3.1. The Mechanism of the ROAC of CHO/PA Catalyzed by PPNCl/Urea
The mechanism of the ROAC of cyclohexane oxide (CHO)/phthalic anhydride (PA) catalyzed by PPNCl/U2 was calculated. In order to simplify the calculation process, PPNCl was replaced by Cl
− with nucleophilic activity, and the reaction mechanisms (
Figure 1) of both no BnOH as the initiator (path A) and BnOH as the initiator (path B) were considered.
In path A, the Cl− as a nucleophile attacks the carbon (C) atom of the epoxy group in epoxide CHO activated by urea U2 through double hydrogen(H)-bonding interactions to lead to the ring-opening reaction of CHO. This step needs to overcome a Gibbs free energy barrier of 13.7 kcal/mol (TS1) to generate an intermediate INT1. Then, the alkoxy anion attacks PA via a transition state TS2 with an energy barrier of 3.2 kcal/mol to produce an intermediate INT2 containing a CHO/PA copolymer unit. The H1 and H2 atoms of molecule U2 in INT2 stabilize the carboxylate anion formed by PA through H-bonding interactions. Then, the nucleophilic attack of the carboxylic anion on the second CHO takes place via a TS3 with an energy barrier of 28.9 (14.2 − (−14.7)) kcal/mol, generating the alternating copolymerization product INT3, which is the rate-controlling step of the whole reaction process.
In path B, Cl− grabs the H of BnOH to generate an alkoxy anion with nucleophilic activity, then this alkoxy anion attacks the carbonyl C atom of PA activated by U2 to realize the ring-opening of PA. This process goes through a TS1’ with an energy barrier of 10.7 kcal/mol. After that, the intermediate INT1’ with a carboxylate anionic terminal stabilized by H1 and H2 atoms of urea was obtained. Then, one molecule of HCl was removed to form the INT2’ by an energy release of 2.9 kcal/mol. Finally, the nucleophilic attack of the carboxylic anion on CHO overcomes an energy barrier of 29.1 (25.3 − (−3.8), TS2’) kcal/mol to give the copolymer product INT3’.
In contrast, in the absence of BnOH, the polymerization reaction catalyzed by the PPNCl/urea system starts from the ring-opening of CHO, and while BnOH was used as the initiator, the ring-opening of PA occurred first, as reported in previous experiments [
9,
10]. The rate-controlling step in both situations is the ring-opening process of CHO, and they both show similar energy barriers (28.9 vs. 29.1 kcal/mol), suggesting that these two cases have similar copolymerization activities. This is consistent with previous experimental results.
3.2. Catalyst Design
Meng et al. reported the ROAC of CHO/PA catalyzed by four different ureas with different Lewis acidity in coordination with PPNCl (
Figure 2). The results showed that in the catalysis of dicyclohexyl substituted U1 (p
Ka = 26.9), the conversion rate of PA reached 76% in 10 min, which was the highest catalytic activity level. When one cyclohexyl group in U1 was substituted by a phenyl group (U2, p
Ka = 22.8/25.1), the conversion rate of PA was 62%. And the conversion rate of diphenyl-substituted U3 (p
Ka = 20.8) was 38% after 20 min. Based on U3, when three Cl atoms were introduced into the
ortho- and
meso-sites of phenyls (U4, p
Ka = 19.2/19.0), the conversion rate (28%, 20 min) decreased. Therefore, the experimental results showed that the catalytic activity decreased with the increase of urea acidity. To clarify how the structures of ureas regulate polymerization activity, the ROACs of CHO and PA—catalyzed by U1, U2, U3, and U4—with PPNCl were calculated.
As shown in
Figure 3, all polymerization processes follow the same mechanism as that of path A in
Figure 1, and the energy barriers of CHO insertion as the rate-controlling step for U1, U2, U3, and U4 are 28.3, 28.9, 29.0, and 29.6 kcal/mol, respectively. Therefore, the above results show that with the increase of urea acidity, the rate-controlling step barrier increases and the catalytic activity decreases, showing a good agreement with the previously mentioned experimental phenomena.
In order to further clarify the relationship between polymerization activity and urea acidity, energy decomposition analyses for
TS3 in the U1 and U4 cases were performed. Among them, the fragments mono and cat represented the monomer CHO and the remaining catalyst parts in
TS3, respectively. As shown in
Figure 4, the total deformation energy Δ
Edef of
U1_TS3 is 49.3 (26.3 + 23.0) kcal/mol, and the interaction energy Δ
Eint between CHO and catalyst is −35.4 kcal/mol, so the Δ
ETS = Δ
Edef + Δ
Eint = 13.9 kcal/mol. In contrast, the bigger deformation energy Δ
Edef (22.9 + 31.9 = 54.8 kcal/mol) of
U4_TS3 completely shields the advantage of the stronger interaction energy (Δ
Eint = −39.5 kcal/mol), resulting in higher Δ
ETS (15.2 vs. 13.9 kcal/mol). Therefore, the lower activity of U4 than U1 may be due to the larger steric repulsion between CHO and the catalyst.
In order to further clarify the origin of the higher activity of U1 than U4, the geometric structures of
INT2 and
TS3 were analyzed. As shown in
Figure 5, the total energy of the hydrogen bonds (E
HB) H1—O1 and H2—O2 in
U4_INT2 is −16.6 kcal/mol, which is greater than that of
U1_INT2 (E
HB = −12.8 kcal/mol). Likewise, the E
HB of the hydrogen bonds H1—O1 and H2—O1 in
U4_TS3 (E
HB = −14.8 kcal/mol) is greater than that of
U1_TS3 (E
HB = −12.2 kcal/mol). This shows that the H-bonding interactions between H1/H2 in the stronger acidity U4 and the O at the chain end is stronger than that in U1’s case, and the acidity of the urea has a greater influence on H-bonding interactions in
INT2 (∆E
HB = −16.6 − (−12.8) = −3.8 kcal/mol) than that of
TS3 (∆E
HB = −14.8 − (−12.2) = −2.6 kcal/mol). Due to the stronger acidity of U4, the H-bonds in
U4_INT2 are enhanced, making
U4_INT2 too stable. Therefore, the CHO insertion needs to break stronger H-bonding interactions to overcome the greater deformation energy, so the insertion energy barrier increases.
According to above results, it was concluded that reducing the acidity of urea can improve its catalytic activity. Based on U2 and U3, therefore, the electron-donating substituents were used to design ten structures of Ua~Uj (
Figure 2). The energies of their corresponding intermediates
INT2 (∆G
INT2), transition states
TS3 (∆G
TS3), and energy barriers (∆G
‡) were calculated (
Table 1).
Firstly, two methyls (CH3) were introduced to the ortho- and the meso-sites of the phenyl group in U2 to give Ua and Ub, respectively. Under these two catalysts, the energy barriers of rate-controlling steps were 28.5 and 27.3 kcal/mol, respectively. In comparison, the energy barrier in the catalysis of Ub was lower than that in U1 (28.3 kcal/mol), suggesting that higher catalytic activity can be obtained by introducing electron-donating substituents to the meso-sites of phenyl groups. Based on U3, different numbers of CH3 or trifluoromethyl (CF3) groups were introduced to the meso-site of the phenyl to lead to new ureas Uc, Ud, and Uh. Their corresponding energy barriers are 26.9, 27.0, and 27.8 kcal/mol, respectively. Although Ud has more electron-donating CH3 groups, its corresponding energy barrier is higher than that of Uc. This energy barrier (26.9 kcal/mol) of Uc with two unsaturated phenyls is even lower than that of Ub (27.3 kcal/mol) with one cyclohexyl. Therefore, the aforementioned results confirm that it is more beneficial to improve catalytic activity through introducing both two phenyls and an electron-donating substituent at the meso-site of only one of the phenyl groups.
Then, two methyls in Uc are replaced by methoxy(OMe) or amino (NH2) groups to obtain Ue and Uf with energy barriers of 28.0 and 24.5 kcal/mol. Obviously, the strong electron-donating ability of NH2 significantly reduces the reaction energy barrier and improves the polymerization activity. In addition, replacing a phenyl group of Uc with pyridyl was also attempted in order to obtain Ug, during which the rate-controlling step barrier was 27.6 kcal/mol. This suggests that the substitution of a phenyl group with pyridyl reduces the catalytic activity. However, introducing one CH3 (Ui) to the meso-site of pyridyl can increase the catalytic activity (26.6 vs. 27.6 kcal/mol). Finally, the Uj obtained by replacing the two CH3 groups of phenyl of Ui with NH2 groups indicates an energy barrier of 24.8 kcal/mol, which is close to that of Uf (24.5 kcal/mol). Overall, the use of NH2 as a strong electron donor can significantly improve the catalytic activity of ureas.
3.3. The ROAC of Different Epoxides and PA Catalyzed by PPNCl/Urea
In order to explore the influence of different epoxides on catalytic activity, we considered the ROAC of propylene oxide (PO), styrene oxide (SO), and epichlorohydrin (ECH) with PA by PPNCl/urea (U1).
3.3.1. Regioselective ROAC of SO and PA
Due to the electronic properties of SO, nucleophilic attacks can occur at two sites, viz., the methylene site and the methine site, due to different regioselectivity during the insertion process. To further compare the copolymerization activity of different epoxides, here we firstly discuss the regioselectivity of SO insertion in the ROAC of SO and PA by PPNCl/U1 (
Figure 6).
Firstly, the Cl− of PPNCl attacks the methylene and methine sites of SO; meanwhile, the hydrogen atoms H1 and H2 of the urea stabilize the alkoxy anion formed by the ring-opening of SO through H-bonding interactions. These two pathways take place through TS1 and TS1′, with energy barriers of 15.7 and 16.0 kcal/mol, to generate INT1 and INT1′, respectively. The almost-identical energy barriers indicate that the activity levels of the ROP of SO at the two sites are similar in kinetics. Then, the alkoxy anions generated by the ring-opening of SO attack the carbonyl C atom of PA and go through TS2 and TS2′, with the energy barriers of 10.7 (17.2 − 6.5) kcal/mol and 3.6 (14.5 − 10.9) kcal/mol, respectively, leading to the ring-opening of PA to form intermediates INT2 and INT2′, with similar energies (11.6 vs. 11.5 kcal/mol). Finally, the carboxylic anion attacks the methylene and methine sites of SO via TS3 and TS3’, with energy barriers of 26.6 (15.0 − (−11.6)) and 27.2 (15.7 − (−11.5)) kcal/mol, to form INT3 and INT3’, respectively. The energy barrier gap of these two pathways is only 0.6 kcal/mol. Therefore, it is speculated that the PPNCl/U1 catalytic system shows poor regioselectivity for the ROAC of SO and PA.
In order to further improve the regioselectivity of SO insertion, U1, U2, U3, and U4 were selected to catalyze the ROAC of SO and PA. The rate-controlling step
INT2 (
INT2’) →
TS3 (
TS3’) was calculated. Δ
G‡(TS/TS’) represents the energy barriers of rate-controlling steps, and the selectivity is decided by the energy barrier gap (ΔΔ
G‡ = Δ
G‡(TS’) − Δ
G‡(TS)) of two pathways. The computational results are summarized in
Table 2.
The results show that the energy barriers (ΔG‡(TS) and ΔG‡(TS’)) of the two pathways of U2 are 27.9 and 28.6 kcal/mol, respectively, and the ΔΔG‡ is 0.7 kcal/mol. The ΔG‡(TS) and ΔG‡(TS’) in U3’s situation are 28.3 and 29.5 kcal/mol, respectively, and the ΔΔG‡ is 1.2 kcal/mol. The ΔG‡(TS) and ΔG‡(TS’) in U4’s case are 29.4 kcal/mol and 31.0 kcal/mol, respectively, and the ΔΔG‡ is 1.6 kcal/mol. These results indicate that with the increase of urea acidity, both the energy barriers of the two ring-opening manners and the ΔΔG‡ increase, suggesting that increasing the acidity of ureas can improve the regioselectivity of SO insertion in the ROAC of SO/PA.
3.3.2. The ROAC of PO, SO, and ECH with PA Catalyzed by PPNCl/U1
Herein, the copolymerizations of three epoxides—PO, SO, and ECH with PA, catalyzed by PPNCl/U1—were calculated in order to compare their activity. As shown in
Figure 7, the polymerization processes of the three epoxides follow the same mechanism as CHO, and the processes of the second epoxide insertion are the rate-controlling steps. The energy barriers of the rate-controlling steps of PO, SO, and ECH were 27.5 (14.2 − (−13.3)), 26.6 (15.0 − (−11.6)), and 23.7 (9.8 − (−13.9)) kcal/mol, respectively. The energy barriers of PO, SO, and ECH were lower than that of CHO (28.3 kcal/mol). Therefore, PPNCl/U1 showed higher copolymerization activity for the epoxides PO, SO, and ECH. By contrast, the energy barrier of ECH is the lowest, followed by SO. Therefore, the introduction of substituents such as phenyl or chlorine can improve the polymerization activity in comparison with PO.
In order to further explore the reasons for the differences in polymerization activity between the three monomers, the rate-controlling step transition states,
TS3, of three monomers—PO, SO, and ECH—were analyzed by energy decomposition (
Figure 8). Among them, the fragments mono and cat represented the monomer and the remaining catalyst parts in
TS3, respectively. The results show that the interaction energies (∆
Eint) between monomer and catalyst fragments in
TS3_PO,
TS3_SO, and
TS3_ECH are −33.1, −33.5, and −37.6 kcal/mol, respectively, and the total deformation energies (∆
Edef) of the two fragments are 48.5 (22.9 + 25.6), 46.1 (21.2 + 24.9), and 48.8 (24.7 + 24.1) kcal/mol, respectively. Therefore, the energies ∆
ETS corresponding to the three monomers are 15.4 (−33.1 + 48.5), 12.6 (−33.5 + 46.1), and 11.3 (−37.6 + 48.8) kcal/mol, respectively, showing a good agreement with the energy barriers. By contrast, the stability of
TS3_SO in comparison with
TS3_PO was mainly ascribed to the lower deformation (46.1 vs. 48.5 kcal/mol). Meanwhile, the stronger interaction (ECH vs. PO: 37.6 vs. 31.1 kcal/mol) between ECH and the catalyst fragments stabilizes
TS3_ECH, leading to the higher copolymerization activity of ECH and PA in comparison with PO.
Further geometric analyses for intermediate
INT2 and transition state
TS3 in PO, SO, and ECH cases were carried out. As shown in
Figure 9, the total energy of hydrogen bonds (E
HB = −13.0 kcal/mol) H1—O1 and H2—O2 in
INT2_PO is bigger than that in
INT2_SO (E
HB = −12.5 kcal/mol), suggesting that stronger H-bonding interactions stabilize
INT2_PO. As we all know, the dispersion of charge will affect the stability of the structure. Therefore, the NBO charges of the atoms at the reaction centers (O1, O2, C1) of
TS3_PO and
TS3_SO were investigated, and the variance S of the absolute value of the NBO charge was calculated. Generally, the smaller the value of S, the more uniform the charge distribution and the lower the energy of the structure [
18]. The S value (about 0.116) of
TS3_SO is the almost same as that of
TS3_PO, indicating that the stability of the two TSs is similar. Further PO insertions need to break the stronger H-bonding interactions in
INT2_PO, so the increased stability of
INT2_PO inhibits subsequent monomer insertion, leading to lower copolymerization activity.
Then, the total energy of the hydrogen bonds (EHB = −13.0 kcal/mol) H1—O1 and H2—O2 in INT2_ECH is the same as that of INT2_PO, suggesting that the stability of the two INTs is similar. However, the S value in TS3_ECH (about 0.112) is smaller than that in TS3_PO (about = 0.116), suggesting that the strong electron-absorbing Cl atoms enhance the structural stability of the rate-controlling transition state by improving the uniformity of the charge distribution in TS3, thus reducing the reaction energy barrier and increasing the activity of copolymerization.