Shape-Persistent Dendrimers

Dendrimers have a diverse and versatile morphology, frequently consisting of core, linking, and peripheral moieties. Dendrimers with flexible linkers, such as PAMAM, cannot retain the persistent shape of molecules, and this has been widely explored and reviewed previously; nevertheless, dendrimers with stiff linkers can preserve the persistent shape of the dendrimers, which has been reported considerably less. This review thus focuses on addressing shape-persistent dendrimers with rigid linking moieties discovered in recent years, i.e., from 2012 to 2023. Shape-persistent dendrimers with an interstitial gap between the dendritic frames in the solid state may or may not let the intramolecular void space be accessible for guest molecules, which largely depends on whether their peripheral groups are flexible or non-flexible. In this paper, eight articles on shape-persistent dendrimers with a flexible alkyl periphery, which may exhibit mesogenic phases upon thermal treatment, and eight articles on shape-persistent dendrimers with a non-flexible periphery, which may allow external ions, gases, or volatile organic compounds to access the interstitial gaps between dendritic frames, are reviewed.


Introduction
Dendrimers are usually composed of a combination of three constructing moieties, i.e., central cores, linking bridges, and peripheral groups, and since the first discovery of dendrimers in the early 1970s [1], their synthesis and the study of their related physical properties have been ongoing. Dendrimers can be prepared in a controllable way, using convergent, divergent, and combined processes, and thus have a predictable morphology, which gives them an advantage over polymers [2]. Other characteristics of dendrimers include their good solubility in organic solvents and the mono-dispersity of their molecular weights, which allow this kind of macromolecule to be easily purified and re-processed after their usage. In particular, dendrimers can have a two-dimensional or three-dimensional orientation, thus inducing the internal void inside the dendritic framework. Therefore, they have been reported to adsorb metal ions or small molecules in solution for use in drug delivery [3][4][5][6][7][8][9] and catalysis [10][11][12][13][14][15][16]. In addition to central cores and peripheral functionalities, these types of dendrimers usually consist of flexible linkers, and in this case, their persistent molecular conformation is not easy to maintain and the intramolecular pores are not accessible to guest molecules in the solid state. This kind of dendritic molecule may have PPI (polypropylimine), PAMAM (polyamidoamine), Si derivatives (carbosilanes, siloxanes, and carbosilazanes), polyether, and polyester networks. Rigid or mesogenic peripheral groups have been found to be attached to the flexible linkers, and corresponding dendrimers have been broadly investigated for applications in the fields of light harvesting and liquid crystals. These dendrimers have already been reviewed extensively [2,[17][18][19][20][21][22], and will not be included in this article.
To keep the void space in the dendritic framework in the solid state accessible to external molecules, as in metal-organic frameworks (MOFs) [23][24][25], covalent-organic As indicated earlier, shape-persistent dendrimers generally possess rigid linkers in the dendritic frame, and thus their solubility in solvents may become an issue during their purification. To avoid such concerns, flexible groups could be attached at their periphery, and to this end, the convergent approach has been generally used as a synthetic strategy. In 2012, Lai and co-workers prepared two shape-persistent dendrimers using piperazine and 1,3,5-triazine as rigid linkers and NR 2 (R = C 8 H 17 ) as flexible peripheral groups, as shown in Figure 1 [36]. These two dendrimers contain a three-fold symmetry at a molecular level and thus self-assemble into liquid crystals upon thermal treatment (Table S1). Based on powder-XRD studies, both dendrimers were observed to have 2D rectangular packing in their mesogenic state ( Figure 2I); their lattice constants a and b were calculated to be 57.10 and 41.52 Å, respectively, for dendrimer 1 and 64.99 and 60.16 Å, respectively, for dendrimer 2. The confirmation of the rectangular columnar LC phase suggests that dendrimers 1 and 2 have a rigid 2D and planar dendritic frame like a disk plate and are thus able to self-assemble upon thermal treatment to form the columnar phase. Based on the schematic representation of the 2D lattices of columnar rectangular stacking ( Figure 2I) [37], it may be difficult to estimate the average diameter of disk-like molecules because they may have an ellipse shape in the mesogenic state. However, it is reasonable to assume that the average diameter of dendrimer 2 should be greater than that of 1 because dendrimer 2 contains more constructing linkers (piperazine and 1,3,5-triazine) than dendrimer 1. that the average diameter of dendrimer 2 should be greater than that of 1 because den drimer 2 contains more constructing linkers (piperazine and 1,3,5-triazine) than den drimer 1.  Dendrimers 3 and 4, as shown in Figure 3, have the same rigid linkers as those o dendrimers 1 and 2 but different flexible groups, i.e., NR2 and OR (R = C8H17, C6H13), a their periphery [38]. Both dendrimers also exhibited mesogenic properties upon therma treatment (Table S1). As observed from powder-XRD investigation, dendrimers 3 and were also observed to have a 2D disk-like frame. However, dendrimer 4 is arranged in hexagonal packing in the mesogenic state, and its lattice constant a was calculated to b 36.0 Å; dendrimer 3 is arranged in rectangular packing with the lattice constants a = 51. Å and b = 20.2 Å. As shown in Figure 2II, the two column discs along axis a in the hexag onal packing in the mesogenic state are close to each other [37]. Therefore, it is reasonabl to estimate, from the packing of disk-like dendrimer 4, that the average diameter of col umn discs is ~36.0 Å.  that the average diameter of dendrimer 2 should be greater than that of 1 because dendrimer 2 contains more constructing linkers (piperazine and 1,3,5-triazine) than dendrimer 1.  Dendrimers 3 and 4, as shown in Figure 3, have the same rigid linkers as those of dendrimers 1 and 2 but different flexible groups, i.e., NR2 and OR (R = C8H17, C6H13), at their periphery [38]. Both dendrimers also exhibited mesogenic properties upon thermal treatment (Table S1). As observed from powder-XRD investigation, dendrimers 3 and 4 were also observed to have a 2D disk-like frame. However, dendrimer 4 is arranged in hexagonal packing in the mesogenic state, and its lattice constant a was calculated to be 36.0 Å; dendrimer 3 is arranged in rectangular packing with the lattice constants a = 51.5 Å and b = 20.2 Å. As shown in Figure 2II, the two column discs along axis a in the hexagonal packing in the mesogenic state are close to each other [37]. Therefore, it is reasonable to estimate, from the packing of disk-like dendrimer 4, that the average diameter of column discs is ~36.0 Å.  Dendrimers 3 and 4, as shown in Figure 3, have the same rigid linkers as those of dendrimers 1 and 2 but different flexible groups, i.e., NR 2 and OR (R = C 8 H 17 , C 6 H 13 ), at their periphery [38]. Both dendrimers also exhibited mesogenic properties upon thermal treatment (Table S1). As observed from powder-XRD investigation, dendrimers 3 and 4 were also observed to have a 2D disk-like frame. However, dendrimer 4 is arranged in hexagonal packing in the mesogenic state, and its lattice constant a was calculated to be 36.0 Å; dendrimer 3 is arranged in rectangular packing with the lattice constants a = 51.5 Å and b = 20.2 Å. As shown in Figure 2II, the two column discs along axis a in the hexagonal packing in the mesogenic state are close to each other [37]. Therefore, it is reasonable to estimate, from the packing of disk-like dendrimer 4, that the average diameter of column discs is~36.0 Å. that the average diameter of dendrimer 2 should be greater than that of 1 because den drimer 2 contains more constructing linkers (piperazine and 1,3,5-triazine) than den drimer 1.  Dendrimers 3 and 4, as shown in Figure 3, have the same rigid linkers as those o dendrimers 1 and 2 but different flexible groups, i.e., NR2 and OR (R = C8H17, C6H13), a their periphery [38]. Both dendrimers also exhibited mesogenic properties upon therma treatment (Table S1). As observed from powder-XRD investigation, dendrimers 3 and were also observed to have a 2D disk-like frame. However, dendrimer 4 is arranged in hexagonal packing in the mesogenic state, and its lattice constant a was calculated to b 36.0 Å; dendrimer 3 is arranged in rectangular packing with the lattice constants a = 51. Å and b = 20.2 Å. As shown in Figure 2II, the two column discs along axis a in the hexag onal packing in the mesogenic state are close to each other [37]. Therefore, it is reasonabl to estimate, from the packing of disk-like dendrimer 4, that the average diameter of col umn discs is ~36.0 Å.  Dendrimers 1-4 all have rigid cores, linkers, and flexible peripheral groups and thus behave as disk-like molecules. It has been observed that dendrimers with flexible cores, rigid linkers, and flexible peripheral groups also behave accordingly. Dendrimers 5-8, as shown in Figure 4, were prepared using a convergent approach, and all exhibit mesogenic phases in the thermal process [39,40] (Table S1). The powder-XRD studies also confirmed that dendrimers 5-8 all have a 2D disk-like frame. Dendrimers 5, 7, and 8 all have hexagonal packing, and their lattice constant a is estimated to be 38.2, 40.8, and 38.6 Å, respectively; dendrimer 6 shows rectangular packing in the mesogenic state with the lattice constants a = 57.1 Å and b = 41.5 Å. Based on a 2D lattice of columnar hexagonal stacking in the mesogenic state, as demonstrated in Figure 2II [37], the average diameter of the column disc for dendrimer 5 is~38.2 Å, which is slightly less than that of dendrimer 8 (38.6 Å), due to the shorter length of the core in 5. However, the length of the core in dendrimer 7 is shorter than that in dendrimers 5 and 8, but the average diameter of column disc 7 is~40.8 Å, which is much greater than that of dendrimers 5 and 8. According to the literature [40], the molecular volume of dendrimer 7 (~10,533 Å 3 ) is similar to that of 8 (~10,688 Å 3 ) because the molecular weight of 7 (6034 Å 3 ) is similar to that of 8 (6062 Å 3 ). However, the cell volume of 7 (~12,979 Å 3 ) is much greater than that of 8 (~11,628 Å 3 ), meaning that the steric congestion of the core in dendrimer 7 can cause the disk-shaped dendrimers to rearrange into a minor order. In other words, the mutual gliding of dendritic molecules within the same columns may arise due to steric congestion of the central core in dendrimer 7 and thus increase the mean diameter of the column disk in the hexagonal packing. Dendrimers 1-4 all have rigid cores, linkers, and flexible peripheral groups and thus behave as disk-like molecules. It has been observed that dendrimers with flexible cores, rigid linkers, and flexible peripheral groups also behave accordingly. Dendrimers 5-8, as shown in Figure 4, were prepared using a convergent approach, and all exhibit mesogenic phases in the thermal process [39,40] (Table S1). The powder-XRD studies also confirmed that dendrimers 5-8 all have a 2D disk-like frame. Dendrimers 5, 7, and 8 all have hexagonal packing, and their lattice constant a is estimated to be 38.2, 40.8, and 38.6 Å, respectively; dendrimer 6 shows rectangular packing in the mesogenic state with the lattice constants a = 57.1 Å and b = 41.5 Å. Based on a 2D lattice of columnar hexagonal stacking in the mesogenic state, as demonstrated in Figure 2II [37], the average diameter of the column disc for dendrimer 5 is ~38.2 Å, which is slightly less than that of dendrimer 8 (38.6 Å), due to the shorter length of the core in 5. However, the length of the core in dendrimer 7 is shorter than that in dendrimers 5 and 8, but the average diameter of column disc 7 is ~40.8 Å, which is much greater than that of dendrimers 5 and 8. According to the literature [40], the molecular volume of dendrimer 7 (~10,533 Å 3 ) is similar to that of 8 (~10,688 Å 3 ) because the molecular weight of 7 (6034 Å 3 ) is similar to that of 8 (6062 Å 3 ). However, the cell volume of 7 (~12,979 Å 3 ) is much greater than that of 8 (~11,628 Å 3 ), meaning that the steric congestion of the core in dendrimer 7 can cause the disk-shaped dendrimers to rearrange into a minor order. In other words, the mutual gliding of dendritic molecules within the same columns may arise due to steric congestion of the central core in dendrimer 7 and thus increase the mean diameter of the column disk in the hexagonal packing. Dendrimers 9 and 10, as demonstrated in Figure 5, were prepared, and their physical properties were then investigated, further confirming that the steric congestion of dendritic cores may affect the average size of the disc column of the dendrimer in the mesogenic state [41]. The related mesogenic ranges are provided in Table S1. The XRD reflection pattern also indicates that dendrimer 9 has a hexagonal columnar phase with a calculated lattice constant of 41.9 Å, which is much longer than that of dendrimer 5 (~38.2 Å). Both dendrimers 5 and 9 have NY-CH2-CH2-CH2-NY as their central linkers (5: Y = H and 9: Y = CH2-C6H5), but the steric congestion in dendrimer 9 is more significant than that in 5. This is related to the two phenylmethyl substituents on the nitrogen atoms, which affect the morphology of dendrimer 9, resulting in the mutual gliding of dendritic molecules within the same columns. Therefore, the cell volume of 9, ~13,686 Å 3 , is much greater than that of 5 (~11,230 Å 3 ), although the molecular volumes of dendrimers 9 and 5 are not much different (~10,981 and 10,662 Å 3 , respectively) because of their similar molecular weights (9: 6202 and 5: 6022). Very interestingly, dendrimer 10, with the central linker NY-CH2-CH2-CH2-NY (Y = CH2-C6H4-CN), also has a similar XRD pattern to 9 in the mesogenic state, and the corresponding lattice constant was calculated to be 38.4 Å, which is similar to that of dendrimer 5 but much less than that of 9. The CH2-C6H4-CN substituent in the core of dendrimer 10 does not seem to significantly enhance the mutual gliding of Dendrimers 9 and 10, as demonstrated in Figure 5, were prepared, and their physical properties were then investigated, further confirming that the steric congestion of dendritic cores may affect the average size of the disc column of the dendrimer in the mesogenic state [41]. The related mesogenic ranges are provided in Table S1. The XRD reflection pattern also indicates that dendrimer 9 has a hexagonal columnar phase with a calculated lattice constant of 41.9 Å, which is much longer than that of dendrimer 5 (~38.2 Å). Both dendrimers 5 and 9 have NY-CH 2 -CH 2 -CH 2 -NY as their central linkers (5: Y = H and 9: Y = CH 2 -C 6 H 5 ), but the steric congestion in dendrimer 9 is more significant than that in 5. This is related to the two phenylmethyl substituents on the nitrogen atoms, which affect the morphology of dendrimer 9, resulting in the mutual gliding of dendritic molecules within the same columns. Therefore, the cell volume of 9,~13,686 Å 3 , is much greater than that of 5 (~11,230 Å 3 ), although the molecular volumes of dendrimers 9 and 5 are not much different (~10,981 and 10,662 Å 3 , respectively) because of their similar molecular weights (9: 6202 and 5: 6022). Very interestingly, dendrimer 10, with the central linker NY-CH 2 -CH 2 -CH 2 -NY (Y = CH 2 -C 6 H 4 -CN), also has a similar XRD pattern to 9 in the mesogenic state, and the corresponding lattice constant was calculated to be 38.4 Å, which is similar to that of dendrimer 5 but much less than that of 9. The CH 2 -C 6 H 4 -CN substituent in the core of dendrimer 10 does not seem to significantly enhance the mutual gliding of dendritic molecules within the same columns, as demonstrated in 9, thus enlarg-ing the average diameter of the column disc. The molecular volume of 10 was estimated to be~11,226 Å 3 based on the powder-XRD data, which is slightly greater than those of 5 (~10,662 Å 3 ) and 9 (~10,981Å 3 ) because the molecular weight of 10 (6252) is slightly greater than that of 5 (6022) and 9 (6202). The cell volume of 10 was calculated to be 11,510 Å 3 , which is, however, close to that of dendrimer 5 (~11,230 Å 3 ) but much less than that of 9 (~13,686 Å 3 ). According to the literature [41], the distance between dendritic frames within the column in 10 is~13.68 Å, which is slightly larger than that of dendrimers 5 and 9, which demonstrate distances of 13.14 and 13.28 Å, respectively. Based on all these results, it may be concluded that the CN dipole in the central core of the dendrimer increases the distance between dendritic frames within the column and this, to some extent, reduces the steric congestion by the CH 2 -C 6 H 4 -CN moiety, thus resulting in negligible mutual gliding between dendritic molecules.
Molecules 2023, 28, x FOR PEER REVIEW 5 of 15 dendritic molecules within the same columns, as demonstrated in 9, thus enlarging the average diameter of the column disc. The molecular volume of 10 was estimated to be ~11,226 Å 3 based on the powder-XRD data, which is slightly greater than those of 5 (~10,662 Å 3 ) and 9 (~10,981Å 3 ) because the molecular weight of 10 (6252) is slightly greater than that of 5 (6022) and 9 (6202). The cell volume of 10 was calculated to be 11,510 Å 3 , which is, however, close to that of dendrimer 5 (~11,230 Å 3 ) but much less than that of 9 (~13,686 Å 3 ). According to the literature [41], the distance between dendritic frames within the column in 10 is ~13.68 Å, which is slightly larger than that of dendrimers 5 and 9, which demonstrate distances of 13.14 and 13.28 Å, respectively. Based on all these results, it may be concluded that the CN dipole in the central core of the dendrimer increases the distance between dendritic frames within the column and this, to some extent, reduces the steric congestion by the CH2-C6H4-CN moiety, thus resulting in negligible mutual gliding between dendritic molecules. Although dendrimers with rigid linkers and flexible peripheral groups can exhibit a persistent shape, the inner void space inside the dendritic framework is rarely reported to be accessible to external gases in the mesogenic or solid state. Very recently, a dendrimer with a triamidobenzene core, as demonstrated in Figure 6, was synthesized, and it was observed that it can adsorb Xe gas in the mesogenic and solid states based on a 129 Xe-NMR spectroscopy study at various temperatures [42]. The related mesogenic ranges are provided in Table S1. Based on the XRD data, dendrimer 11, with 2D packing, shows a rectangular columnar phase with the lattice constants of a = 57.5 Å and b = 41.9 Å. As shown in the literature [42], the dihedral angle of C1-N2-C3-C4 of 11 in the gas phase was calculated to be 25.0 °C, which forces the central core of dendrimer 11 to be non-coplanar, making the inner pore inside the dendritic framework available for guest gases in the mesogenic or solid state. The NMR study revealed that 129 Xe gas can be absorbed into the free void space inside the dendrimer at a temperature range of about −20~80 °C upon heating and at a range of about 105~8-35 °C upon cooling. According to the literature [42], this is the first report demonstrating that a liquid crystalline dendrimer possesses a free void space in the mesogenic and solid states.  Although dendrimers with rigid linkers and flexible peripheral groups can exhibit a persistent shape, the inner void space inside the dendritic framework is rarely reported to be accessible to external gases in the mesogenic or solid state. Very recently, a dendrimer with a triamidobenzene core, as demonstrated in Figure 6, was synthesized, and it was observed that it can adsorb Xe gas in the mesogenic and solid states based on a 129 Xe-NMR spectroscopy study at various temperatures [42]. The related mesogenic ranges are provided in Table S1. Based on the XRD data, dendrimer 11, with 2D packing, shows a rectangular columnar phase with the lattice constants of a = 57.5 Å and b = 41.9 Å. As shown in the literature [42], the dihedral angle of C1-N2-C3-C4 of 11 in the gas phase was calculated to be 25.0 • C, which forces the central core of dendrimer 11 to be non-coplanar, making the inner pore inside the dendritic framework available for guest gases in the mesogenic or solid state. The NMR study revealed that 129 Xe gas can be absorbed into the free void space inside the dendrimer at a temperature range of about −20~80 • C upon heating and at a range of about 105~8-35 • C upon cooling. According to the literature [42], this is the first report demonstrating that a liquid crystalline dendrimer possesses a free void space in the mesogenic and solid states.
Molecules 2023, 28, x FOR PEER REVIEW 5 of 15 dendritic molecules within the same columns, as demonstrated in 9, thus enlarging the average diameter of the column disc. The molecular volume of 10 was estimated to be ~11,226 Å 3 based on the powder-XRD data, which is slightly greater than those of 5 (~10,662 Å 3 ) and 9 (~10,981Å 3 ) because the molecular weight of 10 (6252) is slightly greater than that of 5 (6022) and 9 (6202). The cell volume of 10 was calculated to be 11,510 Å 3 , which is, however, close to that of dendrimer 5 (~11,230 Å 3 ) but much less than that of 9 (~13,686 Å 3 ). According to the literature [41], the distance between dendritic frames within the column in 10 is ~13.68 Å, which is slightly larger than that of dendrimers 5 and 9, which demonstrate distances of 13.14 and 13.28 Å, respectively. Based on all these results, it may be concluded that the CN dipole in the central core of the dendrimer increases the distance between dendritic frames within the column and this, to some extent, reduces the steric congestion by the CH2-C6H4-CN moiety, thus resulting in negligible mutual gliding between dendritic molecules. Although dendrimers with rigid linkers and flexible peripheral groups can exhibit a persistent shape, the inner void space inside the dendritic framework is rarely reported to be accessible to external gases in the mesogenic or solid state. Very recently, a dendrimer with a triamidobenzene core, as demonstrated in Figure 6, was synthesized, and it was observed that it can adsorb Xe gas in the mesogenic and solid states based on a 129 Xe-NMR spectroscopy study at various temperatures [42]. The related mesogenic ranges are provided in Table S1. Based on the XRD data, dendrimer 11, with 2D packing, shows a rectangular columnar phase with the lattice constants of a = 57.5 Å and b = 41.9 Å. As shown in the literature [42], the dihedral angle of C1-N2-C3-C4 of 11 in the gas phase was calculated to be 25.0 °C, which forces the central core of dendrimer 11 to be non-coplanar, making the inner pore inside the dendritic framework available for guest gases in the mesogenic or solid state. The NMR study revealed that 129 Xe gas can be absorbed into the free void space inside the dendrimer at a temperature range of about −20~80 °C upon heating and at a range of about 105~8-35 °C upon cooling. According to the literature [42], this is the first report demonstrating that a liquid crystalline dendrimer possesses a free void space in the mesogenic and solid states.  Using a convergent and click approach, shape-persistent dendrimers 12-14, as shown in Figure 7, were prepared by Malah et al. [43]. These amphiphilic dendrimers with a disc shape assemble in water to produce cylindrical assemblies that undergo a thermosensitive phase transition from a nanorod to columnar phase. The structure of dendrimer arrays in solution was investigated via small-angle X-ray scattering (SAXS), and the length and radius of the nanorods were measured; the radius of 12, 13, and 14 is about 1.41, 1.86, and 2.31 nm, respectively, and the length of 12, 13, and 14 is about 14.7, 16.8, and 57.7 nm, respectively. Since lengths reflect the number of stacked dendrimer discs in cylindrical columns, it could be concluded that the stacked numbers increase with generation number, being 42, 48, and 165 for 12, 13, and 14, respectively. The use of click approaches for preparing shape-persistent dendrimers was also reported in 2010 by Kakkar [44] and in 2014 by Mullen [45], respectively. The work of Kakkar also involved flexible peripheral groups similar to the dendritic structures investigated by Malah, and thus will only be briefly mentioned here. As indicated, the work of Mullen before 2018 has been already reviewed [34,35] and thus will not be described here in detail.
Molecules 2023, 28, x FOR PEER REVIEW 6 of 15 Using a convergent and click approach, shape-persistent dendrimers 12-14, as shown in Figure 7, were prepared by Malah et al. [43]. These amphiphilic dendrimers with a disc shape assemble in water to produce cylindrical assemblies that undergo a thermosensitive phase transition from a nanorod to columnar phase. The structure of dendrimer arrays in solution was investigated via small-angle X-ray scattering (SAXS), and the length and radius of the nanorods were measured; the radius of 12, 13, and 14 is about 1.41, 1.86, and 2.31 nm, respectively, and the length of 12, 13, and 14 is about 14.7, 16.8, and 57.7 nm, respectively. Since lengths reflect the number of stacked dendrimer discs in cylindrical columns, it could be concluded that the stacked numbers increase with generation number, being 42, 48, and 165 for 12, 13, and 14, respectively. The use of click approaches for preparing shape-persistent dendrimers was also reported in 2010 by Kakkar [44] and in 2014 by Mullen [45], respectively. The work of Kakkar also involved flexible peripheral groups similar to the dendritic structures investigated by Malah, and thus will only be briefly mentioned here. As indicated, the work of Mullen before 2018 has been already reviewed [34,35] and thus will not be described here in detail. Malah et al. further prepared dendrimers 15 and 16 with azobenzene as the central core and long-chain ether branches as peripheral groups (Figure 8), which were observed to self-assemble into highly ordered and uniform nanofibers [46]. The aggregated fibers, characterized by TEM and SEM microscopies, were observed to be uniform with an average diameter of 155.6-250.3 nm, likely resulting from π-stacking of the aromatic core units and the interaction between alkyl chains.  Malah et al. further prepared dendrimers 15 and 16 with azobenzene as the central core and long-chain ether branches as peripheral groups (Figure 8), which were observed to self-assemble into highly ordered and uniform nanofibers [46]. The aggregated fibers, characterized by TEM and SEM microscopies, were observed to be uniform with an average diameter of 155.6-250.3 nm, likely resulting from π-stacking of the aromatic core units and the interaction between alkyl chains. Using a convergent and click approach, shape-persistent dendrimers 12-14, as shown in Figure 7, were prepared by Malah et al. [43]. These amphiphilic dendrimers with a disc shape assemble in water to produce cylindrical assemblies that undergo a thermosensitive phase transition from a nanorod to columnar phase. The structure of dendrimer arrays in solution was investigated via small-angle X-ray scattering (SAXS), and the length and radius of the nanorods were measured; the radius of 12, 13, and 14 is about 1.41, 1.86, and 2.31 nm, respectively, and the length of 12, 13, and 14 is about 14.7, 16.8, and 57.7 nm, respectively. Since lengths reflect the number of stacked dendrimer discs in cylindrical columns, it could be concluded that the stacked numbers increase with generation number, being 42, 48, and 165 for 12, 13, and 14, respectively. The use of click approaches for preparing shape-persistent dendrimers was also reported in 2010 by Kakkar [44] and in 2014 by Mullen [45], respectively. The work of Kakkar also involved flexible peripheral groups similar to the dendritic structures investigated by Malah, and thus will only be briefly mentioned here. As indicated, the work of Mullen before 2018 has been already reviewed [34,35] and thus will not be described here in detail. Malah et al. further prepared dendrimers 15 and 16 with azobenzene as the central core and long-chain ether branches as peripheral groups (Figure 8), which were observed to self-assemble into highly ordered and uniform nanofibers [46]. The aggregated fibers, characterized by TEM and SEM microscopies, were observed to be uniform with an average diameter of 155.6-250.3 nm, likely resulting from π-stacking of the aromatic core units and the interaction between alkyl chains.

2D Shape-Persistent Dendrimers with Co-Planar Rigid Linkers and Bulky Peripheral Groups
Instead of using flexible groups, the problem of solubility in organic solvents for shape-persistent dendrimers may be overcome by introducing a bulky functionality at their periphery. Dendrimer 17, which demonstrated good solubility in THF, was successfully prepared and observed to adsorb CO 2 in the solid state. Based on a CO 2 isotherm at 195 K, the BET (Brunauer-Emmett-Teller) and Langmuir surface areas of 17 were estimated to be 154.32 and 292.92 m 2 ·g −1 , respectively ( Figure 9). Interestingly, dendrimer 17 exhibits low adsorption of N 2 gas, and this is the first time that dendrimers have been reported to exhibit superior selective adsorption of CO 2 over N 2 in the literature [47]. Details of a typical process used for determining the free void spaces of samples have been added as Supplementary Materials.

2D Shape-Persistent Dendrimers with Co-Planar Rigid Linkers and Bulky Peripheral Groups
Instead of using flexible groups, the problem of solubility in organic solvents for shape-persistent dendrimers may be overcome by introducing a bulky functionality at their periphery. Dendrimer 17, which demonstrated good solubility in THF, was successfully prepared and observed to adsorb CO2 in the solid state. Based on a CO2 isotherm at 195 K, the BET (Brunauer-Emmett-Teller) and Langmuir surface areas of 17 were estimated to be 154.32 and 292.92 m 2 g −1 , respectively ( Figure 9). Interestingly, dendrimer 17 exhibits low adsorption of N2 gas, and this is the first time that dendrimers have been reported to exhibit superior selective adsorption of CO2 over N2 in the literature [47]. Details of a typical process used for determining the free void spaces of samples have been added as Supplementary Materials. Dendrimers 18-20 were further prepared and investigated for their porous properties ( Figure 10). As shown in the literature [48], the BET surface areas of 18-20 with the piperazine and triazine linkers are similar to each other despite their various molecular weights (ranging from 1791 to 2890) and are in the range of 136-138 m 2 /g based on the CO2 isotherms of dendrimer 18-20 at 195 K. Because of the strong H-bond interaction between the peripheral R groups of 18-20, the triamidobenzene moiety (TAB) may not imbed in the interstitial space of the bulk dendrimers in the solid state, and therefore the BETs of 13-15 are similar to each other and majorly depend on the void spaces constructed by the piperazine and triazine moieties. This assumption was further supported by the BET value of dendrimer 21 (~47 m 2 /g). This is due to the absence of H-bonding interactions between the peripheral groups of dendrimer 21 ( Figure 10). Interestingly, the BETs of 18-20 were observed to be slightly lower than that of a COF (~165 m 2 /g) prepared from the reaction of piperazine with triazine [49], which is reasonable because some of the void space in 18-20 is occupied by the TAB groups inside the dendritic framework. Dendrimers 18-20 were further prepared and investigated for their porous properties ( Figure 10). As shown in the literature [48], the BET surface areas of 18-20 with the piperazine and triazine linkers are similar to each other despite their various molecular weights (ranging from 1791 to 2890) and are in the range of 136-138 m 2 /g based on the CO 2 isotherms of dendrimer 18-20 at 195 K. Because of the strong H-bond interaction between the peripheral R groups of 18-20, the triamidobenzene moiety (TAB) may not imbed in the interstitial space of the bulk dendrimers in the solid state, and therefore the BETs of 13-15 are similar to each other and majorly depend on the void spaces constructed by the piperazine and triazine moieties. This assumption was further supported by the BET value of dendrimer 21 (~47 m 2 /g). This is due to the absence of H-bonding interactions between the peripheral groups of dendrimer 21 ( Figure 10). Interestingly, the BETs of 18-20 were observed to be slightly lower than that of a COF (~165 m 2 /g) prepared from the reaction of piperazine with triazine [49], which is reasonable because some of the void space in 18-20 is occupied by the TAB groups inside the dendritic framework.
Based on the peripheral triamidobenzene moiety (TAB), dendrimers 22 and 23 were further prepared, and their void spaces were then studied ( Figure 11). The BET surface areas of 22 and 23, on the basis of the CO 2 isotherm at 195 K, were calculated to be 191.8 and 212.3 m 2 /g, respectively, which are correspondingly 41 and 56% higher than that of 18 (136.0 m 2 /g) [50]. As shown in the literature [48], the TAB group does not imbed in the dendritic framework in the solid state, so the surface areas of 22 and 23 should be greater due to the longer chain length of their central cores. Dendrimers 22 and 23 were further used for adsorbing pyridines, and it was demonstrated that one molecule of 22 and 23 can adsorb 7 and 24 equivalents of pyridine, respectively. According to the literature, the adsorption capacity of 23 in pyridine is equivalent to 946.2 mg/g, which is the best value reported so far, being over twice the amount (400.8 mg/g) reported in the literature [51]. Based on the peripheral triamidobenzene moiety (TAB), dendrimers 22 and 23 were further prepared, and their void spaces were then studied ( Figure 11). The BET surface areas of 22 and 23, on the basis of the CO2 isotherm at 195 K, were calculated to be 191.8 and 212.3 m 2 /g, respectively, which are correspondingly 41 and 56% higher than that of 18 (136.0 m 2 /g) [50]. As shown in the literature [48], the TAB group does not imbed in the dendritic framework in the solid state, so the surface areas of 22 and 23 should be greater due to the longer chain length of their central cores. Dendrimers 22 and 23 were further used for adsorbing pyridines, and it was demonstrated that one molecule of 22 and 23 can adsorb 7 and 24 equivalents of pyridine, respectively. According to the literature, the adsorption capacity of 23 in pyridine is equivalent to 946.2 mg/g, which is the best value reported so far, being over twice the amount (400.8 mg/g) reported in the literature [51].

2D or 3D Shape-Persistent Dendrimers with Highly Twisted Rigid Linkers
Another approach to increasing the solubility of shape-persistent dendrimers in organic solvents is to introduce highly twisted moieties such as polyphenylenes as rigid linkers. Based on this strategy, a few porous shape-persistent dendrimers have been prepared; among them, several well-known 2D or 3D dendrimers with rigid polyphenylene  Based on the peripheral triamidobenzene moiety (TAB), dendrimers 22 and further prepared, and their void spaces were then studied ( Figure 11). The BET areas of 22 and 23, on the basis of the CO2 isotherm at 195 K, were calculated to and 212.3 m 2 /g, respectively, which are correspondingly 41 and 56% higher tha 18 (136.0 m 2 /g) [50]. As shown in the literature [48], the TAB group does not imbe dendritic framework in the solid state, so the surface areas of 22 and 23 should b due to the longer chain length of their central cores. Dendrimers 22 and 23 were used for adsorbing pyridines, and it was demonstrated that one molecule of 22 an adsorb 7 and 24 equivalents of pyridine, respectively. According to the literature sorption capacity of 23 in pyridine is equivalent to 946.2 mg/g, which is the be reported so far, being over twice the amount (400.8 mg/g) reported in the literatu

2D or 3D Shape-Persistent Dendrimers with Highly Twisted Rigid Linkers
Another approach to increasing the solubility of shape-persistent dendrime ganic solvents is to introduce highly twisted moieties such as polyphenylenes linkers. Based on this strategy, a few porous shape-persistent dendrimers have b pared; among them, several well-known 2D or 3D dendrimers with rigid polyph linkers have been prepared and studied by Mullen and Hammer et a

2D or 3D Shape-Persistent Dendrimers with Highly Twisted Rigid Linkers
Another approach to increasing the solubility of shape-persistent dendrimers in organic solvents is to introduce highly twisted moieties such as polyphenylenes as rigid linkers. Based on this strategy, a few porous shape-persistent dendrimers have been prepared; among them, several well-known 2D or 3D dendrimers with rigid polyphenylene linkers have been prepared and studied by Mullen and Hammer et al. These polyphenylene dendrimers can be used as sensors for volatile organic compounds or nanocarriers for small molecules, which have been extensively reviewed in 2018 [34] and 2016 [35], and therefore, the related works before 2018 will not be further addressed in this article. Instead of sensing and delivering molecules, dendrimers 24-26, which are based on polyphenylene linkers, as shown in Figure 12, have been recently studied regarding their emission variation in response to the stimuli of external light, mechanical force, and volatile organic vapors. Due to the steric effect on the peripheral group, which leads to various kinds of packing in the solid state, the sensitivity of emission variation, therefore, is significantly dependent on the external stimuli [52].
polyphenylene dendrimers can be used as sensors for volatile organic compounds or nanocarriers for small molecules, which have been extensively reviewed in 2018 [34] and 2016 [35], and therefore, the related works before 2018 will not be further addressed in this article. Instead of sensing and delivering molecules, dendrimers 24-26, which are based on polyphenylene linkers, as shown in Figure 12, have been recently studied regarding their emission variation in response to the stimuli of external light, mechanical force, and volatile organic vapors. Due to the steric effect on the peripheral group, which leads to various kinds of packing in the solid state, the sensitivity of emission variation, therefore, is significantly dependent on the external stimuli [52].

3D Molecules with Three-Dimensional Rigid Linkers or Cores
Three-dimensional rigid linkers or central cores can also be incorporated to increase the solubility of shape-persistent dendrimers in organic solvents. A 3D rigid linker of a silane derivative was used to prepare dendrimers 27-29 with porphyrin as a central core ( Figure 13). Because of the introduction of a tetraphenylsilane linker, dendrimers 27-29 can be purified efficiently. However, only a slight bathochromic shift in the Soret and Q bands of the porphyrins was observed in the UV-Vis spectra compared to the non-dendritic porphyrins [53]. The shape-persistent dendrimers containing a 3D central core may be more effective in maintaining void space when compared with those with 3D rigid linkers. This strategy was reported previously by Ma and Pei et al. [54]. In a similar approach, Torneiro et al. prepared dendrimers 30 and 31 using a tetraphenylmethane unit as the dendritic core ( Figure 14) [55]. Such structures with tetraphenylmethane units at their core and nodes are connected by rigid rod-like ethynylene linkers in a convergent synthetic approach. Alternatively, a divergent synthetic route has also been proposed by Torneiro et al. [56]. The first generation of the dendrimer has a star-like shape with a diameter of 3 nm, whereas the second generation shows a branched, porous, and well-defined globular structure with a hydrophobic interior. The second generation of dendrimer has a very

3D Molecules with Three-Dimensional Rigid Linkers or Cores
Three-dimensional rigid linkers or central cores can also be incorporated to increase the solubility of shape-persistent dendrimers in organic solvents. A 3D rigid linker of a silane derivative was used to prepare dendrimers 27-29 with porphyrin as a central core ( Figure 13). Because of the introduction of a tetraphenylsilane linker, dendrimers 27-29 can be purified efficiently. However, only a slight bathochromic shift in the Soret and Q bands of the porphyrins was observed in the UV-Vis spectra compared to the non-dendritic porphyrins [53].
polyphenylene dendrimers can be used as sensors for volatile organic compounds or nanocarriers for small molecules, which have been extensively reviewed in 2018 [34] and 2016 [35], and therefore, the related works before 2018 will not be further addressed in this article. Instead of sensing and delivering molecules, dendrimers 24-26, which are based on polyphenylene linkers, as shown in Figure 12, have been recently studied regarding their emission variation in response to the stimuli of external light, mechanical force, and volatile organic vapors. Due to the steric effect on the peripheral group, which leads to various kinds of packing in the solid state, the sensitivity of emission variation, therefore, is significantly dependent on the external stimuli [52].

3D Molecules with Three-Dimensional Rigid Linkers or Cores
Three-dimensional rigid linkers or central cores can also be incorporated to increase the solubility of shape-persistent dendrimers in organic solvents. A 3D rigid linker of a silane derivative was used to prepare dendrimers 27-29 with porphyrin as a central core ( Figure 13). Because of the introduction of a tetraphenylsilane linker, dendrimers 27-29 can be purified efficiently. However, only a slight bathochromic shift in the Soret and Q bands of the porphyrins was observed in the UV-Vis spectra compared to the non-dendritic porphyrins [53]. The shape-persistent dendrimers containing a 3D central core may be more effective in maintaining void space when compared with those with 3D rigid linkers. This strategy was reported previously by Ma and Pei et al. [54]. In a similar approach, Torneiro et al. prepared dendrimers 30 and 31 using a tetraphenylmethane unit as the dendritic core ( Figure 14) [55]. Such structures with tetraphenylmethane units at their core and nodes are connected by rigid rod-like ethynylene linkers in a convergent synthetic approach. Alternatively, a divergent synthetic route has also been proposed by Torneiro et al. [56]. The first generation of the dendrimer has a star-like shape with a diameter of 3 nm, whereas the second generation shows a branched, porous, and well-defined globular structure with a hydrophobic interior. The second generation of dendrimer has a very The shape-persistent dendrimers containing a 3D central core may be more effective in maintaining void space when compared with those with 3D rigid linkers. This strategy was reported previously by Ma and Pei et al. [54]. In a similar approach, Torneiro et al. prepared dendrimers 30 and 31 using a tetraphenylmethane unit as the dendritic core ( Figure 14) [55]. Such structures with tetraphenylmethane units at their core and nodes are connected by rigid rod-like ethynylene linkers in a convergent synthetic approach. Alternatively, a divergent synthetic route has also been proposed by Torneiro et al. [56]. The first generation of the dendrimer has a star-like shape with a diameter of 3 nm, whereas the second generation shows a branched, porous, and well-defined globular structure with a hydrophobic interior. The second generation of dendrimer has a very narrow dimensional distribution, with a hydrodynamic radius of about 2.3 nm, as measured via dynamic light scattering. Both dendrimers, especially the second generation, showed exceptional fluorescent properties, with a quantum yield at room temperature of 65% and a very narrow emission band. narrow dimensional distribution, with a hydrodynamic radius of about 2.3 nm, as measured via dynamic light scattering. Both dendrimers, especially the second generation, showed exceptional fluorescent properties, with a quantum yield at room temperature of 65% and a very narrow emission band. Dendrimers 32 and 33 with a tetraphenylmethane moiety as a dendritic core were also prepared by Lai et al to study their void space ( Figure 15). The BET surface areas of 32 and 33 based on the CO2 isotherm at 195 K were calculated to be 177.6 and 213.7 m 2 /g, respectively [57]. The void space of 32, as studied by means of CO2 absorption, is slightly less than that of 33, and therefore, one molecule of 32 and 33 can adsorb 1.37 and 1.80 equivalents of toluene, respectively, which is rather consistent with the void space inside their dendritic framework. However, one molecule of 32 and 33 can adsorb 4.07 and 16.07 equivalents of benzonitrile, respectively, which is very surprising. This suggests that when more and more benzonitrile is adsorbed, the frameworks of dendrimers 32 and 33 progressively expand. Thus, the frameworks of 32 and 33 can be regarded as flexible. Because dendrimer 33 contains more TAB moieties at the periphery than dendrimer 32, the framework of 33 provides more H-bond interaction sites for guest molecules than dendrimer 32, allowing more benzonitrile to be adsorbed correspondingly.

Possible Applications
Although 2D or 3D shape-persistent dendrimers may contain void space inside their frameworks because of their rigid linkers, this can often lead these molecules to have low solubility in organic solvents. To solve this problem for easy purification during their preparation or reprocessing after use, 2D rigid dendrimers are usually constructed with flexible alkyl chains at their periphery, thus yielding mesogenic phases upon heat Dendrimers 32 and 33 with a tetraphenylmethane moiety as a dendritic core were also prepared by Lai et al to study their void space ( Figure 15). The BET surface areas of 32 and 33 based on the CO 2 isotherm at 195 K were calculated to be 177.6 and 213.7 m 2 /g, respectively [57]. The void space of 32, as studied by means of CO 2 absorption, is slightly less than that of 33, and therefore, one molecule of 32 and 33 can adsorb 1.37 and 1.80 equivalents of toluene, respectively, which is rather consistent with the void space inside their dendritic framework. However, one molecule of 32 and 33 can adsorb 4.07 and 16.07 equivalents of benzonitrile, respectively, which is very surprising. This suggests that when more and more benzonitrile is adsorbed, the frameworks of dendrimers 32 and 33 progressively expand. Thus, the frameworks of 32 and 33 can be regarded as flexible. Because dendrimer 33 contains more TAB moieties at the periphery than dendrimer 32, the framework of 33 provides more H-bond interaction sites for guest molecules than dendrimer 32, allowing more benzonitrile to be adsorbed correspondingly.
narrow dimensional distribution, with a hydrodynamic radius of about 2.3 nm, as measured via dynamic light scattering. Both dendrimers, especially the second generation, showed exceptional fluorescent properties, with a quantum yield at room temperature of 65% and a very narrow emission band. Dendrimers 32 and 33 with a tetraphenylmethane moiety as a dendritic core were also prepared by Lai et al to study their void space ( Figure 15). The BET surface areas of 32 and 33 based on the CO2 isotherm at 195 K were calculated to be 177.6 and 213.7 m 2 /g, respectively [57]. The void space of 32, as studied by means of CO2 absorption, is slightly less than that of 33, and therefore, one molecule of 32 and 33 can adsorb 1.37 and 1.80 equivalents of toluene, respectively, which is rather consistent with the void space inside their dendritic framework. However, one molecule of 32 and 33 can adsorb 4.07 and 16.07 equivalents of benzonitrile, respectively, which is very surprising. This suggests that when more and more benzonitrile is adsorbed, the frameworks of dendrimers 32 and 33 progressively expand. Thus, the frameworks of 32 and 33 can be regarded as flexible. Because dendrimer 33 contains more TAB moieties at the periphery than dendrimer 32, the framework of 33 provides more H-bond interaction sites for guest molecules than dendrimer 32, allowing more benzonitrile to be adsorbed correspondingly.

Possible Applications
Although 2D or 3D shape-persistent dendrimers may contain void space inside their frameworks because of their rigid linkers, this can often lead these molecules to have low solubility in organic solvents. To solve this problem for easy purification during their preparation or reprocessing after use, 2D rigid dendrimers are usually constructed with flexible alkyl chains at their periphery, thus yielding mesogenic phases upon heat

Possible Applications
Although 2D or 3D shape-persistent dendrimers may contain void space inside their frameworks because of their rigid linkers, this can often lead these molecules to have low solubility in organic solvents. To solve this problem for easy purification during their preparation or reprocessing after use, 2D rigid dendrimers are usually constructed with flexible alkyl chains at their periphery, thus yielding mesogenic phases upon heat treatment, as shown previously. Because their liquid crystalline properties allow shape-persistent dendrimers to possess a good self-assembling ability over a long range, these dendrimers have more uniform stackings in the mesogenic states and possess potential applications for opto-electronic devices [58][59][60][61]. For example, carbon nanotubes or dendritic emitters can be uniformly dispersed in liquid crystalline materials, thus reducing the quenching effect in an organic light-emitting diode device [58,59]. Mesogenic dendrimers with an aromatic core, such as the structures 12-14 as cores and linkers, may show good charge mobility in related devices, such as organic field-effect transistors, because of their proper arrangement, which is characterized by a long-range order [60,61]. In particular, one mesogenic dendrimer with shape-persistent morphology has been recently observed to adsorb Xe in the mesogenic and solid states [42], which may increase the applicability of 2D shape-persistent dendrimers in the area of sensing gases. Due to their good ordering, this kind of dendrimer should show a good gas-detecting ability. Recently, a small amount of graphene was mixed with a 2D shape-persistent dendrimer, and a significant increase in the adsorption of Li ions in the solid state was discovered [62]. Therefore, a convenient application in the optimization of batteries can be anticipated.
In addition, since 2D shape-persistent dendrimers with bulky peripheral groups or highly twisted linkers or 3D shape-persistent dendrimers generally have void spaces that are accessible to external molecules, they can be applied in adsorbing volatile organic compounds (VOCs), as mentioned previously. It is worth noting that the frameworks of shape-persistent dendrimers are flexible because they are generally stabilized by H bonding or strong dipole-dipole interactions. When more molecules (VOCs, such as pyridine and benzonitrile), are adsorbed into the void spaces of the shape-persistent dendrimers, the mutual interaction between H bonding and dipole-dipole interactions changes, thus allowing more VOCs to enter the pore of dendrimers, as shown in the literature [50,57]. Compared with MOFs, COFs, or COPs, shape-persistent dendrimers have the advantages of easy purification and reprocessing after usage due to their good solubility in organic solvents. Additionally, because of their flexible frameworks, their capacities for adsorbing volatile organic compounds are comparable with those of MOFs, as reported in the literature [50,57], although their void spaces under CO 2 are generally smaller than those of MOFs.

Conclusions
Shape-persistent dendrimers are properly categorized into 2D or 3D molecules in this article, and their corresponding physical properties are briefly described. To allow the void space inside the dendritic frameworks in the solid state to be accessible to external gases, metal ions, or volatile organic compounds and maintain good solubility in organic solvents for the purpose of their application in industry, a 3D central core, suitable rigid linkers, or proper peripheral groups should be incorporated at proper stages of their preparation. Therefore, new shape-persistent dendrimers may be synthesized by varying the corresponding cores, linkers, or peripheral functionalities. In our opinion, a convenient method would be to introduce a different rigid linker into the frame of the dendrimer at certain stages, such as using bipiperidine to replace piperazine in the structures. Because bipiperidine contains a longer chain length than piperazine, this may increase the interstitial gap between the dendritic frame, thus, to some extent, improving the solubility of the dendrimer. This strategy may be applied for preparing 2D or 3D shape-persistent dendrimers, as solubility in organic solvents is a major challenge during their preparation. Once the difficulty of preparation due to their solubility is overcome, other physical attributes and potential uses will be investigated in the future. For example, dendrimer 34 not only maintains a larger intramolecular space arising from the incorporation of biperidine in the central core for adsorbing gases but may also exhibit a mesogenic phase upon thermal treatment. Similarly, dendrimer 35 with a biperidine moiety can also be synthesized, and a larger void space in the solid state may be expected for adsorbing volatile organic compounds ( Figure 16). Due to its larger void space, the dendrimer may be used to adsorb environmental contaminants from the aqueous media, which is a new application prospect. to adsorb environmental contaminants from the aqueous media, which is a new application prospect. Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1. Scheme S1: measurement of void space; Table S1: DSC data of dendrimers 1-11. Ref. [47,[63][64][65][66]   Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28145546/s1. Scheme S1: measurement of void space; Table S1: DSC data of dendrimers 1-11. Refs. [47,[63][64][65][66]