Understanding low-pressure CO₂ insertion chemistry in epoxide–CO₂ copolymerization catalysis

Abstract

Despite many CO₂ use strategies being reliant on fast and selective CO₂ insertion reactions into metal-alkoxide bonds, in-depth studies into this chemistry remain rare. Here the effect of CO₂ pressure on the CO₂ insertion chemistry is studied using epoxide–CO₂ copolymerizations. Five high-performance literature catalysts are investigated under systematically varied CO₂ pressures, revealing kinetic profiles indicative of CO₂ insertion equilibria. For each catalyst, two key parameters describing the CO₂ insertion chemistry are determined: the equilibrium constant, K_eq, and the saturation CO₂ pressure above which catalytic performance is maximized, P_threshold. Generalizable correlations between copolymerization activity, K_eq and P_threshold are uncovered and used to predict performances for four further catalyst–monomer combinations. These correlations are a direct link between CO₂ insertion chemistry and process operating conditions, providing a mechanistic framework and testing protocols to accelerate future catalyst development. These results should help deliver efficient scalable CO₂ use technologies, operating with minimal energy.

Main

The chemical industry remains dependent on unsustainable, fossil carbon sources^1,2,3. To move towards a circular carbon economy, there is an urgent need to replace them with renewable carbon, for example from biomass or waste CO₂, and to ensure the lowest possible energy consumption^1,2,3. Scalable CO₂ use technologies are, therefore, essential for the future chemical industry, but should operate under the lowest feasible pressure and deliver maximum rates^1,4,5,6. To effectively transform CO₂ into valuable products, catalysis is vital^7,8,9,10. CO₂ insertion into metal-alkoxide bonds (M–OR) is a common step across many catalytic transformations, for example CO₂ coupling with epoxides to form cyclic carbonates or polycarbonates or with alcohols to form dialkyl carbonates^8,10,11. In nature, the metalloenzyme Rubisco catalyses atmospheric CO₂ transformation into 3-phosphoglycerate, involving CO₂ insertion into a transient Mg(II)ene-diolate (alkoxide) species^5,12. Related CO₂ insertions into metal hydroxide or aqua bonds (M–OH or M–H₂O) are implicated in the industrial high pressure catalytic reverse water gas shift reaction⁵. These CO₂ insertion steps are often proposed to occur rapidly and to be pre-rate limiting, challenging their direct investigation^9,13,14. Increasing the scale and efficiency of these CO₂ transformations requires better understanding of the kinetics and thermodynamics of CO₂ insertion into metal-alkoxide bonds¹⁵.

Most previous investigations of CO₂ insertion chemistry have applied stoichiometric reactions with metal alkoxides and/or hydroxides^16,17. For example, zinc hydroxide complexes were shown to react with CO₂ in chemical equilibria^18,19. Whilst stoichiometric studies can be useful, caution should be applied in generalizing their findings to catalytic processes. Such CO₂ insertions relevant to utilization catalysis should be studied under real process operating conditions.

In this work, we target carbon dioxide and epoxide ring-opening copolymerization (ROCOP) using catalysts that produce perfectly alternating polycarbonates and maximize carbon dioxide uptake^20,21. These catalytic cycles also involve metal-alkoxide intermediates that react with carbon dioxide to produce a metal-carbonate species; in this field it is desirable to identify carbon dioxide insertion chemistry that is effective at low catalyst (metal-alkoxide) concentrations and low CO₂ pressures. Previous kinetic and computational investigations, using a range of different catalysts, were generally conducted using higher carbon dioxide pressures (10–30 bar) and nearly always showed a zero order in CO₂ pressure; as a consequence, in this field catalysts were not designed or optimized for low CO₂ pressure insertion chemistry^{13,14,22,23,24,25}. Very recently, we discovered the ROCOP of CO₂ and propene oxide (PO) using a heterodinuclear Co(III)K(I) catalyst, which showed good activity and selectivity at very low pressures. The catalyst also showed rates that depend on the CO₂ pressure applied over the range 2–12 bar. At higher pressures (12–30 bar), the rates are independent of pressure and are maximized¹³. Experimental kinetics and density functional theory calculations suggested that CO₂ insertion occurs by an equilibrium reaction between metal-alkoxide and metal-carbonate intermediates^13,14 (Fig. 1b). The CO₂ insertion equilibrium controls the effective concentration of the metal-carbonate intermediate, which is the catalytic species involved in the polymerization rate-determining step. Further, it influences catalyst selectivity, as the cyclic carbonate by-product forms from the metal alkoxide¹³. Before our work, only one other group reported two β-diiminate Zn(II) catalysts, used for cyclohexene oxide (CHO)–CO₂ ROCOP, that also showed pressure-dependent rates^26,27. These previous reports, together with some suggestions of CO₂ pressure-dependent rates in other CO₂ insertion reactions^18,19,28, motivate the current in-depth investigation into how CO₂ pressure influences rates more generally in this field of copolymerization catalysis.

Fig. 1: The ROCOP of epoxides and carbon dioxide.

a, ROCOP of epoxides and CO₂ with the two most commonly studied epoxides: propene oxide (PO) and cyclohexene oxide (CHO). b, The proposed catalytic cycle for a high-performance Co(III)K(I) catalyst. The CO₂ insertion is proposed as an equilibrium and incorporated into the rate law¹³.

For industrially operable polymerizations, energy efficiency is important and this may be achieved by conducting reactions at moderate temperatures so as to balance rates, selectivity and polymer viscosity²⁹. Further, reactions should be conducted at the lowest catalyst loadings feasible, particularly if residues must be removed before polymer use. In the past, there have been extensive investigations into the influences of catalyst loading and process temperature but much less understanding of how carbon dioxide pressure influences the catalysis^14,21,30,31. Nonetheless, when copolymerization catalysts are effective at low carbon dioxide pressures (P_CO2 ≤ 10 bar), the resulting process financial costs (capex) and greenhouse gas emissions associated with gas compression are expected to be substantially lower²⁹. To illustrate this point, Aspen Plus was used to estimate the changes to cost and energy input during poly(propene carbonate) (PPC) production due to CO₂ compression from 1 bar to 5 bar, 10 bar, 20 bar or 50 bar, respectively. These estimates suggest that increasing the CO₂ pressure from 5 bar to 20 bar, results in an increase of ~50% to the capital cost and >200% to the process energy requirement (Supplementary Table 1). These results highlight the economic and environmental benefits for lower pressure copolymerization catalysts.

Here the CO₂ insertion chemistry occurring during CO₂ and epoxide ROCOP catalysis is examined under industrially relevant process operating conditions, that is low catalyst loading (1:4,000 catalyst:epoxide), moderate temperature (50 °C) and minimized but fixed carbon dioxide pressure^9,20,32 (Fig. 1a). Epoxide–CO₂ ROCOP is an efficient CO₂ utilization process, forming useful polycarbonate products with high CO₂ uptakes, for example 43 wt% CO₂ in PPC^{9,13,33,34,35,36}. These alternating polycarbonates are useful as surfactants, electrolytes and binders in batteries, thermoplastic elastomers, pressure sensitive adhesives and as engineering plastics^{1,37,38,39,40}. To understand the influence of CO₂ pressure on copolymerization rates, we selected five known high-performance catalysts and investigated the influence of the carbon dioxide pressure applied to each of their polymerization rates. In all cases, the CO₂ pressure applied during the catalysis influences the copolymerization kinetics and for each catalyst the CO₂ insertion equilibrium constant is quantified. Combining the different catalyst threshold pressures and insertion equilibria, we reveal a general method to evaluate, optimize and compare new catalysts. For new catalysts it is possible using a single experiment to predict the lowest CO₂ pressure required to achieve maximum rates and selectivity.

Results and discussion

Catalyst selection

Direct comparisons between catalysts in this field is challenging as rates are reported under individually selected and/or optimized conditions. Analysis of the literature shows many require high CO₂ pressures and moderate temperatures, challenging the selection of catalysts operating at the low pressures and higher temperatures desirable for scale-up (Supplementary Fig. 1). To select catalysts suitable for in-depth kinetic investigations of CO₂ pressure dependence, we evaluated the literature for catalysts with precedent for good activity (turnover frequency >100 h⁻¹) and selectivity (>90%) at low CO₂ pressures (≤10 bar) (Supplementary Fig. 1 and Supplementary Table 2). We also selected catalysts that retain their performances at medium to high temperatures (45–100 °C), so as to maximize rates while minimizing polymer viscosity²⁹. From a long list of catalysts showing optimum performances at pressures below 30 bar, catalysts 1–4 were selected^13,33,34,41. They fulfil the performance criteria, are synthetically accessible and represent different classes including both mono-metallic or multi-metallic catalysts and catalysts operating with or without cocatalysts (Fig. 2). The rates for each of these catalysts were determined under varied CO₂ pressures (2–30 bar) and using otherwise identical conditions^33,34,41. The results of these experiments are compared to the previously reported Co(III)K(I) catalyst 5 for which the CO₂ insertion equilibrium was proposed¹³ (Fig. 2).

Fig. 2: Catalysts studied in this work.

The structures and key data for the catalysts 1³³, 2³⁴, 3³⁴, 4⁴¹ and 5¹³. The figure includes turnover frequency (TOF) and selectivity for polycarbonate data at the lowest carbon dioxide pressure reported in the original publications. ^tBu, tertiary butyl (–C(CH₃)₃); OBzF₅, pentafluorobenzoate (–OCOC₆F₅); Ph, phenyl (–C₆H₅); PPNCl, bis(triphenylphosphine)iminium chloride; OAc, acetate (–OCOCH₃).

All these leading catalysts are cobalt complexes, as it outperforms other metal choices^21,33,35,42 (Supplementary Table 2). Since the leading commercial epoxide is PO, PO–CO₂ ROCOP catalysts were investigated first^9,35. However, the copolymerization of CHO (CHO–CO₂ ROCOP) is also a commonly used catalyst benchmark in the field, hence catalyst 3 was investigated for CHO–CO₂ ROCOP³⁴.

Kinetics

Catalysts 1–5 were prepared according to literature procedures^13,33,34,41, characterized using infrared and ultraviolet-visible light spectroscopy and, where possible, using ¹H and ¹³C NMR spectroscopy (Supplementary Figs. 2–33).

To investigate whether catalysts 1–4 exhibit behaviours consistent with a metal-alkoxide and CO₂ insertion equilibrium, kinetic analyses were conducted using each catalyst. All reactions were conducted in neat epoxide since these conditions are desirable at scale (no organic solvents). Catalysts should also control the polycarbonate molar mass, dispersity and polymer chain end-groups, specifically maintaining activity when using excess (di)alcohols, controlling for (di)hydroxyl polymer end-groups⁴³. All polymerizations were therefore conducted in the presence of trans-1,2-cyclohexanediol in neat epoxide, that is [catalyst]:[diol]:[epoxide] = 1:20:4,000 at 50 °C.

Taking catalyst 2 as a representative example of the experiments conducted for each of the catalysts, first, a series of polymerizations were conducted under CO₂ pressures from 2 bar to 25 bar. At a fixed pressure, polymerizations were monitored using in situ infrared spectroscopy allowing for the calculation of a pseudo first-order rate constant, k_obs, from the semi-logarithmic plot of ln([epoxide]/[epoxide]₀) versus time (Fig. 3b,c). Experiments were conducted at least in duplicate to enable quantification of errors. Next the k_obs values were plotted against the applied CO₂ pressures, showing a linear increase in rate from 2–14 bar (Fig. 3d). The same data plotted as ln(k_obs) versus ln(P(CO₂)) have a gradient of 0.97, indicating a first-order rate dependence on CO₂ pressure (Fig. 3e). At pressures above 14 bar CO₂, the rates were constant and no further increase in k_obs was observed. Above the threshold pressure (14 bar), P_threshold, there is a zero-order dependence on CO₂ pressure (Fig. 3d). Polymerization rates were also plotted against [CO₂], showing the same trends^13,44 (Supplementary Figs. 43–46).

Fig. 3: Kinetic analysis conducted using catalyst 2.

a, Structure of catalyst 2. b, In situ infrared spectrum, showing the peaks corresponding to PPC (1,750 cm⁻¹). c, Exemplar semi-logarithmic plot of [PO]/[PO]₀ versus time, where the rate constant, k_obs, is the slope of the graph, using the rate data for the polymerization at 25 bar CO₂. It has previously been shown that values for such initial rates compare very well with integrated rates determined over wider conversion ranges (20–80%)⁵¹. d, Experimentally determined rates (k_obs) versus P(CO₂). All rate constants were determined as the average of n = 2 independent runs, with errors indicated as ± the standard error from the mean, typically falling ±10%. k_max is the maximum polymerization rate constant, determined as the mean of the k_obs values in the CO₂ pressure independent regime. e, Plot of ln(k_obs) versus ln(P(CO₂)) showing a gradient of 0.97. All ln(k_obs) values were determined from k_obs values obtained as the average of n = 2 independent runs, with errors indicated as ± the standard error from the mean. f, Concentration versus time plot showing the excellent agreement between the experimental data and data generated using the rate law and modelled using COPASI software (Supplementary Fig. 34 and Supplementary Tables 3–6).

Source data

The experimental kinetic data for all the catalysts were collected and analysed in the same way as for catalyst 2. All catalysts showed two different regimes of activity versus CO₂ pressure, and for each catalyst a threshold pressure was identified as the lowest operating pressure for maximum rates (Supplementary Figs. 43–46). These kinetic data indicate that catalysts 1–4 all show metal-alkoxide and CO₂ insertion equilibria (Fig. 1b). These data are interpreted by low pressures resulting in CO₂ insertion equilibria controlling the effective concentration of the carbonate intermediate, which is the key intermediate in the catalytic rate-determining step. Above the threshold CO₂ pressure, the equilibrium lies towards the carbonate and maximum rates result¹³.

The CO₂ insertion equilibrium constant was determined for all five catalysts in the same way. In brief, in the CO₂ pressure independent regime, the equilibrium lies entirely towards the carbonate intermediate, hence [catalyst]₀ = [carbonate], assuming the catalyst can only be speciated as an alkoxide or carbonate intermediate (that is, no catalyst decomposition occurs). The carbonate intermediate concentration at a given pressure, [carbonate]_p, was determined from the ratio of the rate constant at that pressure and the maximum rate constant, multiplied by maximum carbonate concentration. Accordingly, the CO₂ insertion equilibrium constant, K_eq, was determined at each pressure and an average value determined (Supplementary Tables 7–12).

$${K}_{{\rm{eq}}}=\frac{[{\rm{carbonate}}]}{[{\rm{alkoxide}}][{{\rm{CO}}}_{2}]}$$

(1)

The five catalysts show K_eq values that vary from 0.25 ± 0.02 M⁻¹ for catalyst 4 to 3.10 ± 0.26 M⁻¹ for catalyst 3 (Supplementary Tables 7–12). A common rate law was proposed that accounts for the influence of the CO₂ insertion equilibrium and the concentration of the metal-alkoxide intermediate: this rate law applies at all CO₂ pressures (equation 2). Next, for each catalyst the experimental conversion versus time data was compared to data modelled using the rate law (Fig. 3f for catalyst 2 and Supplementary Fig. 34). All catalysts showed an excellent agreement between the experimental and kinetic model data over the entire data range. This finding, applicable to all five catalysts, underscores the generality of the rate law and utility of quantifying the CO₂ insertion equilibria (K_eq).

$${\rm{Rate}}={k}_{{\rm{p}}}{K}_{{\rm{eq}}}\left[{\rm{alkoxide}}\right][{{\rm{CO}}}_{2}]\left[{\rm{epoxide}}\right]$$

(2)

Variable substrate concentration-rate dependencies, observed with CO₂ pressure in this work, are also known in other fields, for example enzyme kinetics⁴⁵. The data for catalyst 2 were also fit using a Michaelis–Menten kinetic model. Plotting the initial rate, v_i, against [CO₂], and fitting with the Michaelis–Menten model, revealed K_eq = 0.49 M⁻¹ and v_max = 6.6 × 10⁻⁴ Ms⁻¹, which are in good agreement with the values for K_eq = 0.62 ± 0.09 M⁻¹ and v_max = 5.8 × 10⁻⁴ Ms⁻¹ determined using the rate law presented in this work (Supplementary Fig. 52). The benefit of using our experimental and kinetic methods are that they directly determine the carbon dioxide insertion equilibrium constant K_eq and the threshold CO₂ pressure P_threshold, the latter is absent from saturation kinetic models.

Generality of metal alkoxide and CO₂ insertion equilibrium

According to the common rate law, the CO₂ insertion equilibrium constant directly correlates with the polymerization rate. Therefore, we plotted the CO₂ insertion equilibrium constant, K_eq, for each of catalysts 1–5, against their rates, measured at 5 bar CO₂ and 50 °C (k_obs,5 bar). The plot reveals a clear exponential correlation between carbon dioxide insertion equilibrium constant and rate (Fig. 4b and Supplementary Fig. 53). The highest performing catalyst (3) exhibits the highest CO₂ insertion equilibrium constant, 3.10 ± 0.26 M⁻¹. Conversely, the lowest performing catalyst (4) has the lowest CO₂ insertion equilibrium constant, 0.25 ± 0.02 M⁻¹ (Fig. 4b–d).

Fig. 4: Relating the CO₂ insertion equilibrium constant, K_eq, to polymerization rates.

a, General reaction scheme for epoxide–CO₂ ROCOP showing the proposed CO₂ insertion equilibrium between a Co-alkoxide and a Co-carbonate intermediate. b, Plot showing all catalysts and values for K_eq versus k_obs at 5 bar CO₂ pressure and 50 °C. All k_obs values were determined as the average of n = 2 independent runs, with errors indicated as ± the standard error from the mean, typically falling ±10%. Values for K_eq and corresponding errors were calculated as indicated in Supplementary Tables 7–12. c, Plot showing data for all catalysts with P_threshold versus K_eq. Values for K_eq and corresponding errors were calculated as indicated in Supplementary Tables 7–12. d, Plot showing data for all catalysts with P_threshold versus k_obs, at 5 bar CO₂ pressure and 50 °C. All k_obs values were determined as the average of n = 2 independent runs, with errors indicated as ± the standard error from the mean, typically falling ±10%. In all plots, squares represent PO–CO₂ ROCOP and triangles represent CHO–CO₂ ROCOP. The symbol colours correspond to the catalysts colour with their associated numbering as defined in Fig. 2. Data for catalyst 5 were taken from ref. ¹³.

Source data

These activity correlations underline the importance of CO₂ insertion equilibria across the different catalysts and provide a new way to compare and design better catalysts. To interpret the data, a mechanism whereby the rate-determining step involves catalyst carbonate attack on the epoxide is invoked (Fig. 1b). The concentration of this key catalyst species (metal carbonate) is controlled by the CO₂ insertion equilibrium. Thus, catalysts with favourable CO₂ insertion equilibria, for example catalyst 3, show greater catalytic performance. The slower and less selective catalysts, for example catalysts 1 or 4, show low CO₂ insertion equilibrium constants, consistent with higher concentrations of residual alkoxide intermediate.

The threshold CO₂ pressure, P_threshold, values describe the minimum CO₂ pressure to achieve the maximum rate. These values are likely to be very important to any process to make polymers^1,4,5,6. The values vary considerably for catalysts 1–5 from 7–16 bar CO₂. Plotting, P_threshold against K_eq, for catalysts 1–5 reveals a linear correlation (Fig. 4c). The better performing catalysts have higher equilibrium constants and lower P_threshold: that is, they reach maximum performance at lower CO₂ pressures. P_threshold also exponentially correlates to the measured k_obs,5 bar (Fig. 4d). This kinetic treatment directly links two measurable variables: the rate constant, k_obs,5 bar and P_threshold, a parameter central to low energy process operation. Such a correlation is particularly important, since it identifies how to maximize performances while minimizing the operating pressure with its associated economic and environmental costs (Supplementary Table 1).

Prediction of equilibrium parameters

There are clear correlations between rate, equilibrium and threshold pressure that apply to all five catalytic systems, which span a wide range of different catalyst classes (Fig. 2). One consequence is that these correlations could be generalizable to other epoxide–CO₂ copolymerizations, conducted isothermally, with experiments in this work all being conducted at 50 °C. It may be that the carbon dioxide insertion K_eq and P_threshold are predictable for any catalyst or monomer using a single measurement of rate coefficient, k_obs, which is set in this work at 5 bar. To experimentally test this hypothesis, a previously reported heterodinuclear Co(II)Mg(II) catalyst (6), not included in the original catalyst selection, was synthesized and examined for CHO–CO₂ ROCOP⁴⁶ (Supplementary Fig. 54 and Supplementary Table 13). Catalyst 6 was selected as it showed very high performances in the copolymerization catalysis, including operating at low loadings and temperatures. In addition, catalysts 1, 2 and 5, previously investigated for PO–CO₂ ROCOP, were each examined for a second monomer combination: CHO–CO₂ ROCOP. First, each catalyst was monitored for CHO–CO₂ ROCOP, at 5 bar CO₂ pressure, to obtain the rate coefficient k_obs,5 bar. Using k_obs,5 bar, the CO₂ insertion equilibrium constant, K_eq, and threshold pressure, P_threshold, were predicted using the exponential relationships that were previously uncovered (Figs. 4 and 5 and Supplementary Table 13). The predicted equilibrium constants for catalysts 1, 5 and 6 are comparable, with K_eq = 0.27 M⁻¹ (1), 0.85 M⁻¹ (5) and 0.28 M⁻¹ (6) (Supplementary Table 13). They also show similar, high, values for the predicted P_threshold = 16 bar (1 and 6) and 14 bar (5). In contrast, catalyst 2 has a substantially higher predicted CO₂ insertion equilibrium constant, K_eq = 23.4 M⁻¹ and a notably lower predicted P_threshold (Fig. 5). To further investigate the general predictability of K_eq, a previously reported organoborane catalyst was tested for CHO–CO₂ ROCOP⁴⁷ (Supplementary Fig. 54 and Supplementary Table 13). However, the observed activities were too low under these conditions to warrant further equilibrium or rate analysis.

Fig. 5: Prediction of threshold pressures for maximum catalytic performance.

a, Plot of threshold pressure for maximum catalytic performance (P_threshold) versus polymerization rate constant, k_obs, at 5 bar CO₂ pressure and 50 °C. Squares represent k_obs for the PO–CO₂ ROCOP, and triangles for CHO–CO₂ ROCOP. k_obs values were determined as the average of n = 2 independent runs, with errors indicated as ± the standard error from the mean, typically falling ±10%. Data for catalyst 5 were taken from ref. ¹³. Crosses represent measured values of k_obs,5 bar and predicted P_threshold values for catalysts 1, 2, 5 and 6 for the CHO–CO₂ ROCOP (Supplementary Table 13). b, Table showing the predicted P_threshold and the measured catalytic performance at P_threshold and at a pressure above it (20 bar) for catalysts 1, 2, 5 and 6. The rate data, k_obs, were obtained at 50 °C, using catalyst (0.025 mol%, 2.5 mM), CHO (6 ml, 9.9 M), trans-1,2-cyclohexanediol (0.5 mol%, 49 mM). c, Structures of the catalysts 1, 2, 5 and 6 for which P_threshold was successfully predicted. The symbol colours in the graphs correspond to the catalysts colour with their associated numbering as defined in Fig. 2.

Source data

Following the predictions of P_threshold and K_eq, the accuracy of the predicted values for catalysts 1, 2, 5 and 6 was tested experimentally. For catalyst 5, CHO–CO₂ ROCOP was investigated at pressures from 5 bar to 25 bar, with the P_threshold being 14 bar and matching the predicted value (Supplementary Fig. 55). For catalyst 1 and 6, the value of the predicted pressure threshold is tested by conducting CHO–CO₂ ROCOP at the predicted P_threshold (16 bar CO₂, Fig. 5), and at a higher pressure than the threshold (20 bar CO₂). If the predicted P_threshold is accurate, the catalytic performance should remain unchanged and indeed, the k_obs is equivalent at each of those pressures (k_obs,16 bar = 0.85 × 10⁻⁵ s⁻¹, k_obs,20 bar = 0.86 × 10⁻⁵ s⁻¹ for catalyst 1 and k_obs,16 bar = 0.91 × 10⁻⁵ s⁻¹, k_obs,20 bar = 0.77 × 10⁻⁵ s⁻¹ for catalyst 6). Catalyst 5 was applied at pressures of 14 (predicted threshold pressure) and 20 bar; it showed very similar rates at both pressures (k_obs,14 bar = 3.90 × 10⁻⁵ s⁻¹, k_obs,20 bar = 4.10 × 10⁻⁵ s⁻¹) once again validating the successful identification of the threshold pressure.

Since catalyst 2 performs far better at 5 bar than the other two catalysts, its P_threshold was predicted to be below 5 bar. This result implies that catalyst 2 has already achieved its maximum rates at 5 bar. Hence, catalyst 2 showed the same catalytic performance at both 5 bar and 20 bar (k_obs,5 bar = 3.86 × 10⁻⁵ s⁻¹, k_obs,20 bar = 3.91 × 10⁻⁵ s⁻¹), strongly suggesting that its P_threshold is <5 bar (Fig. 5 and Supplementary Table 13). These experiments are surprising since the data generated using PO–CO₂ ROCOP can be used to successfully predict P_threshold for CHO–CO₂ ROCOP and to accelerate identification of the optimum operating conditions, that is, minimum pressure for maximum rate. The results obtained using catalysts 1, 2, 5 and 6 for the CHO–CO₂ ROCOP indicate that the kinetic methods may be further generalizable to other monomers. It is particularly helpful to use a single kinetic evaluation (k_obs,5 bar) to identify and predict the optimum operating conditions for that catalyst.

The general applicability of K_eq as a predictor of catalytic performance is further illustrated by three other known catalysts for which pressure-dependent kinetics were reported^26,27,48. An antimony catalyst (with bis(triphenylphosphine)iminium chloride co-catalyst) showed an equilibrium constant of <1 bar⁻¹ in CHO–CO₂ ROCOP, resulting in a P_threshold > 20 bar (Supplementary Fig. 56). A similar P_threshold above 20 bar was reported for a di-Zn(II) β-diiminate catalyst. By contrast, a zinc β-diiminate catalyst 7 showed a threshold pressure <5 bar CO₂ pressure²⁶. In the original reports no equilibrium constants were determined; however, we estimated K_eq <1 M⁻¹ and K_eq ~ 3.67 M⁻¹ for the zinc catalysts, respectively (Fig. 6, catalyst 7).

Fig. 6: Relating the value of CO₂ insertion equilibrium constants to threshold pressures for maximum catalytic performance.

Plot of the combined data for all catalysts showing the carbon dioxide threshold pressure values, P_threshold, and CO₂ insertion equilibrium constants, K_eq, determined in this investigation (with colours identifying different catalysts and square markers referring to PO–CO₂ ROCOP, triangles to CHO–CO₂ ROCOP). The plot shows that only catalyst 2 applied for CHO–CO₂ ROCOP achieves the target low pressure (<10 bar) and high insertion equilibrium (>10 M⁻¹) performance.

Source data

The kinetic prediction method indicates that only catalysts with k_obs,5 bar > 2.5 × 10⁻⁵ s⁻¹ (K_eq > 10 M⁻¹), are expected to show CO₂ pressure independent performances below 10 bar. The PO–CO₂ ROCOP catalysts examined all show K_eq < 5 M⁻¹, and at 5 bar all show performances that depend on carbon dioxide pressure (squares, Fig. 6). Even in the broader literature there are not yet any PO–CO₂ ROCOP catalysts known or reported to enter the target regime: that is, showing high rates and selectivity at <10 bar pressure. The methods presented here should help accelerate new catalyst testing and identify catalyst structure–performance relationships, particularly focused on how catalyst structure drives carbon dioxide insertion chemistry. In contrast, for CHO–CO₂ ROCOP, catalyst 2 already shows a K_eq > 10 M⁻¹ and achieves excellent performances at <5 bar CO₂ pressure (Fig. 6). The literature also reveals other CHO–CO₂ ROCOP catalysts reported to exhibit high rates at low CO₂ pressures; these catalysts are recommended for evaluation using the methods reported here to confirm whether pressure independent performances are achieved at <10 bar. Where such criteria are achieved, the catalysts may even function using more dilute CO₂ sources (that is, <1 bar pressure): a regime that is very rarely explored in this field of catalysis^46,49.

Both catalyst structure and monomer choice influence the CO₂ insertion chemistry, highlighting the value in using the CO₂ insertion parameters, K_eq and P_threshold, as metrics for catalyst comparison. One benefit of these metrics is that they inform directly on the process operating conditions with respect to catalytic performance. Comparing catalysts using these parameters may be more informative than the conventional use of activity (that is, turnover frequency) as figure of merit. It is well known that such activity measurements are both monomer and condition dependent; in contrast, K_eq allows for comparisons over a range of CO₂ pressures and different epoxides. The ability to rapidly predict the carbon dioxide insertion K_eq or P_threshold values drastically reduce the experimental work needed to compare new catalysts and to identify the lowest pressure operating conditions for them.

The correlations and the practical experimental protocols should be especially useful in selecting catalysts for larger-scale use, and in identification of their optimum operating conditions⁵⁰. One question raised by this work is the extent to which similar CO₂ insertion equilibria, and threshold pressures, may apply to other CO₂ utilization catalyses? The use of the methods outlined in this report is recommended to explore CO₂ insertion equilibria in other catalytic cycles. The methods may be particularly useful in identifying operable, fast and selective catalysts that are needed to implement large-scale, energy efficient CO₂ uses.

Conclusions

The influence of CO₂ pressure on its insertion reactions into metal-alkoxide bonds was investigated using structurally diverse, high-performance epoxide and carbon dioxide ROCOP catalysts. Systematic experiments, conducted using epoxide and CO₂ at pressures from 2 bar to 30 bar, revealed that all five catalysts show pressure-dependent CO₂ insertion equilibria. A rate law, applicable under all pressures, was presented and interpreted by a mechanism accounting for differing extents of carbon dioxide insertion. Two reaction parameters are identified and methods to quantify them are presented: the CO₂ insertion equilibrium constant (K_eq) and the threshold carbon dioxide pressure above which rates are maximized (P_threshold). Direct correlations were uncovered between catalytic rate and the CO₂ insertion equilibrium constant and threshold pressure. The data, and parameter inter-relationships, were used to successfully predict the performances for known catalysts using new monomers (CHO–CO₂). The use of one measurement, rather than full kinetic analyses, substantially reduces the experimental work required to identify the lowest pressure process operating conditions and provides a reliable set of metrics by which to compare catalysts. The findings are particularly important for future catalyst design, specifically the under-recognized importance of design for CO₂ insertion, and in enabling scale-up of catalysts resulting in the lowest energy demand. Given the importance of CO₂ insertion equilibria in influencing this field of carbon dioxide copolymerization catalysis, it seems possible, if not likely, that other catalysts may also show related CO₂ pressure dependence. Identifying and quantifying the lowest energy conditions for such CO₂ insertions is really important to accelerate delivery of large-scale CO₂ utilization processes and products.

Methods

CHO–CO₂ and PO–CO₂ ROCOP procedures and experimental apparatus

The same procedures were followed when conducting the CHO–CO₂ and PO–CO₂ ROCOP. A representative method for the CHO–CO₂ ROCOP is detailed here.

The catalyst (0.015 mmol), trans-1,2-cyclohexanediol (35 mg, 0.3 mmol) and mesitylene (21 µL, 0.15 mmol, internal standard for monomer conversion quantification) were dissolved in CHO (6 ml, 59 mmol), under a nitrogen atmosphere. The solution was injected into a 100-ml Parr reactor fitted with an in situ attenuated total reflectance-infrared spectroscopy probe, under a flow of CO₂. The reactor was pressurized to the desired CO₂ pressure and heated to 50 °C. Mass flow controllers were used to ensure fixed and constant CO₂ pressure throughout the reaction. The reaction was monitored by changes to infrared peaks at 1,750 cm⁻¹ (polycarbonate) and 1,820 cm⁻¹ (cyclic carbonate). The polymerization was stirred continually at the desired temperature and pressure until >30% polycarbonate formation. The reaction was then cooled and quenched by exposure to air and addition of benzoic acid (2 mg, 0.016 mmol). The epoxide conversion data was externally calibrated by ¹H NMR spectroscopy using a crude reaction aliquot, using the added mesitylene as the internal standard.

The reaction rate coefficient, k_obs was determined as the gradient of plots of ln([epoxide]/[epoxide]₀) versus time (Supplementary Figs. 39–42), typical epoxide conversions are 5–20%. For each catalyst, epoxide–CO₂ polymerizations were conducted under the same reaction conditions ([catalyst]:[diol]:[epoxide] = 1:20:4,000). For catalysts 1 and 4, [catalyst]:[cocatalyst] = 1:1. Polymerizations were conducted at 50 °C at a fixed CO₂ pressure, with values systematically increased from 2 bar to 35 bar CO₂, using the reaction set up outlined above. All reactions were run in duplicate, with generally ±10% error. Using previously reported data for the solubility of CO₂ in PO and CHO^13,44, polymerization rates were plotted against both [CO₂] and CO₂ pressure.

Catalyst syntheses

The catalysts 1–5 were synthesized according to literature reports. Detailed synthetic procedures for each of catalysts 1³³, 2³⁴, 3³⁴, 4⁴¹ and 5¹³ are provided in the Supplementary Information.