# Depolymerisation of polyisoprene by olefin cross-metathesis at equilibrium

Alexis Perrot, Julien Renault, Isabelle Dez

► To cite this version:

Alexis Perrot, Julien Renault, Isabelle Dez. Depolymerisation of polyisoprene by olefin cross-metathesis at equilibrium. Polymer Degradation and Stability, 2025, 241, pp.111529. 10.1016/j.polymdegradstab.2025.111529. hal-05219126

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# Depolymerisation of polyisoprene by olefin cross-metathesis at equilibrium

Alexis Perrot,\* Julien Renault,ª Isabelle Dezª,\*

Université Caen Normandie, ENSICAEN, Université Rouen Normandie, INSA Rouen Normandie, CNRS, Institut CARMEN UMR 6064, 14050 CAEN, France

## Abstract

Chemical valorisation of polymers gained a massive interest in the recent years, as it represents a more sustainable approach for the management of plastic waste. In particular, depolymerisation of polydienes by olefin cross metathesis is a powerful strategy to access telechelic oligomers with a variety of end groups. Despite the multiplication of investigations aimed at developing new materials from these oligomers, there has been little interest in the prediction of their molecular weight after depolymerisation, even though it represents a major parameter influencing macromolecular properties; in fact, most studies only rely on a kinetic approach to obtain a targeted molar mass. Here, we demonstrate that the equilibrium molecular weight of the oligodienes can be calculated from the amount of chain-transfer agent incorporated in the polymer. Equilibrium was achieved by performing several additions of catalyst, and the molar mass could be predicted from a simple statistical model. While we could not predict the conversion of chain-transfer agent beforehand, this statistical approach still provides an easy tool to establish the degree of polymerization of the products and, hence, have a better control over the final materials properties.

*Keywords:* metathesis, depolymerization, chemical recycling, rubber, polyisoprene

## 1. Introduction

Environmental pollution of plastics is a global and pressing issue. Over 350 million tons of plastics are produced every year worldwide [1] and, among them, approximately 1 billion tires reach their end-of-life, 50% of which being discarded in landfills [2,3]. While governmental efforts encourage the recycling of rubber waste [4], the main industrial 5 strategies rely on the pyrolysis or mechanical shredding of the discarded materials, which generates greenhouse gases or only delays their uncontrolled release in the environment.

Chemical recycling represents a promising alternative for the re-use of rubber waste. Commercial elastomers mostly consist of lightly vulcanised polyisoprene (PI), polybutadiene (PB), and their copolymers [5]. Consequently, devulcanisation of the networks has been widely investigated to obtain a reprocessable raw material that can be 10 reshaped and reused [6]. Alternatively, since these polymers are alkene-rich, oxidative cleavage of the carbon-carbon double bonds has also been thoroughly explored, leading to telechelic oligomers functionalized with hydroxyl- or
carbonyl-containing end-groups [7]. These methods, however, cannot lead to a wide range of chemical functions that
could be further exploited to design a variety of materials for higher-end applications.

On the contrary, chemical recycling of polydienes by olefin cross metathesis allows for the simultaneous depolymerization and end-functionalisation of polydienes with a high tolerance to many end groups. It relies on the 5 insertion of a functionalized short alkene, called the chain-transfer agent (CTA), into the polymer backbone, usually in the presence of ruthenium-based Grubbs catalyst following Chauvin's mechanism (Figure 1) [8,9]. A wide library of telechelic oligomers has been reported [7], for instance with acetate [10], silyl ether [11,12], alkylborane [13], and trithiocarbonates [14] end groups. This obtained raw reactant can then be used to prepare new materials with tailored properties, leveraging the newly incorporated chemical groups [15].

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Mechanism of the depolymerization of polydienes by olefin cross-metathesis in the presence of a functional CTA, leading to telechelic oligomers.</figcaption></figure>
More recently, olefin cross-metathesis with CTAs was judiciously used to finely control the molecular weight of polyalkenamers obtained by Ring-Opening Metathesis Polymerization (ROMP). After polymerization, telechelic polymers are obtained, which could be further involved in the preparation of block copolymers[16,17], polymer networks[18], or telechelic polyethylene after hydrogenation[19]. Interestingly, polydienes can also be used as macro-5 CTAs during this process, leading to statistical copolymers [20].

However, we noticed that the final molecular weight of the telechelic oligomers obtained by metathesis depolymerization varied significantly among different studies, including ours [10,21–23]. Yet, the degree of polymerization is a major parameter affecting the thermomechanical properties of polymer materials and, hence, it would be highly beneficial to predict it knowing the initial reaction conditions. We hypothesized that the high discrepancy between these reports was caused by the stability of the Grubbs catalyst, which is known to decompose over time despite its robustness, especially for long reactions [24–26]. Once the catalyst is decomposed, the depolymerization stops and the equilibrium molecular weight may not be achieved. 10

Here, we present a systematic study of the metathesis depolymerization of linear polyisoprene (PI) at equilibrium. PI was chosen because it does not form cyclic products in metathesis condition, as evidenced by previous studies 15 where Matrix-Assisted Laser Desorption Ionization – Time of Flight (MALDI-ToF) supported the absence of macrocycles [27], and because it represents a good model system for natural rubber; on the other hand, polybutadiene (PB), although a good model for rubber as well, tends to form cyclic species in metathesis conditions by backbiting, especially at low concentrations [28]. Equilibrium is reached by adding fresh Grubbs II catalyst several times until there is no more evolution of the degree of polymerization. Moreover, we demonstrate that a simple statistical model 20 can be used to determine the degree of polymerization of the oligomers given the amount of CTA that reacted.

**2. Experimental section**

**2.1. Materials**

Unless otherwise stated, solvents and reactants were purchased from VWR or Fisher and used without any further purification. The Grubbs II catalyst M204 ((1,3-Bis(2,4,6-trimethylphenyl)-2-25 imidazolidinylidene)dichloro(phenylmethylene)(tricyclohexylphosphine)ruthenium) was purchased from Sigma-Aldrich and used as received. *cis*-1,4-dihydroxybut-2-ene was distilled prior to use. Bio-Beads S-X1 Resin was purchased from Bio-Rad. Silica 60 M for column chromatography was purchased from Macherey-Nagel. Polyisoprene (97% *cis*-1,4, M<sub>n,SEC</sub> = 296,000 g mol<sup>-1</sup> and M<sub>w,SEC</sub> = 837,000 g mol<sup>-1</sup>) was purchased from Scientific Polymer Products, containing a small amount of butylated hydroxytoluene (BHT) as an antioxidant (~0.1 mol% respective to 30 isoprene repeating unit according to ¹H NMR).

**2.2. Characterisation**

NMR spectra were recorded at 298 K on Bruker Neo 600 MHz spectrometer. Chemical shifts (δ) are reported in parts per million (ppm) relative to the residual peak of the deuterated solvent (CDCl₃, ¹H: 7.26 ppm, ¹³C: 77.16 ppm).
The coupling constants *J* are reported in Hertz (Hz). Abbreviations used are as follows: s (singlet), d (doublet), t (triplet), m (multiplet), br (broad). High-Resolution Mass Spectrometry (HR-MS) were performed on a Xevo G2-XS QTOF WATERS spectrometer using ESI-MS in positive ion mode, with: source temperature, 120 °C; desolvation temperature, 250 °C; capillary voltage, 3 kV; cone voltage, 50 V; at mass range: 100–1000 m/z. Size exclusion chromatography (SEC) was performed using a UFLC Shimadzu Separations Module equipped with a Shimadzu RID-20A refractive index detector and three Shodex columns (KF 802–5, KF 804, and KF 807). The SEC analyses were performed at 40 °C using tetrahydrofuran as eluent at a flow rate of 1.0 mL min⁻¹, polyisoprene standards from Agilent were used for calibration.

## 2.3. Synthesis of the CTA

The experimental procedures are detailed in the Supplementary Information.

cis-1,4-diacetoxybut-2-ene (1a). **¹H NMR** (CDCl₃, 600 MHz, 295 K) $\delta$ 5.75 (t, 2H, *J* = 4.4 Hz), 4.67 (d, 4H, *J* = 4.4 Hz), 2.07 (s, 6H). **¹³C NMR**-{¹H} (CDCl₃, 151 MHz, 295 K) $\delta$ 170.9, 128.2, 60.1, 21.0. **HRMS** (ESI+) Calcd for C₈H₁₂O₄ [M+Na]⁺: 195.0633, found 195.0629.

trans-1,4-diacetoxybut-2-ene (trans-1a). **¹H NMR** (CDCl₃, 600 MHz, 295 K) $\delta$ 5.90–5.82 (m, 2H), 4.62–4.54 (m, 15 4H), 2.08 (s, 6H). **¹³C NMR**-{¹H} (CDCl₃, 151 MHz, 295 K) $\delta$ 170.8, 128.2, 64.0, 21.0. **HRMS** (ESI+) Calcd for C₈H₁₂O₄ [M+Na]⁺: 195.0633, found 195.0632.

cis-1,4-bis(dimethylphosphate)but-2-ene (1c). **¹H NMR** (CDCl₃, 600 MHz, 295 K) $\delta$ 5.83 (t, 2H, *J* = 4.4 Hz), 4.64 (dd, 4H, *J*<sub>H-P</sub> = 8.3 Hz, *J*<sub>H-H</sub> = 4.4 Hz), 3.77 (d, 12H, *J*<sub>H-P</sub> = 10.9 Hz). **¹³C NMR**-{¹H} (CDCl₃, 151 MHz, 295 K) $\delta$ 128.6 (d, *J*<sub>C-P</sub> = 6.6 Hz), 62.9 (d, *J*<sub>C-P</sub> = 5.4 Hz), 54.5 (d, *J*<sub>C-P</sub> = 6.1 Hz). **³¹P NMR**-{¹H} (CDCl₃, 243 MHz, 295 K) $\delta$ 1.44 (s). **HRMS** (ESI+) Calcd for C₈H₁₈O₈P₂ [M+Na]⁺: 327.0375, found 327.0378.

## 2.4. Depolymerisation of polyisoprene by Ru-catalysed olefin cross-metathesis

In a typical procedure, PI (204 mg, 3.00 mmol of isoprene repeating units) cut into pieces of approximately 0.5 × 0.5 cm² was dispersed in CH₂Cl₂ (2 mL) and the CTA (at varying concentrations, in mol% relative to the concentration of repeating units) was added. Grubbs catalyst M204 (2.5 mg, 3.00 µmol) was then added to the reaction medium, and the mixture was left to stir at room temperature for 4 h. This step was repeated a total of 4 times. Full dissolution of the polymer was observed after 2–3 h of reaction; PI is soluble in dichloromethane but the dissolution takes hours considering the high degree of polymerisation, which was accelerated by the depolymerisation into smaller chains. Hence, the reaction is heterogeneous in the first few hours. Aliquots for kinetic studies were quenched by dropping in methanol and were collected only after full dissolution of the polymer. At the end of the reaction, the catalyst was quenched by addition of ethyl vinyl ether (100 µL) and the reaction was pursued for 3 h more. The mixture was dried under reduced pressure and the crude was analysed by NMR. The polymers could be purified either on Bio-Beads with CH₂Cl₂ as eluent for *M*<sub>w</sub> < 5,000 g mol⁻¹, or on silica gel with pentane as eluent for *M*<sub>w</sub> > 5,000 g mol⁻¹. The pure polymers were obtained in very good to quantitative yields as light brown oils.

a,ω-diacetoxypolyisoprene. **¹H NMR** (CDCl₃, 600 MHz, 295 K) $\delta$ 5.24–4.95 (br t, n × 1H), 4.65–4.45 (set of d, 35 4H), 2.15–1.92 (br, n × 4H), 1.70–1.62 (br, n × 3H).
α,ω-dichloropolyisoprene. ¹H NMR (CDCl₃, 600 MHz, 295 K) δ 5.24-4.95 (br t, n × 1H), 4.14-3.98 (set of d, 4H), 2.15-1.92 (br, n × 4H), 1.70-1.62 (br, n × 3H).

α,ω-bis(dimethylphosphate)polyisoprene. ¹H NMR (CDCl₃, 600 MHz, 295 K) δ 5.24-4.95 (br t, n × 1H), 4.64-4.46 (set of t, 4H), 3.81-3.71 (set of d, 12H), 2.15-1.92 (br, n × 4H), 1.70-1.62 (br, n × 3H). ³¹P NMR-{¹H} (CDCl₃, 5 243 MHz, 295 K) δ 1.73 (s), 1.68 (s), 1.52 (s), 1.46 (s), 1.34 (s).

Note that, in all cases, the signals due to the end groups (in ¹H and ³¹P NMR) appeared in sets of several signals, due to the presence of either terminal butadiene or isoprene motifs, both in cis or trans configuration.

## 2.5. Theoretical considerations

10. Supposing an equal reactivity of all carbon-carbon double bonds during the reaction, regardless of them being part of a CTA or a polymer chain, the mole fraction X of polymers with a degree of polymerization n can be determined by a statistical approach [29,30]:

$$X(QM_n Q) = X(Q)^2 X(M)^n (n + 1) \quad (1)$$

$$\sum X(QM_n Q) = 1 \quad (2)$$

15. with Q the end-group, M the repeating unit, and X(Q) and X(M) their respective molar fractions.

The average degree of polymerisation $\bar{n}$, the number-average molecular weight $\bar{M}_n$, the weight-average molecular weight $\bar{M}_w$ and the dispersity $D$ can then be determined as well:

$$\bar{n} = \sum n X(QM_n Q) \quad (3)$$

$$\bar{M}_n = \sum X(QM_n Q) M(QM_n Q) \quad (4)$$

$$\bar{M}_w = \frac{\sum X(QM_n Q) M(QM_n Q)^2}{\sum X(QM_n Q) M(QM_n Q)} \quad (5)$$

$$D = \frac{\bar{M}_w}{\bar{M}_n} \quad (6)$$

20

with M(QMnQ) the molar mass of the polymer with a degree of polymerization n.

In particular, equation (3) can be rewritten as (see SI for the demonstration):

$$\bar{n} = 2\left(\frac{1}{x(Q)} - 1\right) \quad (7)$$

25. X(Q) can be measured by ¹H NMR by determining the relative integration of the unreacted CTA, the isoprene repeating unit, and the end-groups. Hence, a theoretical $X_{th}(Q)$ can be computed by supposing that the reacted CTA leads to two end-groups, from which a theoretical $\bar{n}_{th}$ can be derived; this value can be compared to the actual $\bar{n}_{NMR}$ obtained by end-group analysis (see SI for details on the computation). $X_{th}(Q)$ was calculated by considering the consumption of CTA in non-scissile events, which we estimated as being equal to the concentration of terminal alkenes present in 3,4-units and alkene end-groups (0.7 mol% of repeating units, Figure S1); this correction was of major importance because it represents a significant fraction of CTA when used at low concentrations.

30

Quantitative ¹H NMR was ensured by acquiring the spectra with longer relaxation times, so we estimate the integration error to be of the order of 3%. All oligomers were short (< 8 kg mol⁻¹) and the NMR samples were rather
concentrated (~ 10 mg mL⁻¹), ensuring a good signal-to-noise ratio. Finally, all experiments were reproduced in triplicates to ensure reproducibility.

Importantly, Eqn (1) was reported to be valid only for high CTA content ($X(Q) \gg X(M)$) [30]. We demonstrate here that, in fact, it is valid over a range of moderate concentrations (<20 mol% compared to repeating unit), as 5 described later.

# 3. Results and discussion

## 3.1. Kinetics vs. thermodynamics

The extent to which the polymer depolymerises may depend on several parameters. At a first glance, the concentration of isoprene repeating units [M], the concentration of chain-transfer agent [CTA], the concentration of Grubbs II catalyst [GII], the solvent, and the temperature may alter the final molecular weight of the telechelic oligomers.

We benchmarked our study by varying these parameters in the depolymerisation of polyisoprene with *cis*-1,4-diacetoxybut-2-ene 1a and determining the molecular weight of the oligomers after 24 h of reaction. Increasing [M], [CTA] or [GII] leads to a decrease in the average molecular weight of the final oligomers (Table S1), which has already been reported by us and others [10,21]. However, this evolution may only be the consequence of faster kinetics caused by a higher concentration of reactants and catalyst and, hence, does not provide any information on the reaction equilibrium.

In addition, we conducted the depolymerisation in toluene, dichloromethane and THF at different temperatures (Table S2). At room temperature, the shortest oligomers are obtained in toluene and the longest in THF, which reflects the stability of the Grubbs II catalyst in these solvents [31,32]. Moreover, while moderately increasing the temperature (<70 °C) favours depolymerisation, high temperatures (>100 °C) lead to longer oligomers, which may also be due to catalyst degradation. Therefore, the decomposition of the Grubbs II appears to be a significant limiting factor for the metathetic depolymerisation of polyisoprene and may be the source of a high variability between different studies.

Notably, the deactivation of the catalyst may also be caused by the presence of additives in the polyisoprene. Here, the commercial polyisoprene used in this study contains ~0.1 mol% of butylated hydroxytoluene (BHT) that may interact with the Grubbs catalyst and decrease its activity over time.

We evidenced the impact of catalyst deactivation by monitoring the average degree of polymerisation over the course of depolymerisation upon sequential additions of fresh Grubbs II to the depolymerisation mixture (Figure 2). 0.1 mol% of Grubbs II (respective to [M]) were added every 4 h a total of 4 times, hence keeping moderate reaction times and having an overall low content of catalyst compared to the content of CTA (2 mol% respective to [M]). Catalyst decomposition results in a decrease in reaction kinetics and addition of fresh Grubbs II increases the depolymerisation rate to reach shorter oligomers (Figure 2).

The average degree of polymerisation plateaus after several additions of catalyst (Figure 2). The first two additions lead to a significant decrease in $\overline{n}_{NMR}$ (–98.4% and –40.8% respectively) while the last two only slightly affect the degree of polymerisation (–17.9% and –13.2% respectively). The last addition only decreases the degree of
polymerisation by 4–5 repeating units. Therefore, we considered equilibrium was reached after 4 additions of 0.1 mol% of catalyst spaced by 4 h and the average molecular weight of the oligomers was reproducible over at least three samples.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Evolution of $\overline{n}_{RMN}$ as a function of time with sequential additions of Grubbs II. [M] = 1.8 M, [GII] = 4 × 0.1 mol% and [CTA] = 5 mol% respective to [M], $\overline{n}_{0}$ = 4,300. Dotted line is a guide to the eye and error bars indicate the standard deviation over three samples.</figcaption></figure>

In addition, these initial investigations evidenced a good adequation between the molecular weights obtained by 5 NMR and by SEC with PI standards (Table S1, Figure S13), showing that cyclisation or branching does not seem to occur significantly with polyisoprene at this concentration. All telechelic oligomers obtained had good dispersities close or lower than 2. Thus, for convenience, we conducted our consequent investigations with a characterisation by ¹H NMR.

## 3.2. Depolymerisation of polyisoprene at equilibrium

A major parameter affecting the final molecular weight of the oligomers is the quantity of CTA added to the depolymerisation medium. As such, we first varied the CTA content from 1 mol% to 20 mol% relative to the concentration of repeating units (Table 1). Increasing the relative concentration of CTA from 1 mol% to 5 mol% decreases $\overline{n}_{NMR}$ accordingly and with a great correspondence to the expected $\overline{n}_{th}$ (Entries 1-5). Therefore, despite previous reports indicating that the statistical description of the depolymerization only holds for very high content of CTA [30], we found here that it works well for our system and the molecular weight of the end-functional oligomers can be predicted from the amount of CTA that reacted.

This correspondence, however, does not hold for higher content of CTA when keeping [M] at 1.5 mol L⁻¹ (Table 1, Entries 6 and 7). When 10 mol% or 20 mol% of CTA are added, $\overline{n}_{NMR}$ is unexpectedly high. In both cases, the mixture contains a large amount of CTA and, hence, less solvent is used to keep the volume constant. Consequently, we believe polyisoprene becomes less soluble in the reaction mixture and does not undergo depolymerization as efficiently. Hence, we changed the reaction conditions for these two concentrations where the total concentration of
double bonds ([CTA] + [M]) was kept constant at 1.5 mol L⁻¹ (Entries 8 and 9). Satisfyingly, $\overline{n}_{th}$ and $\overline{n}_{NMR}$ decreased further and very short telechelic oligomers with $\overline{M}_{n,NMR}$ around 1,300 g mol⁻¹ were obtained.

<table><caption>**Table 1.** Molecular weights of acetoxy-terminated oligomers obtained by depolymerization of polyisoprene. Reactions were conducted with [M] = 1.5 mol L⁻¹ at 20 °C in CH₂Cl₂ with 4 × 0.1 mol% of Grubbs II. a Determined with Eqn (7). b Determined by end-group analysis. c Computed from $\overline{n}_{NMR}$, multiplying it by the molar mass of isoprene (68.13 g mol⁻¹) and adding the molar mass of the end-groups (172.18 g mol⁻¹). Standard deviations were obtained over three samples. * [CTA] + [M] = 1.5 mol L⁻¹.</caption><thead><tr><th rowspan="2">Entry</th><th>[1a]</th><th rowspan="2">n<sub>th</sub><sup>a</sup></th><th rowspan="2">n<sub>NMR</sub><sup>b</sup></th><th rowspan="2">M<sub>n,NMR</sub><sup>c</sup><br>(kg mol<sup>-1</sup>)</th></tr><tr><th>(mol% relative<br>to [M])</th></tr></thead><tbody><tr><td>1</td><td>1</td><td>131 ± 5</td><td>115 ± 26</td><td>8.0 ± 0.4</td></tr><tr><td>2</td><td>2</td><td>58.6 ± 1.1</td><td>58.5 ± 7.5</td><td>4.2 ± 0.5</td></tr><tr><td>3</td><td>3</td><td>37.6 ± 0.1</td><td>27.9 ± 1.0</td><td>2.1 ± 0.1</td></tr><tr><td>4</td><td>4</td><td>28.0 ± 0.5</td><td>24.8 ± 1.2</td><td>1.9 ± 0.1</td></tr><tr><td>5</td><td>5</td><td>23.4 ± 1.5</td><td>20.5 ± 2.2</td><td>1.6 ± 0.1</td></tr><tr><td>6</td><td>10</td><td>23.6</td><td>26.9</td><td>2.0</td></tr><tr><td>7</td><td>20</td><td>12.6</td><td>34.8</td><td>2.5</td></tr><tr><td>8*</td><td>10</td><td>16.1 ± 2.7</td><td>16.9 ± 1.0</td><td>1.3 ± 0.1</td></tr><tr><td>9*</td><td>20</td><td>11.6 ± 3.2</td><td>17.2 ± 1.5</td><td>1.3 ± 0.1</td></tr></tbody></table>

Importantly, the minimum molecular weight that can be achieved seems to plateau despite the addition of much more CTA to the depolymerization mixture. $\overline{M}_{n,NMR}$ approximately reaches 1 600 g mol⁻¹ with 5 mol% of CTA but 5 only reaches 1 300 g mol⁻¹ when this quantity is multiplied by four (Table 1, Entries 5 and 9). As explained later (section 3.3), we suggest that it is caused by the metathesis equilibrium between the unreacted CTA and the end groups.

The overall concentration of the depolymerization mixture should not, in theory, have a significant impact on the 10 molecular weight of the oligomers if equilibrium is reached. Therefore, we tested this hypothesis by conducting the depolymerization at three different [M] (Table 2). The depolymerisation proceeded more slowly at low concentration

<table><caption>**Table 2.** Molecular weights of acetoxy-terminated oligomers obtained by depolymerization of polyisoprene at different [M]. Reactions were conducted with [1a] = 2 mol% relative to [M] at 20 °C in CH₂Cl₂ with 4 × 0.1 mol% of Grubbs II. a Determined with Eqn (7). b Determined by end-group analysis. c Computed from $\overline{n}_{NMR}$, multiplying it by the molar mass of isoprene (68.13 g mol⁻¹) and adding the molar mass of the end-groups (172.18 g mol⁻¹). Standard deviations were obtained over three samples. * 6 additions of Grubbs II.</caption><thead><tr><th>Entry</th><th>[M]<br>(mol L<sup>-1</sup>)</th><th>n<sub>th</sub><sup>a</sup></th><th>n<sub>NMR</sub><sup>b</sup></th><th>M<sub>n,NMR</sub><sup>c</sup><br>(kg mol<sup>-1</sup>)</th></tr></thead><tbody><tr><td>1</td><td>7.3</td><td>55.3 ± 0.1</td><td>57.9 ± 8.7</td><td>4.1 ± 0.6</td></tr><tr><td>2</td><td>1.5</td><td>56.9 ± 2.1</td><td>58.5 ± 7.5</td><td>4.2 ± 0.5</td></tr><tr><td>3*</td><td>0.73</td><td>64.1 ± 8.8</td><td>64.7 ± 8.2</td><td>4.6 ± 0.6</td></tr></tbody></table>
(0.73 mol L⁻¹) and hence necessitated 2 more additions of catalyst. We observed again a good correspondence between $\overline{n}_{th}$ and $\overline{n}_{NMR}$ in all cases. While a slight increase in degree of polymerisation is observed at low concentrations, the difference is not statistically significant; hence, in our opinion, the concentration is not a major parameter to control the final molecular weight of the oligomers at equilibrium.

Depolymerisation of polyisoprene by olefin cross-metathesis works efficiently with a variety of functional groups. Hence, we extended our study to two other CTA: 1,4-dichlorobut-2-ene (1b) and 1,4-bis(dimethylphosphate)but-2-ene (1c) (Table 3). Overall, and as observed previously, $\overline{n}_{th}$ and $\overline{n}_{NMR}$ are close, even with different CTA. Compared with 1a (Table 1), the depolymerization of polyisoprene with 1b leads to slightly lower $\overline{n}_{NMR}$, while it tends to be slightly higher when 1c is used. Nonetheless, this difference is not significant in most cases; the highest differences are observed when 2 mol% or 5 mol% of 1c are added to the reaction (Table 3, Entries 4 and 5) with a high estimation of $\Delta\overline{n}_{NMR}$ of 14.2 and 6.1, respectively, compared to when 1a is used. We attribute this highest discrepancy to the bulkiness of the dimethylphosphate end-groups in the case of 1c, since steric hindrance may limit the activity of the ruthenium catalyst [33–35] and, hence, hinder the depolymerization. Still, the final molecular weight of the obtained telechelic oligomers is not drastically impacted when different CTA are used.

<table><caption>**Table 3.** Molecular weights of telechelic oligomers obtained by depolymerization of polyisoprene with different CTA. Reactions were conducted with [M] = 1.5 mol L⁻¹ at 20 °C in CH₂Cl₂ with 4 × 0.1 mol% of Grubbs II. a Determined with Eqn (7). b Determined by end-group analysis. c Computed from $\overline{n}_{NMR}$, multiplying it by the molar mass of isoprene (68.13 g mol⁻¹) and adding the molar mass of the end-groups (124.99 g mol⁻¹ for 1b, 304.17 g mol⁻¹ for 1c). Standard deviations were obtained over three samples.</caption><thead><tr><th>Entry</th><th>[CTA]<br>(mol% relative<br>to [M])</th><th>n&#773;<sub>th</sub><sup>a</sup></th><th>n&#773;<sub>NMR</sub><sup>b</sup></th><th>M&#773;<sub>n,NMR</sub><sup>c</sup><br>(kg mol<sup>-1</sup>)</th></tr></thead><tbody><tr><td colspan="5"><strong>1b</strong></td></tr><tr><td>1</td><td>2</td><td>55.9 ± 0.8</td><td>45.1 ± 5.8</td><td>3.2 ± 0.4</td></tr><tr><td>2</td><td>5</td><td>22.0 ± 1.4</td><td>21.6 ± 0.5</td><td>1.6 ± 0.1</td></tr><tr><td>3</td><td>10</td><td>19.6 ± 3.1</td><td>22.8 ± 7.6</td><td>1.7 ± 0.5</td></tr><tr><td colspan="5"><strong>1c</strong></td></tr><tr><td>4</td><td>2</td><td>62.6 ± 7.9</td><td>69.2 ± 3.9</td><td>5.0 ± 0.3</td></tr><tr><td>5</td><td>5</td><td>25.2 ± 3.8</td><td>29.5 ± 3.0</td><td>2.3 ± 0.2</td></tr><tr><td>6</td><td>10</td><td>16.4 ± 2.2</td><td>21.0 ± 1.0</td><td>1.7 ± 0.1</td></tr></tbody></table>

Despite altering several parameters of the depolymerization of polyisoprene by olefin cross-metathesis, an excellent correspondence between $\overline{n}_{th}$ and $\overline{n}_{NMR}$ was kept in most cases. This trend can be highlighted by plotting $\overline{n}_{NMR}$ as a function of $1/X(Q)$ for all obtained data and comparing it to the ideal case scenario of Eqn (7) (Figure 3). The fitting is excellent, suggesting that Eqn (7) provides a robust model to predict the molecular weight of the telechelic oligomers obtained after depolymerization of polyisoprene by olefin cross metathesis, as long as the amount of reacted CTA is known. Therefore, it appears that assuming a similar reactivity between all double bonds involved in the depolymerisation, from which our model is built upon, is valid. Consequently, it implies that a repeating unit is equally
as likely to react with another repeating unit of the same or another polymer chain than with CTAs; yet, we do not observe cyclisation from self-metathesis, so the formation of short linear oligomers is favoured over the one of macrocycles at the end of the reaction, possibly because of entropic considerations.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** $\overline{n}_{NMR}$ as a function of $1/X(Q)$ determined by ¹H NMR (black dots) and comparison with the ideal value calculated from Equation (7) (grey line). Error bars indicate the standard deviations over three samples.</figcaption></figure>

### 3.3. Equilibrium composition

As stated earlier, the degree of polymerization appears to reach a plateau even at high content of CTA. Despite increasing the concentration up to 20 mol% relative to [M], the conversion of CTA never reaches 100 % (Table 4). When CTA **1a** is used, the conversion is close or higher than 90% up to a CTA content of 5 mol% (Entries 1-5) but drastically drops to 57% and 38% when 10 mol% and 20 mol% are added, respectively (Entries 6 and 7). The same trend is observed for CTA **1b** and **1c**.

<table><caption>**Table 4.** Average CTA conversion obtained with different CTA. Standard deviations were obtained over three samples.</caption><thead><tr><th rowspan="2">Entry</th><th rowspan="2">[CTA]<br>(mol% relative<br>to [M])</th><th colspan="3">Conversion of CTA (%)</th></tr><tr><th>1a</th><th>1b</th><th>1c</th></tr></thead><tbody><tr><td>1</td><td>1</td><td>96.2 ± 3.0</td><td>-</td><td>-</td></tr><tr><td>2</td><td>2</td><td>95.4 ± 1.7</td><td>99.1 ± 1.3</td><td>97.4 ± 1.0</td></tr><tr><td>3</td><td>3</td><td>94.9 ± 0.3</td><td>-</td><td>-</td></tr><tr><td>4</td><td>4</td><td>93.9 ± 1.7</td><td>-</td><td>-</td></tr><tr><td>5</td><td>5</td><td>89.3 ± 5.3</td><td>94.9 ± 5.4</td><td>84.8 ± 9.9</td></tr><tr><td>6</td><td>10</td><td>57.3 ± 1.5</td><td>54.1 ± 7.7</td><td>63.7 ± 7.7</td></tr><tr><td>7</td><td>20</td><td>37.9 ± 4.6</td><td>-</td><td>-</td></tr></tbody></table>
We attempted to rationalize this low conversion by considering the similarity between the depolymerization of polyisoprene by olefin cross metathesis and the depolymerization of polyesters by hydrolysis (Scheme 1). In the former case, the depolymerization occurs because of the insertion of the CTA in the polymer chain, leading to chain scission; in the latter, the depolymerization is caused by the insertion of water in the polyester, forming new alcohol 5 and carboxylic end groups.

a.

b.

**Scheme 1.** a. Depolymerisation of polyisoprene by olefin cross-metathesis. b. Depolymerisation of polyesters by hydrolysis, showing the similarity between the two reactions.

We evidenced that the cross metathesis depolymerization of polyisoprene is at equilibrium by adding some Grubbs II to a pure short telechelic oligomer that did not contain any remaining CTA (Figure 4). The initial oligodiene ($\overline{M}_{n,NMR}$ = 2,700 g mol⁻¹) was obtained by metathesis depolymerization of polyisoprene in the presence of **1a**, as described in the previous section, which was then thoroughly purified on BioBeads to remove any unreacted CTA. When fresh 10 Grubbs II was added to these pure telechelic chains, in the same conditions as for the depolymerization, a small quantity of *trans*-1a was formed back after a few hours of reaction. Therefore, just as end-functional polyesters chains can condense to form a new ester linkage and release water, telechelic oligoisoprene chains can also condense to form a new isoprene unit and release a molecule of CTA in the presence of ruthenium catalyst.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** ¹H NMR spectrum (CDCl₃, 600 MHz, 295 K) of α,ω-diacetoxypolyisoprene before (top) and after (bottom) additions of 4 × 0.1 mol% of catalyst, demonstrating the apparition of *trans*-1a in the reaction medium.</figcaption></figure>

Consequently, an equilibrium constant *K* for the metathesis depolymerization can be defined similarly as the one 15 of polycondensation [36]:

$$K = \frac{[Q]^2}{4[CTA][M]} \qquad (8)$$
where the factor 4 comes from the fact that a repeating unit and a CTA can react in four equivalent ways to form a new end-group. Pursuing our analogy with polycondensation systems, K can be expressed as a function of Flory's extent of reaction [37] (see SI, section 5, for details):

$$K = \frac{(1-p_e+p_0)(1-p_e)^2}{r+x-p_e+p_0} \quad (9)$$

5 with $p_0$ and $p_e$ the extent of reaction for polycondensation systems, defined as $1 - 1/n$, at the start of the reaction and at equilibrium, respectively; r the molar ratio of the CTA to the repeating unit; and x the molar ratio of Grubbs catalyst to the repeating unit.

We hypothesized that K would explain the incomplete conversion of the CTA at the end of the depolymerization: at low CTA content, the excess of isoprene units pushes the equilibrium forward and, at higher CTA content, when 10 the concentration becomes comparable to the one of the repeating units, a balance between the forward and backward reaction is more evident.

We found that K was not constant over the whole range of concentrations (Table 5). The evolution of K follows two trends: it first increases from $3.8 \times 10^{-3}$ for 1 mol% of CTA 1a to $24.8 \times 10^{-3}$ for 5 mol%, and then decreases above 5 mol% to reach $13.9 \times 10^{-3}$ at 20 mol%. The initial increase of K is similar to observations reported for 15 polycondensation systems with polyesters where the polymerisation constant was found to decrease for lower degrees of polymerisation because Flory's principle of equal reactivity did not fully hold [36,37]. Hence, in the case of depolymerisation, K should increase with lower degrees of polymerisation and higher CTA content. However, the value obtained for 1 mol% is comparatively low, which we attribute to the higher fraction of CTA that is involved in non-scissile side reactions. Moreover, this trend does not hold for CTA content higher than 5 mol%. We suggest that 20 it may be caused by competing equilibria that are more likely to be impactful when a high concentration of CTA is used, such as cis-trans isomerisation of the CTA, depolymerisation with the trans-CTA, or depolymerisation with non-cis regioisomers. Therefore, although K values can be computed by analogy with polycondensation (Scheme 1), this parallel cannot fully reflect the different equilibria at play in the case of metathetic depolymerization.

<table><caption>**Table 5.** Average equilibrium constants K obtained with different CTA following Equation (9). Standard deviations were obtained over three samples.</caption><thead><tr><th rowspan="2">Entry</th><th rowspan="2">[CTA]<br>(mol% relative<br>to [M])</th><th colspan="3">K (×10<sup>-3</sup>)</th></tr><tr><th>1a</th><th>1b</th><th>1c</th></tr></thead><tbody><tr><td>1</td><td>1</td><td>3.8 ± 1.5</td><td>-</td><td>-</td></tr><tr><td>2</td><td>2</td><td>13.1 ± 2.7</td><td>11.3 ± 2.2</td><td>5.8 ± 0.5</td></tr><tr><td>3</td><td>3</td><td>19.1 ± 1.0</td><td>-</td><td>-</td></tr><tr><td>4</td><td>4</td><td>20.2 ± 1.6</td><td>-</td><td>-</td></tr><tr><td>5</td><td>5</td><td>24.8 ± 4.0</td><td>22.3 ± 0.8</td><td>13.9 ± 2.2</td></tr><tr><td>6</td><td>10</td><td>22.9 ± 2.4</td><td>16.8 ± 7.0</td><td>15.7 ± 1.2</td></tr><tr><td>7</td><td>20</td><td>13.9 ± 2.4</td><td>-</td><td>-</td></tr></tbody></table>
$K$ values for CTAs **1b** and **1c** were also determined with Equation (9) (Table 5). As expected, they reflect the same trends observed when comparing the average degrees of polymerisation. The values obtained for **1a** and **1b** are statistically identical, leading to oligomers with similar molecular weights, while different values of $K$ are obtained for **1a** and **1c** at 2 mol% and 5 mol%, reflecting the different degrees of polymerisation observed (Tables 1 and 3).

Therefore, our simple analogy with polycondensation does not allow for the full prediction of the equilibrium composition since $K$ cannot be easily estimated from the initial reaction conditions, which would probably require a more complete modelling of the system. Nonetheless, we strongly believe that this similarity provides a good starting point for further elucidating the equilibrium composition of the reaction mixture, which would then allow for the full prediction of the molecular weight of the final telechelic oligomers.

## 4. Conclusion

Depolymerisation of polyisoprene by olefin cross metathesis is a powerful tool to access short telechelic oligomers. We showed that, despite previous reports, the final molecular weight of the oligomers appears to be independent from the total concentration of the polymer and from the nature of CTA. The degree of polymerization can be predicted from the amount of reacted CTA using a simple model that proved to be robust over a wide range of conditions. We strongly believe that this work provides a stepping stone towards the fine control and prediction of the macromolecular structure of poly- and oligomers obtained by metathesis depolymerization.

## Corresponding Authors

* Alexis Perrot, alexis.perrot@ensicaen.fr; Isabelle Dez, isabelle.dez@ensicaen.fr.

## Author Contributions

**Alexis Perrot**: Conceptualisation, Methodology, Validation, Formal Analysis, Investigation, Writing – Original Draft, Writing – Review & Editing, Visualization; **Julien Renault**: Validation, Investigation, Writing – Review & Editing; **Isabelle Dez**: Conceptualisation, Resources, Writing – Review & Editing, Supervision, Project Administration, Funding acquisition.

## Acknowledgments

25 This work was supported by the Région Normandie and the University Caen Normandie who are gratefully thanked for their financial support. The authors from the Normandie University thank the Graduate School of Research XL-Chem (ANR-18-EURE-0020 XL-CHEM), Labex SynOrg (ANR-11-LABX-0029), Labex EMC³ (ANR-10-LABX-09-01) and Carnot Institute I2C. We thank Dr R. Legay and Dr H. Elsiblani for fruitful discussions on NMR characterisation.
## Supplementary materials

Supplementary material (PDF) can be found in the online version of this article.

## Data availability

Data will be available upon reasonable request.

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