In this paper, the dynamical properties of the electrochemical double layer following an electron transfer are investigated by using Brownian dynamics simulations. This work is motivated by recent developments in ultrafast cyclic voltammetry which allow nanosecond time scales to be reached. A simple model of an electrochemical cell is developed by considering a 1:1 supporting electrolyte between two parallel walls carrying opposite surface charges, representing the electrodes; the solution also contains two neutral solutes representing the electroactive species. Equilibrium Brownian dynamics simulations of this system are performed. To mimic electron transfer processes at the electrode, the charge of the electroactive species are suddenly changed, and the subsequent relaxation of the surrounding ionic atmosphere are followed, using nonequilibrium Brownian dynamics. The electrostatic potential created in the center of the electroactive species by other ions is found to have an exponential decay which allows the evaluation of a characteristic relaxation time. The influence of the surface charge and of the electrolyte concentration on this time is discussed, for several conditions that mirror the ones of classical electrochemical experiments. The computed relaxation time of the double layer in aqueous solutions is found in the range 0.1 to 0.4 ns for electrolyte concentrations between 0.1 and 1 mol L(-1) and surface charges between 0.032 and 0.128 C m(-2).
Two examples of charged media in water are studied by numerical simulations:
aqueous solutions of highly asymmetrical electrolytes (large and highly charged
spherical particles surrounded by small and slightly charged counterions) and a
swelling clay (charged plane sheets surrounded by small counterions). In the
former example, Brownian dynamics (BD) showed that the mean number of
counterions in the vicinity of polyions nearly balances the charge of the macroion
and that the turnover of the small ions in this region is important. The effect of
hydrodynamic interactions on the dynamics is weak for small ions but
is great for macroions. On the other hand, the relative decrease of the
macroion self-diffusion coefficients is more important than that of counterions.
Moreover, the small ions retain a relatively high self-diffusion coefficient at the
highest concentration, a concentration at which the macroions freeze. BD
simulation was also used to obtain the distribution of counterions Na+
between the sheets of a fairly hydrated montmorillonite. The obtained
profile was very similar to those we obtained by atomic simulations (Monte
Carlo and molecular dynamics) and by a Poisson–Boltzmann treatment.
It justifies the description of the solvent as a continuum as soon as the
system is hydrated enough. However, for less hydrated states of the clay
(mono-or bi-layer of water), only atomic simulations can bring exploitable
information. We showed that, according to whether the counterion is
Na+ and/or Cs+, the behaviours in the bihydrated clay are very different:
although Na+ is easily hydrated and is located in the middle of the pores, Cs+
remains close to the negative surfaces of the sheets and its preferential paths
along the surface sites can be underscored from obtained trajectories.
Das Verhalten eines Ensembles aus wenigen Molekülen sollte ausgeprägt stochastisch sein und somit deutlich von den Geschwindigkeitsgesetzen üblicher chemischer Reaktionen abweichen. Diese Gegensätzlichkeit wurde am Beispiel der elektrochemischen Oxidation eines PAMAM‐Dendrimers mit 64 redoxaktiven Ruthenium‐Einheiten theoretisch untersucht (siehe Bild). Die maximale Anzahl adsorbierter Moleküle, für die noch stochastisches Verhalten beobachtet wird, kann entweder direkt oder anhand von instrumentellen Verzerrungen ermittelt werden.
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