Apparent rate constants propagation

The latter seem to be the only species contributing to propagation, and hence the apparent rate constant of propagation is given by... 

The observed ion-pair propagation constant kj is an apparent rate constant, kj is a composite of the rate constants for the contact ion pair (kc) and solvent-separated ion pair (ks) according to... 

In all but one of these studies the apparent rate constants of propagation were determined. The observed apparent propagation rate constant (kSPP) is a summ of products of rate constants on various forms of active centers (e.g. free ions, ion-pairs, aggregates) and their fractions in the polymerizing mixture... 

It is interesting to note that this relation was verified for polymerizations of styrene, p-methoxystyrene, and isobutylvinylether with iodine by Kanoh and Higashimura (19). They have demonstrated that the apparent rate constants of termination, propagation, and monomer transfer increased with increasing dielectric constant of solvent, and the rates of the increase for these three rate constants were of the order of Eq. (21). 

Figure 9 gives the apparent rate constants of propagation (kp) as a function of the inverse square root of the living end concentration with and without an electric field for styrene with Li+ gegenions in binary... 

If this three-state polymerization mechanism is accepted, we have for the apparent rate constant of propagation kp,... 

Besides the field influence on the monomer reactivity ratio mentioned in the previous sections, living anionic systems present strong evidence against the electroinitiated polymerization mechanism. First of all, the experimental fact, that the apparent rate constant of propagation was increased by the presence of an electric field, rules out a possibility that the observed field-accelerating effect resulted only from the initiation reaction enhanced by the field. The finding that the field had no influence on the dependences of the polymerization rate on monomer and initiater concentrations, but did influence the rate constant, implies that the reaction mechanism was unaltered by the application of the field. These results confirm our very low opinion of the electroinitiated polymerization mechanism. 

In the case of polymerisations with SbFg counterion, addition of Ag0S02CF3 has predictably the reverse effect, producing significant proportions of dormant macroester molecules, and reducing the value of the apparent rate constant for propagation. 

Why are we so ignorant about the magnitude of propagation rate constants Apparent rate constants kA are dependent on the total Nd-concentration (cNd), the fraction of active Nd (ejffNd), the functionality of Nd (fNd) and the propagation rate constant kp ... 

Thus, the concentration of each species must be determined to determine the absolute rate constant(s) of propagation. If not, only the apparent rate constant of propagation is obtained. 

However, the low yield of carbenium ions (< 1%) and often incomplete initiation in these classic cationic systems resulted in very low apparent rate constants of propagation (/rpapp = 1 mol L sec 1). In the past 20 years, three methods have been developed to obtain more accurate rate constants for carbocationic propagation. They are based on direct measurement of the concentration of growing species by rapid spectroscopic techniques, on systems initiated by -y-irradiation, and on systems initiated by trityl salts which are consumed slowly. The latter method follows the concentration of unreacted initiator spectroscopically. Although all three methods have some disadvantages, they provide consistent carbocationic propagation rate constants (kp 105 mol-,L-sec l at 0° C) [207]. 

The ratio of the reactivities of ions and ion pairs (kp+/kp ) are also included in Table 13. They were determined from kinetic studies of the apparent rate constants at either different acid concentrations which vary the extent of dissociation into free ions, or in the presence of tetrabutylam-monium salts with common counteranions such as perchlorates and triflates. This results in ratios of the reactivities of ions and ion pairs of approximately 6 to 24. However, addition of an equimolar amount of salt to triflic acid may lead conjugation of acid with anions [215], with complete deactivation of the system. Therefore, the lower rate constants of propagation for ion pairs may be partially due to removal of the acid from the system. Thus, the values reported in Table 13 can be considered the upper limit of kp+/kp. The true ratio might be lower, with very similar reactivities for ions and ion pairs as in model systems [4]. Miscalculations of the ratio of reactivities of ions and ion pairs has led to unrealistic values of activation parameters calculated for propagation by ions (Ep = 51 kJmol-, ASP = +54 Jmol- K-1) and ion pairs (Ep = 21 kJmol- ASP = -84-mol-,-K l) [17] the latter values are similar to the overall activation parameters for ionic propagation and are quite reasonable. Extrapolation of Kunitake s data to - 80° C shows ion pairs being 30 times more reactive than ions [17], which contradicts the available experimental data [213]. 

This ternary system reduces to a binary system involving only ion pairs and covalent species if free ions are suppressed. This can be accomplished in nonpolar solvents and/or in the presence of salts with common counteranions. The rate of monomer consumption is then expressed using either the apparent rate constant and the assumption that initiator converts quantitatively to active species [Eq. (74)], or using the ionic propagation rate constant and assuming that only ions pairs propagate even though covalent species prevail ( 1 1) [Eq. (75)]. 

Because the reactivities of ions and ion pairs are similar and only weakly affected by the structure of the counteranions, kp + or kp determined by either stopped-flow studies or y-radiated systems (cf., Section IV. 13) can be used in Eq. (75). The equilibrium constant of ionization can then be estimated from the apparent rate constant of propagation and the rate constant of propagation by carbenium ions [Eq. (77)]. For example, Kf 10-s mol-,L in styrene polymerizations initiated by R-Cl/SnCl4 [148]. Kt for vinyl ether polymerization catalyzed by Lewis acids can also be estimated by using the available rate constant of ionic propagation (kp- = 104 mol Lsec-1 at 0° C) [217], The kinetic data in Ref. 258 yields Kj == 10 3 mol - l L in IBVE polymerizations initiated by HI/I2 in toluene at 0° C and Kf 10-1 mol- -L initiated by HI/ZnI2/acetone can be calculated from Eq. (76). 

Deactivation of growing carbenium ions by reaction with sulfides is evidently very fast. Sulfonium ion formation is exothermic (AH = -40 kJ/mol) and exoentropic (AS = -74 J/mol-K) [271]. High equilibrium constants (Keq = 104 moI-1L) for sulfonium ion formation were calculated from the apparent rate constants of propagation and the rate constants of carbocationic growth. Dynamic NMR experiments of model systems with tetrahydrothiophene indicate that the bimolecular deactivation rate constant is kdeacl 106 mol-1-Lsec-1 at 0° C (AH = 20 kJ/mol, AS = -37 J-mol-K), and that activation is faster than bimolecular exchange (k act foe) [67]. 

A comparison of Eq. (22) with Eq. (23) reveals that the apparent rate constant, k, equals the product kp K. Thus, the rate of polymerization is affected by the concentrations of monomer, initiator, and Lewis acid, as well as by the rate and equilibrium constants. Although the ionic propagation rate constant is not very sensitive to the nature of the counterion, solvent and temperature, the equilibrium constant K usually depends strongly on the temperature, solvent, Lewis acid, and the leaving group X. 

The equilibrium constants for sulfonium ion formation were calculated from the apparent rate constants of propagation and the rate constants of carbocationic propagation [257], using Eq. (31) obtained by the combination of Eq. (30) with Eqs. (28) and (29). 

The overall polymerization rates and the apparent rate constants of propagation (/c/pp = RP/[M][I]0) for the same initiating system are, however, very different for each class of monomers. For example, the same initiating system, that will polymerize a-methylstyrene (aMeSt) in 1 h, will complete polymerization of vinyl ether within less than 1 min but would require a few days to polymerize styrene and isobutene under otherwise identical conditions. This trend is due to the equilibria between dormant and active species. In this case the apparent rate constant of propagation is the product of the rate constant of propagation (weakly depending on monomer structure) and the ionization constant (kpapp = kp + -Kf). This equilibrium constant is much higher for more stable cations derived from vinyl ethers than from aMeSt, than styrene or isobutene. 

Differences in reactivity ratios must be taken into account in the synthesis of block copolymers. Synthetic aspects of block copolymerization are discussed in detail in Chapter 5. Ideally, cross-propagation should occur from the more reactive growing species to the more reactive monomer. Here, by more reactive growing species we mean not the more reactive cation but the species that will have a higher apparent rate constant... 

Thus, how should block copolymers between styrene and a vinyl ether be prepared Starting with styrene or with a vinyl ether In the former system, the propagating styryl cation is intrinsically more reactive but present at much lower concentration. A rough estimate of the ratio of cation reactivities is = 103 but the ratio of carbocations concentrations is = I0 S. Thus, the ratio of apparent rate constants of addition is 10-2. Macromolecular species derived from styrene should add to a standard alkene one hundred times slower than those derived from vinyl ethers. Thus, one cross-over reaction St - VE will be accompanied by =100 homopropagation steps VE - VE. Therefore, in addition to a small amount of block copolymer, a mixture of two homopolymers will be formed. Blocking efficiency should be very low, accordingly. 

The polymers possess one sulfonyl group per chain, which can be utilized as end-functional polymers as discussed later (section III.B.l). Narrower MWDs (MJMn = 1.2—1.4) were obtained in MMA polymerization with 1-32 as well as 1-33 and 1-34 in conjunction with CuCl/L-1 in />xylene at 90 °C.175 In a homogeneous system with CuCl/L-4,1-32 can afford narrow MWDs MJMn = 1.1—1.3) for styrene, MMA, and nBA.176 The fast addition of the sulfonyl radical to these monomers was evidenced by H NMR analysis of the reactions, where the apparent rate constants of initiation are 4 (for styrene and MMA), 3 (nBA), and 2 (MA) orders of magnitude higher than those of propagation. A similar controlled and homogeneous polymerization of MMA with 1-32 (X = CH3)/ CuBr/L-4 was reported in diphenyl ether at 90 °C.178 A better control of molecular weights and MWDs with 1-32 (X = CH3)/CuBr/L-9 in diphenyl ether was also... 

Moreover, the apparent rate constant of propagation kp > Rp/[M][C] Increases on decreasing the concentration of living centers. The reaction order In active centers Is nearly equal to 0.25 for a concentration range between 8 x 10 3 and 9 x 10 mole.l. This could be explained by the presence of associations of the lithium sllanolates which are not destroyed by the ligand. Viscosity measurements of living and deactivated PDMS solutions performed In toluene with LI + [221] show a tremendous change. However, It Is not possible to make a quantitative study of the phenomena. 

Here kp should more appropriately be called an apparent rate constant or overall rate constant since both undissociated (ion pair) and dissociated (free ions) species usually exist and their propagation rate constants are different (discussed later). Integration of this pseudo-first-order rate equation gives the time dependence of the monomer concentration as... 

Calculate an estimate pf the apparent rate constant for propagation. Which of the systems given in the table would yield the highest molecular-weight polymer at 90% conversion ... 

The initiation rate was low in this system, kinetic curves showed marked acceleration periods. Analysis of the initial periods of kinetic curves, considering the slow initiation-fast propagation process 19), yielded of an apparent rate constant of initiation kj = 1.6 1(T3 mol-1 1 s 1 (C6H5C1, 70 °C) 18> (k = 8.5 mol"1 I s-1 for the same conditions cf. next paragraph). 

Equations (8.66) and (8.71) allow one to obtain k, and K from the experimental values of overall or apparent rate constant kp determined in the absence and presence of added common ion. While a plot of kp versus 1/[M ] in the absence of added common ion yields a straight line whose slope and intercept are k - kp)K and kp, respectively, a plot of kp versus 1 /[C ]sait in the presence of added conunon ion yields a straight line [cf. Eq. (8.71)] whose slope and intercept are kp-kp)K and kj, respectively, thus affording the values of k, kp, and K, individually (see Problems 8.9 and 8.10). It should be noted that the observed ion pair propagation constant k" is, in fact, an apparent rate constant as it is a composite of rate constants for the contact ion pair and the solvent-separated ion pair (see Problem 8.11). 

---