3.1. Experimental Study
Recently, the kinetics and thermodynamics for a model series of reversible networks based on DA cycloadditions were experimentally determined [
11]. While the same furan-maleimide cycloaddition reactions were studied, the molecular architecture of the amorphous networks (and the corresponding glass transition temperature and thermomechanical properties) could be altered by using different spacer lengths (and thus concentrations of hydroxyl and ether groups) of the furan and maleimide compounds in the mixtures (see
Figure 2 in
Section 2.1. Materials). A mechanistic model with four rate constants as shown in
Figure 1 was used, considering the equilibrium reactions between the furan and maleimide functional groups and the
endo and
exo DA cycloadducts. Non-isothermal microcalorimetric (normalized) heat flow data, measured from 20 °C to 90 °C, in combination with isothermal data at 55 °C, were used to fit the model parameters. One unique set of kinetic and thermodynamic equilibrium parameters was optimized in ref. [
11] (see
Table S1 in the Supplementary Materials), describing in a satisfactory way the reaction rates of the full set of reversible networks from low to high reaction conversions and for temperatures ranging from 20 °C to 90 °C, taking into account the effect of forward and backward DA reactions along the reaction path. Although all model networks contained different concentrations of hydroxyl and ether functionalities in their respective spacers, no extra reaction steps in the model were needed for an accurate description of all measured heat flow profiles.
3.1.1. Model Series of Reversible Networks: Effect of Concentrations of Hydroxyl and Ether Functional Groups on Initial Reaction Rate and Forward DA Rate Constant
To further examine the potential influence of secondary H-bonding interactions on the furan-maleimide kinetics, an alternative experimental approach solely based on isothermally measured initial DA reaction rates (at reaction time t = 0) is followed in this paper.
For this purpose, the DA rates of different stoichiometric mixtures of furans and maleimides, giving rise to the model series of reversible networks, are experimentally determined by microcalorimetry in isothermal conditions at 20 °C. The measured rates are extrapolated to initial DA rates (v
0) at reaction time t = 0, using the optimized kinetic parameter set of ref. [
11] (see
Table S1 and
Section 2.2. Methods). The initial reaction rates v
0 are further normalized against the starting concentrations of the furan and maleimide functional groups in the reaction mixtures. This ratio v
0/([F]
0 [M]
0) at 20 °C is equal to the experimental forward DA rate constant k
DA at 20 °C, i.e., the rate constant for the formation of the sum of
endo and
exo cycloadducts without any interference of the retro DA (backward) reactions (see Equation (4) in
Section 2.2.2. Kinetic calculations). The average experimental value of k
DA for this model series of DA reactions is <k
DA> = 2.29 ± 0.24 10
−5 kg (mol s)
−1 (see
Table S3 in the Supplementary Materials). A reliable and constant value of <k
DA> is obtained with a limited standard deviation (SD = 0.24 10
−5 kg (mol s)
−1), certainly if slight potential errors in the stoichiometric mixing ratio of all independently prepared mixtures are taken into account (as a result of small uncertainties on the average functionalities of the furan and maleimide compounds and the fast mixing protocol to limit reaction conversion during preparation outside the analytical instrument) (see
Section 2.1 Materials,
Table S1, and Ref. [
11]).
3.1.2. Extended Series: Effect of Hydroxyl-free Systems and Increased Concentration of Hydroxyl Groups on Initial Reaction Rate and Forward DA Rate Constant
The model series of networks is further extended with a hydroxyl-free furan-maleimide network (based on 4F400-ester, see
Supplementary Materials) and some hydroxyl-free linear or branched furan-maleimide DA systems (based on the monofunctional furan FGE). On the other hand, the hydroxyl concentration in the stoichiometric furan-maleimide mixtures is also increased by adding different amounts of PPG425 as a third component (see
Section 2.1. Materials).
The DA rates of these additional stoichiometric mixtures of furans and maleimides (plus PPG425 additive) are experimentally determined by microcalorimetry in isothermal conditions at 20 °C and interpreted in the same way as discussed in
Section 3.1.1. The average experimental value of k
DA (=v
0/([F]
0 [M]
0) at 20 °C) for the extended series of DA reactions (model series of 3.1.1. plus OH-free systems and systems with PPG425) is <k
DA> = 2.27 ± 0.21 10
−5 kg (mol s)
−1 (see
Table S3). Very similar values of <k
DA> and SD are obtained as for the model series in 3.1.1. The experimental <k
DA> of this extended series is slightly lower than the value calculated with the optimized kinetic parameters from
Table S1 (k
DA (
endo plus
exo at 20 °C) = 2.42 10
−5 kg (mol s)
−1). This slight deviation (6%) is acceptable in view of the extra experimental systems involved and the different experimental approaches (vide supra). Note also that a deviation of 6% on k
DA is within the SD limits, which can be expressed as equivalent to minor temperature changes of (less than) ± 1 °C around the average reaction temperature of 20 °C.
To examine the influence of the concentration of hydroxyl or ether functionalities on k
DA at 20 °C and to detect potential trends, all data of the extended series are presented in
Figure 3. The ratio in the studied extended series = v
0/([F]
0 [M]
0) at 20 °C is plotted as a function of the concentration of additional functional groups in these systems, i.e., OH (
Figure 3a) and ether (
Figure 3b–d). Nearly constant values for k
DA are observed in all plots, in agreement with the limited SD on <k
DA>. Moreover, no obvious trends are found as a function of hydroxyl or ether concentration in the mixtures. The addition of extra OH-groups by the PPG425 additive, up to a doubled concentration in the mixture 4F400-2M400, also has no effect on the forward DA rate constant (see “+” symbols in
Figure 3). A strong support for the absence of H-bond catalysis is the observation that the OH free linear or branched systems with FGE (FGE-2M230, FGE-2M400, and FGE-3M) and the OH free network (4F400-ester-2M400), in which
no H-bonding is interfering, have a similar experimental value of k
DA (within the standard deviation of 0.21 10
−5 kg (mol s)
−1) and are in line with all data in
Figure 3 (see symbols on y-axis of
Figure 3a).
It can be concluded that the H-bonding catalytic effect of the hydroxyl groups of the furan compounds, interacting with ether groups of the spacers and carbonyl groups of the maleimides, on the DA reactivity seems to be absent or at most very limited in the studied extended series (even if the hydroxyl concentration is increased by the PPG425 additive). In the following section a computational study is performed to validate these experimental results.
3.2. Preliminary DFT Study
In the preliminary study, the strength of hydrogen bonding (HB) that may occur in the formation of the reversible polymer network is estimated using the model compounds in combination with a glycol molecule serving as hydrogen bond donor. Both Furan and Maleimide contain a variety of HB acceptor sites, as displayed in
Figure 4, with these being the furan’s ring oxygen and side-group’s ether functionality, and the maleimide’s carbonyls and ring nitrogen, as well as an ether functionality in the side group. Moreover, we also considered the intramolecular hydrogen bond that can be formed between the hydroxyl end group of the furan’s sidechain and the furan’s ring oxygen, termed in this paper as Furan_IHB. We found that hydrogen bonding interactions with Maleimide are stronger than with Furan. However, none of the interactions result in stable HB complexes. In addition, Furan with a linear side group is preferred over Furan with an intramolecular HB. A more comprehensive analysis can be found in the
Supplementary Materials.
Next to the HB strength, a detailed look at the frontier molecular orbitals of the two compounds and their complexes with glycol is included, so that the possible favorable effect of HB coordination on the HOMO-LUMO energy gap can be scrutinized.
In Diels–Alder reactions, a diene, e.g., Furan, combines with a dienophile, e.g., Maleimide, to form a cycloadduct. DA reactions can be categorized into normal or inverse electron-demand reactions depending on which frontier orbital interactions are dominating: in the case of normal demand the HOMO of the diene strongly interacts with the LUMO of the dienophile, whereas for an inverse demand DA reaction, the diene’s LUMO and dienophile’s HOMO combination shows the smallest energy gap. It is also widely known that the orbital energy gap can be additionally reduced or increased by inclusion of electron-accepting or -donating substituents on the diene or dienophile. Moreover, DA reactions can be further accelerated by adding Lewis acids that can coordinate to one of the reagents or through suitable noncovalent interactions such as hydrogen bond donation [
20,
34,
35,
40,
41,
42]. For normal electron-demand DA reactions, this has been commonly attributed to a stabilization of the LUMO of the dienophile, as such reducing the orbital energy gap and lowering the activation energy to cycloaddition [
24,
25]. However, two very recent contributions by Vermeeren et al. [
43,
44] question this general assertion. The authors concluded that, even though Lewis acids may induce a considerable HOMO-LUMO gap reduction, the total orbital interactions between the reagents are not enhanced, and that the increased reactivity is due to diminished Pauli repulsion between the
-systems of the approaching reactants.
Nevertheless, we explored the impact of hydrogen bonding at the different coordination sites on the frontier orbital levels to probe possible catalytic activity through secondary interactions.
Table S5 indicates that glycol interaction with the HB acceptor atoms in Furan stabilizes both the HOMO and LUMO levels compared to uncoordinated Furan, with the effect being slightly larger for the LUMO energy. When glycol forms a HB with one of the maleimide’s carbonyl groups, again a lowering of both of Maleimide’s frontier orbital energy levels is observed, but in this case it is less pronounced for the LUMO energy. Remark that in the case of Maleimide_gly, the occupied orbital that may combine with the diene’s LUMO is in fact the HOMO-3, since the HOMO to HOMO-2 orbitals are mainly located on the glycol and/or the maleimide’s side group (see
Figure S1). A different situation is encountered for coordination to the ether’s oxygen of Maleimide_cocgly, for which a minor stabilization of the HOMO level is computed whereas the LUMO energy level is slightly destabilized.
Table 2 summarizes the HOMO-LUMO orbital energy differences between the LUMO of the maleimide and the HOMO of the furan, on the one hand, and maleimide’s HOMO and furan’s LUMO, on the other. From the tabulated values, it is clear that the furan-maleimide cycloaddition can be categorized as a normal electron-demand DA reaction. Focusing on the normal-demand orbital interactions, a HOMO-LUMO energy gap reduction is only registered for the Furan-Maleimide_gly combination, with a relatively modest value of 0.21 eV. The largest gaps are associated with the intramolecularly hydrogen bonded furan derivative, which showed the largest stabilization of the HOMO level.
A simplified orbital diagram, showing the relevant frontier orbitals for the uncoordinated and glycol-coordinated maleimide in combination with Furan, is depicted in
Figure 5. The HOMO and LUMO almost fully reside on the main furan and maleimide structure, respectively. Based on the computed orbital gaps, we conjecture that only HB coordination to the carbonyl groups in Maleimide may result in a catalytic effect, as should be reflected in a lower activation energy compared to the DA reaction without considering secondary interactions. In the next section, the impact of hydrogen bonding, with a hydroxyl group as HB donor, on the DA reaction profiles will be examined in detail for both
endo and
exo cycloaddition.
3.3. Influence of Hydrogen Bonding on Diels–Alder Energetics of Substituted Furan and Maleimide
We calculated the reaction profiles of the
endo and
exo cycloaddition reactions without and with hydrogen bonding interactions present. The energetics were computed at the same level of theory as the complexation energies in the
Supplementary Materials. and are tabulated in
Table 3 (enthalpy
H at 298.15 K),
Table S6 (internal energies at 0 K) and
Table S7 (Gibbs free energies at 298.15 K). In all cases, two distinct conformations were considered, with the ether functionality of the maleimide’s side group pointing away (conformation A) or towards (conformation B) the furan molecule, as depicted in
Figure 6.
When no secondary interactions are present, the lowest enthalpy of activation is found for the formation of the endo cycloadduct in conformation B, with a value of 18.6 kcal mol−1. Even though endo conformation B is slightly more stable for the reactant complex and adduct compared to conformation A, the transition state of endo B is even lower in energy, as such yielding the lowest barriers for both the forward and reverse DA reactions. The values for the exo DA reactions in conformations A and B are distinctly higher than their respective endo reactions, by 0.6 to 1.2 kcal mol−1 for the forward DA and 1.5 to 1.9 kcal mol−1 for the retro DA. Please note that when the reaction profiles for exo cyclization in conformations A and B are compared, it is found that conformation B results in lower enthalpies (with respect to the separate reagents) for the reactant complex and transition state structures but not for the exo adduct. When entropic contributions are also added, the stationary point structures in conformation A are energetically less destabilized than those in conformation B. However, this does not impact the trends we found for the activation and reaction enthalpies, which still indicate that endo cycloaddition is kinetically favored over exo cyclization (with also here a preference for conformation B) and that the exo products are more stable than their endo equivalents.
In a next step, we investigated the possibility of hydrogen bonding between the two reagents, in which the hydroxyl functionality in the furan’s side group is interacting with one of the carbonyl groups of the maleimide. For both
endo and
exo cycloaddition in conformations A and B, reaction profiles were obtained, which are denoted as M[C=O] + F[-OH] in
Table 3,
Table S6 and S7. The stabilizing effect of the hydrogen bonds is more pronounced in the
endo than in the
exo reactant complexes, but similar for the A and B conformations. In the transition state structures, the hydrogen bonding is around 1–2 kcal mol
−1 more stabilizing than in the RCs. The different TS conformations are visualized in
Figure S4. Please note that the magnitude of the energy lowering for the different stationary points does not correlate with the measured hydrogen bond lengths (-C=O…HO-) (
Table 4), indicating that steric interactions also play a role.
Hence, for both
endo and
exo conformations, the hydrogen bonding gives rise to a reduction in the activation enthalpies by 0.8 to 1.7 kcal mol
−1. The lowest barriers are found for conformation B, again with a difference of around 1 kcal mol
−1 in favor of
endo cyclization. The barriers for the
exo retro DA reactions remain the same and reduce by ~1.5 kcal mol
−1 for the
endo retro DA (conformations A and B). When the Gibbs free energy profiles (
Table S7) are considered, 4 reactions show a quantifiable reduction in barrier compared to the situation without HB: forward
endo and
exo conformation A and the retro
endo DA reactions. Generalizing over both conformations, a minor to no measurable catalytic effect for the forward
endo and
exo cycloadditions and retro
exo DA reactions is observed; theoretically, only the reverse DA reaction for
endo adducts may be accelerated by hydrogen bonding, by a factor of 18 at most.
3.3.1. Influence of Hydrogen Bonding of Additive on Diels–Alder Energetics of Substituted Furan and Maleimide
Besides this intermolecular hydrogen bonding between the reagents, we also examined the effect of possible hydrogen bond donation of polypropylene glycol (PPG) additives to one of the reagents. This type of HB was modeled by adding an ethane-1,2-diol or ethylene glycol molecule to the elementary DA reactions. Both Furan and Maleimide bear two types of hydrogen bond acceptor positions. Based on our orbital interaction study, only HB with the maleimide’s carbonyl groups is anticipated to induce a reduction of the energy barriers of the forward DA reaction, whereas coordination to the ring oxygen of furan is expected to increase the DA barriers.
First, Furan’s ring oxygen is considered, denoted as F[(O)] + glycol in
Table 3. The enthalpy barriers at 25 °C for the forward and retro DA reactions are in almost all cases considerably larger than their respective “uncatalyzed” reactions. Only for the forward
exo conformation B reaction is a similar activation enthalpy found. The same trends apply for the Gibbs free energetics. At first sight, it seems that coordination of glycol to Furan’s oxygen has a more adverse impact on the
endo reactions compared to the
exo reactions. This can be associated with an additional hydrogen bond formed between the second hydroxyl of glycol and the OH functionality of Furan and is only present in the reactant complexes. We therefore also computed the
endo reaction paths using 2-methoxyethanol as a possible catalyst. The results are listed in
Table S8. The energy barriers reduce by approximately 1.5 kcal mol
−1 and are therefore more in line with what is observed for the
exo reactions.
The second coordination site we examined is one of the carbonyl groups in Maleimide, listed as M[C=O] + glycol, for which the orbital diagrams conjecture a potential catalytic effect. Based on the enthalpy values in
Table 3, hydrogen bonding causes a clear decrease in forward and retro DA reaction barriers for both
endo and
exo. This decrease is maintained upon inclusion of entropy. The barriers are ±1 kcal mol
−1 lower than when the hydrogen bond arises from the actively involved furan reactant, except for forward
endo conformation A for which a smaller decrease is distinguished and the retro
endo conformation B which has a nearly identical barrier.
Finally, the ether groups part of Furan (F[-O-] + glycol) or Maleimide’s sidechain (M[-O-] + glycol) were also examined. In the case of Furan coordination, the and values are similar or slightly larger than for the “uncatalyzed” equivalents, both for the forward and retro cycloadditions. Looking at Maleimide’s ether hydrogen bonding, a ~1.5 kcal mol−1 lowering of the Gibbs free activation energy (but not for ) is found for the forward endo and exo conformation B cycloadditions. For endo, this can be partially explained by increased steric repulsion due to the proximity of the furan reactant and the glycol-coordinated side group of the maleimide, as can be witnessed by the less stabilized reactant complex (RC) for this reaction though less so for the corresponding TS.
3.3.2. Influence of Ester Substitution on Diels–Alder Energetics of Substituted Furan and Maleimide
To further elucidate the influence of hydrogen bonding on the experimental reaction rates, additional computational work was carried out in which the hydroxyl groups near the furans were replaced by ester functions, as such excluding any HB formation within the network.
Table 5 lists the enthalpies H, computed at 298.15 K, for all stationary points along the reaction path of the [4+2] cycloaddition between Maleimide and Furan, but having an ester replacing the hydroxyl functionality. Again, the separate reagents are taken as reference. The 0K and Gibbs free energy (298.15 K) results are collected in
Table S9.
Comparing the enthalpies in
Table 5 to the first four entries of
Table 3 (no HB), the ester-containing reactant complexes and TS structures are 0.6 to 1.8 kcal mol
−1 less stable than their hydroxyl equivalents. The differences are even more pronounced for the products. However, the forward reaction barriers (TS − RC) are almost identical, whereas the retro DA barriers are on average about 2 kcal mol
−1 lower. More importantly, these discrepancies nearly completely disappear for the Gibbs free energy values. Therefore, if the Maleimide-Furan DA reactions are not catalyzed through hydrogen bonding interactions (for the cases without and in the presence of PPG additive), then their reaction rates should match (within experimental deviations) with those obtained for the hydroxyl-free reactions. This is indeed demonstrated in
Figure 3 of the experimental study, described in
Section 3.1.
We can conclude that for all cases the endo formation remains kinetically favored, whereas the exo formation is thermodynamically favored, which is in agreement with our experimental findings. The discussed data indicate that, in theory, hydrogen bonding through functional groups present in the network polymers can act as a catalyst for both the forward and retro Diels–Alder reactions, if the maleimide’s carbonyl or possibly nearby ether groups are involved and with hydroxyl groups of furan or PPG as the possible hydrogen bond donors.
To allow for a more direct comparison with the experimental data in this study, rough estimates of the second-order rate constants were determined based on the computed Gibbs free energy profiles in
Table S7 and compared to the experimental measurements listed in
Table S3. First, the rate constants at 20 °C of all
endo and
exo cycloadditions in
Table S7, i.e., without and with hydrogen bonding (furan-based or glycol-based), were calculated using the Eyring–Polanyi equation from transition state theory (
Table S10). Next, the rate constants were weighted via the Boltzmann populations of the reactant complexes for three different scenarios: (1) not accounting for hydrogen bonding, (2) considering hydrogen bonding between the two reagents, Furan and Maleimide, (3) including for hydrogen bonding via glycol additives as well. Moreover, the weighted rate constant of the DA reaction between Maleimide and the OH-free, ester-substituted furan (
Table S11) was estimated starting from the energetics in
Table S9. The total DA reaction rate constants were taken as the sum of the rate constants obtained for
endo and
exo adduct formation and are listed in
Table S12 together with the experimental second-order rate constants k
DA of the corresponding experimental systems.
Table 6 contains the predicted vs. the experimentally measured relative DA rate constants, with the average of the Model Series taken as the reference. A first observation is that possible hydrogen bonding between Furan and Maleimide does not affect the total rate constant. The rate constant for the ester-functionalized Furan-Maleimide cycloaddition is +/−1.5 times larger than for the ester system, for which no change was experimentally measured (cf. 4F400-ester-2M400). Note, however, that this relates to a Gibbs free activation energy difference of merely 0.3 kcal mol
−1, which can be due to different errors as a result of the level of theory. Finally, the influence of the addition of glycol on the initial rate was evaluated. Theoretically, a non-negligible rate enhancement of a factor of 3.5 is seen, which is not reflected in the experimental data of 4F400-2M400 with PPG425 against the Model Series (average values).
In summary, hydrogen bonding via addition of a HB donor to the DA system can in theory catalyze the reaction to some degree if the majority of the OH groups, being from the furans’ side groups or glycols, are coordinated to sites that result in a lowering of the Gibbs free energy of activation. However, the experimental results clearly rule out this supposition. It is indeed very unlikely that every Diels–Alder reaction taking place during the formation of the reversible network will be catalyzed, mainly because the hydroxyl groups can interact with a range of different sites of which (not so nearby) ether functionalities in the spacers are the most abundant (cf.
Figure 3) and which have no catalytic activity.