Towards designer polyolefins: highly tuneable olefin copolymerisation using a single permethylindenyl post-metallocene catalyst

Using a highly active permethylindenyl-phenoxy (PHENI*) titanium catalyst, high to ultra-high molecular weight ethylene–linear-α-olefin (E/LAO) copolymers are prepared in high yields under mild conditions (2 bar, 30–90 °C). Controllable, efficient, and predictable comonomer enchainment provides access to a continuum of copolymer compositions and a vast range of material properties using a single monomer-agnostic catalyst. Multivariate statistical tools are employed that combine the tuneability of this system with the analytical and predictive power of data-derived models, this enables the targeting of polyolefins with designer properties directly through predictive alteration of reaction conditions.

PHENI* catalysts 1-3 were synthesised according to a literature procedure, 5 and the indenyl-PHENICS complex 4 according to a modified literature procedure. 6Ethylene was supplied by BOC Ltd. and was passed through pre-activated molecular sieves before use.Solid polymethylaluminoxane (sMAO, 3 rd generation) was supplied by SGC Chemicals PLC as a slurry in toluene which was dried under vacuum before use.

Experimental details
High-throughput screening was performed at Xplore s.r.l.(University of Naples Federico II) by V. Busico, R. Cipullo, L. Rongo, and A. Mingione.Polymerisation experiments were conducted in a FreeSlate Parallel Pressure Reactor (PPR) platform consisting of 48 reaction cells contained within a MBraun LabMaster glovebox, which has been described extensively elsewhere. 7Heptane solvent (5 mL) and TIBA scavenger (10 μmol) were added to the PPRs via robotic syringes which were then heated to the required temperature and pressurised to 120 psi (8.3 bar) with ethylene.Pre-catalyst (0.05-0.80 mg in heptane slurry) and 1-hexene were injected with robotic syringes.The reactions were run for 1 hour or until a certain ethylene uptake was reached, after which the reactions were quenched with an excess of dry air.The polymer samples were transferred to a Genevac EZ-Plus centrifugal evaporator to remove the volatiles and then dried under vacuum overnight.
Copolymerisation of ethylene with linear α-olefins.In a typical procedure, 150 mg triisobutylaluminium (TIBA) was added into a vial and 10 mL of hexanes was added.This mixture was introduced into a 150 mL Rotaflo ® ampoule containing a stirrer bar and swirled around the glassware.10 mg supported catalyst was added to the ampoule and washed in with a further 35 mL hexanes.To a sidearm the desired amount of comonomer was added and washed in with sufficient hexanes to keep the total reaction volume at 50 mL.The ampoule was sealed, cycled onto a Schlenk line, and degassed under reduced pressure.It was cycled a further two times using ethylene as a purge gas while the vessel was brought to temperature in a thermostatic oil bath with the stirring set at 1000 rpm.The stopcock was opened to ethylene at a pressure of 2 bar simultaneously with the introduction of the comonomer solution from the sidearm and the timer was started.On completion of the run, the vessel was degassed under partial vacuum then either filtered on a sintered glass frit (porosity 3), and washed with 2 x 25 mL pentane, or precipitated by decanting into a 500 mL round-bottomed flask containing dilute aqueous hydrochloric acid and rotary evaporation of the organic solvent, from which the polymer could be manually separated.Polymers were dried under vacuum until constant weight.All runs were carried out at least in duplicate to ensure reproducibility.

Ethylene/1-hexene copolymer.
Multivariate regression analysis.Data analysis and prediction was performed using the JMP® Pro software suite. 8A standard full factorial least squares model was used to construct models of A, Tm, α, Mw, PDI, x against Tp, c, n, Tp 2 , c 2 , n 2 , Tpn, Tpc, and cn.Analysis of variance (ANOVA) tests the assumptions of homoscedasticity and normality of residuals.Effect test analysis shows which predictors are significant.
The prediction profiler was used with defined desirability functions to determine the experimental conditions for a defined set of copolymer properties.
Conversions between wt% and mol%:

Fineman-Ross analysis
in copolymer, and knm is the rate constant for the insertion of monomer m after monomer n.

Multiple linear regression
When attempting to analyse the various LAO copolymerisation systems simultaneously, all of the relevant variables must first be identified.The explanatory variables are identified as the temperature of polymerisation (Tp), the identity of the comonomer (enumerated as the number of carbon atoms in the LAO, n), and the comonomer concentration (c).Other factors such as pressure, solvent, scale, scavenger, catalyst ligand, and stirring speed have been held constant in these studies but are likely to have an influence over the polymer properties.In particular, the ethylene pressure is expected to have a dramatic influence -at sufficiently high values, it is anticipated that the observed diffusion-controlled regime would be replaced by a kinetic regime in which the reactivity ratios of the catalyst to the two monomers becomes the dominating factor.The response variables are then identified as catalytic activity (A), polymer melting point (Tm), crystallinity (α), molecular weight (Mw), dispersity (PDI, Đ) and comonomer incorporation (x).Taken together, this 9-dimenstional dataset (N = 75) encompasses all of the reaction-space explored in the slurry-phase copolymerisation of ethylene with α-olefins using the PHENI* catalyst 1/TIBA.
From an inspection of the scatterplot matrix (Figure 3), it is immediately clear that some of these factors are more strongly correlated than others.As would be expected, the physical properties of the polymers depend strongly on comonomer incorporation, which is in turn strongly correlated with comonomer concentration.While it has been shown that LAO incorporation is also influenced heavily both by the polymerisation temperature and the identity of the comonomer, the bivariate plots do not show a strong correlation, though incorporation does increase slightly with Tp.This is consistent with the interdependency of these two variables and is itself strong motivation for pursuing further multivariate analysis.Of the polymer properties, Tm shows a strong linear correlation decreasing with increasing incorporation, while α, Mw, and PDI all show decreasing but non-linear correlations.As the relationships plotted in Figure S31 are generally nonlinear, multivariable regression was performed using polynomial combinations of the explanatory variables, up to quadratic terms (Tp, c, n, Tp 2 , c 2 , n 2 , Tpn, Tpc, cn).This resulted in a nonlinear model (model 1, M1) after least squares regression was applied to the dataset.This model allows for a detailed statistical analysis of regression, in particular the coupling of the explanatory variables to each other and the strength of their influence on the response variables.On the basis of likelihood ratio tests, Tp and c explain much of the variation of M1, with -log10(p-values) of 33.0 and 24.9 respectively, and all of the polynomial terms apart from n 2 have significant relationships at the .01level of hypothesis testing.The model is predictive with R 2 values of: A (0.65), Tm (0.85), α (0.81), Mw (0.96), PDI (0.50), x (0.85).Linear regression models assume linearity, homoscedasticity, and residual normality.In this dataset, visual inspection of the distribution of the residuals, confirms that these assumptions approximately hold.Linear models are unable to fit limiting behaviour, and so the empirical lower bounds, particular of Mw, are likely to be poorly accounted for.
F ratios are a measure of signal-to-noise and are defined as the ratio between the partial variation explained by the model, relating to each predictor, and the unexplained variation.
Larger values indicate a stronger relationship between a predictor and a response, and a value close to unity indicates no statistically significant effect.Activity is determined mostly by Tp and Tp 2 (F ratio 16.6 and 53.2), with the quadratic term reflecting the maxima around 60 °C (Table S10).Other key factors are Tpc and c 2 (F ratio 13.3 and 14.4) which highlight the temperature-concentration coupling that is observed qualitatively in.The quadratic concentration term goes some way to account for the initial decrease in activity before a positive comonomer effect becomes apparent at higher concentrations.Concentration effects are confounded by the change in diffusion regime from the formation of free-flowing polymer particles to soluble gels at higher concentrations which lead to a reduction in activity associated with mass-transport processes.The cross term Tpc (24.2) is the principal controlling predictor for PDI, which also has moderate contributions to both Mw (20.0) and Tm (16.5).The anticipated dependency of Mw on both Tp and c is reflected in large F ratios for these predictors, 678.3 and 330.3 respectively.Interestingly, of the cross terms, Tpn (44.9) had the largest F ratio, showing that temperature-chain length coupling is a more important factor than concentration-chain length.This is suggestive of a mechanistic interpretation, with larger energy barriers associated with larger monomers interacting with the thermal energy in the system; since polymer molecular weight is ultimately governed by the ratio of chain propagation to termination rate, such a phenomenon is to be expected.

F ratio, p-value
Incorporation is determined almost linearly by concentration, with c being the dominant predictor, alongside a contribution from Tp.The thermal properties of the polymer -Tm and αdepend largely on Tp and c, and therefore secondarily on x.The regression analysis reveals that while Tm is determined principally by the temperature-concentration couple, crystallinity depends more strongly on the side chain length, with the predictors nc, n 2 and Tpn all having statistically significant contributions.This is consistent with physical expectations: increased comonomer concentration (and therefore, incorporation) increases the degree of branching, which reduces the intermolecular forces between polymer chains and lowers the melting point. 10The branches are generally excluded from the crystalline lamellae, disrupt chain folding and lead to defective crystallisation, 11 with the length of the side chain controlling crystallinity. 12rough this analysis, it is possible to quantify many of the features of this system that are observed qualitatively in this work.That the relatively simple regression model M1 captures so much of the chemical and physical behaviour of this highly non-trivial reaction system demonstrates not only the power of large datasets for the delineation of interrelated variables, but also the potential ability to leverage the tuneability of the PHENI* catalyst system towards parameter-space optimisation.
Full details of the model and analysis of variance (ANOVA) are available from the authors upon reasonable request.

Designer LLDPE
Table S11 Target, predicted, and measured parameters for the polymerisations P1-3.M1 shown with a ± 95% confidence interval, experimental data shown as mean ± standard deviation.In addition to the statistical insight afforded by this highly multidimensional analysis, the real power of statistical models is predictive.Given the immense tuneability afforded by the PHENI* catalyst platform in olefinic copolymerisations, it would be highly desirable to be able to exploit control over the reaction conditions to synthesise polymers with predefined properties.To explore this, three sets of LLDPE properties were devised and translated into desirability functions corresponding to M1, consisting of unimodal functions maximised at the desired value (Figure S32).Following multivariate optimisation of total desirability, the calculated values for Tp, Cn, and [LAO] were rounded to an experimentally relevant degree.The expected values of the predicted output properties were found with a 95% confidence interval based on the covariance matrices.These copolymerisations were then performed with otherwise identical conditions to those used throughout this work: 50 mL hexanes, 150 mg TIBA, 2 bar ethylene, and 30 minutes (Figure S33).This morphological variation has been noted, and is not explicitly included in M1.Furthermore, the predictions for activity (M1 3424 kgLLDPE molTi -1 h -1 bar -1 ; expt.3175 ± 271 kgLLDPE molTi -1 h -1 bar -1 ), crystallinity (M1 39 %; expt.40 ± 7 %), and PDI (M1 4.1; expt.4.1 ± 0.4) were also closely aligned with M1.

Activity /kgLLDPE mol
Incorporation, x, (M1 7.8 %; expt.37.8 ± 4.7 %) showed a large discrepancy between the prediction of M1 and the experimental result.This is surprising both because incorporation as a function of Tp, n, and c is one of the best-defined aspects of M1 and because x determines many of the other well-predicted properties such as Tm and α.This may in part be due to the borderline solubility of LLDPE of this composition impacting the interpolation.The generally excellent agreement between the desired, predicted, and experimental values highlights the power and utility of a large dataset and statistical modelling in the production of polymers with designer properties.
Samples P2 and P3 were optimised in a more constrained fashion with four variables determined simultaneously.P2 (Mw = 500 kDa; PDI = 5.0; Tm = 100 °C; α = 45%) was interpolated within the scope of previously synthesised copolymers.For P3 (Mw = 200 kDa; PDI = 6.5;Tm = 80 °C; α = 25%), the combination of high incorporation -required for the low crystallinity and melting point -and large PDI is unlike any E/LAO copolymer previously synthesised within this work.As before, in both cases, activity was maximised, and incorporation was unconstrained.Simultaneous quadruplex optimisation resulted in a poorer match between the desired properties and those predicted by the optimised reaction conditions.In particular, the extrapolated properties desired for P3 resulted in poor agreement and large 95% confidence intervals for the predicted values.
P2 was synthesised at Tp = 80 °C, with [C6] = 47.0 mM.The experimental melting point (116.5 ± 0.3 °C) is both larger than the desired value and that predicted by M1.The molecular weight (153 ± 7 kDa) is much less than the desired and predicted values.Otherwise, there is good agreement between M1 and experimentation.The generally good agreement between the predicted and experimental data further demonstrates the power of M1, but the poorer match with the desired properties compared to P1 shows the limits of this methodology for simultaneous optimisation of many intercorrelated parameters.
P3 was synthesised at Tp = 32 °C, with [C6] = 168 mM.The desirability functions were poorly optimised, with the desired values of Tm and PDI (80 °C; 6.5) falling outside the 95% confidence interval of the predicted values of Tm and PDI (95 °C; 5.1).This reflects the lack of data for copolymers having both high incorporation and a high PDI, and perhaps suggests that 1/TIBA cannot produce such polymers under these conditions.Polymer melting temperature and dispersity (58 ± 2 °C; 3.0 ± 0.1) were substantially lower than both the target and predicted value, and Mw (355 ± 35 kDa) was found to be increased compared with the desired and predicted values.Only crystallinity (23 ± 2%) was well optimised and predicted.In addition to the relatively poor desirability optimisation and low-confidence predictions, this clearly demonstrates the limitations of extrapolating to property-space much beyond the data used to construct the model.

S47
Despite the obvious limitations, the potential of synthesising designer polyolefins using a single catalyst on the basis of a statistical model has been demonstrated in principle, and is of potentially enormous industrial significance.Parallelised high-throughput reaction platforms would enable more time-and resource-efficient dataset collection and including additional experimental parameters such as pressure would allow finer control and increase the accuracy of simultaneous multiplex optimisations.Incorporating mechanical and material characterisation into the modelling would further enable a dramatically expanded scope of tunability and control, with the ultimate goal of entirely application-directed synthesis.

Figure S2 Figure
Figure S2 Mean comonomer incorporation, as a function of concentration of 1-hexene, of LLDPE-C6 synthesised by 1/TIBA, obtained from GPC-IR or 13 C NMR spectroscopic measurements.Error bars shown at one standard deviation.

Figure S5 Figure
Figure S5 Mean comonomer incorporation, as a function of concentration of 1-octene, of LLDPE-C8 synthesised by 1/TIBA, obtained from GPC-IR or 13 C NMR spectroscopic measurements.Error bars shown at one standard deviation.

Figure S8 Figure
Figure S8 Mean comonomer incorporation, as a function of concentration of 1-dodecene, of LLDPE-C12 synthesised by 1/TIBA, obtained from GPC-IR or 13 C NMR spectroscopic measurements.Error bars shown at one standard deviation.

Figure S31
Figure S31 Scatterplot matrix of the PHENI*/E/LAO dataset, showing 2-dimensional scatter plots as functions of pairs of experimental variables.Shaded nonparametric density contours shown at the 50% and 90% quantiles.N = 75.

Sample
P1 was optimised to a relatively unconstrained high Mw (1 MDa) high Tm (110 °C) LLDPE copolymer, the likes of which have already been synthesised within this work.Additionally, the activity and crystallinity were maximised and the PDI minimised.The model M1 converged on a set of conditions (Tp = 61 °C, n = 8, c = 55.5 mM) consistent with the optimised properties and with relatively narrow 95% confidence intervals (Tm = 112 °C; Mw = 846 kDa).Experimentally, the copolymer melting point and molecular weight (112 ± 3 °C; 606 ± 281 kDa) showed a close qualitative fit with the predictions of M1.The relatively large standard deviation in experimental Mw results from the reaction being at the boundary of the insoluble and soluble regimes, with poor reproducibility between runs.

Figure S33
Figure S33 Polymerisation parameters of P1-P3 predicted by the regression model M1 (95% confidence intervals shown) and experimental results.Horizontal lines indicated the target values which determined the optimisation functions for calculating experimental conditions.Polymerisation conditions: 50 mL hexanes, 150 mg TIBA, 2 bar ethylene, and 30 minutes.

Table S10
Summary of partial effect tests in model M1: F ratios and p-values for each predictor on each response.Predictors composed of Tp (temperature of polymerisation), n (chain length of LAO), and c (LAO concentration).N = 75.

Table S12
Points specifying desirability functions for the optimisation of model M1 towards the properties of P1-3.