The Minimal Total Irregularity of Graphs

In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as \hskip3.3cm $\rm irr_{t}$$(G) = \frac{1}{2}\sum_{u,v\in V}|d_{G}(u)-d_{G}(v)|,$ \noindent where $d_{G}(u)$ denotes the vertex degree of a vertex $u\in V$. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research.Comment: 13 pages, 4 figure

The Maximal Total Irregularity of Bicyclic Graphs

In 2012, Abdo and Dimitrov defined the total irregularity of a graph G=(V,E) as irrtG=1/2∑u,v∈VdGu-dGv, where dGu denotes the vertex degree of a vertex u∈V. In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs on n vertices

Surface-to-Bulk Redox Coupling through Thermally Driven Li Redistribution in Li- and Mn-Rich Layered Cathode Materials.

Li- and Mn-rich (LMR) layered cathode materials have demonstrated impressive capacity and specific energy density thanks to their intertwined redox centers including transition metal cations and oxygen anions. Although tremendous efforts have been devoted to the investigation of the electrochemically driven redox evolution in LMR cathode at ambient temperature, their behavior under a mildly elevated temperature (up to ∼100 °C), with or without electrochemical driving force, remains largely unexplored. Here we show a systematic study of the thermally driven surface-to-bulk redox coupling effect in charged Li1.2Ni0.15Co0.1Mn0.55O2. We for the first time observed a charge transfer between the bulk oxygen anions and the surface transition metal cations under ∼100 °C, which is attributed to the thermally driven redistribution of Li ions. This finding highlights the nonequilibrium state and dynamic nature of the LMR material at deeply delithiated state upon a mild temperature perturbation

Plasma-Assisted Chemical Vapor Deposition of Titanium Oxide Films by Dielectric Barrier Discharge in TiCl4/O-2/N-2 Gas Mixtures

National Natural Science Foundation of China [10875025, 20803007]; Fundamental Research Funds for Central Universities of China [DC12010116, DC13010106]; Program for Liaoning Excellent Talents in University [LJQ20l3128]Low-pressure dielectric barrier discharge (DBD) TiCl4/O-2 and N-2 plasmas have been used to deposit titanium oxide films at different power supply driving frequencies. A home-made large area low pressure DBD reactor was applied, characterized by the simplicity of the experimental set-up and a low consumption of feed gas and electric power, as well as being easy to operate. Atomic force microscopy, scanning electron microscopy, energy dispersive spectroscopy, and contact angle measurements have been used to characterize the deposited films. Experimental results show all deposited films are uniform and hydrophilic with a contact angle of about 15 degrees. Compared to titanium oxide films deposited in TiCl4/O-2 gas mixtures, those in TiCl4/O-2/N-2 gas mixtures are much more stable. The contact angle of titanium oxide films in TiCl4/O-2/N-2 gas mixtures with the addition of 50% N-2 and 20% TiCl4 is still smaller than 20 degrees, while that of undoped titanium oxide films is larger than 640 when they are measured after one week. The low-pressure TiCl4/O-2 plasmas consist of pulsed glow-like discharges with peak widths of several microseconds, which leads to the uniform deposition of titanium oxide films. Increasing a film thickness over several hundreds of nm leads to the film's fragmentation due to the over-high film stress. Optical emission spectra (OES) of TiCl4/O-2 DBD plasmas at various power supply driving frequencies are presented

Plasma-assisted chemical vapor deposition of titanium oxide films by dielectric barrier discharge in TiCl4/O2/N2 gas mixtures

Low-pressure dielectric barrier discharge (DBD) TiCl4/O2 and N2 plasmas have been used to deposit titanium oxide films at different power supply driving frequencies. A homemade large area low pressure DBD reactor was applied, characterized by the simplicity of the experimental set-up and a low consumption of feed gas and electric power, as well as being easy to operate. Atomic force microscopy, scanning electron microscopy, energy dispersive spectroscopy, and contact angle measurements have been used to characterize the deposited films. Experimental results show all deposited films are uniform and hydrophilic with a contact angle of about 15°. Compared to titanium oxide films deposited in TiCl4/O2 gas mixtures, those in TiCl4/O2/N2 gas mixtures are much more stable. The contact angle of titanium oxide films in TiCl4/O2/N2 gas mixtures with the addition of 50% N2 and 20% TiCl4 is still smaller than 20°, while that of undoped titanium oxide films is larger than 64° when they are measured after one week. The low-pressure TiCl4/O2 plasmas consist of pulsed glow-like discharges with peak widths of several microseconds, which leads to the uniform deposition of titanium oxide films. Increasing a film thickness over several hundreds of nm leads to the film's fragmentation due to the over-high film stress. Optical emission spectra (OES) of TiCl4/O2 DBD plasmas at various power supply driving frequencies are presented