Thermal Oxidation Kinetics of Unvulcanized Unstabilized Polyisoprene

2007 ◽  
Vol 80 (4) ◽  
pp. 621-641 ◽  
Author(s):  
X. Colin ◽  
L. Audouin ◽  
J. Verdu

Abstract The thermal oxidation of an unvulcanized, unstabilized polyisoprene rubber (IR) has been studied in the 40–140 °C temperature range. Ageing was monitored by FTIR determination of double bonds and carbonyl groups, mass uptake measurement, and weight average molar mass determination. A mechanistic scheme based on the standard scheme for radical chain oxidation, but taking into account the diversity of initiation processes and the existence of inter and intramolecular radical additions to double bonds, was built. The kinetic model derived from this scheme is composed of seven differential equations to be solved in discretized thickness layers to take into account the kinetic control by oxygen diffusion. This system was numerically solved using a Matlab program dedicated to stiff systems of differential equations. The elementary rate constants and other kinetic parameters were then determined from experimental data, using an inverse approach. A set of physically reasonable parameter values was obtained, allowing thus to envisage lifetime predictions at low temperature (long term). The results lead to observations difficult to make from classical analytical studies, for instance the predominance of bimolecular hydroperoxide decomposition among other initiation modes or the competition between intermolecular hydrogen abstraction and intramolecular addition of peroxy radicals to double bonds.

SIMULATION ◽  
2021 ◽  
pp. 003754972110216
Author(s):  
Zhang Lei ◽  
Li Jie ◽  
Wang Menglu ◽  
Liu Mengya

Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.


2020 ◽  
Author(s):  
Jüri Majak ◽  
Mart Ratas ◽  
Kristo Karjust ◽  
Boris Shvartsman

The study is focused on the development, adaption and evaluation of the higher order Haar wavelet method (HOHWM) for solving differential equations. Accuracy and computational complexity are two measurable key characteristics of any numerical method. The HOHWM introduced recently by authors as an improvement of the widely used Haar wavelet method (HWM) has shown excellent accuracy and convergence results in the case of all model problems studied. The practical value of the proposed HOHWM approach is that it allows reduction of the computational cost by several magnitudes as compared to HWM, depending on the mesh and the method parameter values used.


2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.


Science ◽  
2018 ◽  
Vol 361 (6406) ◽  
pp. 997-1000 ◽  
Author(s):  
K. O. Johansson ◽  
M. P. Head-Gordon ◽  
P. E. Schrader ◽  
K. R. Wilson ◽  
H. A. Michelsen

Mystery surrounds the transition from gas-phase hydrocarbon precursors to terrestrial soot and interstellar dust, which are carbonaceous particles formed under similar conditions. Although polycyclic aromatic hydrocarbons (PAHs) are known precursors to high-temperature carbonaceous-particle formation, the molecular pathways that initiate particle formation are unknown. We present experimental and theoretical evidence for rapid molecular clustering–reaction pathways involving radicals with extended conjugation. These radicals react with other hydrocarbon species to form covalently bound complexes that promote further growth and clustering by regenerating resonance-stabilized radicals through low-barrier hydrogen-abstraction and hydrogen-ejection reactions. Such radical–chain reaction pathways may lead to covalently bound clusters of PAHs and other hydrocarbons that would otherwise be too small to condense at high temperatures, thus providing the key mechanistic steps for rapid particle formation and surface growth by hydrocarbon chemisorption.


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