Since Roth and Mayr1 published a propagation rate constant (kp) of 6 ± 4 × 108 L mol−1 s−1 for isobutylene (IB) polymerization in their seminal article in 1996, there has been disagreement among research groups regarding rate constants for propagation in carbocationic polymerizations, especially for IB and styrene (St). Before Roth and Mayr's article, it was asserted that reliable rate constants of attack on an alkenic monomer by an unpaired carbenium ion, solvated mainly by the monomer, were in the range of k ∼ 103–106 L mol−1 s−1, depending on the reaction conditions.2 Tables 1–5 list rate constants published for various carbocationic polymerizations.1–34 High values (kp > 107 L mol−1 s−1) were reported before Roth and Mayr's work for polymerizations initiated by high energy, with researchers arguing that the high values were due to the lack of counteranions. It was also argued that differently solvated carbocations would have different rate constants (kp± for solvent-separated ion pairs and k for unpaired or free ions). Mayr35 since has shown that the kp he measured is largely independent of the solvent, counterion, and degree of ion separation (kp± = k). These findings are currently enthusiastically debated in the polymer chemistry community.
Table 1. Rate Constants of Propogation for St and Its Derivativesa
What are the true rate constants and why is such a large difference between values measured by different methods? This issue has now been debated from the point of view of organic chemistry, physical chemistry, and polymer chemistry. This article highlights the debate from a different angle and proposes a possible explanation for the discrepancies from a reaction engineering point of view. This article may not fit into a narrowly defined category of a classical review: it is a hybrid of a review and kinetic simulation exercises. We feel that these are necessary to demonstrate alternative pathways. Before a detailed discussion, a short anecdote will be provided.
In 1991, the corresponding author of this article joined the Butyl Technology Group of the Rubber Division of Bayer, Inc. (now Lanxess, Inc.) in Sarnia, Ontario, Canada. Butyl rubber is produced commercially by the carbocationic copolymerization of IB with a small amount (1–3 mol %) of isoprene (IP) with AlCl3 as a catalyst in the diluent methylene chloride at very high monomer concentrations (5–6 mol/L).36, 37 An analysis of the production data at the company revealed that the rate constant must be very high, close to the diffusion limit.38 These findings were presented to a group of scientists assigned to investigate the kinetics of the butyl process. (G. Langstein, W. Baade, R. Heinrich, and J. E. Puskas were called “the gang of four”). Langstein suggested asking Professor Herbert Mayr, a physical organic chemist, to measure the rate constant of propagation in IB polymerization. Roth and Mayr1 published the results, thereby initiating the current debate. The significance of this story is that this revolution originated from industry. Industrial scientists often do not have visibility, and their contributions are not recognized. Therefore, this article is dedicated to all the innovators in industry and specifically to Dr. Gerhard Langstein.
Roth and Mayr measured the rate constant of IB polymerization by the diffusion clock method. This method is based on direct competition experiments. A carbocation R+ is generated in situ and is reacted with the monomer (M) and another compound (X) for which the rate constant of reaction (kx) is known: Figure 1 shows the simplified scheme. With excess M and X, the product ratio RM/RX will be equal to kp/kx. When kx is diffusion-controlled (kx ∼ 3 × 109 L mol−1 s−1), the method is called the diffusion clock method.39 In the case of IB, X was 2-methallyl trimethyl silane, and R+ was generated in the reaction of 2-chloro-2,4,4-trimethylpentane (TMPCl) and 2-chloro-2,4,4,6,6-pentamethylheptane (PMHCl) with TiCl4, GaCl3, and AlCl3. Since then, it has been shown that TMPCl reacts about three times more slowly than PMHCl and a polyisobutylene-36-mer, these latter two being equivalent.40 On the basis of extensive studies of organic reactions between electrophiles and nucleophiles, Mayr and his group41 developed a linear free energy relationship (LFER) type correlation to predict rate constants (k):
Equation 1 uses three parameters: s is a nucleophile-specific parameter, N is a nucleophilicity parameter, and E is an electrophilicity parameter for the electrophile. The nonconventional form of this relationship, shown in eq 2, was used to experimentally obtain electrophilicity and nucleophilicity parameters for a large number of compounds, so that Mayr's group was able to quantitatively describe a large variety of electrophile–nucleophile combinations:41–45
In principle, rate constants of propagation in carbocationic polymerizations can be determined from eq 2, where E is the electrophilicity of the propagating cation and N and s are the nucleophilicity parameters for the monomer obtained experimentally by the measurement of the rate of reaction between diarylcarbenium ions and various monomers with ultraviolet–visible (UV–vis) spectroscopy. Mayr warned that for very fast reactions (kp > 108 L mol−1 s−1), eq 2 can be considered only a prediction with a large error. However, this equation worked remarkably well in several carbocationic polymerizations. For instance, Mayr's LFER predicts high kp values for carbocationic IB polymerizations, in agreement with those obtained by competition experiments (Table 2). Recently, Shaikh et al.46 measured r1 (IB) = 1.17 ± 0.01 and r2 (IP) = 0.99 ± 0.02 in IB–IP copolymerization with in situ Fourier transform infrared (FTIR) spectroscopy. Mayr's LFER predicts k11 = 5.51 × 108, k12 = 4.17 × 108, k22 = 1.66 × 109, and k21 = 2.26 × 108 L mol−1 s−1, so that r1 (=k11/k12) = 1.32 and r2 (=k22/k21) = 0.74. In contrast, the Q–e scheme47 predicts the opposite trend (r1 = 0.87, r2 = 1.13).
After Mayr's work, Faust and his group12, 18, 19 also measured high kp values for IB polymerizations (Table 2). However, discrepancies between high and low values and the associated debate remain. For carbocationic St polymerization, similar discrepancies exist between the LFER prediction or data obtained by direct competition measurements and previously accepted reliable rate constants obtained from kinetic measurements2 (see Table 1). In the case of 2,4,6-trimethylstyrene (TMS), the situation is even more complex. Vairon's group9 investigated the carbocationic polymerization of TMS initiated by trimethylstyryl chloride (TMSCl)/BCl3 in CH2Cl2 under high-purity conditions and reported kp = 1.35 × 104 L mol−1 s−1 at −70°C. Subsequently, Faust's group11 reported kp = 2.8 × 104 L mol−1 s−1, using a different method. In contrast, using N = 0.68, s = 1.08, and E = 6.1, Mayr's48 LFER predicts k20°C = 2.4 × 107 L mol−1 s−1. With the activation enthalpy published by Vairon's group,9 we calculate kp = 4.9 × 106 L mol−1 s−1 for −70°C. Although Mayr warned that in the case of very fast reactions LFER is only an estimate accurate to 1–2 orders of magnitude, it is interesting to explore why there is a difference of nearly three orders of magnitude between the kp value for TMS obtained by kinetic measurements and that predicted by LFER.
CARBOCATIONIC POLYMERIZATION OF TMS: A CASE STUDY
Vairon's group expressly selected TMS for their investigations for several reasons: with this monomer, side reactions, such as indanyl cyclization or intermolecular Friedel–Crafts alkylation, which normally plague carbocationic St polymerization,49–52 are absent because of the three methyl substituents on the ring; BCl3 exclusively forms monomeric BCl4− counteranions (Fig. 2); and ki ≈ kp can be assumed.9 With Ki ≈ K1, a relatively simple mechanistic model of the polymerization can be drawn as shown in Figure 3. The initiator (I; TMSCl) and Lewis acid (LA; BCl3) form the active initiating ion pair (I+LA−) through an equilibrium involving rate constants k1 and k−1. The trimethylstyryl cation can then add monomer, and this leads to growth of the active chain. An active growing chain of any length n can produce dormant chains Pn and free Lewis acid through the equilibrium involving k−1 and k1. The rate of propagation was derived by Vairon et al.11 and is shown in eqs 3 and 4:
where [M]0 is the initial monomer concentration, [M] is the monomer concentration, and [I]0 is the initial initiator concentration. The molar extinction coefficient of the trimethylstyryl cation, obtained in the reaction of excess GaCl3 with TMSCl that led to full ionization, was obtained by UV–vis spectroscopy.9Ki = K1 = 2.3 × 10−3 L mol−1 was then measured in the TMSCl/BCl3/CH2Cl2 system at −70°C by UV spectroscopy from the plot of the absorbance at 334 nm versus the BCl3 concentration. The ionization was carried out with TMSCl = 0.1 mol/L in CH2Cl2 in the presence of a proton trap [di-tert-butylpyridine (DtBP)].9, 11 Polymerizations were then conducted with [TMSCl]0 = 0.001 mol L−1, [BCl3]0 = 0.053 mol L−1, and [TMS]0 = 0.136 mol L−1. The experimental data extracted from the graphs in ref.11 are shown in Table 6.
Table 6. Experimental Monomer Consumption and Molecular Weight Date in TMS Polymerizationa
[M] (mol L−1)
Mn (g mol−1)
The data were taken from ref.11. [M] = monomer concentration; Mn = number-average molecular weight; Mw = weight-average molecular weight.
kp was calculated in two different ways. One method calculated [P] under the polymerization conditions from K1 = [P]/([I][LA]), finding [P] = 2 × 10−7 M. kapp was obtained from the experimental semilogarithmic rate plot, and kp was calculated from eq 3 as kp = kapp/[P]. The other method, presented in a symposium lecture,11 involved calculating kp from eq 4, where kapp = kpK1[I]0[LA]0. Both methods yielded kp = 1.35 × 104 L mol−1 s−1.9, 11 The capping rate constant k−1 was calculated from eq 5, which was developed by Müller et al.:53
where X is the monomer conversion and DPw/DPn is the polydispersity. β = 104.38 was obtained by the best fit of eq 5 to TMS polymerization data, and k−1 = 1409 s−1 was calculated from β with [I]0 = 0.001 mol L−1 and kp = 1.35 × 104 L mol−1 s−1.9, 11 De et al.11 also calculated kp± from limiting molecular weight data, using eq 5:
where DPn∞ is the limiting number-average degree of polymerization and [πNu]0is the initial concentration of the π nucleophile 2-chloropropene. With a known kc value of 21 L mol−1 s−1, kp = 2.8 × 104 L mol−1 s−1 was calculated.
The aforementioned methods are all based on the reaction mechanism shown in Figure 3. Against this background, in this article we use parameter estimation within the Predici polyreaction package54 to extract rate constants from experimental data and to simulate measured monomer consumption plots, molecular weights, and molecular weight distributions (MWDs).9, 11 Parameter estimation is an accepted and very powerful tool in kinetic data analysis.55, 56 It can be used to screen and discard reaction mechanisms and obtain rate constants from experimental data. Although good agreement between experimental and simulated kinetic data cannot be regarded as proof of any reaction mechanism, a disparity can signal that the proposed mechanism is unreasonable. Kinetic modeling can also give insight into the effects of various reaction conditions. The following analysis investigates TMS polymerization from the polymer reaction engineering point of view and presents an alternative mechanism.
Parameter Estimation and Simulation
Vairon's Model (VM)
Based on Figure 3, the model illustrated in Table 7 was constructed with the Predici polyreaction package. The Predici polymerization software is based on the discrete Galerkin method and allows the rigorous computation of molecular weights and MWDs. Unrestricted input of various reaction rate constants, monomers and reaction species, polymer species, reaction steps, and polymerization conditions such as temperature and pressure is possible. In addition, parameter estimation may be conducted for unknown rate constants and parameters with experimental information, and correlations between reaction rate parameters can be implemented with interpreter functions.54, 56 Parameter estimation requires the input of the mechanistic model and initial guesses of the relevant rate constants. The parameter estimation routine is based on the damped Gauss–Newton method and has the ability to converge well even with inaccurate starting estimates. Table 8 lists kp values estimated with various scenarios.
Table 7. Predici Model 1 Using Scheme 1
I + LA ↔ I+ LA−
k1, k−1; k1 = K1 × k−1
I+LA− + M → P1+LA−
ki ≈ kp
Pn+LA− + M → Pn + 1+LA−
Pn+LA− → Pn + LA
Pn + LA → Pn+LA−
k1 = K1 × k−
Table 8. Parameter Estimation Based on Model 1 and Experimental Data11
Rate Constant (Unit)
CI = 95% confidence interval.Bolded numbers = estimated parameters.
For starting estimates, in set 1 (Table 8) we accepted K1 = 2.3 × 10−3 L mol−1 (measured) and k−1 = 1400 s−1 (calculated by Vairon). k1 was calculated from k1 = K1k−1, and kp was estimated from the experimental monomer consumption data in Table 6 with Predici. An estimate of kp = 1.36 × 104 ± 5.91 × 103 L mol−1 s−1 obtained in this way agrees well with Vairon's and Faust's values. The initial guess for kp was varied from 1 to 1 × 106 L mol−1 s−1 and still converged to nearly the same final value.
VM, Set 2
Alternatively to Müller's approach to calculating k−1, we used the method introduced earlier by Puskas et al.57 The authors suggested the concept of a run number, l, defined as the average number of monomer units added per productive ionization. For batch polymerizations, the initial value (l0) or l at an intermediate conversion can be calculated by eqs 7 and 8, respectively:
where l0 is equal to (kp/k−1)[M]0, defined as the run number at [M] = [M]0. Table 9 lists l0 data calculated from MWD data with eq 7 for various systems coinitiated by BCl3.28, 57 For TMS polymerization, we calculated l0 = 3.6. From eq 7, kp/k−1 = 26.5 L mol−1, and with kp = 1.35 × 104 L mol−1 s−1, the backward rate constant is calculated to be k−1 = 510 s−1. Thus, the Puskas equation leads to a different capping rate constant than that calculated by Vairon using the Müller equation. When k−1 = 510 s−1 was used as a starting value in the parameter estimation using monomer consumption data, with k1 being directly correlated as k1 = K1k−1 (set 2, Table 7), kp = 1.364 × 104 ± 5.86 × 103 L mol−1 s−1 was obtained, regardless of the initial estimate being varied between 1 and 1 × 106 L mol−1 s−1. This kp value also agrees well with that reported by Vairon and Faust.
Table 9. Run Length Calculations for BCl3-Coinitiated Polymerizationsa
In set 3, k−1 was arbitrarily set to 107 s−1, with k1 = 2.3 × 104 L mol−1 s−1 to keep K1 fixed at the experimentally determined value. A re-estimation of kp with these initiation parameters fixed caused the propagation rate parameter to converge to kp = 1.37 × 104 ± 5.43 × 103 L mol−1 s−1, which is again very close to the estimates for kp obtained from sets 1 and 2. Simulations of monomer consumption, molecular weight, and MWD plots with these parameters are shown in Figures 4–6. There were no discernible differences in the rate and number-average molecular weight prediction with the VMs (sets 1–3) and measured profiles, with the exception of the MWD profile, which was overestimated (Fig. 6). These parameter estimation and simulation results illustrate that k1 and k−1 can be varied independently, but as long as their ratio (i.e., K1) is kept constant, parameter estimation using monomer consumption data will yield the same kp value. Consequently, we believe that it is insufficient to experimentally measure K1 alone, and k1 and k−1 should be measured independently to estimate a reliable kp value.
Pre-Equilibrium Model (PEM)
Our research group proposed that evoking a pre-equilibrium in the carbocationic polymerization model of IB could explain the apparent discrepancy between high and low kp values.27, 55 According to this view, the initiator and Lewis acid first form an intermediate through an initial pre-equilibrium K0, and this intermediate subsequently dissociates into ion pairs in an equilibrium governed by K1. This concept, applied to the TMS/BCl3 system, is shown in Figure 7. This is not an unreasonable proposal; Kaszas and Puskas58 as well as others9, 59, 60 have suggested the formation of a polarized dipole intermediate in the reaction of tertiary chloride initiators or PIB-Cl with Lewis acids (BCl3, TiCl4, etc.) before ion-pair formation (Winstein spectrum). In Figure 7, first the initiator (TMSCl) and Lewis acid (BCl3) form an intermediate, I*LA, through an equilibrium involving rate constants k0 and k−0. The intermediate species dissociate into ion pairs through an equilibrium involving rate constants k1 and k−1. This active ion pair can polymerize monomers, leading to chain growth. An active growing chain of any length n can transform back to a polymer/Lewis acid intermediate through an equilibrium involving k−1 and k1. Based on Figure 7, the kinetic model shown in Table 10 was constructed in Predici.
Table 10. Predici Model 2 Using Scheme 2
I + LA ↔ I * LA
K0 = k0/k−0
I * LA ↔ I+LA−
K1 = k1/k−1
I+LA− + M → Pn+LA−
Pn+LA− + M → Pn+1+LA−
Pn+LA− → Pn * LA
Pn * LA → Pn+LA−
Pn * LA → Pn + LA
Pn + LA → Pn * LA
To obtain reasonable starting estimates for the rate constants in Figure 7 and Table 10, the polymerization rate equation derived recently for living TMPCl/TiCl4/IB polymerizations dominated by monomeric counteranions was used:56
From the data of De et al.,11kapp = 1.65 × 10−3 s−1. Applying the pre-equilibrium concept to Vairon's measurement of the equilibrium constant shown in Figure 2, we find Ki = K0K1 = 2.3 × 10−3 L mol−1. Substituting this and [I]0 = 0.001 mol L−1 and [LA]0 = 0.053 mol L−1 into eq 10, we have
With kp = 107 L mol−1 s−1, eq 11 reduces to K0 = 1.39 × 104 L mol−1. With kp/k−0k−1 = 26.47 L mol−1 s and k−0 set to 1, k−1 = 4.17 × 105 s−1 and k1 = 0.07 s−1 are calculated. In comparison, Storey and Thomas34 published k−1 = 1.9 × 107 s−1 for St polymerization.34
PEM, Set 1
Simulations (not shown) carried out with the parameters listed in Table 11 (k−0 = 1 s−1, k0 = 1.39 × 104 L mol−1 s−1, k1 = 0.07 s−1, k−1 = 4.17 × 105 s−1, and kp = 107 L mol−1 s−1) matched the experimental monomer conversion plot as well as the VM in Figure 4; however, the MWD plot was broader than both the experimental data and the plot obtained with the VM (Fig. 6). When the initial value of k0 and k−0 was set to 1 L mol−1 s−1 (i.e., considering no pre-equilibrium), the model did not converge with kp = 107 L mol−1 s−1. Thus, the Predici parameter estimation using the PEM reinforces that the VM is not consistent with a high kp.
Table 11. Parameter Estimation Based on Model 241 and Experimental Data18, 40
Parameter estimations were carried out with the initial parameter values listed in PEM, set 1, with all parameters being estimated simultaneously. The model converged with the values shown in Table 11, but with high error (it has been shown that k0 and k−0 are highly correlated and cannot be estimated simultaneously55, 56). This parameter set also matched the experimental monomer consumption plot, but the MWD remained broader than the experimental values.
PEM, Set 3
As a result of trial and error simulations, keeping key ratios constant, we were able to match simultaneously the experimental monomer consumption, the molecular weight, and the MWD–conversion plots (Fig. 6), using the following parameters: k−0 = 0.2 s−1, k0 = 2.78 × 103 L mol−1 s−1 (K0 = 1.39 × 104 L mol−1), k1 = 0.31 s−1, k−1 = 1.89 × 106 s−1, and kp = 1.01 × 107 ± 4.19 × 106 L mol−1 s−1. The very large K0 value indicates that, in the dynamic equilibria between active carbocationic and dormant species, the Lewis acid complexed species would dominate (Fig. 6). Without pre-equilibrium, at any given time, free Lewis acid and dormant initiator or polymer dominate the dynamic equilibria. With this, the composite capping rate constant is k−0k−1 = 3.78 × 105 s−2, and the ratio of the propagation rate constant to the composite capping rate constant remains kp/k−0k−1 = 26.47 L mol−1 s. The results of the simulation remain the same as long as the ratio of k0 to k−0 is maintained.
The purposes of this case study were to highlight some reasons for the apparent discrepancy in the rate constants of propagation measured by different methods for TMS and to estimate the propagation rate constant from experimental data with mechanistic/kinetic modeling coupled with parameter estimation. The results of the parameter estimation illustrate that whatever model is considered, rate prediction is sensitive only to the ratio of the propagation rate constant to the capping rate constant(s). At the same time, MWD is very sensitive to the actual values of the forward and backward rate constants in the dynamic equilibria, but not to their ratios (equilibrium constants). The broad MWD in the TMSCl/GaCl3/CH2Cl2 system,9 in which the initiator and chain ends should be fully ionized, may be described with a PEM and the adjustment of k0 and k−0. Therefore, we believe that measuring the equilibrium constant of the ionization alone, without independent proof of the mechanism, cannot be used to determine the true propagation rate constant.
The mechanism in Figure 7 provides one plausible solution to the apparent discrepancy between the low rate constants obtained from monomer consumption data and deemed reliable60 and the much higher diffusion-controlled values. Plesch60 proposed another explanation involving the formation of a monomer-solvated carbocation intermediate, and in this case a high monomer concentration would result in first-order propagation with the intermediate, giving misleading kp values. Sigwalt et al.10 argued that this suggestion was not convincing because the high kp values of Mayr were obtained at low monomer concentrations. Also, a high monomer concentration in the butyl process still yielded high kp values.38 Sigwalt et al.10 suggested two-step propagation with the formation of solvated carbocationic intermediates. With this mechanism, the apparent second-order rate constant obtained in kinetic experiments would be kp,app = KSM × kp, where KSM is the constant for the equilibrium between solvated carbocation and monomer-complexed solvated carbocation, the latter propagating by a unimolecular rearrangement. This form is similar to the pre-equilibrium concept but cannot be reconciled with Mayr's diffusion clock measurements. The existence and chemical nature of the intermediate in the PEM have not been proven independently yet but are consistent with the Winstein spectrum. However, in the absence of another model that describes seemingly contradictory experimental data such as low and high kp values for the same system, varying MWDs, and first- and second-order TiCl4 dependence observed in IB polymerization, PEM does not seem to be unreasonable. The next section of this review addresses this latter phenomenon.
LIVING CARBOCATIONIC POLYMERIZATION OF IB
Puskas and Lanzendörfer27 proposed a comprehensive model that described two kinetic pathways, as shown in Figure 8. Paths A and B are first- and second-order in TiCl4, respectively. These authors argued that this mechanism accommodates experimental observations of shifting orders between one and two as the ratio of the initiator to Lewis acid changes, and they used this mechanism to simulate the kinetics of living IB polymerization.56 Other authors also reported first-order kinetics in TiCl4 under various conditions.32, 61 Thomas and Storey33 recently challenged Puskas and Lanzendörfer's27 and Paulo et al.'s29 experiments in detail. Thomas and Storey argued that the analysis published in these articles neglected to consider temperature effects. Figure 9 is a reproduction of Figure 2 from Thomas and Storey's article. The authors pointed out rate deceleration in the first few seconds, whereas the temperature rose from −82 to about −81°C. In Figure 9, from a reaction time of 50 to about 250 s (ca. 70% conversion), the logarithmic rate plot seems to be linear. Within this time, the temperature steadily increased from −81 to −66°C, and at 170 s (55% conversion), the temperature started decreasing to −68°C. Beyond this, the plot started to curve upward, indicating rate acceleration, whereas the temperature decreased to about −75°C. Thus, according to these experimental data, the temperature had little effect on the linearity of the semilogarithmic rate plot between about 10 and 70% conversion. According to Roth and Mayr,1 the kp value of 6 ± 4 × 108 L mol−1 s−1 measured for IB has practically zero activation enthalpy. It can be argued that the temperature should affect various equilibrium constants, but these effects may cancel one another out, leading to practically steady rate plots. The cause of rate acceleration at high conversions is not clear, and Thomas and Story did not offer an explanation.
To obtain a better understanding of the effects of the temperature and monomer concentration on the rate plots, we carried out a sequential monomer addition experiment, while simultaneously monitoring the monomer conversion by in situ FTIR spectroscopy and the temperature with a resistance detector (RTD). Figures 10–12 show the results.
IB consumption was monitored with a transmission (TR) probe, following the 1780-cm−1 band (CH2 wagging overtone), which has been found to be proportional to the IB concentration in the 0.3–6 mol L−1 concentration range.62 The peak at 1780 cm−1 disappeared at 1000 s after initiation by the addition of chilled TiCl4. It should be noted here that the disappearance of the 1780-cm−1 peak does not signal complete conversion; as mentioned previously, the peak disappears into the baseline at a concentration of about 0.3 mol/L so the plot levels out at that value. The second IB increment was added after an hour. The peak at 1780 cm−1 sharply reappeared and then decreased with the reaction time. The temperature monitored by RTD increased from −76 to −65.5°C, at which it peaked at 400 s, and then decreased to its initial value (−76°C) at 1980 s. The dotted line in Figure 10 represents 50% monomer consumption (400 s), which coincided with the temperature maximum (−65.5°C). The second IB increment was added after the temperature decreased to −76°C. The temperature rose again to −66.5°C, at which it peaked at about 50% IB conversion. Figures 11 and 12 show the ln([M]0/[M])–time plots.
The following important observations can be made: first, both plots are linear (R2 = 0.99) up to about 40% conversion, with no initial rate deceleration (Fig. 12); second, a slight rate acceleration can be seen after about 500 s during both stages, with the second showing an additional deceleration toward high conversion; and third, the reaction rate of the second stage is significantly lower than that of the first increment (ca. half). Except for the first 50 s, our findings related to the first IB increment are very similar to those reported by Thomas and Storey.33 Figure 10 shows that cooling was also slower during the second stage of polymerization. This, together with the slower rate, may be due to a viscosity increase, but similarly to Thomas and Storey, we have no explanation for the upward curvature of the semilogarithmic rate plots. To avoid possible misinterpretation, the initial slope of nonlinear logarithmic rate plots can be used to obtain apparent rate constants of polymerization, as shown in eq 3, without any assumptions being made about the mechanism of polymerization. We re-evaluated a large number of IB polymerization experiments reported in the literature. To be able to compare experiments carried out with different initiator and TiCl4 concentrations, we normalized the apparent rate constants. For experiments believed to be dominated by first-order kinetics, that is, at high [TMPCl]0/[TiCl4]0 ratios, we carried out normalization, considering both first- and second-order TiCl4 dependence and using eqs 12 and 13:
In the case of excess TiCl4 over initiator, k values were calculated with both eqs 13 and 14,27 the latter representing paths A and B proceeding simultaneously:
The apparent activation enthalpies were calculated from Arrhenius plots (eq 15):
where A is the pre-exponential factor, ΔH is the apparent activation enthalpy of propagation, and R is the universal gas constant (8.314 J mol−1 K−1). Table 12 summarizes data available for path A ([I]0 > [TiCl4]0) experiments in the literature.27, 29, 33, 58, 63 Bold numbers represent calculated values. Figure 13 is a reproduction of the Arrhenius plot in ref.29 published by Puskas's laboratory, which used k values calculated from the slope of the ln([M]0/[M])–time plot, reporting ΔH −25.6 kJ mol−1 with R2 = 0.998. The negative apparent activation enthalpy was consistent with earlier reports.29, 64, 65 Except for [DtBP], Thomas and Storey33 reproduced one of Paulo et al.'s experiments from ref.29 ([TMPCl]0 = 0.054 mol L−1, [TiCl4]0 = 0.04 mol L−1, [IB]0 = 2.0 mol L−1, temperature = −80°C, MeCHx/MeCl = 60/40 v/v, and [DtBP] = 0.002–0.008 mol L−1 for Puskas), from which we calculated k = 1.9 L2 mol−1 s−1. In comparison, Paulo et al.29 reported k = 1.7 L2 mol−1 s−1 when using anhydrous MeCHx and emphasized the importance of solvent quality, demonstrating much slower rates in freshly distilled MeCHx (k = 0.6 L2 mol−1 s−1).
Table 12. Literature Data from Experiments with [TMPCl]0>[TiCl4]0
A direct comparison of the temperature and concentration dependence measured in the two laboratories is not possible because of different absolute concentrations and an insufficient number of data points for any given condition. The best correlation from ref. 33 was found for [TiCl4]0 = 0.025 mol L−1, [TMPCl]0 = 0.025 mol L−1, and [IB]0 = 1 mol L−1,33 yielding ΔH = −28.9 kJ mol−1 with R2 = 0.99, as shown in Figure 14, which is somewhat higher than Paulo et al.'s29 ΔH = −26.4 kJ mol−1.
Figure 15 shows Arrhenius plots for kp,appA data from the two laboratories, regardless of the experimental conditions. Data from our and Storey's laboratory show identical temperature dependence trends with ΔH = −25.6 kJ mol−1 and R2 = 0.91 and 0.67, respectively. The evaluation of the same data, under the assumption of second-order TiCl4 dependence (kp,appB), yielded ΔH = −26.7 and −22.0 kJ mol−1, with R2 = 0.92 and 0.75, respectively. The data have large scatter because of the different reaction conditions, but the temperature dependence trends of the polymerization rate seem to be the same in both laboratories.
Table 13 lists data published for IB polymerizations initiated by TMPCl/TiCl4 for low [TMPCl]0/[TiCl4]0 ratios (<0.3) from Faust's laboratory,19, 65 evaluated with eqs 13 and 14, and the Arrhenius plot for k data is shown in Figure 16. Faust's data is linear with ΔH = −34.5 kJ mol−1 and R2 = 0.99 with both k and k. Most of our experiments (Table 13) were carried out at −80°C, with only two other points at −76.5°C and −50°C. However, our limited data (also shown in Fig. 16) trended with ΔH = −33.4 kJ mol−1, which is very close to Faust's value.
Table 13. Normalized Apparent Rate Constants of Propagation for Low [TMPCl]0/[TiCl4]0 Ratios
kapp (103 s−1)
k (L3mol−3 s−1)
k (L3mol−3 s−1)
[IB]0= 2.0 M [TMPCl]0= 0.002 M; [DtBP]= 0.006 M; Hx/MeCl = 60/40 v/v.
[IB]0= 1.54 M [TMPCl]0= 0.002 M; [DtBP]= 0.003 M; Hx/MeCl = 60/40 v/v.
[IB]0= 2.0 M [TMPCl]0= 0.004 M; [DtBP]= 0.007 M; Hx/MeCl = 60/40 v/v.
[IB]0= 2.0 M [TMPCl]0= 0.002 M; [DtBP]= 0.007 M; Hx/MeCl = 60/40 v/v.
[IB]0= 2.0 M [TMPCl]0= 0.016 M; [DtBP]= 0.007 M; Hx/MeCl = 60/40 v/v.
We argue that the apparent activation enthalpy values of ΔH = −26.329 (Fig. 13) and −28.9 kJ mol−1 (calculated from ref. 33; Fig. 14) are significantly different from ΔH = −34.5 kJ/mol19, 65 (Fig. 16). We interpret this as a clear indication of two simultaneous pathways, whose dominance changes with the reaction conditions.67
Table 14 summarizes literature data34, 64, 66 for systems with cumyl-based aromatic initiators, for low [I]0/[TiCl4]0 ratios, and Figure 17 shows the corresponding Arrhenius plot. ΔH = −38.4 kJ/mol (R2 = 0.96), considering both pathways (kappAB; ΔH = −40.1 kJ mol−1, R2 = 0.96 with only kappB), is higher than all of those previously mentioned for TMPCl, and this indicates that the initiating mechanism has a strong influence on the temperature dependence of living IB polymerizations.
Table 14. Normalized Apparent Rate Constants of Propagation for Low [I]0/[TiCl4]0 Ratiosa
In an interesting comparison, our analysis of recent data from Wu's lab68 indicates that the presence of dimethylacetamide (DMA), a strong electron-pair donor, seems to have a profound influence on the temperature dependence of living IB polymerization. In the absence of DMA, uncontrolled polymerization was reported, but DMA mediated the living conditions. The data were evaluated with eqs 13 and 14, and the Arrhenius plot for kp,appB is shown in Figure 18. Both equations yielded ΔH = −12.0 kJ mol−1 with R2 = 0.96. The ΔH value calculated for this case is much lower than in all the other cases discussed previously. This supports earlier suggestions that DMA is not merely a proton trap in living IB polymerizations.
In summary, an evaluation of new and previously published experimental data for living IB polymerization was used to illustrate differences in the apparent negative activation enthalpies of propagation in systems with high and low initiator/TiCl4 ratios. The large differences seem to support the existence of competitive pathways in living IB polymerizations coinitiated by TiCl4. DMA, a strong donor, decreased ΔH significantly, and this indicates that donors are not merely proton scavengers in living IB polymerizations.
Recently evidence has been presented that first- and second-order pathways operate simultaneously in carbocationic St polymerizations initiated by TMPCl/TiCl4 as well.69 This proposal requires further investigation.
This article provides a critical review of our current understanding of the kinetics and mechanisms of carbocationic polymerizations. It is proposed that the discrepancy in the propagation rate constants reported for various carbocationic polymerizations is due to different mechanistic interpretations and assumptions. In the case study of TMS presented in this article, the simulated values for the propagation rate constant are equal to 1.35 × 104 and 1.01 × 107 L mol−1 s−1 when two different kinetic mechanisms are used. We found that the higher value agrees with Mayr's LFER. This case study underlines the importance of the method of rate constant measurement, suggesting that true rate constants can be obtained only from direct competition experiments or from kinetic interpretation based on independently proven mechanisms. A critical analysis of current mechanistic interpretations of living IB polymerizations based on activation enthalpy also shows a significant range from −12 to −40 kJ mol−1. This underlines the complexity of carbocationic polymerizations. Further study will be needed to reveal their elementary reactions, which consequently will lead us to the true rate constants.
Financial support by the Natural Sciences and Engineering Research Council of Canada, Lanxess, Inc. (formerly the Rubber Division of Bayer, Inc.), American Chemical Society Petroleum Research Fund 37143-SE, and the contributions of Dr. Y. Kwon and Dr. Chattopadhyay are acknowledged.
JUDIT E. PUSKAS
Dr. Judit E. Puskas holds the Lanxess (previously Bayer) Chair in Polymer Science at the College of Polymer Science and Polymer Engineering of the University of Akron. She is a regional editor and member of the advisory board of European Polymer Journal and a member of IUPAC Working Party IV.2.1 (“Structure–Property Relationships of Commercial Polymers”). Puskas has been published in more than 200 publications, is an inventor or coinventor of 16 U.S. patents (three of which are licensed), and has been the chair or organizer of a number of international conferences. She is the recipient of several awards, including the Bayer/Natural Science and Engineering Research Council of Canada Industrial Research Chair in 1998, the 1999 Professional Engineers of Ontario Medal in Research & Development, the 2000 Premier's Research Excellence Award (Ontario), and the 2004 Mercator Professorship Award from the German Research Foundation. Her present interests include living carbocationic polymerization, polymerization mechanisms and kinetics, thermoplastic elastomers, and polymer structure–property relationships, with a focus on the biomedical applications of polymers and the combination of biopolymers and synthetic polymers.
KIMBERLEY B. MCAULEY
Dr. Kimberley B. McAuley is a professor at Queen's University, where she chairs the Engineering Division of the School of Graduate Studies and Research. McAuley has coauthored more than 50 refereed journal publications and has been an organizing committee member and cochair for international conferences on polymer reaction engineering and process systems engineering. Her research interests include the mathematical modeling of chemical reactors and polymerization mechanisms and kinetics. She is the recipient of the Governor General's Gold Medal, the Natural Science and Engineering Research Council of Canada Women's Faculty Award, the Premier's Research Excellence Award, and three teaching awards.
Dr. Gabor Kaszas is Principal Scientist of Research & Development at Lanxess, Inc. (formerly the Rubber Division of Bayer, Inc., Canada). He has been with the company since 1989. He is involved in product and process development and serves as an advisor to management and young scientists. He has 16 U.S. patents and more than 100 publications. His work is cited in Polymer Handbook. He studies with Professor Kennedy in Akron and with Professors Kelen and Tüdös in Hungary. At Lanxess, he has mentored several co-op students and young professionals. His current interests include process simulation, rubber structure–property relationships, and processing.