Dependence of Polymerization Rate on Initiator

Equation 3-32 describes the most common case of radical chain polymerization. It shows the polymerization rate to be dependent on the square root of the initiator concentration. This 

Alternately, the termination mode may change from the normal bimolecular termination between propagating radicals to primary termination, which involves propagating radicals reacting with primary radicals [Berger et al., 1977 David et al., 2001 Ito, 1980]  

This occurs if primary radicals are produced at too high a concentration and/or in the presence of too low a monomer concentration to be completely and rapidly scavenged by monomer (by Eq. 3-14a). If termination occurs exclusively by primary termination, the polymerization rate is given by 

derived by combining the rate expressions for Eqs. 3-14a, 3-15d, and 3-33a, shows that the polymerization rate becomes independent of the initiator concentration (but not kf) and second-order in monomer concentration. 

Primary termination and the accompanying change in the order of dependence of Rp on [I] may also be found in the Trommsdorff polymerization region (Sec. 3-10). Situations also arise where the order of dependence of Rp on [I] will be greater than one-half. This behavior may be observed in the Trommsdorff region if the polymer radicals do not undergo termination or under certain conditions of chain transfer or inhibition (Sec. 3-7). 

---

Scott, T.F., Kloxin, C.J., Draughon, R.B., Bowman, C.N., 2008. Nonclassical dependence of polymerization rate on initiation rate observed in thiol-ene photopolymerizations. Macromolecules 41, 2987—2989. 

We can tentatively conclude, therefore, that the effect of chain transfer is still making itself felt in the polymerization of vinyl caproate in spite of its low water solubility. Except at the lowest particle concentrations, chain transfer is important. The polymerization in these regions is midway betwen Case I and Case II. When variables are considered separately, there is some dependence of polymerization rate on particle concentration, and also some dependence on initiator concentration. In addition, at constant organic volume, while the rate of polymerization increases as the particle concentration increases (Rp oc 2V- ), the rate per particle decreases as the particles get smaller. This shows that transferred radicals are mainly trapped in the particles, but some diffuse out and can undergo termination with other growing radicals. 

The general resemblance of these systems to typical emulsion polymerization has been stressed by several investigators. Thus the number of particles per cc can be varied by altering the concentration of initiator or dispersing agent, but the rate per particle is reasonably constant so long as aggregation is avoided. Dependence of polymerization rate on soap concentration has been established empirically in several cases. 

The value of equilibrium concentration of the monomer in relation to the dissolved polymer, as estimated from the dependence of polymerization rate on the initial monomer concentration, correlates well with the value of this concentration measured by independent methods35. ... 

The Smith-Ewart kinetic theory of emulsion polymerization is simple and provides a rational and accurate description of the polymerization process for monomers such as styrene, butadiene, and isoprene, which have very limited solubility in water (less than 0.1%). However, there are a number of exceptions. For example, as we indicated earlier, large particles (> 0.1 to 0.5 cm diameter) may and can contain more than one growing chain simultaneously for appreciable lengths of time. Some initiation in, followed by polymer precipitation from the aqueous phase may occur for monomers with appreciable water solubility (1 to 10%), such as vinyl chloride. The characteristic dependence of polymerization rate on emulsifier concentration and hence N may be altered quantitatively by the absorption of emulsifier by these particles. Polymerization may actually be taking place near the outer surface of a growing particle due to chain transfer to the emulsifier. 

Finally, let us notify that the first order of dependence of polymerization rate upon initiation rate at the adsorptive immobilization on the surface of filler of polymeric initiator can also be explained by the essential contribution of reactive diffusion to chain termination, i.e., supplying the reactive centers of macroradicals to one another at the expense of their propagation [18]. 

Among recent references to cationic polymerization in the presence of carbon black is the report of a graft polymerization of poly(lV-vinyl-2-pyrrolidone) (NVP) onto a carbon black substrate. Typical carbon black surface structures include carboxylic acid groups. From the dependence of polymerization rate on the concentration of these groups and the effects of surface treatments with basic compounds the inference is drawn that the carboxylic acids initiate cationic polymerizations. In the case of NVP grafting the mechanism would presumably involve proton initiation followed by termination on the residual anionic surface groups. 

FIG U RE 9.9 Dependence of polymerization rate on the initiator concentration in log-log scale. Temperature = 70°C, [NIPAM] = 48.51 mmol, [MBA] = 3 mmol, and total volume = 250 mL [7] , I V50 initiator concentration). (From Meunier, F., Synthese et caractdrisation de supportpolymdres particulaires hydrophiles a base de A-isopropylacrylamide, Elaboration de conjugues particules/ODN et leur utilisation dans le diagnostic medical, Thbse, 1996.)... 

An especially interesting case of inhibition is the internal or autoinhibition of allylic monomers (CH2=CH—CH2Y). Allylic monomers such as allyl acetate polymerize at abnormally low rates with the unexpected dependence of the rate on the first power of the initiator concentration. Further, the degree of polymerization, which is independent of the polymerization rate, is very low—only 14 for allyl acetate. These effects are the consequence of degradative chain transfer (case 4 in Table 3-3). The propagating radical in such a polymerization is very reactive, while the allylic C—H (the C—H bond alpha to the double bond) in the monomer is quite weak—resulting in facile chain transfer to monomer... 

Dependence of the polymerization rate on initiator concentration is confounded with variation in particle concentration. In the only place where a direct relationship can be found, runs 41, 42, and 43, there is zero dependence. For the other runs, there is a dependence on Np0-75 this gives Rp oc I012, using runs 26, 27, and 28 and correcting to constant Np. 

There followed a very important series of papers coocenung the emulsifier-free system (Machi et al., 1978, I9 9a-d)- The equipment used was a modification of that used eailier, but the tetrafluoroethylene pressure was continuously recorded with the use of a strain gauge. In the first paper of the series (Machi er cl., 1978) the rate of polymerization was shown to be proportional to the 1.0 and 1.3 powers of the dose rate and the initial pressure, respectively. The activation energies were 0.8 above and —5.2 kcal/mol below 70°C. There was a maximum in the molecular weights at about the same temperature. This behavior is reminiscent of the behavior of ethylene and was again attributed to the increased mobility of the growing chains above the maximum temperature. The very low mobility would also account for the first-order dependence of the rate on the dose rate below 70 C. As before, n-hexadecane proved to be an excellent inhibitor of polymerization in the gas phase. Particle sizes in the range of 0.1-0.2 microns were obtained. 

Lam and coworkers (4 ) developed kinetic models in which initiation of monomer by electron impact is followed by propagation and termination. They showed that activation of monomer in the gas phase followed by propagation and termination on the electrode surface gave an excellent description of the plasma polymerization process. The predicted functional dependence of deposition rate/On pressure (p) and current density (J) is R p 3. ... 

Many free radical reactions (e.g., polymerization) can be initiated by a light-sensitive substance, P, the molecules of which dissociate into two free radicals upon absorption of a photon. Subsequent reactions are either propagation, in which one radical, R-, is produced for each radical consumed, or termination, in which two radicals combine to form nonradical products. Tbe bulk of the chemical change is due to the propagation step. A small steady-state concentration of free radicals prevails throughout. Explain how such a mechanism accounts for the dependence of the rate on the square root of the light intensity, /. 

This was first detected in 1962 by Firsov et al. [28, 29] and Natta at al. [30] in studies of propene polymerization with TiCl3 at low propene concentrations (propene pressure <1 atm). Polymerization proceeded with an initial acceleration to a constant rate, and the effect of propene concentration on the polymerization rate was tested during the steady state phase of the process. It was shown that the dependence of polymerization rate order on monomer concentration increases from first order to some intermediate between first and second order with a reductimi in monomer concentration (Figs. 1 and 2). 

Equation (15) thus illustrates the dependency of the overall rate of polymerization on the concentrations of initiator and monomer. The half-power dependence of the rate on the initiator concentration appears to be a universal feature of the free radical mechanism and has been used as a diagnostic test for the operation of this mechanism. 

Based on the temperature dependences of polymerization rate, the effective activation energy of polymerization in the presence of TMT was calculated to be equal to 45 4 kJ/mol. This value is markedly lower than that in the case of initiation by PB only (80 4 kJ/mol). 

The results obtained are presented in Figure 8 in the form of In. Rp/(C" ) versus In. (M). A remarkable effect of adding even a small amount of methylene chloride is observed. The rate drops from 53.0 to 13.8 x 10 M sec. on the addition of only 0.4% of solvent. After 12% there is a strict first order polymerization and no further effect of the solvent is observed. The first order dependence of the rate on the monomer concentration is in agreement with the results reported in the literature for the chemically induced "free" cationic polymerization of the vinyl ether in dilute methylene chloride solution. The estimated rate constant for propagation in the first order region is 2.1+0.4 x 10 M. sec. , only about one-tenth the values reported with chemical initiation at the same temperature. 

It has been reported that if the quantity peroxodisulfate is sufficient to maintain the reaction with Fe and FS, its concentration in the aqueous phase has practically no influence. However, peroxodisulfate is necessary in the redox initiation system as a raw material from which the initiating free radicals are formed, but the polymerization rate and the final conversion depend mainly on the concentration of FS and Fe. That is why the determination of the reaction order with respect to [peroxodisulfate] is not easy. Maintaining, however, the optimum constant ratio of the redox system components, the dependence of the rate on the initiator concentration was studied. It was found that ... 

Emulsion polymerization of vinyl chloride was also carried out at subsaturation conditions by Butucea et al. [127] who followed the effect of monomer, emulsifier and initiator on the polymerization behavior. Some results from these investigations are summarized in Table 9. This table shows that the rate of polymerization increases with increasing concentration of all these reaction components. From these results the following semiempirical equation for the dependence of the rate on the initiator, monomer (in water) and emulsifier concentrations was suggested. 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

Here M is the transition metal and L are other ligands of the initial organometallic compounds. In this case individual organometallic compounds are considered to be true catalysts, and the question of the dependence of the polymerization rate on the character of metal-ligand bonds in the initial organometallic compounds is discussed (123). 

The activity of initiators in ATRP is often judged qualitatively from the dispersity of the polymer product, the precision of molecular weight control and the observed rates of polymerization. Rates of initiator consumption are dependent on the value of the activation-deactivation equilibrium constant (A") and not simply on the activation rate constant ( acl). Rate constants and activation parameters are becoming available and some valuable trends for the dependence of these on initiator structure have been established.292"297... 

---