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 γ0 defined as the ratio of nanoparticle valence Z0 to the number of Bjerrum lengths lB = e2/(εkT) per nanoparticle size (γ0 = Z0lB/(2r0) for spherical nanoparticles with radii r0 or γ0 = Z0lB/L for cylindrical particles with length L), where ε is solution dielectric permittivity, e is elementary charge and kT is thermal energy. Depending on the magnitudes of the condensation parameter γ0 and nanoparticle volume fraction ϕ, 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. The magnitude of electrostatic energy of a condensed counterion with respect to solution locations with zero electric field is larger than thermal energy kT, and the fraction of condensed counterions increases from less than half in the weak condensation regime to the majority of all counterions in the strong condensation regime. The condensed counterions are not bound to the nanoparticle surface but instead are localized within the condensed counterion zone near the charged particle. The thickness of the condensed counterion zone varies with the condensation parameter γ0, the nanoparticle shape and volume fraction ϕ, and the salt concentration and can be as narrow as Bjerrum length (∼nm) or as large as the particle size (∼L the length of charged cylinder).

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. To further develop EC-ethanol injection as an ablative therapy, the present study evaluates the extent to which salient injection parameters govern the injected fluid distribution. METHODS: Utilizing ex vivo swine liver, injection parameters (infusion rate, EC%, infusion volume) were examined with fluorescein added to each solution. After injection, tissue samples were frozen, sectioned, and imaged. RESULTS: While leakage was higher for ethanol and 3%EC-ethanol at a rate of 10 mL/hr compared to 1 mL/hr, leakage remained low for 6%EC-ethanol regardless of infusion rate. The impact of infusion volume and pressure were also investigated first in tissue-mimicking surrogates and then in tissue. Results indicated that there is a critical infusion pressure beyond which crack formation occurs leading to fluid leakage. At a rate of 10 mL/hr, a volume of 50 µL remained below the critical pressure. CONCLUSIONS: Although increasing the infusion rate increases stress on the tissue and the risk of crack formation, injections of 6%EC-ethanol were localized regardless of infusion rate. To further limit leakage, multiple low-volume infusions may be employed. SIGNIFICANCE: These results, and the experimental framework developed to obtain them, can inform optimizing EC-ethanol to treat a range of medical conditions.