate, nitrateOxidation of Ferrion by bromate, nitratePopulation model and Sir modelPopulation model and Sir model

For thermal autocatalysisFor thermal autocatalysis

C={2(κ/cC={2(κ/cppσ)k(T)/Bσ)k(T)/B22}}0.50.5

G ApplicationG Application1. from speed to calculate k or D.1. from speed to calculate k or D.2. life science of infection disease2. life science of infection disease3. safety science3. safety science

H. circular effect H. circular effect Diluted effect of autocatalysis because out arc is longer than iDiluted effect of autocatalysis because out arc is longer than i

nner arc, hence, wave advances slowly.nner arc, hence, wave advances slowly.

2.3 Osicillatory and nonplanar fronts2.3 Osicillatory and nonplanar frontsWhat are situation when DWhat are situation when Daa is not equal to D is not equal to Dbb??How to make the different DHow to make the different Daa and D and Dbb??① ① different sizes different sizes ② ② adsorption: ion exchange resins, ligand,adsorption: ion exchange resins, ligand, I- : cyclodextrin I- : cyclodextrin Fe(II): cation-exchange resinFe(II): cation-exchange resinA DB>>DAA DB>>DAFeature: spatial oscillations of state vaviables Feature: spatial oscillations of state vaviables Speed oscillations Speed oscillations Example: flameExample: flame Explaination: local temperature arise of supercatalysis, Explaination: local temperature arise of supercatalysis, front advances quickly->heat transfer-front advances quickly->heat transfer-heat drop-----Front speed become slow.heat drop-----Front speed become slow.Experiment: pyrotechnic mixture forest fire Experiment: pyrotechnic mixture forest fire

Open system? Two dimension? Three dimension?Open system? Two dimension? Three dimension?

B. DA>DBB. DA>DB In long, thin two dimension strip In long, thin two dimension strip

Wiggle front Wiggle front Why: diffusion of reactant is main role for frontWhy: diffusion of reactant is main role for front

Perturbation produces Convex and ConcavePerturbation produces Convex and Concave

Convex: reaction is enhanced, local speed is highConvex: reaction is enhanced, local speed is high

Concave: reactant is diluted to make speed slowlyConcave: reactant is diluted to make speed slowly Perturbation is reinforced Perturbation is reinforced Front: line- cell- chaosFront: line- cell- chaos• Two dimensionsTwo dimensions

three dimensions three dimensions

The formation of earthThe formation of earth