Step polymerization rate constants

The size of the polymer molecules increases at a relatively slow rate in step polymerization compared to chain polymerization due to the lower rate constants in the former since k is of the order of 10 3-10 liter/mole-sec. One proceeds slowly from monomer to dimer, trimer, tetramer, pentamer, and so on until eventually large polymer molecules have been formed. Any two molecular species containing respectively the two different functional groups can react with each other throughout the polymerization. The average size of the molecules increases slowly with time and high molecular weight polymer is not obtained until near the very end of the reaction (i.e., above 95% conversion). ... 

It is normally assumed that the stmctuie of tim trandtkm state is close to that of tlw product. If one assumes farther that the pressure affects primarily the propagation step, AV% may be. repla( by the volume change of polymerizatitm AVpoi and so the followup aj noximate relation should exist between the pressure coeffident of the rate constant of polymerization, Apoi, and the volume dbange of pol3mietization per addition of a monomer unit, AV. ... 

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... 

In the literature on radical polymerization, the rate constant for propagation, ( is often taken to have a single value (i.e. kp( I) - kv(2) - kvQ) - kp(n) - refer Scheme 4.45). However, there is now good evidence that the value of k is dependent on chain length, at least for the first few propagation steps (Section 4.5.1), and on the reaction conditions (Section 8.3). 

Pulsed laser photolysis (PLP) has emerged as the most reliable method for extracting absolute rate constants for the propagation step of radical polymerizations,343 The method can be traced to the work of Aleksandrov el al.370 PLP in its present form owes its existence to the extensive work of Olaj and eoworkers 71 and the efforts of an 1UPAC working party/45"351 The method has now been successfully applied to establish rate constants, /rp(overall), for many polymerizations and copolymerizations. 

Phenomenological evidence for the participation of ionic precursors in radiolytic product formation and the applicability of mass spectral information on fragmentation patterns and ion-molecule reactions to radiolysis conditions are reviewed. Specific application of the methods in the ethylene system indicates the formation of the primary ions, C2H4+, C2i/3+, and C2H2+, with yields of ca. 1.5, 1.0, and 0.8 ions/100 e.v., respectively. The primary ions form intermediate collision complexes with ethylene. Intermediates [C4iZ8 + ] and [CJH7 + ] are stable (<dissociation rate constants <107 sec.-1) and form C6 intermediates which dissociate rate constants <109 sec. l). The transmission coefficient for the third-order ion-molecule reactions appears to be less than 0.02, and such inefficient steps are held responsible for the absence of ionic polymerization. 

It was possible to formulate a rule describing how the copolymerization parameters depend on the polarity of the solvent used. This rule is a result of contemplation about the connection between the copolymerization parameters and propagation rate constants during the cationic polymerization as well as about the changes of solvation of educts and activated complexes of the crossed propagation steps in solvents with varied polarity 14 U7). The rule is as follows ... 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

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. 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

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. 

Consider the following mechanism for step-change polymerization of monomer M (Px) to P2, P3,..., Pr,. The mechanism corresponds to a complex series-parallel scheme series with respect to the growing polymer, and parallel with respect to M. Each step is a second-order elementary reaction, and the rate constant k (defined for each step)1 is the same for all steps. 

As far as propagation is concerned, comparison of rates is hazardous because under some conditions the rate-determining step for isobutene [85], like propene [86], may be a unimolecular process, i.e., of zero order with respect to monomer (see sub-section 5.2). Moreover, comparison is complicated further by the consideration that in every system free cations and cations forming part of an ion-pair or higher aggregate may participate in the polymerization, and that therefore the extent of such participation must be ascertained before meaningful rate constants can be evaluated. This matter will be discussed in Section 6. 

I do not propose any explanation for the great differences in kpl W, and therefore probably in the kpl, for the two VE, but the fact that both rate constants (k+p and kpl) are so different indicates some profound difference in the kinetic properties of these two monomers. The exceptional kinetic position of secondary alkyl ethers is not news, since Eley Saunders (1954) found cyclohexyl VE to be eight times more reactive than EVE in polymerizations initiated by iodine. The dramatic drop in rate at the first dilution step for IPVE is different in magnitude and shape from what was seen with EVE, and the ideas used in the following sections to explain apparently similar phenomena with other monomers and solvents do not seem to be applicable here it remains a mystery. 

Figure 4. Catalytic activity of the pyridine-Cu catalyst in DMSO-benzene solvent (a) and activity of the PSP-Cu catalyst in DMSO (b) (O) oxidative polymerization rate of XOH (A) rate constant of electron transfer step (ke) (0) rate constant of catalyst reoxidation step...

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 ... 

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