Supporting Information Transformation of Engineered Nanomaterials through the Prism of Silver Sulfidation

The USAXS instrument uses Bonse-Hart type crystal optics to extend the lower end of the scattering q range of SAXS to 10-4 Å-1, a value that is normally inaccessible to SAXS instruments in the pinhole geometry. Here, q = 4π/λ × sin(θ), where λ is the X-ray wavelength and θ is one half of the scattering angle 2θ. The USAXS instrument measures absolute scattering intensity, i.e., the differential scattering cross section dΣ/dΩ, where Σ is the scattering cross section per unit sample volume and Ω is the solid angle. For the experiments reported in this study, we conducted the USAXS experiments in the standard 1-D collimated geometry. X-ray wavelength λ was 0.05904 nm, which corresponds to an X-ray energy of 21.0 keV. The relative wavelength spread Δλ/λ ≈ 10-4. At the sample position, the X-ray photon flux was ≈ 1013 photon/s/mm2. The beam size for USAXS experiment was 0.4 mm × 0.4 mm.


Introduction
Due to their novel physical and chemical properties, engineered nanomaterials (ENMs) have found increasing applications in medicine, 1 energy, 2 sensor technologies, 3 and consumer industries. 4 Once deployed, ENMs are subject to their working environments, where ENM structural transformation oen occurs. 5 A proper assessment of the efficacy, safety, and environmental impact of ENMs requires an understanding of the transformation pathway of these materials. 6 ENM transformation and its related kinetics, however, have only been explored very limitedly, largely due to the complexity arisen from concurrent transformations at different length scales in situ. A rigorous and comprehensive determination of ENM transformation in a mechanistic way requires not only advanced materials characterization tools but also in-depth knowledge of the materials system to allow proper modeling of complex data. This lack of understanding presents a major challenge in fullling the promises of these novel and attractive materials.
ENM transformation comes in the form of chemical transformations such as oxidation, suldation, or reduction reactions, physical transformations such as aggregation and agglomeration, and biologically and environmentally mediated transformations such as surface adsorption of macromolecular ligands or ions. [7][8][9][10][11][12] This vast parameter space makes elucidation of ENM transformation difficult. Nevertheless, to predict ENM performance and environmental impacts, knowledge of the extent and rate of specic transformations must be acquired.
Due to their antimicrobial capabilities, silver nanoparticles (AgNPs) are among the most widely used ENMs. 13 For ENMs, one central concern is their environmental impact and consequent social cost. 6 For AgNPs in particular, while they can effectively release silver ions in targeted applications, they can also pose signicant risks to the ecosystem and overall environment. [14][15][16] Thus, it is important to characterize and understand AgNP transformation and its kinetics in realistic environmental settings to elucidate their toxicological behavior. Once discharged into the environment, AgNPs are particularly subject to physiochemical interactions with natural organic matter (NOM), especially humic substances, which act to modify the stability and mobility of AgNPs through electrosteric interactions or hydrophobic effects. [17][18][19] Consequently, humic substances inuence the stability, dissolution, and aggregation behaviors of AgNPs and affect their transport properties and environmental persistence. [20][21][22] To determine suldation kinetics of AgNPs, most existing studies relied on proxy measurements such as ion selective electrodes and colorimetric analysis to measure the transformation rates and to infer the mechanism. [23][24][25] A separate study of ours strongly suggests that results from such indirect measurements alone can be inadequate and even misleading and that direct measurements that monitor the chemical changes of the metallic NPs are necessary to elucidate the underlying structure transformation. 26 From the structure point of view, the phase and morphology of AgNPs transform in the environment. The transformation pathway has been extensively investigated in both lab-based and realistic environment settings. 25,[27][28][29][30][31][32] However, a unied picture of AgNP transformation pathway is yet to emerge. An accurate determination of the kinetics remains elusive. On the one hand, experimental ndings from different studies oen present contradicting results, preventing general conclusions from being drawn and making it difficult, if not impossible, to establish thermodynamic models with high predictability. On the other hand, it has been considered that "the large number of permutations of nanomaterials and environmental systems makes (comprehensive individual-based case studies) impossible in practice". 5 Hence, simplied yet controlled studies of ENM transformations in representative environments may be best positioned to unveil the underlying transformational mechanisms.
Meanwhile, the characterization of structural transformations in ENMs presents a well-documented fundamental challenge. 5,24,28 While various ex situ analytical techniques play a central role, they usually focus on the nal transformation product and do not reveal transient states. Thus, ex situ methods oen fail to directly capture the rate and extent of the transformations, an issue so signicant that a recent Consensus Study Report from the Unites States National Academies 33 identies in situ and in vivo methods to determine the potential and rate of fundamental ENM transformation processes as an urgent research priority.
One key aspect of the characterization challenge is that structural transformations of ENMs generally occur across a broad range of length scales. For example, chemical transformation and dissolution of ENMs oen occur at the atomic level whereas aggregation and agglomeration occur at the nanoand micro-meter scales. To overcome this challenge, various synchrotron-based in situ X-ray techniques have been developed recently to probe nanoparticle synthesis, growth, and transformation in a liquid environment. In particular, one representative work published in Science in 2017 by Sun et al. constitutes one of the rst papers that detail the ENM transformations in real time (oxidation process of colloidal Fe-Fe x O y NPs). 34 Similarly, to offer a possible solution to this metrological challenge, with the overarching goal of a more solid understanding of the structural transformational pathway of ENMs, we have conducted a series of studies of AgNPs using ex situ transmission electron microscopy (TEM) and both in situ and ex situ synchrotron-based ultra-small angle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD). TEM presents direct visual evidence of the morphology and extent of the transformation of individual ENMs. In situ X-ray studies allow characterization of the rate and extent of the transformation on a statistically signicant basis. Importantly, when USAXS, SAXS, and XRD are combined, they encompass a continuous length-scale range from sub-angstrom to several micrometers, [35][36][37][38] which allows both chemical and physical transformation of ENMs to be determined simultaneously. Ex situ X-ray studies allow the crystallinity and extent of the structure transformation of the end-product to be understood comprehensively. Comparing with the techniques used in Sun et al., 34 our approach has the added advantage of being able to unambiguously determine the aggregation state of the AgNPs, due to the broader accessible q range of USAXS. 39 When used together, these techniques provide a window to peer into the intricate transformational kinetics of ENMs.
Our study is conducted in a controlled model system, where suldation is investigated for monodisperse, polyvinylpyrrolidone (PVP) coated AgNPs suspended in water with NOM (Suwannee River fulvic acid). ENM reactivity is strongly related to particle size. 40 The narrow size distribution of AgNPs used in this study allows the suldation transformation process to be differentiated from other processes, quantitatively characterized, and the transformation rate to be established precisely. Suldation is the key environmental structural transformation of interest for AgNPs. 41,42 The transformation of AgNPs in the presence of NOM is of intense current research interest because of the pervasiveness of ENM interactions with NOM in realistic environmental settings. We hope that our controlled study provides insights into the specic structural transformations and their kinetics associated with suldation of AgNPs in increasingly complex and realistic environmental settings, and more generally, helps establish a methodology that determines the transformation rate and potential of ENMs.

Starting materials ‡
The AgNPs are derived from NIST Reference Material (RM 8017, NIST, Gaithersburg MD), with a nominal core diameter of 75 nm and coated with PVP of average molecular weight of 40 kDa. 43 Sodium sulde nonahydrate ($99.99% trace metal basis) was acquired from Sigma-Aldrich (St. Louis, MO) and used without further treatment. We acquired Suwannee River Fulvic Acid Standard I (FA) from the International Humic Substances Society (St. Paul, MN). 44 The moderately hard reconstituted water (MHRW) solution was prepared following a protocol established by the U.S. Environmental Protection Agency. 45 TEM measurements TEM images were acquired using a probe-corrected FEI Titan transmission electron microscope operated at 300 kV. Highangle annular dark eld scanning TEM (HAADF-STEM) images were acquired using a Fischione Model 3000 detector and the inner collection angle was set to z71 mrad. Electron energy loss spectroscopy (EELS) data were collected with an outer collection angle of z11 mrad. For EELS and HAADF-STEM a convergence angle of z13.5 mrad was used and the probe current was typically 20 pA to 30 pA. Nanobeam electron diffraction (NBED) patterns were collected with a semi convergence angle of z1 mrad. Tomography datasets were acquired in 3 steps. The probe convergence angle was z9 mrad and a detector inner collection semi-angle of z42 mrad or z58 mrad was used. The probe current was z10 pA. The tilt series data was aligned and reconstructed using Inspect 3D and OpenMBIR, 46 respectively. Data visualization was performed using Avizo.
The lyophilized AgNP RM containing 2 mg of Ag and 20 mg of PVP was reconstituted by redispersion in 2 mL of deionized water. The resulting suspension was puried by centrifugal ultraltration using Amicon Ultra-4 centrifugal lter units with nominal molecular weight limit of 100 kDa (EMD Millipore, MA). Mixture of FA solution and MHRW was pH adjusted using NaOH to 7.0 AE 0.2. AgNPs were added to the mixture. Mixing of AgNPs was achieved by manual shaking for 10 s. Freshly prepared Na 2 S solution was nally introduced to avoid potential interaction between the sulde and NOM. 29 In the nal stock suspension, the mass concentration of AgNPs was 1.62 mg L À1 , and the mass ratio between FA and Ag and the molar ratio between S and Ag were 5.0 and 0.72, respectively. TEM aliquots were taken at 8 min, 30 min, 1 h, 8 h, and 24 h aer Na 2 S was introduced. Puried samples were deposited onto Ni grids with a carbon support lm stored in a vacuum box and examined typically within 2 days of preparing the grid.

Synchrotron measurements
Synchrotron USAXS, SAXS, and XRD experiments were performed at the USAXS facility at the Advanced Photon Source (APS), Argonne National Laboratory. 47,48 The X-ray wavelength was 0.05904 nm. The absolutely-calibrated USAXS measurements were conducted using the instrument's standard 1-D collimated geometry. 49 The SAXS and XRD experiments were conducted using two standalone Pilatus 2-D area detectors (Model: 100K-S, Dectris, Baden, Switzerland). 50 The data acquisition times for USAXS, SAXS, and XRD were 90 s, 30 s, and 30 s, respectively.
The in situ measurements were conducted with a continuous ow of the sample suspension through a custom-made ow cell, following the steps below: (1) 1.5 mL of pH adjusted (pH 7) FA solution (64.86 mg FA was dissolved in 0.7 mL water and 0.8 mL MHRW) was added into 6 mL of puried AgNP suspension (Ag concentration 2.16 mg mL À1 ) in a vial to achieve a mass ratio for FA to AgNPs of 5 : 1. Aer vigorous shaking for 1 min, the combined USAXS/ SAXS/XRD dataset was collected as the baseline of the pristine state of the AgNP suspension.
(2) 0.022 g crystalline Na 2 S$9H 2 O was dissolved in 0.5 mL of DI water. AgNP concentration aer the addition of Na 2 S was 1.62 mg mL À1 . In situ experiments were started aer the Na 2 S solution was added to the AgNP suspension by conducting a repeated sequence of USAXS, SAXS, and XRD measurements. Each set of USAXS/SAXS/XRD measurements took z5 min.
The ex situ samples were prepared approximately 10 days before the synchrotron measurements following a similar protocol to that of the in situ sample with the same starting materials. The main difference with the ex situ samples was that the molar ratio between S and Ag was adjusted systematically from 0 to 5. Details of these samples can be found in Table 1. The ex situ measurements were conducted using standard liquid cells available at the beamline. Necessary scattering data correction steps with liquid cells are described elsewhere. 51 More details about the synchrotron measurements can be found in the ESI. †

Results and discussion
Ex situ TEM characterization TEM provides direct visualization of nanoparticle structure and morphology, and has been used extensively to determine the fate of AgNPs upon environmental exposure. 27,29,30,[52][53][54] In this study, we used a suite of TEM-based analytical techniques to characterize the morphology, atomic structure, and elemental distribution of individual AgNPs at different stages in the sul-dation process. The pristine AgNP specimens showed no aggregation under TEM. 43 Analysis of 96 particles showed a particle diameter of 67.5 AE 5.1 nm. The AgNPs were in the form of polyhedrons predominately with {111} and {100} surface terminations. The vertices of the particle were nominally {110} terminated, and the particle edges oen had a rounded appearance resulting from surface steps and higher-order surface terminations, a feature identied earlier in a silver cube nanoparticle system. 55 Highresolution images and an atomistic model of pristine AgNPs illustrating the most commonly observed AgNP geometry are shown in ESI. † Chemical mapping by STEM-EELS identies the spatial distribution of elements within the reacted AgNPs. An example of colorized elemental maps from AgNP reacted for 1 h is shown in Fig. 1. The composite image in Fig. 1(b) shows that the reacted AgNP is composed of Ag and S. The distribution of Ag and S, however, is not uniform. As shown by Fig. 1(c) and (d), S is enriched near the surface, while Ag is identied in all parts of AgNP. The HAADF image in Fig. 1(a) reects this compositional inhomogeneity as the image contrast of this technique is sensitive to atomic number. As reported previously, 29 when pH $ 7, Ag binds strongly with S in natural system following a direct conversion: 4Ag + 2HS À + O 2 / 2Ag 2 S + 2OH À . The STEM-EELS result suggests initially suldation is dominated by a surface reaction between Ag and S with the silver core intact, suggesting a direct exchange mechanism rather than a vacancy exchange mechanism observed in the Kirkendall effect. 25 The atomic number contrast provided by HAADF-STEM can be used to track the extent of the structural transformation from Ag to Ag 2 S. Typical TEM images of aliquots taken at 8 min, 1 h, 8 h, and 24 h aer Na 2 S was introduced are shown in Fig. 2. Here all the AgNPs were h111i oriented to facilitate intuitive comparison. The reacted nanoparticles contained a bright core and less bright regions growing at particle vertices along the {110} terminations, as shown in Fig. 2(a). With increasing reaction time, the overall particle size increased slightly, the relative volume of the Ag cores decreased, and the relative volume of the Ag 2 S domains increased. The growth of the Ag 2 S domains eventually led to their impinging on one another ( Fig. 2(b-d)). Aer 24 h, unreacted silver core was clearly visible, indicating incomplete conversion. More HAADF-STEM data, as well as tomographic reconstructions of two AgNPs suldized for 8 m and 24 h, can be found in Fig. S3-S8 in ESI and the Movies. † We used NBED to examine the degree of crystallinity of the Ag 2 S domains and Ag core during the structural transformation. Typical diffraction patterns are shown in Fig. 3(a). Both Ag core and Ag 2 S domains are crystalline. Ag has a structure of Fm 3m with lattice parameter a ¼ 0.409 nm. Ag 2 S has a structure of More NBED data are shown in Fig. S9. † It is worth noting that at all reaction intervals, our results show Ag core and Ag 2 S domain were fully crystalline, a result in contradiction to some reports in literature. 25,32 For example, Levard et al. found that without NOMs, with the S/Ag ratio in the range of 0.019 and 0.719, PVP-coated AgNPs transformed to amorphous Ag 2 S. 32 NOMs are known to affect colloidal stability and Fig. 1 The contrast of the HAADF image of a Ag 2 S/Ag particles after 1 h (a) is sensitive to the atomic number difference between the Ag 2 S and Ag domains. (b) Colorized EELS spectrum images from the same particle where green is sulfur (c) and silver is blue (d).
dissolution of AgNPs. Our results infer that NOMs may also regulate the atomic-scale structure transformation during silver suldation.
Interestingly, our results demonstrate that the suldation process is sensitive to the faceting of the Ag surface, as shown in Fig. 3(b). The {111} surfaces at the top and bottom of the AgNPs remained passivated for all aliquots examined (up to 24 h). Amorphous passivation layers formed with nm layer thickness. It was not possible to conclusively conrm the phase of this passivation layer. However, based on the HAADF image contrast and strong reactivity between Ag and S makes Ag 2 S most likely. This result is in good agreement with a recent study of Ag-Ag 2 S triangular hybrid nanoprisms by Mirkin et al., where a thin passivation layer of Ag 2 S on the Ag {111} facets was indirectly observed. 56 The {110} terminated vertices, on the other hand, did not passivate, which allow Ag 2 S nucleation and growth. {100} and {111} surfaces located at the AgNP sides were not observed to function as separates sites for the nucleation and growth of Ag 2 S, but were eventually transformed to Ag 2 S as the reaction front proceeds inwards from the tips towards the core. The conversion, starting from the vertices, proceeds macroscopically along the h110i directions, however the atomic level mechanism of the reaction front appears to be the collective response of the transformation occurring along of multiple crystal planes as illustrated from slices of a tomographic reconstruction shown in Fig. S10. † The dependence of reactivity of Ag surface on its crystallographic orientation was known for bulk Ag, where it was shown that the formation of Ag 2 S adlayer can only occur without signicant reconstruction of the outermost atomic layer of the substrate. 57 For nanosilver, however, the reaction energetics can be further complicated by geometrical effectsfacets at the tip may have energetically unfavorable atomic structures that lead to higher reactivity, which may contribute to our observation of suldation progression from the vertices of the AgNPs, an observation also made by others. 58,59 Elucidation of the reactivity will require density functional theory calculations, and is out of scope of this paper. Nevertheless, our observation of different reactivity along different crystallographic orientations is clear.

In situ SAXS/XRD
Synchrotron-based SAXS and XRD, as an analytical tool, can reveal kinetics associated with nanoparticle transformation, aggregation, and agglomeration. 60 In our in situ SAXS/XRD study, we used SAXS to investigate the morphological transformation kinetics of the AgNPs, and XRD to investigate the structural transformation of the AgNPs, acquiring complimentary structural information across a sub-nanometer to micrometer length scale. Time-dependent SAXS data are shown in the inset of Fig. 4, with acquisition time indicated by a color scale. As time increases, the scattering curves shi to smaller q, indicating a gradual increase of particle size, consistent with TEM observations, which show growth of Ag 2 S domains along the {110} facets. The growth of Ag 2 S domains is also supported by the change in color of the AgNP suspension during the in situ study. The color of the initial AgNP suspension was gray. Soon aer the introduction of Na 2 S solution, we observed the suspension color changed to, and remained, black until the end of the measurements, which is consistent with reported optical properties of Ag 2 S. 28 The Bessel oscillations in the scattering curves persisted throughout the duration of the measurements, indicating that a narrow particle-size distribution was maintained. A distinct plateau is always identiable in the low-q regime of the scattering curves, showing that the AgNPs did not form aggregates (i.e., they did not coalesce) as they were being suldized and the particles remained well dispersed. 36 Thus, the retained colloidal stability of the AgNPs in suspension during the suldation process under the conditions measured is conclusively established.
We analyzed the time-dependent evolution of the mean particle size assuming that the particle volume-size distribution follows a Gaussian form using the SAXS analysis package, Irena. 61 As we show later, it can be established that, under our experimental conditions, the total mass of Ag in the transformed Ag/Ag 2 S nanoparticles is preserved during the suldation process. Treating this simply as an assumption here, we derived the conversion ratio, dened as the ratio of Ag mass in reacted Ag 2 S product within any one nanoparticle to its starting pristine (pure Ag metal) Ag mass value, from the mean size of the particles. Details of the SAXS analysis are provided in the ESI. † For pristine (unreacted) AgNPs, we found that the particle diameter with standard uncertainty is (68.6 AE 6.4) nm. Because in situ SAXS experiments characterized z1.5 Â 10 8 AgNPs at one time, this result is statistically-representative and conrmed that the AgNPs had a very narrow size distribution. It is known that the size of nanoparticles is strongly tied to their activation energy and reaction rate constant. 62 For kinetic rate determination of the AgNP transformation, a goal of the current in situ study, we emphasize that the identied monodispersity of the pristine AgNPs is important, and we recommend that the size monodispersity be carefully controlled in future rate studies. Additionally, we point out that X-rays are sensitive to high-Z elements because of their high X-ray scattering-length density. The SAXS NP diameters measured concern the physical dimensions of the AgNPs and the subsequent reacted Ag/ Ag 2 S NPs only, but they provide no direct information regarding the PVP coating and presence of NOM materials near the surface of the NPs. 36 Fig . 4 shows the time-dependent conversion ratio of Ag to Ag 2 S, a transformation conclusively demonstrated by TEM. Hence, this conversion curve is directly related to the suldation kinetics of AgNPs. The conversion was rapid initially, then gradually slowed down, approaching a plateau. We analyzed the kinetic rate using a pseudo-rst order rate model (in the form of exponential decay), similar to one previously used to describe the suldation kinetics of AgNPs. 29 We found that the rate constant is (0.0107 AE 0.0005) min À1 . Interestingly, this value is smaller than the kinetic rate identied for 30 nm nanoparticles in Liu et al., 29 where the suldation kinetics is deduced from the time-resolved depletion of sulde. While it might be tempting to conclude that the larger specic area of smaller AgNPs leads to a faster suldation, important differences between these two experiments must be noted. In contrast to probing the suldation of AgNP powder with no coating by Na 2 S in water, our experimental conditions approximate more closely to a realistic environmental setting, where factors such as the presence of NOM, surface functionality, as wells as particle size, can all affect the rate of transformation kinetics. Such differences point to the challenges in predictive modeling, where complexity due to a large set of parameters must be expected. 63 Our TEM and SAXS results unequivocally demonstrated that under our experimental conditions, AgNPs did not aggregate aer 24 h of reaction. We also conducted further studies, where we investigated the role of pH, the presence of fulvic acid, and the type of humic substance, on the colloidal stability during suldation of the same type of AgNP suspension in both water and MHRW. These results, to be reported elsewhere, again show consistent colloidal stability of the AgNPs over a long period of time (hours to days). This consistent colloidal stability contrasts with some of the existing studies of AgNPs in real and simulated environmental systems, where aggregation behaviors were observed for AgNPs. 24,27,31,64,65 Furthermore, while recent work has suggested that the presence of humic substances may aid the colloidal stability of AgNPs, 29,66,67 Zhu et al. reported that humic acid modied the surface coverage of PVP via adsorption or ligand exchange and suldation removed PVP from the particle surface and consequently reduced the colloidal stability of AgNPs. 20 This wide spectrum of reported results is not surprising. The colloidal stability of nanoparticles requires a delicate balance between forces such as van der Waals attraction, steric repulsion, coulombic interaction, and depletion forces. In ENMs, it is oen the surface ligand and coating that plays a central role in controlling their colloidal stability and aggregation state. 40 Our results, as additional evidence, invite a systematic investigation of the detailed role of sterically protecting polymers and NOMs on the colloidal stability of model AgNP systems during suldation, an essential component of ENM processing and application. 40 While SAXS probes the physical morphological transformation of the AgNPs, XRD, being a diffraction technique, provides structural ngerprints of the phases present and their evolution. We devised a XRD data reduction procedure for weak diffraction intensity of ENMs in solution, documented in the ESI. † Fig. 5 shows the time-resolved XRD results, which illustrate in real time the variation of crystalline phases of the AgNPs. Initially (Fig. 5(a)), the pristine AgNPs were single-phase silver, demonstrated by the diffraction data perfectly matching the simulated Ag XRD reference stick pattern (the reference stick patterns here and hereinaer were simulated using the space group and lattice parameters identied in the TEM section). Fig. 5(b) presents a two-dimensional contour plot of the in situ XRD patterns recorded at different times during the suldation process. It is evident that with increasing reaction time (from bottom to top), the primary silver peak intensities decreased, and concurrently a family of weak diffraction peaks emerged with increasing intensity, indicating a gradual structure transformation. Fig. 5(c) shows the XRD pattern acquired at 368 min into the reaction. A comparison with the XRD reference stick patterns of Ag and Ag 2 S clearly shows the presence of Ag 2 S, again proving Ag was transformed to crystalline Ag 2 S. Ag XRD peaks persisted at 368 min, albeit at a lower intensity compared with their counterparts in the pristine state, a result that is in good agreement with the TEM ndings.
We performed quantitative analyses on the peak proles of two stand-alone peaks: the Ag 2 S (112) peak and the Ag (220) peak, as highlighted in Fig. 5(b), to investigate the crystalline transformation kinetics. These results are shown in Fig. 5(d) and (e). Here, we normalized the integrated peak intensity of Ag (220) peak to that of the pristine Ag, translating XRD peak intensity to the molar ratio of Ag transformed to Ag 2 S. We performed a least-squares analysis on the intensity evolution of these two peaks using the same exponential decay model as in the SAXS kinetics analysis. The acquired rate constants from the XRD analysis are summarized in Table 2. The rate constants acquired from the declining Ag (220) peak and the increasing Ag 2 S (112) peak are equivalent within the uncertainties, which suggests that Ag transformed to Ag 2 S without signicant dissolution. Furthermore, a comparison of the SAXS and XRD kinetic time scales shows that they are similar, indicating that both SAXS and XRD probed fundamentally the same process, i.e., the increase in particle morphology (size) is directly related to the chemical transformation from Ag to less dense Ag 2 S.
Notably, at the end of the in situ experiment, SAXS and XRD results demonstrate remarkable consistency and pointed to the same conversion ratio of Ag to Ag 2 S (SAXS: 0.46 AE 0.04, XRD: 0.50 (c) XRD pattern recorded from AgNP suspension at 368 min after the sulfidation process was initiated. The reference stick patterns were simulated using the space groups and lattice parameters shown in the TEM section. (d) shows the conversion ratio of Ag to Ag 2 S, based on the integrated intensity of Ag (220) peak shown in its inset. (e) shows timedependent evolution of the integrated intensity of Ag 2 S (112) peak. In (d) and (e), the solid lines represent least-squares fits of the kinetics data using an exponential decay function. Table 2 Kinetic rate and time scales acquired from morphological analysis of the AgNPs and the peak profiles analyses of Ag (220) peak and Ag 2 S (112) peak Rate constant (min À1 ) USAXS/SAXS 0.0107 AE 0.0005 XRD, Ag (220) peak 0.0138 AE 0.0005 XRD, Ag 2 S (112) peak 0.0132 AE 0.0012 AE 0.05). Interestingly, despite an abundance of sulde ions during the in situ experiment, only 50% of Ag was transformed. The reason for this is unclear. It is known that sulde depletion can occur when humic substances are present, even without AgNPs. 29 We speculate that possible sulde-NOM complexing may reduce the availability of sulde during this initial stage of suldation.

Ex situ SAXS/XRD
While the in situ SAXS/XRD experiments provide insights into the kinetic rate of the AgNP transformation during suldation, they nevertheless cannot capture the entire transition pathway due to limitations imposed by beam time availability. To understand the impact that the molar S/Ag ratio has on the structure and morphology of the end-product, we conducted ex situ SAXS/XRD measurements on samples that had been subject to suldation at different S/Ag ratios for approximately 10 days.
We note that at this AgNP concentration and pH, the oxidation rate of AgNPs is very slow. Repeated single-particle inductively coupled plasma mass spectrometry (ICP-MS) measurements of 1 mg mL À1 AgNP suspensions did not show any signicant change in particle size over >200 days. Hence, we can assume the change in the particle morphology and crystal structure is due to the suldation reaction, alone. Fig. 6 presents the SAXS results for the ex situ samples listed in Table 1. When the S/Ag molar ratio was between 0 and 1, the colloidal stability of AgNPs was maintained, and the narrow size distribution and the overall particle morphology were preserved as evidenced by the continued presence of the Bessel oscillations. However, at S/Ag ¼ 5, such observations were no longer valid. Here, we observed scattering signatures from aggregates, as well as visible sedimentation, leading to a signicant decrease of the scattering intensity as q / 0. For S/Ag # 1, the mean radius increased monotonically with increasing S/Ag ratio (Fig. 5(b)), indicating that AgNP suldation progressed in accordance with the total amount of available sulde in the starting solution. Fig. 7(a) captures the phases present in the ex situ AgNP samples aer suldation reactions have occurred with different S/ Ag ratios. A comparison with the Ag and Ag 2 S reference stick patterns shows that, on increasing the S/Ag ratio, the Ag peak intensities monotonically decreased and Ag 2 S peak intensities monotonically increased. This reveals a systematic transformation from Ag to Ag 2 S depending on the availability of sulde in the solution. It is worth highlighting that at S/Ag ¼ 1, the characteristic Ag diffraction peaks disappeared altogether. With the high sensitivity of the synchrotron XRD experiment, this strongly indicates that the transformation from Ag to Ag 2 S was practically complete. At S/Ag ¼ 5, these observations again broke down, with only amorphous diffraction patterns observed. Together with the SAXS observation of nanoparticle aggregation at this S/Ag ratio, these abnormalities suggest that the transformation pathway for Ag suldation strongly depends on the availability of sulde in the solution, with a switchover point between S/Ag ¼ 1 and S/Ag ¼ 5 for both colloidal stability and structural transformation.
The integrated peak intensities of the Ag (220) peak and the Ag 2 S (112) peak are shown in Fig. 7(b) and (c). Notably, in both plots, when S/Ag is between 0 and 0.5, the integrated intensities demonstrate a linear dependence on S/Ag. A linear least-squares regression analysis yields that for Ag, I Ag (220) ¼ 0.01665(38) À 0.02828(185) Â S/Ag, and for Ag 2 S, I Ag 2 S (112) ¼ 0.0006(6) + 0.0048(19) Â S/Ag. XRD data at S/Ag ¼ 1 shows the Ag to Ag 2 S transition to be complete. Hence, we can assume that the integrated intensities at S/Ag ¼ 1 represent the terminal intensities, which are plotted as the dashed horizontal lines in Fig. 7(b) and (c). The intersects between the dashed lines and the linear ts, therefore, point to the threshold Ag/S ratios necessary for the full transition from Ag to Ag 2 S to occur. Based on this, we found that for the Ag (220) plot ( Fig. 7(b)), the intersect is located at S/Ag ¼ 0.589 AE 0.052, whereas for the Ag 2 S (112) plot (Fig. 7(c)), the intersect is located at S/Ag ¼ 0.604 AE 0.030. This excellent agreement reveals that the full atomic structure transformation requires z0.6 S/Ag molar ratio, which is higher than the 0.5 molar ratio that the stoichiometry of Ag 2 S dictates. In the context of the peroxidation of Na 2 S during storage and potential complexing between S and humic substances, 29,68,69 this may not be completely surprising. We further deduced the mass of silver within individual nanoparticles in the ex situ samples. In particular, data shown in Fig. 7(a) established that with S/Ag ¼ 0, the nanoparticle composition is silver only, and that with S/Ag ¼ 1, the composition is Ag 2 S only. From the SAXS analysis, we determined that the particle radii at S/Ag of 0 and 1 are (33.5 AE 0.3) nm and (39.5 AE 0.4) nm, respectively. With Ag and Ag 2 S densities being 10.49 g cm À3 and 7.23 g cm À3 , respectively, we calculated that the Ag mass per nanoparticle is (1.652 AE 0.015) Â 10 À15 g for S/ Ag ¼ 0 sample (ES0) and (1.626 AE 0.017) Â 10 À15 g for the S/Ag ¼ 1 sample (ES4), respectively. The equivalence of these two masses strongly indicates mass preservation of Ag during the suldation process. In other words, although oxidation is a necessary step of the suldation reaction, when excess S 2À is available, Ag + reacts with near-surface sulde and remains part of the Ag/Ag 2 S nanoparticle. Hence, no Ag is leached to the solution in the form of soluble Ag + ions. This result is consistent with a previous proposal concerning the suldation mechanism by Liu et al., where it was suggested that when the concentration of sulde is high ([sulde] ¼ 0.025 mg L À1 ), AgNPs directly transform to Ag 2 S without intermediate dissolution and reprecipitation. 29 The absence of Ag dissolution is critically important because dissolved Ag + ions provide the main basis for the antimicrobial properties of AgNPs and the main cause for environmental concerns associated with AgNPs. 24 With our analysis, we are able to show that when S/Ag is below the aforementioned unknown threshold value (higher than 1 but less than 5), in the system that we investigated, suldation not only reduces the toxicity of AgNPs due to the extremely low solubility of Ag 2 S, 31 but more importantly, it prohibits soluble Ag + ions from leaching into the solution, thus signicantly limiting the environmental impact of AgNPs. It is also worth noting that while the kinetics of AgNP suldation may be affected by the surface state of the nanoparticles, previous studies have asserted that the thermodynamics may not strongly depend on the surface coverage of AgNPs due to stability constant considerations. 70,71 The validity of this assertion can be further tested by in situ and ex situ studies similar to what is now reported in this work.

Conclusions
Quantitative understanding of the transformation pathway and its related kinetics of ENMs is a major challenge that impacts the application and certication of these promising materials. Using one of the most prevalent and industrially and environmentally relevant ENMs transformation as an example, in this paper, we have systematically investigated the fundamentally important structural transformation of AgNPs during their suldation in water in the presence of natural organic matter. Our methodology involves using a model system where the narrow size distribution of the AgNPs was carefully controlled, a prerequisite for statistically meaningful rate determination due to the well-known strong dependence of nanoparticle reactivity on particle size. Taking advantage of the high quality of the colloidal AgNPs, we applied the synchrotronbased in situ USAXS, SAXS, and XRD techniques, which are sensitive to the NP size, morphology, electron density, and phases, to precisely track the suldation process of the colloidal AgNPs-Ag/Ag 2 S NPs in real time. By combining rigorous ex situ structure determination using analytical TEM, in situ and ex situ synchrotron SAXS and XRD, we addressed some of the major unanswered questions about AgNP transformation in environmental settings such as the rate and extent of the suldation, as well as the aggregation and dissolution behavior.
We found that the extent of suldation of faceted AgNPs has a strong preference on the crystallographic faceting. Passivation layers with nm-scale layer thicknesses developed on {111} surfaces, and Ag 2 S nucleation and growth proceeded inward from the vertices of the AgNPs along the h110i directions. Our extensive NBED results clearly demonstrated that the crystallinity of Ag was preserved, and that the precipitated Ag 2 S domains were also fully crystalline in all the TEM aliquots. TEM conclusively demonstrated that suldation at S/Ag ¼ 0.72 is a slow process with a large fraction of silver in the middle of the AgNPs remaining unreacted aer 24 h of suldation.
In situ SAXS and XRD allowed simultaneous determination of the real-time morphological changes of the AgNPs and the rate of suldation. Both SAXS and XRD results strongly indicate that suldation follows rst-order reaction kinetics. The changes in particle size extracted from SAXS analysis and the conversion kinetics extracted from XRD analysis follow similar kinetic rates, establishing the coupling between particle morphology and extent of atomic structure transformation. The rates can be used to serve as benchmarks to validate thermodynamic models and potentially enable high-delity predictions of the fate and environmental impacts of AgNPs. Importantly, SAXS results also present denitive evidence proving at a high S/Ag ratio of 0.72, the lack of aggregation in the entire duration of the in situ study in this model system involving common ligands and natural organic matter.
We also probed the long-term fate of the AgNPs under different S/Ag ratios using ex situ SAXS/XRD. We found that the converted volume of Ag (Ag 2 S) is linearly related to the initial availability of sulde in the range of S/Ag between 0 and 1 with the individual characteristic of the AgNPs well preserved, suggestive of suldation being a well-regulated reaction. A careful analysis also establishes that the silver mass in the AgNP and transformed Ag/Ag 2 S NP is preserved. This result strongly indicates no dissolved Ag + ions were leached into the solution, a result with profound environmental implication.
While our results are specic to the materials system under investigation, we emphasize that the combined nondestructive methodology can be readily extended to directly probe and unfold the structure transformation pathway and the relevant kinetics in a broad range of model ENM systems. TEM allows indepth characterization of localized structures in the ENMs, and in situ SAXS/XRD provides statistically signicant knowledge regarding the kinetic rate and the extent of the transformation. Together, these complementary techniques present a detailed structure transformation landscape that is critically missing in our understanding of the behaviors of ENMs. 5,6,24 It is also important to acknowledge that due to the contrast mechanism of both TEM and X-ray scattering, this methodology is sensitive to the transformation in the metallic core alone and cannot reveal deterministic information related to the surfactant (organic) and nanoparticle (inorganic) interface, which as an inuential critical review puts, "(surface structure) is a major unknown factor because there are currently no methods available for determining nanoparticle surface structure at the molecular level". 24 Recent developments in attenuated total reectance-Fourier transform infrared spectroscopy have shown promise in the quantitative determination of molecular adsorption on various ENMs. 28,72 Use of the H/D isotope contrast effect in neutron scattering methods may also provide insights regarding the surfactant-surface interaction. Together with the structure evolution of the metallic core enabled by the methodology presented in this paper, we may be positioned to understand the contributing factors that determine the fate and elucidate the risks of ENMs in complex environmental settings.

Conflicts of interest
There are no conicts to declare.