Chain propagation activation volumes

The over-all rates for free radical polymerizations increase with increasing pressure. This means simply that the pressure-induced retardation of the initiator decomposition rate is more than offset by the increase in the rate of chain propagation and the decrease in the rate of chain termination. This is formally stated in terms of activation volumes in Equation 4 (15)... 

Oxidative Pyrolysis. Autoxidation of polypropylene below its melting point has been investigated quite thoroughly with our own laboratory among the most active ones (21, 22, 23,24). This is not the proper place to discuss that topic a chapter written by one of us dealing with the subject can be found in this volume. It suffices to say that the main chain propagating species is the peroxy radical and the chain branching species is the hydroperoxide. 

A theoretical derivation [72] was based on the idea, that linear chain termination is the act of self-burial of macroradical s active center and manifests itself as the act of chain propagation, leading into a trap. Taking into account the fractal properties of pol5mier chain and assuming that a set of traps in its conformational volume is a fractal as well, we obtain the expression similar to Eq. (54) ... 

As anticipated for a chemically controlled reaction, CO2 has only a minor influence on the rate coefficient for chain-transfer to DDM and to the MMA tri-mer in MMA and styrene homo- and copolymerizations. Going from bulk polymerization to solution polymerization with 40 wt%> CO2 present enhances Cx by about 10%, but leaves the associated activation volume, AV (Cx), unchanged [48]. As pointed out in the previous section, the observed lowering of kp,app upon increasing CO2 content is no true kinetic effect, and the propagation rate coefficient kp,kin most likely remains unaffected by the presence of CO2. Thus, ktr for DDM and for the MMA trimer should not be significantly varied by the presence of CO2. 

Thus, the probability of monomolecular chain termination first of all depends on the concentration of traps which, in turn is determined by the conformation of a propagating polymeric chain. From this point of view any additive that does not contain a functional group able to induce polymerization, displacing the monomer from the conformation volume of propagating polymeric chain, increases the traps concentration. In other words, the probability that the active center of a radical will be blocked from the functional groups of a monomer is increased. The stronger this effect, the longer the chain, namely its conformation volume. 

For this example the procedures for the hybrid model design and the sub-model design, as described above, are followed. As a consequence of the requirements, for the hybrid model, all known balances involved are incorporated density balance, energy balance and component balances for monomer, hydrogen, non-activated catalyst, and activated catalyst. The volume of the reactor is constant. The reaction rates for the chain propagation, chain termination, catalyst activation and catalyst deactivation, determine the shifts between the component balances. For these rates, fuzzy relationships are birilt. 

This equation was used to compute the quantity AVf — AV ), the standard state diSerence in activation volume for transfer and propagation, from chain-transfer data in homogeneous bulk polymeriaation at two widely separated pressures (75). Note that the standard states of the pure components are assumed to correspond to the pressure of... 

As stated in the introduction to this section the subcritical crack growth in a polymer is due to the thermomechanical activation of different molecular deformation processes such as chain slip and orientation or void opening. The energy dissipated depends on the frequency, nature, kinetics, and interaction of these processes. But there are many and notable attempts to treat the subcritical crack propagation as one thermally activated multi-step process characterized by one enthalpy or energy of activation and one activation volume. Several of these kinetic theories of fracture have been treated in Chapters 3 and 8. 

The overall activation volume is composed of the activation volumes of the different polymerization steps, initiation, or initiator decomposition, chain propagation and chain termination ... 

In the chain propagation reaction, the decrease in the distance between the radical and the monomer molecule is greater than the increase in length of the double bond of the monomer. Hence the activation volumes An listed in Section D are always negative. The data for An are measured at high pressures by the method of the rotating sector together with An, the activation volume of ehain termination. 

The difference in the activation volumes of the various component reactions results in a different influenee of the pressure on the rate eonstants and leads to modified polymers. Beeause of its larger negative aetivation volume the chain propagation reaction is more favored by high pressures than the termination. The ehain length and consequently the tensile strength as well as the tensile... 

Chain-transfer reactions would be expected to increase in rate with increasing pressure since transfer is a bimolecular reaction with a negative volume of activation. The variation of chain-transfer constants with pressure, however, differ depending on the relative effects of pressure on the propagation and transfer rate constants. For the case where only transfer to chain-transfer agent S is important, Cs varies with pressure according to... 

The conception of a chain reaction in which the breaking off of the chains on the walls depends on the dimensions of the vessel or on the location of the point of ignition is untenable, since the chemical reaction in the propagation of a flame takes place in a narrow zone, the thickness of which is thousands of times less than the dimensions of the vessel and the reaction time of an individual volume element and even of the entire explosive mixture in the vessel is many times less than the time of diffusion of active centers to the walls of the vessel. 

Propagation In olefin derivatives, etc., the intermolecular distances vanish and the volume of activation is negative. Since rings usually have greater molar volumes than the corresponding linear chain compounds, ringopening polymerizations are also favored by increase in pressure. 

To develop their model, Wen and McCormick adopted a number of simplifying assumptions. These are (1) initiation produces two equally reactive radicals, (2) chain transfer reactions are neglected, (3) the rate constants for radicals of different sizes are assumed identical, (4) the propagation rate constant kp, termination rate constant kp and the rate constant for radical trapping kb are all simple functions of free volume as shown below, and (5) there is no excess free volume. The material balance equations for the initiator, the functional group, the active radical, and the trapped radical concentrations... 

Where kp is the rate constant of propagation, C is the active site concentration and M is the monomer concentration. Calculation of kp requires the knowledge of Rn, [C ], and [M]. The uncertainty in the determinations of [C ] by various techniques has been discussed by Tait in this volume. Depending upon the catalyst system, the active sites may all be present initially, or more may be produced as the catalyst agglomerates or crystals fracture during polymerization. If there is catalyst deactivation by either chain termination, chain transfer or poison, [C ] may decrease with time. At the initial stage of reaction [M] is the concentration of monomer dissoved in the diluent. If, during reaction, the catalyst is completely encapsulated by the polymer... 

---