Rate constants step-growth polymerization

Propagation steps lead to the incorporation of additional monomers to the polymer at the growing end of the chain. We make the assumption that the rate of addition is constant, regardless of the chain length, because the reaction itself is the same. This is the same assumption we made for the overall polymerization process in step growth polymerization. The reaction can be represented as shown in Eq. 4.10. 

No real simplification is possible until an assumption is made. Fundamental to all analyses of polymerization kinetics is the assumption of equal reactivity, i.e. kj = k for all j>0. This proves to be a reasonable assumption. The possibility that the rate constants are dependent on polymer chain length has been discussed by Zeman and Amundson [18,19] and Saidel and Katz [20]. More recently, Durand and Bruneau [21], Gandhi and Babu [22] and Gupta and Kumar [23-25] have analysed the effect of unequal reactivity in step-growth polymerizations. 

Based on the experimental results of Table 3.1, we can postulate a simple kinetic model for the study of step-growth polymerization in which all of the rate constants are assiuned to be independent of chain length. This is referred to as the equal reactivity hypothesis. The following section shows that this assumption leads to a considerable simplification of the mathematical analysis. However, there are several systems in which this hypothesis does not hold accmately, and the analysis presented here must be accordingly modified [2,8-14]. 

Example 3.1 Consider the ARB step-growth polymerization in which monomer Pj reacts with P (for any n) with a different rate constant, as follows ... 

The chain polymerization of formaldehyde CH2O was the first example of a chemical conversion for which the low-temperature limit of the rate constant was discovered (see reviews by Goldanskii [1976, 1979]). As found by Mansueto et al. [1989] and Mansueto and Wight [1989], the chain growth is driven by proton transfer at each step of adding a new link... 

The initiation step of chain growth creates a reactive site that can react with other monomers, starting the polymerization process. Before the monomer forms the reactive site, the initiator ( ) (which maybe either a radical generator or an ionic species) first creates the polymerization activator (A) at a rate defined by the rate constant kv This process can be represented as shown in Eq. 4.7. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

In Scheme I, we present a kinetic scheme for tubulin polymerization in the absence of hydrolysis. The rate constants are written such that the (+) signs refer to the association steps and the (-) signs refer to the dissociation steps. The rates of growth at each end may be written as follows ... 

This is a first-order reaction. The half-life of benzoyl peroxide at 100°C is 19.8 min. (a) Calculate the rate constant (in min ) of the reaction, (b) If the half-life of benzoyl peroxide is 7.30 h, or 438 min, at 70°C, what is the activation energy (in kJ/mol) for the decomposition of benzoyl peroxide (c) Write the rate laws for the elementary steps in the above polymerization process, and identify the reactant, product, and intermediates, (d) What condition would favor the growth of long, high-molar-mass polyethylenes ... 

For ring-opening polymerizations of variPlls cyclic ethers, kp is in the range 10- -10-3 L/mol-s (Chien et al., 1988 Mijangos and Leon, 1983 Penczek and Kubisa, 1989). These values are seen to be much closer to the rate constants for step-growth polyesterification than to those for various chain polymerizations. 

We illustrate the start of the polymerization with azoisobutyronitril and the first two steps of growth of the chain with styrene in Fig. 17.1. The notation follows the usual in literature. The initiator decomposes into two initiator radicals that are adding successively to monomers resulting in polymer radicals. At the end of the kinetic chain, the radicals deactivate mutually. The rate constants are assumed to be independent of the degree of polymerization. 

Several pulse radiolysis studies have provided evidence that the 450-500-nm transients assigned to 1,4-acyclic radical cations react with the parent styrenes in nonpolar solvents. The rate constants for these reactions are generally in the 10 -10 M" s range, several orders of magnitude slower than the intial addition of the monomer radical cation. The reactions have been attributed to the trimerization reaction that is the first step in the chain growth in cationic polymerizations (Eq, 27). 

The initiator, I-I, is homolyticaUy broken into two free radicals by either absorption of a photon, hv, or by collision with another molecule, B. In either case there must be sufficient energy to break the center bond of the initiator. Once formed, each free radical, written as I, can start a polymerization reaction by adding monomer molecules. The first step leads to the free radical monomer, I-A , also written as Mj. The next step of the reaction produces a free radical called Mj. Each step of the chain reaction has up to this point its own specific rate constant. Addition of further monomers goes, however, substantially with the same rate, so that one can write during the main growth period of the molecule for each step the fourth reaction equation in Fig. 3.23, where x is the degree of polymerization. Ultimately, the reaction may be stopped by a termination reaction of the chain. The example of the termination reaction shown is a combination of two free radicals. The special case for... 

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