Rate of Formation of Industrial Lubricant Additive Precursors from Maleic Anhydride and Polyisobutylene.

The Alder-ene reaction of neat polyisobutylene (PIB) and maleic anhydride (MAA) to produce the industrially important lubricant additive precursor polyisobutylene succinic anhydride (PIBSA) is studied at 150-180 °C. Under anaerobic conditions with [PIB] ∼ 1.24 M (550 g mol-1 grade, >80% exo alkene) and [MAA] ∼ 1.75 M, conversion of exo-PIB and MAA follows second-order near-equal rate laws with k obs up to 5 × 10-5 M-1 s-1 for both components. The exo-alkene-derived primary product PIBSA-I is formed at an equivalent rate. The less reactive olefinic protons of exo-PIB also react with MAA to form isomeric PIBSA-II (k obs up to 6 × 10-5 M-1 s-1). Some exo-PIB is converted to endo-PIB (containing trisubstituted alkene) in a first-order process (k obs ∼ 1 × 10-5 s-1), while PIBSA-I is difunctionalized by MAA to bis-PIBSAs very slowly. The MAA- and PIB-derived activation parameter ΔG ‡(150 °C) 34.3 ± 0.3 kcal mol-1 supports a concerted process, with that of PIBSA-I suggesting a late (product-like) transition state.

Introduction

Lubricating oils and emulsifiers are important global additives with a myriad of technological applications. The total global dispersant market (2021) has been valued at >$6 billion.[1] Polyisobutylene succinic anhydride (PIBSA, Scheme ) occupies a critical market position in the automotive sector and is manufactured on bulk scales (>104 tons per year) with an estimated 2022 value of ca. $1.5 billion.[2] Presently, most PIBSA is attained by a direct thermal reaction of α-olefin-terminated polyisobutylene (PIB) and maleic anhydride (MAA) (Scheme ).[3−5] This reaction is believed to proceed via a classical (uncatalyzed) Alder-ene reaction[3,6] and requires high temperatures (>150 °C) and long reaction times (>20 h) even when the neat reagents are combined.

Scheme 1

Industrial Preparation of PIBSA-I (R = Polymer Chain) and Calculated[7] Model ene Transition State (A, R = t-Bu), Showing Interatomic Distances in Å

Although the reaction is industrially valuable, the vigorous reaction conditions associated with the industrial process have largely precluded quantitative mechanistic rate investigations. Such investigations could offer insights into how to reduce the present demanding reaction times and temperatures used in current generation industrial PIBSA plants. As it is produced at bulk scales under vigorous conditions, small increases in the reaction efficiency disproportionally improve the environmental credentials of the reaction in terms of reduced carbon footprint and related UN sustainable development goals.[8] Even in the most general sense, studies of the kinetics of the Alder-ene reaction are surprisingly limited, and all of these have been carried out under dilute solvent-based conditions, which are unrepresentative of the true industrial process.[6,9,10] Additionally, there are ad hoc observations from production runs that the PIB/MAA Alder-ene reaction is rather sensitive to the presence of traces of oxygen (or other radical promotors), leading to the formation of alternative products via different mechanisms.[3,4,6,11] A recent (2021) computational study modeled a concerted Alder-ene [4 + 2] pericyclic transition state (A) between MAA and 2,4,4-trimethylpent-1-ene (t-BuCH2C(=CH2)Me), as a surrogate for the end of a PIB chain (Scheme ).[7] This study provided a calculated Gibbs activation energy of 36.6 kcal mol–1 (at 150 °C) with an associated enthalpy change (ΔH‡) of 15.8 kcal mol–1. A similar activation barrier (36.7 kcal mol–1) has been calculated (2021) for the uncatalyzed ene reaction between propene and but-3-en-2-one.[12] Both of these papers[7,12] suggest that a significant rate acceleration should be realized in the presence of AlCl3 due to Lewis acid catalysis. We were, therefore, interested in contrasting the theoretical energy barrier for the uncatalyzed reaction to those attained experimentally under conditions that closely simulate the industrial process. Herein, we describe a detailed kinetic study of the direct thermal reaction of PIB with MAA and comment briefly on the effect of small amounts of AlCl3 on the reaction. The true industrial thermal “ene” synthesis is more complex than the headline summary of Scheme . A cascade of competing processes (Scheme ) occurs during the overall production of PIBSA.

Scheme 2

Full Product Distribution of Species Formed in Industrial PIBSA Production (R = Polymer Chain)

Typically, high vinylidene PIB is used in industrial synthesis, containing >80% α-olefin-terminated PIB (exo-PIB), with the remaining composition being β-olefins (endo-PIB, >10%) and some tetra-substituted alkenes (tetra-PIB). These latter two alkenes are not active in Alder-ene chemistry. However, the allylic protons of exo-PIB (Ha and Hb in Scheme ) react with MAA to generate isomeric PIBSA-I and PIBSA-II, respectively. Further reaction of equivalent allylic protons (labelled Hb and Hc) within PIBSA-I lead to the formation of the bis-PIBSA structures shown. Fortunately, although conformation-induced peak broadening and some overlaps occur, diagnostic 1H NMR peaks of all the species within Scheme are available and assigned from the literature precedent,[3] allowing their complete quantification as a function of time. Tetra-PIB cannot be monitored by NMR during PIBSA synthesis due to the overlap of assigned NMR peaks with those of product PIBSAs.

Results and Discussion

Monitoring of reactions of neat PIB and MAA is complicated by three factors: (i) MAA is only readily soluble in PIB above ca. 100 °C and separates stochastically on rapid cooling (invalidating aliquot sampling); (ii) MAA is volatile and lost to the reaction headspace under the reaction conditions, causing mass balance/reaction homogeneity issues; (iii) competing radical-based reaction pathways are easily[3] promoted by trace amounts of oxygen (air), leading to alternative byproducts. Preliminary studies showed that aliquot sampling from a single vessel led to very poor reproducibility/induction periods. In standard glassware, the major (but batch-dependent) product was PIBSA-III, assigned by us as the structure given in Figure , on the basis of our NMR data. A regioisomeric structure has also been proposed by Balzano and co-workers,[3] but in either case, its formation is favored by radical initiators, especially trace oxygen.[11] Such issues have previously prevented accurate kinetic analyses of this reaction, even in the presence of radical inhibitors.[6]

Figure 1

Structure of PIBSA-III, a common impurity in aerobic compromised PIBSA generation (see also the Supporting Information).

Issues (i)–(iii) were overcome using minimal headspace glass ampoules with Young’s tap seals and thorough degassing (see the Experimental Section). By accounting for the different t1 relaxation values of 550 g mol–1PIB and its derivatives versus lighter MAA and nitrobenzene NMR standard used, it was possible to obtain quantitative composition-time information from 1H NMR spectra (see the Supporting Information for details) for all PIB-containing components. A small series of experiments were conducted to model the background variation in the distribution of PIB structures, in the absence of MAA, at 150, 165, and 180 °C for 4, 8, 15, 20, and 24 h. No statistically significant variation in the composition occurred, indicating that PIB is stable to the reaction conditions in the absence of other components.

Kinetic investigations of the reaction of PIB with MAA were then completed at 150, 160, 165, 170, and 180 °C, and the composition–time data was extracted by NMR. The nominal molarity of each species was calculated from each spectrum, accounting for the density of PIB observed at the experimental temperatures. These results are consistent and reproducible for PIB and PIBSA species for identical runs (±1–2%), but the quantity of MAA present was variable. This variation is due to the poor solubility of MAA in PIB at room temperature. Although there was no loss of reaction mass, the consumption of MAA cannot be monitored by our NMR approach due to its irreproducible precipitation in PIB mixtures. The MAA content could be quantified by gas chromatography (GC) after solubilizing the total ampoule contents in CH2Cl2, although this procedure had a lower reproducibility (ca. 5% error).

The experimental concentration–time data are found to best fit the integrated rate laws (1) to (4)[13] for MAA, PIB, and PIBSA species when using nonlinear least squares regression to determine rate constant values (kobs) and goodness-of-fit.[14−16] Statistical analysis of each data set was carried out using SolverStat.[17] This indicated that the second-order near equal concentrations regime best fitted the decay of exo-PIB, eq , and MAA, eq , and growth of PIBSA-I and PIBSA-II, eq , where Δ0 = [MAA]0 – [PIB]0.[13] Growth of endo-PIB is best modeled using first-order kinetics, eq . The observed rate constants, kobs, derived from fitted experimental data for the decay or formation of each species monitored are given in Table . Pseudo-first-order rate constants, k1, necessary for subsequent reaction parameter calculations were obtained by (i) multiplication of kobs (M–1 s–1) by [MAA]0 for exo-PIB, PIBSA-I, and PIBSA-II, (ii) multiplication of kobs (M–1 s–1) by [PIB]0 for MAA, and (iii) division of kobs (M s–1) by [MAA]0 for bis-PIBSAs. Endo-PIB forms under first-order conditions, so kobs = k1 (s–1). The worst errors were associated with the formation of bis-PIBSAs and endo-PIB due to their low concentrations, especially at lower temperatures. Interestingly, the generation of endo-PIB is marginally faster in the presence of MAA and PIBSAs than in the presence of PIB alone. We attribute this to the adventitious generation of trace acid catalyst for C=C bond isomerization.

Table 1

Rate Constants for the Processes of Scheme a

process	temp (°C)	kobs (M–1 s–1)	k1 (s–1)
consumption of MAA	150	8(3) × 10–6	1.0(4) × 10–5
	160	3(1) × 10–5	4(1) × 10–5
	165	2(1) × 10–5	3(1) × 10–5
	170	4(1) × 10–5	5(1) × 10–5
	180	5.0(1) × 10–5	6(1) × 10–5
consumption of exo-PIB	150	3.9(6) × 10–6	7(1) × 10–6
	160	1.6(3) × 10–5	2.8(4) × 10–5
	165	1.7(2) × 10–5	3.0(4) × 10–5
	170	2.6(3) × 10–5	4.5(6) × 10–5
	180	4.1(6) × 10–5	7(1) × 10–5
formation of PIBSA-I	150	3(2) × 10–6	5(3) × 10–6
	160	5(4) × 10–6	9(6) × 10–6
	165	1.4(4) × 10–5	2.5(6) × 10–5
	170	2.4(8) × 10–5	4(1) × 10–5
	180	6(1) × 10–5	1.1(3) ×10–4
formation of PIBSA-II	150	1.6(6) × 10–5	3(1) × 10–5
	160	5(4) × 10–6	8(7) × 10–6
	165	1(2) × 10–6	1(4) × 10–6
	170	2.1(5) × 10–5	3.6(8) × 10–5
	180	6(1) × 10–5	1.0(2) × 10–4

For the formation of endo-PIB and bis-PIBSAs, see the Supporting Information. The number in parentheses is the standard deviation in the preceding digit.

Exact forms of the integrated rate law equation for two consecutive second-order reactions (to simulate the formation of bis-PIBSA) are not available.[18] However, due to the significant excess of exo-PIB and MAA compared to bis-PIBSA, this reaction became near zeroth order and was modeled as such. Alternative attempts to extract the composite second-order rate constants through Excel-based simulation methods[19] were unsuccessful.

Owing to the occurrence of exo to endo alkene isomerization, the formation of both PIBSA-I and -II structures from exo-PIB and the consumption of PIBSA-I to form bis-PIBSAs at higher temperatures, all measured components were treated separately. The rate of consumption of MAA or PIB somewhat exceeds the rate of formation of PIBSA-I. This difference is attributed to the accelerated formation of minor species not detected by the NMR assay as the temperature rises and agrees with mass balance loss discussed later. This is also in accord with the minor mass balance issues sometimes noted in plant scale operations over time. A good correlation of the models of eqs –4 is attained, with most individual data fits in the range 0.79–0.96 (R2). This is acceptable and still generates meaningful data, especially considering the challenging sampling procedure required. The most significant sources of error are in the GC-based measurement of [MAA] and in the determinations of [endo-PIB]t and [bis-PIBSA] (particularly the latter two, which are only present at low concentrations). Attempts to extend our study above 180 °C were not successful with our present setup.

The Eyring–Polanyi equation (eq ) allows estimation of the Gibbs free energy of activation (ΔG‡) for a reaction and its deconvolution into ΔH‡ and ΔS‡ (see the Supporting Information). Plotting the derived ΔG‡ values for MAA, exo-PIB, and PIBSA-I versus temperature is informative (Figure ). Both MAA and exo-PIB show increasing ΔG‡ with increasing temperature. Such behavior either indicates significant ordering in the transition state (i.e., a strong negative ΔS‡ term) or that additional reaction manifolds (requiring higher ΔG‡) are becoming available as the reaction temperature increases. Conversely, the ΔG‡ values attained from the rate of PIBSA-I formation fall as temperature rises. Even allowing for the experimental error, the difference between ΔG‡ of the starting materials and product is beyond the error bar.

Figure 2

Overall ΔG‡ vs temperature for transformations of Scheme based on MAA and exo-PIB consumption and PIBSA-I formation.

While the experimental ΔG‡(150 °C) values from MAA, exo-PIB, and PIBSA-I (34.1 ± 1.5, 34.8 ± 2.2, and 35.4 ± 2.2 kcal mol–1, respectively), compare well to those (36.6 kcal mol–1) derived from density functional theory (DFT) studies,[7,12] the relative slopes of Figure point to a more complicated picture. Table presents the Eyring-Polanyi ΔH‡ and ΔS‡ values deconvoluted from the MAA, exo-PIB, and PIBSA-I ΔG‡ data. As no literature ΔH‡ or ΔS‡ experimental values are available for individual components of the Alder-ene reaction of PIB and MAA, Arrhenius plots of each dataset (MAA, exo-PIB, and PIBSA-I) were also made (see the Supporting Information) to determine the activation energy (Ea) from each of these components (eq and Table ).

Table 2

ΔH‡, ΔS‡, and Ea Values from the MAA, exo-PIB and PIBSA-I Rate Dataa

reaction process	ΔH‡ (kcal mol–1)	ΔS‡ (eu)	Ea (kcal mol–1)
consumption of MAA	21(7)	–33(15)	21.6(66)
consumption of exo-PIB	28(5)	–16(11)	29.0(47)
formation of PIBSA-I	40(4)	11(9)	40.9(40)

The number in parentheses is the standard deviation in the preceding digit.

Literature activation energies (Ea) of all published Alder-ene reactions using maleic anhydride are presented in Table , together with how the values were attained.[9−11] No literature value exists for the PIB and MAA system for direct comparison; Martuano has attempted this previously but was unable to reproducibly quantify the reaction components using high-performance liquid chromatography or GC methods.[6] The activation energy of the ene reaction between MAA and polypropylene (Mn ∼2010 g mol–1, Mw ∼10,300 g mol–1) has been calculated as 22.0 kcal mol–1 from an IR-derived rate of consumed MAA.[10] These studies[6,9,10] all conclude that MAA-ene reactions are first order with respect to both alkene and enophile and second order overall, in line with our own findings. However, as far as we can determine, no previous Eyring analysis of all of the components of an Alder-ene synthesis has previously been undertaken, even though the reaction is 80 years old. While the PIB system can be expected to have a slower rate due to the increased steric bulk of the polymeric alkene, the (reproducible) activation parameters of PIBSA-I (Table ) are not in accord with the large-ΔS‡ term seen for classic pericyclic reactions. One potential rationale for the data in Table is that the MAA and PIB consumption data is “contaminated” by competing higher energy processes. In line with this, some deviation between the calculated reaction composition data and the observed amounts of PIB and MAA is observed. At 150 °C, 11% of the mass balance is unaccounted for after 24 h. At 180 °C, this figure rises to ca. 30%. We can detect no mass loss from our reactions, implying that depolymerization of PIB to isobutylene is not an issue. This indicates the production of additional product(s) undetected by the NMR and GC assays. These products must be insoluble in CDCl3 or be sufficiently line broadened to not have clear NMR peaks. Gel permeation chromatography (GPC) analysis additionally did not reveal any more information, and the mass balance loss does not correlate to the IR signal that has been assigned to poly(maleic anhydride) species.[10] The undetected byproducts are most likely high-molecular-weight solid polymers.

Table 3

Available Kinetic Data for Alder-ene Reactions Using MAA

alkene	Ea (kcal mol–1)	ΔS‡ (eu)	how determined	conditions	ref
4-phenylbut-1-ene	16.1 ± 0.1	–47.3 ± 0.2	MAA data alone; GC method	C6H3Cl3 solution; excess MAA; 4% quinol vs [ene]	(6)
2,4-dimethyl-4-phenylpent-1-ene	12.5 ± 0.3	–52.8 ± 0.7	MAA data alone; GC method	C6H3Cl3 solution; excess MAA; 7% quinol vs [ene]	(6)
C6–C10 1-alkenes	21.5 ± 0.7	–36.4 ± 1.1	averaged k2 from alkene, MAA and product data; GC method	C6H4Cl2 solution; 2% quinol vs [ene]	(9)
trans-dec-5-ene	18.1 ± 1.5	–42.6 ± 3.5	averaged k2 from alkene, MAA and product data; GC method	C6H4Cl2 solution; 2% quinol vs [ene]	(9)
allylbenzene	ca. 20	n/a	MAA data alone; titration method	C6H4Cl2 solution	(11)
polypropylene	22.0 ± 2.6	n/a	MAA data alone; FTIR method	DMF solution; TEMPO (conc. not specified)	(10)

The PIBSA-I data in Table , if correct, suggests a late (product-like) transition state where the developing C–H bond is already well established. This is in line with the recent (2021) DFT calculations that triggered our investigation.[7,12] In a final comparison with these in silico studies, we tested the efficacy of the Lewis acid catalyst AlCl3, which is predicted to provide strong rate acceleration. At loadings of 3–8 mol % (with respect to PIB), conversion of MAA and PIB to PIBSA-I and II was essentially unaffected compared to the background reaction. The proportion of endo-PIB increased compared to uncatalyzed conditions as catalyst loading increased. This outcome is in agreement with the literature that suggests evolution of HCl from catalysts accelerates the exo-olefin to endo-olefin isomerization.[20] Given the clear calculated drivers for Lewis acid acceleration and the fact that this is a successful strategy in other Alder-ene reactions,[12] it is likely that the minor byproducts affecting the recorded rate data for MAA and PIB are also strong sequestering agents for AlCl3.

Previous kinetic studies of the ene reaction( see Table ) have predominately included a radical inhibitor, such as quinol, or a scavenger, such as TEMPO. A smaller series of reactions was conducted with 2% quinol at 165 °C and monitored by our quantitative NMR methods. The rate of consumption of exo-PIB fell to 1.4(4) × 10–5 M–1 s–1, which is equal to the rate of formation of PIBSA-I in the absence of the radical inhibitor in Table . No difference in the rate was observed in the presence of 2% quinol and 5% AlCl3 after 4 h at 150 °C (data in the Supporting Information).

Despite these underlying factors, the models of eqs –4 and the rate constants derived here do provide a good model for the PIBSA process. Figure shows the calculated reaction composition across 24 h at each of the temperatures studied. These profiles are in good accord with the reaction profiles seen at industrial scales.

Figure 3

Final simulated reaction composition of the Alder-ene reaction between PIB and MAA at 150, 160, 165, 170, and 180 °C across 24 h using eqs –4 and the data in Table .

Conclusions

A kinetic model of the Alder-ene reaction of neat PIB and MAA to produce the industrially produced lubricant precursor PIBSA has been developed. Rate data attained from all observable reaction components between 150 and 180 °C can accurately reproduce bulk plant behavior as a function of temperature.[21] Detailed extraction of the key kinetic parameters (ΔG‡, ΔH‡, ΔS‡, and Ea) leads to the conclusion that MAA and PIB are coproducing small amounts of undetected (by NMR, GC, and GPC) byproducts that engender two negative effects. First, this coproduction skews the acquired activation data attained for the process, complicating its analysis, and second, the same byproducts apparently sequester AlCl3 that otherwise would be a good catalyst for the process. Kinetic data from the PIBSA-I product of the reaction are unaffected by AlCl3 and point to a late (product-like) transition state, where C–H bond formation is already appreciably developed, as seen in recent computational models. Understanding these features points to the need to develop catalysts that are active well below current PIBSA plant operating temperatures, avoiding inhibition of byproduct formation, but using alternative activation modes for PIB and/or MAA. Such approaches would allow new optimization strategies for this important reaction and provide a significant opportunity to reduce the manufacturing footprint.

Experimental Section

High vinylidene 550 g mol–1 molecular weight polyisobutylene (PIB) used was of an identical grade to that used for industrial lubricant synthesis (Lubrizol). This PIB sample contained 80 mol % α-olefins, 15 mol % β-olefins, and 5 mol % tetra-substituted olefins by 1H NMR spectroscopy; GPC studies confirmed its molecular weight and indicated a polydispersity of MW/Mn = 1.5. MAA was commercial (Alfa Aesar), equivalent to that used in the industrial process; its purity was confirmed as >98% by 1H NMR spectroscopy.

Experimental Set-Up

Kinetic runs were conducted using bespoke pressure-resistant glass ampoules with Young’s tap seals (internal diameter, 6 mm; external diameter, 12 mm; height, 120 mm; total volume, 6 mL) (Figure ). This reaction setup mimics the minimum headspace designs of current industrial PIBSA plants and allows multiple duplicate reactions (that give identical conversion-time outputs between batches within ±1–2%) to be set up simultaneously when determining the rates controlling the PIBSA cascade (Scheme ).

Figure 4

Representative ampoules used in this study: (a) before charging, (b) during degassing, (c) during a typical kinetic run (170 °C), and (d) at the completion of the reaction.

Kinetic Runs

Solid MAA (0.816 g, 8.32 mmol, 1.4 equiv), a 10 mm stir bar, and PIB (3.270 g, 5.95 mmol, 1.0 equiv) were charged to the ampoule, and Young’s tap was sealed. The reaction mixture was left to settle for 12–16 h to facilitate degassing, which was achieved by 3× vacuum (1 mbar)/N2 gas cycles. Young’s tap was closed under a flow of N2, and the ampoule was fully submerged in a preheated oil bath (150, 160, 165, 170, or 180 °C), and the kinetics clock started. Sealed reactions were shielded by a blast screen during heated runs. Individual duplicates of the reactions were stopped hourly to provide data over a 24 h window. Owing to the laboratory (covid) open hour restrictions, no data for 11–13 h periods could be collected. To prevent loss of volatile MAA, individual reaction samples were cooled to room temperature before the ampoules were opened. Control runs indicated that nominally identically charged ampoule compositions provided identical conversions at given time points (±1–2% conversion). Independent experimental estimates of the densities of PIB–MAA mixtures in the temperature ranges studied allow the use of molarity, as opposed to molality, units in the kinetic analyses. Amounts of MAA were determined by GC and all other species by 1H NMR spectroscopy (see the Supporting Information for details). Radical inhibitors were not found to be necessary under these conditions and were not used to avoid potential additional rate data being needed. Conversion in the presence of freshly sublimed AlCl3 (3–8 mol % vs PIB) was checked at 150 °C, 4 h and found to be comparable to background conversion within the experimental error (see the Supporting Information). Conversion in the presence of 2% quinol (vs PIB) was calculated at 165 °C at 3, 6, 9, 15, 18, 21, and 24 h and revealed a rate of consumption of exo-PIB equal to the formation of PIBSA-I in the absence of the radical inhibitor (see the Supporting Information).

Data Analyses

Experimental data were fitted to all kinetic models of eqs –4 using Solver Microsoft Excel add-in.[14−16] Data fits were optimized by nonlinear least squares regression of the sum of ([observed species] – [calculated species])2 as a function of kobs and where relevant [PIBSA]final, at fixed [PIB]0 and [MAA]0 values. A near equal concentration (second order overall)[13] rate law gave the best fit to the data based on R2, except for the isomerization of exo-PIB to endo-PIB (which fitted first order) and the formation of bis-PIBSAs (which was zeroth order). The SolverStat tool was used to return regression statistics on all coefficients, including the standard deviations and R2 values (see the Supporting Information).[17] Derived parameters (Ea, ΔH‡, ΔS‡, and ΔG‡) were calculated from kobs. The standard deviations for the derived ΔG‡ values were calculated using eqs –11. Full details are given in the Supporting Information.

All other details and primary data are in the Supporting Information.