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Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone
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Polarization caging in diffusion-controlled electron transfer reactions in solution.

Rakesh Sharan Singh1, Masanori Tachiya, Biman Bagchi

  • 1Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-12, India.

The Journal of Physical Chemistry. B
|September 3, 2010
PubMed
Summary

This study develops a new theory for electron transfer reactions, revealing how solvent polarization and ion movement affect reaction rates. Slowing solvent relaxation significantly impacts reaction outcomes, especially in the normal and barrierless regions.

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Area of Science:

  • Chemical Physics
  • Physical Chemistry
  • Theoretical Chemistry

Background:

  • Electron transfer (ET) reactions are fundamental in chemistry and biology.
  • Ion recombination (IR) is a key example of a diffusion-controlled ET reaction.
  • Simultaneously modeling solvent polarization and diffusion in ET reactions is complex and largely unsolved.

Purpose of the Study:

  • To develop a dynamic theory combining solvent polarization and diffusion for bimolecular ET reactions.
  • To investigate the interplay between polarization relaxation and translational dynamics in ion recombination.
  • To provide a theoretical framework for understanding reaction rates and yields in complex systems.

Main Methods:

  • Developed a dynamic theory integrating ET reaction concepts and barrierless chemical reactions.
  • Employed two-dimensional coupled Smoluchowski equations to model reactant and product probability distributions.
  • Solved the equations numerically using an alternate direction implicit (ADI) scheme.
  • Defined a reaction line based on equal energy for initial and final states.

Main Results:

  • Slow longitudinal polarization relaxation drastically decreases escape probability due to solvent caging.
  • Escape probability and average rate depend significantly on initial solvent polarization in the slow relaxation limit.
  • In the fast polarization relaxation limit, escape probability and rate are independent of initial polarization.
  • The dependence of escape probability and rate on initial polarization is stronger in the normal and barrierless regions than in the inverted region.
  • Observed non-Marcus (asymmetrical parabolic) energy gap dependence of the rate due to dynamics along the R coordinate.

Conclusions:

  • Solvent polarization relaxation and ion diffusion are coupled and critical factors in bimolecular ET reactions.
  • Polarization caging significantly influences reaction dynamics, particularly under slow relaxation conditions.
  • The developed theory provides new insights into the complex kinetics of ion recombination and related ET processes.