Templated Ring-Opening Metathesis (TROM) of Cyclic Olefins

Aug 3, 2018 - Zhe Zhou and Edmund F. Palermo*. Materials Science and Engineering, ... Wang, Cooper, He, Li, and Yang. 2018 51 (15), pp 6111–6118...
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Templated Ring-Opening Metathesis (TROM) of Cyclic Olefins Tethered to Unimolecular Oligo(thiophene)s Zhe Zhou and Edmund F. Palermo* Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States

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S Supporting Information *

ABSTRACT: We developed a fully abiotic approach to template the synthesis of discrete unimolecular polyolefins. Discrete, unimolecular oligo(thiophene)s with alternating sequence were obtained by iterative convergent/divergent couplings and then functionalized with pendant cyclic olefin monomers in the side chains. Upon treatment with the Grubbs third-generation catalyst in dilute solution (0.15 mM in DCM at 0 °C), the pendant monomers undergo templated ring-opening metathesis (TROM). Then, the daughter olefin is liberated from the parent thiophene by hydrolysis. Cyclooctenes undergo TROM to afford macrocyclic products that exactly replicate the chain length of the parent oligomer, as evidenced by MALDI MS/MS and NMR. Norbornene derivatives also undergo TROM and replicate unimolecular chain lengths, but in contrast, they exclusively form the linear oligomeric products with styrenic end groups. A template that was functionalized with one norbornene unit at the α chain end, followed by five cyclooctene units along the template, underwent TROM to afford the macrocyclic daughter olefin. Intertemplate metathesis is suppressed by tuning the concentration and reaction time. Using this strategy, we can effectively replicate the unimolecular nature of a template, made by labor-intensive iterative synthesis, to produce a discrete daughter oligomer by chain growth. We also demonstrate that the templates are recyclable upon hydrolytic cleavage of daughter oligomer, attachment of fresh daughter monomer, and repetition of the TROM process.



INTRODUCTION Naturally occurring biopolymers are rich with chemical information, precisely organized into unimolecular chain lengths, defined sequences, and programmed conformations, which endow a highly sophisticated function.1 Synthetic copolymers typically possess statistical sequence distributions, relatively disperse chain length distributions, and limited conformational control. These materials have been extensively studied due to their interesting physical properties,2 but control of their macromolecular structure is still rudimentary compared to biopolymers. To approach or even exceed nature’s level of control in synthetic polymers3−9 is a goal that has been called the “Holy Grail” of polymer science.10 Strategies for precision control of polymer structure generally fall into two categories: fully synthetic and biological−synthetic hybrid approaches. The use of preexisting or synthetically engineered biopolymers has expanded the cannon of protein structures,11,12 for example, but these methods typically lack the broad chemical diversity of fully synthetic © XXXX American Chemical Society

means. Sequence control in fully synthetic copolymers is possible for step-growth polymerizations in which each individual linkage is formed in an iterative manner.13 The classical Merrifield solid phase peptide synthesis,14 and other synthetic variants,15,16 give well-defined oligomers, albeit with limitations on yield and MW. Johnson and co-workers combined iterative exponential growth (IEG) with orthogonal side-chain functionality (IEG+)17 to synthesize a polymer with sequence-controlled moieties. The Alabi group has employed liquid-phase fluorous supports to prepare sequence-controlled oligomers in one pot.18−20 For chain growth polymerization, methods to control sequence have included precise kinetic control by Lutz and co-workers21 as well as cleverly designed polymerizations of diverse functionalized monomers by Kamigaito,22 Hillmyer,23 Received: May 9, 2018 Revised: July 16, 2018

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and Hawker,6 although these sequence-defined polymers still possess some extent of chain length dispersity. Heroic efforts have been made toward linking one repeat unit at a time (enabling both sequence fidelity and unimolecular chain length, in principle): an ATRP free radical initiator reacts with 1 equiv of allyl alcohol, which is then oxidized and esterified to give an active center for the next single monomer insertion.24 Leigh and co-workers constructed an exceptionally complex molecular machine, based on rotoxanes and amino acids, which showed the ability to form a tripeptide in a fully automated, predetermined series of reactions.25 While certainly laudable, these heroic efforts seem to suggest that scalability and generalization to high-MW polymers will continue to be major challenges. It has long been recognized that template polymerization is an intriguing approach to controlled polymer synthesis.26 In 1954, Szwarc (best known as the father of “living” polymerization) presciently introduced the concept of “replica” polymerization, drawing analogy to biological polymers.27 Acrylic acid was polymerized in the presence of polyvinylpyrrolidone (PVP) as a template via hydrogen-bonding interactions.28 The authors noted rate acceleration but did not see precise replication of chain length from parent to daughter. Weck reported template-assisted ring-opening metathesis polymerization of norbornene monomers associated with polynorbornenes by hydrogen-bonding interactions, which also showed a rate enhancement and narrow polydispersity.29 Similarly, Luh used a polynorbornene template to obtain narrow dispersity in π-conjugated polymers.30 Naturally occurring biopolymers can also be used to template the polymerization of synthetic polymers.31−34 Using base pairs to associate daughter monomers to parent polymer, O’Reilly and co-workers polymerized a vinyl daughter polymer within a micelle composed of a block segment in the parent polymer.35,36 Though highly promising, these current template methods utilized parent polymers that are disperse in terms of chain length and are not sequence controlled. Thus, current template approaches will produce a batch of daughter polymer with similar molecular weight distributions but are not truly unimolecular replication schemes. A convergent/divergent iterative Stille coupling route affords perfectly regioregular and unimolecular poly(3-hexylthiophene), up to 36 repeating units, on the multigram scale.37 Although labor intensive, the method provides an attractive route to polythiophenes that possess side-chain functionality in a defined sequence. Here, we hypothesize that typical monomers for chain growth polymerization could be covalently attached to the side chains of the sequence defined, unimolecular “parent” polymer and then subjected to common chain growth polymerization conditions to yield a unimolecular “daughter” polymer with the potential to also control sequence. In such a scheme, the iterative method used to make the parent is effectively translated to a chain growth replica polymerization of vinyl monomers, for which iterative coupling schemes are very rare or challenging. Moreover, replica polymerization can produce multiple batches of daughter polymer by recycling the template parent polymer. Recyclability of the template justifies the initial investment required for iterative couplings.

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RESULTS AND DISCUSSION Template Synthesis. We prepared alternating sequence oligo(thiophene)s, with precisely positioned side-chain functionality, by modifications to a previously reported37 iterative Stille coupling scheme (Figure 1). Briefly, brominated 3-

Figure 1. Iterative Stille couplings yield alternating sequence oligo(thiophene)s.

hexylthiophene was coupled to a stannylated thiophene containing a pendant −OTBS group to afford the heterodimer with side-chain functionality. Then, the dimer was divided into two parts: one was brominated and the other stannylated, each regioselectivity. Repetition of the Stille coupling process enables growth of the regioregular thiophene chains. At each stage of the iterative process, a small sample of the discrete oligomer was deprotected with tetrabutylammonium fluoride (TBAF). The resulting hydroxyl side chains were coupled to cyclooctene (COE) carboxylic acid, activated by diisopropylcarbodiimide (DIC), a common activation reagent for esterification (Figure 2). The same methods were used to incorporate norbornene derivatives in the side chains of the parent thiophene as well. With minor modifications, a thiophene template with one norbornene unit at the α chain end, followed by a string of n cyclooctene monomers, was also readily accessible (Figure 3). Thus, we prepared a library of thiophene oligomers bearing discrete numbers of cyclic olefin side chains covalently bound to the “parent” polythiophene chain. Thiophene hexamers with three pendant cyclic alkenes positioned at every other location along the thiophene parent chain were loaded with a variety of daughter monomer sequences: (1) three COE monomers, which we refer to as C3, (2) three NB monomers, N3, and (3) one NB monomer at the α position, followed by two COE monomers, N1C2 (Figure 4). Templated Ring-Opening Metathesis (TROM). The ring-opening metathesis polymerization (ROMP) of eightmembered cyclic olefins, with a diverse range of functional groups, is a well-established field.38,39 We sought to further expand the cannon of ROMP to include cyclooctenes (COE) covalently immobilized onto rigid π-conjugated templates. Thus, we examined the reactivity of C3 upon exposure to the Grubbs third-generation catalyst (G3) in dilute solution (0.1− 1 mM in DCM at 0 °C). The catalyst loading in each case is catalyst:template = 1:1, which corresponds to a catalyst:monomer ratio of 1:n, where n is the number of monomers per template. For example, when G3:C3 = 1:1, the G3:COE ratio is 1:3. The resulting parent−daughter conjugate (termed PC3) was analyzed by matrix-assisted laser desorption ionization B

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Figure 2. Synthesis of a parent template by iterative Stille coupling, covalent attachment of daughter monomers in the side chains, template ringopening metathesis (TROM), and hydrolysis to liberate daughter oligomers. The template can be replenished with additional monomer and resubjected to TROM.

Figure 3. Synthesis of a parent template containing one norbornene unit positioned at the α end of the chains and n cyclooctene units positioned at all other units. These hetero templates were subjected to the same TROM conditions as the homo templates.

Figure 4. (A) Thiophene hexamers bearing COE and NB daughter monomers and (B) their 1H NMR spectra.

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show only the molecular ion by MALDI since the desorption− ionization process is efficient via charge transfer, and thus cationization salts are not needed.44 Fragmentation of this peak by MS/MS gives three signals, each corresponding to the parent compound with loss of one (1132.9), two (978.8), or three (824.3) COE monomer units, presumably via McLafferty rearrangements. After TROM (1.5 × 10−4 M, 0 °C, DCM, 60 min), the NMR spectra show nearly complete disappearance of the cyclic olefin at δ ∼ 5.6 ppm and appearance of a new vinyl signal at δ ∼ 5.2 ppm, indicative of the product PC3 (Figure 6). The monomer conversion was 92%. The MALDI spectra of PC3 showed a single peak at the same mass as the starting material (1286.9). Considering the high monomer conversion, we hypothesized that the resulting structure is the macrocyclic trimer of COE without end groups. Indeed, strong evidence of this structure was obtained from the MALDI MS/MS fragmentation of the peak at 1286.9; the major fragment of mass 824.5 is consistent with the hexameric thiophene backbone bearing three vinylic side chains (theor m/z 824.3), which is expected to form by the simultaneous loss of all three COE side chains (Figure 4A). The persistence of the peaks at 1132.9 and 978.8 are indicative of the unreacted monomer, consistent with the slightly less than quantitative conversion by NMR (∼92%). Considering the much higher statistical likelihood of losing one COE relative to losing all three at once, it is clear that the pendant monomers must have undergone ROM on the template. MALDI of PC3 shows no trace of higher MW byproducts. At longer reaction times and/ or high concentrations, higher MW peaks, corresponding to double and triple the mass of the template (e.g., 2574 and 3861), are observed. At even higher concentrations (∼1 M), the reaction mixture rapidly forms an insoluble, cross-linked gel. This is expected because the template C3 contains three polymerizable units and, thus, will form a network upon intertemplate metathesis. The 1H NMR spectra of the C3 template before TROM exhibit sharp peaks indicative of a precisely defined oligomer

time-of-flight/time-of-flight mass spectroscopy/mass spectroscopy (MALDI-TOF/TOF-MS/MS). This powerful technique enables selective fragmentation of individual molecular ion signals in the primary MALDI-TOF spectra to elucidate complex macromolecular structures.40−42 The parent−daughter conjugates are ladder-type polymers denoted with a single set of brackets that span both repeat units, according to IUPAC rules.43 Before TROM, the compound C3 displays a single MALDI peak at m/z 1286.8, in agreement with the theoretical exact mass of 1286.6 (Figure 5). It is typical for poly(thiophene)s to

Figure 5. MALDI and MS/MS data for C3 and PC3 (after TROM).

Figure 6. 1H NMR spectra of the bare template X3, the template loaded with daughter monomers C3, the parent−daughter ladder polymer product of TROM PC3, and the recycled template recovered after hydrolysis of the daughter. Note that the NMR spectra and HRMS of the liberated daughter product are given in Figure 7. D

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theoretical values (527.3343, 522.3289, and 543.3082, respectively). In the ESI spectrum, very minor peaks appear around m/z 491.3 and 473.3, corresponding to DC3 missing one and two CH3 groups, respectively, which indicates that some minor extent of ester hydrolysis in the side chains. Also, a minor peak around m/z 337.2, corresponding to the cyclic dimer of COE, is also observed, which is consistent with slightly less than quantitative monomer conversion (∼94%). There is no evidence of the linear polymer containing any end groups present. The full range ESI mass spectra are given in the Supporting Information (Figure S7c). The formation of the macrocycle is a surprising result because it would presumably require the active chain end of the trimer C3=[Ru] to cross onto the styrenic end group, which is typically considered stable to ROMP conditions. Although the details of the TROM mechanism are unclear at present, and beyond the scope of this report, one may speculate that the colocalization of alkenes on the template (very high local concentration of monomer despite very low overall concentration) promotes reactivity that is otherwise not observed in traditional conditions. Selective formation of COE dimers and trimers has been observed in the case of unsymmetrical Ru-NHC catalysts.45 Moreover, the final ringclosing event ejects the catalyst from the template into dilute solution, allowing for diffusion, which may kinetically stall the reverse ring-opening process. Thus, it is possible that the DC3 macrocycle is a kinetically trapped species even if the linear species is thermodynamically favored. Alternatively, the macrocyclization may be promoted by the presence of the carbonyl linkage between template and daughter. The presence of such groups in proximity to olefin has been shown to alter reactivity by chelation of the carbonyl oxygen to the ruthenium metal center, favoring otherwise challenging macrocyclizations.46 Next, we investigated the template bearing three pendant norbornene units (Figure 8). Before TROM, the template N3 shows a single peak by MALDI at the expected m/z ratio

(Figure 6). After TROM, PC3 exhibits substantial peak broadening in the aromatic and alkene regions of the spectrum. Upon liberation of the daughter oligomer by hydrolysis, we recover the original thiophene hexamer bearing three hydroxyl substituents, dubbed X3. The NMR spectrum of the recovered template is identical to that of the virgin template prior to loading with COE monomers. All peaks in recovered X3 regain their sharp intensity upon liberation of the daughter oligomer (Figure 6), which suggests that peak broadening in PC3 is attributable to the conformational restrictions imposed on the parent−daughter ladder-type conjugate. The ensemble of many different conformers locked in by the TROM process is expected to give rise to peak broadness in the NMR. The broadness is not attributable to molecular/compositional heterogeneity (as is usually the case for polymers) because the spectral features regain sharpness upon hydrolytic cleavage. We also isolated the cyclic daughter oligomer DC3 (as the methyl ester derivative) and characterized it by 1H and 13C NMR as well as electrospray ionization high-resolution mass spectroscopy (ESI HRMS). Indeed, the macrocyclic structure was unambiguously confirmed by NMR (Figure 7A). No

Figure 7. (A) 1H NMR spectra and (B) ESI HR-MS of the methyl ester derivative of the daughter oligomer DC3.

styrenic end-group signals are observed in the 1H or 13C NMR spectra, which are fully consistent with the formation of the macrocycle. Convincingly, the ESI HRMS shows a most prominent peak (m/z 505.3537) that matches well with the theoretical mass of the proton adduct ([M + H]+ = 505.3529) for the proposed structure DC 3 (Figure 7B). Peaks corresponding to DC3 adducts with sodium [M + Na]+ (527.3344), ammonium [M + NH4]+ (522.3298), and potassium [M + K]+ (543.3082) perfectly match the

Figure 8. MALDI and MS/MS data for N3 and PN3. E

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template (Figure 9). The 1H NMR spectrum of N1C2 before TROM contains two olefin signals: one at δ ∼ 5.6 ppm (COE)

(1238.5). Fragmentation of this peak by MALDI MS/MS gives a series of three peaks, each corresponding to the loss of 1 equiv (1172.8), 2 equiv (1106.7), and 3 equiv (1040.7) of cyclopentadiene, as expected from the retro-Diels−Alder fragmentation mechanism. The loss of one cyclopentadiene unit is by far the major fragment, with the loss of two being statistically less likely, and the loss of three representing only a trace amount. TROM of N3, in the same conditions as above (1.5 × 10−4 M, 0 °C, DCM, 60 min), yielded only the linear product PN3 as evidenced by NMR and MALDI with no trace of the macrocyclic daughter product. In the 1H NMR spectra, the template N3 displays an olefinic signal at δ ∼ 6.1 ppm. This peak disappears and is replaced by a broad feature at δ ∼ 5.1 ppm, indicating near complete monomer conversion (Supporting Information, page S22). The MALDI of PN3 shows a dominant peak at m/z ∼ 1343, which is consistent with the linear trimer of norbornene containing a styrenic end groups (m/z 1238 + 104), derived from initiation with the Grubbs third-generation catalyst. Apparently, the macrocyclic ringclosing observed in the case of PC3 is not operative in the case of PN3 under identical TROM conditions. This is consistent with the fact that ROMP on norbornenes does not suffer from the same backbiting reaction encountered in the case of ROMP on cis-cyclooctenes. The simplest explanation for the lack of macrocycle formation on PN3 is that the norbornenes are either sterically or conformationally forbidden from undergoing metathesis between daughter monomers on the α and ω positions. There is a minor peak in the MALDI spectra of PN3 at 2581.6, which is consistent with the product of intertemplate propagation that doubles the MW of the ion, plus the mass of the styrenic end groups (1238.5 × 2 + 104 = 2581). Thus, we find that TROM of N3 is more prone to intertemplate propagation as directly compared to C3 in identical TROM conditions, which is unsurprising because the higher ring-strain NB polymerizes much faster than COEs in ROMP.47−49 The higher mass peak is eliminated when TROM is run at higher dilution or for a shorter time, albeit at the expense of somewhat less than quantitative monomer conversion. The MS/MS fragmentation pattern of the PN3 peak at 1342.9 does not show any signals in the range of 1040−1173, which confirms that no unreacted NB monomer is present in the reaction product (in agreement with approximately quantitative conversion by NMR). The major peak is observed at 824.6, which results from three McLafferty rearrangements as discussed above for the PC3 compound. This is particularly informative, since the TROM product PN3 does not contain any units that can undergo the retro-Diels−Alder mechanism; thus, formation of the putative daughter product is the only plausible explanation that remains. Interestingly, there is also a fragment peak at m/z ∼ 741, which can be explained as the loss of one of the C6H13 side chains. The 741 peak intensifies as the laser power is increased. These observations, combined with the relatively low signal-to-noise ratio in the MS/MS spectra, strongly suggest that the liberation of daughter olefin from the thiophene parent oligomer in PN3 requires substantially more energy than the loss of one or two unreacted norbornene monomers from N3, which is intuitively reasonable. Third, we pursued a hybrid sequence-specific template containing one norbornene side chain at the α position and two COE monomers at the other positions, dubbed the N1C2

Figure 9. MALDI and MS/MS data for N1C2 and PN1C2.

and another at ∼6.1 ppm (norbornene), with integrated areas in the expected 2:1 ratio. The MALDI spectrum of N1C2 shows a single peak at m/z 1270.7, which matches the theoretical value for the loaded template. The fragmentation of this peak by MALDI MS/MS shows three signals: 1204.9 (loss of one cyclopentadiene by retro-DA), 1050.6 (loss of one cyclopentadiene and one COE), and 896.4 (loss of one cyclopentadiene and two COEs). Upon subjecting N1C2 to TROM conditions, the olefinic signals in the NMR disappear and are replaced with one broad feature centered at δ ∼ 5.1 ppm, as expected for PN1C2. The MALDI spectrum displays a predominant peak at 1270.5, consistent with the macrocyclic daughter olefin. Fragmentation of this peak gives a signal at m/ z = 824, which is the vinylic template upon three McLafferty rearrangements (as in the case of PN3). There are no higher MW peaks observed in the spectra, which suggests that no intertemplate cross-linking occurred. There is a minor peak at m/z 1403, which is the linear daughter product with the added mass of styrene end group (+104), as expected, but also includes the extra mass of ethylene (+28), the latter of which was unanticipated. We speculate that the quenching of the TROM process with ethyl vinyl ether (EVE) somehow leads to ethenolysis of the daughter product, although the details of this mechanism remain unclear at present and will be the subject of future investigations. We had initially suspected that the EVE was thermally degraded over time and was thus contaminated with traces of ethylene; however, repeating the experiment with a fresh bottle of EVE gave the same result. It may be possible that addition of EVE to liberated G3 in solution generates a small amount of the methylidine complex that undergoes cross-metathesis with the daughter oligomer. Curiously, however, this effect is only ever seen in the case of the hybrid templates bearing both norbornene and cyclooctene (of type PN1Cn). The templates bearing only norbornenes (PNn), and those bearing only cyclooctenes (PCn), never showed any evidence of ethenolysis. F

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Figure 10. MALDI and MS/MS data for N1C5 and PN1C5.

Encouraged by our preliminary studies on hexameric templates, we proceeded to synthesize a thiophene undecamer with one norbornene (at the α position) and five cyclooctene monomers, denoted as N1C5 (Figure 10). The MALDI spectrum of N1C5 shows a single sharp peak at m/z 2391 and fragments by MS/MS into a prominent peak at 2325 (loss of one norbornene), a less intense peak at 2070 (loss of one NB and one COE), and a very minor peak at 2016 (loss of one NB and two COEs). There were no discernible fragments corresponding to the loss of four or more daughter monomers from the side chains. After N1C5 was subjected to TROM (10−4 M in DCM, 0 °C, 50 min), quantitative conversion of cyclic olefin to polyolefin structure PN1C5 was confirmed by NMR. The MALDI spectrum of PN1C5 showed a major peak at 2391 (the macrocyclic product) as well as a minor signal at 2523 (M + 132; the linear polyolefin with a styrene end group, plus ethylene). The major peak did not display any substantial fragmentation by MS/MS, except for a trace peak indicating loss of one unreacted COE monomer. This observation is unsurprising when we consider that it would require one retro-DA and five McLafferty rearrangements to occur, on the same molecule, almost simultaneously, the probability of which is vanishingly small. The linear peak at m/z 2523 fragments via loss of the mass of ethylene, to give a weak signal at 2495 (2391 + 104), which matches the mass of linear daughter olefin with a styrene end group. The provenance of this fragmentation is unclear at present and will be the subject of future mechanistic investigations. Finally, we hydrolyzed PN1C5 and repeated the MALDI experiment. We observed the hydroxyl-functionalized thiophene template at m/z 1589, but the daughter oligomer was not observed in the α-cyano-4-hydroxycinnamic acid (CHCA) matrix. When the MALDI matrix trans-2-[3-[(4-tert-butylphenyl)-3-methyl-2-propenylidene]malonitrile (DCTB) was used instead, a peak appeared at m/z 904, corresponding to

the daughter oligomer, a 48-membered macro-bicyclic compound containing six carboxylic acid groups (Figure 10). Efforts to scale up the reaction and isolate this daughter oligomer (as an ester derivative) are currently underway. We found it surprising, on first inspection, that a template of 11 thiophene units could possibly yield a daughter oligomer of macrocyclic structure because the ring-closing metathesis would require the two chain ends of the fairly rigid πconjugated template molecule to come within a distance of less than 20 Å. To assess the feasibility of such a structure, we examined 3D molecular models of the putative reaction product PN1C5 (Figure 11). Indeed, the template-bound olefin

Figure 11. Molecular model of the parent−daughter conjugate PN1C5 generated in ChemBio3D with MM2 steric minimization. The contour of the parent thiophene is highlighted in red and the daughter olefin in blue. The dotted line indicates the end-to-end distance R. G

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confirmed by 1H NMR spectroscopy (identical to template assynthesized, before attachment of daughter monomer; see Figure 6). The recovered template was then functionalized again with another 3 equiv of COE monomer and resubjected to TROM conditions, which gave the same result as the virgin TROM. Thus, we demonstrate for the first time, to our knowledge, the recycling and reuse of a template polymer for repeated ROM with unimolecular control (Figure 12).

macrocycle imposes substantial, though not unfathomable, curvature on the oligothiophene backbone: end-to-end distances in the range of ∼12−17 Å are observed with reasonably unstrained bond angles and dihedral angles for the thiophene units. Literature values for the persistence length of regioregular poly(3-alkyl thiophene)s are approximately lp = 30 Å, a length scale that corresponds to about 6 or 7 thiophene units.50−52 Indeed, π-conjugated polythiophenes (C∞ ∼ 13) are more rigid than common polyolefins (C∞ ∼ 7), but only by a factor of about 2. With those data in mind, the arc of the thiophene backbone seen in the molecular model is not so unreasonable. The thiophene 11-mer has a contour length of Nl ∼ 4.2 nm, which is similar to the persistence length of P3HT, suggesting that this oligomer is not a strictly rigid-rod limit but rather a semiflexible segment. It seems logical to speculate that there exists some upper limit for macrocyclic ring-closing to occur on a template, beyond which the probability of two chain ends residing within a through-space distance of