Nonequilibrium pulsed heating freezes sintering of supported metal nanocatalysts

Domain: physics
Published: 2026-01-23
Editorial outcome: major_revision

Abstract
Supported metal nanoparticles always experience thermal-induced sintering that severely depresses their catalytic performance and durability. Recently, ultrafast heating technology has been widely adopted in synthesizing diverse metal nanoparticles or even single atoms on supporting materials, offering enhanced anti-sintering capabilities compared to conventional heating protocols. However, the mechanisms and kinetics underlying this anti-sintering behavior during ultrafast heating processes remain poorly understood. Here, using in situ scanning transmission electron microscopy and theoretical analysis, we microscopically reveal a metastable state for supported metal nanoparticles induced by ultrafast heating pulses, which significantly mitigates the thermal-induced sintering while effectively improves the crystallization degree of metal nanoparticles together with the metal/support interfaces. Our results show that Pt nanoparticles supported on graphene flakes are thermodynamically unstable yet kinetically stable across the ultrafast heating pulses; as a consequence, the Pt/graphene interface is gradually optimized in a lattice scale, leading to remarkable sintering resistance for Pt nanoparticles. These atomic-scale insights provide thorough fundamental understandings for ultrafast heating in stabilizing metal nanoparticles and may further guide the high-throughput production of robust supported metal nanocatalysts.

Introduction
The development of highly efficient and stable nanocatalysts represents one of the central objectives in current materials science, driven by their extensive applications expanding from energy transformation to chemical manufacturing fields. Particularly, most of these state-of-the-art nanocatalysts are metal nanoparticles (NPs, ranging from single atoms to several nanometers in size) supported on inert substrates, designing for maintaining the enormous surface areas as well as the high catalytic efficiencies of metal NPs in complex catalytic environments. However, the synthesis and deployment of supported metal nanocatalysts inevitably involve high-temperature treatments (for decomposing the precursors, or improving the crystallization degrees of metal NPs during the synthesis, or activating the catalytic reactions during the applications of nanocatalysts), which usually include a sequential heating/holding/cooling program lasting for several hours. In this context, a common issue, which is the sintering of metal NPs, occurs due to thermodynamic reasons (i.e., to reduce the surface energy of NPs) and leads to the merging of small NPs into large ones. This sintering effect significantly reduces the specific surface area and active sites of metal NPs, ultimately degrading the catalytic performance of supported nanocatalysts. Therefore, minimizing thermal-induced sintering is an urgent and critical challenge for advancing the applications of supported metal nanocatalysts.

Recently, ultrafast heating has emerged as an intriguing high-temperature synthesis method for producing ultrafine metal NPs or even single atoms on a wide range of supports. This approach enables flash heating/cooling of metal precursors on supports within extremely short timescales (several tens to hundreds of milliseconds), facilitating the instantaneous formation of metal nanocatalysts with a high loading rate and good dispersity. For example, Tian et al. report the synthesis of high-density and ultrasmall NPs uniformly dispersed on two-dimensional (2D) porous carbon by the direct carbothermal shock pyrolysis of metal-ligand precursors in just ~100 ms; remarkably, this method not only achieves rapid NP formation but also provides sufficient activation energy for the NPs to overcome the crystallization barrier, instantly forming highly crystallized metal NPs. Furthermore, an emerging form of pulsed heating that uses a periodic on-off heating pattern has shown promise in stabilizing metal NPs or single atoms. For instance, Hu et al. demonstrate a high-temperature-shockwave method to synthesize and stabilize metal single atoms; they suggest that the activation energy and ultrafast kinetics provided by this method enable the single-atom dispersion and promote the formation of stable bonds with defects on the substrate. Despite its immense potential for controllable synthesis of sintering-resistant nanocatalysts, the mechanisms governing the formation of small, well-crystallized NPs under such kinetics-dominant, thermodynamically nonequilibrium conditions of pulsed heating remain largely unknown. In situ (scanning) transmission electron microscopy, (S)TEM, with its rapid technological advances in simulating practical working environments, has shown the ability to examine nanoscale dynamics on catalysts and other nanomaterials at an ultra-high spatiotemporal resolution. It also provides us a potential opportunity to elucidate the real-time sintering dynamics underlying nonequilibrium processes such as pulsed heating.

Herein, by designing in situ (S)TEM experiments, we show a direct comparative observation on dynamic behaviors in the synthesis of graphene-supported Pt NPs (a suitable catalytic system with a clean interface) under ultrafast pulsed heating (heating/cooling rate of 150 oC s-1 to 1000 oC and pulse width of 50 ms) vs. conventional heating (heating rate of 1 oC s-1). Our results microscopically suggest that pulsed heating promotes the formation of uniform Pt NPs on graphene flakes with great sintering resistance, whereas conventional heating leads to severe sintering of Pt NPs. Coupled with density functional theory (DFT) and molecular dynamics (MD) simulations, we further extract that the significant anti-sintering capacity of Pt NPs under pulsed heating originates from a thermodynamically unstable yet kinetically stable state, which restrains the NPs from long-range diffusion on graphene surface as well as sintering; in contrast, conventional heating allows for free migration and coalescence of Pt NPs on graphene surface. Besides, repeated heating pulses facilitate a gradual improvement in the crystallization degrees of Pt NPs and a progressive optimization of Pt/graphene interfaces, culminating in the formation of stable supported nanocatalysts. Our findings provide a valuable guidance for understanding ultrafast heating process and may stimulate a paradigm shift in the synthesis and applications of supported nanocatalysts.

Results
Experimental design
To trace atomic-scale sintering dynamics of Pt NPs on graphene flakes upon pulsed heating, in situ (S)TEM heating experiments are proceeded by utilizing a heating holder equipped with a heating E-chip specimen support, which consists of a spiral-like copper electrode on a silicon nitride (SiNx) membrane with ten holes (covered with amorphous carbon film), as schematically shown in Fig. 1a. The heating process can be initiated by applying a controlled current through the conductive copper spiral. To guarantee a clean interface across Pt/graphene, graphene flakes are initially dispersed on the heating E-chip and then treated by Ar+/O2- bombardment. This treatment preserves the structural integrity of the graphene flakes, as confirmed by the high-angle annular dark-field STEM (HAADF-STEM) images (Supplementary Fig. 1, no visible damage is found throughout the process).

Subsequently, an appropriate amount of platinum precursor (NH3)4Pt(NO3)2 is applied on the pretreated graphene flakes, as illustrated in Fig. 1b (see “Methods” for the details). The sample is then subjected to a programmed pulsed heating process with precise controls over heating/cooling rate, peak temperature, on-off duration, and repetition cycles. As depicted in Fig. 1c, the pulsed heating protocol involves rapid heating/cooling at a rate of 150 oC s-1 and each pulse of 1000 oC for a short duration of 50 ms over a certain number of cycles (the heating pattern is set based on recent reports and the initial 10-pulse condition is selected to complete the decomposition of precursors and to capture the crystallization process of metal NPs). Particularly, the design of ultrafast cooling rate is essential, as the quenching process is critical for stabilizing the metastable structures formed at high temperatures. For comparison, another in situ experiment under conventional heating is parallelly conducted, involving a slow heating rate of 1 oC s-1 to 1000 oC and a subsequent cooling rate of 5 oC s-1 to room temperature (RT) (Fig. 1d; the temperature holding duration is the same as the pulsed heating). It should be of special notice that the holding time at elevated temperatures during conventional heating for the preparation or application of nanocatalysts typically lasts for several hours, which is far longer than that in our case. In both heating modes, Pt precursor is expected to be thermally decomposed into Pt atoms or NPs on the graphene support during initial heating. Prior to the in situ experiment, HAADF-STEM images and corresponding elemental mapping for C and Pt (Supplementary Fig. 2) confirm the uniform distribution of Pt precursor on graphene flakes.

Sintering dynamics of Pt NPs in two heating modes
We first explore the sintering pattern of Pt NPs on graphene flakes under pulsed heating. Figure 2a–d shows the sequential in situ STEM images of Pt NPs on graphene support against the repeated heating pulses (also see Supplementary Fig. 3). Upon the first pulse, Pt precursor rapidly decomposes, yielding dense Pt NPs on the graphene flake. And after ten pulses, the Pt NPs remain their small size (less than 3 nm, 51% of which are 1-2 nm) (see the corresponding size distributions as insets; additional TEM images of the same area are shown in Supplementary Fig. 4a–c, also confirming the small size of Pt NPs). These observations highlight the strong sintering resistance of Pt NPs under pulsed heating. In a sharp contrast, supported Pt NPs which are subjected to conventional heating display significantly weaker sintering resistance; as shown in the sequential STEM images in Supplementary Fig. 5 (with the selected frames shown in Fig. 2e–h) and TEM images in Supplementary Fig. 4d–f, the number of Pt NPs progressively decreases and the size also increases above 500 oC (also refer to the corresponding size distributions as insets), implying a considerable evaporation and sintering of Pt NPs. Although the lattice-resolved TEM images of Pt NPs formed by both heating modes (Supplementary Fig. 6) reveal a consistent lattice fringe spacing of 0.20 or 0.23 nm (corresponding to the Pt (200) or (111) crystal plane, respectively), the Pt NPs formed via conventional heating exhibit significantly larger particle sizes compared to those formed by pulsed heating, indicating more severe particle agglomeration under slow heating conditions. The above observations are the first microscopic evidence for the anti-sintering characteristics of pulsed heating and are well aligned with the previous synthesis efforts.

Moreover, to quantitatively analyze the above sintering behaviors, we examine the number and average size of Pt NPs during heating under the two modes. As shown in Fig. 2i, the number of Pt NPs on graphene under pulsed heating (red line) slowly drops with the increasing pulse number, remaining approximately 71% of the initial number after 10 pulses. In contrast, the number of Pt NPs on graphene under conventional heating (blue line) slowly drops before 500 oC, but the tendency becomes sharp after this temperature; specifically, the number of Pt NPs reduces by about 67% at 500–1000 oC (remaining only 17% after 1000 oC). Besides, Fig. 2j shows the results of particle size vs. heating time/pulses. Pt NPs under pulsed heating (red line) exhibit a slow and steady increase in size, stabilizing at approximately 1.6 nm after 1000 s/10 pulses, which is still within the typical size range (<3 nm) for high-performance nanocatalysts. Conversely, Pt NPs under conventional heating (blue line) grow rapidly in size until 800 oC, reaching ~1.4 nm. Notably, after 800 oC, a slight decrease in size to around 1.3 nm is observed, which is attributed to the intense diffusion of Pt atoms above the Tammann temperature (namely, diffusion of materials becomes significant above an empirical value of about half of the melting temperature on the Kelvin scale; ~750 oC for Pt). At these elevated temperatures, the weak graphene-Pt interaction allows Pt atoms to diffuse easily, leading to evaporation of small clusters or single atoms, thereby significantly reducing the number of Pt NPs above 800 oC. This explains the particle size-heating time profile observed for the conventional heating. In addition, although the average sizes of Pt NPs are comparable in the above observations, the size distribution from conventional heating is broader due to the existence of many large particles (maximum size up to 5 nm), indicating a more severe sintering. Repeated in situ observations of Pt NPs heated under the two heating protocols further support our interpretation (refer to Supplementary Figs. 7 and 8). We propose that the stark difference in sintering behaviors is primarily attributed to the heating/cooling rate; during the ultrafast pulsed heating, particle migration or atomic diffusion is largely inhibited, whereas the slow heating rate together with the continuous heating in conventional mode allow for more significant atomic diffusion and particle aggregation, which will be discussed later.

To further explore the effect of heating modes on the crystallinity of Pt NPs, which is highly related to the catalytic performance, we track the atomic-scale microstructural evolution for individual NPs. As shown in Fig. 2k, in the pulsed heating, Pt NP immediately forms visible (111) lattice fringes after a single pulse and it becomes clearer with the increasing number of pulses, maintaining the exposed crystal plane and the particle size throughout the process (also proved by the corresponding fast Fourier transform (FFT) patterns in Supplementary Fig. 9a). In contrast, the exposed crystal plane for Pt NP under the conventional heating process changes from (200) to (111) after 500 oC (Fig. 2l) and this NP displays poor crystallinity (see the corresponding FFT pattern in Supplementary Fig. 9b); the underlying reasons for this observation are the continuous size increase (due to the successive merging of nearby NPs) and the thermodynamic-driven shape changes. Figure 2m shows the relative crystalline order of the NPs calculated from their FFT patterns (refer to Supplementary Fig. 9) with respect to time, which further indicate that the NP formed by the pulsed heating possesses a higher crystallinity (the comparison after cooling is also provided in Supplementary Fig. 10 to exclude the temperature difference). Notably, the intensity comparison is also evident at a similar particle size (500 s) for the set two heating modes. Besides, to illustrate the evolutions of Pt/graphene interface in the two heating processes, we record the core-loss C K-edge electron energy loss spectroscopy (EELS) spectra for graphene support as a function of time. Each C K-edge spectrum consists of a peak at ~284 eV (the transitions from 1s spin level to empty π* orbitals of the sp2-bonded atoms) and a step at ~289 eV (the excitations to empty σ* orbitals at both sp2 and sp3 bonded atoms). As shown in Fig. 2n, the π* excitation of C K-edge gradually shifts toward lower energy loss values during pulsed heating (noticeable shift begins at the 4th pulse, likely due to the close contact between NPs and support), which can be a result of strong bonding and charge transfer between Pt NPs and graphene support that modify the electronic structure around the active sites; yet it hardly shifts in the conventional heating. These results show that strong metal-support interactions are established in Pt/graphene interface during pulsed heating, which is of key importance to the stability for supported nanocatalysts.

Atomic-scale behaviors of Pt NPs in pulsed heating
As the sintering rate of Pt NPs remains nearly linear during the first ten pulses of heating, we further extend the pulse number to 100 for understanding the effect of pulses on the sintering stability of Pt NPs. Sequential in situ STEM images (Fig. 3a–f, also see Supplementary Fig. 11) show that, even after 100 pulses, Pt NPs undergo slight sintering, maintaining a nanoscale size and nearly the same particle distribution throughout the heating process. The elemental mappings and the line scan together with the corresponding HAADF-STEM images of Pt/graphene interface are provided as Supplementary Fig. 12, indicating the dense and synchronous distribution of Pt NPs on graphene flake after 100 pulses. Furthermore, the number and average size of Pt NPs during 100 pulses are also analyzed as functions of pulses, as shown in Fig. 3g, h. Both curves behave a tendency to flatten out as the number of pulses increases, ultimately stabilizing with an average size of 2.0 nm and a particle number retention of 63%; this indicates that the Pt NPs are gradually stabilized on graphene support after repeated heating pulses. In addition, the C K-edge EELS results of graphene support before and after 100 heating pulses confirm its structural integrity under repeated heating pulses (Supplementary Fig. 13).

It is also worth noting that the morphology of Pt NPs evolves during the pulsed heating process (Fig. 3a–f), showing a gradual development from quasi-spherical to faceted NPs (high-resolution TEM (HRTEM) images of the Pt NPs after 100 pulses in Supplementary Fig. 14 exhibit hexagonal NPs with dominant {111} facets and occasional (200) planes). This observation reflects that the Pt NPs undergo crystallization improvement and structural optimization on graphene support during the pulsed heating, which are crucial for the stability of nanocatalysts. To clarify the above process, we further analyze the orientation relationship between Pt NPs and graphene flake after 100 pulses, as metal particles tend to form an epitaxial orientation on 2D supporting materials during their growth. Selected-area electron diffraction (SAED) pattern of a graphene support is shown in Fig. 3i, displaying its single-crystalline nature along with [0001] zone axis, and the corresponding atomic structure is schematically shown in Fig. 3j. To define the relative orientation of Pt NPs against graphene flakes, we set the angle between them as 0o when the graphene [10-10] direction (brown line) aligns with the Pt [111] direction (black line). When the Pt NP orientation (blue dashed line) deviates from the graphene orientation, the angle is denoted as θ, as shown in Fig. 3j and Supplementary Fig. 15. Then, we measure the θ angles of approximately 200 Pt NPs, as statistically shown in Fig. 3k. We find that the distribution of θ angles is mainly around 0o, 60o, 120o, and 180o, indicating that the Pt NPs align their crystallographic orientations with graphene support during pulsed heating. This high degree of orientational alignment between Pt NPs and graphene support minimizes the interfacial energy, thereby driving the formation of a thermodynamically stable structure.

In order to directly disclose the structural optimization of Pt NPs, we accordingly capture the HRTEM images of graphene-supported Pt NPs with representative structures along with the increasing heating pulses. As shown in Fig. 4, the structural optimization of Pt NPs can be divided into three stages. In the first stage (during the first 10 pulses, Fig. 4a, b), the Pt NPs, which are newly formed from the decomposition of the precursor, are irregularly elliptical in shape with a poor crystalline nature (displaying only the (200) plane). In the second stage (~10–40 pulses, Fig. 4c, d), Pt NPs slightly grow and form an elongated hexagonal shape with well-defined crystalline lattices, resulting from the actions of facet development. In the final stage (up to 100 pulses, Fig. 4e–h), for minimizing the system energy, Pt NPs undergo persistent surface atomic rearrangement and ultimately form a regular hexagonal outline. The corresponding inverse FFT (iFFT) patterns show their distinct atomic arrangements (Fig. 4i-l), and the entire structural evolution of Pt NPs on graphene is schematically shown in Fig. 4m. In contrast, Pt NPs under conventional heating generally retain an irregularly elliptical shape (Supplementary Fig. 16), which is likely due to the slower heating kinetics; in this scenario, NPs have sufficient time for atomic diffusion and particle agglomeration, leading to the formation of thermodynamically stable spherical structures. Conversely, the rapid heating kinetics under pulsed heating suppress such agglomeration; and aided by the interfacial effects of graphene substrate, the pulsed heating finally results in the formation of faceted structures. Again, repeated in situ observations of Pt NPs sustained 100 heating pulses further support this deduction (refer to Supplementary Fig. 17). It is worth mentioning that the above structural evolution process emphasizes the advantages of pulsed heating in modulating the exposed crystal plane of metal nanocatalysts. It also demonstrates a distinct, particle-centered, and kinetic-controlled pathway in which pulsed heating drives stepwise structural optimization of NPs, in contrast to previous reports where a single high-energy pulse induces support reconstruction and defect generation to stabilize NPs.

In addition, to assess the thermal stability of the Pt/graphene nanocatalyst formed after 100 heating pulses, we conduct an extended heating test by maintaining it at 1000 oC for 1 h. As shown in Supplementary Fig. 18, no obvious coarsening or change in particle morphology occurs within the observation, demonstrating that the as-produced nanostructures are robust even under continuous high-temperature exposure. The marked sintering resistance can be attributed to the formation of strong Pt-C interfacial bonding and the progressive structural alignment of NPs with graphene substrate, both of which arise during the prior heating pulses. To demonstrate that pulsed heating stabilizes NPs through a kinetically constrained pathway rather than a short high-temperature exposure, we further perform an extended pulsed heating of 1000 pulses with a 1s peak duration (cumulative exposure of 1000 s at 1000 oC). Again, Pt NPs remain stable without observable sintering (Supplementary Fig. 19), and the evolutions for number and average size of Pt NPs during the first 100 pulses follow similar trends as those in Fig. 3.

Sintering kinetics of pulsed heating
Summarizing from the above results, we infer that the enhanced sintering stability of Pt NPs under pulsed heating is attributed to two main factors: first, the as-revealed structural optimization and orientational alignment of Pt NPs during pulsed heating lead to an energetically stable configuration; and second, NPs are kinetically hindered from undergoing effective migration due to the brief duration of heating pulses, which is the key mechanism underlying their sintering resistance. To further support this hypothesis, DFT calculations are thereby performed. Figure 5a–c display the DFT calculated patterns of Pt NPs with (001), (011) or (111) planes bound onto graphene. The corresponding binding energies are also shown in Fig. 5d, from which it can be concluded that the Pt (111) NP exhibits the lowest binding energy among the three configurations; this indicates that the attachment of Pt NPs on graphene flakes is more energetically favorable at their (111) facets. This is the direct reason that Pt/graphene interfaces are gradually optimized and stabilized during the pulsed heating (Fig. 4).

Moreover, in order to comprehend the kinetic aspects for sintering behaviors of Pt NPs under the two heating modes, we further perform MD simulations on a Pt/graphene system with different temperature profiles. Considering the difference in time scales between simulations (usually on a picosecond scale) and experiments, we use two distinct heating processes: a temperature ramping process (from 25 to 1000 oC over 20 ps, Supplementary Fig. 20a) to model the pulsed heating experiment and a temperature holding process (at 1000 oC for 20 ps, Supplementary Fig. 20b) to simulate the conventional heating process due to its extremely slow heating rate compared to the pulsed heating. As a result, the system energies as functions of the simulation time for these two processes show their remarkable differences (Supplementary Fig. 20), in which the temperature ramping process shows a gradual increase in energy while the temperature holding process starts at a higher energy state, and the average energy of the former is obviously lower than that of the latter. The simulations also clearly depict the structural evolutions of Pt NPs under two heating methods (Fig. 5e, f); in the temperature ramping process, the Pt NP maintains its integrity on graphene support without apparent diffusion or migration, while a significant diffusion of Pt atoms occurs and the NP eventually wets the graphene surface in the temperature holding process. Although this result clearly suggests that ultrafast heating leads to a mitigation for sintering, it also implies that the NPs can still be thermodynamically unstable as their structure and position both change (Fig. 5e). This means that the as-observed sintering resistance for pulsed heating is not solely induced by thermodynamic causes, kinetic factors may also play important roles. To further verify the kinetic stability of Pt NPs, we track their sintering behavior during the first pulse by rapidly heating them to 1000 oC and then holding for a duration (Fig. 5g). At this early stage, the interaction between the NPs and the support has not yet developed. It is then found that no noticeable sintering occurs at the beginning of temperature holding (<6 s; be noted that this time is much longer than the pulse width); nonetheless, after that, sintering dramatically occurs (Fig. 5h). The finding well agrees with the recent report by Zeng et al. (the critical relaxation threshold for sintering is ~10 s), which appropriately indicates that Pt NPs are kinetically stable in the case of short heating pulses.

Methods
Precursor preparation
A 5 mL graphene oxide solution was initially freeze-dried to form solid blocks, which were subsequently reduced under H2 atmosphere at 500 oC for 5 h to obtain graphene blocks. The graphene blocks were dispersed in ethanol solution and sonicated for 20 min to produce the precursor of graphene flakes. The precursor was dropped onto a heating E-chip specimen support and dried under ambient conditions. The graphene surface was then treated using a Gatan Solarus II plasma cleaner, subjected to Ar+/O2- bombardment at a flow rate of 30 sccm for 60 s. The system pressure was maintained at 350 mTorr, with the plasma power set to 40 W. Next, ammonium platinum nitrate (NH3)4Pt(NO3)2 was dissolved in ethanol to prepare a Pt precursor solution, which was sonicated for 20 min prior to use. Finally, the Pt/graphene precursor was prepared by drop-casting the Pt precursor solution onto the graphene-coated heating E-chip.

In situ (S)TEM experiments
In situ (S)TEM experiments were performed using a DENSsolutions Wildfire heating holder. TEM experiments were conducted on a JEOL JEM-F200 cold-field-emission TEM operated at 200 kV, equipped with an EDS and a Gatan Continuum S EELS. TEM images were acquired using a Gatan OneView IS camera with an optimized exposure time. STEM images were captured with a Gatan PEELS camera using an exposure time of approximately 30 s (except for the images in Fig. 5g, which had an exposure time of 2 s). Core-loss EELS spectra were collected in STEM mode; the energy resolution was 0.72 eV with a dispersion of 0.15 eV per pixel and the acquisition time was about 1 s per frame (total acquisition time ≈ 20 s). With this setup, the convergence and collection angles were 0 and 100 mrad, respectively. For pulsed heating experiments, the sample was subjected to a heating/cooling rate of 150 oC s-1 to 1000 oC for 50 ms, and (S)TEM images were acquired at RT after each pulse (separation of pulses: 100 s). In conventional heating experiments, the sample was heated from RT to 1000 oC at a ramping rate of 1 oC s-1; and the cooling rate was 5 oC s-1. All in situ experiments were repeated to ensure reproducibility of the structural evolution dynamics. The electron beam was blanked whenever possible to minimize beam effects on the nanocatalysts.

Computational details
All theoretical calculations were performed with the Vienna Ab initio Simulation Package (VASP, version 5.4.4) code. DFT calculations were performed with projector-augmented wave method, and the Perdew-Burke-Ernzerhof method of generalized gradient approximation was used to describe the exchange-correlation functional. Grimme’s DFT-D3 method was applied for the van der Waals corrections. Energy and force convergence criteria were set as 10-5 eV and 0.02 eV Å-1, respectively. A 6×6 matrix was used to model graphene and a vacuum layer with a thickness of more than 15 Å was added to avoid spurious interactions between cells. Ab initio MD simulations were performed in the NVT ensemble with Nosé-Hoover thermostat, and the timestep was set as 2 ps.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript, Huang et al. report ultrafast pulsed heating as a nonequilibrium strategy to suppress the sintering of supported Pt nanoparticles, using graphene as the support. Through a combination of in situ STEM analysis, EELS, DFT, and MD simulations, the authors reveal that pulsed heating induces a thermodynamically unstable yet kinetically stable state, enabling improved crystallinity and enhanced metal–support interactions while effectively inhibiting particle migration and coalescence. This work provides a novel atomic-scale understanding of metastable states in nanocatalysts and offers an alternative route to sintering-resistant catalyst synthesis beyond thermodynamic constraints. Overall, the authors present a solid and well-validated study, and this manuscript will be of high interest to researchers working on nanocatalysts. The methodology is rigorous, and the mechanistic insights are valuable. This manuscript can be considered for publication in Nature Communications. However, the following points should be addressed before publication to further improve the quality of this work.\n1. The authors mention that the heating pattern was designed based on recent reports; however, a more detailed description of the temperature profile, particularly the cooling rate following each pulsed heating, is necessary. Since cooling kinetics are critical for the formation of metastable nanostructures, quantifying the cooling behavior would greatly enhance the mechanistic understanding. Additionally, the selection of the 10-pulse condition as the primary reference over the 1-pulse case remains unclear. Could the authors clarify and comment on the potential effects of a single, higher-temperature pulse?\n2. The authors mention that ultrafast pulsed heating effectively suppresses atomic diffusion and aggregation of nanoparticles. However, in several recent studies, including direct-joule heating-based redispersion/atomization (Journal of the American Chemical Society 142,41, 2020, 17364-17371., Science 359, 6383, 2018, 1489-1494.), and photothermal effect-driven redispersion/atomization (metal oxide redispersion (Advanced Materials, 2025, 2419790.), Pt atomization (Chem 8, 4, 2022, 1014-1033.)), it has been shown that ultrafast high-temperature treatment can actually promote atomic diffusion while simultaneously restricting aggregation, resulting in smaller or even atomically dispersed particles. Could the pulsed heating strategy used in this study also induce redispersion or partial atomization of Pt nanoparticles, especially at elevated pulse temperatures or with increased pulse counts? In such cases, atomic mobility could be activated while aggregation remains kinetically suppressed due to short exposure durations. The authors are encouraged to comment on whether such size reduction or dispersion behavior could emerge under more intensive pulse conditions and whether this pathway has been experimentally tested or theoretically predicted.\n3. The manuscript reports the application of up to 100 successive heating pulses, yet no notable structural or chemical change in the graphene support is discussed. Could the authors elaborate on the methods used to evaluate the integrity of the graphene after repeated thermal treatments? In particular, were any atomic-level characterizations (e.g., Raman spectroscopy, EELS, or aberration-corrected TEM) conducted to assess possible cumulative damage or defect generation?\n4. The discussion compares the appearance of the Pt (111) facet after a single pulsed heating step with the delayed emergence of the same facet under conventional heating (initially showing the (200) facet). Given that (111) is thermodynamically more stable than (200), it would be more accurate to highlight the rapid stabilization of (111) as a merit of pulsed sintering rather than concluding a higher degree of crystallinity. Moreover, as Figure S12 also shows the appearance of the (200) facet under pulsed heating, please address this apparent contradiction.\n5. A noticeable shift in the peak position begins at the 4th pulse. Please provide a discussion on this phenomenon. Additionally, prior to comparing 10-pulse treatment with conventional heating for 1000 seconds, consider providing comparative data at intermediate temperatures to better contrast single-pulse effects.\n6. In the interpretation of Figure 3j, clarify the rationale for lattice matching discussion between 3D Pt nanoparticles and 2D graphene sheets. In particular, provides more detail on how the crystallographic orientation was determined from FFT patterns.\n7. Only four images are shown for the 100-pulse case in Figure 4(e-h). Please revise the layout for consistency across all pulse conditions or clarify the rationale behind the image selection.\n8. Confirm whether the TEM image in Figure S13 was obtained along the same zone axis as those shown in Figure 4. This is important for accurate structural comparison.", "reviewer_2": "The manuscript titled “Defying thermodynamics: Nonequilibrium pulsed heating freezes sintering of supported metal nanocatalysts” explores the behavior of Pt nanoparticles supported on graphene under ultrafast pulsed heating, using in situ (S)TEM observations in combination with DFT and MD simulations. The study aims to demonstrate that pulsed heating leads to a metastable, kinetically stabilized state that can inhibit nanoparticle sintering more effectively than conventional heating. While the experimental design is technically sound and the integration of microscopy with modeling is methodologically appropriate, the current version of the manuscript raises several concerns that must be addressed before it can be considered for publication. The mechanistic claims, particularly regarding structural optimization, interface effects, and the generality of the proposed anti-sintering mechanism, require clearer justification and more critical discussion. Additionally, the manuscript would benefit from a more rigorous evaluation of the crystallinity data, the role of the substrate, and the absence of catalytic performance validation. Therefore, I recommend major revisions. Specific comments are provided below to help the authors improve the manuscript’s clarity, depth, and scientific rigor..\n1. In Figure 2m, The lower crystallinity of Pt NPs under conventional heating may be biased by the different thermal states during which the measurements were taken—if FFT was performed at high temperature, thermal vibrations and atomic diffusion could artificially reduce apparent crystallinity. In contrast, pulsed heating benefits from repeated cooling, effectively annealing the structure. A fair comparison should assess crystallinity after cooling in both cases, or this limitation should be clearly discussed to avoid misinterpretation. Including such a control or at least discussing this thermal-state-dependent artifact would significantly enhance the credibility of the crystallinity comparison and deepen our understanding of the thermal evolution of NP structure in both regimes.\n2. In Figure 2n, the electron energy loss spectroscopy (EELS) results suggest changes at the metal-support interface, but the chemical state evolution of Pt (e.g., oxidation state, bonding environment) is not fully explored. Complementary characterization would help clarify the electronic effects contributing to NP stabilization.\n3. In Figure 3, the manuscript claims a “high degree of lattice matching” between Pt NPs and graphene supports. However, this terminology is not strictly accurate. Pt(111) has a lattice spacing of ~0.227 nm, while the in-plane lattice spacing of graphene (e.g., (10-10)) is ~0.213 nm, and their crystallographic symmetries (fcc vs. hexagonal) differ. Thus, this interface should not be described as lattice-matched. A more appropriate term would be “orientation alignment” or “epitaxial-like interfacial relationship.” The authors are advised to revise this statement for precision.\n4. In the part of “Sintering kinetics of pulsed heating”, The manuscript attributes the sintering resistance under pulsed heating to both interfacial structural optimization and kinetic suppression. It would strengthen the mechanistic understanding if the authors discuss whether kinetic limitation alone—without crystallographic alignment or structural optimization—would be sufficient to ensure long-term stability. This distinction is important to evaluate whether the observed robustness is primarily due to the heating profile or also critically dependent on support-induced ordering\n5. Although 100 pulses demonstrate improved sintering resistance, the net thermal exposure remains short relative to real catalytic conditions. The authors are encouraged to address how these metastable structures behave under extended heating, cyclic heating, or in the presence of reactive environments, either through additional data, cited references, or detailed discussion.\n6. While structural stabilization is clearly demonstrated, the manuscript lacks direct correlation with catalytic performance. A brief experimental validation (e.g., a model reaction demonstrating enhanced durability or activity of pulsed-heated Pt NPs) or a robust discussion on how the observed microstructural advantages may translate into catalytic improvements would significantly enhance the relevance of the study."}, "author_response": "Point-by-point response\nWe sincerely thank the reviewers for their comments and suggestions on our manuscript.\nWe have addressed all the concerns raised by the referees in full and revised the\nmanuscript accordingly. Our responses to the reviewers’ comments are given below.\nThe content is organized as following:\nSection Ⅰ: Response for Reviewer 1 (p2-p16)\nSection Ⅱ: Response for Reviewer 2 (p17-p25)\nP\nA\nG\nE\nResponse for Reviewer #1\nIn the manuscript, Huang et al. report ultrafast pulsed heating as a nonequilibrium\nstrategy to suppress the sintering of supported Pt nanoparticles, using graphene as the\nsupport. Through a combination of in situ STEM analysis, EELS, DFT, and MD\nsimulations, the authors reveal that pulsed heating induces a thermodynamically\nunstable yet kinetically stable state, enabling improved crystallinity and enhanced\nmetal–support interactions while effectively inhibiting particle migration and\ncoalescence. This work provides a novel atomic-scale understanding of metastable\nstates in nanocatalysts and offers an alternative route to sintering-resistant catalyst\nsynthesis beyond thermodynamic constraints. Overall, the authors present a solid and\nwell-validated study, and this manuscript will be of high interest to researchers working\non nanocatalysts. The methodology is rigorous, and the mechanistic insights are\nvaluable. This manuscript can be considered for publication in Nature Communications.\nHowever, the following points should be addressed before publication to further\nimprove the quality of this work.\n(1) The authors mention that the heating pattern was designed based on recent reports;\nhowever, a more detailed description of the temperature profile, particularly the cooling\nrate following each pulsed heating, is necessary. Since cooling kinetics are critical for\nthe formation of metastable nanostructures, quantifying the cooling behavior would\ngreatly enhance the mechanistic understanding. Additionally, the selection of the 10-\npulse condition as the primary reference over the 1-pulse case remains unclear. Could\nthe authors clarify and comment on the potential effects of a single, higher-temperature\npulse?\nOur response: Thanks very much for the positive comment and kind suggestion from\nthe reviewer. We would like to respond for your concerns as follows.\n1) Regarding the reviewer’s comments on the temperature profile, we emphasize that\nboth the heating rate and, in particular, the cooling rate of 150 oC/s in our pulsed heating\nexperiment are well within the capabilities of the DENSsolutions Wildfire heating\nP\nA\nG\nE\nsystem.1,2 Furthermore, direct temperature measurements recorded by the Impulse\nsoftware during an individual heating pulse confirm the uniformity of the designed\nheating/cooling rate (Table R1).\nSecond, we agree with the reviewer that the cooling kinetics indeed play a decisive role\nin the formation of metastable structures. The cooling rate achieved in our pulsed\nheating experiments is markedly higher than that of conventional heating, enabling the\nsuppression of atomic diffusion and thereby stabilizing the metastable structures\nformed at elevated temperatures.3,4 In contrast, conventional cooling rates keep the\nsystem much close to thermodynamic equilibrium, which facilitates the crystallization\nof metal nanoparticles and the evolution of thermodynamically stable structures.\nConsequently, the cooling behaviors of the two approaches differ fundamentally. To\nfurther address this point, we have now included detailed descriptions of the cooling\nrate in the revised text, which read as “Particularly, the design of ultrafast cooling rates\nis essential, as the quenching process is critical for stabilizing the metastable structures\nformed at high temperatures.45,46” and “For comparison, another in situ experiment\nunder conventional heating was parallelly conducted, involving a slow heating rate of\n1 oC s-1 to 1000 °C and a subsequent cooling rate of 5 oC s-1 to room temperature”.\n2) Regarding the reviewer’s questions on the design of pulse conditions, we note that\nthe choice of a 10-pulse sequence follows the approach reported by Yao et al.;5 since\nboth the decomposition of metal precursors and the nucleation/growth of metal NPs\nrequire sufficient time, and a single heating pulse is typically inadequate to complete\nthese processes. Approximately 10 pulses are therefore necessary to obtain uniformly\ndispersed NPs, which then provides a meaningful basis for investigating the sintering\nbehavior of supported nanocatalysts.\nFurthermore, while a single, higher-temperature pulse can indeed accelerate precursor\ndecomposition, organics volatilization, and NP crystallization,6 it does not alter the\nintrinsic tendency for sintering or structural evolution under pulsed heating; rather, it\nmerely accelerates the kinetics. Thus, we consider higher-temperature pulses with fewer\nP\nA\nG\nE\npulse numbers cannot be the ideal parameter. We also wat to remind you that our focus\nlies on the understanding of sintering dynamics, structural evolution of NPs, and\ninterface optimization that occur during pulsed heating; therefore, employing relatively\nlower-temperature pulses slows down these transformations, thereby enabling more\nconvenient observations.\nTo clarify the reason for the design in our work, we have now added the following\ndescription in the updated text: “the heating pattern was set based on recent reports and\nthe initial 10-pulse condition was selected to complete the decomposition of precursors\nand capture the crystallization process of metal NPs”.\nReferences:\n(1) van Swieten, T. P. et al. Mapping elevated temperatures with a micrometer\nresolution using the luminescence of chemically stable upconversion nanoparticles.\nACS Appl. Nano Mater. 4, 4208-4215 (2021).\n(2) Vijayan, S., Wang, R., Kong, Z. & Jinschek, J. R. Quantification of extreme thermal\ngradients during in situ transmission electron microscope heating experiments. Microsc.\nRes. Techniq. 85, 1527-1537 (2021).\n(3) Han, Y.-C., Cao, P.-Y. & Tian, Z.-Q. Controllable synthesis of solid catalysts by\nhigh-temperature pulse. Acc. Mater. Res. 4, 648-654 (2023).\n(4) Deng, B. et al. Phase controlled synthesis of transition metal carbide nanocrystals\nby ultrafast flash Joule heating. Nat. Commun. 13, 262 (2022).\n(5) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(6) Chen, L., Liu, J., Volpe, R. & Grasso, S. Impact of repeated heat pulses on the\nconsolidation and grain growth of 3YSZ consolidated via ultrafast high-temperature\nsintering (UHS). J. Eur. Ceram. Soc. 45, 117395 (2025).\nP\nA\nG\nE\nTable R1. The actual temperature measurement of a single heating pulse.\nExperiment time / s Temperature Setpoint / oC Temperature Measured / oC\n0 20 20.507456\n1.982 347.413451 305.582642\n3.965 628.539899 651.154297\n6.610 1003.617347 1012.758667\n8.591 768.879477 800.145874\n10.571 487.144688 474.15567\n13.542 20 20.297533\n(2) The authors mention that ultrafast pulsed heating effectively suppresses atomic\ndiffusion and aggregation of nanoparticles. However, in several recent studies,\nincluding direct-joule heating-based redispersion/atomization (Journal of the\nAmerican Chemical Society 142,41, 2020, 17364-17371., Science 359, 6383, 2018,\n1489-1494.), and photothermal effect-driven redispersion/atomization (metal oxide\nredispersion (Advanced Materials, 2025, 2419790.), Pt atomization (Chem 8, 4, 2022,\n1014-1033.)), it has been shown that ultrafast high-temperature treatment can actually\npromote atomic diffusion while simultaneously restricting aggregation, resulting in\nsmaller or even atomically dispersed particles. Could the pulsed heating strategy used\nin this study also induce redispersion or partial atomization of Pt nanoparticles,\nespecially at elevated pulse temperatures or with increased pulse counts? In such cases,\natomic mobility could be activated while aggregation remains kinetically suppressed\ndue to short exposure durations. The authors are encouraged to comment on whether\nsuch size reduction or dispersion behavior could emerge under more intensive pulse\nconditions and whether this pathway has been experimentally tested or theoretically\npredicted.\nP\nA\nG\nE\nOur response: We sincerely thank the reviewer for this important suggestion. We\nclarify that no redispersion or atomization behavior has been observed in our pulsed\nheating experiments, as evidenced by the size evolution of Pt NPs over 100 heating\npulses (Figure 3h, shown here as Figure R1).\nOne possible reason is the size effect: pulsed heating decomposes the precursors into\nwell-dispersed NPs with diameters below 2 nm, which are much smaller than the\nredispersed NPs reported in the literature cited by the reviewer. Such ultra-small NPs\npossess very high surface energies, making further redispersion unfavorable. More\nimportantly, as noted in previous reports,7-9 redispersion or atomization typically\nrequires two key conditions: (i) sufficiently high temperatures to break atomic bonds\nwithin the NPs and overcome diffusion barriers, thus causing the NPs to split and move\non the support; (ii) strong metal–support interactions, such as spatial (MOFs, COFs) or\nchemical (surface functional groups, dangling bonds) confinements, are also essential\nto stabilize the redistributed atoms or ultra-small clusters.\nTherefore, in our opinion (and under the current experimental conditions),\nredispersion/atomization cannot be induced solely by elevated pulse temperatures or\nincreased pulse counts because the nature of the support is also critical. In our system,\nthe graphene support provides an atomically smooth surface with negligible\nconfinement, preventing particles/atoms trapping. We emphasize it here that this design\nis intentional, as it allows us to focus on the sintering behaviors of NPs under pulsed\nheating.\nReferences:\n(7) Lang, Z. et al. Destabilization of single-atom catalysts: characterization,\nmechanisms, and regeneration strategies. Adv. Mater. 37, 2418942 (2025).\n(8) Li, L. & Zhang, N. Atomic dispersion of bulk/nano metals to atomic-sites catalysts\nand their application in thermal catalysis. Nano Res. 16, 6380-6401 (2023).\n(9) Morgan, K., Goguet, A. & Hardacre, C. Metal redispersion strategies for recycling\nof supported metal catalysts: a perspective. ACS Catal. 5, 3430-3445 (2015).\nP\nA\nG\nE\nFigure R1. (Figure 3h) Average size of Pt NPs as a function of pulse number across\n(a-f). Error band represents the 95% confidence interval of the mean.\n(3) The manuscript reports the application of up to 100 successive heating pulses,\nyet no notable structural or chemical change in the graphene support is discussed.\nCould the authors elaborate on the methods used to evaluate the integrity of the graphene\nafter repeated thermal treatments? In particular, were any atomic-level\ncharacterizations (e.g., Raman spectroscopy, EELS, or aberration-corrected TEM)\nconducted to assess possible cumulative damage or defect generation?\nOur response: We thank the reviewer for this professional suggestion. While we did\nnot initially emphasize the changes in the graphene support during 100 heating pulses,\nit is well established that graphene possesses excellent thermal stability as a catalyst\nsupport, as frequently documented in previous studies.10,11 Additionally, there are also\nstudies indicating that surface defects generated during preparation can be repaired\nunder prolonged heating,12 but the extremely short duration of each pulse in our\nexperiments makes it unlikely that successive pulses would significantly affect the\nstructure of graphene. Moreover, the graphene samples were sintered at 500 oC for 30\nminutes prior to our in situ heating experiments, which further ensures their thermal\nstability.\nTo directly assess potential cumulative damage or defect generation of graphene\nsupport, we collected the EELS spectra of pristine graphene before and after 100\nP\nA\nG\nE\nheating pulses (Figure R2). The absence of noticeable changes in the C–K edge\nconfirms that pulsed heating exerts negligible influence on the graphene structure. We\nhave now added the corresponding discussion on the integrity of graphene under\nrepeated pulses in the revised manuscript, which reads as “In addition, the C K-edge\nEELS results of the graphene support before and after 100 heating pulses confirm its\nstructural integrity under repeated heating pulses (Figure S13).”. We also added Figure\nR2 in the updated Supplementary Information as Figure S13.\nReferences:\n(10) Jang, I. et al. Instantaneous thermal energy for swift synthesis of single-atom\ncatalysts for unparalleled performance in metal–air batteries and fuel cells. Adv. Mater.\n36, 2403273 (2024).\n(11) Qiao, Y. et al. 3D-printed graphene oxide framework with thermal shock\nsynthesized nanoparticles for Li-CO batteries. Adv. Funct. Mater. 28, 1805899 (2018).\n2\n(12) Liu, L., Qing, M., Wang, Y. & Chen, S. Defects in graphene: generation, healing,\nand their effects on the properties of graphene: a review. J. Mater. Sci. Technol. 31, 599-\n606 (2015).\nFigure R2. (Figure S13) (a, b) STEM image and C K-edge EELS spectra of graphene\nsupport before and after 100 heating pulses.\n(4) The discussion compares the appearance of the Pt (111) facet after a single pulsed\nheating step with the delayed emergence of the same facet under conventional heating\n(initially showing the (200) facet). Given that (111) is thermodynamically more stable\nthan (200), it would be more accurate to highlight the rapid stabilization of (111) as a\nP\nA\nG\nE\nmerit of pulsed sintering rather than concluding a higher degree of crystallinity.\nMoreover, as Figure S12 also shows the appearance of the (200) facet under pulsed\nheating, please address this apparent contradiction.\nOur response: We appreciate the reviewer’s insightful comment on that pulsed heating\npromotes the rapid formation of the thermodynamically stable (111) facet. However,\nthe conclusion we drew in the text regarding higher crystallinity was not directly linked\nto the emergence of the (111) plane. Instead, it was based on the brightness contrast of\nthe diffraction spots in the FFT patterns (Figure S9 and Figure 2m, attached here as\nFigure R3 and Figure R4, respectively), where pulsed heating produced stronger\ndiffraction contrasts, qualitatively indicating a higher degree of NP crystallinity.13 To\navoid potential misunderstanding caused by our earlier wording, we have revised the\n revised the\ncorresponding statement in the manuscript as: “In contrast, the exposed crystal plane\nfor Pt NPs under the conventional heating process changed from (200) to (111) after\n500 oC (Figure 2l) and these NPs displayed poor crystallinity (see the corresponding\nFFT pattern in Figure S9b);”.\nRegarding the appearance of the (200) facet after 100 heating pulses, we clarify that\nwhile this is possible, it remains a rare phenomenon, likely arising from anchoring\neffects of surface defects or localized interfacial forces. Importantly, the overall trend\nis the preferential formation of the more stable (111) facets, as shown in Figure R5,\nwhere the ratio of (111) facet exceeds 90%. To illustrate this point more clearly, we\nhave replaced the original Figure S12 with Figure R5 in the updated Supplementary\nInformation and revised the corresponding text, which read as “high-resolution TEM\nimages of the Pt NPs after 100 pulses in Figure S14 exhibit hexagonal NPs with\ndominant {111} facets and occasional (200) planes”.\nReference:\n(13) Fei, L. et al. Observable two-step nucleation mechanism in solid-state formation\nof tungsten carbide. ACS Nano 13, 681-688 (2019).\nP\nA\nG\nE\nFigure R3. (Figure S9) (a) FFT pattern series corresponding to pulsed heating process\nin Figure 2k. (b) FFT pattern series corresponding to conventional heating process in\nFigure 2l.\nFigure R4. (Figure 2m) Evolutions of relative crystalline orders for Pt NPs throughout\n(k) and (l) against time. The amounts of crystalline order were determined from the spot\nintensity of the corresponding FFT patterns (see Figure S9), comparing the value from\na NP with the same crystal orientation (whose crystalline order is set as 100, heated\nwith 10 pulses).\nP\nA\nG\nE\nFigure R5. (Figure S14) High-resolution TEM images showing the crystallographic\nanalysis of Pt NPs after 100 heating pulses. NPs that expose their (111) and (200) crystal\nplanes are marked with green and yellow circles, respectively. The result indicates the\ndominance of the stable (111) crystal plane.\n(5) A noticeable shift in the peak position begins at the 4th pulse. Please provide a\ndiscussion on this phenomenon. Additionally, prior to comparing 10-pulse treatment\nwith conventional heating for 1000 seconds, consider providing comparative data at\nintermediate temperatures to better contrast single-pulse effects.\nOur response: We sincerely thank the reviewer’s constructive comment.\n1) The phenomenon of peak shift noticed by the reviewer can be explained by the fact\nthat the first few pulses primarily drive the decomposition of precursor, during which\nthe newly formed NPs are not yet in intimate contact with the support due to residual\norganics at the interface. By the 4th pulse, the NPs may have established closer contacts\nwith the graphene support, enabling charge transfer, as reflected by the peak shift in the\nEELS spectra (Figure 2n, attached here as Figure R6). That charge transfer between\ngraphene and Pt NPs has been confirmed (both experimentally and theoretically) in our\nprevious work.14 To clarify this point, we have added the corresponding description in\nthe updated text, which read as “As shown in Figure 2n, the π* excitation of C K-edge\ngradually shifts toward lower energy loss values during pulsed heating (noticeable shift\nbegins at the 4th pulse, likely due to the NPs initiate close contacts with the support),\nwhich can be a result of strong bonding and charge transfer between Pt NPs and\ngraphene support that modify the electronic structure around the active sites;”.\nP\nA\nG\nE\n2) Regarding the EELS results under conventional heating (Figure 2n), we clarify that\nthese measurements were conducted during the heating process rather than under\nisothermal conditions at 1000 oC. Comparative spectra at intermediate temperatures\nhave therefore been included in Figure 2n.\nReference:\n(14) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\n29183 (2024).\nFigure R6. (Figure 2n) C K-edge EELS spectra for the graphene supports as a function\nof heating time under pulsed heating and conventional heating modes.\n(6) In the interpretation of Figure 3j, clarify the rationale for lattice matching\ndiscussion between 3D Pt nanoparticles and 2D graphene sheets. In particular,\nprovides more detail on how the crystallographic orientation was determined from FFT\npatterns.\nOur response: Thanks very much for the constructive comments from the reviewer.\n1) For your concern on Figure 3j, our intention for this scheme focuses on the\ncrystallographic orientation relationship between the [111] direction of Pt NPs and the\n and the\n[10-10] direction of graphene flakes (you may also refer to Figure 5c for the side-view\nof this interfacial relationship), which has been well explored in previous studies.15 To\nP\nA\nG\nE\nclearly illustrate this orientation relationship and to avoid potential misunderstanding,\nwe have revised the original Figure 3j with Figure R7 in the updated manuscript.\nIn addition, to clarify the validity of the “lattice matching” statement in the manuscript,\nwe have calculated the lattice mismatch between the Pt (111) plane and the graphene\n(10-10) plane, which is 6.57%. Since this value exceeds the typical lattice matching\ncriterion (<5%), the original statement of “lattice matching” was indeed inappropriate.\nWe apologize for this oversight, and following the suggestion of Reviewer #2, we have\nnow revised the description of “lattice matching” to “orientational alignment” in the\nupdated text.\n2) In response to how the crystallographic orientation was derived from the FFT\npatterns, we first determined the crystallographic orientation of the graphene flake from\nthe FFT pattern (Figure 3i, shown here as Figure R8); subsequently, the corresponding\ncrystallographic orientation of Pt NPs supported by the above graphene flake were\nmeasured (Figure R9). Then the θ angles between the graphene [10-10] direction and\nthe Pt [111] direction were determined to assess the orientation alignment. We found\nthat the distributions of θ angle were mainly around 0°, 60°, 120°, and 180°, indicating\nthat the Pt NPs adopted preferred orientations aligned with the graphene support during\nthe pulsed heating process. To illustrate the acquisition of crystallographic orientation,\nwe have added Figure R9 in the updated Supplementary Information as Figure S15\nand revised the corresponding text, which reads as “When the Pt NP orientation (green\ndashed line) deviated from the graphene orientation, the angle was denoted as θ, as\nshown in Figure 3j and Figure S15.”.\nReference:\n(15) Cai, P.-Y. et al. Atomic structures of Pt nanoclusters supported on graphene grown\non Pt(111). J. Phys. Chem. C 122, 28, 16132-16141.\nP\nA\nG\nE\nFigure R7. (Figure 3j) Atomic schematic illustrating the orientation of Pt NPs with\nrespect to graphene support.\nFigure R8. (Figure 3i) SAED pattern of the graphene support, showing its single-\ncrystalline nature.\nFigure R9. (Figure S15) (a, b) HRTEM images and corresponding FFT pattern of Pt\nNPs supported on graphene support, showing their crystallographic orientation\nrelationships against graphene flakes.\n(7) Only four images are shown for the 100-pulse case in Figure 4(e-h). Please revise\nthe layout for consistency across all pulse conditions or clarify the rationale behind the\nimage selection.\nP\nA\nG\nE\nOur response: Thank the reviewer very much for this meticulous comment. We clarify\nthat the structural evolution of Pt NPs shown in Figure 4 (attached here as Figure R10)\ndoes not represent an in situ sequence. In fact, to ensure experimental reproducibility,\nwe conducted three independent experiments and selected Pt NPs with representative\nstructures at different pulse numbers to illustrate the structural adjustment process. In\nparticular, typical NPs observed along the [01-1] zone axis after 100 heating pulses are\npresented in Figure 4e-h, as this configuration is relatively the most stable and\nrepresents the eventual structural tendency of Pt NPs under pulsed heating. To avoid\nambiguity, we have revised the description in the updated text, which read as “In order\nto directly disclose the structural optimization of Pt NPs, we accordingly captured the\nhigh-resolution TEM images of graphene supported Pt NPs with representative\nstructures along with the increasing heating pulses.”.\nP\nA\nG\nE\nFigure R10. (Figure 4) Atomic-scale evolutions of Pt NPs in 100 heating pulses. High-\nresolution TEM images showing the lattice structure of representative Pt NPs after (a,\nb) 10 pulses, (c, d) 40 pulses, and (e-h) 100 heating pulses. Scale bar in (a) also applies\nto (b-h). (i-j) False-colored iFFT pattens showing the atomic arrangements of Pt NPs\ncorresponding to (e-h), respectively. (m) Schematic illustration for the structural\nevolution of Pt NPs on a graphene support via pulsed heating.\n(8) Confirm whether the TEM image in Figure S13 was obtained along the same zone\naxis as those shown in Figure 4. This is important for accurate structural comparison.\nOur response: Thanks very much for the reviewer’s reminder. The TEM images in\nFigure S13 and Figure 4 were not acquired along the same zone axis. As indicated in\nthe manuscript, the repeated pulsed heating promotes Pt NPs to adopt a stable structure\nalong the [01-1] zone axis on graphene, whereas conventional heating in our\nexperiments does not allow the NPs to fully reach the most thermodynamically stable\nstate due to the relatively short heating duration. As a result, NPs under conventional\nheating may form along multiple zone axis, such as the [01-1] and [1-21] zone axis, as\nshown in Figure R11. It should be noted that the crystallographic configuration shown\nin Figure S13 is the dominant structure in our TEM observations. For a more accurate\nstructural comparison, we have replaced the original Figure S13 with Figure R11 in\nthe updated Supplementary Information.\nFigure R11. (Figure S16) HRTEM images and corresponding FFT patterns of Pt NPs\nalong the (a, b) [01-1] and (c, d) [1-21] zone axis after conventional heating.\nP\nA\nG\nE\nResponse for Reviewer #2\nThe manuscript titled “Defying thermodynamics: Nonequilibrium pulsed heating\nfreezes sintering of supported metal nanocatalysts” explores the behavior of Pt\nnanoparticles supported on graphene under ultrafast pulsed heating, using in situ\n(S)TEM observations in combination with DFT and MD simulations. The study aims to\ndemonstrate that pulsed heating leads to a metastable, kinetically stabilized state that\ncan inhibit nanoparticle sintering more effectively than conventional heating. While the\nexperimental design is technically sound and the integration of microscopy with\nmodeling is methodologically appropriate, the current version of the manuscript raises\nseveral concerns that must be addressed before it can be considered for publication.\nThe mechanistic claims, particularly regarding structural optimization, interface\neffects, and the generality of the proposed anti-sintering mechanism, require clearer\njustification and more critical discussion. Additionally, the manuscript would benefit\nfrom a more rigorous evaluation of the crystallinity data, the role of the substrate, and\nthe absence of catalytic performance validation. Therefore, I recommend major\nrevisions. Specific comments are provided below to help the authors improve the\nmanuscript’s clarity, depth, and scientific rigor.\n(1) In Figure 2m, the lower crystallinity of Pt NPs under conventional heating may be\nbiased by the different thermal states during which the measurements were taken—if\nFFT was performed at high temperature, thermal vibrations and atomic diffusion could\nartificially reduce apparent crystallinity. In contrast, pulsed heating benefits from\nrepeated cooling, effectively annealing the structure. A fair comparison should assess\ncrystallinity after cooling in both cases, or this limitation should be clearly discussed\nto avoid misinterpretation. Including such a control or at least discussing this thermal-\nstate-dependent artifact would significantly enhance the credibility of the crystallinity\ncomparison and deepen our understanding of the thermal evolution of NP structure in\nboth regimes.\nOur response: We thanks very much for the positive comment and kind suggestion\nP\nA\nG\nE\nfrom the reviewer. Following the reviewer's suggestion, we have further compared the\ncrystallinity of the Pt NPs after cooling under both pulsed and conventional heating.\nThe HRTEM image and corresponding FFT pattern of the same Pt NP after\nconventional heating and cooling are shown in Figure R12a, and the relative\ncrystallinity of Pt NPs after cooling is added to the original Figure 2m, which is shown\nhere as Figure R12b. As expected, high temperatures reduce the crystallinity of Pt NPs,\nas indicated by the lower FFT intensity for samples heated to 1000 °C under\nconventional heating (Figure R12b). After cooling, the crystallinity under conventional\nheating increases slightly but remains lower than that observed under pulsed heating.\nThis result suggests that pulsed heating does improve the crystallinity of the NPs,\npossibly due to its merit of repeated cooling process.\nTo better illustrate this point, the results (Figure R12) have been added to the updated\nSupplementary Information as Figure S10, and the corresponding discussion has been\nrevised in the manuscript, which reads as “(the comparison after cooling is also\nprovided in Figure S10 to exclude the temperature difference)”.\nFigure R12. (Figure S10) (a) HRTEM image and corresponding FFT pattern of the\nsame Pt NP in conventional heating (Figure 2l) after cooling to RT. (b) Evolutions of\nrelative crystalline orders for Pt NPs throughout the pulsed heating and conventional\nheating, including the crystallinity comparison after cooling.\n(2) In Figure 2n, the electron energy loss spectroscopy (EELS) results suggest changes\nat the metal-support interface, but the chemical state evolution of Pt (e.g., oxidation\nstate, bonding environment) is not fully explored. Complementary characterization\nP\nA\nG\nE\nwould help clarify the electronic effects contributing to NP stabilization.\nOur response: Thank the reviewer very much for this important suggestion. We\nattempted to probe the chemical state of Pt using EELS; however, due to the relatively\nhigh energy-loss of Pt and the considerable thickness, the signal was too weak to\nreliably determine the chemical state of Pt, as shown in Figure R13.\nInstead, we examined the chemical state evolution of Pt indirectly through the changes\nin the C K-edge EELS spectra. First, EELS spectra of pristine graphene before and after\n100 heating pulses were collected (Figure R14), showing no significant changes. In\ncontrast, a notable C K-edge shift was observed at the Pt NP-graphene interface (Figure\n2n), suggesting that this shift originates from charge transfer between Pt NPs and\ngraphene rather than from the graphene itself. In addition, our previous work has\ndemonstrated that charge transfer generally occurs from Pt NPs to graphene, resulting\nin a decrease in the C valence and a corresponding increase in the Pt valence.16\nAccordingly, this charge transfer during pulsed heating leads to partial oxidation of Pt\nand the formation of strong Pt-C bonds, which contribute to NP stabilization.\nWe have revised the corresponding discussion in the revised manuscript, which reads\nas “As shown in Figure 2n, the π* excitation of C K-edge gradually shifts toward lower\nenergy loss values during pulsed heating (noticeable shift begins at the 4th pulse, likely\ndue to the NPs initiate close contacts with the support), which can be a result of strong\nbonding and charge transfer between Pt NPs and graphene support that modify the\nelectronic structure around the active sites;” and “In addition, the C K-edge EELS\nresults of the graphene support before and after 100 heating pulses confirm its structural\nintegrity under repeated heating pulses (Figure S13).”. We also added Figure R14 in\nthe updated Supplementary Information as Figure S13.\nReference:\n(16) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\nP\nA\nG\nE\n29183 (2024).\nFigure R13. EELS spectra taken from a Pt NP after pulsed heating for the Pt-M edge.\nsupport before and after 100 heating pulses.\n(3) In Figure 3, the manuscript claims a “high degree of lattice matching” between Pt\nNPs and graphene supports. However, this terminology is not strictly accurate. Pt(111)\nhas a lattice spacing of ~0.227 nm, while the in-plane lattice spacing of graphene (e.g.,\n(10-10)) is ~0.213 nm, and their crystallographic symmetries (fcc vs. hexagonal) differ.\nThus, this interface should not be described as lattice-matched. A more appropriate\nterm would be “orientation alignment” or “epitaxial-like interfacial relationship.” The\nauthors are advised to revise this statement for precision.\nOur response: Thank the reviewer very much for this significant suggestion. To clarify\nthe validity of the “lattice matching” statement in the manuscript, we have calculated\nthe lattice mismatch between the Pt (111) plane and the graphene (10-10) plane, which\nP\nA\nG\nE\nis 6.57%. Since this value exceeds the typical lattice matching criterion (<5%), the\noriginal statement of “lattice matching” was indeed inappropriate. We apologize for this\noversight, and following your suggestion, we have now revised the description of\n“lattice matching” to “orientational alignment” in the updated text.\n(4) In the part of “Sintering kinetics of pulsed heating”, The manuscript attributes the\nsintering resistance under pulsed heating to both interfacial structural optimization and\nkinetic suppression. It would strengthen the mechanistic understanding if the authors\ndiscuss whether kinetic limitation alone—without crystallographic alignment or\nstructural optimization—would be sufficient to ensure long-term stability. This\ndistinction is important to evaluate whether the observed robustness is primarily due to\nthe heating profile or also critically dependent on support-induced ordering.\nOur response: Thanks very much for the reviewer’s reminder.\nFirst, in the supported catalyst systems without noticeable interfacial interaction,\npulsed heating alone can still effectively limit sintering,17,18 suggesting that pure kinetic\nconfinement is sufficient to inhibit particle migration. Similarly, the Pt/graphene system\nused in our study exhibits weak metal-support interactions.19 In particular, during the\nfirst few heating pulses, when NPs have not yet established good contacts with\ngraphene support, sintering is thoroughly suppressed by kinetic blocking of atomic\ndiffusion and particle migration. Therefore, we conclude that even under a single pulse,\nor cumulatively across 100 pulses, kinetics alone can prevent sintering.\nSecond, repeated pulses lead to structural and interfacial optimization that enhances\nmetal-support interactions, further contributing to sintering resistance. Nonetheless,\nkinetic suppression remains the dominant factor. We have incorporated this discussion\nin the revised manuscript, which reads as “and second, the NPs are kinetically hindered\nfrom undergoing effective migration due to the brief duration of heating pulses, which\nis the key mechanism underlying their sintering resistance.”.\nP\nA\nG\nE\nReferences:\n(17) Yao, Y. et al. In situ high temperature synthesis of single-component metallic\nnanoparticles. ACS Cent. Sci. 3, 294-301 (2017).\n(18) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(19) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\n29183 (2024).\n(5). Although 100 pulses demonstrate improved sintering resistance, the net thermal\nexposure remains short relative to real catalytic conditions. The authors are\nencouraged to address how these metastable structures behave under extended heating,\ncyclic heating, or in the presence of reactive environments, either through additional\ndata, cited references, or detailed discussion.\nOur response: Thanks very much for the reviewer’s reminder. First, numerous studies\nhave shown that nanocatalysts synthesized via pulsed heating exhibit excellent catalytic\nstability under prolonged heating or reactive environments,20-22 which have been\nattributed to the formation of metastable structures and/or the strong metal-support\ninteractions. Second, to directly assess the thermal stability of the Pt/graphene\nnanocatalyst formed after 100 heating pulses in our work, we conducted an extended\nheating test by maintaining the metastable nanostructure at 1000 oC for 1 hour. As\nshown in Figure R15, the Pt NPs retained excellent thermal stability with no obvious\nsintering. This stability can be attributed to the strong bonding between Pt\nnanostructures and the graphene support, which arises from the combined effects of\nkinetic suppression and interface optimization during pulsed heating, effectively\npreventing NP sintering even under prolonged high-temperature exposure.\nWe have now added the result (Figure R15) to the updated Supplementary Information\nas Figure S18 and integrated this discussion in the revised manuscript, which reads as\n“In addition, to assess the thermal stability of the Pt/graphene nanocatalyst formed after\n100 heating pulses, we conducted an extended heating test by maintaining it at 1000 oC\nP\nA\nG\nE\nfor 1 hour. As shown in Figure S18, the Pt NPs retained excellent thermal stability with\nno obvious sintering.”.\nReferences:\n(20) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(21) Li, C. et al. Ultrafast self-heating synthesis of robust heterogeneous nanocarbides\nfor high current density hydrogen evolution reaction. Nat. Commun. 13, 3338 (2022).\n(22) Du, P. et al. In-situ Joule-heating drives rapid and on-demand catalytic VOCs\nremoval with ultralow energy consumption. Nano Energy 102, 107725 (2022).\nFigure R15. (Figure S18) In situ STEM images showing the time-lapsed thermal\nstability of Pt/graphene nanocatalyst formed after 100 heating pulses at 1000 oC.\n(6) While structural stabilization is clearly demonstrated, the manuscript lacks direct\ncorrelation with catalytic performance. A brief experimental validation (e.g., a model\nreaction demonstrating enhanced durability or activity of pulsed-heated Pt NPs) or a\nrobust discussion on how the observed microstructural advantages may translate into\ncatalytic improvements would significantly enhance the relevance of the study.\nP\nA\nG\nE\nOur response: We sincerely thank the reviewer for this constructive comment. As we\naddressed in the response above, the Pt/graphene nanocatalyst formed by 100 heating\npulses in our work exhibits great thermal stability under extended heating, as shown in\nFigure R15, which is crucial for practical catalytic performance.\nThen, we will clarify the relationship between the microstructural advantages resulting\nfrom pulsed heating and the catalytic performance in terms of size, structure and metal-\nsupport interaction for nanocatalysts.\nFirst, the ultrafast heating/cooling kinetics of pulsed heating limit the sintering effect,\nproducing ultra-small metal NPs (<3 nm) with high dispersibility. This results in a large\nspecific surface area and abundant active sites, directly enhancing catalytic activity.23,24\nSecond, the high crystallinity of NPs achieved under pulsed heating, particularly the\nmetastable structure arising from multistep optimization, reduces lattice defects (and\ninactive sites) while increasing resistance to atomic migration and sintering.25-27 This\ncontributes to higher intrinsic activity and provides a structural basis for long-term\nstability.\nThird, strong electronic metal-support interaction (ESMI), induced by charge transfer\nduring pulsed heating, effectively anchors the metal NPs, suppressing migration,\nagglomeration, and Ostwald ripening during catalysis.28,29 This mechanism underlies\nthe minimization of performance degradation over prolonged operation. In addition,\nESMI can modulate the electronic structure of the metal surface, optimize the\nadsorption strength of the reactants/intermediates and potentially influence the reaction\npath.30\nTherefore, we have now added the corresponding discussion on how the observed\nmicrostructural advantages translate into catalytic improvements in the updated text,\nwhich reads as “On the basis of above analysis, we want to finally discuss the\nmicrostructural advantages of those pulsed heating-derived NPs in catalytic\napplications: 1) the ultra-small (<3 nm) and highly dispersed NPs provide abundant\nP\nA\nG\nE\nactive sites, which are promising for improving the mass-specific catalytic activity;22,47\n2) the high-crystalline NPs together with the metastable metal/support structure ensure\nhigh intrinsic activity as well as excellent sintering resistance;49,58,59 and 3) the\nconsequential metal-support interaction (i.e., charge transfer) enhances substantial\ninterfacial stability and modulates the electronic structure of metal NPs, which are\nbeneficial for long-term catalytic stability and reaction selectivity.53,54,60 The synergistic\neffect of these structural advantages directly underpins the catalytic performance and\nlong-term stability of these catalysts, demonstrating the great potential of pulsed\nheating for precise and facile regulations of supported nanocatalysts.”.\nReferences:\n(23) Dai, Y., Lu, P., Cao, Z., Campbell, C. T. & Xia, Y. The physical chemistry and\nmaterials science behind sinter-resistant catalysts. Chem. Soc. Rev. 47, 4314-4331\n(2018).\n(24) Liu, L. & Corma, A. Metal catalysts for heterogeneous catalysis: from single atoms\nto nanoclusters and nanoparticles. Chem. Rev. 118, 4981-5079 (2018).\n(25) Dou, X. et al. Structure–reactivity relationship of zeolite-confined Rh catalysts for\nhydroformylation of linear α-olefins. J. Am. Chem. Soc. 147, 2726-2736 (2025).\n(26) Chen, Q. et al. Rapid synthesis of metastable materials for electrocatalysis. Chem.\nSoc. Rev. 54, 4567-4616 (2025).\n(27) Li, Z. et al. Well-defined materials for heterogeneous catalysis: from nanoparticles\nto isolated single-atom sites. Chem. Rev. 120, 623-682 (2020).\n(28) Xu, M. et al. Renaissance of strong metal–support interactions. J. Am. Chem. Soc.\n146, 2290-2307 (2024).\n(29) Hu, X., Xu, D. & Jiang, J. Strong metal‐support interaction between Pt and TiO\n2\nover high-temperature CO hydrogenation. Angew. Chem. Int. Ed. 64, e202419103\n2\n(2025).\n(30) Li, J. et al. Highly active and stable metal single-atom catalysts achieved by strong\nelectronic metal–support interactions. J. Am. Chem. Soc. 141, 14515-14519 (2019).\nP\nA\nG\nE\nPoint-by-point response\nWe sincerely thank the reviewers for their comments and suggestions on our manuscript.\nWe have addressed all the concerns raised by the referees in full and revised the\nmanuscript accordingly. Our responses to the reviewers’ comments are given below.\nThe content is organized as following:\nSection Ⅰ: Response for Reviewer 1 (p2)\nSection Ⅱ: Response for Reviewer 2 (p3-p9)\nP\nA\nG\nE\nResponse for Reviewer #1\nIn the manuscript, Huang et al. report ultrafast pulsed heating as a nonequilibrium\nstrategy to suppress the sintering of supported Pt nanoparticles, using graphene as the\nsupport. Through a combination of in situ STEM analysis, EELS, DFT, and MD\nsimulations, the authors reveal that pulsed heating induces a thermodynamically\nunstable yet kinetically stable state, enabling improved crystallinity and enhanced\nmetal–support interactions while effectively inhibiting particle migration and\ncoalescence. This work provides a novel atomic-scale understanding of metastable\nstates in nanocatalysts and offers an alternative route to sintering-resistant catalyst\nsynthesis beyond thermodynamic constraints. Overall, the authors present a solid and\nwell-validated study, and this manuscript will be of high interest to researchers working\non nanocatalysts. The methodology is rigorous, and the mechanistic insights are\nvaluable. This manuscript can be considered for publication in Nature Communications.\nHowever, the following points should be addressed before publication to further\nimprove the quality of this work.\n(1) The authors mention that the heating pattern was designed based on recent reports;\nhowever, a more detailed description of the temperature profile, particularly the cooling\nrate following each pulsed heating, is necessary. Since cooling kinetics are critical for\nthe formation of metastable nanostructures, quantifying the cooling behavior would\ngreatly enhance the mechanistic understanding. Additionally, the selection of the 10-\npulse condition as the primary reference over the 1-pulse case remains unclear. Could\nthe authors clarify and comment on the potential effects of a single, higher-temperature\npulse?\nOur response: Thanks very much for the positive comment and kind suggestion from\nthe reviewer. We would like to respond for your concerns as follows.\n1) Regarding the reviewer’s comments on the temperature profile, we emphasize that\nboth the heating rate and, in particular, the cooling rate of 150 oC/s in our pulsed heating\nexperiment are well within the capabilities of the DENSsolutions Wildfire heating\nP\nA\nG\nE\nsystem.1,2 Furthermore, direct temperature measurements recorded by the Impulse\nsoftware during an individual heating pulse confirm the uniformity of the designed\nheating/cooling rate (Table R1).\nSecond, we agree with the reviewer that the cooling kinetics indeed play a decisive role\nin the formation of metastable structures. The cooling rate achieved in our pulsed\nheating experiments is markedly higher than that of conventional heating, enabling the\nsuppression of atomic diffusion and thereby stabilizing the metastable structures\nformed at elevated temperatures.3,4 In contrast, conventional cooling rates keep the\nsystem much close to thermodynamic equilibrium, which facilitates the crystallization\nof metal nanoparticles and the evolution of thermodynamically stable structures.\nConsequently, the cooling behaviors of the two approaches differ fundamentally. To\nfurther address this point, we have now included detailed descriptions of the cooling\nrate in the revised text, which read as “Particularly, the design of ultrafast cooling rates\nis essential, as the quenching process is critical for stabilizing the metastable structures\nformed at high temperatures.45,46” and “For comparison, another in situ experiment\nunder conventional heating was parallelly conducted, involving a slow heating rate of\n1 oC s-1 to 1000 °C and a subsequent cooling rate of 5 oC s-1 to room temperature”.\n2) Regarding the reviewer’s questions on the design of pulse conditions, we note that\nthe choice of a 10-pulse sequence follows the approach reported by Yao et al.;5 since\nboth the decomposition of metal precursors and the nucleation/growth of metal NPs\nrequire sufficient time, and a single heating pulse is typically inadequate to complete\nthese processes. Approximately 10 pulses are therefore necessary to obtain uniformly\ndispersed NPs, which then provides a meaningful basis for investigating the sintering\nbehavior of supported nanocatalysts.\nFurthermore, while a single, higher-temperature pulse can indeed accelerate precursor\ndecomposition, organics volatilization, and NP crystallization,6 it does not alter the\nintrinsic tendency for sintering or structural evolution under pulsed heating; rather, it\nmerely accelerates the kinetics. Thus, we consider higher-temperature pulses with fewer\nP\nA\nG\nE\npulse numbers cannot be the ideal parameter. We also wat to remind you that our focus\nlies on the understanding of sintering dynamics, structural evolution of NPs, and\ninterface optimization that occur during pulsed heating; therefore, employing relatively\nlower-temperature pulses slows down these transformations, thereby enabling more\nconvenient observations.\nTo clarify the reason for the design in our work, we have now added the following\ndescription in the updated text: “the heating pattern was set based on recent reports and\nthe initial 10-pulse condition was selected to complete the decomposition of precursors\nand capture the crystallization process of metal NPs”.\nReferences:\n(1) van Swieten, T. P. et al. Mapping elevated temperatures with a micrometer\nresolution using the luminescence of chemically stable upconversion nanoparticles.\nACS Appl. Nano Mater. 4, 4208-4215 (2021).\n(2) Vijayan, S., Wang, R., Kong, Z. & Jinschek, J. R. Quantification of extreme thermal\ngradients during in situ transmission electron microscope heating experiments. Microsc.\nRes. Techniq. 85, 1527-1537 (2021).\n(3) Han, Y.-C., Cao, P.-Y. & Tian, Z.-Q. Controllable synthesis of solid catalysts by\nhigh-temperature pulse. Acc. Mater. Res. 4, 648-654 (2023).\n(4) Deng, B. et al. Phase controlled synthesis of transition metal carbide nanocrystals\nby ultrafast flash Joule heating. Nat. Commun. 13, 262 (2022).\n(5) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(6) Chen, L., Liu, J., Volpe, R. & Grasso, S. Impact of repeated heat pulses on the\nconsolidation and grain growth of 3YSZ consolidated via ultrafast high-temperature\nsintering (UHS). J. Eur. Ceram. Soc. 45, 117395 (2025).\nP\nA\nG\nE\nTable R1. The actual temperature measurement of a single heating pulse.\nExperiment time / s Temperature Setpoint / oC Temperature Measured / oC\n0 20 20.507456\n1.982 347.413451 305.582642\n3.965 628.539899 651.154297\n6.610 1003.617347 1012.758667\n8.591 768.879477 800.145874\n10.571 487.144688 474.15567\n13.542 20 20.297533\n(2) The authors mention that ultrafast pulsed heating effectively suppresses atomic\ndiffusion and aggregation of nanoparticles. However, in several recent studies,\nincluding direct-joule heating-based redispersion/atomization (Journal of the\nAmerican Chemical Society 142,41, 2020, 17364-17371., Science 359, 6383, 2018,\n1489-1494.), and photothermal effect-driven redispersion/atomization (metal oxide\nredispersion (Advanced Materials, 2025, 2419790.), Pt atomization (Chem 8, 4, 2022,\n1014-1033.)), it has been shown that ultrafast high-temperature treatment can actually\npromote atomic diffusion while simultaneously restricting aggregation, resulting in\nsmaller or even atomically dispersed particles. Could the pulsed heating strategy used\nin this study also induce redispersion or partial atomization of Pt nanoparticles,\nespecially at elevated pulse temperatures or with increased pulse counts? In such cases,\natomic mobility could be activated while aggregation remains kinetically suppressed\ndue to short exposure durations. The authors are encouraged to comment on whether\nsuch size reduction or dispersion behavior could emerge under more intensive pulse\nconditions and whether this pathway has been experimentally tested or theoretically\npredicted.\nP\nA\nG\nE\nOur response: We sincerely thank the reviewer for this important suggestion. We\nclarify that no redispersion or atomization behavior has been observed in our pulsed\nheating experiments, as evidenced by the size evolution of Pt NPs over 100 heating\npulses (Figure 3h, shown here as Figure R1).\nOne possible reason is the size effect: pulsed heating decomposes the precursors into\nwell-dispersed NPs with diameters below 2 nm, which are much smaller than the\nredispersed NPs reported in the literature cited by the reviewer. Such ultra-small NPs\npossess very high surface energies, making further redispersion unfavorable. More\nimportantly, as noted in previous reports,7-9 redispersion or atomization typically\nrequires two key conditions: (i) sufficiently high temperatures to break atomic bonds\nwithin the NPs and overcome diffusion barriers, thus causing the NPs to split and move\non the support; (ii) strong metal–support interactions, such as spatial (MOFs, COFs) or\nchemical (surface functional groups, dangling bonds) confinements, are also essential\nto stabilize the redistributed atoms or ultra-small clusters.\nTherefore, in our opinion (and under the current experimental conditions),\nredispersion/atomization cannot be induced solely by elevated pulse temperatures or\nincreased pulse counts because the nature of the support is also critical. In our system,\nthe graphene support provides an atomically smooth surface with negligible\nconfinement, preventing particles/atoms trapping. We emphasize it here that this design\nis intentional, as it allows us to focus on the sintering behaviors of NPs under pulsed\nheating.\nReferences:\n(7) Lang, Z. et al. Destabilization of single-atom catalysts: characterization,\nmechanisms, and regeneration strategies. Adv. Mater. 37, 2418942 (2025).\n(8) Li, L. & Zhang, N. Atomic dispersion of bulk/nano metals to atomic-sites catalysts\nand their application in thermal catalysis. Nano Res. 16, 6380-6401 (2023).\n(9) Morgan, K., Goguet, A. & Hardacre, C. Metal redispersion strategies for recycling\nof supported metal catalysts: a perspective. ACS Catal. 5, 3430-3445 (2015).\nP\nA\nG\nE\nFigure R1. (Figure 3h) Average size of Pt NPs as a function of pulse number across\n(a-f). Error band represents the 95% confidence interval of the mean.\n(3) The manuscript reports the application of up to 100 successive heating pulses,\nyet no notable structural or chemical change in the graphene support is discussed.\nCould the authors elaborate on the methods used to evaluate the integrity of the graphene\nafter repeated thermal treatments? In particular, were any atomic-level\ncharacterizations (e.g., Raman spectroscopy, EELS, or aberration-corrected TEM)\nconducted to assess possible cumulative damage or defect generation?\nOur response: We thank the reviewer for this professional suggestion. While we did\nnot initially emphasize the changes in the graphene support during 100 heating pulses,\nit is well established that graphene possesses excellent thermal stability as a catalyst\nsupport, as frequently documented in previous studies.10,11 Additionally, there are also\nstudies indicating that surface defects generated during preparation can be repaired\nunder prolonged heating,12 but the extremely short duration of each pulse in our\nexperiments makes it unlikely that successive pulses would significantly affect the\nstructure of graphene. Moreover, the graphene samples were sintered at 500 oC for 30\nminutes prior to our in situ heating experiments, which further ensures their thermal\nstability.\nTo directly assess potential cumulative damage or defect generation of graphene\nsupport, we collected the EELS spectra of pristine graphene before and after 100\nP\nA\nG\nE\nheating pulses (Figure R2). The absence of noticeable changes in the C–K edge\nconfirms that pulsed heating exerts negligible influence on the graphene structure. We\nhave now added the corresponding discussion on the integrity of graphene under\nrepeated pulses in the revised manuscript, which reads as “In addition, the C K-edge\nEELS results of the graphene support before and after 100 heating pulses confirm its\nstructural integrity under repeated heating pulses (Figure S13).”. We also added Figure\nR2 in the updated Supplementary Information as Figure S13.\nReferences:\n(10) Jang, I. et al. Instantaneous thermal energy for swift synthesis of single-atom\ncatalysts for unparalleled performance in metal–air batteries and fuel cells. Adv. Mater.\n36, 2403273 (2024).\n(11) Qiao, Y. et al. 3D-printed graphene oxide framework with thermal shock\nsynthesized nanoparticles for Li-CO batteries. Adv. Funct. Mater. 28, 1805899 (2018).\n2\n(12) Liu, L., Qing, M., Wang, Y. & Chen, S. Defects in graphene: generation, healing,\nand their effects on the properties of graphene: a review. J. Mater. Sci. Technol. 31, 599-\n606 (2015).\nFigure R2. (Figure S13) (a, b) STEM image and C K-edge EELS spectra of graphene\nsupport before and after 100 heating pulses.\n(4) The discussion compares the appearance of the Pt (111) facet after a single pulsed\nheating step with the delayed emergence of the same facet under conventional heating\n(initially showing the (200) facet). Given that (111) is thermodynamically more stable\nthan (200), it would be more accurate to highlight the rapid stabilization of (111) as a\nP\nA\nG\nE\nmerit of pulsed sintering rather than concluding a higher degree of crystallinity.\nMoreover, as Figure S12 also shows the appearance of the (200) facet under pulsed\nheating, please address this apparent contradiction.\nOur response: We appreciate the reviewer’s insightful comment on that pulsed heating\npromotes the rapid formation of the thermodynamically stable (111) facet. However,\nthe conclusion we drew in the text regarding higher crystallinity was not directly linked\nto the emergence of the (111) plane. Instead, it was based on the brightness contrast of\nthe diffraction spots in the FFT patterns (Figure S9 and Figure 2m, attached here as\nFigure R3 and Figure R4, respectively), where pulsed heating produced stronger\ndiffraction contrasts, qualitatively indicating a higher degree of NP crystallinity.13 To\navoid potential misunderstanding caused by our earlier wording, we haven revised the\ncorresponding statement in the manuscript as: “In contrast, the exposed crystal plane\nfor Pt NPs under the conventional heating process changed from (200) to (111) after\n500 oC (Figure 2l) and these NPs displayed poor crystallinity (see the corresponding\nFFT pattern in Figure S9b);”.\nRegarding the appearance of the (200) facet after 100 heating pulses, we clarify that\nwhile this is possible, it remains a rare phenomenon, likely arising from anchoring\neffects of surface defects or localized interfacial forces. Importantly, the overall trend\nis the preferential formation of the more stable (111) facets, as shown in Figure R5,\nwhere the ratio of (111) facet exceeds 90%. To illustrate this point more clearly, we\nhave replaced the original Figure S12 with Figure R5 in the updated Supplementary\nInformation and revised the corresponding text, which read as “high-resolution TEM\nimages of the Pt NPs after 100 pulses in Figure S14 exhibit hexagonal NPs with\ndominant {111} facets and occasional (200) planes”.\nReference:\n(13) Fei, L. et al. Observable two-step nucleation mechanism in solid-state formation\nof tungsten carbide. ACS Nano 13, 681-688 (2019).\nP\nA\nG\nE\nFigure R3. (Figure S9) (a) FFT pattern series corresponding to pulsed heating process\nin Figure 2k. (b) FFT pattern series corresponding to conventional heating process in\nFigure 2l.\nFigure R4. (Figure 2m) Evolutions of relative crystalline orders for Pt NPs throughout\n(k) and (l) against time. The amounts of crystalline order were determined from the spot\nintensity of the corresponding FFT patterns (see Figure S9), comparing the value from\na NP with the same crystal orientation (whose crystalline order is set as 100, heated\nwith 10 pulses).\nP\nA\nG\nE\nFigure R5. (Figure S14) High-resolution TEM images showing the crystallographic\nanalysis of Pt NPs after 100 heating pulses. NPs that expose their (111) and (200) crystal\nplanes are marked with green and yellow circles, respectively. The result indicates the\ndominance of the stable (111) crystal plane.\n(5) A noticeable shift in the peak position begins at the 4th pulse. Please provide a\ndiscussion on this phenomenon. Additionally, prior to comparing 10-pulse treatment\nwith conventional heating for 1000 seconds, consider providing comparative data at\nintermediate temperatures to better contrast single-pulse effects.\nOur response: We sincerely thank the reviewer’s constructive comment.\n1) The phenomenon of peak shift noticed by the reviewer can be explained by the fact\nthat the first few pulses primarily drive the decomposition of precursor, during which\nthe newly formed NPs are not yet in intimate contact with the support due to residual\norganics at the interface. By the 4th pulse, the NPs may have established closer contacts\nwith the graphene support, enabling charge transfer, as reflected by the peak shift in the\nEELS spectra (Figure 2n, attached here as Figure R6). That charge transfer between\ngraphene and Pt NPs has been confirmed (both experimentally and theoretically) in our\nprevious work.14 To clarify this point, we have added the corresponding description in\nthe updated text, which read as “As shown in Figure 2n, the π* excitation of C K-edge\ngradually shifts toward lower energy loss values during pulsed heating (noticeable shift\nbegins at the 4th pulse, likely due to the NPs initiate close contacts with the support),\nwhich can be a result of strong bonding and charge transfer between Pt NPs and\ngraphene support that modify the electronic structure around the active sites;”.\nP\nA\nG\nE\n2) Regarding the EELS results under conventional heating (Figure 2n), we clarify that\nthese measurements were conducted during the heating process rather than under\nisothermal conditions at 1000 oC. Comparative spectra at intermediate temperatures\nhave therefore been included in Figure 2n.\nReference:\n(14) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\n29183 (2024).\nFigure R6. (Figure 2n) C K-edge EELS spectra for the graphene supports as a function\nof heating time under pulsed heating and conventional heating modes.\n(6) In the interpretation of Figure 3j, clarify the rationale for lattice matching\ndiscussion between 3D Pt nanoparticles and 2D graphene sheets. In particular,\nprovides more detail on how the crystallographic orientation was determined from FFT\npatterns.\nOur response: Thanks very much for the constructive comments from the reviewer.\n1) For your concern on Figure 3j, our intention for this scheme focuses on the\ncrystallographic orientation relationship between the [111] direction of Pt NPsn and the\n[10-10] direction of graphene flakes (you may also refer to Figure 5c for the side-view\nof this interfacial relationship), which has been well explored in previous studies.15 To\nP\nA\nG\nE\nclearly illustrate this orientation relationship and to avoid potential misunderstanding,\nwe have revised the original Figure 3j with Figure R7 in the updated manuscript.\nIn addition, to clarify the validity of the “lattice matching” statement in the manuscript,\nwe have calculated the lattice mismatch between the Pt (111) plane and the graphene\n(10-10) plane, which is 6.57%. Since this value exceeds the typical lattice matching\ncriterion (<5%), the original statement of “lattice matching” was indeed inappropriate.\nWe apologize for this oversight, and following the suggestion of Reviewer #2, we have\nnow revised the description of “lattice matching” to “orientational alignment” in the\nupdated text.\n2) In response to how the crystallographic orientation was derived from the FFT\npatterns, we first determined the crystallographic orientation of the graphene flake from\nthe FFT pattern (Figure 3i, shown here as Figure R8); subsequently, the corresponding\ncrystallographic orientation of Pt NPs supported by the above graphene flake were\nmeasured (Figure R9). Then the θ angles between the graphene [10-10] direction and\nthe Pt [111] direction were determined to assess the orientation alignment. We found\nthat the distributions of θ angle were mainly around 0°, 60°, 120°, and 180°, indicating\nthat the Pt NPs adopted preferred orientations aligned with the graphene support during\nthe pulsed heating process. To illustrate the acquisition of crystallographic orientation,\nwe have added Figure R9 in the updated Supplementary Information as Figure S15\nand revised the corresponding text, which reads as “When the Pt NP orientation (green\ndashed line) deviated from the graphene orientation, the angle was denoted as θ, as\nshown in Figure 3j and Figure S15.”.\nReference:\n(15) Cai, P.-Y. et al. Atomic structures of Pt nanoclusters supported on graphene grown\non Pt(111). J. Phys. Chem. C 122, 28, 16132-16141.\nP\nA\nG\nE\nFigure R7. (Figure 3j) Atomic schematic illustrating the orientation of Pt NPs with\nrespect to graphene support.\nFigure R8. (Figure 3i) SAED pattern of the graphene support, showing its single-\ncrystalline nature.\nFigure R9. (Figure S15) (a, b) HRTEM images and corresponding FFT pattern of Pt\nNPs supported on graphene support, showing their crystallographic orientation\nrelationships against graphene flakes.\n(7) Only four images are shown for the 100-pulse case in Figure 4(e-h). Please revise\nthe layout for consistency across all pulse conditions or clarify the rationale behind the\nimage selection.\nP\nA\nG\nE\nOur response: Thank the reviewer very much for this meticulous comment. We clarify\nthat the structural evolution of Pt NPs shown in Figure 4 (attached here as Figure R10)\ndoes not represent an in situ sequence. In fact, to ensure experimental reproducibility,\nwe conducted three independent experiments and selected Pt NPs with representative\nstructures at different pulse numbers to illustrate the structural adjustment process. In\nparticular, typical NPs observed along the [01-1] zone axis after 100 heating pulses are\npresented in Figure 4e-h, as this configuration is relatively the most stable and\nrepresents the eventual structural tendency of Pt NPs under pulsed heating. To avoid\nambiguity, we have revised the description in the updated text, which read as “In order\nto directly disclose the structural optimization of Pt NPs, we accordingly captured the\nhigh-resolution TEM images of graphene supported Pt NPs with representative\nstructures along with the increasing heating pulses.”.\nP\nA\nG\nE\nFigure R10. (Figure 4) Atomic-scale evolutions of Pt NPs in 100 heating pulses. High-\nresolution TEM images showing the lattice structure of representative Pt NPs after (a,\nb) 10 pulses, (c, d) 40 pulses, and (e-h) 100 heating pulses. Scale bar in (a) also applies\nto (b-h). (i-j) False-colored iFFT pattens showing the atomic arrangements of Pt NPs\ncorresponding to (e-h), respectively. (m) Schematic illustration for the structural\nevolution of Pt NPs on a graphene support via pulsed heating.\n(8) Confirm whether the TEM image in Figure S13 was obtained along the same zone\naxis as those shown in Figure 4. This is important for accurate structural comparison.\nOur response: Thanks very much for the reviewer’s reminder. The TEM images in\nFigure S13 and Figure 4 were not acquired along the same zone axis. As indicated in\nthe manuscript, the repeated pulsed heating promotes Pt NPs to adopt a stable structure\nalong the [01-1] zone axis on graphene, whereas conventional heating in our\nexperiments does not allow the NPs to fully reach the most thermodynamically stable\nstate due to the relatively short heating duration. As a result, NPs under conventional\nheating may form along multiple zone axis, such as the [01-1] and [1-21] zone axis, as\nshown in Figure R11. It should be noted that the crystallographic configuration shown\nin Figure S13 is the dominant structure in our TEM observations. For a more accurate\nstructural comparison, we have replaced the original Figure S13 with Figure R11 in\nthe updated Supplementary Information.\nFigure R11. (Figure S16) HRTEM images and corresponding FFT patterns of Pt NPs\nalong the (a, b) [01-1] and (c, d) [1-21] zone axis after conventional heating.\nP\nA\nG\nE\nResponse for Reviewer #2\nThe manuscript titled “Defying thermodynamics: Nonequilibrium pulsed heating\nfreezes sintering of supported metal nanocatalysts” explores the behavior of Pt\nnanoparticles supported on graphene under ultrafast pulsed heating, using in situ\n(S)TEM observations in combination with DFT and MD simulations. The study aims to\ndemonstrate that pulsed heating leads to a metastable, kinetically stabilized state that\ncan inhibit nanoparticle sintering more effectively than conventional heating. While the\nexperimental design is technically sound and the integration of microscopy with\nmodeling is methodologically appropriate, the current version of the manuscript raises\nseveral concerns that must be addressed before it can be considered for publication.\nThe mechanistic claims, particularly regarding structural optimization, interface\neffects, and the generality of the proposed anti-sintering mechanism, require clearer\njustification and more critical discussion. Additionally, the manuscript would benefit\nfrom a more rigorous evaluation of the crystallinity data, the role of the substrate, and\nthe absence of catalytic performance validation. Therefore, I recommend major\nrevisions. Specific comments are provided below to help the authors improve the\nmanuscript’s clarity, depth, and scientific rigor.\n(1) In Figure 2m, the lower crystallinity of Pt NPs under conventional heating may be\nbiased by the different thermal states during which the measurements were taken—if\nFFT was performed at high temperature, thermal vibrations and atomic diffusion could\nartificially reduce apparent crystallinity. In contrast, pulsed heating benefits from\nrepeated cooling, effectively annealing the structure. A fair comparison should assess\ncrystallinity after cooling in both cases, or this limitation should be clearly discussed\nto avoid misinterpretation. Including such a control or at least discussing this thermal-\nstate-dependent artifact would significantly enhance the credibility of the crystallinity\ncomparison and deepen our understanding of the thermal evolution of NP structure in\nboth regimes.\nOur response: We thanks very much for the positive comment and kind suggestion\nP\nA\nG\nE\nfrom the reviewer. Following the reviewer's suggestion, we have further compared the\ncrystallinity of the Pt NPs after cooling under both pulsed and conventional heating.\nThe HRTEM image and corresponding FFT pattern of the same Pt NP after\nconventional heating and cooling are shown in Figure R12a, and the relative\ncrystallinity of Pt NPs after cooling is added to the original Figure 2m, which is shown\nhere as Figure R12b. As expected, high temperatures reduce the crystallinity of Pt NPs,\nas indicated by the lower FFT intensity for samples heated to 1000 °C under\nconventional heating (Figure R12b). After cooling, the crystallinity under conventional\nheating increases slightly but remains lower than that observed under pulsed heating.\nThis result suggests that pulsed heating does improve the crystallinity of the NPs,\npossibly due to its merit of repeated cooling process.\nTo better illustrate this point, the results (Figure R12) have been added to the updated\nSupplementary Information as Figure S10, and the corresponding discussion has been\nrevised in the manuscript, which reads as “(the comparison after cooling is also\nprovided in Figure S10 to exclude the temperature difference)”.\nFigure R12. (Figure S10) (a) HRTEM image and corresponding FFT pattern of the\nsame Pt NP in conventional heating (Figure 2l) after cooling to RT. (b) Evolutions of\nrelative crystalline orders for Pt NPs throughout the pulsed heating and conventional\nheating, including the crystallinity comparison after cooling.\n(2) In Figure 2n, the electron energy loss spectroscopy (EELS) results suggest changes\nat the metal-support interface, but the chemical state evolution of Pt (e.g., oxidation\nstate, bonding environment) is not fully explored. Complementary characterization\nP\nA\nG\nE\nwould help clarify the electronic effects contributing to NP stabilization.\nOur response: Thank the reviewer very much for this important suggestion. We\nattempted to probe the chemical state of Pt using EELS; however, due to the relatively\nhigh energy-loss of Pt and the considerable thickness, the signal was too weak to\nreliably determine the chemical state of Pt, as shown in Figure R13.\nInstead, we examined the chemical state evolution of Pt indirectly through the changes\nin the C K-edge EELS spectra. First, EELS spectra of pristine graphene before and after\n100 heating pulses were collected (Figure R14), showing no significant changes. In\ncontrast, a notable C K-edge shift was observed at the Pt NP-graphene interface (Figure\n2n), suggesting that this shift originates from charge transfer between Pt NPs and\ngraphene rather than from the graphene itself. In addition, our previous work has\ndemonstrated that charge transfer generally occurs from Pt NPs to graphene, resulting\nin a decrease in the C valence and a corresponding increase in the Pt valence.16\nAccordingly, this charge transfer during pulsed heating leads to partial oxidation of Pt\nand the formation of strong Pt-C bonds, which contribute to NP stabilization.\nWe have revised the corresponding discussion in the revised manuscript, which reads\nas “As shown in Figure 2n, the π* excitation of C K-edge gradually shifts toward lower\nenergy loss values during pulsed heating (noticeable shift begins at the 4th pulse, likely\ndue to the NPs initiate close contacts with the support), which can be a result of strong\nbonding and charge transfer between Pt NPs and graphene support that modify the\nelectronic structure around the active sites;” and “In addition, the C K-edge EELS\nresults of the graphene support before and after 100 heating pulses confirm its structural\nintegrity under repeated heating pulses (Figure S13).”. We also added Figure R14 in\nthe updated Supplementary Information as Figure S13.\nReference:\n(16) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\nP\nA\nG\nE\n29183 (2024).\nFigure R13. EELS spectra taken from a Pt NP after pulsed heating for the Pt-M edge.\nsupport before and after 100 heating pulses.\n(3) In Figure 3, the manuscript claims a “high degree of lattice matching” between Pt\nNPs and graphene supports. However, this terminology is not strictly accurate. Pt(111)\nhas a lattice spacing of ~0.227 nm, while the in-plane lattice spacing of graphene (e.g.,\n(10-10)) is ~0.213 nm, and their crystallographic symmetries (fcc vs. hexagonal) differ.\nThus, this interface should not be described as lattice-matched. A more appropriate\nterm would be “orientation alignment” or “epitaxial-like interfacial relationship.” The\nauthors are advised to revise this statement for precision.\nOur response: Thank the reviewer very much for this significant suggestion. To clarify\nthe validity of the “lattice matching” statement in the manuscript, we have calculated\nthe lattice mismatch between the Pt (111) plane and the graphene (10-10) plane, which\nP\nA\nG\nE\nis 6.57%. Since this value exceeds the typical lattice matching criterion (<5%), the\noriginal statement of “lattice matching” was indeed inappropriate. We apologize for this\noversight, and following your suggestion, we have now revised the description of\n“lattice matching” to “orientational alignment” in the updated text.\n(4) In the part of “Sintering kinetics of pulsed heating”, The manuscript attributes the\nsintering resistance under pulsed heating to both interfacial structural optimization and\nkinetic suppression. It would strengthen the mechanistic understanding if the authors\ndiscuss whether kinetic limitation alone—without crystallographic alignment or\nstructural optimization—would be sufficient to ensure long-term stability. This\ndistinction is important to evaluate whether the observed robustness is primarily due to\nthe heating profile or also critically dependent on support-induced ordering.\nOur response: Thanks very much for the reviewer’s reminder.\nFirst, in the supported catalyst systems without noticeable interfacial interaction,\npulsed heating alone can still effectively limit sintering,17,18 suggesting that pure kinetic\nconfinement is sufficient to inhibit particle migration. Similarly, the Pt/graphene system\nused in our study exhibits weak metal-support interactions.19 In particular, during the\nfirst few heating pulses, when NPs have not yet established good contacts with\ngraphene support, sintering is thoroughly suppressed by kinetic blocking of atomic\ndiffusion and particle migration. Therefore, we conclude that even under a single pulse,\nor cumulatively across 100 pulses, kinetics alone can prevent sintering.\nSecond, repeated pulses lead to structural and interfacial optimization that enhances\nmetal-support interactions, further contributing to sintering resistance. Nonetheless,\nkinetic suppression remains the dominant factor. We have incorporated this discussion\nin the revised manuscript, which reads as “and second, the NPs are kinetically hindered\nfrom undergoing effective migration due to the brief duration of heating pulses, which\nis the key mechanism underlying their sintering resistance.”.\nP\nA\nG\nE\nReferences:\n(17) Yao, Y. et al. In situ high temperature synthesis of single-component metallic\nnanoparticles. ACS Cent. Sci. 3, 294-301 (2017).\n(18) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(19) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\n29183 (2024).\n(5). Although 100 pulses demonstrate improved sintering resistance, the net thermal\nexposure remains short relative to real catalytic conditions. The authors are\nencouraged to address how these metastable structures behave under extended heating,\ncyclic heating, or in the presence of reactive environments, either through additional\ndata, cited references, or detailed discussion.\nOur response: Thanks very much for the reviewer’s reminder. First, numerous studies\nhave shown that nanocatalysts synthesized via pulsed heating exhibit excellent catalytic\nstability under prolonged heating or reactive environments,20-22 which have been\nattributed to the formation of metastable structures and/or the strong metal-support\ninteractions. Second, to directly assess the thermal stability of the Pt/graphene\nnanocatalyst formed after 100 heating pulses in our work, we conducted an extended\nheating test by maintaining the metastable nanostructure at 1000 oC for 1 hour. As\nshown in Figure R15, the Pt NPs retained excellent thermal stability with no obvious\nsintering. This stability can be attributed to the strong bonding between Pt\nnanostructures and the graphene support, which arises from the combined effects of\nkinetic suppression and interface optimization during pulsed heating, effectively\npreventing NP sintering even under prolonged high-temperature exposure.\nWe have now added the result (Figure R15) to the updated Supplementary Information\nas Figure S18 and integrated this discussion in the revised manuscript, which reads as\n“In addition, to assess the thermal stability of the Pt/graphene nanocatalyst formed after\n100 heating pulses, we conducted an extended heating test by maintaining it at 1000 oC\nP\nA\nG\nE\nfor 1 hour. As shown in Figure S18, the Pt NPs retained excellent thermal stability with\nno obvious sintering.”.\nReferences:\n(20) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(21) Li, C. et al. Ultrafast self-heating synthesis of robust heterogeneous nanocarbides\nfor high current density hydrogen evolution reaction. Nat. Commun. 13, 3338 (2022).\n(22) Du, P. et al. In-situ Joule-heating drives rapid and on-demand catalytic VOCs\nremoval with ultralow energy consumption. Nano Energy 102, 107725 (2022).\nFigure R15. (Figure S18) In situ STEM images showing the time-lapsed thermal\nstability of Pt/graphene nanocatalyst formed after 100 heating pulses at 1000 oC.\n(6) While structural stabilization is clearly demonstrated, the manuscript lacks direct\ncorrelation with catalytic performance. A brief experimental validation (e.g., a model\nreaction demonstrating enhanced durability or activity of pulsed-heated Pt NPs) or a\nrobust discussion on how the observed microstructural advantages may translate into\ncatalytic improvements would significantly enhance the relevance of the study.\nP\nA\nG\nE\nOur response: We sincerely thank the reviewer for this constructive comment. As we\naddressed in the response above, the Pt/graphene nanocatalyst formed by 100 heating\npulses in our work exhibits great thermal stability under extended heating, as shown in\nFigure R15, which is crucial for practical catalytic performance.\nThen, we will clarify the relationship between the microstructural advantages resulting\nfrom pulsed heating and the catalytic performance in terms of size, structure and metal-\nsupport interaction for nanocatalysts.\nFirst, the ultrafast heating/cooling kinetics of pulsed heating limit the sintering effect,\nproducing ultra-small metal NPs (<3 nm) with high dispersibility. This results in a large\nspecific surface area and abundant active sites, directly enhancing catalytic activity.23,24\nSecond, the high crystallinity of NPs achieved under pulsed heating, particularly the\nmetastable structure arising from multistep optimization, reduces lattice defects (and\ninactive sites) while increasing resistance to atomic migration and sintering.25-27 This\ncontributes to higher intrinsic activity and provides a structural basis for long-term\nstability.\nThird, strong electronic metal-support interaction (ESMI), induced by charge transfer\nduring pulsed heating, effectively anchors the metal NPs, suppressing migration,\nagglomeration, and Ostwald ripening during catalysis.28,29 This mechanism underlies\nthe minimization of performance degradation over prolonged operation. In addition,\nESMI can modulate the electronic structure of the metal surface, optimize the\nadsorption strength of the reactants/intermediates and potentially influence the reaction\npath.30\nTherefore, we have now added the corresponding discussion on how the observed\nmicrostructural advantages translate into catalytic improvements in the updated text,\nwhich reads as “On the basis of above analysis, we want to finally discuss the\nmicrostructural advantages of those pulsed heating-derived NPs in catalytic\napplications: 1) the ultra-small (<3 nm) and highly dispersed NPs provide abundant\nP\nA\nG\nE\nactive sites, which are promising for improving the mass-specific catalytic activity;22,47\n2) the high-crystalline NPs together with the metastable metal/support structure ensure\nhigh intrinsic activity as well as excellent sintering resistance;49,58,59 and 3) the\nconsequential metal-support interaction (i.e., charge transfer) enhances substantial\ninterfacial stability and modulates the electronic structure of metal NPs, which are\nbeneficial for long-term catalytic stability and reaction selectivity.53,54,60 The synergistic\neffect of these structural advantages directly underpins the catalytic performance and\nlong-term stability of these catalysts, demonstrating the great potential of pulsed\nheating for precise and facile regulations of supported nanocatalysts.”.\nReferences:\n(23) Dai, Y., Lu, P., Cao, Z., Campbell, C. T. & Xia, Y. The physical chemistry and\nmaterials science behind sinter-resistant catalysts. Chem. Soc. Rev. 47, 4314-4331\n(2018).\n(24) Liu, L. & Corma, A. Metal catalysts for heterogeneous catalysis: from single atoms\nto nanoclusters and nanoparticles. Chem. Rev. 118, 4981-5079 (2018).\n(25) Dou, X. et al. Structure–reactivity relationship of zeolite-confined Rh catalysts for\nhydroformylation of linear α-olefins. J. Am. Chem. Soc. 147, 2726-2736 (2025).\n(26) Chen, Q. et al. Rapid synthesis of metastable materials for electrocatalysis. Chem.\nSoc. Rev. 54, 4567-4616 (2025).\n(27) Li, Z. et al. Well-defined materials for heterogeneous catalysis: from nanoparticles\nto isolated single-atom sites. Chem. Rev. 120, 623-682 (2020).\n(28) Xu, M. et al. Renaissance of strong metal–support interactions. J. Am. Chem. Soc.\n146, 2290-2307 (2024).\n(29) Hu, X., Xu, D. & Jiang, J. Strong metal‐support interaction between Pt and TiO\n2\nover high-temperature CO hydrogenation. Angew. Chem. Int. Ed. 64, e202419103\n2\n(2025).\n(30) Li, J. et al. Highly active and stable metal single-atom catalysts achieved by strong\nelectronic metal–support interactions. J. Am. Chem. Soc. 141, 14515-14519 (2019)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "This study played a crucial role in elucidating the mechanism for rational nanostructured catalyst design through heat treatment in a metastable state.\nFurthermore, I believe it is fully acceptable for accurately answering the questions posed.", "reviewer_2": "Many concerns have been addressed. However, after careful review of the revised manuscript and rebuttal, there are still major questions for this paper.\n1. What dose the authors mean about “defying thermodynamics”. How did you achieve that and how can anyone defy thermodynamics? A mere anti-sintering behavior is not defying thermodynamics.\n2. The particle formation and migration process have been previously studied by Nat. Commun. 2020, 11 (1), 6373, and others.\n3. What is the safe region for ultrafast heating to maintain particle stability, for example, T range, t or pulse times range, and heating/cooling ranges. The authors should dig into the mechanism of this kinetic stabilization and propose design principles, instead of just listing one example.\n4. The authors used stability under pulsed heating as improved stability and sintering-resistance. This is far from enough as thermochemical reactions occur at continuous high T rather than pulses. The true isothermal stability is therefore important to evaluate if the particles are stable or not.\n5. The conclusion—that pulsed heating achieves a higher degree of crystallinity than conventional heating—should be discussed more cautiously. A conventional heating and a slow cooling provide sufficient time for atoms to diffuse and rearrange into their lowest-energy, most stable lattice positions, thereby minimizing defects and yielding a highly ordered structure. This process (i.e., annealing) is the widely accepted standard method for improving the crystallinity of materials."}, "author_response": "Point-by-point response\nWe sincerely thank the reviewers for their comments and suggestions on our manuscript.\nWe have addressed all the concerns raised by the referees in full and revised the\nmanuscript accordingly. Our responses to the reviewers’ comments are given below.\nThe content is organized as following:\nSection Ⅰ: Response for Reviewer 1 (p2)\nSection Ⅱ: Response for Reviewer 2 (p3-p9)\nP\nA\nG\nE\nResponse for Reviewer #1\nThis study played a crucial role in elucidating the mechanism for rational\nnanostructured catalyst design through heat treatment in a metastable state.\nFurthermore, I believe it is fully acceptable for accurately answering the questions\nposed.\nOur response: We sincerely appreciate the reviewer's positive comment and\nrecommendation for publication.\nP\nA\nG\nE\nResponse for Reviewer #2\nMany concerns have been addressed. However, after careful review of the revised\nmanuscript and rebuttal, there are still major questions for this paper.\n(1) What dose the authors mean about “defying thermodynamics”. How did you\nachieve that and how can anyone defy thermodynamics? A mere anti-sintering behavior\nis not defying thermodynamics.\nOur response: We thank the reviewer for this careful and important question. We fully\nagree that no process can literally “violate” the thermodynamic laws, and we regret any\nambiguity caused by the phrasing. By using “defying thermodynamics”, we intended\nto describe a process in which pulsed heating drives the system along a nonequilibrium,\nkinetically constrained pathway that is inaccessible under conventional, near-\nequilibrium heating. In other words, pulsed heating does not break thermodynamic laws;\ninstead, it changes the accessible energetic landscape by drastically limiting the time\navailable for diffusion and equilibration, thereby trapping the system in metastable\nconfigurations rather than allowing it to evolve toward the global thermodynamic\nminimum.\nIn our experiments, this nonequilibrium pathway is realized through three interrelated\neffects, all directly supported by the in situ observations: i) Ultrafast heating and cooling\n(up to 150 °C s⁻¹) suppress long-range atomic diffusion and particle migration,\npreventing the system from thermodynamically favorable sintering. ii) Repeated short\npulses kinetically freeze intermediate configurations and then allow stepwise structural\nrelaxation and interface optimization rather than full equilibration, as evidenced by the\nevolution of NP size (Figure 3h), the enhanced FFT diffraction-spot contrast\n(indicating improved crystallinity) (Figure 2m), and the EELS C K-edge shifts\nconsistent with charge transfer and strengthened metal–support interactions (Figure\n2n). iii) The resulting nanostructures are stabilized by improved crystallinity and\nstronger interfacial bonding; consequently, they exhibit remarkable resistance to\ncoarsening even during extended continuous heating at 1000 °C for 1 h (Figure S18).\nP\nA\nG\nE\nThus, our work goes beyond a simple “anti-sintering” phenomenon. Pulsed heating not\nonly suppresses thermodynamically driven coarsening, but also routes nanoparticles\nalong a distinct formation pathway that yields robust structures with specific\ncrystallography and interfacial chemistry thought a thermodynamically unstable yet\nkinetically stable state (that is difficult for conventional heating to realize). This ability\nto access useful nonequilibrium configurations by kinetic control is what we intended\nto convey by the phrase “defying thermodynamics,” not a literal violation of\nthermodynamic principles. To avoid the possible ambiguity, we have changed this\nwording in the revised manuscript as “Beyond thermodynamics”.\n(2) The particle formation and migration process have been previously studied by Nat.\nCommun. 2020, 11 (1), 6373, and others.\nOur response: We thank the reviewer for pointing out the relevant literature. Regarding\nthe Nat. Commun. 2020 paper, it reports fundamentally different experimental facts and\nmechanisms as compared with this work. In that paper, a single, high-energy pulse is\nused to modify the support (for example, transforming amorphous carbon into highly\ndefective turbostratic graphite), thereby providing nucleation and anchoring sites for\nnanoparticles. This process therefore depends on support modification as the\nstabilization route.\nIn contrast, our study establishes a particle-centred, kinetic-controlled strategy that does\nnot rely on support transformation. Through repeated short pulses, we kinetically\nsuppress diffusion-driven sintering and allow the metal particles themselves to undergo\nmultistep structural evolution (including improved crystallinity, facet selection, and\nprogressive strengthening of the metal-support interface). This dynamic optimization\nprocess yields highly supported nanocatalysts even on atomically smooth\ngraphene.\nThis distinction, between support modification and intrinsic nanoparticle kinetic\nP\nA\nG\nE\noptimization, represents the key conceptual advance of our work. It is further\nsubstantiated by our in situ TEM evidence (particle-size evolution, FFT contrast\nenhancement, and C K-edge shifts) and by the extended isothermal stability test.\nWe have cited this paper (Nat. Commun. 2020, 11 (1), 6373) and clarified this\nmechanistic difference in the revised manuscript, which now reads as follows: “It also\ndemonstrates a distinct, particle-centred, and kinetic-controlled pathway in which\npulsed heating drives stepwise structural optimization of NPs, in contrast to previous\nreports where a single high-energy pulse induces support reconstruction and defect\ngeneration to stabilize NPs.35”\n(3) What is the safe region for ultrafast heating to maintain particle stability, for\nexample, T range, t or pulse times range, and heating/cooling ranges. The authors\nshould dig into the mechanism of this kinetic stabilization and propose design principles,\ninstead of just listing one example.\nOur response: We sincerely thank the reviewer for this insightful comment.\nFirst, we wish to emphasize that the central aim of our study is indeed to elucidate the\nstabilization mechanism of supported metal nanoparticles under pulsed heating. Our\nfindings demonstrate that the pulsed-heating process enables the formation of robust\nsupported NPs through kinetic control—that is, by confining atomic diffusion and\nstructural evolution within a non-equilibrium regime. This kinetic stabilization\nmechanism remains generally applicable across a broad range of pulsed-heating\nconditions and is not highly sensitive to minor variations in individual parameters such\nas pulse duration or cycle number. The experimental parameters selected in this work\ntherefore represent a successful realization within this kinetically accessible regime.\nSecond, regarding the reviewer’s request for the “safe region” of ultrafast heating, we\nnote that it cannot be defined by a universal, fixed temperature or time range. Instead,\nthe stability regime should be viewed as a “kinetic window” jointly determined by the\nP\nA\nG\nE\ninterplay among heating/cooling rates, pulse duration, and peak temperature. Besides,\nthe exact boundaries of this “window” depend on the physicochemical properties of the\nmetal-support system (e.g., melting point, interfacial adhesion energy, atomic\ndiffusivity) and the specific experimental environment.\nNevertheless, our in situ TEM results offer clear mechanistic insights that can guide the\nrational design of pulsed-heating protocols. Specifically, nanoparticle stabilization can\nbe achieved when: (i) the heating rate is sufficiently rapid to access a non-equilibrium\nregime before extensive atomic diffusion occurs; (ii) the pulse duration is short enough\nto prevent long-range sintering; and (iii) the temperature is high enough to activate local\natomic rearrangements that enhance crystallinity and metal–support bonding. Together,\nthese criteria define a broadly applicable kinetic-controlled principle for constructing\nstable nanocatalysts through pulsed or otherwise temporally modulated thermal stimuli.\nWe believe this provides both a mechanistic foundation and a conceptual framework\nfor extending the strategy to diverse material systems.\nAccordingly, we have added the corresponding discussion in the revised manuscript,\nwhich now reads as “Consequently, our work offers clear mechanistic insights that NP\nstabilization for a specific metal during pulsed heating can be achieved within a kinetic\nwindow (which should be jointly governed by heating/cooling rates, pulse duration, and\npeak temperature); under such conditions, diffusion-driven sintering is kinetically\nconfined while local structural rearrangements are activated, enabling the formation of\nthermally robust nanostructures.”\n(4) The authors used stability under pulsed heating as improved stability and sintering-\nresistance. This is far from enough as thermochemical reactions occur at continuous\nhigh T rather than pulses. The true isothermal stability is therefore important to\nevaluate if the particles are stable or not.\nOur response: We fully agree that isothermal stability under continuous high\nP\nA\nG\nE\ntemperature is essential for practical catalysis. To address this, we have performed an\nextended isothermal test on the Pt/graphene sample prepared after 100 pulsed-heating\ncycles by holding it at 1000 °C for 1 hour. As shown in the supported data (Figure S18),\nthe Pt NPs show no obvious coarsening or sintering after this prolonged exposure,\nindicating that the pulsed-heating protocol produces nanostructures that are not only\ntransiently protected by kinetic effects but are also thermally robust under continuous\nhigh-T conditions. We interpret this robustness as arising from the combination of\nimproved crystallinity and strengthened metal-support interactions produced during\npulsed heating: these features stabilize the kinetically accessed nanostructures against\nfurther coarsening even under extended isothermal annealing.\nWe have added the extended-heating data to the Supplementary Information (Figure\nS18, also shown here as Figure R1) and discussed the result in the main text to make\nthis point explicit, which reads as “In addition, to assess the thermal stability of the\nPt/graphene nanocatalyst formed after 100 heating pulses, we conducted an extended\nheating test by maintaining it at 1000 oC for 1 hour. As shown in Figure S18, no obvious\ncoarsening or change in particle morphology occurs within the experiment,\ndemonstrating that the produced nanostructures are excellent robust even under\ncontinuous high‑temperature exposure.”\nP\nA\nG\nE\nFigure R1. (Figure S18) In situ STEM images showing the time-lapsed thermal\nstability of Pt/graphene nanocatalyst formed after 100 heating pulses at 1000 oC.\n(5). The conclusion—that pulsed heating achieves a higher degree of crystallinity than\nconventional heating—should be discussed more cautiously. A conventional heating\nand a slow cooling provide sufficient time for atoms to diffuse and rearrange into their\nlowest-energy, most stable lattice positions, thereby minimizing defects and yielding a\nhighly ordered structure. This process (i.e., annealing) is the widely accepted standard\nmethod for improving the crystallinity of materials.\nOur response: We thank the reviewer for this constructive comment. There might be\nsome misunderstanding caused by our previous wording. Our intention was not to claim\nthat pulsed heating yields a crystallinity higher than that achieved through conventional\nlong-term annealing with slow cooling. Rather, our conclusion highlights that under\nrepeated ultrafast heating pulses, the crystallinity of nanoparticles can be progressively\noptimized through a unique, kinetically governed pathway. Each heating pulse allows\npartial structural relaxation and defect healing without enabling extensive diffusion-\nP\nA\nG\nE\ndriven coarsening, leading to a stepwise improvement of crystalline order. This process\ndiffers fundamentally from conventional equilibrium annealing and reflects a\nnonequilibrium structural optimization mechanism.\nTo avoid ambiguity, we have revised the relevant statement in the manuscript to\nemphasize this kinetic improvement of crystallinity, rather than a direct superiority over\nconventional annealing, which now reads as “As a result, repeated heating pulses drives\nprogressive improvement in the crystallization degrees of Pt NPs and promotes their\ninterfacial optimization with graphene support, leading to structurally refined and\nthermally robust supported nanocatalysts.”\nP\nA\nG\nE\nPoint-by-point response\nWe sincerely thank the reviewers for their comments and suggestions on our manuscript.\nWe have addressed all the concerns raised by the referees in full and revised the\nmanuscript accordingly. Our responses to the reviewers’ comments are given below.\nThe content is organized as following:\nSection Ⅰ: Response for Reviewer 1 (p2)\nSection Ⅱ: Response for Reviewer 2 (p3-p14)\nP\nA\nG\nE\nResponse for Reviewer #1\nThis study played a crucial role in elucidating the mechanism for rational\nnanostructured catalyst design through heat treatment in a metastable state.\nFurthermore, I believe it is fully acceptable for accurately answering the questions\nposed.\nOur response: We sincerely appreciate the reviewer's positive recommendation for our\nmanuscript.\nP\nA\nG\nE\nResponse for Reviewer #2\nThe authors did not really address the previous concerns. As shockwave heating to\nstabilize nanoparticles or nano clusters has been well documented before, using the\nexact shock method. Now the authors re-performed the experiments under TEM, which,\nto some degree, provides a fresh perspective. However, if this nanoscale perspective is\nnot well-utilized for an in-depth understanding, then little science would be gained from\nthe current study. Importantly, the origin of such kinetic stabilization is still not revealed,\nand many of the experimental designs are not scientifically sound or even conflict with\neach other. To name a few:\n(1) There is a significant discrimination between major control samples (Fig.1c vs.\nFig.1d). They have very different thermal histories at high T, and, understandably, they\nshow different dispersions. Instead of controlling the total time (~1000 s or only 10\npulses), the authors should do 10,000-20,000 pulses (500-1000s at high temperature)\nfor a fair comparison. The so-called kinetic stability may not be valid because of the\nkinetic advantages, but may largely be from a much shorter duration at high\ntemperature. This can sabotage the foundation of this paper.\nOur response: We thank the reviewer for raising this important concern. We fully agree\nthat a fair comparison between pulsed heating and conventional heating must consider\nthe total time the nanoparticles (NPs) spend at high temperature. Below we clarify our\nexperimental design and provide additional experiments that directly address this point.\nFirst, the comparison shown in Figure 1c and Figure 1d is initially designed to isolate\nthe roles of heating/cooling rate in pulsed heating and conventional heating by ensuring\nthat both methods share the same holding time at 1000 °C (50 ms). Although this\ncomparison highlights the effect of rapid thermal cycling, we understand that it does\nnot fully address the reviewer’s request for an equal total high-temperature exposure.\nFollowing the reviewer’s suggestion, we thereby compare conventional heating (∼1200\ns total time under high-T) with 100 heating pulses (∼1300 s cumulative high-T\nP\nA\nG\nE\nexposure), where the total durations represent the sum of heating/cooling and\nisothermal holding periods. As shown in Figure 3 and Figure S17, Pt NPs subjected to\n100 heating pulses retain markedly better size stability and dispersion than those treated\nby conventional heating (Figure 2e-h and Figure S7) under this time-normalized\ncondition.\nTo determine whether the observed stabilization arises from the intrinsic kinetic\npathway of pulsed heating rather than simply from a shorter high-T duration, we\nconduct a new control experiment in which we significantly increase both peak duration\nand pulse number. Specifically, the sample was held at 1000 °C for 1 s per pulse and\nsubjected to 1000 heating pulses (i.e., 1000 s of cumulative exposure at 1000 °C).\nAs shown in Figure R1 (also refer to the updated Supplementary Information as Figure\nS19), the evolutions for number and average size of Pt NPs during the first 100 pulses\nfollow same trends as those in Figure 3, and critically, they remain stable without\nobservable sintering even after 1000 pulses. This finding directly demonstrates that\npulsed heating stabilizes NPs through a kinetically constrained pathway: the ultrafast\nheating/cooling rate and short high-T residence within each pulse limit long-range\natomic diffusion and coalescence, while still allowing local structural relaxation and\ninterface strengthening. By contrast, under conventional heating, the NPs are held well\nabove the Tamman temperature (namely, diffusion of materials becomes “significant”\nabove an empirical value of about half of the melting temperature)1 of Pt (~750 °C) for\nlong periods, leading to bond breaking and therefore NP migration and coalescence.\nIn this revision, we have added the above result to the revised manuscript together with\nthe following text: “To demonstrate that pulsed heating stabilizes NPs through a\nkinetically constrained pathway rather than a short high-temperature exposure, we\nperform an extended pulsed heating of 1000 pulses with a 1 s peak duration (cumulative\nexposure of 1000 s at 1000 °C). Again, Pt NPs remain stable without observable\nsintering (Figure S19), and the evolutions for number and average size of Pt NPs during\nthe first 100 pulses follow similar trends as those in Figure 3.”.\nP\nA\nG\nE\nReference:\n(1) Golunski, S. E. Why use platinum in catalytic converters? Platinum Met. Rev. 51,\n162 (2007).\nFigure R1. (Figure S19) (a) In situ STEM image series showing the evolution of Pt\nNPs on graphene support during 1000 heating pulses, with a heating/cooling rate of 150\noC s-1 and a peak temperature duration at 1000 oC for 1 s. (b) Number and average size\nP\nA\nG\nE\nof Pt NPs as functions of pulse number for (a). Error bars represent the 95% confidence\ninterval of the mean.\n(2) In the last round, the authors were asked to test the isothermal stability of\nPt/graphene. They responded that this material can sustain 1000 oC for 1 hour without\nsintering (reply 4, Fig. S18). This result conflicts directly with Fig. 5g-h where\nnanoparticles show sintering starting at 6 seconds.\nThe reviewer tends to believe that the latter is the true case, as sintering is much easier\nat 1000℃, where nanoparticles want to sinter and the graphene substrate is graphitized.\nAs long as you do not have strong Pt-C/O bonds, the sintering is almost unavoidable.\nIn the paper, the authors discussed having some crystalline affinity of Pt and the\ngraphene, but no direct bond formation. Then the Pt clusters can not be stabilized at\nsuch a high temperature. This will be contrary to common sense.\nFig. 5g-5h showing sintering in 6 seconds at 1000℃:\nReply and Fig. S18 showing anti-sintering in 1 hour at 1000℃:\nOur response: We thank the reviewer for this comment and for highlighting the need\nto clarify the apparent discrepancy between the isothermal test (Figure S18) and the\nsintering behavior observed in Figure 5g-h.\nFirst, we would like to clarify that the two experiments as mentioned by the reviewer\nprobe two distinct structural states of Pt NPs, which induces different thermal responses.\nFigure 5g-h captures the behavior immediately after the first pulsed-heating step to\n1000 °C, during which the Pt precursor has only just decomposed into nascent clusters\n(i.e., “fresh” NPs). At this early stage, the metal-support interaction is undeveloped, and\nthe NPs have not yet undergone any structural or interfacial relaxation. As a result, when these\nfreshly formed clusters are held at 1000 °C for several seconds, substantial\nsintering occurs (as expected for weakly bound Pt on a pristine graphene surface). In\ncontrast, Figure S18 examines the isothermal stability of the fully evolved Pt/graphene\nnanocatalyst produced after 100 heating pulses (i.e., “annealed” NPs). Over the course\nP\nA\nG\nE\nof these repeated pulses, the Pt NPs gradually undergo crystallographic refinement,\nfacet selection, and interfacial reorganization (Figures 3k, 4, and 5d), and they develop\nmuch stronger interactions with the graphene support. Our EELS analysis (Figure 2n)\ntogether with our previous work2 demonstrates interfacial charge transfer as well as\nformation of strong Pt–C interfacial bonds. In short, the stable behavior observed in\nFigure S18 DOESN’T conflict with Figure 5g-h; rather, the two experiments highlight\ntwo different stages of NP evolution: an initially unstable state vs. a kinetically\noptimized, strongly anchored state.\nTo avoid potential ambiguity, we have revised the manuscript to clarify this point. The\nrelevant sentence now reads as: “To further verify the kinetic stability of Pt NPs, we\ntrack their sintering behavior during the first pulse by rapidly heating them to 1000 °C\nand then holding for a duration (Figure 5g). At this early stage, the interaction between\nthe NPs and the support has not yet developed.”.\nSecond, the stability of Pt/graphene nanocatalysts produced by pulsed heating is\nattributed to two mechanistic factors. (i) The structural adjustment during 100 heating\npulses yields NPs with improved crystallinity and orientations aligned with the\ngraphene support, producing lower-energy, more stable configurations (Figures 3k, 4,\nand 5d). (ii) The strengthened interfacial interaction (evidenced by C K-edge shifts in\nEELS in Figure 2n) is consistent with our previous findings, which indicates\nsubstantial charge transfer and the formation of strong Pt-C bonding at the interface.2\nThese synergistic effects collectively generate the thermally robust nanostructures\nobserved in the 1 h isothermal test (Figure S18). This conclusion is also consistent with\nreports showing that pulsed-heated nanocatalysts exhibit superior stability during\nextended thermal or reactive operation, attributed to metastable structures and/or\nenhanced metal-support coupling.3-5\nFinally, we should explain that the graphene support does not undergo notable\ngraphitization under our pulsed-heating conditions. The C K-edge spectra after 100 and\n1000 pulses (Figures R2 and R3) show no detectable change; this agrees with the well-\nP\nA\nG\nE\nestablished high thermal stability of graphene as a catalyst support.6,7 Hence, the\nobserved stabilization of Pt NPs arises from the NP-support interface evolution rather\nthan the chemical transformation of support.\nUnder this circumstance, we have inserted additional discussion in the updated text,\nwhich read as “The marked sintering resistance can be attributed to the formation of\nstrong Pt-C interfacial bonding and the progressive structural alignment of NPs with\ngraphene substrate, both of which arise during the prior heating pulses.”.\nReferences:\n(2) Gan, M. et al. Incomplete charge transfer bestows significant sintering resistance\nfor metal nanoparticles on two-dimensional graphyne. J. Mater. Chem. A 12, 29174-\n29183 (2024).\n(3) Yao, Y. et al. High temperature shockwave stabilized single atoms. Nat. Nanotechnol.\n14, 851-857 (2019).\n(4) Li, C. et al. Ultrafast self-heating synthesis of robust heterogeneous nanocarbides\nfor high current density hydrogen evolution reaction. Nat. Commun. 13, 3338 (2022).\n(5) Du, P. et al. In-situ Joule-heating drives rapid and on-demand catalytic VOCs\nremoval with ultralow energy consumption. Nano Energy 102, 107725 (2022).\n(6) Jang, I. et al. Instantaneous thermal energy for swift synthesis of single-atom\ncatalysts for unparalleled performance in metal–air batteries and fuel cells. Adv. Mater.\n36, 2403273 (2024).\n(7) Qiao, Y. et al. 3D-printed graphene oxide framework with thermal shock\nsynthesized nanoparticles for Li-CO batteries. Adv. Funct. Mater. 28, 1805899 (2018).\nA\nG\nE\nFigure R2. (Figure S13) (a, b) STEM image and C K-edge EELS spectra of graphene\nsupport before and after 100 heating pulses.\nFigure R3. (a, b) STEM image and C K-edge EELS spectra of graphene support before\nand after 1000 heating pulses.\n(3) This question is not answered at all in the last round.--- What is the safe region for\nultrafast heating to maintain particle stability, for example, T range, t or pulse times\nrange, and heating/cooling ranges? The authors should dig into the mechanism of this\nkinetic stabilization and propose design principles, instead of just listing one example.\nWe understand the current pulse enables stability under 10 pulses. What we don’t know\nis where the kinetic boundary is and the reason behind this boundary, for example, the\nkinetic competition between interparticle diffusion and the pulsed heating freezing. The\nauthor also mentioned heating rate is particularly important, but is this supported by\nexperimental proof (must with fair controls)? Quantitative or numeric study will be\nlargely preferred to understand this kinetic stability or its safe boundaries.\nOur response: We sincerely thank the reviewer for this important and insightful\nquestion. Following your suggestion, we have explicitly mapped out the kinetic\nboundary (“kinetic window”) within which pulsed heating suppresses sintering in this\nrevision (using the Pt/graphene system as a model).\nWe provide quantitative boundaries that define the conditions under which sintering is\neffectively suppressed. These boundaries emerge from the interplay between bond-\nP\nA\nG\nE\nbreaking/diffusion and the limited time NPs spend above the Tamman temperature\nduring each ultrafast pulse. Our new experiments address all three key parameters\nrequested by the reviewer (i.e., heating/cooling rate, pulse duration, and peak\ntemperature) and establish clear mechanistic design principles.\n1) The heating/cooling rate sets the onset of the kinetic regime. Prior studies typically\ndefine ultrafast heating as rate ≥100 °C s⁻¹,8 and our side-by-side in situ TEM\nexperiments confirm this threshold. At 100 °C s⁻¹, the evolution of Pt NPs over 100\npulses mirrors the stabilization behavior observed at 150 °C s⁻¹ (Figure R4), whereas\nfurther reducing the rate to 50 °C s⁻¹ results in continuous coarsening with no sign of\nconvergence in particle number or size (Figure R5). This arises because the slower\nheating rate prolongs the dwell above the Tamman temperature of Pt (~750 °C),\nresulting in long-range diffusion. Thus, heating/cooling rate ≥100 °C s⁻¹ is required to\nrestrict the time available for bond breaking and migration of NPs.\n2) The allowable dwell time at high temperature imposes a complementary kinetic\nconstraint. While earlier single-pulse tests suggested that holding at 1000 °C for <6 s\nmitigates sintering (Figure 5g), our systematic study across multiple durations (50 ms,\n2 s, 3 s, 4 s, 5 s, and 6 s, each repeated sequentially for 10 pulses) reveals a sharper\nboundary. As shown in Figure R6, pulse durations ≤4 s well maintain the stabilization\nbehavior, whereas the durations of 5–6 s trigger rapid coalescence (Figure R6). These\nresults establish ~4 s as the time boundary for pulsed heating at 1000 °C.\n3) As the aim of pulsed heating is to produce well-crystallized NPs with an appropriate\nsize distribution, the temperature window itself is bounded by the precursor\ndecomposition threshold (~400 °C) and the melting point of Pt NPs (~1005 °C for 2 nm\nparticles).9 Within this range, higher temperatures increase the thermodynamic driving\nforce for sintering, and our experiments show that even near the melting point (1000 °C),\nsintering remains effectively suppressed as long as the rate and duration remain within\nthe kinetic window (Figure R4). This ensures complete precursor decomposition, rapid\ncrystallization, and access to kinetically controlled structural relaxation pathways.\nP\nA\nG\nE\n4) We also note that the number of pulses does not dictate kinetic stability. Even after\n1000 pulses, corresponding to a cumulative 1000 s at 1000 °C, Pt NPs remain stable\n(Figure R1). Additional pulses primarily refine particle crystallinity and strengthen the\nmetal–support interface, with these processes largely completed within ~100 pulses.\nIn summary, our supplementary quantitative analysis shows that pulsed heating\nsuppresses sintering when three criteria are met simultaneously: (i) heating/cooling rate\n≥100 °C s⁻¹ to minimize the effective diffusion time, (ii) high-temperature dwell time\n≤4 s to prevent the onset of long-range coalescence, and (iii) peak temperature between\nprecursor decomposition and melting point of NPs. These experimentally defined limits\nestablish a clear kinetic mechanism and a practical design framework for applying\npulsed or otherwise temporally modulated thermal stimuli to stabilize supported\nnanostructures.\nReferences:\n(8) Chen, Q. et al. Rapid synthesis of metastable materials for electrocatalysis. Chem.\nSoc. Rev. 54, 4567-4616 (2025)\n(9) Wang, G., Xu, Y.-S., Qian, P. & Su, Y.-J. The effects of size and shape on the\nstructural and thermal stability of platinum nanoparticles. Comput. Mater. Sci. 169,\n109090 (2019).\nP\nA\nG\nE\nFigure R4. (a-j) In situ STEM image series showing the evolution for Pt NPs on\ngraphene support during 100 heating pulses, with a heating/cooling rate of 100 oC s-1.\n(k) Number and average size of Pt NPs as functions of the pulse number for (a-j).\nError bars represent the 95% confidence interval of the mean. The evolution of NPs over 100\nheating pulses aligns with the previous observations at rate of 150 °C s-1 (Figure 3a-h),\nwherein the NPs gradually stabilize on the support, indicating that the rate of 100 °C s-\n1 remains within the kinetic window of sintering resistance. Combined with the results\nat a heating/cooling rate of 50 °C s-1 shown in Figure R5, we therefore conclude that\nthe kinetic boundary for heating/cooling rates is ≥100 °C s-1.\nP\nA\nG\nE\nFigure R5. (a-j) In situ STEM image series showing the evolution for Pt NPs on\ngraphene support during 100 heating pulses, with a heating/cooling rate of 50 oC s-1. (k)\nNumber and average size of Pt NPs as functions of the pulse number for (a-j). Error\nbars represent the 95% confidence interval of the mean. The NPs exhibit continuous\nsintering throughout the 100 heating pulses, indicating that this rate is far from the\nkinetic window.\nP\nA\nG\nE\nFigure R6. (a) In situ STEM image series showing the evolution for Pt NPs on graphene\nsupport during 60 heating pulses, with a varying duration of 50 ms, 2 s, 3 s, 4 s, 5 s, and\n6 s for each duration within 10 pulses. (b) Number and average size of Pt NPs as\nfunctions of the pulse number for (a). Error bars represent the 95% confidence interval\nof the mean. The number and size of NPs gradually stabilize during the heating pulses\nwith durations ≤4 s; however, as the duration increase to ≥5 s, sintering recommences\nand becomes more pronounced, indicating that the kinetic stability has been disrupted.\nThese results confirm that the safe range for pulse duration is ≤4 s.\nP\nA\nG\nE\nPoint-by-point response\nWe sincerely thank the reviewers for their comments and suggestions on our manuscript.\nWe have addressed all the concerns raised by the referees in full and revised the\nmanuscript accordingly. Our responses to the reviewers’ comments are given below.\nThe content is organized as following:\nSection Ⅰ: Response for Reviewer 1 (p2)\nSection Ⅱ: Response for Reviewer 2 (p3-p8)\nP\nA\nG\nE\nResponse for Reviewer #1\nThis study played a crucial role in elucidating the mechanism for rational\nnanostructured catalyst design through heat treatment in a metastable state.\nFurthermore, I believe it is fully acceptable for accurately answering the questions\nposed.\nOur response: We sincerely appreciate the reviewer's positive assessment and\nrecommendation for publication.\nP\nA\nG\nE\nResponse for Reviewer #2\nThe authors have made a substantial effort to address the concerns raised in the\nprevious round by providing more in situ TEM evidence. Overall, the revised\nmanuscript is largely improved in rigor and scope, and it convincingly demonstrates\nthat pulsed heating can yield supported Pt nanoparticles with markedly enhanced\nresistance to sintering. However, one key concept and (mis)understanding should be\nclarified.\n1. It remains insufficiently clarified on the roles of pulsed heating (PH) and Pt–C\ninterfacial bonding in governing the long-term stability of the nanoparticles. In\ncomment #2, the authors showed that, under PH operation, Pt NPs are not stable for\nthe initial stage because their crystallinity and interfacial bond are not yet formed; The\nPt NPs then become stable after ~100 PH cycles, even when annealed under isothermal\nheating at 1000 oC (does this mean isothermal heating can also freeze sintering?).\nThis experimental data indicate that the stability or long-term anti-sintering of Pt NPs\nis NOT (at least not entirely) from pulsed heating effect, but rather, and importantly,\nfrom the strong interaction with the substrate. This conclusion is understandable and\nconvincing, but it is in strong contradiction to the authors’ claim that pulsed heating\nfreezes sintering in supported metal nanoparticles.\nA clearer separation of the early-stage kinetic suppression of sintering and the late-\nstage chemical or interfacial stabilization, along with a discussion of the exact role of\npulsed heating, would substantially strengthen the mechanistic clarity of the work.\nIt seems that, compared with slow continuous heating, PH is effective in building strong\nmetal-support interaction at the initial stage by competing with sintering and\ngraphitization behaviors. But, the long-term stability of nanoparticles under PH is not\nbecause of PH freezing, but because of the formation of strong interfacial bonding. The\nauthors should either prove experimentally or theoretically that pulsed heating can\nindeed freeze sintering, or attribute the true role of PH to first forming the strong\nP\nA\nG\nE\nbonding, and then ensuring stability.\nOverall, the discussion of beyond thermodynamics, pulsed heating freezes sintering, the\nthermodynamically unstable yet kinetically stable state under PH, etc, lacks scientific\nrigor and experimental/theoretical proof. The authors should elaborate the paper\nstrictly based on their observations.\nAnother one, why are responses and data in comment #3 not revealed in either the main\ntext or SI? The discussion of possible kinetic competition among crystallization, bond\nformation, sintering, and graphitization is helpful for readers to understand the role\nand design of PH.\nOur response: We thank the reviewer for this thoughtful and technically important\ncomment. We fully agree with the reviewer’s constructive comment on the role of\npulsed heating in suppressing sintering. Actually, we have clearly stated that pulsed\nheating is currently adopted in the synthesis of supported nanocatalysts in the\nmanuscript, and we are thereby working on the underlying mechanisms for these\nsynthesis efforts in this work (which is “the early-stage” as raised by the reviewer).\nBesides, in response to the reviewer’s question regarding previous Comment #3, we\nhave now included the full datasets (Figs. R1-R3) defining the kinetic window\n(heating/cooling rate, pulse duration, and peak temperature) in the Supplementary\nInformation (Supplementary Figs. 21-23) and explicitly integrated the corresponding\ndiscussion into the revised manuscript and Supplementary Information, which reads as\n“Consequently, our work offers clear mechanistic insights that NP stabilization for a\nspecific metal during pulsed heating can be achieved within a kinetic window (which\nshould be jointly governed by heating/cooling rate (Supplementary Figs. 21 and 22),\npulse duration (Supplementary Fig. 23), and peak temperature, as discussed in\nSupplementary Discussion);” and “Using the Pt/graphene system as an example, we\ndefine the kinetic boundaries in which pulsed heating suppresses NP sintering. In situ\nSTEM experiments show that heating/cooling rates ≥100 °C s⁻¹ stabilize Pt NPs over\nP\nA\nG\nE\n100 pulses, whereas slower rates allow coarsening (Supplementary Figs. 21 and 22).\nPulse durations ≤4 s at 1000 °C preserve progressive convergence of particle size and\nnumber, while longer pulses trigger rapid coalescence (Supplementary Fig. 23).\nBesides, the temperature window lies between the precursor decomposition (~400 °C)\nand the size-dependent Pt melting point (~1005 °C), with sintering effectively\nsuppressed even near 1000 °C if rate and duration criteria are met (Supplementary Fig.\n21). Pulse number does not affect stability, although additional pulses further improve\ncrystallinity and metal-support bonding (Supplementary Fig. 19). These results\nestablish a clear kinetic mechanism and provide design rules for NP stabilization via\npulsed or temporally modulated heating: rates ≥100 °C s⁻¹, dwell ≤4 s, and temperatures\nbetween decomposition and melting.”.\nP\nA\nG\nE\nFig. R1. (Supplementary Fig. 21) (a-j) In situ STEM image series showing the\nevolution for Pt NPs on graphene support during 100 heating pulses, with a\nheating/cooling rate of 100 oC s-1. (k) Number and average size of Pt NPs as functions\nof the pulse number for (a-j). Error bars represent the 95% confidence interval of the\nmean.\nP\nA\nG\nE\nFig. R2. (Supplementary Fig. 22) (a-j) In situ STEM image series showing the\nevolution for Pt NPs on graphene support during 100 heating pulses, with a\nheating/cooling rate of 50 oC s-1. (k) Number and average size of Pt NPs as functions\nof the pulse number for (a-j). Error bars represent the 95% confidence interval of the\nmean.\nP\nA\nG\nE\nFig. R3. (Supplementary Fig. 23) (a) In situ STEM image series showing the evolution\nfor Pt NPs on graphene support during 60 heating pulses, with a varying duration of 50\nms, 2 s, 3 s, 4 s, 5 s, and 6 s for each duration within 10 pulses. (b) Number and average\nsize of Pt NPs as functions of the pulse number for (a). Error bars represent the 95% confidence\ninterval of the mean. The number and size of NPs gradually stabilize during the heating pulses\nwith durations ≤4 s; however, as the duration increase to ≥5 s, sintering recommences\nand becomes more pronounced, indicating that the kinetic stability has been disrupted.\nThese results confirm that the safe range for pulse duration is ≤4 s.\nP\nA\nG\nE"}]

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