Determination of homopolymerization kinetics and copolymerization with methyl methacrylate of diethyl 9-(methacryloyloxy)-2-oxo-nonylphosphonate, 9-(methacryloyloxy)-2-oxo-nonylphosphonic acid and diethyl 9-(methacryloyloxy)-nonylphosphonate

3.1.1 Conversion-time dependences for diethyl phosphonate monomer M1

Monomer M1, was polymerized in methanol, at 60°C, in three different concentrations – 0.25, 0.5, and 0.75 mol/l. AIBN (0.025 mol/l) was used as an initiator. Conversion was followed by FTIR spectroscopic measurements. After polymerization, methanol was evaporated and the residual polymer–monomer mixture was dissolved in 1.5 ml of chloroform. The changes of the part of the FTIR spectra are shown in Figure 1.

Figure 1:

Changes of the FTIR spectra of M1 during homopolymerization; [M1]=0.5 mol/l, [AIBN]=0.025 mol/l, MeOH, T=60°C, 1.5 ml CHCl₃, NaCl, d=0.18 cm.

Conversions were calculated from the height as well as from integrals of the relatively broad peak at 1637 cm⁻¹ which belongs to the symmetric vibration of the double bond.

The effect of the monomer concentration on the course of polymerization is shown in Figure 2 in the form of conversion-time dependences for 0.25, 0.5, and 0.75 mol/l monomer concentrations. The polymerization is very fast from the beginning without any induction period. A reflection of this are the high initial polymerization rates. The following values of Rp were obtained. For concentration of M1 of 0.25 mol/l Rp is 3.33×10⁻⁵ mol/l·s, for 0.5 mol/l Rp=7.22×10⁻⁵ mol/l·s and for 0.75 mol/l Rp=14.4×10⁻⁵ mol/l·s.

Figure 2:

Monomer conversion of M1 during homopolymerization.

[AIBN]=0.025 mol/l, T=60°C.

By plotting ln Rp against ln [M1] (Figure 3) the intensity exponent to the monomer concentration was determined. The experimental points are satisfactorily correlated with the line and the slope (tga) 1.31 is a little bit higher than the theoretical value of 1. The kinetic theory of the ideal free radical polymerization predicts Rp=K [I]^0.5 [M]¹. Nevertheless, if we admit that the value 1.31 lies in experimental uncertainty we should suppose that termination depends on length of the growing polymer chains or does not proceed solely by the mutual interaction of polymer radicals (20). The initiator primary radicals probably contribute to radical termination.

Figure 3:

Dependence of M1 initial polymerization rates on monomer starting concentrations in methanol at 60°C; [AIBN]=0.025 mol/l.

The polymerization of M1 was subsequently performed at 60°C using three different concentrations of AIBN. Similarly as in a previous case the polymerization rates Rp were calculated. Then initial polymerization rates Rp at 60°C in dependence on 0.025, 0.05, 0.075 [mol/l] of AIBN at 0.5 mol/l monomer concentration confirm nearly ideal free radical polymerization behavior of the M1 monomer. The logarithmic dependence of the Rp on AIBN concentration is linear with the slope 0.42. The coefficient is a little lower than the predicted value 0.5 but the deviation is small enough to accept typical behavior for free radical polymerization kinetics with prevailing termination of growing polymer radicals, mainly by disproportionation beside the recombination. Nevertheless the participation of the termination of primary radicals cannot be excluded.

The last studied dependency was the effect of temperature on the course of M1 homopolymerization. The M1 polymerization at 40, 50 and 60°C (0.025 mol/l AIBN and 0.5 mol/l of M1) showed that conversion started from the beginning of polymerization for the temperature at 50 and 60°C. There was short induction period for the polymerization at 40°C. It is likely that the temperature was not enough to produce sufficient concentration of initiating radicals to eliminate the traces of stabilizer and start polymerization from the beginning. The natural logarithm of the effective reaction rate Rp is plotted versus reciprocal absolute temperature in Figure S1 (Supplementary section) indicating an Arrhenius temperature dependence. The activation energy should be differentiated as a statistical quantity from the threshold energy, the minimum energy that must be attained by a pair of colliding particles for a given elementary reaction to occur. An apparent obtained activation energy of 86.2 kJ/mol is consistent with literature reports for bulk polymerization of MMA ranging from 78 to 86 kJ/mol (21), (22), (23), (24), (25). It means that the presence of a long alkyl chain and a keto group in the β-position, as well as the nature of terminal functional group, has no meaningful effect on the monomer reactivity and polymerization mechanism.

The lifetime of a growing radical is 1 s or less, and this period is negligible compared to the total reaction time. Polymer chain lengths result from a competition between the rate of propagation and the rate of termination. High molar-mass polymer is generated from the start of the polymerization. The number-average molecular weights (M_n) change during the polymerization. M_n decreases as the polymerization proceeds, as monomer concentration decreases, whereas the concentration of grooving radicals R remains essentially constant.

The rate of monomer consumption is faster than initiator primary radical production and M_n decreases with conversion, leading to an increase in dispersity as is shown in Table 2 for three runs of polymerization with different monomer concentrations.

3.1.2 Conversion-time dependences for phosphonic acid monomer M2

The main structural difference between previous monomers M1 and M2 is that while M1 is a phosphonate M2 is corresponding free phosphonic acid having a much more polar phosphonic acid group. Concerning the solubility of both monomers they are soluble in many solvents. The is a remarkable difference in the solubility of the homopolymers. While the homopolymer of M1 was soluble in chloroform, acetone and THF, homopolymer of M2 was soluble only in methanol and water. Hence, after polymerization the monomer conversion in the reaction mixture was calculated from the concentration decrease of double bonds after dilution in methanol by FTIR spectroscopy. Methanol is not typical solvent for FTIR spectroscopic measurements but fortunately in the region of interest (1800–1600 cm⁻¹) there is a window sufficient for FTIR spectroscopic measurements. Peak intensities collected directly from original spectra were exactly the same as those obtained from the spectra after subtraction of methanol. ATR-FTIR spectroscopic measurements were applied after methanol evaporation for all samples too. Both methods provided the same results.

The effect of the monomer concentration on the course of polymerization is shown in Figure S2 (Supplementary section) in the form of conversion-time dependences for 0.25, 0.5, and 0.75 mol/l of M2 concentrations. As in the case of M1, the polymerization under these conditions is very fast from the beginning without any induction period. The following values of Rp were obtained: for a concentration of M2 of 0.25 mol/l Rp was 3.34×10⁻⁵ mol/l·s, for 0.5 mol/l Rp=6.25×10⁻⁵ mol/l·s and for 0.75 mol/l Rp=10.45×10⁻⁵ mol/l·s. For the first two concentrations of M2 the rates of homopolymerization are very similar as for homopolymerization of M1. Only the rate for the highest concentration (0.75 mol/l) Rp=10.45 mol/l·s is lower than for M1 (Rp=14.4×10⁻⁵ mol/l·s). Plotting ln Rp against ln concentration of M2 (Figure S3 in Supplementary section) the intensity exponent to monomer concentration was determined. The experimental points are satisfactorily correlated with a line and the obtained slope 1.05 is almost exactly the same as the theoretical value of 1.

The effect of initiator AIBN concentration on the conversion curves for M2 is shown in Figure S4 (Supplementary section). Polymerization rates Rp at 60°C in dependence on 0.025, 0.05, 0.075 [mol/l] of AIBN at 0.5 mol/l monomer concentrations confirms nearly ideal free radical polymerization behavior for M2. The following values of Rp were obtained. For concentration of AIBN of 0.025 mol/l Rp was 7.41×10⁻⁵ mol/l·s, for 0.05 mol/l Rp=10.4×10⁻⁵ mol/l·s and for 0.075 mol/l Rp=14.6×10⁻⁵ mol/l·s. The logarithmic dependence of the Rp on the AIBN concentration (Figure S5 in Supplementary section) is linear with the slope 0.60, which is almost exactly the same as the theoretical value of 0.5 for typical free radical polymerization.

The dependency of temperature on the course of M2 homopolymerization was the last studied effect. The courses of M2 polymerization at 45, 55 and 65°C (0.025 mol/l AIBN and 0.5 mol/l monomer M2) are shown in Figure S6 (Supplementary section). As in the case of M1, conversion starts from beginning of polymerization for higher temperatures 55 and 65°C and there is also a short induction period for the polymerization at 45°C. It is likely that traces of impurities or stabilizers preferentially react with radicals produced from the initiator. The ln Rp dependence on reciprocal temperature 1/K (Figure S7 in Supplementary section), gives straight line with slope that relates to the polymerization overall activation energy Ea=86.4 kJ/mol.

3.1.3 Conversion-time dependences for the phosphonate M3

M3 is similar to M1 is diethyl phosphonate. Contrary to M1, M2 does not contain a carbonyl group in the β-position in respect to the phosphonate group, only a long alkyl chain is present. As regards the solubility of this monomer and homopolymer, the situation is practically the same as for M1 and the same procedures as for M1 were used for conversion evaluation.

The effect of the monomer concentration on the course of polymerization is shown in Figure S8 (Supplementary section) in the form of conversion-time dependences for 0.25, 0.5, and 0.75 mol/l of M3 concentrations. As in the case of M1, the polymerization is very fast from the beginning without any induction period. The following values of Rp were obtained: for concentration of M3 of 0.25 mol/l Rp was 3.11×10⁻⁵ mol/l·s, for 0.5 mol/l Rp=7.22×10⁻⁵ mol/l·s and for 0.75 mol/l Rp=12.2×10⁻⁵ mol/l·s. For first two concentrations of M3 the rates of homopoly-merization are very similar to the homopolymerization of M1. Only the rate for concentration 0.75 mol/l is a little bit lower for M3 (Rp=12.2×10⁻⁵ mol/l·s) than for M1 (Rp=14.4×10⁻⁵ mol/l·s).

But generally we can conclude that the carbonyl in the β-position in respect of the phosponic group has no meaningful effect on the rate of homopolymerization. Plotting ln Rp against ln concentration of M3 (Figure S9 in Supplementary section) the intensity exponent to the monomer concentration was determined and the slope of 1.24 points on termination rate dependence on the chain length.

The effect of initiator AIBN concentration on the conversion curves are shown in Figure S10 (Supplementary section). Polymerization rates Rp at 60°C in dependence on 0.025, 0.05, 0.075 [mol/l] of AIBN at 0.5 mol/l M3 concentrations confirm a nearly ideal free radical polymerization behavior for monomer M3.

The logarithmic dependence of the Rp on AIBN concentration (Figure S11 in Supplementary section) is linear with the slope 0.53. The coefficient is also a little higher than predicted value 0.5 but as in the previous case the deviation is small enough to accept typical free radical polymerization kinetic behavior with prevailing termination of growing polymer radicals mainly by disproportionation.

Finally, the dependency of temperature on the course of M3 homopolymerization was studied at 40, 50 and 60°C ([AIBN]=0.025 mol/l, [M3]=0.5 mol/l) and are shown in Figure S12 (Supplementary section). A short induction period for the polymerization at 40°C was observed as in the case of monomers M1 and M2. The ln Rp dependence on the reciprocal temperature 1/K (Figure S13 in the Supplementary section), gives a straight line with slope that relates to the polymerization overall activation energy Ea=77.6 kJ/mol.

4.1.1 Copolymerization of MMA with M1

Both monomers are methacrylates with different substituents on the ester bond: a methyl group in MMA and a 2-oxo-nonyl-phosphonate in M1. The changes in their ¹H-NMR spectra during copolymerization can be seen on Figure 4 (for M1:MMA molar ratio 3:1) and on Figure S14 (Supplementary section, for molar ratio M1:MMA=1:2.9). The two non-equivalent olefinic hydrogens from MMA as well as from M1 represent two singlets and possess exactly the same chemical shifts at 5.58 and 6.06 ppm, respectively. Only the total conversion can be calculated on the base of these peaks. The methyl ester group from MMA appears as a sharp singlet at 3.71 ppm, while this group in copolymer appears at 3.6 ppm as a broader singlet. It is a bit more difficult for co-monomer M1. The signals for six protons consisting from two protons of the CO-O-CH₂- group as well as for four protons of two P-O-CH₂-groups in monomer M1 appear at 4.15 ppm as overlapping multiplets. In the polymer we can see only the new peak from the two protons of CO-O-CH₂- as the broad singlet at 3.95 ppm. The signal of four protons of two P-O-CH₂- groups is not much affected by the polymerization process and stay at the same position, which brings some difficulties for calculation. There are another couple of peaks coming from methylene -CH₂- group next to the β-carbonyl in the region 2.5–2.7 ppm. In the monomer it appears in the form of a triplet at 2.6 ppm and during polymerization a new peak is growing at 2.64 ppm. But as can be seen in Figure 4 for the ratio M1:MMA=3:1, there is an overlap of these two peaks and quantification from integration is questionable. Using of the four earlier mentioned sufficiently separated peaks allows us to follow the kinetics of copolymerizations as well as the composition of copolymers.

Figure 4:

Details of the ¹H-NMR spectra of the copolymerization of M1 with MMA (ratio M1: MMA=3:1) at various time, deuterated methanol, T=55°C.

Total monomer concentration=0.5 mol/l, [AIBN]=0.025 mol/l.

The integral of these peaks is proportional to the concentration of monomers during the copolymerization and they were evaluated for the time conversion plot as well as for the feed composition at the beginning as well as during the copolymerization.

Figure 5A shows a typical time-conversion plot for the short time scale of polymerization. The M1 is converted a little bit faster than MMA. This also follows from the dependence of comonomer ratio M1:MMA in feed versus time (Figure 5C). This ratio is slowly decreasing with polymerization time. Starting from an initial ratio 3.0, it reaches a value 2.1 after 180 min of polymerization. In this stage of copolymerization at conversion ca 60% the content of MMA in the rest of monomer mixture is higher than at the beginning of polymerization. The courses of polymerization at the long time scale shown in Figure 5B indicate that the conversion of M1 after 10 h of polymerization is almost 100%, while conversion of MMA is only 85%.

Figure 5:

Monomer conversions of M1, MMA and total conversion during the copolymerization of mixture M1:MMA=3:1; (A) short time scale (B) long time scale; (C) comonomer ratio M1:MMA in feed versus time.

A very similar situation was in the case of molar ratio M1:MMA=1:2.9 – Figure S15a (Supplementary section). Only the difference between conversion of M1 and MMA was much smaller. Similarly the changes of feed ratio shown in Figure S15b (Supplementary section) are less marked as in the previous case. The excess of MMA could be the reason for this distortion as will be seen from the copolymerization parameters.

The determination of reactivity ratio in the Jaacks method is simplified by using of an excess of one monomer (M1=M₁) at a time that is large enough that the copolymers will have a very small content of the other monomer (MMA=M₂). In this case chain propagation takes place almost exclusively by the addition to a polymer radical with a terminal M₁ –unit (P₁*) and monomer consumption by the propagation of P₂* may be neglected (8). The slope of dependency of the rate of M1 consumption against the rate of MMA consumption gives the reactivity ratio r_M1 as is shown in Figure S16 (Supplementary section). The reactivity ratio r_MMA was obtained from copolymerization with an excess of MMA and the Jacks plot is shown in Figure S17 (Supplementary section). The received copolymerization parameters were r_M1=1.31 and r_MMA=1.01.

The Fineman-Ross method has been applied for numerous systems. This method is a linearized graph of F=[M₁]/[M₂] versus f=[m₁]/[m₂]. [M₁]/[M₂] is the molar ratio of monomer units in the feed, [m₁]/[m₂] is the molar ratio of monomer units in the copolymer (9). The Fineman-Ross plot graphs F(f–1)/f versus F²/f and for the copolymerization of M1 with MMA is shown in Figure S18 (Supplementary section). The received copolymerization parameters were r_M1=1.28 and r_MMA=1.08. The value is a little lower than the values obtained from the Jaacks method for M1 (r_M1=1.31) and higher in MMA r_MMA=1.08 when compared with r_MMA=1.01 but the differences are very small especially for M1.

The last method for evaluation of the copolymerization parameters is the nonlinear least square method. The copolymerization diagram plots the instantaneous copolymer composition F as a function of the initial feed composition f (t=0). The variables are defined as shown in following equations:

f1=1−f2=[M1][M1]+[M2]

F1=1−F2=r1f12+f1f2r1f12+2f1f2+r2f22

The data from the kinetic experiments can be fit to these equations with the nonlinear least square method (10). The fit is shown in Figure S19 (Supplementary section) and the resulting r parameters are in very good agreement with those values from the Fineman-Ross method: r_M1=1.31 and r_MMA=1.1. Both parameters are bigger than 1. It means that grooving macro radical with the ultimate M1 structure prefers reaction with M1 and vice versa. However, this preference is minor in MMA. Small heterogeneous samples are expected from the free radical copolymerization of M1 with MMA. Reactivity ratios determined by different method are summarized in Table 3.

4.1.2 Copolymerization of MMA with M2

Contrary to previous M1 cases the phosphonic acid M2 does not contain two P-O-CH₂- groups from diethylester so in the NMR spectra there is only a triplet at 4.15 ppm coming from the CO-O-CH₂- group of M2 (Figure 6). This makes the calculation for the conversion of the monomer much clearer. As in the previous case there are two non-equivalent olefinic hydrogens from MMA as well as from M2 which represent two singlets and possess exactly the same chemical shifts at 5.58 and 6.06 ppm for both co-monomers, respectively.

Figure 6:

Details of the ¹H-NMR spectra of the copolymerization of M2 with MMA at various time, deuterated methanol, T=55°C. Molar ratio M2:MMA=1:2.9=0.34, total monomers concentration=0.5 mol/l, AIBN=0.025 mol/l.

So they are useless for copolymerization monitoring. Only the total conversion can be calculated on the base of these peaks. The methyl ester group from MMA appears as a sharp singlet at 3.72 ppm while this group in the copolymer appears at 3.63 ppm as a broader singlet. Similarly for M2, the triplet of the O-CH₂- group in the monomer appears at 4.14 ppm while in the polymer it changes to a broad singlet at 3.95 ppm. These four sufficiently separated peaks allow us to follow the kinetics of copolymerizations as well as the composition of copolymers. The changes of this part of the ¹H-NMR spectra during copolymerization for this pair at molar ratio M2:MMA=1:2.9 are shown in Figure 6.

Contrary to the previous case, where the conversion of M1 was faster than conversion of MMA, in this case (as follows from Figure S20 in Supplementary section) the conversion of MMA is very similar to the conversion of M2. As in the previous case it is the copolymerization of two mathacrylates with different ester groups. The methyl group in MMA as well as the long alkyl chain containing free phosphonic acid seems to have the same electronic effect on the vinyl groups of comonomers. The reactivity of both possible grooving radicals with both comonomers is the same. Consequently, the comonomer ratio of M2:MMA is almost constant during the copolymerization as it is shown in Figure S20b; in the supplementary section for starting ratio M2:MMA=0.345. This is confirmed by the obtained copolymerization parameters using the Jaacks method (Figure S21 in Supplementary section). In this case there is excess of MMA and copolymerization parameter for MMA is r_MMA=0.90.

The same behavior has been obtained for the ratio M2:MMA=5.9:1. Time conversion dependence (shown in Figure S22a; in the supplementary section) is a little bit different in comparison with the course for the ratio M2:MMA=1:2.9 (shown in Figure S20a; in the supplementary section). In this case it is the typical auto-acceleration process showing S-shape dependence. The conversion of two monomers as well as total conversion calculated from peak of vinyl is exactly the same. As in the previous case the monomer ratio shown in Figure S22b; in the supplementary section is almost constant during the whole polymerization time. The composition of copolymers at any conversion is almost the same as the composition of the feed at the beginning of copolymerization. In this case of M2 excess copolymerization parameter for M2 is r_M2=0.98 as it follows from the Jaacks plot (Figure S23 in Supplementary section). The copolymerization parameters summarize in Table 3 pointed out a very similar reactivity of both comonomers. There is no preference for growing radical terminated with M2 or MMA to react preferentially with the monomer M2 or MMA. Due to this the final composition of copolymers being exactly the same as the composition of monomer mixture.

4.1.3 Copolymerization of MMA with M3

Both monomers are methacrylates with different substituents on the ester bond, a methyl group in MMA and the long nonyl-phosphonate group at the end in M3. As in the case for couples M1 and M2 with MMA, two non-equivalent olefinic hydrogens from MMA as well as from M1, M2 and M3 represent two singlets which possess exactly the same chemical shifts at 5.58 and 6.06 ppm, respectively. The total conversion can be calculated on the base of these peaks. The methyl ester group from MMA appears as a sharp singlet at 3.75 ppm, while this group in the copolymer appears at 3.50 ppm as a broader singlet. A smaller difficulty occurs for co-monomer M3. The changes of the ¹H-NMR spectra during copolymerization for this pair are very similar as for the pair M1/MMA, and are shown in Figure 7.

Figure 7:

Details of the ¹H-NMR spectra of the copolymerization of M3 with MMA (ratio M3:MMA=1:3.4) at various time, deuterated methanol, T=55°C.

Total monomers concentration=0.5 mol/l, [AIBN]=0.025 mol/l.

Contrary to M1, where signals of two protons consist of the CO-O-CH₂- group and the signal for four protons of two P-O-CH₂-groups in the monomer appear as one signal at 4.1 ppm (Figures S14 and 4) in the case of M3 these two groups appeared as two signal in different positions. A signal for two protons consisting of the CO-O-CH₂- group is in the form of a triplet at 4.13 ppm and a signal for four protons of two P-O-CH₂-groups in the monomer appear at 4.1 ppm as a sharp multiplet. Using of these peaks for quantification after integration is ambiguous due to the overlapping of these two signals at the later stages of polymerization. But in the polymer we can see the new peak from two protons of CO-O-CH₂- as the broad singlet at 3.95 ppm. Signal of four protons of two P-O-CH₂- groups is not affected by the polymerization process and stay at the same position. Use of these four sufficiently separated peaks allows us to follow the kinetics of copolymerizations as well as the composition of copolymers.

The time-conversion plot for copolymerization of the mixture of M3 and MMA (feed ratio M3:MMA=1:3.4=0.29) is shown in Figure S24 (Supplementary section). As can be seen in Figure S24a; the conversion of MMA is only a little bit faster than the conversion of M3. The feed ratio is almost constant during the whole polymerization process as it is shown in Figure S24b. The reactivity ratio r_MMA was obtained from copolymerization with excess of MMA and the Jaacks plot gives the value r_MMA=1.37. The copolymerization parameter based on the Jaacks method for M3 is r_M3=1.03 (Figure S25 in the Supplementary section). A little bit lower value for r_MMA=1.25 and higher for r_M3=1.1 were obtained by application of the Fineman-Ross method.

Reactivity ratios, summarized in Table 3, show that both parameters are bigger than 1. It means that grooving macro radical with the ultimate M3 structure prefers to react with M3 and vice versa, however, this preference is minor in M3. Small heterogeneous samples are expected from the free radical copolymerization of M1 with MMA. MMA is built a little faster than M3. So it means that at a lower conversion the copolymer contains a smaller amount of poly(MMA) than corresponds to starting mixture and the copolymer produced at higher conversion contained more poly(M3).