Partial Fluxes of Phosphoric Acid Anions through Anion-Exchange Membranes in the Course of NaH2PO4 Solution Electrodialysis

Electrodialysis (ED) with ion-exchange membranes is a promising method for the extraction of phosphates from municipal and other wastewater in order to obtain cheap mineral fertilizers. Phosphorus is transported through an anion-exchange membrane (AEM) by anions of phosphoric acid. However, which phosphoric acid anions carry the phosphorus in the membrane and the boundary solution, that is, the mechanism of phosphorus transport, is not yet clear. Some authors report an unexpectedly low current efficiency of this process and high energy consumption. In this paper, we report the partial currents of H2PO4−, HPO42−, and PO43− through Neosepta AMX and Fujifilm AEM Type X membranes, as well as the partial currents of H2PO4− and H+ ions through a depleted diffusion layer of a 0.02 M NaH2PO4 feed solution measured as functions of the applied potential difference across the membrane under study. It was shown that the fraction of the current transported by anions through AEMs depend on the total current density/potential difference. This was due to the fact that the pH of the internal solution in the membrane increases with the growing current due to the increasing concentration polarization (a lower electrolyte concentration at the membrane surface leads to higher pH shift in the membrane). The HPO42− ions contributed to the charge transfer even when a low current passed through the membrane; with an increasing current, the contribution of the HPO42− ions grew, and when the current was about 2.5 ilimLev (ilimLev was the theoretical limiting current density), the PO43− ions started to carry the charge through the membrane. However, in the feed solution, the pH was 4.6 and only H2PO4− ions were present. When H2PO4− ions entered the membrane, a part of them transformed into doubly and triply charged anions; the H+ ions were released in this transformation and returned to the depleted diffusion layer. Thus, the phosphorus total flux, jP (equal to the sum of the fluxes of all phosphorus-bearing species) was limited by the H2PO4− transport from the bulk of feed solution to the membrane surface. The value of jP was close to ilimLev/F (F is the Faraday constant). A slight excess of jP over ilimLev/F was observed, which is due to the electroconvection and exaltation effects. The visualization showed that electroconvection in the studied systems was essentially weaker than in systems with strong electrolytes, such as NaCl.

Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders

In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents at T = 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [1, 2] with some improvements and unitary notations.

Relativistic persistent currents in ideal Aharonov–Bohm rings

The exact solutions of the complete Dirac equation for fermions moving in ideal Aharonov–Bohm rings are used for deriving the exact expressions of the relativistic partial currents. It is shown that as in the nonrelativistic case, these currents can be related to the derivative of the fermion energy with respect to the flux parameter. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent current at T = 0 is evaluated giving its analytical expression and showing how this depends on the ring parameters.

Revealing of hydrodynamic and electrostatic factors in the center-of-mass velocity of an expanding plasma generated by pulsed laser ablation

Time-of-flight spectra of C, Fe, and Si ions produced with the use of a KrF excimer laser have been analyzed. Ion currents were collected by Faraday cups and their responses were analyzed using a detector signal function. This function was derived from shifted Maxwell-Boltzmann velocity distribution, in order to uncover the contribution of partial currents of all the ionized species constituting the expanding plasma plume. The deconvolution method allowed to estimate parameters of the plasma, such as the ion temperature and the center-of-mass velocities of expanding ionized species. Furthermore, the linear charge-state dependence of the center-of-mass velocity has revealed the contribution of hydrodynamic and electrostatic forces to the expansion velocity of the plasma. The nearly isotropic distribution of the center-of-mass velocity indicates that the shape of the plasma plume is determined mainly by the angular distribution of the ionization degree of ions.