The ROMP copolymerization of NBE with CP was conducted in CH
2Cl
2 solutions at 0 °C (
Scheme S3). The copolymerizations were allowed to proceed to low conversion (less than 20%, except for sample 80/20 for which the conversion was 39%), in all cases, satisfying the differential copolymerization equation. The molecular characteristics of the samples are given in
Table 1. Different copolymers are symbolized by the various feed molar ratios of the monomers; for example, sample 20/80 indicates the copolymer for the synthesis where 20% NBE and 80% CP were employed as the molar feed composition. The molecular weights were measured by SEC using a calibration curve constructed by polystyrene standards. It is obvious that rather high molecular weight copolymers of relatively broad molecular weight distributions were obtained in agreement with previous results describing the homopolymerization of NBE and CP under similar experimental conditions [
41]. The SEC traces of the copolymers and a characteristic
1H-NMR spectrum are given in the SI (
Figures S1 and S2).
2.1.1. Monomer Reactivity Ratios and Statistical Analysis of the Copolymers
The monomer reactivity ratios were determined using the Finemann-Ross (FR) [
42], inverted Finemann-Ross (IFR) [
42], and Kelen-Tüdos (KT) [
43] graphical methods. A computer program, called COPOINT, was also employed [
44]. According to the Finemann-Ross method, the monomer reactivity ratios can be obtained by the equation:
where the reactivity ratios, r
NBE and r
CP correspond to the NBE and CP monomers, respectively. The parameters G and H are defined as follows:
with
M
NBE and M
CP are the monomer molar compositions in feed and dM
NBE and dM
CP the copolymer molar compositions.
The inverted Finemann-Ross method is based on the equation:
The plots of the G vs. H values and the G/H vs. 1/H values yield the reactivity ratios rNBE and rCP from the intercept and the slope of the graphs.
Alternatively, the reactivity ratios can be obtained using the Kelen-Tüdos method which is based on the equation:
where η and ξ are functions of the parameters G and H:
and α a constant which is equal to (H
max·H
min)
1/2, H
max, H
min being the maximum and the minimum H values, respectively, from the series of measurements. From the linear plot of η as a function of ξ, the values of η for ξ = 0 and ξ = 1 are used to calculate the reactivity ratios according to the equations:
The copolymerization data for all samples are provided in
Table 2. The sample 80/20 was not taken into account for the calculation of the reactivity ratios, since the conversion of the polymerization reaction was much higher than the other samples, thus deviating from the copolymerization equation. The FR graphical plot is given in
Figure 1, whereas the other plots concerning the methods previously reported are given in
Figures S3 and S4 in the SI, whereas the reactivity ratios are summarized in
Table 3. All plots for the different graphical methods were linear, thus indicating that these reactions follow conventional copolymerization kinetics and that the reactivity of the active polymerization chain end is determined only by the terminal monomer unit.
The computer program COPOINT evaluates the copolymerization parameters using comonomer/copolymer composition data as obtained from copolymerization experiments with finite monomer conversion. Although the mathematical treatment can be applied up to full monomer conversion, it is recommended not to exceed 20–30 mol %. COPOINT numerically integrates a given copolymerization equation in its differential from. The copolymerization parameters can be obtained by minimizing the sum of square differences between measured and calculated polymer compositions. Errors of the fitted parameters are estimated from the statistical error of the sum of square differences, as well as from a quadratic approximation of this sum in the vicinity of the optimized values of the copolymerization parameters.
Table 2.
Copolymerization data for the copolymers.
Table 2.
Copolymerization data for the copolymers.
Sample | X | Y | H | G | η | ξ |
---|
20/80 | 0.277 | 0.960 | 0.080 | −0.011 | −0.030 | 0.212 |
40/60 | 0.675 | 1.325 | 0.344 | 0.166 | 0.259 | 0.538 |
50/50 | 0.946 | 1.703 | 0.525 | 0.390 | 0.475 | 0.640 |
60/40 | 1.491 | 2.030 | 1.095 | 0.757 | 0.544 | 0.788 |
α = 0.295 | | | | | | |
20/80P | 0.250 | 1.000 | 0.062 | 0 | 0 | 0.199 |
40/60P | 0.667 | 1.631 | 0.272 | 0.258 | 0.493 | 0.520 |
50/50P | 1.000 | 1.778 | 0.562 | 0.437 | 0.537 | 0.691 |
60/40P | 1.500 | 2.226 | 1.011 | 0.826 | 0.654 | 0.801 |
α = 0.251 | | | | | | |
Figure 1.
FR plot of the statistical copolymers.
Figure 1.
FR plot of the statistical copolymers.
Table 3.
Reactivity ratios.
Table 3.
Reactivity ratios.
Method | rNBE | rCP | rNBE | rCP |
---|
in the Absence of PPh3 | in the Presence of PPh3 |
---|
F-R | 0.76 ± 0.06 | 0.06 ± 0.003 | 0.84 ± 0.06 | 0.02 ± 0.002 |
i F-R | 0.78 ± 0.07 | 0.07 ± 0.004 | 0.96 ± 0.12 | 0.06 ± 0.004 |
KT | 0.82 ± 0.10 | 0.07 ± 0.005 | 0.87 ± 0.07 | 0.02 ± 0.004 |
COPOINT | 0.77 ± 0.14 | 0.02 ± 0.001 | 0.96 ± 0.23 | 0.03 ± 0.001 |
Other catalytic systems a |
IrCl3/1,5-COD | 5.6 | 0.07 | | |
WCl6/EtAlCl2 | 13 | 0.32 | | |
WCl6/Ph4Sn | 2.6 | 0.55 | | |
WCl6/Bu4Sn | 12 | 0.27 | | |
WCl6/Ph4Sn/EAc | 2.2 | 0.62 | | |
It is obvious that all methods provide similar data concerning the reactivity ratios for both monomers. According to the data obtained by the Kelen-Tüdos method r
NBE = 0.82 and r
CP = 0.07. These results imply that the rate of NBE incorporation into the copolymer structure is much higher than the rate of CP incorporation and is in agreement with the much higher rate of NBE homopolymerization compared to the rate of CP homopolymerization in ROMP procedures [
45,
46,
47,
48,
49,
50]. This case is referred to as a non-ideal non-azeotropic copolymerization [
51]. Previous studies employing catalysts based on Ir and W provided similar results in terms of the reactivity ratios [
34,
35,
36]. However, the difference in reactivity was even higher than in the present study. Grubbs’ catalysts in the presence of MoCl
5 or WCl
6, RuCl
3-phenol and modified Grubbs’ catalysts have been previously employed to provide alternating PNBE/PCP copolymers [
37,
38,
39,
40]. This is direct evidence that the catalytic system greatly influences the reactivity ratios of the two monomers.
The statistical distribution of the dyad monomer sequences M
NBE-M
NBE, M
CP-M
CP, and M
NBE-M
CP were calculated using the method proposed by Igarashi [
52]:
where X, Y, and Z are the mole fractions of the M
NBE-M
NBE, M
CP-M
CP, and M
NBE-M
CP dyads in the copolymer, respectively, and Φ
NBE corresponds to the NBE mole fractions in the copolymer. Mean sequence lengths μ
NBE and μ
VNBE were also calculated using the following equations [
53]:
The data are summarized in
Table 4 (dyad monomer sequences X, Y, Z and mean sequence length). The variation of the dyad fractions with the NBE mole fraction in the copolymers is displayed in
Supplementary Figure S5 of the SI. These results provide a clear picture of the copolymer structures as well as the distribution of the monomer units in the copolymer chain. It is obvious that the mole fraction of the M
CP-M
CP dyads is the minority component for almost all copolymer compositions. On the contrary, the mole fraction of the M
NBE-M
NBE dyads is very high for all the samples. This is direct evidence of the huge difference of the two monomer reactivity ratio values.
Table 4.
Dyad monomer sequences X = MNBE-MNBE, Y = MCP-MCP, Z = MNBE-MCP dyads and mean sequence lengths.
Table 4.
Dyad monomer sequences X = MNBE-MNBE, Y = MCP-MCP, Z = MNBE-MCP dyads and mean sequence lengths.
Sample | X | Y | Z | μNBE | µCP |
---|
20/80 | 0.089 | 0.109 | 0.801 | 1.79 | 1.07 |
40/60 | 0.186 | 0.046 | 0.769 | 2.09 | 1.05 |
50/50 | 0.284 | 0.024 | 0.692 | 2.40 | 1.04 |
60/40 | 0.356 | 0.016 | 0.628 | 2.66 | 1.03 |
20/80P | 0.058 | 0.058 | 0.883 | 1.87 | 1.02 |
40/60P | 0.249 | 0.009 | 0.741 | 2.42 | 1.01 |
50/50P | 0.287 | 0.007 | 0.705 | 2.55 | 1.01 |
60/40P | 0.384 | 0.004 | 0.611 | 2.94 | 1.01 |
2.1.2. Kinetics of the Thermal Decomposition of the Statistical Copolymers
The kinetics of the thermal decomposition of the statistical copolymers was studied by TGA measurements. The activation energy, E, of mass loss upon heating was calculated using the isoconversional Ozawa-Flynn-Wall (OFW) [
54,
55,
56] and Kissinger [
57,
58] methods. The OFW approach is a “model free” method, which assumes that the conversion function F(α), where α is the conversion, does not change with the alteration of the heating rate, β, for all values of α. The OFW method involves the measuring of the temperatures corresponding to fixed values of α from experiments at different heating rates β. Therefore, plotting lnβ
vs. 1/T in the form of
should give straight lines with slopes directly proportional to the activation energy, where
T is the absolute temperature,
A is the pre-exponential factor (min
−1), and
R is the gas constant (8.314 J/K·mol). If the determined activation energy is the same for the various values of α, then the existence of a single-step degradation reaction can be concluded with certainty. The OFW method is the most useful method for the kinetic interpretation of thermogravimetric data, obtained from complex processes like the thermal degradation of polymers. It can be applied without the knowledge of the reaction order.
The activation energy E was also calculated from plots of the logarithm of the heating rate over the squared temperature at the maximum reaction rate, T
p2,
vs. 1/T
p in constant heating experiments, according to the Kissinger method using the equation:
where T
p and α
p are the absolute temperature and the conversion at the maximum weight-loss and n is the reaction order. The E values can be calculated from the slope of the plots of ln(β/T
p2) versus 1/T
p.
The statistical copolymers were thermally degraded at different heating rates. The detailed results are given in the Supporting Information Section (
Figures S6–S8, Tables S1–S6), whereas an example of the recorded thermograms under different heating rates is displayed in
Figure 2. Differential thermogravimetry, DTG, showed that a single decomposition peak appears for both homopolymers. The thermal decomposition of PCP starts and is completed at lower temperatures than that of PNBE. However, the temperature at the maximum rate of decomposition of PCP is higher than that of PNBE. These results imply that the mechanism of decomposition is different between the two homopolymers reflecting the differences in their chemical structure. DTG revealed that a single decomposition peak appears for the statistical copolymers as well. The temperature at the maximum rate of their decomposition lies between the values of the respective homopolymers.
The linearity of the OFW diagrams in a broad range of conversions proves that it is an efficient method for the analysis of the thermal decomposition of the copolymers. A characteristic example is given in
Figure 3. More examples are incorporated in the SI Section (
Supplementary Figures S9 and S10). However, deviations from the linearity were observed in very low or very high conversions, since these results refer to the decomposition of parts of the macromolecules that are not representative of the overall copolymeric chains, due to the statistical character of the distribution of the different monomer units.
Figure 2.
Derivative weight loss with temperature for the sample 50/50 under different heating rates.
Figure 2.
Derivative weight loss with temperature for the sample 50/50 under different heating rates.
Figure 3.
Ozawa-Flynn-Wall plots lnβ vs. 1/T for the sample 20/80 at different heating rates.
Figure 3.
Ozawa-Flynn-Wall plots lnβ vs. 1/T for the sample 20/80 at different heating rates.
The activation energy values of the PCP homopolymer decrease upon increasing the decomposition conversion, whereas the opposite behavior was obtained for the PNBE homopolymer due to the different decomposition mechanism of the two samples. The activation energy values of the copolymers change considerably upon changing the decomposition conversion, indicating that the decomposition mechanism is complex during the thermal decomposition. This behavior resembles that of the PNBE homopolymer, due to the very high content in NBE units along the copolymer chains, which reflects the much higher reactivity ratio of NBE, compared to that of CP. The data from the OFW diagrams are provided in
Table 5. The observed relatively-good agreement of the Ea values obtained between the OFW and the Kissinger methods can be attributed to the same effect. The Ea values obtained from the Kissinger method are given in
Table 6, whereas characteristic plots are provided in
Figures S11–S14 in the SI.
Table 5.
Activation energies for the homopolymers and the statistical copolymers from the OFW method for different degrees of decomposition.
Table 5.
Activation energies for the homopolymers and the statistical copolymers from the OFW method for different degrees of decomposition.
Weight Loss | PCP | PNBE | 80/20 | 60/40 | 50/50 | 40/60 | 20/80 | 20/80P | 40/60P | 50/50P | 60/40P | 80/20P |
---|
10 | 340.46 | - | 36.681 | 105.75 | - | 174.59 | - | 191.26 | 105.10 | - | - | - |
20 | 326.49 | - | 64.583 | 157.38 | - | 201.36 | 225.14 | 239.50 | 188.00 | 188.20 | - | - |
30 | 302.21 | - | 117.89 | 252.66 | 17.351 | 273.86 | 267.63 | 243.78 | 211.01 | 210.91 | 176.30 | 176.66 |
40 | 289.24 | 296.81 | 164.37 | 269.96 | 249.50 | 290.49 | 274.11 | 255.06 | 226.03 | 225.70 | 218.32 | 225.88 |
50 | 275.61 | 377.79 | 206.77 | 273.53 | 328.57 | 251.33 | 279.77 | 253.71 | 233.46 | 233.52 | 242.20 | 231.98 |
60 | 266.88 | 332.89 | 253.41 | 268.46 | 336.38 | 205.11 | 281.26 | 254.62 | 238.20 | 238.22 | 251.72 | 262.36 |
70 | 260.73 | 308.28 | 316.18 | 267.63 | 320.26 | 43.964 | 284.09 | 254.25 | 239.55 | 235.10 | 255.00 | 267.26 |
80 | 257.65 | - | 287.08 | 300.30 | 283.09 | 32.316 | 290.99 | 253.87 | 242.52 | 242.60 | 254.75 | 274.41 |
90 | 255.90 | - | 225.23 | - | 243.77 | - | 318.92 | 256.23 | 250.26 | 250.29 | 187.75 | 267.26 |
Table 6.
Activation energies for the homopolymers and the statistical copolymers from the Kissinger method.
Table 6.
Activation energies for the homopolymers and the statistical copolymers from the Kissinger method.
Sample | Ea |
---|
PCP | 227.24 |
PNBE | 247.11 |
20/80 | 190.30 |
40/60 | 214.21 |
50/50 | 316.54 |
60/40 | 214.49 |
80/20 | 275.64 |
20/80P | 253.69 |
40/60P | 249.55 |
50/50P | 243.62 |
60/40P | 236.62 |
80/20P | 259.13 |