Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Onset of energy dissipation in ballistic atomic wires

Electronic transport at finite voltages in free-standing gold atomic chains of up to seven atoms in length is studied at low temperatures using a scanning tunneling microscope. The conductance vs voltage curves show that transport in these single-mode ballistic atomic wires is nondissipative up to a finite voltage threshold of the order of several mV. The onset of dissipation and resistance within the wire corresponds to the excitation of the atomic vibrations by the electrons traversing the wire and is very sensitive to strain.

Electrochemical generation of oxygen-containing groups in an ordered microporous zeolite-templated carbon

Zeolite templated carbon (ZTC) was electrochemically oxidized under various conditions, and its chemistry and structural evolution were compared to those produced by conventional chemical oxidation. In both oxidation methods, a general loss of the original structure regularity and high surface area was observed with increasing amount of oxidation. However, the electrochemical method showed much better controllability and enabled the generation of a large number of oxygen functional groups while retaining the original structure of the ZTC. Unlike chemical treatments, highly microporous carbons with an ordered 3-D structure, high surface area (ranging between 1900 and 3500 m2/g) and a large number of oxygen groups (O = 11,000–3300 μmol/g), have been prepared by the electrochemical method. Some insights into the electrooxidation mechanism of carbon materials are proposed from the obtained polarization curves, using ZTC as a model carbon material.

Generation of nitrogen functionalities on activated carbons by amidation reactions and Hofmann rearrangement: Chemical and electrochemical characterization

Nitrogen functionalization of a highly microporous activated carbon (BET surface area higher than 3000 m2/g) has been achieved using the following sequence of treatments: (i) chemical oxidation using concentrated nitric acid, (ii) amidation by acyl chloride substitution with NH4NO3 and (iii) amination by Hoffman rearrangement. This reaction pathway yielded amide and amine functional groups, and a total nitrogen content higher than 3 at.%. It is achieved producing only a small decrease (20%) of the starting microporosity, being most of it related to the initial wet oxidation of the activated carbon. Remarkably, nitrogen aromatic rings were also formed as a consequence of secondary cyclation reactions. The controlled step-by-step modification of the surface chemistry allowed to assess the influence of individual nitrogen surface groups in the electrochemical performance in 1 M H2SO4 of the carbon materials. The largest gravimetric capacitance was registered for the pristine activated carbon due to its largest apparent surface area. The nitrogen-containing activated carbons showed the highest surface capacitances. Interestingly, the amidated activated carbon showed the superior capacitance retention due to the presence of functional groups (such as lactams, imides and pyrroles) that enhance electrical conductivity through their electron-donating properties, showing a capacitance of 83 F/g at 50 A/g.