Indentation analysis of nano-particle using nano-contact mechanics models during nano-manipulation based on atomic force microscopy

Atomic force microscopy is applied to measure intermolecular forces and mechanical properties of materials, nano-particle manipulation, surface scanning and imaging with atomic accuracy in the nano-world. During nano-manipulation process, contact forces cause indentation in contact area between nano-particle and tip/substrate which is considerable at nano-scale and affects the nano-manipulation process. Several nano-contact mechanics models such as Hertz, Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS), Burnham–Colton–Pollock (BCP), Maugis–Dugdale (MD), Carpick–Ogletree–Salmeron (COS), Pietrement–Troyon (PT), and Sun et al. have been applied as the continuum mechanics approaches at nano-scale. In this article, indentation depth and contact radius between tip and substrate with nano-particle for both spherical and conical tip shape during nano-manipulation process are analyzed and compared by applying theoretical, semiempirical, and empirical nano-contact mechanics models. The effects of adhesion force, as the main contrast point in different nano-contact mechanics models, on nano-manipulation analysis is investigated for different contact radius, and the critical point is discussed for mentioned models.     

TWO-VARIABLE JACOBI POLYNOMIALS FOR SOLVING SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Two-variable Jacobi polynomials, as a two-dimensional basis, are applied to solve a class of temporal fractional partial differential equations. The fractional derivative operators are in the Caputo sense. The operational matrices of the integration of integer and fractional orders are presented. Using these matrices together with the Tau Jacobi method converts the main problem into the corresponding system of algebraic equations. An error bound is obtained in a two-dimensional Jacobi-weighted Sobolev space. Finally, the efficiency of the proposed method is demonstrated by implementing the algorithm to several illustrative examples. Results will be compared with those obtained from some existing methods.     

Vertex and Edge Orbits of Fibonacci and Lucas Cubes

The Fibonacci cube \({\Gamma_{n}}\) is obtained from the n-cube Q _n by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube \({\Lambda_{n}}\) is obtained. The number of vertex and edge orbits, the sets of the sizes of the orbits, and the number of orbits of each size, are determined for the Fibonacci cubes and the Lucas cubes under the action of the automorphism group. In particular, the set of vertex orbit sizes of \({\Lambda_{n}}\) is \({\{k \geq 1; k |n\} \cup \{k \geq 18; k |2n\}}\), the number of vertex orbits of \({\Lambda_{n}}\) of size k, where k is odd and divides n, is equal to \({\sum_{d | k} \mu (\frac{k}{d})F_{\lfloor{\frac{d}{2}}\rfloor+2}}\), and the number of edge orbits of \({\Lambda_{n}}\) is equal to the number of vertex orbits of \({\Gamma_{n-3}}\). Dihedral transformations of strings and primitive strings are essential tools to prove these results.     

在色氨酸存在下利用多壁碳纳米管糊电极和萘酚介质构成的伏安传感器测定N-乙酰半胱氨酸(英文)

A multiwall carbon nanotube modified electrode prepared by incorporating multiwall carbon nanotubes in the electrode of a sensor and naphthol green as a homogeneous mediator was used as a voltammetric sensor for the determination of N‐actylcysteine(N‐AC) in the presence of trypto-phan(Trp). The voltammograms of differential pulse voltammetry of N‐AC in a mixture with Trp were separated from each other by a potential difference of 200 mV, which allowed the determina-tion of both N‐AC and Trp simultaneously. Under the optimum conditions, the electrocatalytic cur-rents increased linearly with N‐AC concentration in the range of 0.25–400 μmol/L(two linear seg-ments with different slopes). The detection limit for N‐AC was 0.08 μmol/L. The kinetic parameters of the system were determined using electrochemical methods. The method was applied for the determination of N‐AC in drug and urine samples.     

K7[PW11CoO40]: Efficient and Ecofriendly Catalyst for the Enamination of β-Dicarbonyl Compounds

Condensation of a variety of β-dicarbonyl compounds with primary and secondary amines carried out in the presence of catalytic amounts of K₇[PW₁₁CoO₄₀]. From this reaction N-substituted β-enamino esters and ketones were obtained in high yields.     

The Effect of a Covalent and a Noncovalent Small-Molecule Inhibitor on the Structure of Abg β-Glucosidase in the Gas-Phase

The effects of binding two small-molecule inhibitors to Agrobacterium sp. strain ATCC 21400 (Abg) β-glucosidase on the conformations and stability of gas-phase ions of Abg have been investigated. Biotin-iminosugar conjugate (BIC) binds noncovalently to Abg while 2,4-dinitro-2-deoxy-2-fluoro-β-d-glucopyranoside (2FG-DNP) binds covalently with loss of DNP. In solution, Abg is a dimer. Mass spectra show predominantly dimer ions, provided care is taken to avoid dissociation of dimers in solution and dimer ions in the ion sampling interface. When excess inhibitor, either covalent or noncovalent, is added to solutions of Abg, mass spectra show peaks almost entirely from 2:2 inhibitor-enzyme dimer complexes. Tandem mass spectrometry experiments show similar dissociation channels for the apo-enzyme and 2FG-enzyme dimers. The +21 dimer produces +10 and +11 monomers. The internal energy required to dissociate the +21 2FG-enzyme to its monomers (767?±?30 eV) is about 36 eV higher than that for the apo-enzyme dimer (731?±?6 eV), reflecting the stabilization of the free enzyme dimer by the 2FG inhibitor. The primary dissociation channels for the noncovalent BIC-enzyme dimer are loss of neutral and charged BIC. The internal energy required to induce loss of BIC is 482?±?8 eV, considerably less than that required to dissociate the dimers. For a given charge state, ions of the covalent and noncovalent complexes have about 15 % and 25 % lower cross sections, respectively, compared with the apo-enzyme. Thus, binding the inhibitors causes the gas-phase protein to adopt more compact conformations. Noncovalent binding surprisingly produces the greatest change in protein ion conformation, despite the weaker inhibitor binding.

Cupric Sulfate Pentahydrate: A Mild and Efficient Catalyst for the Chemoselective Synthesis of 1,1-Diacetates from Aldehydes in a Solvent-Free System

Cupric sulfate pentahydrate was found to be an efficient catalyst for the protection of aldehydes as 1,1-diacetates in high yields in a solvent-free system at room temperature. Ketones are not affected under these reaction conditions.