Mathematical simulation of the kinetics of radiation induced hydroxyalkylation of aliphatic saturated alcohols

Competition Kinetics of the Nonbranched‐Chain Addition of Free Radicals to Olefins, Formaldehyde, and Oxygen

“…Earlier mathematical simulation [8] demonstrated that replacing the adduct radical R 3 with the radical R 2 [5] in the reaction between identical radicals and in the reaction involving R 1 gives rise to a peak in the curve of the 1 : 1 adduct formation rate as a function of the concentration of the unsaturated component. Reaction (1b), which is in competition with reaction (1a), is responsible for the maximum in the curve described by (2), and reaction (4), which is in competition with reaction (3), is responsible for the maximum in the curve defined by (1).…”

“…For the same purpose, the rate constant of reaction (2) in the kinetic equation can be replaced with its analytical expression k 2 = αl m 2k 5 V 1 /x 2 m , which is obtained by solving the quadratic equation following from the reaction rate extremum condition ∂V 3,4 (1 : 1 Adduct)/∂x = 0, where V 3, 4 (1 : 1 Adduct) = V 3 + V 4 . After these transformations, the overall formation rate equation for the 1 : 1 adducts R 3 A and R 3 B (which may be identical, as in the case of R 3 H [5,8,9,12,13,[18][19][20][21]), appears as…”

“…We will consider kinetic variants for the case of comparable component concentrations with an excess of the saturated component [10,11] and the case of an overwhelming excess of the saturated component over the unsaturated component [8,9,12].…”

“…It covers free radical additions to alkenes [10,11], their derivatives [8,9], formaldehyde (first compound in the aldehyde homological series) [8,9,12], and oxygen [13,14] (which can add an unsaturated radical as well) yielding various 1 : 1 molecular adducts, whose formation rates as a function of the unsaturated compound concentration pass through a maximum (free radical chain additions to the C=N bond have not been studied adequately). In the kinetic description of these nontelomerization chain processes, the reaction between the 1:1 adduct radical and the unsaturated molecule, which is in competition with chain propagation through a reactive free radical ( • PCl 2 , C 2 H 5…”

“…This publication presents a comprehensive review of the nonbranched-chain kinetic models developed for particular types of additions of saturated free radicals to double bonds [8][9][10][11][12][13][14]. It covers free radical additions to alkenes [10,11], their derivatives [8,9], formaldehyde (first compound in the aldehyde homological series) [8,9,12], and oxygen [13,14] (which can add an unsaturated radical as well) yielding various 1 : 1 molecular adducts, whose formation rates as a function of the unsaturated compound concentration pass through a maximum (free radical chain additions to the C=N bond have not been studied adequately).…”