Brownian dynamics 2-2 electrolytes

Both MC and MD simulation, can be applied to MM and BO Hamiltonian models of electrolyte solutions. MD at the MM level is known as Brownian dynamics simulation. It has gained some importance for the study of large ions in solution. At the BO level only concentrated solutions can be considered due to the restricted number of solvent molecules per number of ions in the simulation box. 

The Metropolis MC method in the canonical ensemble is the most frequently used simulation approach to solve the primitive model of electrolytes. Averages of static properties are taken from a large set of Boltzmann-weighted configurations. Molecular dynamics and Brownian dynamics constitute two other methods to determine static and dynamic properties of molecular systems. Their implementations are, however, comphcated for systems possessing impulsive forces in combination with other forces. Hence, a soft-sphere repulsion is frequently used instead of the hard-sphere one when simulating such systems with these methods. 

More complex systems such as solutions containing macroions and short flexible coimterions have recently been simulated using the primitive model of electrolytes [112]. Solutions of macroions with simple coimterions at different amounts of oppositely charged polyelectrolyte have also been investigated, and the sequence complexation phase separation redissolution was observed [113]. Similar simulations where the macroion represented lysozyme have also been performed [114]. Finally, by using a related soft-sphere model, the dynamics and, in particular, the self-diffusion of the macroions and the counterions have been investigated by employing Brownian dynamics simulation [115]. 

Perhaps the simplest phase transition for a pol5mieric system is the collapse of a single chain. There is much current interest in collapse transitions in relation to the protein folding problem (455). These simulations are often done with Brownian dynamics, and may include electrolyte effects. Low dimensional simulations (456) are of use in helping to imderstand this problem, particularly because theories of 1-D systems, which can be compared with simulations, are much easier to construct than for 2-D and 3-D. 

Several applications of brownian dynamics were made for electrolyte solutions and for biochemical systems with the aim to computing rate constants or characterizing chemical species. 

II) LANGEVIN DYNAMICS OF ELECTROLYTES an example of brownian dynamics... 

Brownian dynamics has been applied with this kind of potentials to 1-1 and 2-2 electrolytes and to some models of polyelectrolytes. 

As an example, the brownian dynamics results of the simulation of associated and non associated electrolytes in water at IM show that different cluster densities can be evaluated from this simulation. 

In order to understand these new features, we will recall briefly the basic principles of brownian dynamics cluster analysis for electrolytes. 

It is obviously possible to compute single particle densities as well as pair, triplet or higher order cluster densities. In fact these cluster densities are significant only for the structure of the solution, if one substracts the corresponding values for a brownian dynamic simulation at random i.e. a simulation in wich one removed the interactions between the particles. We present on Fig. 2a the values for a l-1 electrolyte in water... 

KAPRAL - The results for the equilibrium fractions of clusters in the electrolyte were obtained from long-time averages over the Brownian dynamics simulation. These results could be checked by direct Monte-Carlo simulations on the primitive model electrolyte. Has this been done ... 

This model has been applied to electrolytes since about 10 years and has been proved to be a successful tool in the derivation of dynamical and kinetic properties of electrolyte solutions with Mac-Millan Mayer solute-solute interactions and continuous brownian solvent . ... 

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