Bjerrum length

Abstract: We present results of molecular dynamics simulations of linear polyelectrolytes in solution. The fundamental model for polyelectrolytes in solution is studied. Specifically, simulations are performed for multichain systems of a flexible chain model of charged polymers. The full Coulomb interactions of the monomers and counterions are treated explicitly. Experimental measurements of the osmotic pressure and the structure factor are reproduced. The simulations reveal a new picture of the chain structure based on calculations of the structure factor, persistence length, end‐to‐end distance, etc. We present a detailed discussion of the chain structure and a comparison with present theories. In contrast to the predicted dilute limit of rodlike chains, we find that the chains have significant bending at very low densities. Furthermore, the chains contract significantly before they overlap. We also show that counterion condensation dramatically alters the chain structure.

Abstract: The interaction between charged objects in an electrolyte solution is a fundamental question in soft matter physics. It is well known that the electrostatic contribution to the interaction energy decays exponentially with object separation. Recent measurements reveal that, contrary to the conventional wisdom given by the classic Poisson-Boltzmann theory, the decay length increases with the ion concentration for concentrated electrolytes and can be an order of magnitude larger than the ion diameter in ionic liquids. We derive a simple scaling theory that explains this anomalous dependence of the decay length on the ion concentration. Our theory successfully collapses the decay lengths of a wide class of salts onto a single curve. A novel prediction of our theory is that the decay length increases linearly with the Bjerrum length, which we experimentally verify by surface force measurements. Moreover, we quantitatively relate the measured decay length to classic measurements of the activity coefficient in concentrated electrolytes, thus showing that the measured decay length is indeed a bulk property of the concentrated electrolyte as well as contributing a mechanistic insight into empirical activity coefficients.

Abstract: Because micro-ions accumulate around highly charged colloidal particles in electrolyte solutions, the relevant parameter to compute their interactions is not the bare charge, but an effective (or renormalized) quantity, whose value is sensitive to the geometry of the colloid, the temperature or the presence of added-salt. This nonlinear screening effect is a central feature in the field of colloidal suspensions or polyelectrolyte solutions. We propose a simple method to predict effective charges of highly charged macro-ions, that is reliable for monovalent electrolytes (and counterions) in the colloidal limit (large size compared to both screening length and Bjerrum length). Taking reference to the non linear Poisson–Boltzmann theory, the method is successfully tested against the geometry of the macro-ions, the possible confinement in a Wigner–Seitz cell, and the presence of added salt. Moreover, our results are corroborated by various experimental measures reported in the literature. This approach provid...

Abstract: Screening of a surface charge by an electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.