Tianwen Bai*a,
Jun Ling
bc and
Thieo E. Hogen-Esch*b
aCollege of Biological, Chemical Sciences and Engineering, Jiaxing University, Jiaxing 314001, China. E-mail: baitw@zjxu.edu.cn
bDepartment of Chemistry and Loker Hydrocarbon Research Institute, University of Southern California, Los Angeles, CA 90089-1661, USA. E-mail: hogenesc@gmail.com
cMOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
First published on 7th May 2025
The stereochemistry of t-BuLi initiated styrene polymerization in cyclohexane yields isotactic-rich polystyrene in the presence of sodium 4-methylbenzenesulfonate (SMBS). Herein, we report the results of DFT calculations in cyclohexane, both in the presence and absence of SMBS, using the B3PW91 hybrid functional and 6-311++G(d,p) basis set with DFT-D3 correction, allowing for the detailed evaluation of the transition state structures confirmed by benchmark analysis. We focus on the addition of a single styrene to a 1-lithio-1,3(S)-diphenyl-pentane (LDPP) model dimer anion, producing the expected four stereoisomers of 1-lithio-1,3,5-triphenylheptane (LTPH). The addition proceeds through four styrene stereoisomeric complexes, consisting of two pseudo-enantiomeric sets with the corresponding transition states (TSs), which exhibit similar Gibbs free energy (≤0.1 kcal mol−1), in agreement with previously reported results. The geometries of the complexes and transition states are consistent with the major rotational (rather than lateral) motions of the aryl and vinyl groups as the complexes evolve into transition states and trimer anions. In the presence of SMBS, similar but higher energy monomer complexes are formed that surprisingly have nearly the same free energy. However, the TS free energy barriers increase in the following order: m-pro-m <r-pro-m ≅ m-pro-r <r-pro-r. For instance, the TS energies for monomer addition differ by as much as 1.4 kcal mol−1 for the r-pro-r compared to the m-pro-m transition states. However, due to the 1.9 kcal mol−1 lower free energy of the pro-r compared to the pro-m dimer anions, the corresponding activation energies differ by as much as 3.3 kcal mol−1. This would tend to favor the formation for mm triads over rr dyads by a factor of about 1.9 × 102, which is consistent with the prevailing isotactic stereochemistry.
Anionic styrene isotactic polymerization involving alkali metal complexes has been reported as early as 1960.6 However, the origin of this process was later attributed to the presence of impurities that are often present.7,8 Worsfold and Bywater reported that the presence of water significantly increased the isotactic content in PS, suggesting that the results were plausibly due to the presence of LiOH formed by adventitious water. Accordingly, Makino et al. demonstrated the synthesis of highly isotactic PS (with triad and pentad contents of 95% and 90%, respectively) at −60 °C, uncontaminated by significant quantities of stereoirregular PS. This was achieved by initiating the polymerization with 3,3-dimethyl-1,1-diphenyl-1-lithiobutane (DMPBL) in the presence of equimolar LiOH, generated in situ in hexane, at temperatures between −30 and −60 °C.9 In the absence of LiOH, only low contents of mm triads (11%) were observed.
Cazzaniga et al. also prepared fractions of isotactic polystyrene (iPS), along with stereoirregular PS at −30 °C using n-BuLi/lithium tert-butoxide (t-BuOLi) complexes.10 They also synthesized semicrystalline ABA type isotactic PS-polybutadiene triblock copolymers.11 The ratio of isotactic polystyrene to polybutadiene (iPS wt% ≥66%) in these copolymers resulted in various microphase-separated morphologies at a scale that is typical of diblock copolymers. However, the synthesis of isotactic PS block copolymers still requires fractionation of the isotactic polystyrene. More recent developments have shown that alkyllithium-alkoxide (RLi/ROMt) with (MtLi, Na, and K) and R2MgOR/KOR-initiated styrene polymerizations in methylcyclohexane at −40 °C gave isotactic-rich PS (mm contents as high as 85%).12
We have recently reported a polymerization of styrene initiated by t-BuLi in hexane or cyclohexane, in the presence of one or less equivalent of sodium dodecylbenzenesulfonate (SDBS), which produces isotactic-rich PS (mm triads and mmmm pentads at 77% and 51%, respectively) at ambient temperature or above with relatively narrow distributions (Mw/Mn = 1.1–1.4).13 Lower temperatures gave inferior results. The advantage of these anionic polymerizations is the formation of isotactic-rich PS at ambient temperatures and the potential to produce the corresponding isotactic PS block copolymers.
Previous DFT calculations using a B3LYP hybrid functional and 6-31G(d) basis set were carried out on 1-lithio-1,3(S)-diphenyl butane (LDPB) in vacuum or cyclohexane as a model for PSLi, and their complexes with sodium 4-methylbenzenesulfonate (SMBS) as a model for SDBS.13 The results suggested that in cyclohexane and similar solvents at ambient conditions, LDPB adequately models the stereochemical properties of PSLi. This includes the predominant formation of unreactive LDPB and PSLi dimers that are in equilibrium with a reactive monomeric LDPB (PSLi) in cyclohexane and similar hydrocarbons, in agreement with calculations by Yakimansky et al.13,14 Furthermore, the absence of spontaneous epimerization of the pro-chiral LDPB ion pair configuration (1-pro-m or 1-pro-r) (Scheme 1), or the formation and dissociation of the dimer has been shown to be consistent with these calculations.13,14
The simulated reactions of 3(S)-LDPB with styrene also indicated a strongly preferred Li side (syn) monomer attack through coordination of the Li ion with styrene to give styrene complexes prior to monomer addition.13 Hence, the relative thermodynamic stabilities of the various pro-chiral Li ion pairs complexes are of interest. In the absence of SMBS, the formation of either 1-pro-S or 1-pro-r LDPB-styrene complexes were found, which burdens the Li ion coordinating either the pro-si or pro-re pro-chiral monomer, with the remaining Li ion coordinated to the penultimate 3-phenyl of LDPB.14 The relative free energies of four stereoisomeric LDPB-styrene complexes were consistent with the demonstrated slight preference for heterotactic and syndiotactic PS triads in the absence of SMBS.13,14 Thus, upon monomer addition, the relative ΔG values of formation of 2-m-pro-m, 2-m-pro-r, 2-r-pro-r and2-r-pro-m LDPB-styrene complexes were calculated as 0, -0.53, −1.23 and −0.85 kcal mol−1, respectively, consistent with the experimental data showing the preferred syndiotactic (rr) and heterotactic (mr) triads. In the presence of SMBS, however, these computations showed a strongly favored (ΔG ≈ −30 kcal mol−1) 1:
1 LDBP-SMBS complex by reaction of the LDPB dimer anion with SMBS.13 The simulated LDPB–SMBS styrene complexes show structures with the Li and Na ions both being close to the benzyl carbanion, with the Na ions being syn with respect to Li and close to the center of the 1-phenyl group. Dimerization of these complexes were shown to be absent. However, the calculations of the transition states corresponding to the monomer addition were inaccessible at the time;15 thus, any conclusions were considered to be tentative.
Here, we report more advanced calculations (B3PW91/6-311++G(d,p)) methods to model the complexes of styrene with a slightly modified 1-lithio-1,3(S)-diphenylpentane (LDPP). The results of the calculations of the detailed structures of LDPP, LDPP-monomer complexes 2, transition 3, and trimer anions 4 in the absence or presence of SMBS are reported. In the absence of SMBS, the free energies of the four isomeric transition states were found to be quite similar, which is consistent with the formation of atactic stereochemistry. However, in the presence of SMBS, the transition state free energies for styrene addition to LDPP are consistent with a preference of isotactic-like polymerizations.
The pro-si or pro-re styrene addition to the two pro-m or pro-r diastereomers of LDPP should give four m-pro-m, m-pro-r, r-pro-r and r-pro-m stereoisomers of 1-lithio-1,3,5-triphenylheptane 4 (LTPH) via the corresponding four stereoisomeric styrene complexes 2 and transition states 3 (Schemes 1–3). First, the results both with respect to atomic positions and dihedral angles are analyzed. We then report on the analogous reactions in the presence of sodium-4-methyl-benzenesulfonate (SMBS).
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Scheme 2 Syn addition of styrene to 1-pro-m LDPP at its pro-si or pro-re faces, giving the 4-m-pro-m or 4-m-pro-r trimer anion via monomer complexes 2, and transition states 3. |
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Scheme 3 Syn addition of styrene to 1-pro-r LDPP at its pro-si or pro-re faces, giving the 4-r-pro-r [t g−g−t] or 4-r-pro-m trimer [t g−g−t] anions. |
The surprisingly similar Li distances to the 1-phenyl carbanion and the 3-phenyl coordinating group of the dimer precursor 1 are of special interest in being very similar (Table S1†). For both the 1- pro-m and 1- pro-r isomers (Table S1†), the Li ion is located much closer to CZ (0.22–0.23 nm, 2.2–2.3 Å) than CE (0.30 nm, 3.0 Å). However, its coordination to the 3-phenyl group depends on stereochemistry with the Li ion of 1-pro-m being more strongly coordinated to the CZ′ carbon (0.23 nm, 2.3 Å) than to the CE′ carbon, while the opposite is the case for the 1-pro-r isomer with distances of 0.27 nm (2.7 Å) and 0.24 nm (2.4 Å), respectively. Although the 1-phenyl torsions are nearly the same but with opposite signs, the torsions of the 3-phenyl groups for 1-pro-m (31.3°) and 1-pro-r (17.2°) are not (Table S1†). As seen above, this is consistent with 1-pro-m and 1-pro-r being epimers. The (C2–C3) gauche dihedral angle in 1-pro-m and the larger 3-phenyl torsion account for its greater conformational strain (1.4 kcal mol−1) compared to the 1-pro-r isomer (Fig. 2). The unusual values of the C1–C2 dihedral angle may be seen as distorted trans-like conformations (t) due to the strong intramolecular Li-3-phenyl interactions (see below).14
A comparison of Tables S1 and S4† show that the distances with respect to the Li ion of the aryl carbons of 1 and 3 (pro-m or pro-r) are nearly identical, as are the magnitudes and torsions of the dihedral angles (CH2–C1–CQ–CZ). For instance, the four isomers of 4 show nearly the same Li–CZ and Li–CE distances in the 1-phenyl carbanion that is nearly independent of stereochemistry, with the Li–CQ (0.21 nm, 2.1 Å) and Li–CZ (0.22–0.23 nm, 2.2–2.3 Å) distances being significantly smaller than that of Li–CE (0.30 nm, 3.0 Å) (Tables S1 and S2†).
This gives four diastereomeric monomer complexes 2, which differ significantly from the two LDPP precursors (Schemes 2 and 3) formed through reaction of 1-pro-m on the si or re face of the monomer. This results in the displacement of the 3-phenyl group, accompanied by rotation of the (C2–C3) bonds, giving all-trans (t t) 2-pro-m-pro-si or 2-pro-m-pro-re complexes with smaller 1-phenyl torsions of −21° and −14° (Tables S1 and S3†). The alternative 2-pro-r-pro-si and 2-pro-r-pro-re monomer complexes are formed similarly, but generate (g− t) complexes with smaller 1-phenyl torsions of 13° and 17° (Table S3†). It is of some interest that the 2-pro-m-pro-si complexes have higher torsions compared with all others, as this may be a factor (but not the only one), considering its much higher free energy compared with the other three, as shown in Fig. 1.
The 2-pro-m-pro-si and 2-pro-r-pro-re complexes have much smaller Li–CZ (0.23 nm, 2.3 Å) than Li–CE (0.31 nm, 3.1 Å) distances. Meanwhile, for the 2-pro-m-pro-re and the 2-pro-r-pro-si complexes, this is almost exactly the reverse, with the Li–CE distances being smallest (0.23 nm, 2.3 Å) compared to the coordinating aryl carbons (Table S3†). Interestingly, the Li distances to the coordinating aryl carbons are much smaller for the 2-pro-m-pro-re or 2-pro-r-pro-si complexes. The aryl carbons all have lower values (0.05–0.07 nm, 0.5–0.7 Å) compared with the other two isomers (Fig. 1), indicating that this may correlate with their lower Gibbs free energies (see below).
The displacement by styrene of the Li-coordinating 3-phenyl group leads to the formation of 2-pro-m or 2-pro-r LDPP monomer complexes, in which the 1-phenyl group is nearly coplanar with the LDPP chain, with the 1-phenyl torsions being much smaller than LDPP with values of about −21°/17° and −14°/13° for 2-pro-m-pro-si/2-pro-r-pro-re and 2-pro-m-pro-re/2-pro-r-pro-si, respectively, and the 3-phenyl groups being sufficiently far away from the carbanions (Table S6†).
Monomer orientations relative to the LDPP chain are represented by intermolecular dihedral angles (C1′–C2′), (C2′–C1) and (C1–C2), where the primes refer to the monomer CH and CH2 vinyl carbons, respectively (Table S6†). It seems plausible that these dihedral angles are consistent with both 2-pro-m-pro-si/2-pro-r-pro-re and 2-pro-m-pro-re/2-pro-r-pro-si being enantiomeric-like. For the 2-pro-m-pro-re//2-pro-r-pro-si pair, the C1′–C2′ and C1–C2 dihedrals are quite close, while these are a little larger (∼6°) for the (C1–C2) dihedrals. However, in all cases, the dihedral angles remain opposite in signs, indicating at least a reasonable argument for pairs of enantiomer-like isomers, given that dihedral angles are far more sensitive measures than the Li aryl carbon distances. In that context, it is interesting that the largest deviation in dihedral angles (16°) is seen for the (C1–C2) dihedral of the 2-pro-m-pro-si/2-pro-r-pro-re pair of complexes, given the extraordinarily large free energy value (9.4 kcal mol−1) for the 2-pro-m-pro-si complex (Fig. 1).
With respect to the LDPP parts of the 2-pro-m-pro-si and 2-pro-m-pro-re (2-pro-m) complexes, this leads to all-trans (t t) conformations with (C1–C2), (C2–C3) and (C3–C4) dihedral angles of about 170°–175° (Table S6†). The two 2-pro-r complexes show (t g t) conformations of LDPP, where the carbanion is likewise fully exposed, but has a single LDPP (C2–C3) gauche conformation. This indicates again that the conformations are much more revealing in the distinction of stereoisomers. As seen from the values of the intermolecular (C2′–C1) dihedrals (Table S6†), the “steepness” of the monomer approach with respect to the chain is greater for 2-pro-m-pro-si/2-pro-r-pro-re and 2-pro-m-pro-re/2-pro-r-pro-si. This is also seen for the dihedrals of the long axes of the monomer and benzyl carbanion that give values of 19° and −6° for set 2-pro-m-pro-si/2-pro-r-pro-re, and −67° and 66° for set 2-pro-m-pro-re/2-pro-r-pro-si (Table S6†).
The very similar magnitudes of the TS dihedrals in each set are consistent with the very small (≤4.0°) transition state free energy differences. This also holds for 4-m-pro-r and 4-r-pro-r (3S-1-pro-r and 3R-1-pro-S), indicating that the 5-phenyl group in trimer anion 4 has little or no effect on stereochemistry, as concluded earlier, and supports both the LDPP and LTPH anions being appropriate models for the anionic styrene polymerization stereochemistry.13
The results of the computations shown in Table 1 list the free energies of 1-pro-m and 1-pro-r, the energies of the four styrene complexes (2-pro-m + S(si), 2-pro-m + S(re), 2-pro-r + S(si), 2-pro-r + S(re)), the corresponding transition states 3, and the resulting 4-m-pro-r, 4-m-pro-m, 4-m-pro-r and 4-m-pro-m trimer anions that are only between 1.1, 1.7, 0.1 and 0.6 kcal mol−1 more stable than 1-pro-m, respectively.
Structures | ΔG of 1 (kcal mol−1) | ΔG of 2 (kcal mol−1) | ΔG± of 3 (kcal mol−1)b | ΔG of 4 (kcal mol−1) |
---|---|---|---|---|
a Free energies of 1-pro-m and 1-pro-r, corresponding complexes: 2-pro-m + (si), 2-pro-m + (re), 2-pro-r + (si), 2-pro-r + (re).b Activation free energies relative to 1-pro-m and 1-pro-r. | ||||
1-m-pro-si | 0 | 9.4 | 17.1 | −1.1 |
1-m-pro-re | 0 | 7.9 | 17.1 | −1.7 |
1-r–pro-si | −1.4 | 8.8 | 18.9 | −0.1 |
1-r-pro-re | −1.4 | 8.1 | 18.8 | −0.6 |
Our calculations shown in Fig. 2 appear to show a slight preference for isotactic-like additions, but this may be offset by a greater tendency for the isotactic chain ends to associate into unreactive dimers. This is fully consistent with a nearly complete absence of stereoregularity when initiated by carefully purified alkyllithium or reactive lithium carbanions occurring in hexane, cyclohexane or similar solvents, which is consistent with our computations.7,9,12
The 5-pro-m and 5-pro-r isomers show (C2–C3) and (C3–C4) dihedral angles with (t g t) and (t t) conformations for the C1–C4 chain segments of the 1-pro-m and 1-pro-r isomers, respectively, with the torsion signs remaining the same in all cases (Tables S2 and S10†).
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Scheme 4 Monomer addition to the 5-pro-m dimer anions. Formation of LTPH (trimer anions) 8-m-pro-m and 8-m-pro-r. |
The changes in the formation of the complexes are major and remarkable (Scheme 4). Thus, the 3-phenyl group is displaced from the Li ion by the styrene monomer, and the Na ion is now only coordinated with the monomer phenyl group being 0.28 nm (2.8 Å), which is nearly equidistant to the phenyl carbons. It remains located above the methylene and methine vinyl carbons at 0.24 (2.4 Å) and 0.27 nm (2.7 Å, Table S11†).
Unlike the complexes of 2, the free energies of the four monomer-SMBS complexes 6 are nearly equal in free energy (<0.7 kcal mol−1, Fig. 2). However, one isomer 6-pro-r + Ssi stands out in having dual coordination of the Li ion by sulfonate (Scheme 5), and the 1-phenyl torsion dihedral angle is lower (5°–9°) than the other three cases, suggesting correlation of the Li charge density and 1-phenyl torsion (Table S11†).
As indicated above, the formation of the monomer complexes 6 involves large changes in the deployment of Li and Na ions. That includes a reversal of 5-pro-m and 5-pro-r having t g t and t t t conformations, respectively, into two 6-pro-m complexes and one 6-pro-r-pro-re complex having t t t and t g t LDPP backbones.
However, the 6-pro-r-pro-si complex has a LDPP gauche-like (g)g− t conformation with an unusual (C1–C2) dihedral angle (∼88.5°). The (C2–C3) and (C3–C4) LDPP dihedrals of 6, not being involved directly in the reaction, are relabeled as (C4–C5) and (C5–C6) dihedrals upon formation of 8 with virtually unchanged values (Table S16†).
As seen before, in the presence of SMBS, the values and signs of the dihedral angles of the complexes, transition states and trimer anions, though consistent with symmetry properties, differ far more than that seen in the absence of SMBS (Tables S6–S8†). For example, although the 6-pro-m-pro-re and 6-pro-r-pro-si complexes have the expected opposite signs, their (C1′–C2′), (C2′–C1) and (C1–C2) dihedral angle values vary by as much as 73° (Table S14†). Thus, symmetry considerations are not suited in interpreting the free energies that are remarkably close (Fig. 2). The value of the LDPP (C1–C2) dihedral angle of the 6-pro-r-pro-si isomer complex has an unusual value of about 88° that evolves into an equally unusual value of 145° for the corresponding 7-pro-r-pro-si TS, suggesting significant steric strain. However, as shown in Fig. 2, the Gibbs free energies of the monomer complexes are almost identical.
Given the lower (−1.7 kcal mol−1) energies of the chain-end r-compared to m-dyads, this leads to increased differences in activation energies with values of 30.2 kcal mol−1 for 7-pro-r-pro-si compared to the lowest value (26.9 kcal mol−1 for 7-pro-m-pro-si, indicating a difference in the free energy of activation of about 3.3 kcal mol−1 (Table 2). This would suggest that the rates of formation of the mm triads would exceed that of the rr triad formation. Of course, that would be misleading, as the activation free energies of formation of mr and rm dyads are quite a bit lower (Table 2, Fig. 2). Given the multiple and plausibly overlapping effects, the above is likely to play a significant role in explaining the virtual absence of rr triads in LTHP. The benchmark results under B3LYP/6-311++G(d,p) and M06-2X/6-311++G(d,p) agreed well with these conclusions, and all key conclusions (e.g., stereoselectivity trends, rate-limiting steps) remained robust across all tested functionals. M06-2X indeed provided improved thermodynamic data for reaction pathways and lower energy barriers (22.8, 23.5, 26.2, 23.9 kcal mol−1).
Isomers | 5 | 6 | 7 | (ΔG≠) b | ΔΔ(G≠)c | kmm/kp d |
---|---|---|---|---|---|---|
a In cyclohexane.b Differences in the activation Gibbs free energy in kcal mol−1 mol−1 (ΔG≠) between 7 and 5.c Differences in the activation free energies compared to the free energy of activation of pro-m-pro-si.d Propagation rate constant kmm for isotactic triad formation at 300 K relative to: kmr, krr and krm from top to bottom. | ||||||
pro-m-pro-si | 0 | 22.8 | 26.9 | 26.9 | 0 | 1.0 |
pro-m-pro-re | 0 | 22.9 | 27.3 | 27.3 | 0.4 | 1.8 |
pro-r-pro-si | −1.9 | 22.8 | 28.3 | 30.2 | 3.3 | 194 |
pro-r-pro-re | −1.9 | 22.2 | 28.0 | 29.9 | 3.0 | 119 |
Provided that LDPP is a reasonable model for the polymer, the low isotactic content (in the absence of SMBS) can be ascribed to the lower degree of association of r-LDPP into dimers (3.3 kcal mol−1), hence favoring the formation of r dyads at the chain ends, and thus slightly favoring the formation syndiotactic chains (Table 3). However, this may be compensated for by the preferred association of the greater steady state concentrations of the pro-r species, thus giving atactic PS without significant fractions of mm triads and or mmm tetrads. The faster rates of the polymerization in the presence of SMBS, the higher free energy and transition states notwithstanding, are due the larger concentrations of the SMBS complexes (5-pro-m, 5-pro-r), as these do not seem to dimerize to any significant extent. This simple model would also be consistent with the kinetics of this polymerization being reported by Yakimanski et al.14 The formation of long meso (m) sequences of isotactic PS for the case of SMBS may be kinetically favored by the lower TS, as discussed above. In addition, there is the possible participation of an uncoordinated 5-pro-m[u] LDPP intermediate that should rapidly form both 6-m-pro-Ssi and 6-m-pro-Sre monomer complexes. Further simulations with other coordinating agents could point to additives with even more stereo-selective properties. This approach could be of interest in applications for block copolymers.
No. | ΔG (kcal mol−1) at 298.2 Kb | |
---|---|---|
a The pro-meso and pro-racemic structures are indicated as m- and r-, respectively.b Calculation details: B3PW91/6-31+G(d,p) in vacuum. Previous data are shown in parentheses.13 | ||
1 | 2 m-LDPB ⇒ (m-LDPB)2 | −19.0 (−21.7) |
2 | 2 r-LDPB ⇒ (r-LDPB)2 | −15.7 (−19.5) |
3 | m-LDPB + r-LDPB ⇒ (m-LDPB-r-LDPB) | −17.5 (−18.0) |
4 | m-LDPB + SMBS ⇒ (m-LDPB-SMBS) | −27.1 (−29.6) |
5 | r-LDPB + SMBS ⇒ (r-LDPB-SMBS) | −26.8 (−30.8) |
6 | 2 SMBS ⇒ (SMBS)2 | −34.5 (−34.7) |
7 | 0.5 (m-LDPB)2 + 0.5 (SMBS)2 ⇒ (m-LDPB-SMBS) | −0.40 (−1.4) |
8 | (m-LDPB)2 + 0.5 (SMBS)2 ⇒ (m-LDPB-SMBS-mLDPB) | −4.50 (−7.2) |
As illustrated in Tables S6–S8,† the changes in the dihedral angles of the monomer and LDPP chain-end provide more details into the nature of the molecular changes that mediate the conversions of complexes into transition states, and of transition states into trimer anions. The magnitudes of the changes are typically 30° or less, and the dihedral signs (positive or negative) remain the same as the intermediates interconvert (Tables S6–S8†). This would be consistent with the relatively rapid (∼10−9 to 10−12 s−1) and large rotations of the phenyl or vinyl groups of the monomer, and the phenyl groups of polymer chain ends compared to translational motions.
A comparison of the dimer and trimer anions ion show that the conformations of the first two asymmetric carbons are nearly identical, as shown by the first two dihedral angles of the chain (Tables S2 and S8†), which is consistent with the lack of any influence of the asymmetric carbon 5(S) in LTPH or 3-C in LDPP. In addition, the intramolecular coordination of the lithium ion by the 3-phenyl groups is quite strong, as suggested by the nearly constant CH2–C1–CZ–CQ dihedral angles (1-phenyl torsions) of the two isomers of LDPP and all four isomers of LTPH being nearly identical (±26°–29°). Meanwhile, the (C1–C2) dihedral angles of the LDPP and LTPH are both between 127° and 130° degrees (Tables S2 and S8†), so that the dimer and trimer anions are equally suitable as models.
As shown in Fig. 2, the transition state free energies decrease by 2.7 kcal mol−1 as follows: 7-r-pro-r > 7-m-pro-r > 7-r-pro-m > 7-m-pro-m. As the rates of formation of 7-m-pro-si and 7-r-pro-re would represent the corresponding formation of mm and rr dyads, this would entail differences in the free energy of activation (below). The corresponding differences in activation free energies decrease by even more (3.3 kcal mol−1), given the lower free energies of the racemic (r,r) dyads. The formation of the mr and rm triads are lower, but these still should have a significant effect. This trend is qualitatively consistent with the considerable non-bonded interactions in the relative free energies of the TS's (Table 2). There are several reasons: (a) the relatively high values value of the intermolecular (C2′–C1) and (C1–C2) dihedral angles of 7-r-pro-si, (∼73° and 76°, respectively) compared to the other three isomers (Table S15†); (b) the 145° intramolecular (C1–C2) dihedral angle of 7-r-pro-r that indicates a severe conformational strain, which should exceed the free energy of a single gauche conformation; (c) the low value (169°) of the intramolecular (C3–C4) dihedral angle of 7-r-pro-r compared to that of the other three isomers; and (d) the higher values of the 1-phenyl torsions (∼27°) of 7-m-pro-re and 7-r-pro-si compared to the other two (19°–20°, Table S15†). Although these are listed separately, there may well be considerable overlap between these factors.
Thus far, interactions of the SMBS phenyl group in any of the intermediates have not been discussed. In general, the benzene sulfonate phenyl group is not in close proximity to any of the aromatic groups of any of the monomer complexes and transition states.
However, there is an exception in that the 7-pro-r-pro-si transition state, there is a proximity of the ortho-carbon or hydrogen atom of the ortho-carbon of the benzene sulfonate phenyl group to the meta carbon (hydrogen) of the 1-phenyl carbanion, as measured by the distance of the 1-phenyl CZ carbon to the ortho-carbon of the SMBS, being on the order of 3.8 Å. The hydrogens are even closer at about 3.4 Å. Even though these interactions may be small and may not appreciably increase the energy of this transition state, this raises the possibility that this proximity effect may be enhanced by the introduction of a methyl or larger group at the ortho-carbon(s) of the benzenesulfonate. Thus, future explorations in this directions would be interesting.
The free energies of activation for the monomer addition for r-pro-r and r-pro-m are 3.3 and 3.0 kcal mol−1 higher, respectively, than that of the competing m-pro-m and m-pro-r additions. Hence, the direct m-pro-m addition in the presence of the styrene monomer is favored to repeat, as the competing m-pro-r process may be “handicapped” by the absence of a directly accessible TS state, and may depend on the occurrence of a spontaneous cleavage of the Li-3-phenyl coordination (Table S5†).
In addition, the monomer vinyl-phenyl dihedral angles for transition states 7-m-pro-re and 7-r-pro-si are unusually low (∼10°) compared with that (∼27°) of the corresponding isomers of the trimer anion 8 (Table S16†), while the other two (7-m-pro-si and 7-r-pro-re) TS isomers both have torsions (∼19°) that are well matched with regard to the 1-phenyl torsions (∼20°), as the complexes are converted into transition states (Tables 2 and S15†). This would result in an additional negative entropy penalty for the conversions of 6-m-pro-re and 6-r-pro-si into 7-m-pro-re and 7-r-pro-si. Thus, the dependence on stereochemistry with respect to the transition state (TS) free energies appear to indicate mainly non-bonded interactions associated with conformational effects.
As shown in Table 3, the formation constants of 2-pro-m or 2-pro-r 1:
1 LDPP-SMBS complexes are very high and nearly identical. In contrast, the LDPP-SMBS complex also dimerizes but with relatively low formation constants (Table 3). Such dimers have been demonstrated for similar carbanions in hydrocarbons, but have been shown to be unreactive.13,14 The same is plausible in the present case, given the data in Table 3. Thus, the computations carried out are based on 1
:
1 LDPP-SMBS complexes with a stoichiometry that is independent of the LDPP stereoisomer, as both pro-m and pro-r LDPP have nearly the same formation constant with SMBS, which are very large and nearly the same order of magnitude (Table 3).
In conclusion: (A) The polymerization mechanism has been shown to undergo a process through four stereoisomeric 1:
1 styrene complexes 2, the corresponding transition states 3 and 1-lithio-1,3,5-triphenylheptane trimer anions 4; (B) LDPP-styrene complexes 2 formed by coordination of Li ion of LDPP to styrene at its pro-si or pro-re faces give 2-pro-m-pro-si/2-pro-m-pro-re or 2-pro-r-pro-si/2-pro-r-pro-re, which are short-lived but stable complexes that equilibrate with the 1-pro-m and 1-pro-r LDPP, and that vary in free energy between 9.0 and 4.7 kcal mol−1, in which the Li-3-phenyl coordination has been disrupted; (C) The four transition states differ from the complexes in that their free energies are nearly equal (within 1.0 kcal mol−1), which is consistent with the formation of atactic polystyrene; (D) The transition state structures closely resemble that of the complexes, but differ primarily through different dihedral angles of the vinyl carbons (C1′, C2′) and the first two carbons of LDPP (C1, C2). Hence, the transition states involve primarily bond rotations of the monomer, as the complexes are transformed into transition states and then into trimer anions. (E) In the resting state, the 1-pro-m and 1-pro-r epimers and the four stereoisomers of 4 have (C1–C2), dihedral angles of about 128°–130°, characterized as distorted trans conformations due to a strong intramolecular coordination of Li to the 3-phenyl group (Tables S2 and S8†). The (C2–C3) and (C3–C4) dihedral angles are either gauche (g ∼67°–73°) or trans (t ∼173°–176°).
Footnote |
† Electronic supplementary information (ESI) available: 3D structures and geometry data of the critical transitions states. See DOI: https://doi.org/10.1039/d5ra00332f |
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