Brownian dynamics polyelectrolytes

Klenin, K., Merlitz, H., and Langowski, J. (1998) A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes. Biophys. J. 74, 780-788. 

According to the fluctuation-dissipation theorem [1], the electrical polarizability of polyelectrolytes is related to the fluctuations of the dipole moment generated in the counterion atmosphere around the polyions in the absence of an applied electric field [2-4], Here we calculate the fluctuations by computer simulation to determine anisotropy of the electrical polarizability Aa of model DNA fragments in salt-free aqueous solutions [5-7]. The Metropolis Monte Carlo (MC) Brownian dynamics method [8-12] is applied to calculate counterion distributions, electric potentials, and fluctuations of counterion polarization. 

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]. 

The adsorption of polyelectrolytes to surfaces is a problem of growing interest stimulated by many industrial applications. Explicit and implicit solvent models were used in studying this problem via computer simulation [39,40]. Using molecular and Brownian dynamics simulations and... 

Brownian dynamics hyperbranched polymers with linear polyelectrolytes under steady shear flow [96]... 

Dalakoglou G, Karatasos K, Lyulin S, Lyulin A (2008) Brownian dynamics simulations of complexes of h3q)erbranched polymers with linear polyelectrolytes effects of the strength of electrostatic interactions on static properties. Mat Sci Eng B-Solid 152(1-3) 114—118. doi 10.1016/j.mseb.2008.06.012... 

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

Chang, R., Yethiraj, A. Brownian dynamics simulations of polyelectrolyte solutions with divalent counterions. J. (Them. Phys. 118, 11315-11324 (2003). doi 10.1063/l.1575731... 

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

Eq. (3.1) describes the diffusive behavior of a chain (i.e., the movement of the center of mass) as well as its conformational rearrangements as a function of time. The equation is stochastic because the chain performs Brownian motion, and it has many different conformations which all have the same probability. The monomer-monomer interactions are described by the Fj. We will assume here that there are no long-range interactions present (in marked contrast to the case of polyelectrolytes ) and that hence the chain s structure is a random or self-avoiding walk. Motion in three-dimensional space is assumed throughout. The diffusion tensor Dy specifies the dynamics. Mathematical consistency of eq. (3.1) requires that Dy is symmetric and positive-definite for all possible golymer conformations (no other property is necessary). In the Rouse case, Dy is simply diagonal. 

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