**Simulation of Polyelectrolyte-Catalysed Reaction
between Divalent Ions **

**Jesus Piñero,**^{1} **Lutful B.
Bhuiyan,**^{1}** Jurij Reščič**^{2}
**and Vojko Vlachy**^{2,*}

^{1}* Laboratory of Theoretical Physics Department of
Physics, University of Puerto Rico, San Juan, Puerto Rico 00931-3343
*

* Corresponding author: E-mail:

**Abstract**

Catalytic potential of linear polyelectrolyte solutions in presence of +2:–2
salts, as evidenced through ionic correlations in the inhomogeneous atmosphere
around a polyion, is studied using Monte Carlo simulation techniques and the
traditional non-linear Poisson-Boltzmann approach. The simulations are performed
on the cylindrical cell model where a uniformly charged hard cylinder mimics the
linear polyion caged in a cylindrical cell containing divalent counterions and
co-ions. Cell (volume) average of the inter-ionic correlations, as reflected in
the pair-correlation functions, is presented as function of the polyion
concentration, the low-molecular electrolyte concentration, and the ion radius.
The volume average of the doublet pair distribution function between counterions
is found to be sensitive to variation of model parameters. The results indicate
large enhancement in the reaction rate between the counterions, while a decrease
in the coion-coion and the coion-counterion reaction rate is noted, all in
comparison with pure electrolyte solutions. The agreement between the
predictions of the Poisson-Boltzmann theory and the simulation results is merely
qualitative in most instances.

**Keywords:** Polyelectrolytes, +2:–2 electrolytes, catalytic
effect, Monte Carlo method, Poisson-Boltzmann theory