The mechanism of the Cannizzaro reaction of Formaldehyde

1954 ◽  
Vol 7 (4) ◽  
pp. 335 ◽  
Author(s):  
RJL Martin
Keyword(s):  
Fourth Order ◽  
Kinetic Data ◽  
Order Reaction ◽  
Rate Equations ◽  
Third Order ◽  
The Third ◽  
Hydride Ion ◽  
Cannizzaro Reaction ◽  
Wide Range ◽  
Mechanism Of The Reaction

For a wide range of concentrations of formaldehyde and alkali, the Cannizzaro reaction of formaldehyde can be described as the sum of a third and a fourth order reaction. However, the concentrations which are used for the rate equations must be corrected for the amount of methylene glycol anion present. The dissociation constant of methylene glycol as determined from the kinetic data is the same magnitude as that derived electrometrically. The mechanism of the reaction is interpreted as a reaction between formaldehyde and the hydride ion donors CH2(O-)(OH) and CH2(O-)(O-) It is shown why the third order reaction proposed by previous workers is not always applicable.

scholarly journals Bounds on the conductivity of a random array of cylinders

1988 ◽  
Vol 417 (1852) ◽  
pp. 59-80 ◽  
Keyword(s):  
Fourth Order ◽  
Volume Fraction ◽  
Effective Conductivity ◽  
Basis Set ◽  
Circular Cylinders ◽  
Third Order ◽  
Entire Volume ◽  
The Third ◽  
Wide Range ◽  
Order Bounds

We consider the problem of determining rigorous third-order and fourth-order bounds on the effective conductivity σ e of a composite material composed of aligned, infinitely long, equisized, rigid, circular cylinders of conductivity σ 2 randomly distributed throughout a matrix of conductivity σ 1 . Both bounds involve the microstructural parameter ξ 2 which is an integral that depends upon S 3 , the three-point probability function of the composite (G. W. Milton, J. Mech. Phys. Solids 30, 177-191 (1982)). The key multidimensional integral ξ 2 is greatly simplified by expanding the orientation-dependent terms of its integrand in Chebyshev polynomials and using the orthogonality properties of this basis set. The resulting simplified expression is computed for an equilibrium distribution of rigid cylinders at selected ϕ 2 (cylinder volume fraction) values in the range 0 ≼ ϕ 2 ≼ 0.65. The physical significance of the parameter ξ 2 for general microstructures is briefly discussed. For a wide range of ϕ 2 and α = σ 2 /σ 1 , the third-order bounds significantly improve upon second-order bounds which only incorporate volume fraction information; the fourth-order bounds, in turn, are always more restrictive than the third-order bounds. The fourth-order bounds on σ e are found to be sharp enough to yield good estimates of σ e for a wide range of ϕ 2 , even when the phase conductivities differ by as much as two orders of magnitude. When the cylinders are perfectly conducting ( α = ∞), moreover, the fourth-order lower bound on σ e provides an excellent estimate of this quantity for the entire volume-fraction range studied here, i. e. up to a volume fraction of 65%.

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.

Synthesis and third-order nonlinear optical properties of novel ethynyl-linked heteropentamer composed of four porphyrins and one pyrene

2009 ◽  
Vol 13 (02) ◽  
pp. 275-282 ◽  
Author(s):  
Ning Sheng ◽  
Jing Sun ◽  
Yongzhong Bian ◽  
Jianzhuang Jiang ◽  
Dong Xu
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Spectroscopic Methods ◽  
Third Order ◽  
Zinc Compounds ◽  
Nlo Properties ◽  
Metal Free ◽  
The Third ◽  
Wide Range

Novel heteropentameric porphyrins-pyrene arrays, in which four meso-tetraphenyl porphyrins are linked to the center unit of pyrene by four acetylenyl bonds, were designed and synthesized. The newly synthesized heteropentameric compounds have been characterized by a wide range of spectroscopic methods. The third-order nonlinear optical (NLO) properties of both the metal-free and zinc compounds of the three-dimensional arrays were investigated by Z-scan experiments, showing enhanced NLO properties compared with that of the porphyrin and pyrene monomers.

scholarly journals The alcoholysis of 1,2,2-trimethylpropyl-methylfluorophosphonate

2000 ◽  
Vol 65 (12) ◽  
pp. 857-866
Author(s):  
Mladjen Micevic ◽  
Slobodan Petrovic
Keyword(s):  
Kinetic Data ◽  
Reaction Rate ◽  
Frequency Factor ◽  
Reaction Rate Constant ◽  
Order Reaction ◽  
Activation Entropy ◽  
Second Order Reaction ◽  
Third Order ◽  
First Order ◽  
Kinetics Of

The alcoholysis of 1,2,2-trimethylpropyl-methylfluorophosphonate (soman) was examined with a series of alkoxides and in corresponding alcohols: methanol, ethanol, 1-propanol, 2-propanol, 2-methoxyethanol and 2-ethoxyethanol. Soman reacts with the used alkoxides in a second order reaction, first order in each reactant. The kinetics of the reaction between 1,2,2-trimethylpropyl-methylfluorophosphonate and ethanol in the presence of diethylenetriamine was also examined. A third order reaction rate constant was calculated, first order in each reactant. The activation energy, frequency factor and activation entropy were determined on the basis of the kinetic data.

scholarly journals Asymptotic formulae for linear equations

1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Don B. Hinton
Keyword(s):  
Asymptotic Behaviour ◽  
Fourth Order ◽  
Linear Equations ◽  
Order Equation ◽  
Third Order ◽  
Fourth Order Equation ◽  
The Third ◽  
Asymptotic Formulae ◽  
Image Position

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation

scholarly journals Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Fundamental Theorem ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third ◽  
Properties Of Materials ◽  
Derivatives Of

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

Structure functions of turbulence in the atmospheric boundary layer over the ocean

1970 ◽  
Vol 44 (1) ◽  
pp. 145-159 ◽  
Author(s):  
C. W. Van Atta ◽  
W. Y. Chen
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Fourth Order ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Order Structure ◽  
Third Order ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Order Quantities

Structure functions of turbulent velocity fluctuations up to fourth order have been measured at several heights in the atmospheric boundary layer over the open ocean, and the results are compared with theoretical predictions for separations in the inertial subrange. The behaviour of second- and third-order quantities shows substantial agreement with the predictions of Kolmogorov's original theory over a wide range of separations, but the results of a recent modification of the theory, attempting to account for intermittency in the local dissipation rate, are also consistent with the data over somewhat shorter separation intervals. The behaviour of the measured fourth-order structure function disagrees with that predicted from Kolmogorov's original work, but good agreement is found with the results of the modified theory.

scholarly journals Comparison of 6 Diode and 6 Transistor Mixers Based on Analysis and Measurement

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
J. Ladvánszky ◽  
K. M. Osbáth
Keyword(s):  
Field Effect Transistors ◽  
Input Power ◽  
Bipolar Transistors ◽  
Large Signal ◽  
Design Environment ◽  
Third Order ◽  
The Third ◽  
Wide Range ◽  
Measurement Results ◽  
Versus Input

Our goal is to overview semiconductor mixers designed for good large signal performance. Twelve different mixers were compared utilizing pn diodes, bipolar transistors, and/or junction field effect transistors. The main aspect of comparison is the third-order intercept point (IP3), and both circuit analysis and measurement results have been considered. IP3 has been analyzed by the program AWR (NI AWR Design Environment) and measured by two-tone test (Keysight Technologies). We provide three ways of improvement of large signal performance: application of a diplexer at the RF port, reduction of DC currents, and exploiting a region of RF input power with infinite IP3. In addition to that, our contributions are several modifications of existing mixers and a new mixer circuit (as illustrated in the figures). It is widely believed that the slope of the third-order intermodulation product versus input power is always greater than that of the first-order product. However, measurement and analysis revealed (as illustrated in the figures) that the two lines may be parallel over a broad range of input power, thus resulting in infinite IP3. Mixer knowledge may be useful for a wide range of readers because almost every radio contains at least one mixer.

New bounds on effective elastic moduli of two-component materials

1982 ◽  
Vol 380 (1779) ◽  
pp. 305-331 ◽  
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Fourth Order ◽  
Geometrical Parameters ◽  
Effective Moduli ◽  
Third Order ◽  
Effective Shear Modulus ◽  
The Third ◽  
Two Component ◽  
Order Bounds

Based on the perturbation solution, we derive new bounds on the effective moduli of a two-component composite material which are exact up to fourth order in δ μ = μ 1 — μ 2 and δ K = K 1 — K 2 , where μ i and K i , i = 1, 2, are the shear and bulk modulus, respectively, of the phases. The bounds on the effective bulk modulus involve three microstructural parameters whereas eight parameters are needed in the bounds on the effective shear modulus. For engineering calculations, we recommend the third-order bounds on the effective shear modulus which require only two geometrical parameters. We show in detail how Hashin-Shtrikman’s bounds can be extended and how Walpole’s bounds can be improved using two inequalities on the two geometrical parameters that appear in the third-order bounds on the effective shear modulus. The third- and fourth-order bounds on the effective moduli are shown to be more restrictive than, or at worst, coincident with, existing bounds due to Hashin and Shtrikman, McCoy, Beran and Molyneux and Walpole.

STANDARD NOMOGRAPHIC FORMS FOR EQUATIONS IN THREE VARIABLES

1935 ◽  
Vol 12 (1) ◽  
pp. 14-40 ◽  
Author(s):  
F. M. Wood
Keyword(s):  
Unit Circle ◽  
Fourth Order ◽  
Third Order ◽  
Rectangular Hyperbola ◽  
Practical Utility ◽  
The Third ◽  
Cubic Curve ◽  
Final Adjustment ◽  
Straight Lines ◽  
Suitable Location

Equations of the third and fourth nomographic order in three variables have been dealt with and classified. Equations of the third order may be reduced to one of two standard forms, α + β + γ = 0 and α + βγ = 0, which give alignment charts composed of three straight lines. Equations of the fourth order may also be reduced to one of two standard forms, resulting in charts composed of (a) two straight lines and a curve, or (b) two scales on a conic, and the third on another curve. Transformations of these four standard forms are given which permit of rapid and easy adjustment of the position and length of the scales for any given example, resulting in a chart of practical utility. Although the underlying theory has been studied by other writers, notably Soreau and Clark, it has possibly never appeared before in such a neat form. On this account, and also because of the standard transformations, it is felt that this article is of particular value.Standard forms have also been developed for third order equations leading to charts composed of two scales on a conic and a third straight scale, and in conclusion a third type of chart, in which all three scales appear on a single cubic curve, has been standardized. The practical value of the last type is questionable, but the conic charts are of use since we may arbitrarily choose the unit circle, or the rectangular hyperbola, for our conic scales. Final adjustment forms which permit suitable location of the scales in particular examples have been obtained in every case.

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