Kinetic chains average lifetime

Equation (4) clearly shows that the number average degree of polymerisation Xn is inversely proportional to the reaction rate Rp, meaning that, in radical chain polymerisation high reaction rates are linked to low molecular masses and vice versa. One way to avoid this dilemma is to use emulsion polymerisation where the lifetime of a radical (i.e., the "kinetic" chain length) is independent of... 

The average lifetime t of the kinetic chain is given by the ratio of the steady-state radical concentration to the steady-state rate of radical disappearance ... 

More detailed information on the activation pathway, which distinguishes the polymeric photoinitiators from the corresponding low-molecular-weight structural models, has been obtained by photophysical measurements [22,27,28] in terms of quantum yield and average lifetime of the triplet excited state of benzophenone moieties in the above systems. However, in order to get a better comprehension of this point, it is necessary to introduce some basic concepts about the kinetic treatment of a photoinitiated chain polymerization. 

The kinetic chain length v is a measure of the average number of monomer units reacting with an active center during its lifetime and is related to x through the mechanism of the termination. Thus, combination means x = 2v, but =v if disproportionation is the only termination reaction. Under steady-state conditions... 

Kinetics at low yields gives only the ratio K( pp)/kl, not the individual rate constants. Thus, one of the two rate constants must be determined by another method. Such a method uses the average lifetime of a chain t, which is defined by... 

The average molecular weight in radical polymerization can be found from the kinetic model, Eq. (5.3.1), as follows. The kinetic chain length, v, is defined as the average number of monomer molecules reacting with a polymer chain radical dining the latter s entire lifetime. This will be the ratio between the rate of... 

Since hydrolysis is a chain scission process, it always induces embrittlement. In initially ductile linear polymers, such as PET or PAll, toughness falls off by two or three decades when the weight average molar mass reaches a critical value Mp of the order of 10-20 mol.kg corresponding to a small multiple of the entanglement molar mass (Fayolle et al., 2008). In the frame of second-order kinetics (rate constant h)> it is possible to determine a lifetime value corresponding to the time to embrittlement ... 

The counteranions derived from MX initiators, in contrast, do not interact as strongly with carbocations as the oxo-acid counteranions, as previously discussed. Therefore, even when two propagating species are formed by these initiators, the interconversion between them is as fast as to allow a propagating chain to take both dissociated and non-dissociated forms during its kinetic lifetime. Under these conditions, product polymers show a rather broad, unimodal MWD whose peak lies at an average of the molecular weights corresponding to the two dissociation states (cf. Fig. 2). 

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