Discrete charge effects in the structure of ions around polyelectrolyte models

摘要

Axial long-range effects in the structure of ions around discretely charged polyelectrolytes are discussed. Specifically, we deal with rigid polyion models with helical or cylindrical symmetry—DNA typically—in which a number of charges are treated. The solvent is described by a dielectric continuum. Firstly, exact and approximate methods for calculating the long-range interactions along the axial direction are introduced. The convergence rate and usefulness of the exact formula is discussed. The replacement of the exact expression by that due to an equivalent homogeneous charge distribution is also checked. It is concluded that such substitution leads to erroneous results for the ionic concentration profiles. This seems in contradiction with previous work showing that infinite systems made of discrete and homogeneous charge distributions exhibit very similar ionic structures. Thus, we have investigated the behaviour of the finite systems (i.e. without long-range interactions). It is concluded that polyelectrolyte finite size effects are dependent on the charge distribution: the system with a discrete charge distribution condenses more counterions than the homogeneous one. As the effect of the long-range correction is just the opposite, they mutually cancel so both infinite systems yield almost identical ionic concentration profiles, in agreement with previous studies.