Concerning the Problem of the Isokinetic Relationship. IV. The Evaluation of the Isosubstituent Hammett Parameter by Means of Isokinetic and Isoequilibrium Temperatures

1986 ◽  
Vol 39 (2) ◽  
pp. 199 ◽  
Author(s):  
W Linert
Keyword(s):  
Temperature Dependence ◽  
Activation Parameters ◽  
Common Point ◽  
Isokinetic Temperature ◽  
Benzoic Acids ◽  
Reaction Series ◽  
Isokinetic Relationship ◽  
The Common ◽  
Point Of Intersection ◽  
Hammett Parameter

The interrelation between the isosubstituent and the isokinetic relationship is developed and tested for several Hammett reaction series. Two methods of approach to relate the temperature dependence of Arrhenius and Hammett plots are given, one utilizing the isoequilibrium temperature of the ionization of benzoic acids and the other the isokinetic temperature of the respective Hammett reaction series. The efficiency of the approaches for the evaluation of the coordinates of the common point of intersection in the Hammett plot, i.e. the characteristics of the isosubstituent relationship, are compared with each other and with experimental results. With the former approach, by using the activation parameters of only one (commonly the unsubstituted ) member of the series, the temperature dependence of a Hammett line can be predicted provided that the isokinetic temperature of the Hammett series does not approach the experimental temperature range. Otherwise the latter approach must be used which, however, needs the temperature dependence of at least two (or better more) members of the reaction series.

Concerning the problem of the isokinetic relationship. I. A statistical mechanical model

1983 ◽  
Vol 36 (10) ◽  
pp. 1903 ◽  
Author(s):  
W Linert ◽  
AB Kudrjawtsev ◽  
R Schmid
Keyword(s):  
Frequency Factor ◽  
Isokinetic Temperature ◽  
Reaction Series ◽  
Empirical Coefficient ◽  
Isokinetic Relationship ◽  
Exponential Factor ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
The Common

The equation for the rate constant derived from the statistical theory of kinetics is compared with the common Arrhenius equation. Thereby the pre-exponential factor and the activation energy can be expressed by means of the theoretical quantities, frequency factor (Z0), oscillator number (s), and potential barrier height (E). In these terms the isokinetic relationship can be represented by the equation (c- c) = b(E-E) where c is s- 1 and the bars denote the means in the reaction series under consideration. The empirical coefficient b, in connection with the numerical value of the isokinetic temperature, is proposed to be used as a criterion for the classification of reaction series. The model is exemplified by means of an organic SN2 reaction.

Thermodynamic Analysis of the Hammett Equation, the Temperature Dependence of ρ, and the Isoequilibrium (Isokinetic) Relationship

1971 ◽  
Vol 49 (17) ◽  
pp. 2803-2807 ◽  
Author(s):  
Loren G. Hepler
Keyword(s):  
Differential Equations ◽  
Temperature Dependence ◽  
Thermodynamic Analysis ◽  
Activation Parameters ◽  
Isokinetic Temperature ◽  
Hammett Equation ◽  
Isokinetic Relationship ◽  
Solvent Interactions ◽  
Independent Constant ◽  
The Relationship

Exact thermodynamic analysis of the Hammett equation has led to four differential equations relating δΔH0, δΔS0, δΔCp0, dρ/dT, and d2ρ/dT2. Similar equations can be obtained in terms of activation parameters ΔH≠, etc. For temperature independent δΔH0 and δΔS0 and therefore δΔCp0 = 0, two of these differential equations lead to ρ = ρ∞ [1–(β1/T)] and the familiar isoequilibrium (isokinetic) equation δΔH0 = β1δΔS0. The "isoequilibrium (isokinetic) temperature" represented here by β1 is a temperature independent constant of integration. For constant non-zero δΔCp0 we similarly obtain more complicated expressions for ρ and the "isoequilibrium (isokinetic) temperature." These findings are considered in relation to a model in which environmental contributions (due to solute–solvent interactions) to δΔH0 and δΔS0 are related by a parameter βc. The relationship between β1, and βc is established, and it is shown that in general β1 ≠ βc.

A result of resonant energy exchange between reactants and their chemical surrounding: The isokinetic relationship

1990 ◽  
Vol 55 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Wolfgang Linert
Keyword(s):  
Energy Transfer ◽  
Energy Exchange ◽  
Equilibrium Constants ◽  
Heat Bath ◽  
Common Point ◽  
Isokinetic Temperature ◽  
Isokinetic Relationship ◽  
Resonant Energy ◽  
Point Of Intersection

Many homologous series of reactions exhibit a common point of intersection in the ln k versus 1/T plots. This can be taken as a profound basis for the appearance of the isokinetic relationship (IKR) defining a temperature where rate (or equilibrium) constants of the series show a minimum in selectivity. The theoretically derived relationship describing the IKR and yielding a correlation between the isokinetic temperature and the frequencies available in an ideal heat bath is examined for real systems. It is shown that the role of the solvent in chemical reactions that exhibit isokinetic relationship is not only due to chemical interactions but also to energy transfer between reactants and solvents and vice versa.

Concerning the Problem of the Isokinetic Relationship. III. The Temperature-Dependance of the hammett Equation

1985 ◽  
Vol 38 (5) ◽  
pp. 677 ◽  
Author(s):  
W Linert ◽  
R Schmid ◽  
AB Kudrjawtsev
Keyword(s):  
Benzoic Acid ◽  
Hammett Equation ◽  
Reaction Series ◽  
Temperature Dependent ◽  
Isokinetic Relationship ◽  
A Value ◽  
The Common ◽  
Point Of Intersection ◽  
Temperature Dependance ◽  
The Relationship

It is shown that the temperature-dependence of the Hammett equation is, in contrast to tradition, both physically and experimentally better described by means of temperature-dependent σ and temperature- independent ρ (termed ρo). The relationship between ρo and the customary (temperature dependent) ρ is ρT = ρo(1/T-1/Tbiso)/(1/T-1/Tbiso) where Tbiso , is the isoequilibrium temperature of the benzoic acid ionization, for which the present analysis suggests a value of -255 K, and T is 298 K. In these terms, the temperature variation of the Hammett equation can be evaluated by supplying merely E(u)a (the activation energy for the reaction of the unsubstituted reactant) and ρo, in that the σ value for the isokinetic substituent , i.e., the abscissa of the common point of intersection in the Hammett plot, is σiso = (1/T-1/Tbiso)E(u)a/(2.303Rρo) = E(u)a/(2630po) Further, ρo I related to energies ρo = E(u)a/(ΔH°u-ΔH°s(iso))where ΔH°u and ΔH°s(iso) are the ionization enthalpies of the parent benzoic acid and that bearing the isokinetic substituent , respectively. Analogous equations apply to thermodynamic reaction series when substituting E(u)a for ΔH°u(series). Along these lines the interpretation of the customary Hammett plot is advanced.

A Program for Linear Regression with a Common Point of Intersection:  The Isokinetic Relationship

2001 ◽  
Vol 41 (5) ◽  
pp. 1141-1144 ◽  
Author(s):  
Carole Ouvrard ◽  
Michel Berthelot ◽  
Thierry Lamer ◽  
Otto Exner
Keyword(s):  
Linear Regression ◽  
Common Point ◽  
Isokinetic Relationship ◽  
Point Of Intersection

Evidence in favour of Exner isokinetic method to determine activation parameters

1985 ◽  
Vol 50 (7) ◽  
pp. 1565-1572
Author(s):  
Pascual Segura
Keyword(s):  
Aqueous Solution ◽  
Ab Initio ◽  
Activation Parameters ◽  
Statistical Evidence ◽  
Reaction Series ◽  
Isokinetic Relationship ◽  
Decarboxylation Reaction

Exner method to ascertain the isokinetic relationship (IKR) and obtain isokinetic activation parameters in a reaction series, although well known, is relatively little applied; A great many chemists do not appear to be convinced of the superiority of isokinetic activation parameters over conventional ones, and the IKR itself is still a controversial matter. From our kinetic results on the decarboxylation of a series of 4-substituted-2,6-dinitrobenzoate ions in aqueous solution, activation parameters were calculated, both by Exner method and by a conventional one. The obtained isokinetic activation enthalpies correlate much better (r = 0.998, 5 points) than the conventional ones (r = 0.97, 5 points), with the energies (calculated at the STO-3G ab initio level) for the formation of substituted aryl anions, the latter being a process expected to be energetically related to the decarboxylation reaction. This is the first example of non-statistical evidence in favour of Exner method to determine activation parameters, a method that we strongly advocate.

On estimating the common point of intersection of curves

2001 ◽  
Vol 135 (2) ◽  
pp. 350-360 ◽  
Author(s):  
Shaul P Ladany ◽  
Israel David
Keyword(s):  
Common Point ◽  
The Common ◽  
Point Of Intersection

A Study on the common point between ‘The art of war’ and ‘laozi’ and modern management

2017 ◽  
Vol 80 ◽  
pp. 229-261
Author(s):  
Myung‑yong Jun ◽  
Yong‑ho Song
Keyword(s):  
Common Point ◽  
Modern Management ◽  
Art Of War ◽  
The Common ◽  
The Art Of War

scholarly journals Zebrafish Models to Study New Pathways in Tauopathies

2021 ◽  
Vol 22 (9) ◽  
pp. 4626
Author(s):  
Clément Barbereau ◽  
Nicolas Cubedo ◽  
Tangui Maurice ◽  
Mireille Rossel
Keyword(s):  
Cognitive Deficits ◽  
Tau Protein ◽  
Common Point ◽  
Transgenic Models ◽  
Synaptic Loss ◽  
Wide Range ◽  
Transgenic Lines ◽  
Functional Consequences ◽  
The Common

Tauopathies represent a vast family of neurodegenerative diseases, the most well-known of which is Alzheimer’s disease. The symptoms observed in patients include cognitive deficits and locomotor problems and can lead ultimately to dementia. The common point found in all these pathologies is the accumulation in neural and/or glial cells of abnormal forms of Tau protein, leading to its aggregation and neurofibrillary tangles. Zebrafish transgenic models have been generated with different overexpression strategies of human Tau protein. These transgenic lines have made it possible to highlight Tau interacting factors or factors which may limit the neurotoxicity induced by mutations and hyperphosphorylation of the Tau protein in neurons. Several studies have tested neuroprotective pharmacological approaches. On few-days-old larvae, modulation of various signaling or degradation pathways reversed the deleterious effects of Tau mutations, mainly hTauP301L and hTauA152T. Live imaging and live tracking techniques as well as behavioral follow-up enable the analysis of the wide range of Tau-related phenotypes from synaptic loss to cognitive functional consequences.

scholarly journals Mechanistic aspects of oxidation on L-tyrosine by diperiodatocuprate(III) complex in alkali media: a kinetic model

2009 ◽  
Vol 7 (4) ◽  
pp. 929-937 ◽  
Author(s):  
Nagaraj Shetti ◽  
Rajesh Hegde ◽  
Sharanappa. Nandibewoor
Keyword(s):  
Alkaline Medium ◽  
Activation Parameters ◽  
Spectral Studies ◽  
Slow Step ◽  
Isokinetic Temperature ◽  
Thermodynamic Quantities ◽  
Radical Intermediate ◽  
Different Temperatures ◽  
Reactive Oxidant ◽  
Reaction Constants

AbstractOxidation of an amino acid, L-tyrosine (L-Tyr) by diperiodatocuprate(III) (DPC) in alkaline medium at a constant ionic strength of 0.1 mol dm−3 was studied spectrophotometrically at different temperatures (288.1–313.1 K). The reaction between DPC and L-Tyr in alkaline medium exhibits 1:4 stoichiometry (L-Tyr:DPC). Intervention of free radicals was observed in the reaction. Based on the observed orders and experimental evidence, a mechanism involving monoperiodatocuprate(III) (MPC) as the reactive oxidant species has been proposed. A suitable mechanism is proposed through the formation of a complex and free radical intermediate. The products were identified by spot test and characterized by spectral studies. The reaction constants involved in the different steps of the mechanism were calculated. The activation parameters with respect to slow step of the mechanism were computed and are discussed. The thermodynamic quantities were determined for different equilibrium steps. Isokinetic temperature was also calculated and found to be 252.3 K.

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