Termination Kinetics in Styrene Bulk Polymerization i
4.3 Relevance of Chain-Length Dependent Termination
The relevance of taking chain-length dependent termination into account may be illustrated by a comparison of the SP–PLP–EPR results with data from both chemically initiated polymerization and from SP–PLP experiments carried out in conjunction with the time-resolved measurement of monomer consumption by near-infrared spectroscopy (SP–PLP–NIR). Chain-length averaged kt values, <kt>, from SP–PLP–NIR yield <kt>(Sty)/<kt>(MMA) = 2.0 for 90 °C and ambient pressure for an activation volume of 14.5 cm3∙mol−1 of both monomers.19,144,145 In contrast, the SP–PLP–EPR measurements result in kt(1,1)(Sty)/kt(1,1)(MMA) = 0.7 for the same temperature.This seeming contradiction may be resolved by considering the average chain length associated with the SP–PLP–NIR data for the two monomers, deduced from the same time interval (0.15 s) after laser pulsing.
4.3 Relevance of Chain-Length Dependent Termination
55
0 1 2 3 4
7.5 8.0 8.5 9.0
log(k t(i,i)/ L⋅mol−1 ⋅s−1 ⋅108 )
log i
Sty Bulk MMA
90 °C
Figure 4.8: Decay of the rate coefficient for termination of two radicals at identical chain length i, kt(i,i) in styrene (Sty) and methyl methacrylate (MMA) bulk polymerization at 90 °C according to their composite-model parameters (see text). The figure servers the purpose of illustrating the seeming contradiction found for kt ratios between MMA and Sty deduced from different types of experiments.
Within 0.15 s,19,144 chain growth at 90 °C occurs up to a maximum chain length of imax(Sty) = 1092 and of imax(MMA) = 2120, respectively.
Based on estimated average chain lengths of <i>(Sty) = 500 and
<i>(MMA) = 1000 and on the composite-model parameters for both monomers, with αs = 0.65, ic = 100, αl = 0.16 for MMA,95,117 an adjusted ratio of about kt(500,500)(Sty)/kt(1000,1000)(MMA) = 2.2 is found, which number is in close agreement with the above-cited ratio of
<kt>(Sty)/<kt>(MMA) from SP–PLP–NIR experiments averaged over the same time period, i.e., of 0.15 s. The detailed analysis of termination behavior thus requires propagation rate and chain-length dependence of termination, as given by the composite-model parameters, to be properly taken into account. The higher kp value of MMA results in larger radicals which in conjunction with higher ic and αs, reduce termination rate and contribute to the bulk polymerization rate of MMA being above the one of styrene under stationary conditions at 80 °C.120 This effect on kt(i,i) is illustrated in Figure 4.8 and is also true for chemically initiated
4 Termination Kinetics in Styrene Bulk Polymerization
56
polymerizations in which chain lengths far above ic are expected. It appears to be a matter of principle that a direct comparison of <kt> data for different monomers should as the consequence be restricted to monomers which are not that different in absolute kp values and composite-model parameters.
The all invasive impact of CLDT on <kt> from chemically initiated polymerizations might be further highlighted if the temperature dependence of <kt>, i.e., the Arrhenius activation energy EA(<kt>), is considered. Taylor et al. measured <ktexp
> for chemically initiated bulk polymerization of styrene120 under steady-state conditions, i.e., in the presence of a broad distribution of chain lengths, between 40 °C and 90 °C.
Important kinetic quantities such as <kt> and the number average degree of polymerization might be correlated with the power-law expression for chain-length dependent kt by Mahabadi146 and by Olaj and his group.147,148 On the basis of this early work, eq ( 4.2) has been proposed for deducing chain-length averaged <kt> from chain-length dependent kt(i,i) =kt0
·i–αl with kt0 being defined in eq ( 2.29)89,90,120. The equation in this form rests on the assumption that only the long-chain regime, i.e., i <ic has to be considered in chemically initiated polymerizations which might be true due to the larger i values of the terminating radicals under typical the experimental conditions.120 The simultaneous impact of initiation, propagation and termination on chain length has been taken into account by this expression. The symbol Г in eq ( 4.2) denotes the gamma function.
The efficiency of initiation, f, the rate coefficient for decomposition of the thermal initiator, kd, as well as the initiator concentration, cI, are available from Ref.120 about 18 per cent below <ktexp> in the temperature range 40 to 90 °C with the experiments covering the range up to 15 % monomer conversion. This minor discrepancy may in part be due to the calculation via eq ( 4.2) being entirely based on parameters for the long-chain regime, but neglect small radicals of i < ic, for which kt(i,i) is higher than predicted by the specific power-law expression underlying eq ( 4.2). Thus <ktCLDT> may slightly underestimate <kt>.
4.3 Relevance of Chain-Length Dependent Termination
<ktPREDICI> as the impact of small radial termination is also ignored within the PREDICI® estimate. The PREDICI® procedure is specified in the Appendices section. It should be noted that the activation energy resulting from the estimate via eq ( 4.2), EA(<ktCLDT polymerizations. This relationship reflects that a faster initiator decay at higher temperature leads to higher radical concentrations and thus to shorter chains of terminating radicals being tantamount to a higher value of <kt>. Note that for αl = 0 , EA(<kt>) equals EA(kt(1,1)).120 steady-state polymerization are both reliable. It appears recommendable to use the kt(i,i) data from SP–PLP–EPR whenever CLDT needs to be explicitly taken into account, whereas <ktexp> provides an adequate description of conventional chain-length averaged termination kinetics.
Obviously, kt(i,i) constitutes the suitable set of rate coefficients for representation of termination with reversible deactivation polymerization of styrene, where growing radicals of more or less identical size react with each other.
4 Termination Kinetics in Styrene Bulk Polymerization chain-length averaged <ktCLDT> for chemically initiated styrene homopolymerization at 90 °C; <ktCLDT> has been deduced from the EPR-derived composite-model parameters for long-chain radicals via eq (4.2), whereas the <ktPREDICI
> data are from PREDICI simulation including the entire set of the four composite-model parameters. The experimental values, <ktexp>, are from Ref.120