The influence of chain length-dependent propagation on the evaluation of the chain length dependence of the rate coefficient of bimolecular termination, 2 - PLP-SEC methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k(t) introduced in the form of a power law and that of propagation k(p) modeled by a Langmuir-type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R](2) while the propagation goes directly with [R], As a consequence there is no general recommendation possible as to which experimental value of k(p) is best taken as a substitute for the correct average of k(p) characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k(t) and its chain length dependence (i.e., plotting some average of k(t) versus the mean chain-length of terminating radicals on a double-logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence, This is especially so for the quantity (K) over bar (t)* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence. [GRAPHICS] Numerically calculated number distributions of dead polymer terminated by disproportionation (x(D))(L) in arbitrary units vs. chain-length L in case of chain length-dependent termination k(t)(L, K) = k(t)((1,1))(L . K)(-b/2) (using parameters k(p)(0) = 100 L (.) mol(-1) (.) s(-1), [M] = 10 mol (.) L-1, t(0) = 0.1 s, C = 5, b = 0.16) for a constant kp (full line) and for a Langmuir-like behavior of k(p) (parameters A = 50 L (.) mol(-1) (.) s(-1), B = 125, broken line; A = 50 L (.) mol(-1) (.) s(-1), B = 250, dashed-dotted line). Points of inflection are marked by full symbols (see Figure 2), the (k) over bar ((n))(p) extracted values of k. (n = 1, 2,3) are given in Table 1.