Where in the world are condensed counterions?

A scaling model of the concentration profiles of both condensed and free counterions is presented for solutions of spherical and cylindrical charged nanoparticles of different charge valences, nanoparticle sizes, and salt concentrations. The distribution of counterions for both spherical and cylindrical charged particles in salt-free solutions is determined by the condensation parameter defined as the ratio of nanoparticle valence to the number of Bjerrum lengths = /() per nanoparticle size ( = /(2) for spherical nanoparticles with radii or = / for cylindrical particles with length ), where is solution dielectric permittivity, is elementary charge and is thermal energy. Depending on the magnitudes of the condensation parameter and nanoparticle volume fraction , we find three qualitatively different regimes for the counterion distribution near charged particles: (i) weakly charged particles with no condensed counterions, (ii) regime of weak counterion condensation with less than half of the counterions condensed, and (iii) regime of strong counterion condensation with the majority of counterions condensed.

Understanding Factors Governing Distribution Volume of Ethyl Cellulose-Ethanol to Optimize Ablative Therapy in the Liver.

Objective: Ethanol ablation, the injection of ethanol to induce necrosis, was originally used to treat hepatocellular carcinoma, with survival rates comparable to surgery. However, efficacy is limited due to leakage into surrounding tissue. To reduce leakage, we previously reported incorporating ethyl cellulose (EC) with ethanol as this mixture forms a gel when injected into tissue.