## Introduction

Metal-organic frameworks (MOFs) are an emerging class of porous materials that have enormous potentials in gas separation1,2,3,4, catalysis5,6,7,8,9,10, drug delivery11,12,13,14,15, and energy storage16,17,18,19. Typically, MOFs are viewed as crystalline lattices with accessible regular-shaped pores. However, the prevalence of defects in MOFs as discovered in recent works has challenged the conventional perception20,21,22. The defects could fundamentally alter the chemical environment23,24,25 as well as the spatial geometry and connectivity of the pore space26,27,28,29. It has been suggested by various studies that the defects could be one of the key contributors to the catalytic activities30,31,32,33,34, and could significantly affect adsorption and transport properties29,35,36,37,38,39. The characterizations of defects are technically challenging as the structure of defect sites may be disordered and heterogeneous, and they could locate internally or at the particle surface40,41. Thermogravimetric analysis42,43 and other measurements44,45,46,47 can only provide limited site-specific information of defects. The recent development of low dose high-resolution transmission electron microscopy (HRTEM) or cryogenic electron microscopy (cryo-EM) has made great progress to directly visualize defect formations48,49,50,51,52,53. Yet the imaging techniques, at the current stage, cannot identify irregularly-distributed defects or provide quantifications of bulk phases. In addition, the chemical functionalities (e.g., hydroxyl, water, and small-molecule modulators) and the acid-base properties are largely absent in the pictures of defects.

Solid-state nuclear magnetic resonance (SSNMR) can thoroughly elucidate the chemical characters of organic moieties and metal centers in the defective framework54,55,56,57,58,59. However, the direct characterizations of defects are limited by resolution and sensitivity, and lack of spatial and volumetric information.25,39,60,61 In this work, we present an indirect strategy that utilizes phosphorus-containing probe molecules to characterize defects in MOFs, which can provide both molecular details and bulk quantifications. The indirect method is more sensitive and background-free (based on the receptive 31P signal), and is highly chemical-specific and quantitative. By varying the size of probe molecules (i.e., by controlling their accessibility to different pores), we can also distinguish between defects of different geometric volumes62 as well as their distributions. Phosphorus-containing probe molecules (e.g., the homologs of trimethylphosphine oxide, TMPO, and trimethylphosphine, TMP) have been adopted to study the acidity of solid-acid catalysts and zeolites63,64,65,66,67. The translation of these methods into MOFs, particularly targeting defects, requires a comprehensive understanding of the host-guest interactions between the probe molecules and the MOF matrices. Here, we combined 31P NMR methods and density functional theory (DFT) calculations to identify the one-to-one correspondence between the 31P signals and the underlying defect structures. The defect sites terminated with or without modulator can be distinguished in 31P spectra from that of the ideal framework. With the molecular understanding of the defect-associated signals, the quantification of defects in MOFs was achieved. It’s expected that our NMR strategy can provide much-needed chemical resolution and quantitative accuracy to the frontier explorations of defects in MOFs and possibly in zeolitic imidazolate frameworks (ZIFs)68,69 and covalent organic frameworks (COFs)70,71 as well.

## Results and discussion

In this work, we focus on the MOF named UiO-66(Zr), as its defects are one of the most researched in the literature. The defective UiO-66 samples are prepared according to the reported procedures25 with or without acetic acid as the modulator (labeled as “dU”). The “ideal” UiO-66 sample is prepared by using HCl to control the pH of solution42 (labeled as “iU”). The formation of defects was determined by the thermogravimetric analysis (TGA) (see the descriptions in the Methods section). Representative transmission electron microscopy (TEM) images of MOF particles are shown in Fig. 1a. In general, the defective UiO-66 appears as separated particles while the ideal ones are aggregated (Supplementary Fig. 1). The powder x-ray diffraction (PXRD) of these samples show expected patterns as the simulated structure (Fig. 1b). The low angle region (2θ = 3°–7°) of our dU samples is largely flat, suggesting the distribution of defects is not as ordered as those in defective UiO-66(Hf) modulated with formic acid53,72.

TMP, TMPO, tributylphosphine oxide (TBPO), and trioctylphosphine oxide (TOPO) (Fig. 1c) are used as the probe molecules in our NMR investigations. The loading of probe molecules is performed on the samples activated under vacuum at 150 °C. The adsorption procedure includes adsorption, equilibration, and solvent removal steps (see Methods section for details). Note that TMP is easily oxidized into TMPO, while TMPO, TBPO, and TOPO are sensitive to moisture. The samples were prepared in Ar or N2 glove boxes to avoid the environmental influence. PXRD patterns of the loaded samples are recorded to ensure that the crystalline structure of UiO-66 is preserved (Supplementary Fig. 2). The nitrogen sorption data were also collected on samples before and after TMPO/TMP adsorption (Supplementary Fig. 3). The probe-loaded samples are packed in solid-state NMR rotors and their 31P spectra are recorded under magic angle spinning (MAS). The detailed experimental procedures and characterization results can be found in the Methods section.

### Identify the local acidity of defects

Both Lewis and Brønsted acid sites can be present in MOFs. The μ-OH that exists in both perfect lattice and defective frameworks are Brønsted acid sites. In a defective MOF, some linkers are missing on defect zirconium atoms. Normally, most of the defect zirconium are compensated by acetate modulators and water (in dU-Ac) creating new Brønsted acid sites. Only a few modulators could fall off, leaving under-coordinated zirconium as Lewis acid sites. In contrast, the under-coordinated zirconium sites could be abundant in structures lack of acetate (in dU-no Ac).

The 31P chemical shift (δ31P) of TMP can be a sensitive probe to distinguish Lewis and Brønsted sites. It has been well researched that, for adsorbed TMP, the 31P signals in the range of −60 to −63 ppm correspond to physical adsorption, those in the range of −25 to −60 ppm correspond to Lewis acid sites, and those in the range of −2 to −5 ppm correspond to Brønsted acid sites66,73. The TMP in ideal UiO-66 has only one signal at −63 ppm indicating only physically adsorbed molecules (Fig. 2a). The TMP does not bond to the μ-OH in ideal UiO-66 suggesting the Brønsted acidity of μ-OH in ideal UiO-66 is relatively weak.

In the defective UiO-66 with acetate modulator (dU-Ac), Brønsted acid sites (δ31P = −2 to −3 ppm) appear. According to the 1H-31P two-dimensional (2D) heteronuclear correlation (HETCOR) spectrum (Fig. 2b), we attribute the Brønsted sites to the defects bonded with water (δ1H = 4.5 ppm). In the defective UiO-66 without acetate modulator (dU-no Ac), we can observe the presence of Lewis acid sites (δ31P = −34 ppm). The Lewis sites are attributed to under-coordinated zirconium atoms which are exposed when there is no acetate modulator. When TMP is coordinated to the Lewis acid sites, the 1H signal of its methyl groups appears as several peaks (δ1H = −0.5–3 ppm) which could be due to the differences in pore environment.

The assignment of TMP signals is further supported by DFT calculations of 31P chemical shift. Figure 2c presents the probable structures for DFT calculation including the physical adsorbed TMP in ideal UiO-66 cages, and TMP at the Brønsted and Lewis defect sites. The calculated shifts (listed in Supplementary Table 1) are in good agreement with experimental results. The calculation shows that the TMP coordinated to the Brønsted site is protonated (i.e., TMPH+). Here, the Brønsted site is formed by the coexistence of water and acetate.25 As UiO-66 was prepared in acidic environment, there are extra protons that may be captured by TMP to form TMPH+. The TMP coordinated to Lewis site may also be accompanied by water or acetate as the neighbor, yet the hydroxyl is improbable due to the unfavorable energetics (Supplementary Fig. 4). The physically adsorbed TMP is likely trapped at the window between the small tetrahedral cage and the large octahedral cage74,75.

Using TMP as the probe, we are able to distinguish the defects with open zirconium sites (Lewis site) from those occupied by water/acetate (Brønsted site). However, in UiO-66 prepared with acetate modulator, Brønsted defect sites dominate. Yet the 31P shift of TMP is not very sensitive to Brønsted acidity, as compared to TMPO. It is because that TMPO has an electron-withdrawing oxygen atom (prefers the H+ of Brønsted sites), while TMP has an electron-donating lone pair (prefers the electron-deficient Lewis sites). In the next section, we use TMPO to reveal the fine structures of Brønsted defect sites.

### The fine structure of Brønsted defects

The 31P spectra of TMPO-loaded UiO-66 samples (Fig. 3a, b) show at least eight different sites (labeled from A to H). In general, these species can be categorized into physically adsorbed species (from 30 to 50 ppm) and chemically adsorbed species (from 50 to 70 ppm)76. Most physically adsorbed and some chemically adsorbed species can be washed away by dichloromethane, yet some chemically adsorbed species cannot be washed away. This suggests the variable bonding strengths and configurations of TMPO in UiO-66. The accurate assignment of these species is challenging and requires a collaborative effort of NMR and DFT calculations.

Let us focus on the physically adsorbed species first. The 31P signals at 32 and 36 ppm (species H and G, respectively) are shifted upfield from that of pure crystalline TMPO (δ31P = 42 ppm). This is an indication of the shielding effect of benzene dicarboxylate (BDC) linkers. Calculations show the H and G species are TMPO being attracted inside or towards the small tetrahedral cages. 2D 31P-31P correlation spectrum (Fig. 3c) shows the cross peaks between the H and G species indicating these two species are in spatial proximity, i.e., in the same or neighboring small cages. The species E (δ31P = 46 ppm) and F (δ31P = 42 ppm) can be attributed to physically adsorbed molecules in the large cage. According to the DFT calculation, the F species is the isolated TMPO while the E species is hydrogen-bonded with water (Fig. 3d). The assignment is corroborated by the intentionally water-treated sample which shows a significant enhancement of E signal (Supplementary Fig. 5).

For chemically adsorbed TMPO, we attribute the signals greater than 60 ppm to the species bonded to Lewis acid sites and the signals between 60 to 50 ppm to those bonded to Brønsted acid sites, based on our DFT calculations (Supplementary Table 2). The A species (δ31P = 62 ppm) only weakly appears in the dU-Ac sample. Since most Lewis sites in dU-Ac are occupied by acetate and water, the weak signal of A is well expected. Both defective and ideal UiO-66 have a strong signal of B species (δ31P = 58 ppm). The B species can be attributed to TMPO bonded to the μ-OH in non-defective cages (Fig. 3d). The species C (δ31P = 55 ppm) and D (δ31P = 53 ppm) only show up in defective UiO-66. Species C is attributed to TMPO bonded to the μ-OH next to a missing BDC linker, while species D can be attributed to TMPO bonded to the defect-associated water. The combinative use of TMP and TMPO probe molecules can provide a holistic and detailed picture of the internal chemistry in MOFs.

### The volumetric accessibility of defects

Besides the chemical properties of defects, the accessibility of defects, based on their pore volume and connectivity, is also important. The accessibility of active sites can have a direct consequence on the catalytic activity, biological functionality, and adsorption properties39,77,78. The evaluation of accessibility can be achieved by varying the size of probe molecules. Here, we use the homologs of TMPO, i.e., TMPO, TBPO, and TOPO which have kinetic diameters of 0.55, 0.82, and 1.1 nm, respectively79.

In ideal UiO-66, the windows between cages are about 0.5–0.7 nm80, which allows the uptake of only TMPO. While in defective UiO-66, the windows open wider and could allow the adsorption of bigger molecules. Therefore, TMPO can access both ideal and defective internal space of UiO-66, while TBPO and TOPO can only access a limited part associated with defects or the outer surface. The quantifications of total adsorbed molecules (measured as the molar concentrations with respect to the BDC linkers) are shown in Fig. 4a, which is achieved by 1H solution-state NMR of the digested samples (Supplementary Fig. 6).

The uptake of TMPO in defective UiO-66 (~0.82) is roughly twice of that in ideal UiO-66 (~0.42). It is estimated that 50% of the pores are defective in this dU sample. The uptake of TBPO in the defective UiO-66 is ~0.36 while its uptake in ideal UiO-66 is only ~0.033. We therefore conclude that most TBPO can only access defective pores. The uptake of TOPO is rather low (<0.01) in both ideal and defective UiO-66. The very few adsorbed TOPO molecules are most likely on the surface of the MOF particles (Fig. 4b).

The 31P chemical shifts of TBPO and TOPO can also provide chemical distinction on sites they adsorb onto. Note that the overall signals of TBPO and TOPO shift about 8 ppm downfield as compared to TMPO79. The separation between chemically and physically adsorbed signals is marked with dotted lines (Figs. 4c, d). For TBPO, the chemically adsorbed species show a similar 31P shift range as that of TMPO (except the 8 ppm offset). There is only one type of physically adsorbed TBPO in UiO-66, which should be attributed to the ones in the large cages. For TOPO, its signals are related to the surface structure of UiO-66 particles which should be interesting for further investigations focused on the surface chemistry of MOFs.

### The quantification of defect concentration

Besides revealing the details of local chemistry and pore geometry in defective MOFs, the 31P signal of probe molecules can also quantify the relative fractions of different adsorption sites. Here, direct polarization (DP) of 31P signals (Fig. 5a) is used to ensure reliable quantification results. The 31P cross-polarization (CP) signals might not be quantitative as the CP efficiency and dynamics81 could vary for different sites (Supplementary Fig. 7). We demonstrate the quantitative results by correlating the intensities of species C and D (Fig. 3d), i.e., the dominant defect-associated 31P signals, to thermogravimetric analysis (TGA) measurements (Supplementary Fig. 8). The plot shows the general linear relation between the two very different measurements. Compared to the conventional TGA method42,43, our 31P NMR methods can provide much-needed molecular details of the defects.

In summary, we established a method based on 31P NMR of probe molecules to characterize the internal chemistry in MOFs with ideal or defective lattices. The Brønsted and Lewis acidity of defects and various bonding configurations of TMP and TMPO adsorption sites have been identified. The volumetric accessibility of pores and defects is revealed by using the homolog series of TMPO with different molecular sizes. The 31P NMR offers both molecular details and reliable quantifications of defects and local environments in MOFs. This method can be adaptable for MOFs with various kinds of pore geometries, metal centers or functional groups. Further utilization of other probe molecules of different chemical affinity or molecular sizes is worthwhile for revealing defects of special chemistry and accessibility.

## Methods

### Synthesis procedures

#### Synthesis of ideal UiO-66

The preparation of ideal UiO-66 follows the procedure described in ref. 42. 5.39 g terephthalic acid (Energy Chemical, China), 3.78 g zirconium tetrachloride (Aladdin, China), and 2.86 mL hydrochloric acid (36-38 wt.%, SCR, China) were added in a flask containing 100 mL of N, N′-dimethylformamide (DMF) (SCR, China). The mixture was stirred at 70 °C to make the solids dissolve completely. The synthesis mixture was transferred to a 150 mL Teflon liner, then sealed in a stainless-steel autoclave. The autoclave was heated in the 220 °C oven for 24 h and UiO-66 particles were formed. The resulting solids were washed with DMF three times. Then, solids were soaked in methanol (SCR, China) for a day to exchange the solvent and the step was repeated three times. Finally, the solids were dried in a 70 °C vacuum oven for 48 h to remove the solvent and then ground into powder.

#### Synthesis of defective UiO-66

The preparation of defective UiO-66 follows the procedure described in ref. 25. 1.00 g terephthalic acid and 1.40 g zirconium tetrachloride were dissolved in 100 mL N, N′-dimethylformamide separately. The solutions were separated into different batches. In each batch, 10 mL of terephthalic acid solution, 10 mL of zirconium tetrachloride solution, and 1–6 mL acetic acid (SCR, China) were mixed in a 40 mL glass vial. The mixtures were placed in an 85 °C oven for 48 h, the washing and drying treatments of resulting UiO-66 particles were the same as above.

#### Adsorption of TMPO and its homologs

The adsorption steps follow the guidance described in ref. 66 with some minor modifications. Before adsorption, the UiO-66 powders were activated at 150 °C under vacuum for 4 h. 100 mg TMPO (or 240 mg TBPO, or 428 mg TOPO) (Alfa Aesar) was dissolved in 15 mL dichloromethane (Yonghua Chemical, China) under Ar atmosphere. 50 mg activated UiO-66 powders were added into the solution with1 h of ultrasonic dispersion. Then the solids were centrifuged out and dried in a 70 °C vacuum oven for 24 h to remove the solvent.

After UiO-66 sample was centrifuged out from TMPO solution, the solids were washed with 10 mL dichloromethane with ultrasonic dispersion. Then the solids were centrifuged out and dried in a 70 °C vacuum oven for 24 h to remove the solvent. Attention: the danger of using dichloromethane must be reminded.82

50 mg activated UiO-66 sample was placed in a glass vial and was transferred into the nitrogen dry box. 0.3 mL TMP (Aldrich) was added into the vial and let it reach equilibrium for 24 h. The sample was vacuumed at room temperature to remove extra TMP.

### Characterization methods

#### Solution-state NMR

1H solution-state NMR spectra were collected on a Bruker AVANCE III 400 MHz NMR spectrometer. The samples of interested were fully dissolved in 2 M NaOH solution (D2O) and loaded in NMR tubes. The recycle delay was set to 6 s. The quantifications of probe molecules were determined by the integrals of their 1H signals, normalized by the integral of the benzene 1H signal of terephthalic acid.

#### Solid-state NMR

All the experiments were performed on a Bruker AVANCE III HD 600 MHz spectrometer at resonance frequencies of 150.84 MHz for 13C, 242.80 MHz for 31P, and 600.13 MHz for 1H. Magic angle spinning (MAS) experiments were performed on 3.2 mm MAS probes at a spinning speed of 15 or 18 kHz. The 1H signals were referenced to those of adamantane at 1.8 ppm. The 31P signals were referenced to that of NH4H2PO4 at 0.81 ppm.

For CPMAS, the 1H-31P cross-polarization contact time was 4.0 ms and the 1H decoupling power was 104 kHz. For 1H-31P heteronuclear correlation (HETCOR), the CP contact time was 2.0 ms and the proton spin diffusion time was 0.1 ms. For 31P-31P 2D correlation spectra, the CP contact time was 2.0 ms and the 10 ms mixing time was filled with radio frequency-driven recoupling (RFDR) pulses.

For 31P direct polarization (DP) quantification experiments, the recycle delay was set to 15 s which is five times of the 31P spin-lattice relaxation time (Supplementary Fig. 7). The 1H decoupling power was 100 kHz. The DP spectra were deconvoluted into eight Gaussian peaks (species A to H) and their molar factions were determined by their integral areas. The total amount of adsorbed molecules was determined by 1H solution-state NMR of digested samples.

#### Powder X-ray diffraction (PXRD)

The PXRD patterns were obtained on a Rigaku Ultima IV diffractometer using Cu-Kα radiation (λ = 1.5418 Å, tube operating at 40 kV and 30 mA), the 2θ range is 3°–50° and the scanning speed is 10°/min.

#### Nitrogen sorption measurements

Nitrogen sorption measurements were performed on a Belsorp max instrument at 77 K. The samples were pretreated under vacuum at 150 °C for 5 h. Approximately 40 mg of activated sample was used in each experiment.

#### Transmission electron microscope (TEM)

TEM images were obtained on a Hitachi HT7700 microscope.

#### Thermogravimetric Analysis (TGA)

TGA experiments were conducted on an SDT Q600 TGA instrument. The samples were heated from room temperature to 700 °C at a rate of 10 °C/min under 120.0 mL/min dry air flow.

The TGA curves can be divided into three parts according to the drops and plateaus: (1) from room temperature to 100 °C, the removal of solvents and adsorbed gases; (2) 100–350 °C, the loss of hydrogen bonding water, hydroxyl groups, and acetate modulator; (3) 350–700 °C, the loss of organic linkers (i.e., BDC) and the UiO-66 breaks down into zirconium oxide, ZrO2.

The final mass of ZrO2 was normalized to 100% (remaining weight at 600 °C). The weight of ideal UiO-66 at 350 °C is 220.2% which agrees with the chemical formula of Zr6O6(BDC)6, In contrast, the weight of defective UiO-66 at 350 °C is below 220.2% suggesting the deficiency of BDC linkers. The defective UiO-66 takes the formula of Zr6O6+x(BDC)6-x where x is the number of linker deficiency. x can be calculated by the equation below.

$$\frac{w\%(350\,{{^\circ }}{{{{{\rm{C}}}}}})-100\%(600\;{{^\circ}}{{{{{\rm{C}}}}}})}{220.2\%-100\%}=\frac{6-x}{6}$$

here, w%(350 °C) is the normalized weight at 350 °C.

Defect concentration is calculated as

$${{{{{\rm{defect\; concentration}}}}}}=\frac{x}{6-x}$$

### Theoretical calculations

The details for theoretical calculations are described in the Supplementary Methods.