Cross-Linking of Polymers: Kinetics and Transport Phenomena

Abstract

The cross-linking process of a complex system was studied at elevated temperature. Partially hydrogenated poly(acrylonitrile-co-1,3-butadiene)/dicumyl peroxide compound was selected as a representative complex polymer/cross-linking agent system. On the basis of the mechanisms of cross-linking reactions, an expression relating reaction rates and population balance equations with rheologically determined concentration of cross-links was applied. Consequently the Eyring equation reflecting the effect of the self-diffusion on reaction rate constants was utilized and was further integrated into the classical Arrhenius equation for reaction rate constants. Diffusion coefficients acknowledging the mutual diffusion were estimated according to the free-volume theory, whereas thermodynamic properties governing the heat transfer, i.e. density, heat capacity, and thermal conductivity, were determined from independent measurements. Plateau storage modulus variation was monitored within the linear viscoelastic regime by dynamic mechanical analysis. Compounds with different initial peroxide concentrations were chosen for the study of the correspondence between model predictions and experimental observations, which proved to be very good.

Kinetic modeling of the peroxide cross-linking of polymer/monomer blends: From a theoretical model framework to its application for a complex polymer/monomer dispersion system

“…However, in contrast to these lumped parameter models, which allow for the initial concentration of peroxide and polymer as the input, the developed model predicts the formation of various species from the initial concentrations of all different polymer, peroxide, and monomer reaction sites and the blend morphology. In addition, the developed population balance model is consistent with experimental observations that several minority species are formed or consumed during the course of reactions even in a simple case of, for example, HPAB cross-linking in the absence of any monomer moieties [22,23].…”

“…1 and 2, as well as in Tables 3 and 4 for concentrations of C S=E,C,P , a general population balance equation is for HPAB/DCP/ZDMA compounds (in the case of HPAB/DCP/TMPTMA and HPAB/DCP/HVA-2 compounds the different specific monomer/polymer chemistry in Table 4 was acknowledged accordingly) as follows [22,23]:…”

“…Using these considerations, a total of 10 rate constants (with k d,i,j,k,l,m,n and k ib,i,j,k , which could not have been obtained from literature [27][28][29][30][31][32]) for all potential substituents had to be determined, that is k iha,i,j,k,l,m,n , k iar,i,j,k,l,m,n,o , k it1,i,j,k,l,m,n , k it2,i,j,k,l,m,n , k ha,i,j,k,l,m,n , k ar,i,j,k,l,m,n,o , k t1,i,j,k,l,m,n , k t2,i,j,k,l,m,n , k b,i,j,k , and k e,i,j,k,l,m,n . The rate constants and the associated activation energies and pre-exponential factors were determined utilizing molecular modeling [22,23,33]. This was achieved by the semi-empirical Parameterized Model number 3 method calculations, using unrestricted Hartree-Fock spin pairing and self-consistent field controls of 0.001 convergence limit and 1000 iterations limit.…”

Investigation on the synthesis of self-crosslinking polyamideamine–epichlorohydrin as in-depth profile control agent and its properties

“…Owing to the chemical structure of PAE, the polymer can be self-crosslinked and can be applied as one-component PCA. [5][6][7] Experimental Materials Adipic acid (ADA), diethylenetriamine (DETA), epichlorohydrin, hydrochloric acid and sodium hydroxide were applied by Sichuan Youte Chemical Co. (Suining, China) and were all of industrial grade. All the materials were applied as original without any other processing.…”

Modeling of chemical kinetics of elastomer/hydroxyl‐ and carboxyl‐functionalized multiwalled carbon nanotubes nanocomposites' cross‐linking

“…The kinetics of the cross‐linking of several elastomers was studied. The kinetic model simulation has to be able to either describe the complete cross‐linking process phenomenologically [4] or mechanistically [5–7] including homolytic cleavage of the peroxide, beta cleavage of the oxy radical, hydrogen abstraction, addition reactions, radical coupling (cross‐link formation), polymer scission, and radical transfer for a wide range of compositions and an assortment of elastomers, using a single set of rate constants.…”