Growth, Properties, and Applications of Branched Carbon Nanostructures

Nanomaterials featuring branched carbon nanotubes (b-CNTs), nanofibers (b-CNFs), or other types of carbon nanostructures (CNSs) are of great interest due to their outstanding mechanical and electronic properties. They are promising components of nanodevices for a wide variety of advanced applications spanning from batteries and fuel cells to conductive-tissue regeneration in medicine. In this concise review, we describe the methods to produce branched CNSs, with particular emphasis on the most widely used b-CNTs, the experimental and theoretical studies on their properties, and the wide range of demonstrated and proposed applications, highlighting the branching structural features that ultimately allow for enhanced performance relative to traditional, unbranched CNSs.


Introduction
The late Stone Age, known as the Neolithic Age (10,000-4500 BC) marked the first extensive use of composite materials in construction-the "mudbrick". The beginnings of an agricultural system also trace back to this period. By-products of agriculture, such as straw, were used as reinforcing materials in these mudbricks, thus providing an early example of "recycling". Mudbricks can therefore be considered as the first recorded artifact containing a branched material as a matrix reinforcing component [1].
Many other biological systems have branched structures where their functional morphology is key to their advanced functionality. For example, the correlation of branching in plants with respect to their functional morphology and mechanical behavior have led to concepts applicable in synthetic branched-fiber materials [2], in the bio-inspired design of polymer nanocomposites [3], in tissue engineering [4], and in superhydrophobicity-the socalled "lotus leaf" effect [5]. Currently, branched carbon nanotubes (b-CNTs) and branched carbon nanofibers (b-CNFs) are of great technological interest due to their electronic and mechanical properties. Although less common, branched CNTs can also be grown onto graphene-based materials, such as reduced graphene oxide (rGO), in a combination of 1D and 2D components to attain 3D hierarchical architectures [6]. All these materials can form 2D and 3D ordered networks, and the aim of this mini-review is to highlight some of their proof-of-principle and proposed applications.

Experimental Studies and Branched CNS Production
Currently, Ni, Co, Fe, and Cu or their alloys are used as catalyst particles to decorate CNFs or CNTs to form branches. The main but by no means only used [7] growth method is some form of chemical vapor deposition (CVD) process [8], which can be further modified, for instance through plasma enhancement, to increase the geometrical diversity of the resulting nanomaterials [9][10][11]. Earlier, Terrones et al. found that sulfur plays an important role in the formation of branched nanotube networks with stacked-cone morphologies [12]. In particular, sulfur acts as a CNT branching promoter, as its interaction with the C atoms favors the formation of non-hexagonal rings in the sp 2 lattice, thus introducing a negative curvature in the case of heptagons (leading to branch opening) or a positive curvature in the case of pentagons (leading to tip closing) [12]. More recently, Huang et al. fabricated branched CNTs by a CVD process in the presence of thiols. They concluded that "sulfur in thiol may reduce the melting point of iron (Fe: 1535 °C, FeS: 1193 °C) during the pyrolysis process. This will result in the enlargement of iron particles which is responsible for nanotube growth." This finding is important, as they noted that these larger particles were more likely to split into smaller ones, leading to branched nanotube growth [13].
Most researchers who do not fabricate their own b-CNTs use the so-called CNSs supplied by Applied Nanostructured Solutions LLC (Lockheed Martin Corporation, MD, US) [14]. The CNSs are fabricated in a CVD process on a moving substrate (e.g., glass fiber) with a growth rate of up to several microns per second. The process uses an iron catalyst, which initializes CNT growth, and then splits, forming Y-junction CNTs. The CNTs within the CNS have a more defective structure than those in a conventional CNT bundle. The CNS bundles consist of aligned CNTs whose inner walls are intact, and the outer walls have defects with 5 or 7 membered carbon rings, which covalently bind to adjacent CNTs. On average, the bundles are 70 μm long and 10 μm thick with multi-wall CNTs (MWCNTs) of ca. 9 nm diameter. "These defective features are characterized by its highly entangled, branched, cross-linked, and wall-sharing architecture" [15].
Malik et al. fabricated branched MWCNTs using commercially available MWCNTs (Baytubes© from Bayer Material Science A.G., Leverkusen, Germany) by introducing defects in the outer tubes, which split and re-rolled to form branched MWCNTs ( Figure  1) with Y-junctions and T-junctions ( Figure 2) [16]. They also found that if they used the same process on thinner MWCNTs, such as triple-walled MWCNTs, then tri-layer graphene ribbons formed. Tri-layer graphene is currently an interesting quantum material [17]. The indications are that only a few outer walls of the branched MWCNTs are defective; nevertheless, enhanced properties emerge, such as a lower percolation threshold. The inner tubes of the branched MWCNTs remain intact and so retain their native electrical and mechanical properties.  (d) outer layers peeling out as a sheet; (e) onset of re-rolling of outer layers. Reproduced from [16].
A simple, one-step co-pyrolysis method was developed to produce branched CNTs with controlled N-doping at the junctions, using hexamethylenetetramine and benzene as nitrogen and carbon sources. The catalyst splitting at the tips of the CNTs led to branching. Interestingly, it was found that the difference in the vapor pressure and the insolubility Nanomaterials 2021, 11, 2728 3 of 22 of the precursors were crucial aspects for the generation of the intratubular junctions connecting the b-CNTs [18].  [16].
A simple, one-step co-pyrolysis method was developed to produce branched CNTs with controlled N-doping at the junctions, using hexamethylenetetramine and benzene as nitrogen and carbon sources. The catalyst splitting at the tips of the CNTs led to branching. Interestingly, it was found that the difference in the vapor pressure and the insolubility of the precursors were crucial aspects for the generation of the intratubular junctions connecting the b-CNTs [18].
Another type of approach to attain branched CNTs is based on the covalent or non-covalent functionalization with branched or dendritic structures to connect the CNTs with each other. The most commonly used procedures rely on grafting onto the CNTs with branched or dendritic polymers [19][20][21]. However, covalent functionalization is well-known to affect the electronic properties of CNSs and requires careful monitoring to preserve the CNS [22]. Alternatively, π-π interactions offer an efficient strategy to non-covalently attach CNTs to aromatic and multi-functional linkers, and, thus, to each other into branched structures. For instance, a molecular clip was designed displaying an open cavity with four anthracene panels that could capture single-walled carbon nanotubes (SWCNTs) to yield highly monodispersed and stable aqueous nanocarbon composites [23].
In recent years, environmental awareness has fostered increasing interest in the development of green production methods for carbon nanostructures [24] and their functionalization with virtually zero waste generation [25]. Diazonium salts have been proposed as covalent linkers for the tips of SWCNTs that were previously wrapped in DNA to protect the sidewalls from undesired functionalization, thus enabling the preferential crosslinking of the CNT ends in water and at room temperature [26]. Environmentally-friendly carbon sources, such as vegetable oils, have also been used to produce b-CNTs [27]. The upcycling of plastic waste for CNT production is another attractive approach to lower its impact on the environment [28] and was also applied to branched CNTs. In particular, Y-type branched MWCNTs were produced through the upcycling of polyethylene terephthalate (PET) waste, through a rotating cathode arc discharge technique. It was found that the soot obtained from the anode contained solid carbon spheres, which were formed at the lower temperature region of the anode (ca. 1700 °C), and which could be converted into long "Y" type branched and non-branched MWCNTs at approximately 2600 °C. Conversely, soot deposited on the cathode was composed of thinner MWCNTs and other nanoparticles (NPs), with the tubes generally featuring a higher graphitization degree, compared to those on the cathode [29].

Theoretical Studies
Theoretical research on branched CNSs has given greater insight into a number of parameters of interest, such as the type and nature of defects, for technological applications. Zang and Glukhova studied the formation of the T-shaped junction between Another type of approach to attain branched CNTs is based on the covalent or noncovalent functionalization with branched or dendritic structures to connect the CNTs with each other. The most commonly used procedures rely on grafting onto the CNTs with branched or dendritic polymers [19][20][21]. However, covalent functionalization is well-known to affect the electronic properties of CNSs and requires careful monitoring to preserve the CNS [22]. Alternatively, π-π interactions offer an efficient strategy to noncovalently attach CNTs to aromatic and multi-functional linkers, and, thus, to each other into branched structures. For instance, a molecular clip was designed displaying an open cavity with four anthracene panels that could capture single-walled carbon nanotubes (SWCNTs) to yield highly monodispersed and stable aqueous nanocarbon composites [23].
In recent years, environmental awareness has fostered increasing interest in the development of green production methods for carbon nanostructures [24] and their functionalization with virtually zero waste generation [25]. Diazonium salts have been proposed as covalent linkers for the tips of SWCNTs that were previously wrapped in DNA to protect the sidewalls from undesired functionalization, thus enabling the preferential crosslinking of the CNT ends in water and at room temperature [26]. Environmentally-friendly carbon sources, such as vegetable oils, have also been used to produce b-CNTs [27]. The upcycling of plastic waste for CNT production is another attractive approach to lower its impact on the environment [28] and was also applied to branched CNTs. In particular, Y-type branched MWCNTs were produced through the upcycling of polyethylene terephthalate (PET) waste, through a rotating cathode arc discharge technique. It was found that the soot obtained from the anode contained solid carbon spheres, which were formed at the lower temperature region of the anode (ca. 1700 • C), and which could be converted into long "Y" type branched and non-branched MWCNTs at approximately 2600 • C. Conversely, soot deposited on the cathode was composed of thinner MWCNTs and other nanoparticles (NPs), with the tubes generally featuring a higher graphitization degree, compared to those on the cathode [29].

Theoretical Studies
Theoretical research on branched CNSs has given greater insight into a number of parameters of interest, such as the type and nature of defects, for technological applications. Zang and Glukhova studied the formation of the T-shaped junction between SWCNTs. They combined a triangulated mesh with molecular dynamics (MDs) to allow for the generation of several topological configurations of the contact point between different carbon nanostructures, such as fullerenes, graphene, and CNTs, including T-, X-, and Y-type junctions with atomistic models [30]. Classical MD simulations were employed to enable better design of b-CNTs, and a comparison was made between the properties of b-CNTs with V-, T-, and Y-junctions and their effects on the performance of the resulting nanopins as part connectors in nanodevices [31]. DFT calculations were combined with the experimental bottom-up synthesis of a junction unit of b-CNTs to study its interesting optoelectronic properties [32].
The heatflow through b-CNTs with T-junctions was studied by atomistic models, with particular attention to the branch length and strain effects on the thermal transport. Remarkably, it was found that the heat flew straight, rather than sideways, inside the T-junction, using an asymmetric temperature setup. Such an observation is in disagreement with the conventional thermal circuit calculations, and may be explained through ballistic phonon transport, phonons with differing interactions or scattering with the defective atoms at the T-junction. Furthermore, the tensile strain proved to be a useful parameter to control the thermal transport, with potential implications for heat management uses [33]. Energy transmission is dependent on the type of junction too, as demonstrated in a detailed study on phonon scattering on T-type and X-type CNT junctions [34].
In silico studies of the mechanism of nanowelding a branched network of SWCNTs were performed for tissue engineering applications [4], whereby CNTs are very promising [35,36], especially to repair the bone [37,38] and conductive tissues [39], such as the nerve [40] and the heart [41]. Defective regions of SWCNTs were found to absorb more energy than defect-free regions, which acted as hot-spots for nanowelding and the formation of b-CNT networks [4]. Further studies demonstrated the importance of the type of structural defects in the contact area of b-SWCNTs on the contact resistance of the T-junction of SWCNTs in the resulting electrical conductivity of the final network [42]. A layered design was proposed using natural polymer matrices, i.e., collagen, albumin, or chitosan, connected via the b-CNTs to provide an electrically conductive network to assist cells in their mutual reconnection during the regenerative process [42].
Finally, a bio-inspired design was proposed for b-CNTs as nanocomposite reinforcement. Coarse-grained MD simulations revealed that the pullout strength of the b-CNTs could be an order of magnitude higher than that of linear CNTs, whereby the enhanced interfacial shearing strength was found to be strongly dependent on various parameters, such as the geometry of nanofibers, the molecular weight of the polymers composing the bulk material, and the pullout velocity [3].

Batteries
Lithium-ion batteries (LIBs) use oxides of the valuable elements Li, Co, Ni, and Mn in their cathode material. This accounts for about a third of the cost of the battery. However, cheaper technologies may not be commercially recyclable. Therefore, the main way to reduce their carbon footprint would be to make them more efficient, so that they are not only cheaper to begin with, but also last longer in service. LIBs mainly use graphitic materials in their anodes as they have good electrical conductivity, high crystallinity, and a layered structure. Graphite has a theoretical intercalation capacity of 372 mA·h·g −1 for the end compound LiC 6 [43]. LIB anodes fabricated with branched CNSs (Table 1) together with transition metal sulfide or oxide NPs have high capacity and good cycle life [44][45][46][47][48][49]. The synergy of these NPs and branched CNSs leads to a hierarchical porous network with a large surface area, good electrical conductivity, and enhanced structural stability compared to conventional amorphous carbon. As an example, Chen et al. fabricated a b-CNT@SnO 2 @carbon sandwich-type heterostructure ( Figure 3) as an LIB anode [44]. Scanning electron microscopy (SEM) images ( Figure 4) confirmed the branched nature of CNTs (Figure 4a), which increased significantly in diameter upon inclusion of SnO 2 in the structure (Figure 4b), which featured a "brush-like" morphology, with SnO 2 nanorods stemming from CNTs (Figure 4c,d). Hierarchical architectures were attained also through iron oxide NP encapsulation inside CNTs, whose 3D networks were ozonized and used as substrates to further grow CNT branches, thanks to a catalytic effect of the iron NPs. This material showed high stability (>98% capacity retention up to 200 cycles at 100 mA·g −1 with a coulombic efficiency >97%, an outstanding rate capability (>70% capacity retention at 50-1000 mA·g −1 rates), and reasonable capacity of ca. 800 mA·h·g −1 at 50 mA·g −1 [50].
1) together with transition metal sulfide or oxide NPs have high capacity and good cycle life [44][45][46][47][48][49]. The synergy of these NPs and branched CNSs leads to a hierarchical porous network with a large surface area, good electrical conductivity, and enhanced structural stability compared to conventional amorphous carbon. As an example, Chen et al. fabricated a b-CNT@SnO2@carbon sandwich-type heterostructure ( Figure 3) as an LIB anode [44]. Scanning electron microscopy (SEM) images ( Figure 4) confirmed the branched nature of CNTs (Figure 4a), which increased significantly in diameter upon inclusion of SnO2 in the structure (Figure 4b), which featured a "brush-like" morphology, with SnO2 nanorods stemming from CNTs (Figure 4c,d). Hierarchical architectures were attained also through iron oxide NP encapsulation inside CNTs, whose 3D networks were ozonized and used as substrates to further grow CNT branches, thanks to a catalytic effect of the iron NPs. This material showed high stability (>98% capacity retention up to 200 cycles at 100 mA•g −1 with a coulombic efficiency >97%, an outstanding rate capability (>70% capacity retention at 50-1000 mA•g −1 rates), and reasonable capacity of ca. 800 mA•h•g −1 at 50 mA•g −1 [50].   1) together with transition metal sulfide or oxide NPs have high capacity and good cycle life [44][45][46][47][48][49]. The synergy of these NPs and branched CNSs leads to a hierarchical porous network with a large surface area, good electrical conductivity, and enhanced structural stability compared to conventional amorphous carbon. As an example, Chen et al. fabricated a b-CNT@SnO2@carbon sandwich-type heterostructure ( Figure 3) as an LIB anode [44]. Scanning electron microscopy (SEM) images ( Figure 4) confirmed the branched nature of CNTs (Figure 4a), which increased significantly in diameter upon inclusion of SnO2 in the structure (Figure 4b), which featured a "brush-like" morphology, with SnO2 nanorods stemming from CNTs (Figure 4c,d). Hierarchical architectures were attained also through iron oxide NP encapsulation inside CNTs, whose 3D networks were ozonized and used as substrates to further grow CNT branches, thanks to a catalytic effect of the iron NPs. This material showed high stability (>98% capacity retention up to 200 cycles at 100 mA•g −1 with a coulombic efficiency >97%, an outstanding rate capability (>70% capacity retention at 50-1000 mA•g −1 rates), and reasonable capacity of ca. 800 mA•h•g −1 at 50 mA•g −1 [50].   Sodium-ion batteries (SIBs) have the advantage that sodium is cheaper and more abundant than lithium. However, sodium ions are much larger than lithium ions, so new electrode materials are being investigated. SIBs do not use graphite, as it is not possible to achieve sodium insertion with the electrolytes commonly used in metal-ion batteries. In theory, 2D carbon materials can have a theoretical intercalation capacity up to 2232 mA·h·g −1 for the end compound Na 6 C 6 [51]. In practice, branched CNSs are amongst the most promising anode materials for SIBs (Table 1) as they have good conductivity and a 2D/3D micro-porous structure. The structure of b-CNT anode material means that the sodium-ion or lithium-ion insertion follows the "house of cards" model [52], which means that both sides of the branches are accessible. These types of anode materials are intrinsically flexible, and so the mechanical stresses on intercalation/de-intercalation are reduced, which leads to greater electrode long-cycle stability. Branched CNSs serve as conductive porous networks with the active NPs, and they not only improve mechanical stability but also enhance the surface area [49,53,54].
The many advantages of branched CNSs in electrocatalysis have been analyzed in detail in many studies. For instance, Li et al. fabricated a tree-like nanostructure with FeOOH leaves growing on MWCNT branches, FeOOH@MWCNTs, as an anode for electrocatalytic water splitting ( Figure 5) [87]. Another work combined the catalytic activity of cobalt NPs with the high conductivity of CNT branches grown onto reduced graphene oxide (rGO), which displays a high surface area and ion diffusion, to produce a hierarchical architecture for electrocatalytic ORR and OER reactions [94]. Bamboo-like branches of CNTs were grown onto rGO, thanks also to iron oxide NPs, to enhance the performance of LIBs and achieve a specific capacity as high as 1757 mA·h·g −1 at 50 mA·g −1 , with a good rate capability of 73% at 1000 mA·g −1 , and a gradual increase from ca. 1500 to ca. 2900 mA·h·g −1 after 100 cycles [95].

Supercapacitors
Branched CNSs are not only used in conventional energy storage systems, such as LIBs and fuel cells, but also as promising materials for supercapacitors [97]. The term supercapacitor encompasses electrostatic double-layer capacitors (EDLCs) [98][99][100][101] and pseudocapacitors [102][103][104]. Carbon-based electrodes tend to be EDLCs, as their porosity lies in the microporous (>2 nm) to mesoporous (2-50 nm) range. In EDLCs, the separation of charge in a Helmholtz double-layer is ca. 0.3-0.8 nm at the interface between the electrode surface and the electrolyte. There is no transfer of charge between the electrode and the electrolyte. The forces leading to the polarization of absorbed molecules are electrostatic; therefore, CNSs are not chemically modified. Table 3 shows examples of branched CNSs with applications in supercapacitor technology. They have a very large surface area and excellent electrical conductivity, which leads to high power and energy density materials. For instance, Xiong et al. have fab-ricated a MWCNT tree-like hybrid nanostructure with graphite platelet (GP) leaves for supercapacitor applications (Figure 6)

Electromagnetic Wave (EMW) Technology
Branched CNSs are used to enhance EMW absorbance (Table 4), which has promising applications in the area of photovoltaics (PV), photo-detectors, and water splitting by photo-electrochemical catalysis. Phan and Yu fabricated tree-like vertically aligned nanostructures (VANS) with MWCNT branches on black silicon (BSi) stems for EMW absorbance applications (Figure 7) [105].

Sensors Technology
Branched CNS fillers enhance the electrical properties of thermoplastic polyurethane (TPU) as they have a low percolation threshold and good electrical conductivity. Application areas include strain sensors and actuators [108][109][110]. In the application area of strain sensors, researchers usually report a gauge factor (G f ), calculated from the ratio of normalized instantaneous resistance change (∆R/R 0 ) to strain (ε). Other sensor applications include highly sensitive electrochemical sensors in so-called nanohybrid sensors [111][112][113][114].

Electromagnetic Wave (EMW) Technology
Branched CNSs are used to enhance EMW absorbance (Table 4), which has promising applications in the area of photovoltaics (PV), photo-detectors, and water splitting by photo-electrochemical catalysis. Phan and Yu fabricated tree-like vertically aligned nanostructures (VANS) with MWCNT branches on black silicon (BSi) stems for EMW absorbance applications (Figure 7) [105].

CNS Type Material Type Specifications
Ref.
Y-junction MWCNTs and carbon flakes TPU/CNS/GNP nanocomposites-melt mix preparation-multifunctional polymer nanocomposites, piezoresistive sensors At 2 wt% filler concentration: TPU/CNS and TPU/CNS/GNP nanocomposites; gauge factor up to 28 and 144, respectively, under 50% strain [112] Tree-like MWCNT-COOH/Ag NP with porous structure MWCNT-COOH/Ag NP nanohybrid CO 2 gas detection Electrochemical CO 2 detection in aqueous medium with a detection limit of 52 nM (surface area 525 ms/g) [113] Hierarchically structured carbon electrodes fabricated from cellulose MWCNT modified carbon fiber: single fiber microelectrode with branched carbon nanotubes for enhanced sensing Tested the detection of NADH oxidation. The overpotential of NADH decreased from over 0.8 V to 0.6 V for the CNT-modified carbon fiber electrode [114] Nanomaterials 2021, 11, x FOR PEER REVIEW 11 of 22 Tree-like. Hollow porous carbon fibers (HPCFs) with MWCNT branches decorated with iron oxide NPs Fe3O4-CNTs-HPCF absorbents with "tree-like'' structure; EM wave absorber.
Lightweight composite material for aerospace applications The bandwidth with a reflection loss <−15 dB from 10 to 18 GHz (1.5-3.0 mm thick layer) and, the minimum reflection loss is −51 dB at 14 GHz (2.5 mm thick layer) [107]

Sensors Technology
Branched CNS fillers enhance the electrical properties of thermoplastic polyurethane (TPU) as they have a low percolation threshold and good electrical conductivity. Application areas include strain sensors and actuators [108][109][110]. In the application area of strain sensors, researchers usually report a gauge factor (Gf), calculated from the ratio of normalized instantaneous resistance change (ΔR/R0) to strain (ε). Other sensor applications include highly sensitive electrochemical sensors in so-called nanohybrid sensors [111][112][113][114]

Composite Performance Enhancement
Researchers have found that branched CNSs significantly enhance the mechanical, electrical, and thermo-conductive properties in a wide range of nanocomposites. Branched MWCNT fillers form stronger networks by comparison with conventional MWCNTs, leading to enhanced mechanical performance of the resulting materials [13,19,21,[115][116][117][118]. Natural catalysts can be used to fabricate branched MWCNTs as reinforcement materials to enhance the mechanical and electrical properties of composites. This was shown with volcanic pumice from the Greek island of Santorini (Figure 9) [116]. Alternatively, hyperbranched polymers can be grafted onto CNTs to favor their interconnection and interfacing with polymer resins, with additional advantages such as lower temperatures for curing [20]. The presence of branched as opposed to linear CNTs can be advantageous for the mechanical properties. For instance, the branched structure allows for a lower rheological percolation threshold at much lower nanofiller content, as shown on thermoplastic polyurethane (TPU) composites that demonstrated enhanced conductive and mechanical properties upon inclusion of b-CNTs as fillers [115].
Using a different strategy, hyperbranched polyesters were grafted onto the surface of carboxylated MWCNTs through an esterification reaction. When included in epoxy resins, the fillers demonstrated stronger interfacial bonding and toughening performance, with higher degree of branching of the polymer [19]. Another hyper-branched polymer used to connect MWCNTs is poly(urea-urethane) so as to provide fillers for polyamide-6. The grafted polymer enhanced the compatibility between the CNTs and the bulk matrix of the composite, enabling hydrogen bonding between them, thus yielding a uniform dispersion and allowing for more efficient load-transfer from the polyamide to the CNTs, as well as lower crystallization temperature and higher crystallization rate and The presence of branched as opposed to linear CNTs can be advantageous for the mechanical properties. For instance, the branched structure allows for a lower rheological percolation threshold at much lower nanofiller content, as shown on thermoplastic polyurethane (TPU) composites that demonstrated enhanced conductive and mechanical properties upon inclusion of b-CNTs as fillers [115].
Using a different strategy, hyperbranched polyesters were grafted onto the surface of carboxylated MWCNTs through an esterification reaction. When included in epoxy resins, the fillers demonstrated stronger interfacial bonding and toughening performance, with higher degree of branching of the polymer [19]. Another hyper-branched polymer used to connect MWCNTs is poly(urea-urethane) so as to provide fillers for polyamide-6. The grafted polymer enhanced the compatibility between the CNTs and the bulk matrix of the composite, enabling hydrogen bonding between them, thus yielding a uniform dispersion and allowing for more efficient load-transfer from the polyamide to the CNTs, as well as lower crystallization temperature and higher crystallization rate and degree [21].
Compression-molded samples were prepared with different polymers (i.e., polypropylene (PP), polycarbonate (PC), and poly(vinylidene fluoride) or PVDF) and different CNT fillers (i.e., SWCNTs, linear or branched MWCNTs). The nanofillers enhanced the conductive properties of the polymers, allowing for a lower electrical percolation threshold already with <0.1% CNT content. Furthermore, inclusion of 2 wt% b-MWCNTs led to resistivity as low as 2 Ω cm (PC), 3 Ω cm (PVDF), or 7 Ω cm (PP). Another additional advantage of b-CNTs is the high homogeneity of the resulting dispersions [117].

Other Technological Applications
Other technological applications for branched CNSs take advantage of aspects of their tunable properties, such as rheology [119] and hydrophobicity [5], as well as their electrical and electronic properties [8,16,18,29,120,121]. Hirtz and Hölscher et al. used an open flame process to fabricate site-specific catalyst supports and also proposed an empirical model for the growth process, as shown in Figure 10, in agreement with SEM micrographs (Figure 11) [122].

Other Technological Applications
Other technological applications for branched CNSs take advantage of aspects of their tunable properties, such as rheology [119] and hydrophobicity [5], as well as their electrical and electronic properties [8,16,18,29,120,121]. Hirtz and Hölscher et al. used an open flame process to fabricate site-specific catalyst supports and also proposed an empirical model for the growth process, as shown in Figure 10, in agreement with SEM micrographs ( Figure 11) [122].  A nanothickening agent for high temperature fracturing fluid in the field of oil and gas production was produced using dendritic structures obtained from the free radical polymerization of acrylamide (AM), acrylic acid (AA), sodium p-styrene sulfonate, dimethyl diallyl ammonium chloride, and MWCNTs. The resulting system demonstrated enhanced thickening capacity, thermoresistance, salt and shear tolerance, viscoelasticity, sand carrying capacity, and gel breaking performance, compared to the pristine polymer and partially hydrolyzed polyacrylamide (HPAM) [119].
Super-hydrophobicity is a desirable property that finds various applications, such as the production of stain proof and advanced textiles. This property can be achieved through the creation of highly rough surfaces, for instance through a biomimicry approach that take inspiration from the microstructure of the lotus leaf, which floats on muddy waters whilst appearing clean. In the case of branched CNTs, lotus-leaf mimicry can be attained in different ways. In one approach, the CNTs were vertically aligned and

Other Technological Applications
Other technological applications for branched CNSs take advantage of aspects of their tunable properties, such as rheology [119] and hydrophobicity [5], as well as their electrical and electronic properties [8,16,18,29,120,121]. Hirtz and Hölscher et al. used an open flame process to fabricate site-specific catalyst supports and also proposed an empirical model for the growth process, as shown in Figure 10, in agreement with SEM micrographs ( Figure 11) [122].  A nanothickening agent for high temperature fracturing fluid in the field of oil and gas production was produced using dendritic structures obtained from the free radical polymerization of acrylamide (AM), acrylic acid (AA), sodium p-styrene sulfonate, dimethyl diallyl ammonium chloride, and MWCNTs. The resulting system demonstrated enhanced thickening capacity, thermoresistance, salt and shear tolerance, viscoelasticity, sand carrying capacity, and gel breaking performance, compared to the pristine polymer and partially hydrolyzed polyacrylamide (HPAM) [119].
Super-hydrophobicity is a desirable property that finds various applications, such as the production of stain proof and advanced textiles. This property can be achieved through the creation of highly rough surfaces, for instance through a biomimicry approach that take inspiration from the microstructure of the lotus leaf, which floats on muddy waters whilst appearing clean. In the case of branched CNTs, lotus-leaf mimicry A nanothickening agent for high temperature fracturing fluid in the field of oil and gas production was produced using dendritic structures obtained from the free radical polymerization of acrylamide (AM), acrylic acid (AA), sodium p-styrene sulfonate, dimethyl diallyl ammonium chloride, and MWCNTs. The resulting system demonstrated enhanced thickening capacity, thermoresistance, salt and shear tolerance, viscoelasticity, sand carrying capacity, and gel breaking performance, compared to the pristine polymer and partially hydrolyzed polyacrylamide (HPAM) [119].
Super-hydrophobicity is a desirable property that finds various applications, such as the production of stain proof and advanced textiles. This property can be achieved through the creation of highly rough surfaces, for instance through a biomimicry approach that take inspiration from the microstructure of the lotus leaf, which floats on muddy waters whilst appearing clean. In the case of branched CNTs, lotus-leaf mimicry can be attained in different ways. In one approach, the CNTs were vertically aligned and branched, so as to create a tree-like structure with extreme non-sticking properties and a water contact angle as high as 165 • [5]. Alternatively, sidewall functionalization of MWCNTs with branched and linear perfluoropolyether (PFPE) was achieved through the generation of reactive radical species from the thermal decomposition of PFPE peroxide precursors. The wettability of the functionalized MWCNTs was significantly reduced, as they acquired super-hydrophobicity [120].
Water purification is another field of potential application for branched CNSs. Purification membranes were obtained through the electrospinning of chitosan fibers and concomitant spraying of carboxylated MWCNTs, and successfully applied for the removal of methylene blue and methyl orange dyes, also with a water flux as high as 3757.36 L/m 2 h, and at a low pressure of 0.2 bar. In this manner, an alternative production method to the common blending process was demonstrated to be useful in wastewater treatment [121].

Conclusions and Future Perspectives
The European Green Deal aims to make Europe climate neutral by 2050, boosting the economy through green technology, creating sustainable industry and transport, and cutting pollution [123]. This means that the commercial success of any of the applications highlighted in this concise review has to be not only scalable but also sustainable. As detailed in this work, both theory and experiments have shown that branched MWCNTs can enhance the mechanical and electrical properties of polymeric materials. One of the advantages of these nanostructures is that the outer layers are branched and so may have degraded properties, but the inner layers are intact and retain desired properties. Further studies to compare the mechanical properties between the different types of junctions and unbranched CNTs are needed. At present, in 2021, SWCNTs have been studied in silico and unsurprisingly revealed a superior mechanical performance relative to branched SWCNTs, with structural damage initiation occurring at non-hexagonal sites, although with various failure modes and strength reduction depending on the exact bonding structure at the junction [124]. In addition to composites' reinforcement, the area of catalysis presents some interesting opportunities. Branched MWCNTs are used, or have proposed applications, as catalyst support materials, both for noble-metal catalysts such as Pt as well as earth abundant catalysts such as Fe and Ni, and even on their own in metal-free electrocatalysis.
The most commonly used fabrication method in this field is some type of CVD, so the produced material would have to have unique properties to be very attractive to a commercial enterprise. Therefore, new production methods that use sustainable, natural resources and are highly efficient are continuously sought after, also to produce branched CNSs for additional advantages, such as the possibility to avoid polymer binders in devices for electrochemical energy storage and conversion, so as to avoid the inclusion of additional components that could increase the resistance and negatively affect the device performance [125]. Understanding the CNT growth mechanisms in detail is key to allowing a leap forward to overcome current critical challenges for their mainstream commercial application [126]. For instance, entirely end-bonded MWCNTs were found to exhibit superconductivity with a transition temperature that was significantly higher than that of ropes of SWCNTs, and such a property is highly sensitive to the CNT junction structure [127]. Furthermore, CNT growth in the CVD chamber is non-linearly dependent with reaction time, and fine adjustment of experimental parameters to maximize the catalyst performance is key to ensure high-quality CNT vertical forests [128,129]. CNT orientation is an important parameter in the determination of the final material physicochemical properties, with CNT-CNT junctions playing a key role [130].
Considering the great research efforts required over the last decades to understand how to control unbranched CNT growth and anisotropic orientation, the translation of such knowledge onto b-CNTs to attain fine control over their production presents further challenges that are currently limiting their large scale use. Availability of commercial suppliers that offer high-grade b-CNTs with defined structures and good batch-to-batch reproducibility is still limited, as is the current market demand that could promote its progress. Clearly, more advances are needed at the fundamental-research level to drive b-CNT development and adoption.
Finally, researchers in this field can take hope from Herbert Krömer (Nobel Prize in Physics 2000) in Krömer's Lemma: "The principal applications of any sufficiently new and innovative technology always have been and will continue to be applications created by that new technology" [131]. For instance, the unique properties of CNS led to a wide array of proposed applications in medicine and the health sector [132][133][134][135], spanning from tissue engineering [35,136] to wearable sensors [137,138], imaging [139,140], diagnostics, and therapy [141], especially leveraging their conductive properties [142]. There are, however, hurdles for their translation into clinical practice [143][144][145], and it can be envisaged that further developments in their covalent attachment into stable and branched nanostructures may allow at least some of these barriers to be overcome, for instance limiting the loss of individual CNSs from the material.