Chapter 7 The End

2 7.9 Energy Transfer Equilibrium Equilibrium between singlet states expected to be quite rare except when linked by a spacer Intermolecular equilibrium for triplets readily achieved Concentration ratio of [A*]/ [D*] is monitored as a fct of time. A cst ratio is indicative of energy transfer equilibration To allow comparison of energy from spectroscopic measurements and energy transfer equilibrium

3 7.9 Electron Transfer Equilibrium In the ground state In the excited state

Chemiluminescent Ion Recombination Ion recombination in solution can lead to an excited state 2 factors a) Marcus inverted region where smaller  G to excited state may be kinetically preferred b) a triplet radical ion pair can populate an excited triplet state of D, but formation of ground state products is spin forbidden

Role of Molecular Diffusion in Energy and Electron Transfer Processes in Solution Delivery Processes 1. Organized Proximity Linked chromophores Ex, Photosynthesis 2. Diffusional Processes Transfer requires proximity and the medium allows mobility of the reaction partners 3. Conducting Medium Ex Trivial Mechanisms for Energy and Electron transfer

Example with Energy Transfer (a) D* and A diffuse through the solution until they meet as collision partners in an encounter complex D*A. (b) Collisions occur between D* and A in the encounter complex D*A, and one of these collisions eventually leads to energy transfer and generation of a new encounter complex DA*. (CAGE EFFECTS) (c) The encounter complex DA* breaks up into free D + A*.

Estimation of Rate Constants for Diffusion Controlled Processes Smoluchowski eqn. For large solute molecules in small solvent molecules Debye eqn. For small solute molecules in large solvent molecules  =2000

8 K diff as a fct of Viscosity You can also make an Arrhenius plot since viscosity is temperature dependent

9 Diffusion-controlled Energy Transfer Experimental Criteria A) k obs close to k calc B) k obs is a fct of T/  C) k obs is invariant for quenchers of widely varying structures D) k obs reaches a limiting value that corresponds to the fastest bimolecular rate constant measured for that solvent Totally diffusion controlled energy transfer processes are rare

10 Reactions that are Near Diffusion-Control Group 1 Spin Statistical Factors come into play They behave as typical diffusion controlled processes but rate constants are a constant fraction of k diff Group 2 First step is reversible K obs <k dif

11 Viscosity and Diffusion-Control Experimental rate constant approach diffusion control rate constants for  ≥2cP in a range considered viscous fluid. Common situation: Ea dif >Ea ET If ET is exothermic, k ET will be temperature indep. So experimentally Ea obs <Ea dif k dif will change more with temperature than k obs And kobs ≈kdif at low temperature

Cage Effect Average frequency of collisions unchanged but distribution in time is changed Secondary cage reeencounter:due to non- uniform distribution of reactants who can react together even when separated by at least one solvent molecule

Distance-Time Relationships for Diffusion Random walk equation Brownian movement

Diffusion Control in Systems Involving Charged Species Charge as well as viscosity, temperature and molecular dimensions play a role in cage effects In the case of electron transfer, coulombic effects may affect the separation of the products Need to add an electrostatic correction to k dif

Effect of Rapid Molecular Processes on the Mechanism of Processes Approaching Diffusion 1) Quenching by diffusional processes Most common regime. Processes with long time scales 2) Quenching influenced by transient effects When conc. are high and lifetimes are short, redistribution of quenchers (A) around the probe molecule (D*) cannot be reestablished during the lifetime of D* Time -dependent rate constant 3) Static quenching No transport of molecules through the solution as in solid matrices (Perrin Formulation)

16 Transient Effects the average path traveled by a molecule with D~ 10 –5 cm 2 s –1 in 100 fs, 10 ps and 1 ns, we find these distances to be 0.14 Å, 1.4 Å and 14 Å, respectively, clearly, in at least the first two cases, distances that are too short for diffusion to be able to re- establish

17 Concentration of Quenchers with Time Rate of quenching at short time scales is faster than those in the diffusional regime s0 s

Energy Transfer in the Absence of Diffusion In rigid systems Possible mechanisms 1) Physical mass transport system not rigid at a molecular level 2) Proximity (Perrin Formulation) D and A are close enough to permit transfer Competing processes are slower in rigid media than in fluid media 3) Conducting Media 4)Energy or Electron migration Molecular wires Hopping occurs in polymeric materials

19 Perrin Formulation (for Static Quenching) No displacement of D* and A during lifetime of D* No quenching from outside the quenching sphere  =0 and  =1 in the quenching sphere  º and  are the efficiencies for donor emission in the absence and presence of quencher(A)