Fundamental Insights into the Reductive Covalent Cross-Linking of

Feb 6, 2018 - The present study shows that the SWCNT functionalization using iodide derivatives leads to the best results in terms of bulk functionali...
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Fundamental Insights into the Reductive Covalent Cross-Linking of Single-Walled Carbon Nanotubes Milan Schirowski, Gonzalo Abellán, Edurne Nuin, Jonas Pampel, Christian Dolle, Vincent Wedler, Tim-Patrick Fellinger, Erdmann Spiecker, Frank Hauke, and Andreas Hirsch J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b12910 • Publication Date (Web): 06 Feb 2018 Downloaded from http://pubs.acs.org on February 6, 2018

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Fundamental Insights into the Reductive Covalent CrossLinking of Single-Walled Carbon Nanotubes Milan Schirowskia,b,§, Gonzalo Abellána,b,§, Edurne Nuina, Jonas Pampelc, Christian Dolled, Vincent Wedlerb, Tim-Patrick Fellingere,f, Erdmann Spieckerd, Frank Haukeb, and Andreas Hirsch*a,b a

Chair of Organic Chemistry II, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Henkestr. 42, 91054 Erlangen, Germany. b Joint Institute of Advanced Materials and Processes, Friedrich-Alexander-Universität Erlangen-Nürnberg, Dr.-Mack-Str. 81, 90762 Fürth, Germany. c Fraunhofer Institute IWS, Winterbergstr. 28, 01277 Dresden, Germany. d Institute of Micro- and Nanostructure Research, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 6, 91058 Erlangen, Germany. e University of Applied Science Zittau/Görlitz, Theodor-Körner Allee 16, 02763 Zittau, Germany. f Department of Technical Electrochemistry, Technical University Munich, Lichtenbergstraße 4, 85748 Garching, Germany. §

These authors contributed equally to this work. cross-linking • SWCNT • covalent functionalization • diazonium salt • TG-MS

ABSTRACT: Single-walled carbon nanotubes (SWCNT) have been covalently cross-linked via a reductive functionalization pathway, utilizing negatively charged carbon nanotubides (KC4). We have compared the use of difunctional linkers acting as molecular pillars between the nanotubes, namely p-diiodobenzene, p-diiodobiphenyl as well as benzene-4,4’-bis(diazonium) and 1,1’biphenyl-4,4’-bis(diazonium) salts as electrophiles. We have employed statistical Raman spectroscopy (SRS), a forefront characterization tool consisting of thermogravimetric analysis coupled with gas chromatography and mass spectrometry (TG-GC-MS), and aberration-corrected high resolution transmission electron microscopy image series at 80kV to unambiguously demonstrate the covalent binding of the molecular linkers. The present study shows that the SWCNT functionalization using iodide derivatives leads to the best results in terms of bulk functionalization homogeneity (Hbulk) and degree of addition. Phenylene linkers yield the highest degree of functionalization, whereas biphenylene units induce a higher surface area with an increase in the thermal stability and an improved electrochemical performance in the oxygen reduction reaction (ORR). This work illustrates the importance of molecular engineering in the design of novel functional materials and provides important insights into the understanding of basic principles of reductive cross-linking of carbon nanotubes.

INTRODUCTION Single-walled carbon nanotube (SWCNT) functionalization has been successfully developed during recent years and several functionalization pathways have been reported, improving their processability and fostering their practical applications.1–7 Among the different synthetic approaches the reduction of SWCNT using alkaline metals in suitable solvents – yielding negatively charged carbon nanotubides – followed by the sidewall addition reactions with electrophiles is probably one of the most efficient routes.8 This approach yields solutions of individualised SWCNTs due to a Coulomb-driven exfoliation of the starting materials and generates activated intermediates for the subsequent covalent addend binding, as has been previously demonstrated for alkyl- and aryl-halides, carbonyl compounds, and diazonium or iodonium salts (λ3 iodanes).3,6,7,9–17 When it comes to the tailored cross-linking of SWCNTs – a promising route for the improvement of the structural, electrochemical, mechanical and electrical properties of nanotubes18–32 – the number of examples is scarce. A

recent report by Shaffer and co-workers using Na/naphthalene as a charge transfer agent and p-diiodobenzene (p-DIB) as dielectrophilic cross-linking agent revealed the formation of carbon-bonded organogels with promising properties as electrode materials in supercapacitors.22 However, a detailed understanding of the intrinsic reactivity principles is still lacking. Moreover, the role of the nanotubes used as starting material, the nature of the electrophile and solvents, the homogeneity of the functionalization process, the role of the unreacted addends, or the influence of side reactions remains largely unknown. For this purpose, we extensively investigated the influence of the selected solvent and starting SWCNT material on two different cross-linking routes, using bisdiazonium and diiodo compounds endowed with linkers having different dimensions, acting as pillars between the SWCNTs (Scheme 1). In this study, we analyzed the functionalized SWCNT by statistical Raman spectroscopy (SRS), aberration-corrected high-resolution transmission electron microscopy (HRTEM),

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N2-adsorption isotherms, as well as a forefront thermogravimetric analysis, coupled with gas chromatographic separation, and mass spectrometric characterization (TG-GC-MS). Our results show that the use of milder iodide derivatives is the most effective route, minimizing the presence of unreacted moieties and achieving the highest degree of functionalization. Moreover, we have evaluated the influence of the different covalent cross-linker on the macroscopic electrochemical performance, studying the oxygen reduction reaction (ORR). Whereas the phenylene linkers exhibit a higher degree of functionalization but limited kinetics, the biphenylene linkers improve the separation of the individual SWCNTs mediating the accessibility of the SWCNT’s surface sites, which leads to a clearly improved electrochemical performance.

Table 1. Experimental information of the reaction products and statistical Raman spectroscopic data (ID/IG values ± standard deviation s).

RESULTS AND DISCUSSION In a first step, the solid-state reduction of pristine nanotubes with potassium was developed under strict inert conditions using an argon-filled glovebox ( 600 single point spectra each. Top: statistical distribution of the ID/IG values at 532 nm (A) and 785 nm (B) laser excitation wavelengths. Bottom: mean spectra at 532 nm (C) and 785 nm (D) laser excitation wavelengths.

Additional insights into the covalent cross-linking and the nature of the organic addends can be obtained from coupled TG-MS measurements. Indeed, the online spectra of the final materials show the detachment of the covalently bound addends (Figure 3).13,49 TG-MS spectra of SWCNT-Ph and SWCNT-BiPh confirmed the presence of the desired molecular linkers, showing the characteristic molecular ion traces of benzene at m/z 78, 77, and 51, and biphenyl at m/z 154, 153

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and 76, respectively. The expected m/z of biradical species was not detected, most likely due to the hydrogen abstraction in the gas phase, as previously observed in aryl-functionalized graphene derivatives.47 Moreover, the presence of linkers connected only by one side can be anticipated in the crosslinked samples. In fact, the characteristic iodobenzene mass trace (m/z = 204) was detected at a lower temperature (ca. 228 °C) along with other typical benzene fragmented ions (m/z 51, 52, and 77), suggesting that alongside the desired bivalent linkers showing a higher thermal stability (284 °C) coexist with halfway-reacted monoiodo compounds on the SWCNTs after the reaction procedure.22 Moreover, the expected mass of iodine was not detected. According to TG-MS analyses, reasonable mass losses ranging from 14.5 % to 12.0 % for SWCNT-Ph and SWCNT-BiPh were observed, which after subtraction of the pristine HiPco SWCNTs contribution (4.6 %), were corrected to 9.9% and 4.6 %, respectively (see Figure 3). The degree of functionalization of cross-linked SWCNTs can be estimated by: 𝑚!"#$%& 𝑚!"#$%& / 𝐷𝑒𝑔. 𝐹𝑢𝑛𝑐𝑡. = 𝑀!"#$%& 𝑀!"#$%& where mmoiety is the mass of the leaving group by the TG mass loss, mcarbon is the remaining mass of the carbon deriving from the SWCNT, Mmoiety is the molar mass of the leaving group (77 g/mol and 153 g/mol for phenyl and biphenyl, respectively), and Mcarbon is 12.01 g/mol. The calculated values of functionalization were 1.83 % and 0.66 % for SWCNT-Ph and SWCNT-BiPh, respectively, which are in agreement with the results obtained by SRS. It should be noticed that this degree of functionalization calculation methodology does not lead to face values – due to the possible contribution of adsorbed unreacted residual moieties or secondary products – and should be considered as an approximation. The obtained results afforded an estimation of ca. 1.5 and 0.5 aryl moieties per 100 carbon lattice atoms for sample SWCNT-Ph and SWCNT-BiPh, respectively, in excellent accordance with previous SWCNT functionalization approaches.13,42,45 With respect to the thermal stability, the ion current traces of SWCNT-Ph and SWCNT-BiPh exhibited a peak at ca. 284 ºC and 326 ºC, respectively, indicative of a slightly higher thermal stability of the biphenylene-linked species of ca. 42 °C despite the smaller degree of functionalization. This fact could be related with the smaller amount of defects introduced in the SWCNT-BiPh carbon lattice and the bulk homogeneity (Hbulk) of the material. In the case of SWCNT-BiPh, instead of finding partially reacted 4-iodobiphenyl (m/z 280), only biphenyl (m/z 154) was found, which originates from the twofold attached biphenylene linker. This is most likely due to the high boiling point of ca. 320 ºC of the former linear molecule, which precludes its detection (vide infra). For the unambiguous proof of the identity of the detached molecular linkers, we took advantage of a TG-GC-MS device, which can provide in operando information on the temperature of cleavage, the integrity of the organic tethers or the formation of side products.13,47 In this device, the evolved gas of the sample can be separated by a classic gas chromatography column, and afterwards analyzed by mass spectroscopy. The chromatogram of SWCNT-Ph revealed the presence of both iodobenzene and benzene, whereas biphenyl was the only

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analyte molecule detected in SWCNT-BiPh, in agreement with the TG-MS results (see Figure 3).

Figure 3. TG-MS spectra of samples SWCNT-Ph (A) and SWCNT-BiPh (B), showing an ion current for all characteristic mass fragments of the corresponding phenylene- and biphenylene linkers. Peak maxima of the most prominent masses (m/z 78 for benzene, and m/z 154 for biphenyl) are highlighted by a dashed line with indicated cleavage temperature on top.

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Figure 5. (A) Temperature-dependent statistical Raman spectroscopy (TDSRS) of SWCNT-Ph in the temperature region between 50 and 400 °C. (B) Mean Raman ID/IG intensity ratio extracted from the temperature-dependent Raman spectra measured using 532, 633, and 785 nm excitation wavelengths. (C) TDSRS of SWCNT-BiPh and (D) its corresponding ID/IG intensity ratios. Figure 4. GC-MS spectra from the TG-GC-MS measurements. (A) SWCNT-Ph at 220 °C (black) and 360 °C (red) injection temperature, both showing iodobenzene and benzene as main analytes; relative peak areas depicted in dashed square. (B) SWCNT-BiPh, showing biphenyl as only analyte. Retention times indicated in black.

Furthermore, in order to estimate the amount of twofold connected linkers, two different injection temperatures (i.e. 220 and 360 ºC) were measured, analyzing the area of the gas chromatogram, which is directly proportional to the amount of evolved gas (Figure 4).13 At the lower injection temperature, the area ratio of benzene/iodobenzene was ca. 4:1. Interestingly, at higher injection temperatures the area ratio is roughly ten times higher (ca. 37:1), in good accordance with the TG-MS results. This further corroborates the assumption that monolinked iodobenzene and double-linked phenylene groups coexist in the sample and moreover demonstrates the higher thermal stability of the twofold connected molecular linkers. In addition, we also increased the injection temperature to 480 °C in order to elucidate the origin of the TG mass loss taking place at higher temperatures. Predominantly, benzene and toluene were revealed in the evolved gas-phase by GC separation. Despite benzene being an indicator for a successful crosslinking, the cleavage temperature is significantly higher than expected for sidewall C-C bond breaking. This fact, next to the presence of toluene, which cannot be explained by the desired reaction, is indicative of a SWCNT degradation presumably deriving from reaction-induced defects. A similar nanomaterial degradation was already reported by our group for graphene, which additionally generated other aromatic gaseous molecules like o-, m-, and p-xylene.47

On the other hand, SWCNT-BiPh exhibit only one peak at ca. 15.2 min (biphenyl) independently of the injection temperature (260 °C or 440 °C), this is probably due to the high boiling point of 4-iodobiphenyl (320 ºC). It is worth to mention that our transfer line in our TG-GC-MS unit has a fixed temperature of 280 ºC, causing condensation of the analyte and thus precluding its detection (Figure 4B). Additionally, we have explored the role exerted by the addend’s dimensions on the cross-linking process using the diiodo compounds. In fact, we synthesized longer 4,4’’diiodo-p-terphenyl and 4,4’’’-diiodo-p-quaterphenyl as linkers (see Figure S5) and performed the same studies. Nonetheless despite all the efforts, characterization based on the analysis of Raman and TG measurements was not satisfactory due to the impossibility to remove the excess of diiodo reactant from the SWCNTs, mainly due to their poor solubility in most organics solvents, precluding any reliable information. Direct confirmation of sp3 carbon formation, and therefore covalent sidewall-bonds of SWCNTs, has been demonstrated by Barron and co-workers by solid-state NMR spectroscopy50, however the limited solubility of our cross-linked SWNTs precludes any study in this direction. Thus, in order to unambiguously demonstrate the covalent binding of the aryl groups we performed a temperature-dependent SRS (TDSRS) analysis of samples SWCNT-Ph and SWCNT-BiPh using three different excitation wavelengths (Figure 5). The D band decreases concomitantly with the rising temperatures for all the samples, indicative of a sp3−sp2 rehybridization of the carbon lattice atoms of the pristine SWCNT. Moreover, the thermal evolution of the mean ID/IG ratio (measured using 532, 633, and 785 nm) nicely correlates with the TG profile, showing an abrupt decrease at ca. 280 °C for SWCNT-Ph and a more continuous decrease with two broad steps at ca. 280 and 370 ºC for SWCNT-BiPh, in good agreement with the online MS results. These experiments confirm the covalent attachment of

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the molecular linkers even at relatively low temperatures, discarding the influence of physisorbed species. We also investigated the morphology of the pristine and crosslinked SWCNTs by transmission electron microscopy (TEM, FEI Titan Themis3 300) at 80 kV accelerating voltage to reduce structural damage. Figure 6 A–C shows bright-fieldTEM overview images, Figure 6 E–F high-resolution-TEM images of the pristine and functionalized CNTs. The TEM data clearly reveals the single wall nature of the tubes with diameter of 1.1-1.4 nm with residual catalyst particles present. In overall, the phenyl and biphenyl functionalized samples exhibit a more dispersed and debundled nature (see Fig. 6 and SI6 for additional images). The separation of the pristine and cross-linked nanotubes has been compared by measuring the distance between tube sidewalls from HRTEM data. For pristine SWCNTs the distance between sidewalls is 3.9 ± 0.3 Å, indicative of van-der-Waals interactions comparable to the inter-layer distance of graphite. In the functionalized case, the distance drops to 3.5 ± 0.3 Å for phenylene linkers and 3.6 ± 0.3 Å for biphenylene units, respectively. This very subtle

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difference in inter-tubular distances is a consequence of the projection phenomenon in TEM. Only in the very unlikely case of a perfectly orthogonal orientation of the linker chain towards the electron beam the expected linker chain length of around 4.6 and 8.0 Å, respectively, would be resolvable. In addition, we repeatedly observed characteristic entanglement between the tubes showing twisting ensembles, probably as a consequence of the random covalent binding between them. Atomic-resolution transmission electron microscopic movies51 revealed interesting collective vibrations in cross-linked SWCNTs that suggest the covalent binding between nanotubes (see Supplementary Information video 1). Moreover, characteristic entanglement has been repeatedly observed. However, owing to the random alignment of functional linker groups on the nanotubes and the alignment of nanotubes towards the electron beam no clear and unambiguous direct microscopic evidence for the linker groups between 2 individual SWNTs could be gained. In any case, strong evidence can be seen in the Supplementary Information video 1, suggesting the presence of the molecular linkers.

Figure 6. A)-C) Overview BF-TEM images of pristine (A), phenyl-functionalized (B) and biphenyl-functionalized SWNT (C). D-F HRTEM of pristine (D) and functionalized SWNTs (E-F) as indicated.

Furthermore, the cleavage of the covalently attached linker groups during electron irradiation is likely to occur. Remarkably, for SWNT-BiPh we were able to retrieve atomically resolved TEM data of a BiPh moiety attached by only one extreme to an isolated SWNT, in excellent accordance to previous TG-GC-MS analysis. Fig. 7 A shows unprecedented experimental data of an addend on a SWNT surface. From the diameter of the tube and the recorded Moiré pattern we con-

cluded the moiety to be attached to a (12,8) SWNT.52,53 This tube, with the covalently attached BiPh moiety was used for HRTEM image simulation, shown in Fig. 7 B. The conformation of the addend changed mentionable during imaging and was cleaved after several seconds of electron irradiation, as can be observed in the video 2 shown in Supplementary Information.

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Figure 7. A) HRTEM image of single-sided attached BiPh moiety on SWNT (scale bar is 2 nm). B) Simulated HRTEM image of BiPh on (12,8) SWNT slightly inclined as shown in model in C. C) HRTEM image simulation by multislice algorithm, paremeters: 80 kV, Cs 10 µm, defocus 4.7 nm, defocus spread 2.5 nm.

In order to gain a deeper insight into the materials’ surface modification and porosity, nitrogen-physisorption measurements were carried out. In Figure 8 the isotherms of SWCNTPh and SWCNT-BiPh are depicted. Thus, the adsorption/desorption isotherms corroborate the influence of the functionalization on the surface and pore structure respectively. The pristine HiPco SWCNTs show a high specific surface area (SSA) of 671 m2·g-1, as evaluated by the Braunauer-Emmett-Teller (BET) method (this is not surprising as the pristine HiPco nanotubes usually exhibit random values of surface areas ranging between ca. 400–1,000 m2·g-1, see supporting information for more details). The functionalization leads to a drop in the SSA to 429 m2·g-1 in case of Ph and 572 m2·g-1 in case of BiPh functionalization, in accordance with the tendency observed in the respective TEM experiments. The isotherm corresponding to the pristine SWCNTs can be described as a type II isotherm with high microporosity and unlimited multilayer formation at high relative pressure. The almost linear increase in the relative pressure range of 0.03 and 0.45 p·p0-1 is indicative of a large external surface area, as can be expected from largely debundled SWCNTs (see Figure S7). However, an additional H3 type hysteresis loop at relative pressures higher than 0.6 is observed, which is indicative of a pore network or interstitial porosity consisting of macropores in agglomerated SWCNTs that are not completely filled with pore condensate. In stark contrast, the functionalized SWCNTs show type IV(a) isotherms with a characteristic plateau at high relative pressures, indicating a limited multilayer formation that can be interpreted as a sign of the cross-linking process. Interestingly, the plateau in the case of the BiPh-functionalized SWCNTs is accompanied with only little reduced external surface area, i.e. multilayer formation in the pressure range of 0.03 and 0.45 p p0-1 is still largely possible. In contrast to the pristine SWCNTs, H1-type hystereses for the functionalized SWCNTs indicate the presence of mesopore cavities. The shallow slopes reflect a wide range of such mesopores, respectively. In case of SWCNT-BiPh there is a fraction of pores that are clearly smaller compared to the ones in the pristine SWCNTs, as can be observed from the hysteresis closing at lower relative pressures.

Figure 8. Nitrogen adsorption-desorption isotherms measured at 77 K of the SWCNT-Ph and SWCNT-BiPh samples.

This can again be interpreted as a stronger agglomeration compared to the pristine sample, but also as a larger stability against pore collapse of the materials compared to the SWCNT-Ph, in agreement with the TG-MS results. The SWCNT-Ph sample shows overall a strongly reduced gas uptake and a strongly reduced external surface area, highlighting the influence of the cross-linker length. Both functionalized SWCNTs have clearly reduced microporosity, however, again more pronounced for the SWCNT-Ph sample. In order to investigate the influence of a covalent cross-linking functionalization of the SWCNTs by phenylene or biphenylene units on the electrochemical performance, the oxygen reduction reaction (ORR) activity of SWCNT-Ph, SWCNT-Biph, and pristine SWCNTs was exemplarily investigated under alkaline conditions in 0.1 M KOH, using a rotating disk electrode (RDE) at 1,600 rpm. The corresponding linear sweep voltammograms (LSVs) reveal different onset potentials, as well as clear differences in the kinetic region (Figure 9 and Figure S8). The phenylene-functionalized SWCNTs show higher onset potentials, but sluggish kinetics. Such slow kinetics can be connected to a low catalytic activity or to a small electrochemically active surface area (i.e. small concentration of active sites). The higher onset potential can be interpreted by catalytically more active sites mediated by the higher phenylene-functionalization as compared to the BiPh-functionalized SWCNTs. The sluggish kinetics are therefore likely caused by a low electrochemically active surface, which goes along with the shorter cross-linking of phenylene groups as indicated by the nitrogen sorption experiments. Interestingly, the SWCNTs that are cross-linked by

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larger biphenylene units apparently provide a lower specific catalytic activity (lower degree of functionalization), the higher external surface area (longer molecular linkers), however, allows for better kinetics and therefore results in 20 % higher current density at 0.7 V. Remarkably, the number of transferred electrons determined by Koutecký-Levich analysis is very similar for both materials indicating that the different active sites still catalyse by the same mechanism (Figure S9). The behavior goes along well with the nitrogen physisorption results. Overall, the results herein show that covalent crosslinking of SWCNT with BiPh compared to Ph improves the separation of the individual SWCNTs mediating the accessibility of the SWCNT’s active surface sites, which leads to a clearly improved electrochemical performance, which is reflected in better kinetics and higher current densities. Moreover, in line with the recently evolving defective carbon catalysts54, it is interesting to prove that catalytically active sites can be introduced by controlled functionalization at low temperature along with a fine tuning of porosity.55

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ty at 0.7 V compared to the phenylene linker. This work provides an important insight into the understanding of the basic principles of reductive SWCNT cross-linking and may serve as a guideline for the design of multifunctional materials of great interest in mechanics, biomedicine, sensing or energy storage and conversion.

ASSOCIATED CONTENT Supporting Information Experimental details, additional Raman, structure of additional molecular linkers, additional TEM analyses, N2-isotherm of pristine SWNT, and Koutecký-Levich analysis of the materials are available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Prof. Andreas Hirsch. E-mail: [email protected]

ACKNOWLEDGMENT The authors sincerely acknowledge Prof. Jens Weber for his kind assistance with the nitrogen adsorption experiments. The Deutsche Forschungsgemeinschaft (SFB 953 “Synthetic Carbon Allotropes”, project A1 and Z2) and the Cluster of Excellence Engineering of Advanced Materials (EAM) are gratefully acknowledged for the financial support. Dr. G.A. thanks the EU for a Marie Curie Fellowship (FP7/2013-IEF-627386) and the FAU for the Emerging Talents Initiative (ETI) grant #WS1617_Nat_04. Dr. E. Nuin thanks the Programm zur Förderung der Chancengleichheit für Frauen in Forschung und Lehre (FFL) – Promoting Equal Opportunities for Women in Research and Teaching – for her postdoctoral fellowship.

REFERENCES Figure 9. RDE polarization curves of the materials in O2saturated 0.1 M KOH with a sweep rate of 5 mV s−1, 1,600 rpm.

These results indicate that control over the molecular linkers at the nanoscale could exert an influence in the macroscopic properties of this synthetic carbon allotrope.

CONCLUSIONS In summary, we developed a screening of two different reductive covalent cross-linking routes for SWCNT, unifying the experimental conditions. These systematic experiments unambiguously show that the SWCNT functionalization using diiodo compounds leads to the best results both in terms of the degree of addition and bulk homogeneity. By combination of advanced analytical tools we elucidated the nature of the organic addends, proving that mono-linked iodobenzene and double-linked phenylene groups coexist in the sample. On the other hand, the biphenylene-functionalized sample exhibited a lower degree of addition but a higher thermal stability. Furthermore, unprecedented aberration-corrected HRTEM images of covalently attached addends have been achieved. Finally, we have evaluated how the increase in the size of the molecular cross-linkers, as well as the degree and type of functionalization is reflected in the macroscopic properties of the samples. Biphenylene-linking exhibits a higher external surface area (increase in ca. 33 % compared to SWCNT-Ph) with the formation of mesoporosity, and better kinetics for the oxygen reduction reaction, enabling for ca. 20 % higher current densi-

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