Self-Assembly and Ionic-Lattice-like Secondary Structure of a Flexible Linear Polymer of Highly Charged Inorganic Building Blocks

Among molecular building blocks, metal oxide cluster anions and their countercations provide multiple options for the self-assembly of functional materials. Currently, however, rational design concepts are limited to electrostatic interactions with metal or organic countercations or to the attachment and subsequent reactions of functionalized organic ligands. We now demonstrate that bridging μ-oxo linkages can be used to string together a bifunctional Keggin anion building block, [PNb2Mo10O40]5– (1), the diniobium(V) analogue of [PV2Mo10O40]5– (2). Induction of μ-oxo ligation between the NbV=O moieties of 1 in acetonitrile via step-growth polymerization gives linear polymers with entirely inorganic backbones, some comprising over 140 000 repeating units, each with a 3– charge, exceeding that of previously reported organic or inorganic polyelectrolytes. As the chain grows, its flexible μ-oxo-linked backbone, with associated countercations, coils into a compact 270 nm diameter spherical secondary structure as a result of electrostatic interactions not unlike those within ionic lattices. More generally, the findings point to new options for the rational design of multidimensional structures based on μ-oxo linkages between NbV=O-functionalized building blocks.


Materials and instruments
. Crystal data and structure refinement details. Table S3-5. Selected bond lengths, bond angles and bond valence sum (BVS) values. Figure S9. 2D Contour map depicting the observed electron density. Figure S10. Sequential 31 P NMR spectra of THA 5 1 in CD 3 CN during its polymerization under ambient air. Figure S11. FTIR spectrum obtained after drying a MeCN solution of polymerized THA 5 1. Figure S12. Small angle X-ray scattering (SAXS), and dynamic and static light scattering (DLS and SLS) data for MeCN solutions of polymerized 1. Figure S13. Unweighted DLS of THA 5 1 after polymerization in MeCN under Ar / air / CO 2 . Table S6. Unweighted DLS of THA 5 1 after polymerization in MeCN under Ar / air / CO 2 . Figure S14. Dry-TEM images of THA 5 1 after polymerization under CO 2 in MeCN.                   Figure S42. Positive-mode ESI-MS of the THA salt of the mixture of Wells-Dawson derivatives after depolymerization in MeCN. References refluxed at 100 °C for two hours (color changed from orange to bright yellow, and a white precipitate appeared). The pH was adjusted to 3.0 by a slow titration with a concentrated solution of NaHCO 3 . The precipitate was removed by filtration, and the volume of the filtrate was reduced to about 40 mL using a rotary-evaporator (if any additional precipitate appeared during this step, it was subsequently filtered off). The solution was then saturated with KCl (about 5 g) at room temperature. Any excess precipitate was immediately filtered off and the solution was heated gently to 30 -40 °C to ensure complete dissolution of the KCl. The solution was transferred to the refrigerator (4 °C). After three hours, any excess KCl that might have precipitated again was filtered off. Yellow needle-like crystals appeared within a few hours and were harvested after four days. Yield: 42.7%. The product K 5  . In order to replace all the alkali metal cations with organic cations, a two-phase system was used, introducing K 5 1 in an aqueous phase and a stoichiometric amount of organic cations in an organic phase. K 5 PNb 2 Mo 10 O 40 (0.2264 g, 1×10 -4 mol) was dissolved in 1 mL H 2 O in a 4 mL vial. Tetrahexylammonium bromide [CH 3 (CH 2 ) 5 ] 4 NBr (THABr) (0.2173 g, 5×10 -4 mol) were dissolved in dichloromethane and added to the aqueous solution of the K 5 1, forming two separate phases. The mixture was vigorously stirred using a magnetic stirring bar. After 5 minutes, the organic phase was separated on a separatory funnel and dried completely using a rotary evaporator at 40 °C to ensure complete dryness. The product was a waxy, yellow solid; yield: 99%. The product ([CH 3 (CH 2 ) 5 ] 4 N) 5  Crystallization of (THA 4 H1) for single crystal X-ray diffraction. THA 5 1 (0.1 g) was dissolved in 1 mL THF solution. The solution was placed in the refrigerator at 4 °C. X-ray quality crystals formed over several months.
Polymerization. The polymerization of [CH 3 (CH 2 ) 5 ] 4 N) 5 PNb 2 Mo 10 O 40 (THA 5 1) was carried out with different concentrations of reactants and other conditions. A typical polymerization reaction was as follows. THA 5 1 (14.4 mg, 4×10 -6 mol) was dissolved in 1.5 mL MeCN and 0.5 mL CD 3 CN (or in some cases, 2 mL MeCN). In all cases, the concentration of THA 5 1 was 2 mM. After adding 10 µL 30% H 2 O 2 (9.77×10 -5 mol) to the POM solution at room temperature, the solution was stirred vigorously for a few minutes, and then transferred into a quartz cuvette sealed with a Teflon cap, and following by UV-Vis spectroscopy. The reaction requires 3-4 days to reach completion. The final product was characterized by 31 P-NMR, FTIR, DLS, SAXS, and cryo-TEM.
The polymerization of THA 5 1 under 1 atm CO 2 (g) was carried out with typical polymerization conditions in a gas-tight quartz cuvette. After adding H 2 O 2 , the cuvette was purged with CO 2 gas for 20 min. The reaction required approximately 3-4 days to reach completion. The final product was characterized by DLS and dry-TEM.
The polymerization of THA 5 1 under 1 atm Ar (g) was carried out with typical polymerization conditions in a Schlenk flask. After adding H 2 O 2 , the solution was frozen in liquid N 2 and the air removed using a pump, then refilled with pure Ar gas. The freeze-pump-thaw cycles were carried out six times. No polymer was observed after five days.
NMR Kinetic study of the polymerization process. Sequential 31 P NMR spectra were obtained during the polymerization process, here carried out in an NMR tube. THA 5 1 (7.2 mg, 2×10 -6 mol) was dissolved in 0.375 mL MeCN and 0.125 mL CD 3 CN, after which 5 µL 30% H 2 O 2 (4.8×10 -5 mol) was added to the POM solution at room temperature. The concentration of THA 5 1 was 4 mM. The solution was stirred vigorously for a few minutes, following by the acquisition of 31 P NMR spectra after constant time intervals.
Exchange of counter cations present in solutions of polymeric 1. (CH 3 ) 4 NCl (TMACl) or LiClO 4 salt were used to exchange counter ions of polymeric 1 in MeCN. With addition of 11 mg TMACl (0.1 mmol) to the polymer solution, yellow precipitate was quickly produced and the solution became colorless. With centrifugation, the supernatant was removed and the precipitate was washed with MeCN. Then 2 mL water was added to dissolve the precipitate, giving a clear solution (TMA1) with pH = 4.18. The solution was characterized by 31 P NMR, 1 H NMR, DLS, dry-TEM, and EDX.
Upon addition of 11 mg LiClO 4 (0.1 mmol) to polymeric 1 (2 mM THA 5 1 ) in MeCN, the solution remained clear. With evaporate, a yellow powder was obtained. After adding 2 mL water and 2 mL DCM to dissolve the powder, two clear layers were obtained. After centrifugation, the water layer (Li1) with pH = 4.43 was collected. The solution was characterized by 31 P NMR, 1 H NMR, DLS, dry-TEM, and EDX.
For compared with 31 P NMR of 1 and polymeric 1, Me 4 NCl or LiClO 4 salts were added to the MeCN solution of THA 5 1. After workup, the obtained powders were dissolved in D 2 O and analyzed by 31 P NMR spectroscopy.  2 The pH of the solution was 5.76. The solution was heated at 60 °C for two hours (the solution became a little cloudy, and the pH had changed to 6.39). KCl was then added (to 2 M KCl), giving a yellow precipitate. The precipitate was filtered and washed with water. Yield: 70.5 % (based on solid K 10 P 2 W 17 O 61 ). The compound was characterized by FTIR and 31 P-NMR. The FTIR spectrum confirmed the compound to possess the Wells-Dawson structure. In 31 P NMR spectra there are four sets of signals: at -10.53 and -12.78 belonging to mono-Nb K 7 P 2 NbW 17 O 62 ; at -10.74 and -12.67 belonging to the mono-Nb peroxo K 7 P 2 NbW 17 O 63 ; at -9.10 and -13.21 belonging to di-Nb K 8 P 2 Nb 2 W 16 O 62 ; at -9.27 and -13.09 belonging to di-Nb peroxo K 8 P 2 Nb 2 W 16 O 64 ; the 2Nb are on the same side of the Wells-Dawson structure. 3 Synthesis of a di-Nb(V) substituted Wells-Dawson (WD) anion (THA salt). The same method was used to change K + countercations of the above mixture of Wells-Dawson anions to organic cations. The K + salt of WD derivative (0.1688 g) was dissolved in 2 mL H 2 O in a 4 mL vial. Tetrahexylammonium bromide [CH 3 (CH 2 ) 5 ] 4 NBr (THABr) (0.1335 g, 3.1×10 -4 mol) was dissolved in dichloromethane and added to the aqueous solution, forming two separate phases. The mixture was vigorously stirred using a magnetic stirring bar. After 5 minutes, the organic phase was separated on a separatory funnel and dried completely using a rotary evaporator at 40 °C. The product was a waxy, yellow solid; yield: 87.5 %. The compound was characterized by FTIR, 31 P-NMR, and ESI-MS. FTIR spectrum could found the compound is Wells-Dawson structure. From 31 P NMR, there are four sets of peaks (the peak at -10.82 and -13.19 belong to mono-Nb THA 7 P 2 NbW 17 O 62 ; the peak at -11.02 and -13.08 belong to mono-Nb peroxo THA 7 P 2 NbW 17 O 63 ; the peak at -9.33 and -13.57 belong to di-Nb THA 8 P 2 Nb 2 W 16 O 62 ; the peak at -9.54 belong to di-Nb peroxo THA 8 P 2 Nb 2 W 16 O 64 ; the 2Nb are on the same side of the Wells-Dawson structure) 3 .

Synthesis of a di-Nb(V) substituted Wells-Dawson (WD) anion (K + salt
Polymerization and depolymerization. The method of polymerization and depolymerization were the same with Keggin structure, only difference was the weight of THA salt of WD derivative (28 mg, about 2 mM). The solution was characterized by 31 P NMR, DLS, cryo-TEM, and ESI-MS. DFT calculations were carried out to determine the relative stability and population of the five distinct isomers of [PNb 2 Mo 10 O 40 ] 5in aqueous solution. Although this anion has not been analyzed theoretically previously, the vanadium derivative [PV 2 Mo 10 O 40 ] 5has been studied in deep by several groups. [6][7][8] All these studies have shown that all five isomers are very close in energy, and that their relative energies depend on solvent, temperature and also might depend on the level of the calculation. A deep analysis of the electronic structure and protonation sites of vanadium molybdates anions can be found in ref 6. Our results for [PNb 2 Mo 10 O 40 ] 5show in general similar behavior. The differences between electronic energies and free energies among all isomers are very small. Hence, the relative free energy values at 25 °C were computed in a range of less than 2 kcal·mol -1 (Table S1). It is worth mentioning that we have found and characterized seven distinct minima. When we introduce the two Nb atoms in positions 1,5 and 1,8 we obtained two minima with different energies. A similar behavior was found for positions 1,6 and 1,7, as shown in Table S1. This is reminiscent of the alternating short and long bond length distortions observed within the ring structures, M n O n , of certain polyoxomolybdates. [9][10] In contrast to molybdates, tungstates fail to show significant ring distortions or they are significantly smaller. 11 DFT calculations show that metal oxide ring distortions originate from a pseudo Jahn-Teller vibronic instability at high symmetry structures. 12  The isomer populations given in Figure 1 were computed considering the partial populations for the seven minima, but considering only five distinct topological isomers a-1,2, a-1,4, a-1,5, a-1,6 and a-1,11 since at room temperature the potential different NMR signals for the two structures identified for each one of isomers a-1,5 and a-1,6 cannot be differentiated. According to our calculations these two isomers are the most abundant with populations of 51% and 30%, respectively. The other three isomers exhibit a much smaller abundance, between 5% and 7%. A similar series of calculations was performed for [PV 2 Mo 10 O 40 ] 5obtaining similar results, with the main difference in the populations of isomers a-1,6 and a-1,5, which are reversed for this anion, with values of 54% and 37%, respectively. The others three isomers also present much lower abundances ranging from 2% to 4%.
All the calculations were performed using Gaussian 09 code with the B3LYP functional under the tight convergence criteria and the ultrafine grid. LANL2DZ pseudopotential was used for V, Nb, Mo, and W atoms, and the 6-31g(d,p) basis set was used for other atoms.     XtalLAB Synergy-S single crystal x-ray diffractometer, which includes a Hy-Pix-6000HE detector and a standard Mo Kα x-ray radiation source (λ = 0.71073 Å). Unit cell dimensions, space group assignment, data reduction and finalization were done by using the CrysAlis PRO software package 13 (ver. 39.49, released 2018). A total of 152862 reflections were collected, of which 24228 were used after merging by SHELXL 14 according to the crystal class and based on Friedel pair equivalency for structure solution. Analytical numeric absorption correction was done using a multifaceted crystal model 15 and empirical absorption correction was done using spherical harmonics 16 . The structure was solved in the monoclinic P2 1 space group (no. 4) by SHELXT 17 via intrinsic phasing and refined by SHELXL using a full-matrix least-squares technique as an inversion twin (Flack parameter = 0.49), graphics were done by the Olex2 software package 18 . The final refinement cycle included the atomic coordinates and anisotropic thermal parameters of all atoms (not including hydrogen atoms), which converged toward R1 = 0.0621, wR2 = 0.1541 and S = 1.020. All non-hydrogen atoms were located expect a single terminal carbon atom of the tetrahexylammonium (THA) cation. The location of the two niobium atoms was found using bond length of the O-M bonds (O = PO 4 3oxygens, M = Mo, Nb metal centers), differences in electron density of the refined structure and bond valence sum method, 19 one atom was located precisely while the other was split due to disorder between two locations with partial occupancies, the anionic part of the structure is shown in Figure S7, polyhedral representation is shown in Figure S8. A summary of crystal data is given in Table S2.   5-anions, THA (four per unit) and two co-crystallized tetrahydrofuran (THF) molecules. The lack of a single tetrahexylammonium cation can be attributed to charge balance by a proton being present from the crystallization process, as protonated structures, including POMs, in organic solvents have been previously reported. [20][21] Also, the bond valence sum calculations support the presence of a proton which is disordered over at least four terminal oxygen atoms (see table S5). The crystallization process involves the addition of THA to an aqueous acidic solution (pH = 3) of the anion, precipitation of [N(C 6 H 13 ) 4 ] 5 [PNb 2 Mo 10 O 40 ] from solution and re-dissolve in THF in order to obtain single crystals suitable for diffraction. The niobium sites were located by considerable differences in the bond distances for the 12 metal sites, the crystalline radius of hexacoordinate Mo(VI) being 0.05 Å shorter compared to hexacoordinate Nb(V), resulting in considerable shorter bond length for Mo and O found in the central phosphate group, ca. 2.47 Å for Mo-O bonds compared to ca. 2.51 Å for Nb-O bond lengths, which corresponds well to the difference of their respective Shannon radii 22 . This observed difference was coupled with a lower electron density around the Nb sites that was accounted for from the electron density map (F o ) of the refined structure ( Figure S9). Finally, bond valence sum method 19 shows that the precisely located Nb atom has 5.127 valence units (v.u.) corresponding to a charge of +5, while the two partially occupied Nb/Mo sites have v.u. in the range of 5.449-5.576, corresponding to a charge of ca. +5.4-5.6, which is the result of the partial occupancy of the atomic site with both Nb(V) and Mo(VI) throughout the crystalline lattice, a comprehensive table is located in Table S5. Hydrogen atoms were placed at calculated positions (C-H = 0.98-0.99 Å) and refined in riding mode, with U iso (H) = 1.2U eq (C) for CH 2 groups and 1.5U eq (C) for CH 3 groups.   Bond valence sum calculation were performed via the KCryst program 23 using the parameters given by Gagne et al. 19 Figure 4A of the text, the scattering-intensity data in Figure S12A were partially number weighted to emphasize the more abundant medium-sized coiled polymers, giving an effective R h of ca. 23 nm, somewhat larger than in the unweighted result ( Figure 4A). For these coiled polymers, Guinier fitting of the SLS data in panel B gives a radius of gyration of R g of 13.27. Notably, to obtain the Zimm plot of SLS data, it is necessary to use the intermediate-angle data, and to remove data obtained at low angles. The low-angle data mainly includes information about the largest species, while the intermediate range data are due to the R h = ca. 23 nm (average) species. Using these DLS and SLS data, that both refer to the intermediate sized species, the ratio between R g and R h is 0.58, definitive for solid, compact spheres of the monomeric units. This conclusion is consistent with the fitting of the SAXS results ( Figure 4B of the text), which also gave compact spheres. Figure S13. Unweighted DLS of THA 5 1 after polymerization in MeCN under Ar / air / CO 2 . Due to the stepgrowth mechanism, the number of larger polymers is small relative to the number of monomers, S18 oligomers and small polymers. This is typical of step-growth polymerization. If we show the number weighted spectra, the scattering from the objects observed by SAXS and TEM will not appear.        Figure S23. Diameter of particles and distance between adjacent particles measured from cryo-TEM images. The diameter of the particles is 2.94 ± 0.13 nm with 95% confidence interval, and the distance between adjacent particles is 1.12 ± 0.06 nm with 95% confidence interval. Hence, the effective radius of each particle (particle and space) is 2.59 ± 0.13 nm with 95% confidence interval. These particle sizes and interparticle distances are larger than those expected for individual Keggin ions and the linkages between them. This, at least in part, is a consequence of working close to the resolution limit of cryo-TEM. Fortunately, by calculating the degree of polymerization (DP) on the basis of these larger observed monomer sizes and linkages, the DP reported in text errs on the side of being smaller than the likely actual value. This is the reason for stating that calculated value as a "minimum estimated DP".               These appear less compact than those prepared from 1 (see Figure 6 of the text), which also may reflect some damage during sample preparation.