IChO 2024 · Theory problem 7

SABIC

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The Saudi Basic Industries Corporation (SABIC) was established in the mid-1970s as part of Saudi Arabia's plan to diversify its economy. Today, SABIC is a global chemical giant, producing 69 million tons of products annually.

Part A

SABIC's own unique ethene oligomerization technology (oligomers are polymers with few monomer units) produces linear alpha olefins (1-alkenes), which are used in numerous industrial applications.

Linear alpha olefins are produced by catalytic oligomerization of ethene, resulting in a range of chain lengths with a distribution. Different catalysts can yield various distributions of products.

In the geometric or Schulz–Flory distribution, each oligomer fraction is related to the previous fraction by the equation, \(T_{n+1}=\alpha T_n\), where \(T_n\) represents the molar amount of the oligomer with \(n\) ethene units, and \(\alpha\) is a constant called the probability of chain propagation. Ethene, the monomer is not a member of the series (\(n\geq2\)).

One catalytic oligomerization process can be described by a relatively simple mechanism:

Figure 1

Although this mechanism is not a classical chain reaction because the final product is not produced within the cycle, the usual kinetic treatment of chain reactions can be applied to it. The three processes shown (1–3) are all chain propagation steps. R is lengthened by each cycle.

All three reactions are first order with respect to the chain carriers. For ethene, use an unknown order \(\rho\), to be determined later.

7.1 Write the rate equations for reactions 1–3 using \(k_1\), \(k_2\), and \(k_3\) as the corresponding rate constants, which are independent of the carbon chain length. 1 pt

Chain termination step, producing the oligomers, is a first order reaction competing with reaction 1.

7.2 Write i) the chemical equation and ii) rate equation of termination. Use \(k_t\) as the corresponding rate constant. 2 pt

7.3 Find the value of \(\rho\) which ensures that the product mixture of olefins shows the required ratio of products in accordance with the Schulz–Flory distribution when the reaction is run in a closed system. Derive a formula for this case that gives \(\alpha\) as the function of rate constants. 4 pt

Aluminum alkyls are used as co-catalysts in the ethene oligomerization process. It was found that they also catalyzed the Friedel–Crafts alkylation of the aromatic solvents used for the oligomerization.

In a typical oligomerization reaction, an alkylated aromatic compound Q was isolated from the complex reaction mixture of ethene oligomerization in toluene as solvent. The alkylated aromatic compound Q has the molecular formula \(\ce{C11H16}\) and its \(\ce{^1H}\) NMR spectrum contains the following peaks.

\(\ce{^1H}\) NMR of Q: \(\delta\) 0.9 (\(t\), 3H); 1.35 (\(m\), 2H); 1.59 (\(m\), 2H); 2.34 (\(s\), 3H), 2.60 (\(t\), 2H); 7.18 (\(d\), 2H); 7.22 (\(d\), 2H).

7.4 Draw the structure of Q. 3 pt

Part B

Vitrimers are adaptive polymers with "reversible" covalent bonds, allowing shape-changing and self-healing under specific conditions. This subtask explores the principles of vitrimer chemistry, an important topic in SABIC's polymer research.

A recently elucidated fast and reversible reaction involving dioxaborolanes can serve as the chemical background for such an adaptable polymer network. The two dioxaborolanes below were prepared by the reaction of phenylboronic acid with 1,2-butanediol and 3,5-dimethylphenylboronic acid with 1,2-propanediol, respectively.

Figure 2

They participate in a model metathesis (exchange) reaction. The two carefully purified compounds were mixed in the absence of solvent and the mixture was kept at \(60\,^\circ\mathrm{C}\) for two hours. Interestingly, the gas chromatograms of the mixture at the start and at the end of the incubation period showed only the peaks below, with equimolar quantities of the components. The peaks in this system separate in a way that correlates with molar mass: compounds with lower mass appear at earlier elution times.

Figure 3

No catalyst, water, diol or acid was detectable in the mixture.

7.5 Draw the compounds associated with peaks I–IV in the chromatogram. 2 pt

Linking functional units to a polymer chain is known as grafting, and the functional units are referred to as grafting agents. In this case, the dioxaborolane units are linked to the polymer chains by maleimide groups via a radical process, in which one maleimide group is coupling to the polymer chain at a random carbon atom. The scheme below introduces a flexible synthesis route towards the dioxaborolane maleimide grafting agent used in the vitrimers.

Figure 4

7.6 Draw the structures of A–C. 3 pt

7.7 Select on the answer sheet which reagent(s) and/or condition is/are appropriate for linking the dioxaborolane maleimide units to polyethylene. 1 pt

Figure 5

The vitrimer was prepared as follows:

  • Polyethylene is grafted with dioxaborolane maleimide. Assume no side reactions between the dioxaborolane maleimide compounds.
  • The reagents are removed from the macromolecules.
  • Propanediol functionalized bis-dioxaborolane is added to enable crosslinking.
Figure 6
  • The mixture is carefully heated for metathesis (exchange) reaction to take place.

To determine the extent of grafting and crosslinking in the vitrimer, infrared (IR) spectroscopy was used at room temperature where the metathesis reaction is extremely slow. Assume a homogeneous vitrimer.

  • All of the small molecules are removed from the polymer.
  • The IR spectrum of a thin polymer film is measured.
  • IR spectrum contains absorption peaks that correspond to specific functional groups.
  • The Beer–Lambert law can be used to quantify the concentration of these functional groups.

The provided data table gives the wavelengths, corresponding molar (related to the specified functional groups) absorption coefficients for relevant characteristic peaks together with the absorbances of the vitrimer sample.

Vibration wavenumber, with the functional group indicated Molar absorption coefficient, \(\epsilon\) \((\mathrm{dm^3\,mol^{-1}\,\mu m^{-1}})\) Sample absorbance at this wave number, \(A\)
Imide group band at \(1710\ \mathrm{cm^{-1}}\) 2.67 0.451
Monosubstituted benzene ring band at \(1600\ \mathrm{cm^{-1}}\) 0.28 0.022
Disubstituted benzene ring band at \(1520\ \mathrm{cm^{-1}}\) 0.68 0.042
\(\ce{CH2}\) groups of polyethylene, band at \(1470\ \mathrm{cm^{-1}}\) 0.021 0.904

7.8 Calculate the grafting density (\(X_g\)) of polyethylene based on the measurements. That is the ratio of the grafted groups over the ethylene units. 3 pt

7.9 Calculate the percentage of the grafted groups that are not part of a crosslink (\(p_{nc}\)). 4 pt

Official English text of the problem.

Answers

  • 7.1 \[ \boxed{v_1=k_1[Z][\ce{C2H4}]^\rho,\qquad v_2=k_2[X],\qquad v_3=k_3[Y].} \]

  • 7.2 \[ \boxed{\ce{Z -> L_nM + CH2=CHCH2CH2R}},\qquad \boxed{v_t=k_t[Z].} \] The released product is a linear terminal alkene, generic SMILES C=CCC[*], where * represents R.

  • 7.3 \[ \boxed{\rho=0,\qquad \alpha=\frac{k_1}{k_1+k_t}.} \]

  • 7.4 Q is 1-butyl-4-methylbenzene, also called \(p\)-\(n\)-butyltoluene: CCCCc1ccc(C)cc1.

  • 7.5 The compounds, in increasing elution time, are:

I: 4-methyl-2-phenyl-1,3,2-dioxaborolane: CC1COB(c2ccccc2)O1.

II: 4-ethyl-2-phenyl-1,3,2-dioxaborolane: CCC1COB(c2ccccc2)O1.

III: 2-(3,5-dimethylphenyl)-4-methyl-1,3,2-dioxaborolane: CC1COB(c2cc(C)cc(C)c2)O1.

IV: 2-(3,5-dimethylphenyl)-4-ethyl-1,3,2-dioxaborolane: CCC1COB(c2cc(C)cc(C)c2)O1.

  • 7.6

A: The furan–maleic anhydride Diels–Alder adduct, represented as exo-7-oxabicyclo[2.2.1]hept-5-ene-2,3-dicarboxylic anhydride:
O=C1OC(=O)[C@H]2[C@@H]1[C@@H]1C=C[C@H]2O1.

B: 3-Aminopropane-1,2-diol: NCC(O)CO.

C: Furan-protected N-[(2-phenyl-1,3,2-dioxaborolan-4-yl)methyl]maleimide, retaining the bicyclic core of A:
O=C1N(CC2COB(c3ccccc3)O2)C(=O)[C@H]2[C@@H]1[C@@H]1C=C[C@H]2O1.

  • 7.7 Select a only, dicumyl peroxide: CC(C)(OOC(C)(C)c1ccccc1)c1ccccc1.

  • 7.8 \[ \boxed{X_g\approx7.8\times10^{-3}=0.78\%.} \]

  • 7.9 \[ \boxed{p_{nc}\approx66\%} \] (the nominal calculation gives \(66.2\%\)).

Solution

7.1 — Propagation rate equations

Ethene, SMILES C=C, enters in reaction 1, where it reacts with chain carrier Z. Reactions 2 and 3 convert X into Y and Y into Z, respectively, without consuming additional free ethene.

Consequently,

\[ v_1=k_1[Z][\ce{C2H4}]^\rho,\qquad v_2=k_2[X],\qquad v_3=k_3[Y]. \]

For rates expressed in \(\mathrm{mol\,dm^{-3}\,s^{-1}}\), \(k_2\) and \(k_3\) have units \(\mathrm{s^{-1}}\), while \(k_1\) has units \[ (\mathrm{mol\,dm^{-3}})^{-\rho}\mathrm{s^{-1}}. \]

7.2 — Termination

Termination competes with ethene capture by Z. It therefore releases the terminal alkene already coordinated to the metal:

\[ \ce{Z ->[k_t] L_nM + CH2=CHCH2CH2R}. \]

This is dissociation: no atoms are added or removed. The released linear terminal alkene has generic SMILES C=CCC[*], with * representing R.

In Z, the alkene is coordinated through its double bond, conventionally described as \(\eta^2\) coordination. Ordinary molecular SMILES does not show this coordination adequately, and the unspecified metal–ligand fragment \(\ce{L_nM}\) has no unique molecular SMILES.

Since termination is first order,

\[ v_t=k_t[Z], \]

where \(k_t\) has units \(\mathrm{s^{-1}}\).

7.3 — Condition for the Schulz–Flory distribution

At each visit to Z, a chain can either propagate through reaction 1 or terminate. Its probability of propagation is therefore

\[ \alpha =\frac{v_1}{v_1+v_t} =\frac{k_1[\ce{C2H4}]^\rho} {k_1[\ce{C2H4}]^\rho+k_t}. \]

If this probability is constant, producing an oligomer with one additional ethene unit requires one additional successful propagation. Thus,

\[ T_{n+1}=\alpha T_n, \]

and, starting with the smallest oligomer at \(n=2\),

\[ T_n=T_2\alpha^{n-2}. \]

In a closed system, ethene concentration decreases as the reaction proceeds. For positive propagation and termination rate constants, the branching probability above is independent of this changing concentration only when

\[ \boxed{\rho=0}. \]

It then becomes

\[ \boxed{\alpha=\frac{k_1}{k_1+k_t}}. \]

The constants \(k_2\) and \(k_3\) determine how quickly the chain passes through X and Y. They do not affect the propagation-versus-termination choice, because neither of those intermediates has a competing termination step in the given mechanism.

7.4 — Identification of Q

For \(\ce{C11H16}\), the degree of unsaturation is

\[ \mathrm{DBE}=\frac{2(11)+2-16}{2}=4, \]

consistent with one benzene ring.

The NMR assignments are:

Signal Assignment
\(\delta 0.9\), triplet, 3H Terminal methyl of an \(n\)-butyl group
\(\delta 1.35\), multiplet, 2H Butyl methylene next to the terminal methyl
\(\delta 1.59\), multiplet, 2H Middle methylene nearer the aromatic ring
\(\delta 2.34\), singlet, 3H Methyl directly attached to the aromatic ring
\(\delta 2.60\), triplet, 2H Benzylic methylene of the \(n\)-butyl group
\(\delta 7.18\) and \(7.22\), two doublets, 2H each Two equivalent pairs of aromatic hydrogens in a para-disubstituted ring

Therefore, draw a benzene ring bearing methyl and straight-chain butyl groups at opposite positions:

\[ \boxed{\text{Q = 1-butyl-4-methylbenzene}} \]

SMILES: CCCCc1ccc(C)cc1.

7.5 — Assignment of chromatographic peaks

The exchange reaction produces all four combinations of the two arylboron groups and the two diol residues. Each product retains a five-membered dioxaborolane ring.

Peak Aryl group attached to boron Diol-derived substituent on the ring Molecular formula
I Phenyl Methyl \(\ce{C9H11BO2}\)
II Phenyl Ethyl \(\ce{C10H13BO2}\)
III 3,5-Dimethylphenyl Methyl \(\ce{C11H15BO2}\)
IV 3,5-Dimethylphenyl Ethyl \(\ce{C12H17BO2}\)

Their names and SMILES are given in Answers 7.5. To draw each structure, place the stated aryl group on boron and the methyl or ethyl substituent on one carbon of the five-membered ring.

Successive formulas in the table differ by \(\ce{CH2}\), so their molar masses increase in exactly the order I–IV. This establishes the elution order using the problem’s stated mass–retention relationship.

The starting materials are II and III; exchange produces I and IV:

\[ \ce{II + III <=> I + IV}. \]

No water, free diol, or free acid is required in this net exchange.

The configurations of the diol-derived stereocentres are not specified in the question; they are therefore left unspecified in the SMILES.

7.6 — Structures A–C

A: Diels–Alder protection. Furan, c1ccoc1, reacts as the diene with maleic anhydride, O=C1OC(=O)C=C1. The cycloaddition gives the oxygen-bridged bicyclic anhydride A:

\[ \ce{C4H4O + C4H2O3 -> C8H6O4}. \]

Draw the bicyclic skeleton shown in the subsequent protected imide, but with the imide nitrogen replaced by the anhydride oxygen. Retain the oxygen bridge, the remaining carbon–carbon double bond, and the cis relationship inherited from maleic anhydride.

The exo representation used here is:

O=C1OC(=O)[C@H]2[C@@H]1[C@@H]1C=C[C@H]2O1.

B: Introduction of the amino diol. The product shown after the \(78\,^\circ\mathrm{C}\) step has an imide nitrogen bearing the side chain \(\ce{-CH2CH(OH)CH2OH}\). Therefore B must be 3-aminopropane-1,2-diol, NCC(O)CO.

Its amino group opens the anhydride; subsequent dehydration forms the imide:

\[ \ce{C8H6O4 + C3H9NO2 -> C11H13NO5 + H2O}. \]

The protected hydroxy imide is furan-protected N-(2,3-dihydroxypropyl)maleimide:

O=C1N(CC(O)CO)C(=O)[C@H]2[C@@H]1[C@@H]1C=C[C@H]2O1.

The coproduct is water, O.

C: Formation of the cyclic boronic ester. Phenylboronic acid, OB(O)c1ccccc1, condenses with the two adjacent hydroxyl groups, eliminating two molecules of water:

\[ \ce{C11H13NO5 + C6H7BO2 -> C17H16BNO5 + 2 H2O}. \]

Thus C is furan-protected N-[(2-phenyl-1,3,2-dioxaborolan-4-yl)methyl]maleimide:

O=C1N(CC2COB(c3ccccc3)O2)C(=O)[C@H]2[C@@H]1[C@@H]1C=C[C@H]2O1.

To draw C, leave the protected imide unchanged and join its two side-chain oxygen atoms to a common boron atom bearing phenyl. This closes the five-membered dioxaborolane ring.

Finally, heating to \(110\,^\circ\mathrm{C}\) causes a retro-Diels–Alder reaction:

\[ \ce{C17H16BNO5 -> C13H12BNO4 + C4H4O}. \]

The products are furan and the required grafting agent, N-[(2-phenyl-1,3,2-dioxaborolan-4-yl)methyl]maleimide:

O=C1N(CC2COB(c3ccccc3)O2)C(=O)C=C1.

7.7 — Radical grafting onto polyethylene

Select a only.

Dicumyl peroxide, CC(C)(OOC(C)(C)c1ccccc1)c1ccccc1, undergoes homolytic cleavage of its peroxide bond on heating. The resulting radicals can abstract hydrogen from polyethylene, generating a polymer radical. Addition of that radical across the maleimide double bond creates the bond connecting the grafting agent to the polymer.

The other choices do not supply the required grafting process:

  • b: Platinum, [Pt], with dihydrogen, [H][H], provides hydrogenation conditions.
  • c: Light at \(454\ \mathrm{nm}\), without a suitable photoinitiating system, does not provide the required radical initiation.
  • d: The bicyclic guanidine base TBD, 1,5,7-triazabicyclo[4.4.0]dec-5-ene, C1CN2CCCN=C2NC1, is not an appropriate initiator for this radical grafting.

7.8 — Grafting density

The Beer–Lambert law is

\[ A=\epsilon c\ell, \]

where \(c\) is in \(\mathrm{mol\,dm^{-3}}\) and film thickness \(\ell\) is in \(\mu\mathrm m\). Consequently, \(A/\epsilon=c\ell\), and the common thickness cancels from concentration ratios.

Each graft contains one imide group. The coefficient is specified per imide group, so its two carbonyl groups must not be counted separately.

For the grafts,

\[ c_g\ell=\frac{0.451}{2.67} =0.168914\ \mathrm{mol\,dm^{-3}}\,\mu\mathrm m. \]

For polyethylene methylene groups,

\[ c_{\ce{CH2}}\ell=\frac{0.904}{0.021} =43.0476\ \mathrm{mol\,dm^{-3}}\,\mu\mathrm m. \]

Each ethylene repeat contains two backbone carbon atoms, represented by the polyethylene repeat fragment [*]CC[*]. Using two methylene groups per repeat,

\[ X_g =\frac{c_g}{c_{\ce{CH2}}/2} =\frac{2(0.451/2.67)}{0.904/0.021} =0.00784777. \]

Thus,

\[ \boxed{X_g\approx7.8\times10^{-3}=0.78\%}. \]

The small correction for conversion of one backbone methylene into a methine per graft gives

\[ X_g=\frac{2c_g}{c_{\ce{CH2}}+c_g}=0.00781709, \]

which rounds to the same result.

7.9 — Grafts that are not part of a crosslink

The added crosslinker is 1,4-bis(4-methyl-1,3,2-dioxaborolan-2-yl)benzene:

CC1COB(c2ccc(B3OCC(C)O3)cc2)O1.

A retained crosslinker can be attached to either one graft or two grafts. Only the latter forms a bridge between grafts. Crosslinkers attached to no grafts are small molecules and have been removed.

Let:

  • \(g\): total concentration of grafts, measured through imide groups;
  • \(m\): concentration of monosubstituted benzene rings;
  • \(d\): concentration of disubstituted benzene rings;
  • \(s\): concentration of crosslinker molecules attached to one graft;
  • \(b\): concentration of crosslinker molecules attached to two grafts.

Each remaining monosubstituted benzene ring belongs to an original phenylboronate attached to one graft. Each retained disubstituted ring belongs to one crosslinker molecule. Therefore,

\[ g=m+s+2b,\qquad d=s+b. \]

Solving,

\[ b=g-m-d,\qquad s=2d-g+m. \]

The non-crosslinked grafts comprise those retaining their original phenylboronate and those attached to a singly attached crosslinker:

\[ g_{nc}=m+s=2m+2d-g. \]

The measured quantities are

\[ \begin{aligned} g\ell&=\frac{0.451}{2.67}=0.168914,\\ m\ell&=\frac{0.022}{0.28}=0.0785714,\\ d\ell&=\frac{0.042}{0.68}=0.0617647, \end{aligned} \]

all in \(\mathrm{mol\,dm^{-3}}\,\mu\mathrm m\).

These give

\[ b\ell=0.0285777,\qquad s\ell=0.0331870. \]

Hence,

\[ \begin{aligned} p_{nc} &=100\frac{m+s}{g}\\ &=100\left[ \frac{2(0.022/0.28)+2(0.042/0.68)} {0.451/2.67}-1 \right]\\ &=66.16\ldots\%. \end{aligned} \]

Therefore,

\[ \boxed{p_{nc}\approx66\%}. \]

Counting only the monosubstituted benzene groups would miss the grafts bearing singly attached crosslinker molecules.

The solution was checked against the official solution.