Chain Reactions

Radical bulk polymerization of styrene in the presence of rubber particles from recycled tires: a kinetic study using DSC

“…By considering the aforementioned limitations and therefore, assuming that the effects of GTR inhibition are already implicit in the values of k i , k p and k t , the overall effective kinetic constants were predicted. Under the hypothesis of LCH (i.e., Long-Chain Hypothesis) and QSSA (i.e., Quasi Steady-State Assumption) for the polymer radicals [29], the differential equation above can then be written as Eq. (3) and then integrated over the initial instances of polymerization (i.e., for low monomer conversion values), by considering that the variation of the initiator concentration is negligible, to yield the expression in Eq.…”

Silver Vapor Supersonic Jets: Expansion Dynamics, Cluster Formation, and Film Deposition

“…In the simulations, we considered the formation of Ag 2 dimers in the Ag-He mixture flow in triple collisions (forward process) and their disintegration through collisions with Ag and He atoms (reverse process) according to the following reactions [ 36 , 51 ]: Ag + Ag + Ag → Ag 2 + Ag, Ag + Ag + He → Ag 2 + He, Ag 2 + Ag → Ag + Ag + Ag, Ag 2 + He → Ag + Ag + He, with the temperature-dependent rate coefficients of forward (Equations (3) and (4)) and reverse (Equations (5) and (6)) reactions being K 12,Ag , K 12,He , K 21,Ag , and K 21,He , respectively.…”

“…The parameters of Equation (7) can be evaluated using the equilibrium size distribution of silver clusters and dimer dissociation energy with A = 10.86 × 10 33 m −3 K, B = −1, and = 1.67 eV [ 52 , 54 ]. The rate coefficients of forward processes (3) and (4) assuming the Arrhenius expression without an activation barrier can be expressed as follows [ 51 ]: …”

“…Reactions (3) and (4) can be considered as a two-step process [ 51 ]: (i) the formation of an excited quasi-dimer in a paired Ag–Ag collision and (ii) the stabilization of the excited cluster by a collision with a third atom (helium or silver). Assuming that the lifetime t L of the quasi-dimer depends on the relative collision velocity as [ 51 , 55 ] (here, is the collision cross-section, is the relative velocity of colliding Ag atoms, and H is a constant) and that any collision with a third atom leads to dimer stabilization, the rate constant of the direct reactions can be presented in the following form [ 55 ]: where are the reference viscosity index, diameter, and relative velocity, respectively, of the VHS model for a dimer–atom collision. is the reduced mass of the atom–dimer system ( is the mass of a Ag atom, and is the mass of the third atom (Ag or He)), and .…”

“…The parameter H was related to the lifetime of a quasi-dimer and could vary in fairly large limits. The minimal value of corresponded to a lifetime equal to the mean time between direct collisions of Ag monomers as hard spheres [ 51 ]. In this case, Equation (9) was reduced to with a coefficient of the order of 1 [ 56 , 57 ].…”