THE PHOTOOXIDATION OF AZOMETHANE. III

1959 ◽  
Vol 37 (9) ◽  
pp. 1546-1560 ◽  
Author(s):  
F. Wenger ◽  
K. O. Kutschke
Keyword(s):  
Carbon Balance ◽  
Bimolecular Reaction ◽  
Major Product ◽  
Performic Acid ◽  
Peroxy Radicals ◽  
Methyl Radicals ◽  
Third Order ◽  
Vibrationally Excited ◽  
The Third ◽  
High Oxygen Pressure

It is confirmed that the yields of all products in the photooxidation of azomethane at relatively high oxygen pressure depend on conversion in a manner which would be explained if a reactive hydrogen donor were produced in the early stages of the reaction. Evidence is presented which indicates that formaldehyde cannot be active as an inhibitor in the system at 162 °C. It is suggested that methyl radicals react with oxygen in two ways. The third order formation of methyl peroxy radicals leads to methoxy radicals and, eventually, to methanol, while the bimolecular reaction between methyl radicals and oxygen leads to a vibrationally excited state of formaldehyde. The latter is thought to undergo oxidization to performic acid, which acts as the inhibitor in the system. Yields of formaldehyde, of nitrogen in excess of that formed in the primary process, and of nitrous oxide are linearly related regardless of the conversion up to about 4%. Methanol is a major product of the oxidation and, if account is taken of its yield, a carbon balance of the order of 90% is obtained.

Kinetics and mechanisms of the thermal decomposition of propane I. The Uninhibited of reaction

1962 ◽  
Vol 270 (1341) ◽  
pp. 242-253 ◽  
Keyword(s):  
Radical Mechanism ◽  
Methyl Radicals ◽  
Methyl Radical ◽  
Third Body ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Free Radical Mechanism ◽  
Pressure Region ◽  
Initiation Reaction

The uninhibited pyrolysis of propane was investigated from 530 to 670 °C and at pressures up to 600 mm. In an unpacked vessel the reaction was of the first order at lower temperatures and higher pressures. A transition to 3/2 order at higher temperatures and lower pressures was observed. The rates were somewhat reduced in a packed vessel, and an apparent order of 1.25 was obtained. The activation energy of the reaction in its first-order region was 67.1 kcal and that of the f-order reaction was 54.5 kcal. Added carbon dioxide had no effect on the rates either in the first-order or 3/2-order region. On the basis of this evidence, and of theoretical arguments, it is concluded that the reaction is largely homogeneous and occurs by a free-radical mechanism. The initiation reaction is considered to be the dissociation of propane into a methyl radical and an ethyl radical, this reaction being in its second-order low-pressure region under the conditions of the experiments. The termination reaction when the overall order is unity is concluded to be the recombination of a methyl and a propyl radical in the presence of a third body. In the 3/2-order region the termination reaction is believed to be the recombination of two methyl radicals, also in the third-order region. These mechanisms are shown to give a satisfactory interpretation of the overall behaviour.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3194
Author(s):  
Adrian Petris ◽  
Petronela Gheorghe ◽  
Tudor Braniste ◽  
Ion Tiginyanu
Keyword(s):  
Harmonic Generation ◽  
Nonlinear Optical ◽  
Laser Pulses ◽  
Third Harmonic Generation ◽  
High Repetition Rate ◽  
Third Order ◽  
Third Harmonic ◽  
The Third ◽  
High Repetition ◽  
Gan Crystal

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary
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