1 MODELING Solution-Phase Nonlinear Dynamics Heterogeneous Dynamics

2 Brief History of Chemical NLD Chemical waves and oscillations rejected –Violate Second Law –Difficult to reproduce Prigogine –No Second Law violation far from equilibrium BZ reaction –Easily reproduced Doubts allayed─new theories, experiments

3 Mechanism and Model Mechanism─elementary steps at molecular level Model─simplified mechanism –Abstract: Lotka-Volterra –Derived: Oregonator, Brusselator –Empirical: Rate Law

4 Calculating Rate Constants Diffusion-controlled limits Marcus theory of electron transfer Eigen theory of proton transfer Eigen theory of metal complex formation

5 Lotka-Volterra Model A + X  2X,k 1 X + Y  2Y,k 2 Y , k 3 dX/dt = k 1 AX - k 2 XY dY/dt = k 2 XY - k 3 Y

6 Lotka-Volterra: Predator-Prey

7 Lotka-Volterra: Increase in Predator Efficiency

8 Empirical Model: Iodate-Sulfite-Ferrocyanide A)IO I - + 6H +  3I H 2 O B)I HSO H 2 O  3I - + HSO H + C)I Fe(CN) 6 4-  3I - + 2Fe(CN) 6 3- D)IO HSO 3 -  I - + 3HSO 4 - E)H + + SO 3 2- = HSO 3 -

9 Derived Model-1: Epstein-Orbán-Edblom (EOE) Concentrations in large excess: iodate, iodide, ferrocyanide, sulfate –Incorporate into rate equation Four variables: A = [SO 3 2- ], X =[HSO 3 - ],Y = [H + ], Z = [I 2 ] Reciprocal residence time, k 0, varied Inflow variables: Y 0, A 0

10 Derived EOE Model-2 A = [SO 3 2- ], X =[HSO 3 - ],Y = [H + ], Z = [I 2 ]

11 EOE: Oscillations in a Flow Reactor

12 EOE: Oscillations in a Flow Reactor; Close-up

13 EOE: Changing k 2N from 6.0e-2 to 6.5e-2 M -1 s -1

14 Photoresponse of the Chlorine Dioxide-Iodine-Malonic Acid Reaction in a Flow Reactor First experimental demonstration of Turing structures Inflow solution A –0.04 M H 2 SO 4 with M I 2 Inflow solution B –varying amounts of –malonic acid (w/wo) starch with chlorine dioxide

15 CDIMA: No Light (1) I 2 + MA  H + + I - + IMA (2) ClO 2 + I -  ½I 2 + ClO 2 - (3) ClO I - + 4H +  Cl - + 2I 2 + 2H 2 O (4) I - + I 2 + Starch  StarchI 3 - (5) StarchI 3 -  I - + I 2 + Starch (6) I 2 + I -  I 3 - (7) I 3 -  I 2 + I - (h1) I 2 + H 2 O  I - + H + + IOH (h2) I - + H + + IOH  I 2 + H 2 O

16 CDIMA Fitting: No Light-Trial 1 k(1)=1e-3, k(2)=1.1e3

17 CDIMA Fitting: No Light-Trial 2 k(1)=1.16e-3, k(2)=1.45e3

18 CDIMA: Light on/off Light on: (8) I 2 + h  I · + I · (9) I · + I ·  I 2 (10) I · + I -  I 2 - (11) I 2 -  I · + I - (12) I · +ClO 2  IClO 2 Recovery-Light off: (13) IClO 2 + H 2 O  IO Cl - + 2H + (14) 5I - + IO H +  3I 2 + 3H 2 O (16) ClO 2 + I 2 -  ClO I 2

19 CDIMA Fitting: Complete Sequence

20 Detection of e aq - in Reductive Processes Electrochemical reductions Sodium amalgams Solid-phase reductants Heterogeneous reactions where yields may be decreased by scavenging precursors such as e aq - and H ·

21 Elementary Steps in the Generation of H 2 from the Reduction of Water by Magnesium Mg(s)  2e aq - + Mg 2+ e aq - + H +  H · e aq - + e aq -  H 2 + 2OH - e aq - + H ·  H 2 + OH - H · + H ·  H 2

22 Benzoate vs. Ethanol with Trichloroacetate Mg + 2H 2 O  Mg(OH) H · e aq e-3 s -1 e aq - + Cl 3 CCOO -  Cl 2 C · COO + Cl - 8.5e10 M -1 s -1 H · + C 6 H 5 COO -  · C 6 H 6 COO - 9.2e8 M -1 s -1 H · + C 2 H 5 OH  CH 3 C · HOH + H 2 1.7e7 M -1 s -1

23 Competitive Scavenging