The End

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Chapter 7

• The End

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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
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7.9 Electron Transfer Equilibrium

• In the ground state
• In the excited state

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7.10 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

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7.11 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

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7.11 Example with Energy Transfer

• (a) D and A diffuse through the solution until
  they meet as collision partners in an encounter
  complex DA.
• (b) Collisions occur between D and A in the
  encounter complex DA, 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.

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7.11 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

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

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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

Kobsltkdif
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Viscosity and Diffusion-Control

• Experimental rate constant approach diffusion
  control rate constants for ?2cP in a range
  considered viscous fluid.
• Common situation
• EadifgtEa ET
• If ET is exothermic,
• kET will be temperature indep.
• So experimentally EaobsltEa dif
• kdif will change more with temperature than k
  obs
• And kobs kdif at low temperature

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7.12 Cage Effect

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

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7.13 Distance-Time Relationships for Diffusion

• Random walk equation
• Brownian movement

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7.14 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

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7.15 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)

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Transient Effects

• the average path traveled by a molecule with D
  10 5 cm2s 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

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Concentration of Quenchers with Time
10-9 s
0 s

• Rate of quenching at short time scales is faster
  than those in the diffusional regime

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7.16 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

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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)