One-, Two-, and Three-Dimensional Self-Assembly of Atomically Precise Metal Nanoclusters

Metal nanoclusters (NCs), which consist of several, to about one hundred, metal atoms, have attracted much attention as functional nanomaterials for use in nanotechnology. Because of their fine particle size, metal NCs exhibit physical/chemical properties and functions different from those of the corresponding bulk metal. In recent years, many techniques to precisely synthesize metal NCs have been developed. However, to apply these metal NCs in devices and as next-generation materials, it is necessary to assemble metal NCs to a size that is easy to handle. Recently, multiple techniques have been developed to form one-, two-, and three-dimensional connected structures (CSs) of metal NCs through self-assembly. Further progress of these techniques will promote the development of nanomaterials that take advantage of the characteristics of metal NCs. This review summarizes previous research on the CSs of metal NCs. We hope that this review will allow readers to obtain a general understanding of the formation and functions of CSs and that the obtained knowledge will help to establish clear design guidelines for fabricating new CSs with desired functions in the future.


Metal Nanoclusters for Nanotechnology
Nanotechnology is technology to precisely manufacture small structures. In many countries, nanotechnology is being promoted as a national policy. Progress of nanotechnology allows information and functions to be integrated in smaller spaces, making it possible to manufacture devices with more functions at the same scale. In addition, since nanotechnology makes it possible to integrate the same function in a smaller volume than is the case for current devices, it is expected that devices will be downsized, which will increase their portability. This eliminates the need for the user to be dependent on the device location, which could solve the problems such as crowding and traffic jams and allow users to manage their time more effectively. In addition, the progress of nanotechnology has many advantages, such as saving resources and energy and decreasing waste and environmental damage [1].
Techniques to fabricate small materials can be roughly divided into two categories. One category is top-down methods, in which a desired structure is produced by decreasing the size of a larger substrate ( Figure 1). Nanotechnology has been supported by the development of top-down methods. For example, increased functionality and miniaturization of electronic devices have been realized by the progress of top-down techniques. However, when a fine structure is manufactured by using tools (light, electron beam, scanning probe microscope, etc.), it is difficult to manufacture nanostructures with finer accuracy than that of the tools. Therefore, in recent years, bottom-up methods that assemble nanostructures from atoms and molecules have attracted attention (Figure 1) [1]. Nanomaterials 2020, 10 2 of 47 nanotechnology has many advantages, such as saving resources and energy and decreasing waste and environmental damage [1].

Controlled Assembly of Metal Nanoclusters
As mentioned above, metal NCs show promise as constituent units of functional nanomaterials. Gold (Au) NCs have already been put to practical use in the fields of sensors, catalysts, and paints. On the other hand, at present, electronic devices are manufactured by top-down methods. Therefore, to replace the components of current devices with metal NCs, it is necessary to grow metal NCs to a size that allows their combination with structures manufactured by top-down methods. Moreover, in other applications, the small size of metal NCs often makes them difficult to handle. To realize nanodevices and next-generation materials with the advantageous characteristics of metal NCs, it is essential to establish techniques to assemble metal NCs to a size that makes them easy to handle.
To form a one-dimensional (1D) arrangement of metal NCs, templates [109,110] and host-guest interactions [111] are extremely effective. Two-dimensional (2D) and three-dimensional (3D) arrays of metal NCs can be fabricated by Langmuir-Blodgett [112] and alternate adsorption methods. There are many reports in which metal NCs are arranged in one, two, and three dimensions by using these methods. However, in the structures produced by these methods, the metal NCs are not regularly arranged in a strict sense. Since the conductivity (σ) of metal NCs changes exponentially with the length of the insulating organic ligands [113], the existence of a distribution in the distances between NCs (i.e., the length of the insulating part) is undesirable when applying the assembled metal NCs in electronic devices. Furthermore, although the Langmuir-Blodgett and alternate adsorption methods are suitable for arranging metal NCs in a wide size area, they are not suitable for arranging those in a tiny area.
Metal NCs are regularly arranged in single crystals. Therefore, it is possible to produce precise structures in which metal NCs are regularly connected in one, two, and three dimensions by crystallizing them while including an ingenious means to connect metal NCs. In fact, many crystals in which metal NCs are regularly linked by such a method have been reported in recent years. These structures contain strong bonds, such as Au−Au, Au−silver (Ag), Ag−oxygen (O), Ag−sulfur (S), Ag−chloride (Cl), Ag−nitrogen (N), cesium (Cs)−S, or hydrogen (H) bonds [114], and weak interactions, such as π−π, anion−π, cation···π, aryl CH···Cl, and van der Waals interactions [115] (Figure 2). Similar to supramolecules, molecular assemblies [116], and metal-organic frameworks (MOFs) [117] that are self-assembled from metal ions and organic molecules, connected structures (CSs) of metal NCs can be formed by self-assembly during crystallization, using these bonds and interactions. Such structures, which could also be called "suprametal NC crystals", exhibit physical/chemical properties different from those of an individual metal NC. Thus, the formation of CSs not only increases the size of the structure, but also enables the application of NCs in new fields. Nanomaterials 2020, 10 3 of 47 nanodevices and next-generation materials with the advantageous characteristics of metal NCs, it is essential to establish techniques to assemble metal NCs to a size that makes them easy to handle.

Contents of This Review
In recent years, it has become possible to control not only the geometrical structure of metal NCs, but also 1D, 2D, and 3D CSs of metal NCs. Further development of these techniques will lead to novel nanomaterials possessing the characteristics of metal NCs. Such development may enable a future in Nanomaterials 2020, 10, 1105 4 of 48 which metal NCs are applied in devices. However, since these studies have been initiated in recent years, there have been few review articles focusing on 1D, 2D, and 3D CSs of metal NCs [118,119].
In this review, we summarize the existing research, with the purposes of understanding the current situation regarding these structures and giving perspective regarding clear design for producing new 1D, 2D, and 3D CSs with desired functions.
This review is structured as follows. Section 2 outlines the fabrication of 1D CSs consisting of metal NCs, their geometrical structures, and physical/chemical properties. Then, Sections 3 and 4 present research on 2D and 3D CSs, respectively. After summarizing this review article in Section 5, a brief future outlook is described in Section 6.
It should be noted that 1D, 2D, and 3D CSs of metal NCs can be formed by methods other than crystallization [120,121]; for example, hydrophilic Au NCs have been arranged in 1D and 3D form by the Xie's group, although these NCs have not been crystallized. However, in this review, only the CSs of metal NCs in crystals are summarized, because our focus is on the regularly CSs in a strict sense. In addition, we described the synthesis methods only for the several examples. Thus, we recommend the readers who want to know the detail of synthesis methods for each example to refer to each original paper.

One-Dimensional Structures
The formation of 1D CSs composed of precise metal NCs is important from the viewpoint of the fabrication of controlled nanodevices by bottom-up methods. In this section, we introduce some typical examples of the construction of 1D CSs by the formation of metal−metal bonds (Figure 2A), formation of Ag−O bonds ( Figure 2B), control of counterions ( Figure 2C), and introduction of linker molecules ( Figure 2D). The connection methods, NCs, linkers, year reported, and reference numbers of 1D CSs are summarized in Table 1. Chemical structures of some of the ligands used in these studies are shown in Scheme 1. The chemical structures of organic molecules used as linkers are illustrated in Scheme 2. Nanomaterials 2020, 10 3 of 47 nanodevices and next-generation materials with the advantageous characteristics of metal NCs, it is essential to establish techniques to assemble metal NCs to a size that makes them easy to handle. To form a one-dimensional (1D) arrangement of metal NCs, templates [109,110] and host-guest interactions [111] are extremely effective. Two-dimensional (2D) and three-dimensional (3D) arrays of metal NCs can be fabricated by Langmuir-Blodgett [112] and alternate adsorption methods. There are many reports in which metal NCs are arranged in one, two, and three dimensions by using these methods. However, in the structures produced by these methods, the metal NCs are not regularly arranged in a strict sense. Since the conductivity (σ) of metal NCs changes exponentially with the length of the insulating organic ligands [113], the existence of a distribution in the distances between NCs (i.e., the length of the insulating part) is undesirable when applying the assembled metal NCs in electronic devices. Furthermore, although the Langmuir-Blodgett and alternate adsorption methods are suitable for arranging metal NCs in a wide size area, they are not suitable for arranging those in a tiny area.
In their study, butanethiolate (S-Bu, Scheme 1(1)) was used as the SR ligand. First, [Au 25 (S-Bu) 18 ] − anion was synthesized by reducing the Au(I)-S-Bu complex by using sodium borohydride (NaBH 4 ). Then, [Au 25 (S-Bu) 18 ] − anion was oxidized into neutral [Au 25 (S-Bu) 18 ] 0 in open column packed with silica gel, and single crystals were grown by slow evaporation. Figure 3A(a) shows the geometrical structure of [Au 25 (S-Bu) 18 ] 0 obtained by single-crystal X-ray diffraction (SC-XRD). Each [Au 25 (S-Bu) 18 ] 0 has almost the same framework structure as that of [Au 25 (SR) 18 ] 0 protected by other SR ligands; e.g., phenylethanethiolate (PET, Scheme 1(2)) and ethanethiolate (S-Et, Scheme 1(3)) ( Figure 3A(b)) [27,53]. However, Au−Au bonds formed between adjacent NCs in the [Au 25 (S-Bu) 18 ] 0 crystal, unlike the case for other [Au 25 (SR) 18 ] 0 crystals ( Figure 3A(a),B(a)). This indicates that [Au 25 (S-Bu) 18 ] 0 is a suitable structural unit to form 1D CSs. The Au−Au distance between adjacent NCs of 3.15 Å was within the range of aurophilic interactions (2.9−3.5 Å) and shorter than the non-bonding Au−Au distance (3.80 Å) estimated from the van der Waals radius of Au. This result indicates that a 1D CS was formed in the crystal structure of [Au 25 (S-Bu) 18 ] 0 via Au−Au bonds. To form such a 1D CS, it was considered that the repulsion between the ligands was suppressed and an attractive force between the ligands was induced because the adjacent NCs twisted and approached each other (twist-and-lock mechanism). It was suggested that 1D CSs did not form when S-Et and PET were used ( Figure 3A(b),B(b)) because S-Et has a short alkyl group that leads to a weak attractive force between ligands and PET with a bulky functional group has large steric repulsion between ligands. In 2017, these researchers also succeeded in forming a 1D CS of [Au 25 (S-Pen) 18 ] 0 (S-Pen = pentanethiolate, Scheme 1(4)) [140]. In the same paper, they reported that the distance between NCs was shorter in this 1D CS than in the 1D CS of [Au 25 (S-Bu) 18 ] 0 ( Figure 3C). In addition, in 2019, they formed 1D CSs of [Au 24 Hg(S-Bu) 18 ] 0 (Hg = mercury) and [Au 24 Cd(S-Bu) 18 ] 0 (Cd = cadmium), in which one Au of [Au 25 (S-Bu) 18 ] 0 was replaced with Hg or Cd [141]. Nanomaterials 2020, 10 5 of 47 physical/chemical properties different from those of an individual metal NC. Thus, the formation of CSs not only increases the size of the structure, but also enables the application of NCs in new fields. [Au25(S-Et)18] 0 at −253 °C . The inset shows the same spectra with normalized peak intensity. The black curve corresponds to the EPR cavity signal, which is subtracted in the inset for clarity. All spectra were obtained by using the following parameters: microwave frequency = 9.733 GHz; microwave power = 150 μW; amplitude modulation = 1 G. Reproduced with permission from References [122,140]. Copyright 2014 American Chemical Society and 2017 American Chemical Society.

Contents of This Review
In recent years, it has become possible to control not only the geometrical structure of metal NCs, but also 1D, 2D, and 3D CSs of metal NCs. Further development of these techniques will lead to novel  18 ] 0 at −253 • C. The inset shows the same spectra with normalized peak intensity. The black curve corresponds to the EPR cavity signal, which is subtracted in the inset for clarity. All spectra were obtained by using the following parameters: microwave frequency = 9.733 GHz; microwave power = 150 µW; amplitude modulation = 1 G. Reproduced with permission from References [122,140]. Copyright 2014 American Chemical Society and 2017 American Chemical Society. The same group also revealed that the 1D CSs had electronic structures and physical properties different from those of individual NCs. Since [Au 25 (S-Bu) 18 ] 0 has unpaired electrons, it exhibits paramagnetism in solution. Conversely, the 1D CS of [Au 25 (S-Bu) 18 ] 0 was non-magnetic ( Figure 3D) [122]. This change was mainly ascribed to the formation of the 1D CS, which led to the close proximity of NCs, allowing the unpaired electrons of adjacent NCs to form electron pairs. Because of the formation of such electron pairs, the conduction band of the 1D CS was full and its valence band was empty, so the obtained 1D CS was predicted to have the properties of a semiconductor [122].
In 2020, we [142] conducted a detailed study on the factors responsible for the formation of 1D CSs via Au−Au bonds by using [Au 4 Pt 2 (SR) 8 ] 0 (Pt = platinum) as the NC. A similar NC, [Au 4 Pd 2 (PET) 8 ] 0 (Pd = palladium), was reported by Wu and colleagues in 2017 ( Figure 4) [143]. Although it was not mentioned in their paper, [Au 4 Pd 2 (PET) 8 ] 0 formed a 1D CS in its crystal ( Figure 4). Because this type of metal NC has a smaller metal core than that of [Au 25 (SR) 18 ] 0 described above (Figure 4), the distribution of the ligands in this type of NC should change depending on the ligand structure. Moreover, Au and Pt form a stronger bond than that between Au and Pd [144]. Therefore, it was expected that changing Pd to Pt would increase the stability of the NC [145], thereby expanding the variety of ligand functional group structures that can be used in 1D CSs. For these reasons, we chose [Au 4 Pt 2 (SR) 8 ] 0 as the building block of their 1D CS. The SR ligands shown in Scheme 1(2),(5)-(8) were used. Because the functional group structures of these SR ligands differ greatly, it was expected that there would be different ligand-ligand interactions between the resulting NCs.  Figure 3C). In addition, in 2019, they formed 1D CSs of [Au24Hg(S-Bu)18] 0 (Hg = mercury) and [Au24Cd(S-Bu)18] 0 (Cd = cadmium), in which one Au of [Au25(S-Bu)18] 0 was replaced with Hg or Cd [141]. The same group also revealed that the 1D CSs had electronic structures and physical properties different from those of individual NCs. Since [Au25(S-Bu)18] 0 has unpaired electrons, it exhibits paramagnetism in solution. Conversely, the 1D CS of [Au25(S-Bu)18] 0 was non-magnetic ( Figure 3D) [122]. This change was mainly ascribed to the formation of the 1D CS, which led to the close proximity of NCs, allowing the unpaired electrons of adjacent NCs to form electron pairs. Because of the formation of such electron pairs, the conduction band of the 1D CS was full and its valence band was empty, so the obtained 1D CS was predicted to have the properties of a semiconductor [122]. In 2020, we [142] conducted a detailed study on the factors responsible for the formation of 1D CSs via Au−Au bonds by using [Au4Pt2(SR)8] 0 (Pt = platinum) as the NC. A similar NC, [Au4Pd2(PET)8] 0 (Pd = palladium), was reported by Wu and colleagues in 2017 ( Figure 4) [143]. Although it was not mentioned in their paper, [Au4Pd2(PET)8] 0 formed a 1D CS in its crystal ( Figure  4). Because this type of metal NC has a smaller metal core than that of [Au25(SR)18] 0 described above (Figure 4), the distribution of the ligands in this type of NC should change depending on the ligand structure. Moreover, Au and Pt form a stronger bond than that between Au and Pd [144]. Therefore, it was expected that changing Pd to Pt would increase the stability of the NC [145], thereby expanding the variety of ligand functional group structures that can be used in 1D CSs. For these reasons, we chose [Au4Pt2(SR)8] 0 as the building block of their 1D CS. The SR ligands shown in Scheme 1(2),(5)- (8) were used. Because the functional group structures of these SR ligands differ greatly, it was expected that there would be different ligand-ligand interactions between the resulting NCs.
In  8 ] 0 is a metal NC that can become a structural unit of 1D CSs via Au−Au bond formation ( Figure 5A); (2) although all [Au 4 Pt 2 (SR) 8 ] 0 NCs have similar structures, the intra-cluster ligand interactions vary depending on the ligand structure. As a result, the distribution of the ligands in [Au 4 Pt 2 (SR) 8 ] 0 changes depending on the ligand structure; (3) the differences in the ligand distributions influence the inter-cluster ligand interactions, which in turn affect the formation of 1D CSs and change their structure ( Figure 5B). These results demonstrate that we need to design intra-cluster ligand interactions, to produce 1D CSs with desired configurations. This study also explored the effects of 1D CS formation on the electronic structure of NCs. The results revealed that the formation of the 1D CS caused the band gap of the NCs to decrease ( Figure 5C,D) [142].  [146]. For (AuAg)34(A-Adm)20 alloy NCs, either monomeric NC or 1D CSs were formed depending on the solvent. Monomeric NC could be converted to 1D CSs by dissolving in an appropriate solvent. In the 1D CS, NCs were connected each other via Ag−Au−Ag bond ( Figure 6A,B). They studied the electronic structure of the obtained 1D CS by density functional theory (DFT) calculations, which predicted that the single crystals of 1D CS have a band gap of about 1.3 eV ( Figure 6C). Field-effect transistors (FETs) fabricated with single crystals of 1D CS ( Figure 6D) showed highly anisotropic p-type semiconductor properties with ~1800fold conductivity in the direction of the polymer as compared to cross directions ( Figure 6E), hole mobility of ≈0.02 cm 2 /Vs, and an ON/OFF ratio up to ~4000. They noted that the conductivity (1.49 × 10 -5 S/m) of these crystals in the c-crystallographic axis is one-to-three orders of magnitude higher than the values reported for 1D CS consisting of Au21 clusters, where 1D CS was formed by modulating the weak interactions in the ligand layers (see Section 2.3). It was interpreted that the conductivity and charge carrier mobility was increased by several orders of magnitude in their 1D CS via direct linking of the metal NCs by the -Ag-Au-Ag-chains in the crystal. They described in  20 alloy NCs (A-Adm = 1-ethynyladamantane; Scheme 1(9)) [146]. For (AuAg) 34 (A-Adm) 20 alloy NCs, either monomeric NC or 1D CSs were formed depending on the solvent. Monomeric NC could be converted to 1D CSs by dissolving in an appropriate solvent. In the 1D CS, NCs were connected each other via Ag−Au−Ag bond ( Figure 6A,B). They studied the electronic structure of the obtained 1D CS by density functional theory (DFT) calculations, which predicted that the single crystals of 1D CS have a band gap of about 1.3 eV ( Figure 6C). Field-effect transistors (FETs) fabricated with single crystals of 1D CS ( Figure 6D) showed highly anisotropic p-type semiconductor properties with~1800-fold conductivity in the direction of the polymer as compared to cross directions ( Figure 6E), hole mobility of ≈0.02 cm 2 /Vs, and an ON/OFF ratio up to~4000. They noted that the conductivity (1.49 × 10 -5 S/m) of these crystals in the c-crystallographic axis is one-to-three orders of magnitude higher than the values reported for 1D CS consisting of Au 21 clusters, where 1D CS was formed by modulating the weak interactions in the ligand layers (see Section 2.3). It was interpreted that the conductivity and charge carrier mobility was increased by several orders of magnitude in their 1D CS via direct linking Nanomaterials 2020, 10, 1105 9 of 48 of the metal NCs by the -Ag-Au-Ag-chains in the crystal. They described in this paper that this result holds promise for further design of functional cluster-based materials with highly anisotropic semiconducting properties. Nanomaterials 2020, 10 9 of 47 this paper that this result holds promise for further design of functional cluster-based materials with highly anisotropic semiconducting properties.  Reproduced with permission from Reference [147]. Copyright 2014 Royal Society of Chemistry.

Connection via Ag−O Bonds
When Ag NCs contain acetic acid ions (CH 3  The Ag 20 (CO 3 ) core of the NC was formed by the aggregation of Ag around CO 3 2− ( Figure 7A) as an anion template. In the crystal, the Ag NCs were connected in one dimension via two Ag−O−Ag bonds ( Figure 7B). The obtained 1D CS was stable in both solid and solution states, had a bandgap of 3.22 eV, and exhibited reversible thermochromic emission.
to build the periodic crystal, and the integration over the Brilloin zone was done in a 4 × 4 × 4 Monkhorst-Pack k-point mesh. The band gap is centered around zero. (D,E) Electrical transport properties of the cluster polymer crystals; (D) structure of the polymer crystal FET; (E) I-V plot of the polymer crystal along a-axis and c-axis, respectively, with the range of corresponding conductivity values shown in the inset. Reproduced with permission from Reference [146]. Copyright 2020 Springer-Nature. Reproduced with permission from Reference [147]. Copyright 2014 Royal Society of Chemistry.

Connection via Ag−O Bonds
When Ag NCs contain acetic acid ions (CH3COO − ), trifluoroacetic acid ions (CF3COO − ), or nitrate ions (NO3 − ) in the ligand layer, it is possible to connect Ag NCs by forming Ag−O bonds. Su et al. [147] first reported the formation of such a 1D CS in 2014. In this study, the 1D CS was obtained by crystallization of the product which was obtained by the reaction between AgSt Bu,  Formation of 1D CSs based on a similar principle was also reported by Mak and co-workers in 2017 [148]. In their report, Ag 18 (CO 3 )(S-t Bu) 10 (NO 3 ) 6 (DMF) 4 was linked by the formation of Ag−O bonds ( Figure 8). The Ag 18 (CO 3 ) core contained CO 3 2− as an anion template at the center, like Ag 20 (CO 3 ).

Control of Counterions
For certain metal NCs, the total number of valence electrons satisfies the number for the closed-shell electronic structure when it is a cation, so they are generated as a cation [151]. For example, [Au 21 (S-c-C 6 H 11 ) 12 (DPPM)] + (S-c-C 6 H 11 = cyclohexanethiolate, Scheme 1(13), and DPPM = bis(diphenylphosphinomethane), Scheme 1 (14)) is synthesized as a cation. In 2018, Jin et al. [152] revealed that [Au 21 (S-c-C 6 H 11 ) 12 (DPPM)] + formed a 1D CS in a crystal by assembling as a pair with the counter anion and that the structure of the 1D CS changed depending on the counterion ( Figure 11A,B).
There are not only metal NCs synthesized as cations but also metal NCs synthesized as anions. Because the total number of valence electrons of [Ag 29 (BDT) 12 (PPh 3 ) 4 ] 3− (BDT = 1,3-benzenedithiolate, Scheme 1(15); PPh 3 = triphenylphosphine, Scheme 1(16)) satisfies the number for a closed-shell electronic structure as the anion, it is generated as the anion [153]. In 2019, Zhu et al. [154] reported that mixing this NC with Cs acetate in DMF induced Cs + attachment to the NC and PPh 3 desorption from the NC, resulting in the formation of [Cs 3 Ag 29 (BDT) 12 (DMF) x ] 0 (x = 5 or 6) and that the obtained [Cs 3 Ag 29 (BDT) 12 (DMF) x ] 0 formed a 1D CS in its crystal. Figure 12A shows the resulting 1D CS. In the crystal, [Cs 3 Ag 29 (BDT) 12 (DMF) x ] 0 was connected by a series of bonds consisting of −Cs + −DMF−Cs + −S−Ag−Ag−S−. This 1D CS was considered to be formed because of the electrostatic attraction between [Ag 29 (BDT) 12 (DMF) x ] 3− and Cs + , Cs−S bond formation, and Cs···π interactions ( Figure 12B). Nanomaterials 2020, 10 11 of 47 first report of the formation of a structure in which V10O28 6− was covered with an Ag NC with SR as a ligand. This 1D CS assembled because two Ag−O bonds were formed between two PhSO3 − in the ligand layer and one Ag44(V10O28)(S-Et)20 NC ( Figure 9B). Schematic diagram of electron hopping in Au21 NC assemblies. Different configurations of the interacting π-π pairs result in tunneling barriers of different heights (white solid squares), thus changing the electron conductivity (e − represents an electron, σ is the conductivity, d is the interparticle distance, and β is the tunneling decay constant). Reproduced with permission from Reference [152]. Copyright 2018 Springer-Nature.

Control of Counterions
For certain metal NCs, the total number of valence electrons satisfies the number for the closedshell electronic structure when it is a cation, so they are generated as a cation [151]. For example, [Au21(S-c-C6H11)12(DPPM)] + (S-c-C6H11 = cyclohexanethiolate, Scheme 1(13), and DPPM = bis(diphenylphosphinomethane), Scheme 1 (14)) is synthesized as a cation. In 2018, Jin et al. [152] revealed that [Au21(S-c-C6H11)12(DPPM)] + formed a 1D CS in a crystal by assembling as a pair with the counter anion and that the structure of the 1D CS changed depending on the counterion ( Figure  11A Figure 12C). This indicates that Cs + attachment and PPh 3 desorption did not markedly change the electronic structure of the Ag 29 (BDT) 12 NCs. In contrast, the absorption and PL spectra of [Ag 29 (BDT) 12

Introduction of Linker Molecules
In the examples described in Section 2.3, 1D CSs were formed by the counterion acting as a linker. When an organic molecule is used as the linker, the distance between NCs in a 1D CS can be freely controlled because the design of the structure of organic molecules is well understood. In fact, the geometry of an MOF is controlled by the design of the linker organic molecule [155]. In recent years, several 1D CSs of metal NCs with organic molecules as linkers have also been reported.  20 -2020 [146] Formation of Ag−O, Ag−S, Ag−Cl bond, etc.
For example, in 2018, Zang et al. [156] reported a 1D CS in which Ag 14 (DT-o-C) 6 NCs (DT-o-C = 1,2-dithiolate-o-carborane, Scheme 1(17)) were linked by pyrazine (Scheme 2(1)). In this study, first, [Ag 14 (DT-o-C) 6 (pyridine/p-methylpyridine) 8 ] (Scheme 2(2),(3)) were identified as Ag NCs with high thermal stability that maintained their framework structure even at 150 • C or higher in air ( Figure 13A). Then, they attempted to synthesize Ag NCs in which the pyridine or p-methylpyridine ligands of these Ag NCs were replaced by pyrazine. As a result, they obtained a 1D CS in which Ag 14 (DT-o-C) 6 NCs were linked by pyrazine ( Figure 13B). In the obtained structure, pyrazine was coordinated to each Ag 14 (DT-o-C) 6 NC at a diagonal position, which caused the 1D CS to rotate in the clockwise direction with respect to the (001) axis. In this study, the researchers also succeeded in forming 2D and 3D CSs composed of Ag 14 (DT-o-C) 6 NCs by changing the structure of the bipyridine ligand, as described later in Sections 3.2 and 4.3, respectively.  Figure 11D).
There are not only metal NCs synthesized as cations but also metal NCs synthesized as anions. Because the total number of valence electrons of [Ag29(BDT)12(PPh3)4] 3− (BDT = 1,3-benzenedithiolate, Scheme 1(15); PPh3 = triphenylphosphine, Scheme 1(16)) satisfies the number for a closed-shell electronic structure as the anion, it is generated as the anion [153]. In 2019, Zhu et al. [154] reported that mixing this NC with Cs acetate in DMF induced Cs + attachment to the NC and PPh3 desorption from the NC, resulting in the formation of [Cs3Ag29(BDT)12(DMF)x] 0 (x = 5 or 6) and that the obtained [Cs3Ag29(BDT)12(DMF)x] 0 formed a 1D CS in its crystal. Figure   NC. Ag = green and pink, S = yellow, C = gray, N = blue, carborane = turquoise. Reproduced with permission from Reference [156]. Copyright 2018 American Chemical Society.

Introduction of Linker Molecules
In the examples described in Section 2.3, 1D CSs were formed by the counterion acting as a linker. When an organic molecule is used as the linker, the distance between NCs in a 1D CS can be freely controlled because the design of the structure of organic molecules is well understood. In fact, the geometry of an MOF is controlled by the design of the linker organic molecule [155]. In recent years, several 1D CSs of metal NCs with organic molecules as linkers have also been reported.  6 NC. Ag = green and pink, S = yellow, C = gray, N = blue, carborane = turquoise. Reproduced with permission from Reference [156]. Copyright 2018 American Chemical Society.
Because N readily coordinates to Ag, bipyridine is often used to connect NCs containing Ag. In 2019, Zang and colleagues formed a 1D CS composed of Ag 18 (PhPO 3 )(S-t Bu) 10 (CF 3 COO) 2 (PhPO 3 H) 4 (PhPO 3 2− = phenylphosphinic diion; PhPO 3 H − = phenylphosphinic acid ion) NC nodes with bipyridine(3-amino-4,4 -bipyridine (bpy-NH 2 , Scheme 2(4)) linkers [157]. In this experiment, NC synthesis, ligation, and crystallization were performed simultaneously in one pot ( Figure 14A). The node Ag 18 (PhPO 3 )(S-t Bu) 10 NCs contained PhPO 3 2− as an anion template in their center. In the crystal, adjacent Ag 18 (PhPO 3 )(S-t Bu) 10 NCs were linked by two bpy-NH 2 to form a 1D CS ( Figure 14B).  (17)) were linked by pyrazine (Scheme 2(1)). In this study, first, [Ag14(DT-o-C)6(pyridine/p-methylpyridine)8] (Scheme 2(2),(3)) were identified as Ag NCs with high thermal stability that maintained their framework structure even at 150 °C or higher in air ( Figure  13A). Then, they attempted to synthesize Ag NCs in which the pyridine or p-methylpyridine ligands of these Ag NCs were replaced by pyrazine. As a result, they obtained a 1D CS in which Ag14(DT-o-C)6 NCs were linked by pyrazine ( Figure 13B). In the obtained structure, pyrazine was coordinated to each Ag14(DT-o-C)6 NC at a diagonal position, which caused the 1D CS to rotate in the clockwise direction with respect to the (001) axis. In this study, the researchers also succeeded in forming 2D and 3D CSs composed of Ag14(DT-o-C)6 NCs by changing the structure of the bipyridine ligand, as The obtained 1D CS was stable up to 110 • C in a nitrogen (N 2 ) atmosphere. When mechanical stimulation was applied to the 1D CS, its PL wavelength changed. When the 1D CS sample subjected to mechanical stimulation was recrystallized, its PL wavelength returned to the original value ( Figure 14C). Thus, the PL of the 1D CS composed of Ag 18 (PhPO 3 )(S-t Bu) 10 NCs exhibited reversible mechanochromism. Because this 1D CS emitted light at two wavelengths and its PL intensity ratio changed with temperature (thermochromism; Figure 14D), the authors suggested that this 1D CS could be applied as a thermometer.
The obtained 1D CS was stable up to 110 °C in a nitrogen (N2) atmosphere. When mechanical stimulation was applied to the 1D CS, its PL wavelength changed. When the 1D CS sample subjected to mechanical stimulation was recrystallized, its PL wavelength returned to the original value ( Figure  14C). Thus, the PL of the 1D CS composed of Ag18(PhPO3)(St Bu)10 NCs exhibited reversible mechanochromism. Because this 1D CS emitted light at two wavelengths and its PL intensity ratio changed with temperature (thermochromism; Figure 14D), the authors suggested that this 1D CS could be applied as a thermometer.
The SC-XRD analysis of the products revealed that Ag10(CF3COO)4(S-Bu)6(CH3CN)2 and Ag10(CF3COO)4(St Bu)6(CH3CN) were the nodes in the 1D CSs with p-iah and o-iah, respectively ( Figure 16A(a),B(a)). These 1D CSs containing p-iah and o-iah had cross-helical and parallel chain structures, respectively ( Figure 16A(b),B(b)). The latter structure also contained hydrogen bonds (N−H···O) between the parallel linker molecules. It is interesting that different 1D CSs formed depending on the position of N in the linker molecule (Scheme 2(6),(7)). Both 1D CSs showed PL and that with o-iah as the linker exhibited weak green PL in highly polar solvents and strong yellow PL in solvents with low polarity. Based on these characteristics, the authors suggested that the 1D CS with o-iah could be used to measure the concentration of dichloromethane (CH2Cl2, Figure 16C) or trichloromethane (CHCl3) in tetrachloromethane (CCl4). Both 1D CSs showed PL and that with o-iah as the linker exhibited weak green PL in highly polar solvents and strong yellow PL in solvents with low polarity. Based on these characteristics, the authors suggested that the 1D CS with o-iah could be used to measure the concentration of dichloromethane (CH 2 Cl 2 , Figure 16C) or trichloromethane (CHCl 3 ) in tetrachloromethane (CCl 4 ).
Xu and co-workers reported the formation of a zigzag-type of 1D CS with Cd6Ag4(S-Ph)16(DMF)(H2O) (S-Ph = benzenethiolate, Scheme 1(18) and Figure 17A) as a node and trans-1,2-bis(4-pyridyl)ethylene (bpe, Scheme 2(8)) as a linker ( Figure 17B) [160]. This 1D CS was obtained by the reaction of Cd6Ag4(S-Ph)16(DMF)3(CH3OH) (CH3OH = methanol) with bpe. In the obtained 1D CS, N of bpe coordinated to Cd not Ag ( Figure 17A). Such a coordination pattern has also been observed in 2D and 3D CSs composed of Cd6Ag4(S-Ph)16 and bpe previously reported by Zhang et al. [161,162].  Figure 17C). In the 1D CS, the optical absorption onset was redshifted to the visible region. They used the 1D CS as a visible light (>420 nm)-responsive photocatalyst to decompose the organic dye Rhodamine B in water. The 1D CS exhibited higher photocatalytic activity toward Rhodamine B degradation than that of the Cd6Ag4(S-Ph)16 NCs ( Figure 17D) and high stability during the photocatalytic reaction.

Two-Dimensional Structures
To date, Ag NCs have been used as the building blocks in almost all 2D CSs. Like Au NCs, Ag NCs have unique electronic and optical properties [68,[163][164][165][166] and are expected to be applied in various fields. However, Ag NCs are less stable than Au NCs against external stimuli, such as light and solvents. Therefore, studies have been actively conducted to improve the stability of Ag NCs by assembly of CSs and thereby improve their physical properties. In Sections 3.1 and 3.2, we focus on the connection of NCs by Ag−O bond formation ( Figure 2B) and introducing linker molecules ( Figure  2D), respectively. Table 2 summarizes the connection methods, NCs, linkers, reported years, and They compared the electronic structures of the resulting 1D CS and individual Cd 6 Ag 4 (S-Ph) 16 (DMF) 3 (CH 3 OH) NCs. The results revealed that the band gap of the NCs was narrowed by the formation of the 1D CS ( Figure 17C). In the 1D CS, the optical absorption onset was redshifted to the visible region. They used the 1D CS as a visible light (>420 nm)-responsive photocatalyst to decompose the organic dye Rhodamine B in water. The 1D CS exhibited higher photocatalytic activity toward Rhodamine B degradation than that of the Cd 6 Ag 4 (S-Ph) 16 NCs ( Figure 17D) and high stability during the photocatalytic reaction.

Two-Dimensional Structures
To date, Ag NCs have been used as the building blocks in almost all 2D CSs. Like Au NCs, Ag NCs have unique electronic and optical properties [68,[163][164][165][166] and are expected to be applied in various fields. However, Ag NCs are less stable than Au NCs against external stimuli, such as light and solvents. Therefore, studies have been actively conducted to improve the stability of Ag NCs by assembly of CSs and thereby improve their physical properties. In Sections 3.1 and 3.2 we focus on the connection of NCs by Ag−O bond formation ( Figure 2B) and introducing linker molecules ( Figure 2D), respectively. Table 2 summarizes the connection methods, NCs, linkers, reported years, and reference numbers of the relevant literature. Several of the ligands used in these studies are shown in Scheme 1. The organic molecules used as linkers are depicted in Scheme 2.
The structures of the SR in these two types of Ag 20 (CO 3 )(SR) 10 NCs were different (S-iPr vs. S-c-C 6 H 11 ), which influenced the formation angle and bond distance between adjacent NCs in the 2D CSs.
The O − of CF 3   In 2019, Sun and co-workers also reported the formation of a 2D CS, using Ag NCs [149]. In this study, a 2D CS consisting of Ag 46 (V 10 O 28 )(S-Et) 23 (19)), in which adjacent NCs are linked by Ag−O bonds. SR, alkyne, or phosphine ligands are generally used in metal NCs. In this study, their aim was to synthesize Ag NCs by using an N-donor ligand, which is not appropriate based on the hard/soft acid/base theory [167], and form corresponding CSs. The three kinds of 2D CSs obtained had similar frameworks regardless of the coordination ions (CF 3 COO − , NO 3 − , or CF 3 SO 3 − ), which means that the framework structure shown in Figure 20B is very rigid. It was found that Ag 11 Cl(N-L) 8 (CF 3 COO) 2 ·2CHCl 3 showed dual-emission behavior and that its PL peaks had different optimal excitation wavelengths.
Nanomaterials 2020, 10 20 of 47 [167], and form corresponding CSs. The three kinds of 2D CSs obtained had similar frameworks regardless of the coordination ions (CF3COO − , NO3 − , or CF3SO3 − ), which means that the framework structure shown in Figure 20B is very rigid. It was found that Ag11Cl(N-L)8(CF3COO)2·2CHCl3 showed dual-emission behavior and that its PL peaks had different optimal excitation wavelengths.

Introduction of Linker Molecules
As described below, in Section 4.3, in 2017, Zang et al. [168] reported the formation of a 3D CS in which Ag 12 (S-t Bu) 8 (CF 3 COO) 4 NCs were linked by bpy. This was a pioneering study on the formation of an MOF, using Ag NCs as nodes, and has greatly influenced subsequent studies. In 2018, they synthesized a 2D CS consisting of Ag 12 NCs and bpy [169]. The core structure of the node was changed (isomerized) by dissolving an Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NC MOF crystal in a mixed solvent consisting of N,N-dimethylethanamide (DMAC) and toluene, which changed the geometrical structure of the entire CS from 3D to 2D ( Figure 21A,B). This result indicates that the solvent selection is important in the design of the structure of metal NCs and their CSs. In the 2D CS consisting of newly formed Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NCs, each Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NC was linked to six adjacent Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NCs via linkers to produce a highly symmetric 2D CS ( Figure 21C). The layers were separated by 7.23 Å, with weak interactions between them. It was also revealed that the reversible structural transformation between 3D and 2D CSs could be induced by appropriate solvent selection ( Figure 21A,B).   Structural deformation of the CSs also induced changes in their electronic structure and PL properties. For example, the 3D CS only showed PL at a single wavelength, regardless of temperature and excitation wavelength, whereas the 2D CS exhibited PL of two colors (blue and red), depending on the excitation wavelength ( Figure 21D). To enhance the blue emission of the 2D CS, the researchers introduced bpy-NH 2 , which itself emits blue light, as a linker, to fabricate a 2D CS containing two types of linkers, bpy and bpy-NH 2 . The intensity ratio of the red and blue PL signals depended on the mixing ratio of linker molecules. At the optimum linker mixing ratio, the PL intensity ratio of the red and blue peaks depended on temperature. Therefore, this 2D CS containing two types of linkers could be used as a temperature sensor ( Figure 21E).

Introduction of Linker Molecules
In 2018, the same group also reported the formation of a 2D CS consisting of Ag 14 (DT-o-C) 6 NCs [156]. The 2D CS with Ag 14 (DT-o-C) 6 , as a structural unit ( Figure 22A), was fabricated by changing the linker structure from that used to form the 1D CS (Section 2.4 and Figure 13) to dipyridin-4-yl-diazene (Scheme 2(9)). The obtained 2D CS possessed a rhombic network structure with Ag 14 (DT-o-C) 6 (CH 3 CN) 4 as nodes ( Figure 22B).   6 dipyridin-4-yl-diazene a 2018 [156] Ag 12 (S-t Bu) 6 (CF 3 COO) 6 TPPA a 2018 [170] Ag 12 (S-t Bu) 6 (CF 3 COO) 3 TPyP   In 2018, Zang et al. [170] reported the formation of a 2D CS consisting of Ag 12 (S-t Bu) 6 (CF 3 COO) 6 and tris(4-pyridylphenyl)-amine (TPPA; Scheme 2(10) and Figure 23A). This structure is interesting because the distance between the 2D layers can be changed. In this 2D CS, DMAC used as a solvent existed between layers immediately after the synthesis and the 2D layers overlapped, as shown in Figure 23B(a),(d). When the DMAC was partially removed from this structure, the overlap of the 2D layers changed, as illustrated in Figure 23B(b),(e). Furthermore, when this structure was immersed again in the mother liquor, the structure changed to that depicted in Figure 23B(c),(f). It was also found that the size of the crystal and its emission characteristics changed in accordance with the overlap manner in the 2D CS.
Recently, this group also formed a 2D CS with Ag 12 (S t Bu) 6 (CF 3 COO) 3 NCs as nodes by using 5,10,15,20-tetra(4-pyridyl)porphyrin (TPyP, Scheme 2(11)) as a linker ( Figure 24A) [171]. TPyP has a photosensitizing effect. Therefore, the ability of the 2D CS to degrade the toxic substance 2-chloroethyl ethyl sulfide (CEES), also called mustard gas, was studied ( Figure 24B). The obtained 2D CS showed higher photocatalytic activity than that of a reported MOF. This high photocatalytic activity was ascribed to the synergistic effect of Ag NCs and TPyP, promoting the production of singlet oxygen, which induced the degradation of CEES ( Figure 24B). The 2D CS maintained its crystallinity after the photocatalytic reaction and was able to be used repeatedly. The authors pointed out that photocatalytic activity could be further increased by selecting appropriate Ag NCs and organic molecular linkers.
Two other types of 2D CSs were also reported in 2019. In their paper on 1D CS formation ( Figure 15 and Section 2.4), Bakr et al. [158] also reported that a 2D CS with Ag 14 Cl(S-t Bu) 8 (CF 3 COO) 5 (DMF) as nodes was formed by changing the concentration of bpy during synthesis ( Figure 25A). This Ag 14 Cl core contained Cl − at its center as an anion template. Compared with the Ag 15 Cl(S-t Bu) 8 (CF 3 COO) 5.67 (NO 3 ) 0.33 (DMF) 2 node of the 1D CS, the node of the 2D CS (Ag 14 Cl(S-t Bu) 8 (CF 3 COO) 5 (DMF)) had one less Ag atom. However, the frameworks of these NCs were similar to each other ( Figure 25B). The 2D CS showed higher thermal stability than those of individual Ag NCs and the 1D CS ( Figure 15D). Unlike individual Ag NCs and the 1D CS, the 2D CS emitted green light with a strong intensity, even at room temperature ( Figure 25C). Based on the results of a DFT calculation, it was interpreted that the enhancement of PL intensity was caused by a linker-to-cluster charge transfer excitation. In addition, Gao et al. [159] recently formed a 2D CS ( Figure 26) with Ag 10 (CF 3 COO) 4 (S-t Bu) 6 (CH 3 CN) 4 nodes, using 3-pyridine carboxylic hydrazide (m-iah, Scheme 2(12)) as a linker, which is the meta equivalent of p-iah and o-iah used to form 1D CSs ( Figure 16).
Thus, 2D CS formation by using a linker leads to the assembly of a structure with high stability and quantum yield (QY). However, 2D CS formation decreases the solubility of NCs, which limits their processability and device applicability. Therefore, Zang et al. [172] recently established a method to polymerize 2D CS to overcome this problem and provide materials suitable for practical use ( Figure 27A). In this study, Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NCs reported in their previous work ( Figure 21) [168] were used as nodes. Moreover, 1,4-bis (pyrid-4-yl)benzenamine (bpz-NH 2 , Scheme 2(13)) was used as the linker. The amino group of the bpz-NH 2 linker played an important role in polymerization. First, 2D CS crystals consisting of Ag 12 (S-t Bu) 6 (CF 3 COO) 6 and bpz-NH 2 were fabricated ( Figure 27B). The crystal size was limited to about 200-300 nm by quenching the reaction within 1 min. A 2D CS film was obtained by reacting the crystals with methacrylic anhydride (MA). MA bound to the amino group of bpz-NH 2 ( Figure 27C) and was then polymerized with acrylate monomers butyl methacrylate (BMA) and triethylene glycol dimethacrylate (TEGDMA), as shown in Figure 27D.   As described below, in Section 4.3, in 2017, Zang et al. [168] reported the formation of a 3D CS in which Ag12(St Bu)8(CF3COO)4 NCs were linked by bpy. This was a pioneering study on the formation of an MOF, using Ag NCs as nodes, and has greatly influenced subsequent studies. In 2018, they synthesized a 2D CS consisting of Ag12 NCs and bpy [169]. The core structure of the node was changed (isomerized) by dissolving an Ag12(St Bu)6(CF3COO)6 NC MOF crystal in a mixed solvent   . Reproduced with permission from Reference [171]. Copyright 2019 American Chemical Society.
As described below, in Section 4.3, in 2017, Zang et al. [168] reported the formation of a 3D CS in which Ag12(St Bu)8(CF3COO)4 NCs were linked by bpy. This was a pioneering study on the formation of an MOF, using Ag NCs as nodes, and has greatly influenced subsequent studies. In 2018, they synthesized a 2D CS consisting of Ag12 NCs and bpy [169]. The core structure of the node was newly formed Ag12(St Bu)6(CF3COO)6 NCs, each Ag12(St Bu)6(CF3COO)6 NC was linked to six adjacent Ag12(St Bu)6(CF3COO)6 NCs via linkers to produce a highly symmetric 2D CS ( Figure 21C). The layers were separated by 7.23 Å , with weak interactions between them. It was also revealed that the reversible structural transformation between 3D and 2D CSs could be induced by appropriate solvent selection ( Figure 21A,B). Structural deformation of the CSs also induced changes in their electronic structure and PL properties. For example, the 3D CS only showed PL at a single wavelength, regardless of temperature and excitation wavelength, whereas the 2D CS exhibited PL of two colors (blue and red), depending on the excitation wavelength ( Figure 21D). To enhance the blue emission of the 2D CS, the researchers introduced bpy-NH2, which itself emits blue light, as a linker, to fabricate a 2D CS containing two types of linkers, bpy and bpy-NH2. The intensity ratio of the red and blue PL signals depended on the mixing ratio of linker molecules. At the optimum linker mixing ratio, the PL intensity ratio of the red and blue peaks depended on temperature. Therefore, this 2D CS containing two types of linkers could be used as a temperature sensor ( Figure 21E).
In 2018, the same group also reported the formation of a 2D CS consisting of Ag14(DT-o-C)6 NCs [156]. The 2D CS with Ag14(DT-o-C)6, as a structural unit ( Figure 22A), was fabricated by changing the linker structure from that used to form the 1D CS (Section 2.4 and Figure 13) to dipyridin-4-yl- Nanomaterials 2020, 10 23 of 47 diazene (Scheme 2(9)). The obtained 2D CS possessed a rhombic network structure with Ag14(DT-o-C)6(CH3CN)4 as nodes ( Figure 22B). In 2018, Zang et al. [170] reported the formation of a 2D CS consisting of Ag12(St Bu)6(CF3COO)6 and tris(4-pyridylphenyl)-amine (TPPA; Scheme 2(10) and Figure 23A). This structure is interesting because the distance between the 2D layers can be changed. In this 2D CS, DMAC used as a solvent existed between layers immediately after the synthesis and the 2D layers overlapped, as shown in Figure 23B(a),(d). When the DMAC was partially removed from this structure, the overlap of the 2D layers changed, as illustrated in Figure 23B(b),(e). Furthermore, when this structure was immersed again in the mother liquor, the structure changed to that depicted in Figure 23B(c),(f). It was also found that the size of the crystal and its emission characteristics changed in accordance with the overlap manner in the 2D CS.
Recently, this group also formed a 2D CS with Ag12(S t Bu)6(CF3COO)3 NCs as nodes by using 5,10,15,20-tetra(4-pyridyl)porphyrin (TPyP, Scheme 2(11)) as a linker ( Figure 24A) [171]. TPyP has a photosensitizing effect. Therefore, the ability of the 2D CS to degrade the toxic substance 2chloroethyl ethyl sulfide (CEES), also called mustard gas, was studied ( Figure 24B). The obtained 2D CS showed higher photocatalytic activity than that of a reported MOF. This high photocatalytic activity was ascribed to the synergistic effect of Ag NCs and TPyP, promoting the production of singlet oxygen, which induced the degradation of CEES ( Figure 24B). The 2D CS maintained its crystallinity after the photocatalytic reaction and was able to be used repeatedly. The authors pointed out that photocatalytic activity could be further increased by selecting appropriate Ag NCs and organic molecular linkers. Two other types of 2D CSs were also reported in 2019. In their paper on 1D CS formation ( Figure  15 and Section 2.4), Bakr et al. [158] also reported that a 2D CS with Ag14Cl(St Bu)8(CF3COO)5(DMF) as nodes was formed by changing the concentration of bpy during synthesis ( Figure 25A). This Ag14Cl core contained Cl − at its center as an anion template. Compared with the Ag15Cl(St Bu)8(CF3COO)5.67(NO3)0.33(DMF)2 node of the 1D CS, the node of the 2D CS (Ag14Cl(S- Thus, 2D CS formation by using a linker leads to the assembly of a structure with high stability and quantum yield (QY). However, 2D CS formation decreases the solubility of NCs, which limits their processability and device applicability. Therefore, Zang et al. [172] recently established a method to polymerize 2D CS to overcome this problem and provide materials suitable for practical use ( Figure 27A). In this study, Ag12(St Bu)6(CF3COO)6 NCs reported in their previous work ( Figure  21) [168] were used as nodes. Moreover, 1,4-bis (pyrid-4-yl)benzenamine (bpz-NH2, Scheme 2(13)) was used as the linker. The amino group of the bpz-NH2 linker played an important role in polymerization. First, 2D CS crystals consisting of Ag12(St Bu)6(CF3COO)6 and bpz-NH2 were fabricated ( Figure 27B). The crystal size was limited to about 200-300 nm by quenching the reaction within 1 min. A 2D CS film was obtained by reacting the crystals with methacrylic anhydride (MA). MA bound to the amino group of bpz-NH2 ( Figure 27C) and was then polymerized with acrylate The resulting membrane exhibited PL with a QY of 14.8%, which was higher than that of the unpolymerized 2D CS crystals ( Figure 28A(a)). The increased PL intensity was ascribed to the polymerization strengthening the structure of the 2D CS, which suppressed molecular vibrations and thus nonradiative decay. The membrane was stable in water regardless of pH ( Figure 28A(b)). The researchers also attempted to use the membrane to sense the harmful substance nitrobenzene in solution. The results revealed that the membrane was able to detect nitrobenzene with a sensitivity of 3.19 ppb ( Figure 28B). This membrane also displayed high reusability ( Figure 28C). These results indicate that polymerizing 2D CSs is an effective approach to obtain Ag NCs suitable for applications. Nanomaterials 2020, 10 25 of 47 monomers butyl methacrylate (BMA) and triethylene glycol dimethacrylate (TEGDMA), as shown in Figure 27D. The resulting membrane exhibited PL with a QY of 14.8%, which was higher than that of the unpolymerized 2D CS crystals ( Figure 28A(a)). The increased PL intensity was ascribed to the polymerization strengthening the structure of the 2D CS, which suppressed molecular vibrations and thus nonradiative decay. The membrane was stable in water regardless of pH ( Figure 28A(b)). The researchers also attempted to use the membrane to sense the harmful substance nitrobenzene in solution. The results revealed that the membrane was able to detect nitrobenzene with a sensitivity of 3.19 ppb ( Figure 28B). This membrane also displayed high reusability ( Figure 28C). These results indicate that polymerizing 2D CSs is an effective approach to obtain Ag NCs suitable for applications.

Three-Dimensional Structures
Ag NCs are often used as nodes in 3D CSs. Because 3D CSs generally possess stronger frameworks than those of 2D CSs, the formation of 3D CSs is effective to enhance the stability of Ag NCs and thereby improve their physical properties. In 3D CS formation, the principles of NC assembly are similar to those in 1D and 2D CS formation, although the ligands used are often different. In Sections 4.1, 4.2, and 4.3, we focus on the assembly of 3D CSs via the formation of Ag−O, Ag−S, or Ag−Cl bonds ( Figure 2B), control of counterions ( Figure 2C), and the introduction of linker molecules ( Figure 2D), respectively. The metal NCs, connection modes, linker molecules, year reported, and reference numbers for these studies are summarized in Table 3. Several of the ligands used in 3D CSs are shown in Scheme 1. The organic molecules used as linkers are illustrated in Scheme 2.

Three-Dimensional Structures
Ag NCs are often used as nodes in 3D CSs. Because 3D CSs generally possess stronger frameworks than those of 2D CSs, the formation of 3D CSs is effective to enhance the stability of Ag NCs and thereby improve their physical properties. In 3D CS formation, the principles of NC assembly are similar to those in 1D and 2D CS formation, although the ligands used are often different. In Sections 4.1-4.3, we focus on the assembly of 3D CSs via the formation of Ag−O, Ag−S, or Ag−Cl bonds ( Figure 2B), control of counterions ( Figure 2C), and the introduction of linker molecules ( Figure 2D), respectively. The metal NCs, connection modes, linker molecules, year reported, and reference numbers for these studies are summarized in Table 3. Several of the ligands used in 3D CSs are shown in Scheme 1. The organic molecules used as linkers are illustrated in Scheme 2.

Connection via Ag−O, Ag−S, or Ag−Cl Bonds
In 2017, Mak et al. [148] formed a 3D CS consisting of Ag 14 (S-iPr) 6 (CF 3 COO) 11 (H 2 O) 3 (CH 3 OH) NCs ( Figure 29A). The NCs were connected via O−Ag−O bonds formed between CF 3 COO − and Ag ions ( Figure 29B,C). Each Ag NC was connected to six other NCs, thereby forming a distorted octahedral-like coordination structure. It was speculated that this 3D CS formed by the assembly of NCs after NC generation.
In 2017, Mak et al. [148] formed a 3D CS consisting of Ag14(S-iPr)6(CF3COO)11(H2O)3(CH3OH) NCs ( Figure 29A). The NCs were connected via O−Ag−O bonds formed between CF3COO − and Ag ions ( Figure 29B,C). Each Ag NC was connected to six other NCs, thereby forming a distorted octahedral-like coordination structure. It was speculated that this 3D CS formed by the assembly of NCs after NC generation. In 2019, Sun and colleagues also produced a 3D CS, and theirs consisted of Ag44(Mo6O19)(S-Et)24(SCl4)3 NCs ( Figure 30A) containing a POM as an anion template ( Figure 30B); these NCs were reported in their paper on 1D CS ( Figure 9) and 2D CS ( Figure 19) formation [149]. In this 3D CS, Mo6O19 2− was used as an anion template, which was different from the case of the 1D and 2D CSs, in which the POM V10O28 6− was located in the center of the cluster. This was the first report in which Mo6O19 2− was used as an anion template of Ag NCs. Mo6O19 2− has octahedral symmetry, and thereby the outer Ag44(S-Et)24 layer also displayed high symmetry ( Figure 30C). The Ag44 shell had six quadrangles and 24 pentagonal faces. Ag at the vertices of these six quadrangles was connected with In 2019, Sun and colleagues also produced a 3D CS, and theirs consisted of Ag 44 (Mo 6 O 19 )(S-Et) 24 (SCl 4 ) 3 NCs ( Figure 30A) containing a POM as an anion template ( Figure 30B); these NCs were reported in their paper on 1D CS ( Figure 9) and 2D CS ( Figure 19) formation [149]. In this 3D CS, Mo 6 O 19 2− was used as an anion template, which was different from the case of the 1D and 2D CSs, in which the POM V 10 O 28 6− was located in the center of the cluster. This was the first report in which Mo 6 O 19 2− was used as an anion template of Ag NCs. Mo 6 O 19 2− has octahedral symmetry, and thereby the outer Ag 44 (S-Et) 24 layer also displayed high symmetry ( Figure 30C). The Ag 44 shell had six quadrangles and 24 pentagonal faces. Ag at the vertices of these six quadrangles was connected with one S atom and four Cl atoms, leading to the formation of a 3D CS consisting of Ag 44 (Mo 6 O 19 )(S-Et) 24 (SCl 4 ) 3 ( Figure 30D). The S and Cl atoms used in the connections were generated by the decomposition of S-Et and CH 2 Cl 2 during the CS synthesis. The 3D CS in which Ag NCs are linked by dithiocarb, reported in 2019 by Gao et al. [173], should also be included in this category. The researchers first synthesized an Ag 11 S(C 5 NS 2 H 10 ) 9 precursor (C 5 NS 2 H 10 = diethyldithiocarbamate, Scheme 1(20)) [174]. The obtained precursor was reacted under high pressure, in an autoclave, to form a 3D CS with Ag 17 (C 5 NS 2 H 10 ) 14 as a repeating unit. This structure consists of Ag 9 NCs bound to twelve C 5 NS 2 H 10 ( Figure 31A) and Ag 5 NCs containing six C 5 NS 2 H 10 ( Figure 31B). The 3D CS ( Figure 31C) was formed by the sharing of S between the two types of NCs. In these structures, the Ag 9 NCs were the nodes for three-point bridges and the Ag 5 NCs were the nodes for four-point bridges. Table 3. Connection modes, NCs, linkers, publication years, and references for 3D CS.  6 1,4-bis(4-pyridyl)benzene a 2018 [156] Ag 10 (S-t Bu) 6 (CF 3 COO) 2 (PhPO 3 H) 2 bpy a 2018 [176] Ag 12 (S-t Bu) 6 (CF 3 COO) 6 CPPP a 2019 [177] Ag 12 (S-t Bu) 6 (CF 3 COO) 6 Ag 8 (S-t Bu) 4 (CF 3 COO) 4 tppe a 2019 [178] Ag + [C(Au-mdppz) 6 ](BF 4 ) 2 a 2014 [179] a See Scheme 2.

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Nanomaterials 2020, 10 27 of 47 one S atom and four Cl atoms, leading to the formation of a 3D CS consisting of Ag44(Mo6O19)(S-Et)24(SCl4)3 ( Figure 30D). The S and Cl atoms used in the connections were generated by the decomposition of S-Et and CH2Cl2 during the CS synthesis.  The 3D CS in which Ag NCs are linked by dithiocarb, reported in 2019 by Gao et al. [173], should also be included in this category. The researchers first synthesized an Ag11S(C5NS2H10)9 precursor (C5NS2H10 = diethyldithiocarbamate, Scheme 1(20)) [174]. The obtained precursor was reacted under high pressure, in an autoclave, to form a 3D CS with Ag17(C5NS2H10)14 as a repeating unit. This structure consists of Ag9 NCs bound to twelve C5NS2H10 ( Figure 31A) and Ag5 NCs containing six C5NS2H10 ( Figure 31B). The 3D CS ( Figure 31C) was formed by the sharing of S between the two types of NCs. In these structures, the Ag9 NCs were the nodes for three-point bridges and the Ag5 NCs were the nodes for four-point bridges. one S atom and four Cl atoms, leading to the formation of a 3D CS consisting of Ag44(Mo6O19)(S-Et)24(SCl4)3 ( Figure 30D). The S and Cl atoms used in the connections were generated by the decomposition of S-Et and CH2Cl2 during the CS synthesis.  The 3D CS in which Ag NCs are linked by dithiocarb, reported in 2019 by Gao et al. [173], should also be included in this category. The researchers first synthesized an Ag11S(C5NS2H10)9 precursor (C5NS2H10 = diethyldithiocarbamate, Scheme 1(20)) [174]. The obtained precursor was reacted under high pressure, in an autoclave, to form a 3D CS with Ag17(C5NS2H10)14 as a repeating unit. This structure consists of Ag9 NCs bound to twelve C5NS2H10 ( Figure 31A) and Ag5 NCs containing six C5NS2H10 ( Figure 31B). The 3D CS ( Figure 31C) was formed by the sharing of S between the two types of NCs. In these structures, the Ag9 NCs were the nodes for three-point bridges and the Ag5 NCs were the nodes for four-point bridges.

Control of Counterions
Very recently, Zhu's group synthesized two types of 3D CSs in which [Au1Ag22(S-Adm)12] 3+ NCs (S-Adm = 1-adamantanethiolate, Scheme 1(21)) were connected in three dimensions via Note that the packing pattern of the right-handed chiral 3D channel framework was the same as that of the left-handed chiral 3D channel framework. Reproduced with permission from Reference [175]. Copyright 2020 Wiley-VCH.
Study of the physical and chemical properties of the 3D CSs revealed that both exhibited red PL in the presence of polar solvents such as CH 3 OH, ethanol, and water, which disappeared when the solvent was evaporated ( Figure 33A). This behavior indicates that the obtained 3D CSs can function as sensors for polar solvents. The 3D CS composed of only the right-or left-handed enantiomer exhibited circularly polarized luminescence (CPL) (Figure 33B). possessed a diamondlike structure ( Figure 32A(f)) consisting of interpenetrating clockwise and counterclockwise optical isomers ( Figure 32A(g)), which led to a small pore diameter of 6.2 Å ( Figure  32A(h)). In the second 3D CS, [Au1Ag22(S-Adm)12](SbF6)3 was a structural unit, and the 3D CS was formed by connecting [Au1Ag22(S-Adm)12] 3+ to three SbF6 − via Ag−F−Ag bonds ( Figure 32B(a)-(c)). This structure only contained clockwise or counterclockwise optical isomers ( Figure 32B(d)). As a result, this 3D CS had a larger pore diameter (15 Å , Figure 32B(e)) than that of the first 3D CS (6.2 Å , Figure 32A).
Study of the physical and chemical properties of the 3D CSs revealed that both exhibited red PL in the presence of polar solvents such as CH3OH, ethanol, and water, which disappeared when the solvent was evaporated ( Figure 33A). This behavior indicates that the obtained 3D CSs can function as sensors for polar solvents. The 3D CS composed of only the right-or left-handed enantiomer exhibited circularly polarized luminescence (CPL) ( Figure 33B).

Introduction of Linker Molecules
The formation of 3D CSs by using linker molecules is a technique often used to fabricate molecular assemblies and MOFs. When a 3D CS composed of metal NCs is formed by such a method, in addition to increasing the stability of the NCs, it is also expected to adsorb gas molecules within its pores and behave as a catalyst with high selectivity because of the narrow pores. Furthermore, because the metal NCs, which are used as nodes, have more diversity in terms of coordination direction than that of metal ions, metal NC-based MOFs may have different connection modes from those of normal MOFs formed by using metal ions as nodes, and thereby they construct novel framework structures. Thus, metal NC-based MOFs possess not only the characteristics of individual metal NCs and MOFs, but also the possibility to produce new functions through synergistic effects.
Zang's group have been energetically researching 3D CSs with linkers, as well as the cases of 1D and 2D CSs. First, in 2017, Zang et al. [168] formed an Ag 12 NC-based MOF (Ag 12 (S-t Bu) 8 (CF 3 COO) 4 (bpy) 4 ) in which Ag 12 (S-t Bu) 8 (CF 3 COO) 4 was bridged by bpy ( Figure 34A). The obtained Ag 12 NC-based MOF possessed a bilayer structure ( Figure 34B). The formation of such a 3D CS markedly improved the stability of the Ag 12 NCs. For example, a crystal of the individual Ag 12 (S-t Bu) 6 (CF 3 COO) 6 (CH 3 CN) 6 NCs discolored in just 30 min when left in the atmosphere. In contrast, the Ag 12 NC-based MOF showed almost no change in crystallinity, even when left in the air for one year ( Figure 34C). The 3D CS also showed high stability during long-term gas adsorption and irradiation with visible light for several hours.

Introduction of Linker Molecules
The formation of 3D CSs by using linker molecules is a technique often used to fabricate molecular assemblies and MOFs. When a 3D CS composed of metal NCs is formed by such a method, in addition to increasing the stability of the NCs, it is also expected to adsorb gas molecules within The formation of the 3D CS greatly changed the PL properties of the NCs. The individual Ag 12 NCs exhibited red PL with low QY. Conversely, the Ag 12 NC-based MOF exhibited green PL under vacuum, which was quenched by O 2 in the atmosphere ( Figure 35A). The PL emission wavelength of the 3D CS under vacuum was independent of temperature and excitation wavelength, and its QY was 60 times higher than that of individual Ag 12 NCs. The authors ascribed this high QY to the efficient suppression of nonradiative decay in the 3D CS. Moreover, the fact that the PL of the 3D CS is quenched by O 2 means that it is highly sensitive to O 2 . The 3D CS showed a fast response to O 2 in experiments in which the atmosphere was repeatedly switched between air and N 2 . No such O 2 response was observed for the individual Ag 12 NCs. Based on these results, they suggested that the Ag 12 NC-based MOF can be applied as an O 2 sensor. In addition, the Ag 12 NC-based MOF was able to adsorb volatile organic compounds (VOCs) in its pores. The VOC-containing Ag 12 NC-based MOF exhibited different PL colors, depending on the kind of VOC ( Figure 35B). This indicates that the Ag 12 NC-based MOF displays solvatochromism and therefore can be used for VOC detection.  Zang's group have been energetically researching 3D CSs with linkers, as well as the cases of 1D and 2D CSs. First, in 2017, Zang et al. [168] formed an Ag12 NC-based MOF (Ag12(St Bu)8(CF3COO)4(bpy)4) in which Ag12(St Bu)8(CF3COO)4 was bridged by bpy ( Figure 34A). The obtained Ag12 NC-based MOF possessed a bilayer structure ( Figure 34B). The formation of such a 3D CS markedly improved the stability of the Ag12 NCs. For example, a crystal of the individual Ag12(St Bu)6(CF3COO)6(CH3CN)6 NCs discolored in just 30 min when left in the atmosphere. In contrast, the Ag12 NC-based MOF showed almost no change in crystallinity, even when left in the air for one year ( Figure 34C). The 3D CS also showed high stability during long-term gas adsorption and irradiation with visible light for several hours.
The formation of the 3D CS greatly changed the PL properties of the NCs. The individual Ag12 NCs exhibited red PL with low QY. Conversely, the Ag12 NC-based MOF exhibited green PL under vacuum, which was quenched by O2 in the atmosphere ( Figure 35A). The PL emission wavelength of the 3D CS under vacuum was independent of temperature and excitation wavelength, and its QY was 60 times higher than that of individual Ag12 NCs. The authors ascribed this high QY to the efficient suppression of nonradiative decay in the 3D CS. Moreover, the fact that the PL of the 3D CS In a paper on Ag 14 (DT-o-C) 6 NCs published in 2018 (Figures 13 and 22), the same group reported that a 3D CS containing Ag 14 (DT-o-C) 6 NCs formed when bpy was used as a linker ( Figure 36A) [156]. The Ag 14 NC nodes in the 3D CS had a face-centered cubic structure like that of other Ag 14 NCs. This 3D CS was formed by connecting the eight vertices of each Ag 14 NC with bpy linker molecules. However, this 3D CS was not stable after solvent evaporation, similar to the case of the corresponding 1D CS ( Figure 13) and 2D CS (Figure 22) [156]. Therefore, they synthesized a 3D CS with an interpenetrating framework by using 1,4-bis(4-pyridyl)benzene (Scheme 2 (14)) as a linker, in order to decrease the pore size and form a 3D CS with a strong framework ( Figure 36B). The obtained 3D CS showed high thermal stability, remaining intact up to 220 • C ( Figure 36C), and possessed pores with a diameter of about 1.12 nm ( Figure 36D). This 3D CS showed optical absorption over a wide wavelength range and thermochromism ( Figure 36E). In a paper on Ag14(DT-o-C)6 NCs published in 2018 ( Figures 13 and 22), the same group reported that a 3D CS containing Ag14(DT-o-C)6 NCs formed when bpy was used as a linker ( Figure 36A) [156]. The Ag14 NC nodes in the 3D CS had a face-centered cubic structure like that of other Ag14 NCs. This 3D CS was formed by connecting the eight vertices of each Ag14 NC with bpy linker molecules. However, this 3D CS was not stable after solvent evaporation, similar to the case of the corresponding 1D CS ( Figure 13) and 2D CS ( Figure 22) [156]. Therefore, they synthesized a 3D CS with an interpenetrating framework by using 1,4-bis(4-pyridyl)benzene (Scheme 2(14)) as a linker, in order to decrease the pore size and form a 3D CS with a strong framework ( Figure 36B). The obtained 3D CS showed high thermal stability, remaining intact up to 220 °C ( Figure 36C), and possessed pores with a diameter of about 1.12 nm ( Figure 36D). This 3D CS showed optical absorption over a wide wavelength range and thermochromism ( Figure 36E).
Zang et al. [176] have also produced several other functional Ag NC-based MOFs. For example, in 2018, they reported the synthesis of a flexible Ag NC-based MOF. This structure consisted of 2D layers of Ag10(St Bu)6(CF3COO)2(PhPO3H)2 NCs linked via bpy, which were stacked through hydrogen bond (O-H···O) and C-H···O interactions, to form the 3D CS ( Figure 37A,B). The 2D CS layers were thus linked by weak interactions, which facilitated the sliding of the layers, allowing the 3D CS to undergo structural deformation in response to guest organic molecules ( Figure 37C). This Ag10 NC-based MOF exhibited green PL in air. Upon inclusion of guest organic molecules, it exhibited PL with an emission color depending on the guest organic molecule ( Figure 37D). As such, this Ag10 NC-based MOF has potential as a sensor for distinguishing VOCs by its PL color. In 2019, they also formed a 3D CS consisting of Ag12(St Bu)6(CF3COO)6 NC nodes and 2,5-bis(4-cyanophenyl)-1,4-bis(4-(pyridine-4-yl)-phenyl)-1,4-dihydropyrrolo[3,2-b]pyrrole (CPPP, Scheme 2(15)) as a linker ( Figure  38A) [177]. This was the first report in which a nitrile group (-CN) was used to link Ag NCs. The Zang et al. [176] have also produced several other functional Ag NC-based MOFs. For example, in 2018, they reported the synthesis of a flexible Ag NC-based MOF. This structure consisted of 2D layers of Ag 10 (S-t Bu) 6 (CF 3 COO) 2 (PhPO 3 H) 2 NCs linked via bpy, which were stacked through hydrogen bond (O-H···O) and C-H···O interactions, to form the 3D CS ( Figure 37A,B). The 2D CS layers were thus linked by weak interactions, which facilitated the sliding of the layers, allowing the 3D CS to undergo structural deformation in response to guest organic molecules ( Figure 37C). This Ag 10 NC-based MOF exhibited green PL in air. Upon inclusion of guest organic molecules, it exhibited PL with an emission color depending on the guest organic molecule ( Figure 37D). As such, this Ag 10 NC-based MOF has potential as a sensor for distinguishing VOCs by its PL color. In 2019, they also formed a 3D CS consisting of Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NC nodes and 2,5-bis(4-cyanophenyl)-1,4-bis(4-(pyridine-4-yl)-phenyl)-1,4-dihydropyrrolo[3,2-b]pyrrole (CPPP, Scheme 2(15)) as a linker ( Figure 38A) [177]. This was the first report in which a nitrile group (-CN) was used to link Ag NCs. The obtained 3D CS exhibited PL with a higher QY (61%) than that of CPPP in solution and solid states because the aggregation-induced quenching of CPPP was suppressed in the 3D CS ( Figure 38B). Nanomaterials 2020, 10 33 of 47 obtained 3D CS exhibited PL with a higher QY (61%) than that of CPPP in solution and solid states because the aggregation-induced quenching of CPPP was suppressed in the 3D CS ( Figure 38B). Reproduced with permission from Reference [176]. Copyright 2018 American Chemical Society.
In the above 3D CSs, the nodes consisted of only one kind of Ag NCs. Tang et al. [178] synthesized an Ag NC-based MOF that had two types of Ag NCs as nodes. This Ag NC-based MOF was composed of 1,1,2,2-tetrakis(4-(pyridin-4-yl)phenyl)-ethene (tppe, Scheme 2(16)), Ag12(St Bu)6(CF3COO)6, and Ag8(St Bu)4(CF3COO)4 ( Figure 39). In the 3D CS, one Ag12(St Bu)6(CF3COO)6 NC and three Ag8(St Bu)4(CF3COO)4 NCs were bound to the four N atoms of tppe. The estimated pore volume of this Ag NC-based MOF was 40.9%. DMAC, which was used as a solvent in the synthesis, was present in the pores of the 3D CS immediately after synthesis ( Figure 40A). When the obtained 3D CS was exposed to the atmosphere, DMAC was removed, while maintaining the framework of the 3D CS. The Ag NC-based MOF thus obtained exhibited PL in the visible region because tppe is a light-emitting molecule. The PL wavelength of the 3D CS depended on the presence or absence of DMAC in its pores ( Figure 40B). When DMAC was present in the pores of the framework, intramolecular rotation of tppe was suppressed, which changed the excited-state dynamics of the 3D CS. The change in the emission behavior of the Ag NC-based MOF induced by DMAC was ascribed to this change of its excited-state characteristics ( Figure 40C).
Wang and colleagues reported the formation of a 3D CS, using metal NCs as linkers, before the use of metal NCs as nodes was developed [179]. In 2014, they succeeded in forming an NbO-type MOF by using Ag ions as nodes and [C(Au-mdppz)6](BF4)2] (mdppz = 2-(3methylpyrazinyl)diphenylphosphine, Scheme 2(17)) NCs as linkers ( Figure 41). [C(Au- In the above 3D CSs, the nodes consisted of only one kind of Ag NCs. Tang et al. [178] synthesized an Ag NC-based MOF that had two types of Ag NCs as nodes. This Ag NC-based MOF was composed of 1,1,2,2-tetrakis(4-(pyridin-4-yl)phenyl)-ethene (tppe, Scheme 2(16)), Ag 12 (S-t Bu) 6 (CF 3 COO) 6 , and Ag 8 (S-t Bu) 4 (CF 3 COO) 4 ( Figure 39). In the 3D CS, one Ag 12 (S-t Bu) 6 (CF 3 COO) 6 NC and three Ag 8 (S-t Bu) 4 (CF 3 COO) 4 NCs were bound to the four N atoms of tppe. The estimated pore volume of this Ag NC-based MOF was 40.9%. DMAC, which was used as a solvent in the synthesis, was present in the pores of the 3D CS immediately after synthesis ( Figure 40A). When the obtained 3D CS was exposed to the atmosphere, DMAC was removed, while maintaining the framework of the 3D CS. The Ag NC-based MOF thus obtained exhibited PL in the visible region because tppe is a light-emitting molecule. The PL wavelength of the 3D CS depended on the presence or absence of DMAC in its pores ( Figure 40B). When DMAC was present in the pores of the framework, intramolecular rotation of tppe was suppressed, which changed the excited-state dynamics of the 3D CS. The change in the emission behavior of the Ag NC-based MOF induced by DMAC was ascribed to this change of its excited-state characteristics ( Figure 40C).
Wang and colleagues reported the formation of a 3D CS, using metal NCs as linkers, before the use of metal NCs as nodes was developed [179]. In 2014, they succeeded in forming an NbO-type MOF by using Ag ions as nodes and [C(Au-mdppz) 6 ](BF 4 ) 2 ] (mdppz = 2-(3-methylpyrazinyl)diphenylphosphine, Scheme 2(17)) NCs as linkers ( Figure 41). [C(Au-mdppz) 6 ](BF 4 ) 2 has a framework with C in the center ( Figure 41A) and is luminescent. The 3D CS was formed by the outer N atom of mdppz (Scheme 2(17)) binding to an Ag ion ( Figure 41B,C). The obtained 3D CS consisted of two interpenetrating frameworks ( Figure 41D,E) with a 1D channel in the c-axis direction ( Figure 41C). Because a luminescent NC was used as the linker, the obtained MOF also showed green PL. The 3D CS displayed a PL QY of 25.6%, which was much higher than that of the luminescent NCs (1.5%). This increase of QY was caused by the strengthening of the framework of the linker NCs upon MOF formation and the excited-state perturbation induced by the coordination of Ag ions. Nanomaterials 2020, 10 34 of 47 mdppz)6](BF4)2 has a framework with C in the center ( Figure 41A) and is luminescent. The 3D CS was formed by the outer N atom of mdppz (Scheme 2(17)) binding to an Ag ion ( Figure 41B,C). The obtained 3D CS consisted of two interpenetrating frameworks ( Figure 41D,E) with a 1D channel in the c-axis direction ( Figure 41C). Because a luminescent NC was used as the linker, the obtained MOF also showed green PL. The 3D CS displayed a PL QY of 25.6%, which was much higher than that of the luminescent NCs (1.5%). This increase of QY was caused by the strengthening of the framework of the linker NCs upon MOF formation and the excited-state perturbation induced by the coordination of Ag ions.   Nanomaterials 2020, 10 34 of 47 mdppz)6](BF4)2 has a framework with C in the center ( Figure 41A) and is luminescent. The 3D CS was formed by the outer N atom of mdppz (Scheme 2(17)) binding to an Ag ion ( Figure 41B,C). The obtained 3D CS consisted of two interpenetrating frameworks ( Figure 41D,E) with a 1D channel in the c-axis direction ( Figure 41C). Because a luminescent NC was used as the linker, the obtained MOF also showed green PL. The 3D CS displayed a PL QY of 25.6%, which was much higher than that of the luminescent NCs (1.5%). This increase of QY was caused by the strengthening of the framework of the linker NCs upon MOF formation and the excited-state perturbation induced by the coordination of Ag ions.     1⊃DMAC, 1⊃THF, 1⊃Toluene, and 1⊃DMF, respectively). Reproduced with permission from Reference [178]. Copyright 2019 Wiley-VCH.

Summary
In this review, representative studies on the formation of 1D, 2D, and 3D CSs in which metal NCs were self-organized and regularly linked were summarized. From this summary, the following points became clear.
(1) Methods. The methods to connect metal NCs that have been reported to date can be roughly divided into the following five categories: (i) direct connection by formation of metal−metal bonds ( Figure 2A); (ii) connection by Ag−O, Ag−S, or Ag−Cl bond formation ( Figure 2B); (iii) connection by counterions ( Figure 2C); (iv) connection by linker molecules ( Figure 2D); and (v) connection by inter-ligand interactions ( Figure 2E; not introduced in this review). (2) Diversity. Among CSs produced by the above methods, there are many examples of the formation of 1D, 2D, and 3D CSs through the use of methods (ii) and (iv). An important point when constructing CSs by these methods is the design of the ligand of the NCs and linker, respectively. It is presumed that the control of these species is relatively easy, which has led to Nanomaterials 2020, 10 36 of 47 the wider utilization of methods (ii) and (iv) than of the other methods. In particular, for method (iv), existing knowledge obtained in the study of normal MOFs can be considered.

Summary
In this review, representative studies on the formation of 1D, 2D, and 3D CSs in which metal NCs were self-organized and regularly linked were summarized. From this summary, the following points became clear.
(1) Methods. The methods to connect metal NCs that have been reported to date can be roughly divided into the following five categories: (i) direct connection by formation of metal−metal bonds ( Figure 2A); (ii) connection by Ag−O, Ag−S, or Ag−Cl bond formation ( Figure 2B); (iii) connection by counterions ( Figure 2C); (iv) connection by linker molecules ( Figure 2D); and (v) connection by inter-ligand interactions ( Figure 2E; not introduced in this review). (2) Diversity. Among CSs produced by the above methods, there are many examples of the formation of 1D, 2D, and 3D CSs through the use of methods (ii) and (iv). An important point when constructing CSs by these methods is the design of the ligand of the NCs and linker, respectively. It is presumed that the control of these species is relatively easy, which has led to the wider utilization of methods (ii) and (iv) than of the other methods. In particular, for method (iv), existing knowledge obtained in the study of normal MOFs can be considered. (3) Metal element. To directly connect metal NCs, it is effective to use Au as a main element because it forms strong aurophilic interactions (intermetal interactions). In the connections involving metal−O or metal−Cl bonds, it is effective to use Ag as a main element because it readily bonds with O or Cl. Moreover, in the connections using bpy as a linker, Ag is attractive as the main element because of the high affinity of N and Ag. (4) Stability. The formation of a CS generally improves the thermal stability of the component metal NCs regardless of the connection mode. (5) Electronic structure. The formation of a CS often causes the band gap of the NC to narrow.
This means that CS formation allows the use of a broader wavelength range of light, opening up the possibility of visible-light-driven photocatalysis by using CSs. (6) PL properties. For 2D and 3D CS using linkers, CS formation often leads to an increase in PL emission intensity. When metal NCs are the PL source, there are many cases in which dual emission peaks appear upon connection with a linker. In addition, the PL color of a CS often changes depending on the kind of VOC trapped in its pores. (7) Electrical conduction. The electron conductivity of CSs changes dramatically depending on the distance between each metal NC and the mode of connection; 1D CS formed by the direct connection via metal−metal bond shows the higher conductivity than 1D CS connected through counter ion. (8) Possible applications. The reported CSs have potential applications in fields such as electronic devices, luminescent devices, gas and temperature sensing, and photocatalysis.
This review allowed us to obtain a common understanding of the CSs reported to date and their functions. We hope that the knowledge thus clarified will lead to clear design guidelines for developing new CSs with desired functions in the future.

Outlook
It is expected that the following studies will be conducted in the future, leading to new CSs.
(1) Use of other metal elements. At present, mostly Au and Ag are used as the metal element in CSs. This is largely related to the high stability of Au and Ag NCs. For Ag NCs, the good connectivity between Ag and linker molecules is also related to this fact. On the other hand, several syntheses of individual copper (Cu) NCs have been reported recently [10,[180][181][182][183]. In addition, other metal ions are often used in normal MOFs with metal ions as nodes [153]. CS formation of NCs based on Cu or other metals may also lead to materials with high thermal stability. In the future, it is expected that many elements will be used in CSs, thereby realizing various functions and decreased cost of such materials. (2) Use of the alloying effect. At present, there are few examples in which alloy NCs are connected to form CSs [142,143,146]. Mixing different elements leads to NCs with physical/chemical properties and functions that are different from those of monometal NCs. In fact, for individual metal NCs, many cases have been reported in which new physical properties/functions appeared because of mixing/synergistic effects [66,[184][185][186][187][188][189][190][191][192][193][194]. The previous studies have established basic techniques for the formation of CSs consisting of Ag NCs. In the future, it is expected that more functional materials will be created by extending such CS formation techniques to Ag-based alloy NCs. (3) Connection of reported metal NCs. Ag NC-based MOFs are interesting because they can be synthesized by a one-pot process. However, in CSs formed by such a method, metal NCs that are stable only in the CS are often found as nodes. For individual metal NCs, many NCs have already been synthesized with atomic precision . In addition, much information has been obtained on methods to generate novel functions in such NCs, including alloying [66][67][68]. In the future, it is expected that a method to more effectively utilize the reported metal NCs in CSs will be found. To achieve this, it may be necessary to establish new connection methods different from those described in this review ( Figure 2). (4) Elucidation of electronic conductivity. We believe that 1D CSs may be applied as nanodevices.
However, at present, few experiments on the conductivity of 1D CSs have been reported [146,152].
In the future, it is expected that the conductivity of 1D CSs will be measured as a basic physical property. It is anticipated that the accumulation of such information will eventually lead to the production of nanodevices based on 1D CSs of metal NCs. (5) Exploration of other possible applications of connected structures. Various applications, such as gas storage, gas separation, gas conversion, and reaction-selective catalysis, have been studied for normal MOFs with metal ions as nodes [117]. It has also been reported that, in the case of self-assembled complexes, a reaction different from that in the case of using an ordinary flask proceeds in the cage structure (i.e., the cage behaves as a nanoflask) [116]. In the future, it is expected that these possibilities will be investigated for metal NC-based MOFs and that their functions will be much higher than those of conventional MOFs and self-assembled complexes.
As mentioned in Section 1, the advance of bottom-up technology is essential for the further development of nanotechnology in the future. In previous research, multiple techniques to generate metal atoms on the molar scale in a solution and to self-organize them to form nanomaterials with the same number of constituent atoms and the same number of molecules have been studied; that is, precise synthesis techniques of metal NCs have been developed. However, to apply these metal NCs as devices and next-generation materials, developing techniques to assemble metal NCs to a size that is easy to handle is necessary (Figure 1). We hope that technologies that allow the self-organization of regularly arranged CSs composed of metal NCs will be further developed in the future. Ultimately, such nanotechnology is expected to enable resource conservation, energy conservation, decreased waste and environmental load, and the better use of time by human society.