On the Spatial Correlations in Nonequilibrium Systems

On example of diffusion-limited reversible A + A ⇋ B reactions we re-examine two fundamental concepts of classical chemical kinetics -the notion of "Chemical Equilibrium" and the "Law of Mass Action". We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance µ apart of each other at time moment t, may associate forming a B particle at the rate k + (µ). In turn, any randomly moving B particle may spontaneously dissociate at the rate k − (λ) into a geminate pair of As "born" at a distance λ apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t = ∞ state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a non-equilibrium steady-state, and that the Law of Mass Action is invalid.The classical concepts hold only in case when the ratio k + (µ)/k − (µ) does not depend on µ for any µ.

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“…[12,13,14,15]. Under certain conditions, it may also take place for reactions in which the particles number is not explicitly conserved [16].…”

Section: Introductionmentioning

confidence: 99%

Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions

Voituriez

Moreau

Oshanin

2005

The Journal of Chemical Physics

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“…The length scale is called the Kuramoto length. [26][27][28][29][30] The Kuramoto length characterizes the spatial correlation of density fluctuations around a uniform concentration state. The density fluctuations beyond the length scale given by the Kuramoto length are independent.…”

Section: Both Cations and Anions Are Discharged At The Electrode Surfacementioning

confidence: 99%

“…Photo-electrochemical (PEC) conversion of water can be an example, but the fundamental results apply to other electrode reactions. We show that the gradient of total ion density (the sum of cation and anion concentrations) is characterized by either the Kuramoto length [26][27][28][29][30][31] Debye length depending on the situation, while the gradient of charge density (the difference between cation and anion concentrations) is characterized by the Debye length in binary monovalent weak electrolytes. The Kuramoto length characterizes the length scale of local density fluctuations around a uniform concentration state.…”

Section: Introductionmentioning

confidence: 95%

“…[26][27][28][29][30][31] In weak electrolytes, the Kuramoto length is given by the length scale of diffusive migration of ions within its life-time; the life-time is determined by the association rate of ions. [26][27][28][29][30][31] Our results indicate that the ion density gradients can also be characterized by the Kuramoto length when both cations and anions are discharged at the electrode in binary monovalent weak electrolytes. For this case, ion density drop caused by electrode reactions is recovered by ion density fluctuations localized within the Kuramoto length.…”

Section: Introductionmentioning

confidence: 99%

“…The Kuramoto length characterizes the length scale of local density fluctuations around a uniform concentration state. [26][27][28][29][30][31] In weak electrolytes, the Kuramoto length is given by the length scale of diffusive migration of ions within its life-time; the life-time is determined by the association rate of ions. [26][27][28][29][30][31] Our results indicate that the ion density gradients can also be characterized by the Kuramoto length when both cations and anions are discharged at the electrode in binary monovalent weak electrolytes.…”

Section: Introductionmentioning

confidence: 99%

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Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson–Nernst–Planck equations involving ionization in a weak electrolyte

Suzuki

Seki

2018

Chemical Physics

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We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson-Nernst-Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the total ion density gradient was given by the Kuramoto length which characterized the distance over which an ion diffuses before association. The charge density gradient is characterized by the Debye length for 1:1 weak electrolytes. We discuss the role of these length scales for efficient water splitting reactions using photo-electrocatalytic electrodes.

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Spatial correlations in reaction-diffusion systems in nonequilibrium conditions

Seki¹,

Kitahara²

1995

Journal of Molecular Liquids

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On the Spatial Correlations in Nonequilibrium Systems

Cited by 9 publications

References 1 publication

Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions

Corrections to the law of mass action and properties of the asymptotic t=∞ state for reversible diffusion-limited reactions

Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson–Nernst–Planck equations involving ionization in a weak electrolyte

Spatial correlations in reaction-diffusion systems in nonequilibrium conditions

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