Introduction

Controlling the catalytic behavior of molecules, especially regulating their adsorption/desorption on heterogeneous catalyst surfaces, is a key technique for emerging green synthetic chemistry1,2. Stronger molecule adsorption enables the stable reactant/intermediate molecule supply, however, on the other hand, this leads to weaker molecule desorption and slower active site release. Therefore, excessively strong or weak molecule adsorption/desorption leads to either active site poisoning or inefficient molecule supply, resulting in a sluggish reaction rate and poor selectivity, especially in complex multi-step catalytic cascade reactions. Nevertheless, for conventional heterogeneous catalysts, thermal inertia in macroscopic reactors needs to be adapted to transfer heat from the reactor wall into the entire reaction space3,4. The constant ambient high temperature makes it difficult for molecules to escape from the active site, causing overreaction and inducing excessive by-products5,6. In contrast, if a nanoreactor (heterogeneous catalyst) can be designed to enclose heat in its interior, that is, only locally high temperature is generated around the nanoreactor while leaving the reaction medium relatively “cool”, it will be expected to drive the regulation of the adsorption–desorption behavior of molecules through the self-pressurizing properties conferred by the temperature difference7,8,9,10,11. However, such excessively strong thermal radiation from inside out, in turn, tends to trigger desorption-dominated catalytic reaction kinetics. This undoubtedly leads to insufficient time for the conversion of intermediates to target products in multi-step cascade reactions.

To achieve the equilibrium of molecule adsorption–desorption, so as to precisely control the reaction depth, requires the delicate structural design of nanoreactors to modulate the microenvironment12,13. To this end, Gaussian curvature engineering of artificial nanoreactors opens new perspectives for tailoring molecule adsorption–desorption behavior to obtain target chemical products with a high selectivity14,15,16. Monte Carlo theory proves that concave surfaces are more suitable for molecular adsorption than convex surfaces17. Meanwhile, concave surface engineering armed with porous shells is conducive to enhancing the thermal energy conversion through light multiple reflections in the curved cavity, which in turn further boosts the internal pressure-driven molecular desorption18. Based on this, the number of molecules for adsorption–desorption in nanoreactors can be quantified through the customized surface curvatures, which is expected to achieve the equilibrium of molecule adsorption–desorption at the active sites19. However, the current regulation of curved surfaces mainly focuses on controlling the size of isotropic spherical hollow structures to change the cavity curvatures, which is centered on the adjustment of a single curvature on the surface (for example, the convex effect on the outer surface, or the concave effect on the inner surface)14,19,20,21,22,23. It is still a great challenge to accurately control the concavity to achieve enhanced molecular enrichment on both the outer and inner surfaces, and further quantitatively reveal the correlation between the nanoreactor curvatures and molecule adsorption–desorption behavior as well as reaction pathways.

Herein, we quantitatively reveal the rational balancing of molecule adsorption/desorption on mesoporous silica self-pressuring nanoreactors with controllable Gaussian curvatures to achieve significantly enhanced catalytic efficiency and selectivity. The modulation of nanoreactors from the concave anisotropic bowl-like to convex droplet-like structures is realized via a programmable nanodroplet buckling strategy. The concave surfaces of nanoreactors are endowed with additional pressure by the liquid–surface-tension, which induces the adsorption of molecules from outside to inside. In contrast, the drastic temperature difference triggered by encapsulating Fe3O4 nanoparticles (~20 nm) with plasmon resonance effect inside the mesoporous silica cavity (~200 nm) (nearly 200 °C of catalyst and 71.4 °C of reaction medium), induces a self-pressurizing concave nanoreactor with inside-to-out molecular desorption. Under this mode, the photothermal concave nanoreactor with catalytic metallic Ru (~5 nm) nanocrystals on the outer shells achieves an efficient cascade conversion of 5-hydroxymethylfurfural (HMF, biomass platform molecule). Moreover, the reaction efficiency is an order of magnitude higher than that of conventional heating, exhibiting a high selectivity of 97.9% for the target product (5-formyl-2-furancarboxylic acid, FFCA). The theoretical calculation and simulation results quantitatively reveal the relationship between molecule adsorption–desorption and Gaussian curvatures. The established equilibrium equation demonstrates that the adsorption–desorption equilibrium point of molecules occurs at 7/8 concavity, where the internal–external pressure of the nanoreactor is in a relative equilibrium state.

Results

Gaussian surface interface engineering strategies

We introduced Gaussian surface engineering to the construction of mesoporous nanoreactors to understand and optimize the catalytic reaction kinetics. Three representative structural models with different Gaussian curvatures (K, defined as the product of the two principal curvatures at a certain point on the surface, representing the degree of local curvature of a surface) are applied, including anisotropic concave (corresponding to length-to-diameter ratio, i.e., concavity C = L/D < 1), isotropic sphere (C = 1), and anisotropic convex structures (convexity C > 1) (Fig. 1a–c and Supplementary Fig. 1). According to Young-Laplace theory, a curved liquid interface induces a pressure directed radially toward the center of curvature (ΔPexternal = 2ϒ/r). This pressure arises from liquid–surface tension acting on Gaussian surfaces via molecular momentum transfer and is manifested as an additional, adsorption-directed force exerted by liquid molecules on the nanoparticle surface (white arrows, Fig. 1d–f and Supplementary Fig. 2). Based on the statistical approximation, the concave/convex region can be regarded as part of a new uniform spherical surface. The calculated external pressure difference (ΔPexternal) acting across the entire concave surface is 19.9 bar (curvature radius r of 72.2 nm) (Supplementary Figs. 3 and 4). This value exceeds the 16.2 bar calculated for the convex surface, where the pressure direction gradually reverses, implying stronger adsorption on the concave surface (r = 88.4 nm) (Fig. 1h and Supplementary Table 1).

Fig. 1: Optimization of nanoreactor structure based on the Gaussian surface effect.
figure 1

Schematic diagram of different Gaussian surfaces and their additional pressures (a, d) anisotropic-concave; b, e isotropic-spherical, and c, f anisotropic-convex. The white arrow represents the direction in which the liquid exerts force on the solid surface. The red arrow indicates the direction in which the solid surface exerts force on the liquid. The Gaussian curvature of a sphere can be simplified as K = 1/r2, r is the curvature radius. Adsorption pressure ΔPexternal = 2ϒ/r, where ϒ is the surface tension of the liquid. g 3D color mapping of cross-sectional temperature spatial distribution through molecular dynamics simulation with internal heat sources. h Variation of adsorption strength (ΔPexternal) and desorption strength (ΔPinternal) within the internally heated nanoreactors with respect to Gaussian curvatures. i Schematic diagram of self-pressurization and the additional pressure co-regulating molecular adsorption–desorption equilibrium in internally heated concave nanoreactors. j Simulation of flow field distributions corresponding to internally heated nanoreactors.

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To balance the external pressure, it is necessary to construct thermal self-beam porous nanoreactors to match the internal pressure, thus further regulating molecule adsorption–desorption equilibrium. Specifically, the crust-like properties of the porous shells confine the heat source overwhelmingly to the inside of the cavity, creating a high-to-low temperature difference between the hot nanoreactor and cool solvent environment (Fig. 1g and Supplementary Fig. 5). The saturated vapor pressure of the liquid in the cavity of different Gaussian surfaces is calculated by the Antoine equation (lgΔPinternal = A-B/(ΔT + C)). The thermal gradient enhances the inside-to-out molecule desorption, which is defined as a negative value (ΔPinternal). The concave surface induces higher thermal (Tcavity = 220.3 °C) and stronger self-pressurization effects (ΔPinternal = −20.8 bar) than the convex surface (Tcavity = 204.7 °C, ΔPinternal = −15.9 bar) (Fig. 1h). At this time, the out-inside adsorption and in-outside desorption show an antagonistic relationship, and the intersection point of the ΔPinternal and ΔPexternal curves lies between the concave and spherical surfaces (ΔPinternal = −18.7 bar, ΔPexternal = 18.3 bar). This inspires the optimization of nanoreactor structures, which is expected to establish a molecular adsorption–desorption equilibrium bridge quantitatively under appropriate curved surface parameters (Fig. 1i, j). Based on the Gaussian curvature effects of nanoreactors, equilibrium equations between the adsorption of molecules under additional pressure and the desorption effect induced by heating-constrained can be established, thus providing theoretical guidance and data support for joint manipulation of molecular behavior and residence time.

Tunable adsorption effects in concave–convex mesoporous nanoreactors

Inspired by the above results, a programmable nanodroplet buckling strategy was proposed to precisely regulate the concave–convex curvatures of mesoporous silica nanoreactors. Specifically, hexadecyltrimethylammonium bromide (CTAB) was used as a soft template to stabilize the nanodroplets at the oil–water (propanol–water) interface. Subsequently, tetraethyl orthosilicate (TEOS) precursors are hydrolyzed to form negatively charged silicate oligomers, which are deposited at the interface to induce the anisotropic growth of silica shells (Fig. 2a). SEM images show that the obtained mesoporous nanoparticles present bowl-like architectures (corresponding concavity, C = 1/2) (Fig. 2b). The concave surface of the nanoparticle approximates a part of a new spherical surface. TEM images show that the subsequent growth of the shells gradually thinned, and the thickness decays from the outer layer (~20 nm) to the inner layer (~8 nm), resulting in the uneven distribution of elements (C, Si, and O) in the hemispherical skeleton (Fig. 2c and Supplementary Fig. 6). Interestingly, changing the alkyl chain lengths of the oil phase from C3 to C7, that is, using different alcohols (e.g., butanol, pentanol, hexanol, and heptanol) as the oil phase, the obtained nanoparticles gradually vary from anisotropic concave to droplet-like convex structures (Fig. 2i and Supplementary Fig. 7). The C value increases from 1/2 (nanoreactor-1) to 3/4 (nanoreactor-2) and further to 7/8 (nanoreactor-3) with the chain length increase from C3 to C5, corresponding to the decrease of concave areas (Fig. 2d–f). When using pentanol with C6 as the oil phase, isotropic spherical nanoparticles are obtained (C = 1) (nanoreactor-4) (Fig. 2g). The morphology of the nanoparticles shifted into convex droplet-like nanoparticles (nanoreactor-5, C = 9/8) with heptanol as the oil phase (C7) (Fig. 2h and Supplementary Table 2). During this process, the concavity gradually decreases and turns into a convexity, corresponding to a gradual increase in the cavity volume from 1.57 × 106 to 5.32 × 106 nm3 (Supplementary Fig. 8).

Fig. 2: Design principles and tunable adsorption effects of concave–convex mesoporous nanoreactors.
figure 2

a Schematic diagram and design principle of the synthesis process of concave mesoporous nanoparticles. b SEM images of the concave mesoporous nanoparticles. c–h TEM images and structural modeling of mesoporous nanoparticles with different concavities (C value). c, d Propanol, e butanol, f pentanol, g hexanol, h heptanol. i Concave degree and curvature radius corresponding to different carbon numbers in the alkyl chain (C3–C7). j O2 adsorption capacity and k number of adsorbed molecules and molecular adsorption equation for concave–convex mesoporous nanoreactors.

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Furthermore, the Brunauer–Emmett–Teller (BET) surface area of the nanoparticles with different curvatures are calculated to be ~354–416 m2 g−1, and all the pore sizes obtained by the Barrett–Joyner–Halenda (BJH) method are centered at ~2.6 nm (Supplementary Fig. 9). The O2 adsorption results confirm that the reduction of Gaussian curvature provides stronger adsorption pressure to enrich O2 molecules (Fig. 2j). The number of molecules colliding on different Gaussian curvature nanoreactors is quantified by proposing a molecular adsorption equation based on the additional pressure of the liquid–surface-tension. The adsorption number of molecules in nanoreactor-1 (4.39 × 1018 pieces/m2) at room temperature is significantly higher than that of nanoreactor-5 (3.58 × 1018 pieces/m2), demonstrating stronger adsorption capacity. The number of adsorbed molecules in the nanoreactor gradually decreases from concave to convex (Fig. 2k).

Tunable desorption effects in photothermal nanoreactors

In addition to the concave enhanced molecule adsorption effect, the matching of the outward desorption effect of molecules (especially for intermediates in cascade reactions) in the internal-heat-confined nanoreactor is also a crucial manifestation to improve the reaction selectivity. Therefore, multifunctional photothermal nanoreactors are constructed by in-situ encapsulating hydrophilic Fe3O4 nanoparticles within cavities can provide the required localized thermal energy, and Ru nanocrystals are implanted on the shells to deliver critical catalytic sites for specific chemical transformations (Fig. 3a, Supplementary Figs. 10–13, and Supplementary Table 3). When bathed in xenon lamp lights, the thermal energy of the Fe3O4 cores confined within the mesoporous silica shell provides localized high temperatures (Fig. 3b). Thermocouples and thermal imaging show that the shell surface temperature of nanoreactor-1 can reach nearly 200 °C, while the reaction medium (solvent) keeps a relatively cool temperature of 73.7 °C after 10 min of irradiation, exhibiting excellent super-photothermal effect and stability (Fig. 3c, d and Supplementary Fig. 14). As the nanoreactor shifts from convex to concave, the shell surface temperatures increase, however, the temperature transfer to the reaction medium shows little difference (63.8–73.7 °C). At this time, the concave nanoreactor exhibits a stronger temperature difference (120.1 °C) and photothermal conversion efficiency (PCE, 80.99%) (Fig. 3e, g and Supplementary Fig. 15). The inside-out hot vapor pressure is directly related to the temperature difference, which implies the tunability of the molecular desorption capacity.

Fig. 3: Tunable thermal properties and desorption effects in photothermal nanoreactors.
figure 3

a Element mapping images of the nanoreactors. b Photothermal images of nanoreactor-1 particles irradiated by lasers of different powers. c Photothermal stability of nanoreactor-1 after four cycles of the on/off laser. d Different curvatures nanoreactor temperature field. e The experimental temperature difference between nanoreactor surfaces and solvents. f Molecular dynamics simulation of thermal distribution images of nanoreactors with different curvatures and corresponding temperature values and thermal vapor pressures. Position 1 (cavity interior), Position 2 (shell), and Position 3 (reaction medium). g PCE of nanoreactors with different curvatures. h Number of desorbed molecules and molecular desorption equation of nanoreactors with different curvatures.

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The temperature distribution within the nanoreactor cavity is obtained by molecular dynamics simulations, further confirming the formation of large temperature gradients at different locations for individual nanoreactors (Supplementary Figs. 16 and 17). The heat accumulates around the nanoreactor under the envelope of the porous shells, and a small amount of heat is transferred to the solvent environment to maintain stability. The large temperature difference between Position 1 (cavity interior) and Position 3 (reaction medium), results in a self-pressurization property of the nanoreactor from the inside out. The maximum temperature difference in concave nanoreactor-1 delivers an obvious inward-outward pressure of 21.79 bar, higher than that of nanoreactor-2 (19.88 bar) and nanoreactor-3 (18.56 bar) with increased C values, much higher than the convex nanoreactor-5 (15.23 bar) (Fig. 3f). The inside-out pressure induces active desorption of molecules from the catalyst surface to the reaction medium. The molecular desorption equation shows that the number of desorption molecules in the nanoreactor-1 (2.76 × 1018 pieces/m2) is significantly higher than that in the nanoreactor-5 (1.76 × 1018 pieces/m2) under the actual thermal effect, demonstrating that the internal pressure induced by concave nanoreactor is more likely to promote molecule desorption (Fig. 3h). These “internal-heating to external-cooling” nanoreactors with different Gaussian curvatures provide potential opportunities to promote mass transfer-desorption dynamics, which lay the foundation for tailoring the reaction pathways of molecules.

Self-pressurizing mesoporous nanoreactors for biomass conversion

To verify the feasibility of photothermal nanoreactors, we used biomass-derived platform feedstock HMF as probe molecules to synthesize high-value-added chemicals, such as FFCA24,25. The reactant HMF typically undergoes a continuous oxidation process from intermediates (e.g., 2,5-diformylfuran or 5-(hydroxymethyl)furan-2-carboxylic acid (HMFCA)) to target products of FFCA (Fig. 4a). Excessively strong or weak adsorption–desorption behaviors of molecules under complex transformation pathways greatly affect the product distribution. The kinetic curve of the photothermal nanoreactor-3 with suitable concave parameters (C = 7/8) shows a decrease in HMF concentration with the conversion of 98.8% and a gradual increase of the target product FFCA with the yield of 96.9% (Fig. 4b). This process reveals that in such a catalytic system with a hot-cool temperature difference, the concave nanoreactor-3 can guarantee the relatively stable adsorption–desorption time of the molecules, and realize the pathway of HMF → HMFCA → FFCA. By contrast, when converted to traditional external conventional heating with the same solvent temperature as photothermal (65 °C), the conversion of HMF is merely 43.3%. The yields of intermediate HMFCA and target product FFCA are only 23.9% and 4.9%, respectively (Fig. 4c). Although increasing the temperature from 65 to 150 °C pulls up the conversion of HMF to 84.6%, a uniform thermal field breeds many by-products, such as maleic acid (MA) and levulinic acid (LA), resulting in a low selectivity for FFCA (46.4%, Fig. 4d). By contrast, the photothermal catalysis process accelerates the directional conversion, increasing the first-order reaction rate (k) by an order of magnitude (from 0.07 to 0.31 h−1) and turnover frequency (TOF) by 2.3 times (from 102.31 to 235.19 h−1) over conventional thermocatalysis (Fig. 4e and Supplementary Fig. 18). Meanwhile, the experimentally measured reaction rate (km = 0.31 h−1) is basically the same as that of predicted rate (kp = 0.34 h−1), indicating that the process is primarily driven by the thermal effect, specifically the presence of a pronounced thermal gradient at the nanoreactor surface (Supplementary Fig. 19). These data fully demonstrate that the photothermal catalytic system significantly outperforms traditional thermocatalysis in both efficiency and selectivity (Table S4).

Fig. 4: Self-pressurizing mesoporous nanoreactors for biomass conversion.
figure 4

a Schematic diagram of photothermal nanoreactor catalyzed HMF oxidation. The inner wall of the nanoreactor is modeled with Fe3O4 nanoparticles, and the outer wall is modeled with Ru nanoparticles. Kinetic plots of catalytic reactions at (b) photothermal and conventional heating (c) 65 °C and d 150 °C in nanoreactor-3. e Comparison of photothermal and thermocatalytic performances in nanoreactor-3 (the first-order reaction rate (k), the turnover frequency (TOF), FFCA selectivity, and HMF conversion). f Desorption time of target products and number of intermediates under photothermal and thermocatalytic catalysis in nanoreactor-3 through simulation. g DFT simulated reaction Gibbs free-energy diagram of HMF oxidation (65 and 150 °C). (h) Numerical simulation of surrounding temperature distributions and velocity vectors during photothermal and thermocatalytic nanoreactors. Flow field distribution around the nanoreactor-3 and simulation snapshots under i photothermal and j conventional heating (enrichment of intermediate molecules on the nanoreactor-3 surface, and the direction of the arrow shows its desorption path in the left panel. Yellow and blue particles represent intermediates and target products, respectively, in the right panel.) Reaction conditions: 50 mg of catalyst, 50 mg of HMF, 20 mL of acetonitrile as solvent, atmospheric pressure, O2, 10 h.

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Density functional theory (DFT) is applied to reveal the temperature-dependent reaction energy of HMF-FFCA pathways (Fig. 4g). When the catalyst temperature is 65 °C, the reaction energy barrier of second-step HMFCA-FFCA (0.88 eV) is significantly higher than that of HMF-HMFCA (0.68 eV), indicating that the second step is the rate-limiting step of the whole reaction. It explains that HMFCA is the main product at 65 °C. In contrast, increasing the temperature to 150 °C can significantly reduce the reaction energy barrier of both HMF-HMFCA and HMFCA-FFCA steps, where the first step becomes the final rate-determining step. Therefore, although the “cool reaction medium” is approximately maintained at 65 °C under photothermal catalysis, the locally high temperature of about 150 °C at the nanoreactor surface (active sites) is enough to overcome the reaction energy barrier of HMFCA-FFCA, which eventually induces the conversion of HMF-FFCA.

Molecular dynamics simulations further show that the heat transfer in conventional heating brings a uniform thermal field, which is completely different from the photothermal nanoreactors with large temperature differences (Fig. 4h and Supplementary Fig. 20). The internally heated convection of the photothermal nanoreactor flows in the same direction as the thermal gradient, and the vortex effect from the inside-out facilitates molecular motion velocity and exchange range (Fig. 4i and Supplementary Video 1). In contrast, externally heated convection occurs at the edge of the nanoreactor, tangent along the surface (Fig. 4j, Supplementary Fig. 21, and Supplementary Video 2). Overall, although the conventional thermo-catalytic process (150 °C) can also cross the reaction energy barrier, the additional pressure and the out-inside heat transfer both make the intermediate molecules more inclined to accumulate on the nanoreactor surface (Supplementary Fig. 22). The residence time of the target product molecule is 97.86 μs for conventional thermal catalytic process, much longer than 30.39 μs for the photothermal catalysis (Fig. 4f). The strong molecule adsorption effect in the overall high-temperature environment leads to the generation of by-products. In addition, even when the thermal temperature difference in nanoreactors with different concavities is adjusted to be the same, the yield of target product FFCA still reduces from 96.9% in nanoreactor-3 to 70.9% in nanoreactor-1 (Supplementary Fig. 23). This means that in the photothermal catalytic system, even though the same self-pressurization is given, the different Gaussian surfaces can still produce a large influence on catalytic behavior.

Molecular adsorption–desorption dynamic equilibrium bridge

Based on the above analysis, we further investigated the catalytic performances of photothermal nanoreactors with different Gaussian curvatures (Fig. 5a and Supplementary Fig. 24). With the increase of C value from 1/2 to 7/8, the HMF conversion increases from 92.8% to 98.8%, and the FFCA yield improves from 76.2% to 96.9%. The further convex nanoreactor (C = 9/8) achieves complete conversion of HMF and HMFCA, but cannot be further fully converted to FFCA (92.5% yield) due to the generation of MA by-products. Notably, the yield of the intermediate HMFCA from nanoreactor-1 to nanoreactor-5 decays gradually, suggesting that the transition of the nanoreactor from concave to convex promotes intermediate conversion (Fig. 5b). The nanoreactor-3 (C = 7/8) delivers the best catalytic performance and the lowest apparent activation barrier (11.08 KJ mol−1). This implies that the reaction energy barrier of FFCA synthesis can be reduced to a greater extent, thus obtaining superior catalytic activity that is unachievable with other curvatures (Fig. 5c). In addition, the surface chemical properties of various photothermal nanoreactors are basically the same, further demonstrating that the difference in catalytic performances are mainly attributed to the curvature structure changes (Supplementary Fig. 8c). The subsequent expansion of the reactants from HMF to furfural and glycerol exhibits similarly optimized selectivity in nanoreactor-3 (Supplementary Fig. 25).

Fig. 5: Nanoreactor Gaussian surface effect induced molecular adsorption–desorption equilibrium.
figure 5

a Yield and b intermediate (HMFCA) reaction kinetics plots of photothermal nanoreactors with different curvatures. c Apparent activation energy (EA) of HMF oxidation in photothermal nanoreactors with different curvatures. d Calculation of the difference between the number of molecules adsorbed and desorbed under different curvature photothermal nanoreactors based on theoretical equations. e The number of intermediates and their (f) desorption time in photothermal nanoreactors with different curvatures. g Arrhenius plots of HMF oxidation in photothermal nanoreactors with different curvatures. h Three-dimensional relationship and i difference between C value, T versus molecular adsorption/desorption strength. j Simulation of enrichment densities of intermediates at adsorption and desorption strength in photothermal nanoreactors with different curvatures. k Equilibrium effect of adsorption and desorption in Gaussian curvature nanoreactors by simulation. Yellow and blue particles represent intermediates and target products, respectively. The arrow direction indicates the desorption pathway of the intermediate. Reaction conditions: 50 mg of catalyst, 50 mg of HMF, 20 mL of acetonitrile as solvent, atmospheric pressure, O2, 10 h.

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According to the proposed equilibrium formula, the microscopic mechanism of molecular adsorption/desorption behavior under photothermal nanoreactors with different C values is probed (Eq. 1). Theoretical calculation shows that the number of adsorbed molecules at concave C = 1/2 and 3/4 is 2.58 × 1018 and 2.50 × 1018 pieces/m2, respectively, which is significantly lower than at room temperature due to thermal effects. The number of molecular desorptions is greater than adsorption (ΔZ is negative) (Figs. 3h and 5d, e). The enrichment number and residence time (23.05 and 26.39 μs at C = 1/2 and 3/4, respectively) of intermediates on the surface of the catalyst are weakened, which is insufficient for the complete conversion to the target products (Fig. 5f and Supplementary Fig. 26). The Arrhenius curves further evolve from curved (nanoreactor-1, 2, and 3) to linear (nanoreactor-4 and 5) type, meaning that the kinetics of the catalytic reaction from concave to convex surface is controlled by diffusion (Fig. 5g). In photothermal convex C = 1 and 9/8, the number of adsorbed molecules (2.35 × 1018 and 2.20 × 1018 pieces at C = 1 and 9/8, respectively) is greater than that of desorbed molecules (ΔZ is positive), and the density distribution of intermediates is denser.

$$\varDelta Z={Z}_{{{\rm{A}}}}-{Z}_{{{\rm{D}}}}=\frac{2\sqrt{2}\Upsilon }{r\sqrt{{{\rm{K}}}_{{\rm{B}}}T}}-\frac{{10}^{{\frac{1}{2}}-\left(A-\frac{B}{\bigtriangleup T+C}\right)}}{5\sqrt{{{\rm{K}}}_{{{\rm{B}}}}{Tm}}}$$
(1)

Where ϒ is the surface tension of the reaction medium, affected by temperature. r is the curvature radius. KB is the Boltzmann constant (1.380649 × 10−23 J/K). T is the thermodynamic temperature. m represents the relative molecular mass. ΔT is the temperature difference between the nanoreactor and the reaction medium. A, B, and C are Antoine constants for the reaction medium.

Although the reactants and intermediates are completely converted, the prolonged molecular desorption time (57.28 and 60.45 μs at C = 1 and 9/8, respectively) leads to excessive oxidation into by-products (Supplementary Fig. 27). Localized photothermal activation overcomes the energy barrier under mild bulk temperature conditions, while Gaussian curvature engineering precisely regulates the adsorption/desorption equilibrium and accelerates mass transfer. The synergistic effect is pivotal to surpassing the traditional thermocatalytic system. Molecular dynamics simulations are applied to explore the correlation between the L/D (C) and temperature (T) versus molecular adsorption/desorption strength (ΔE) (Eq. 2) (Fig. 5h).

$$\varDelta E=40.54\,{C}^{2}+4.57\times {10}^{-5}{T}^{2}-32.04\,C-0.057\,T+7.64$$
(2)

Where C is the length-to-diameter ratio, and T is the thermodynamic temperature.

The two surfaces of adsorption and desorption strengths show an antagonistic relationship and intersect in a spatial curve, where all points on the intersection line are the equilibrium points (Fig. 5i and Supplementary Fig. 28). When the internal temperature is 100–300 °C, the corresponding equilibrium point is in the range of 0.73–0.96 (C value), and all of them are concave nanoreactors (Supplementary Fig. 29). Under experimental temperature, the equilibrium point appears at C = 0.88, which is close to that of nanoreactor-3 (Fig. 5j). These results reveal that the equilibrium point can be tuned dynamically under the coupled influence of Gaussian curvature and thermal effects (Fig. 5k).

Discussion

Correlation of Gaussian curvature and catalytic effects

First, for the different photothermal effects of nanoreactors with different Gaussian curvatures, the unit area of light refraction is affected by the cavity volume, and the light reflection path is shorter and more intense in a relatively small space26. As the structure transitions from convex to concave, the internal cavity volume decreases, leading to a higher temperature gradient under irradiation. This temperature difference elevates the internal pressure, thereby enhancing the outward momentum transfer of molecules and intensifying the desorption process, as calculated by the Antoine equation. Simultaneously, surface tension induces a net inward-directed contraction of the liquid interface, causing the collective momentum transfer of molecules in the direction normal to the concave solid surface (external pressure), promoting molecular adsorption towards the nanoreactor surface, as quantified by the Young-Laplace equation. Therefore, by changing the Gaussian curvatures of the nanoreactor, the internal and external pressure of the nanoreactor can be dynamically adjusted, thus the dynamic regulation of molecule adsorption–desorption can be realized. The molecule adsorption–desorption curves related to nanoreactor curvatures show a relative antagonistic change, demonstrating the close relationship between the molecular diffusion behavior and the nanoreactor structure. For instance, although the concave surface enhances adsorption potential, the overwhelming internal pressure results in a phenomenon where the amount of molecules desorbed significantly exceeds the amount adsorbed (Fig. 5j). Conversely, the relatively larger inner cavity in convex nanoreactor-5 presents a smaller temperature difference under irradiation and consequently lower internal pressure and slower desorption times (60.45 and 23.05 μs for nanoreactor-5 and nanoreactor-1, respectively, Fig. 5f). Thus, regulating the concavity (i.e., corresponding curvature) offers a pathway to balance these opposing forces. The intersection point of the simulated adsorption and desorption curves represents the specific curvatures where dynamic equilibrium is approached. At this equilibrium point (close to the nanoreactor-3), the number of adsorption and desorption cycles approaches dynamic equilibrium, signifying a stable population of molecules interacting with the catalytic surface. This optimized residence time is crucial, as it not only promotes the conversion of reactants and intermediates but also minimizes the duration for which molecules are exposed to conditions conducive to side reactions. Consequently, this dynamic equilibrium state dramatically enhances the selectivity towards the desired target product, aligning perfectly with our experimental observations.

Formation mechanism of tunable concave–convex nanoreactor

Based on the above observations, a programmable nanodroplet buckling strategy is proposed for the synthesis of a series of mesoporous nanoparticles with different concave–convex curvatures. In the water-in-oil (propanol, butanol, pentanol, hexanol, and heptanol) emulsion systems, the spherical nanodroplets are stabilized by surfactant CTAB (other parts migrate into the water phase from the micelles) (Fig. 6a). Subsequently, the introduced precursor TEOS is hydrolyzed to form negatively charged silicate oligomers. The surfactant/silicate composite micelles in the water phase are then attracted by the positively charged CTAB molecules and deposited continuously at the interface (Step 1). This process makes the anisotropic growth of the mesoporous silica shells and triggers the dynamic migration of the oil/water interface. At this stage, the nucleation sites of the oligomers become two locations, one part of which continues to deposit at the interface under the attraction of CTAB (corresponding to the interface growth rate, vi)27,28,29,30. The other part of which continues to deposit on the preformed silica shells in the aqueous phase (seen as shell deposition rate, vs) (Step 2)31. The deposition of oligomers in the aqueous phase makes the initially grown shells gradually thicker, and the subsequent deposition of oligomers at the interface gradually increases the area of the shell encapsulating the nanodroplets. Under the influence of oil–water interfacial energy, the growth rate of the interfacial shells is obviously faster than the deposition rate, which also leads to a gradual thinning of the subsequently grown shells. Under the influence of hydrogen bond forces between oil and water molecules, the oligomeric shell gradually sinks inward towards the interior of the droplet. The growth of the entire shell is also a dynamic deposition-solidification process, the initial thick-shell regions resist this stress, while subsequently formed thin-shell areas lack sufficient structural rigidity32. It can collapse towards the internal droplet along with the migration of the oil–water interface. With the continuous deposition and solidification of silica oligomers at the interface, the concave structure is gradually formed (Step 3) (Supplementary Fig. 30).

Fig. 6: Illustration of the programmable nanodroplet buckling strategy.
figure 6

a The formation of concave mesoporous silica nanoparticles. b Typical simulation snapshots (gray particles represent the solid shell layer, blue particles represent the aqueous phase, and the oil phase constitutes the surrounding environment) and c surface curvature hot spot distribution of nanoparticle depression in the propanol–water (C3) emulsion system. d Diagram of free energy/nucleation barrier against alcohols of different alkane chain lengths (C3–C7). e Simulation of interface growth rate (vi) and shell deposition rate (vs) of mesoporous nanoparticles with different concave and convex curvatures. Simulation of molecular density distribution in alcohol–water emulsion systems with different alkane chain lengths (red particles represent the oil phase, while blue particles represent the water phase) and schematic distribution of curvature hotspots on the concave–convex surface. f C4, g C5, and h C7.

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Molecular dynamics simulations are applied to reveal the interfacial dynamic-driven process (Supplementary Fig. 31). It is found that vi (1.10) is apparently faster than vs (0.11) in the propanol–water emulsion system, and this gap gradually increases with time (Supplementary Fig. 32). The rapid growth of the shells resulted in the oligomers deposited at the oil–water interface not being able to solidify, but gradually collapsing toward the interior of the droplets. During the whole growth process, the droplet surface curvature presents a dynamic change, from the initial spherical shape, gradually buckling and collapsing into a stable hemispherical structure, which further confirms the formation process of the concave structure (Fig. 6b, c and Supplementary Video 3). The nucleation barrier and the critical nucleation number gradually decrease with the increase of alkyl chain lengths (C3–C7), indicating that the interface tends to be stable (Fig. 6d)33,34. It is found that when the alkyl chain length is short, there is no free energy barrier, which means that the oil molecules are unable to aggregate into nucleation, but can be dispersed in water (Supplementary Fig. 33)35.

The nuclear barrier decreases with increasing chain length, thus altering the relative change of vi and vs. Moreover, the vi growth rate gradually slows down with increasing alkyl chain lengths of the oil phase (Fig. 6e). When butanol and pentanol are used as oil phases, the relative velocity differences between vi and vs are about 0.90 and 0.82, respectively, which are 0.09 and 0.17 lower than those of propanol, respectively. This results in an opportunity for interfacial shell growth to solidify and become thicker, so the proportion of its depression into the droplet is reduced (Fig. 6f, g). Further increase in hexanol (C6), the relative velocity difference is further reduced, thus obtaining a hollow spherical-like structure (Supplementary Fig. 34). The whole process is like a chase and encounter process, so when heptanol (C7) is the oil phase, it shows strong interfacial stability, resulting in vs very close to vi. In this process, the newly grown shell can maintain its rigidity without collapse in time, and form convex structures along with the dynamic migration of the interface (Fig. 6h). The dynamic change of droplet surface curvature further confirms the stability of the oil–water interface, that is, the higher the stability, the less prone to collapse, thus accurately regulating the nanostructure concavity and convexity.

In summary, a series of mesoporous nanoreactors from concave to convex structures are designed by a programmable nanodroplet buckling strategy. The precise regulation of thermal-confined self-pressurization and external additional pressure is constructed on a single-nanoreactor level. Bidirectional pressure equilibrium in customized concave nanoreactors implies a balance between molecular adsorption and desorption. Molecular dynamics simulations show that the photothermal-induced temperature difference and thermal vapor pressure promote molecular vortex motion and active desorption. The catalytic efficiency is even an order of magnitude higher than that of conventional heating (k increased from 0.07 to 0.31 h−1), realizing high selectivity at a high HMF conversion (FFCA selectivity increased from 46.4% to 97.9%). Based on this, we propose the molecular adsorption/desorption equilibrium equations to quantify the molecular adsorption–desorption quantities under the coupled influence of Gaussian curvature and photothermal effects. Under the combined influence, when the C value is 1/2 and 3/4, the enriched number and residence time of the intermediate molecules are weakened, which limits the complete conversion to target products. Whereas the molecular enrichment is relatively higher under the convex structure, leading to the generation of by-products. The internal–external pressures tend to be balanced at C = 7/8, and the molecule adsorption–desorption quantities also reach a relative equilibrium state, showing the best catalytic performance. This builds a dynamic equilibrium bridge to explore the strength of molecular adsorption–desorption in more functional nanoreactors.

Methods

Synthesis of mesoporous silica particles

Sonically dissolve 20 mg of hexadecyltrimethylammonium bromide (CTAB) and 1 g of polyvinylpyrrolidone (PVP) in 10 mL of propanol. The 1 mL of ethanol, 0.10 mL of deionized water, 0.10 mL of sodium citrate in water (0.18 M), and 0.10 mL of NH3·H2O (28 wt%) were added to the above solution and subjected to continuous sonication to form a homogeneous emulsion. Subsequently, the emulsion was continued to be sonicated for 10 min, then 0.15 mL of TEOS was added, and the reaction was allowed to stand for 4 h. After three rounds of ethanol centrifugation, it was collected and then extracted with 0.1 M HCl ethanol solution at 60 °C for 12 h. After two consecutive extractions, the residual surfactant could be removed, and the mesoporous SiO2 nanoparticles with 1/2 concave structure could be obtained. Based on the above synthesis system, butanol, pentanol, hexanol, and heptanol were used instead of propanol to obtain mesoporous SiO2 nanoparticles with concave and convex curvatures of 3/4, 7/8, 1, and 9/8, respectively.

Active components loaded on mesoporous SiO2 nanoparticles

To load the Fe3O4 nanoparticles in the inner cavities of mesoporous silica, 0.1 mL of hydrophilic Fe3O4 aqueous solution (2.0 mg/mL) was added to the reaction solution instead of water at the initial stage. Other reaction conditions were consistent with those for the synthesis of silica. Method for implanting Ru nanocrystals into the silica shell: Dissolve SiO2 shell and 20 mg of SiO2 nanoparticles were dissolved in 20 mL of ethanol solution, followed by the addition of 2.0 mL of RuCl3·3H2O (25 mM) and stirring for 2 h. Subsequently, 1 mL of NaBH4 (26 mM) was added and stirred for 1 h until the mesoporous nanoparticles gradually changed from white to dark brown, indicating the formation of Ru nanocrystals. The final product was centrifuged and washed three times with deionized water.

Characterizations

The morphology and structure of the samples were observed by field emission scanning electron microscopy (FESEM, Hitachi Model S-4800). Transmission electron microscopy (TEM) measurements were performed on a JEOL JEM2100F microscope (Japan) operating at 200 kV. Samples for SEM and TEM analysis were prepared by dispersing in ethanol and dropping on Si substrates and Cu grids. The surface area and pore size distribution of the samples were measured by nitrogen adsorption isotherm (Micromeritics Tristar 3020) at 77 K after degassing for more than 12 h at 180 °C under vacuum. The surface area was calculated using the BET method, and pore volume and pore size distribution were calculated using the BJH model. The X-ray diffraction (XRD) spectra of the powders were recorded on a Rigaku D/max-2550VB/PC diffractometer using a Cu Kα (λ = 0.015406 nm). X-ray source at 40 kV and 40 mA. The X-ray photoelectron spectroscopy (XPS) was measured on a Thermo Scientific K-Alpha using an Al Kα (hv = 1486.6 eV) radiation source. Diffuse reflectance spectra were measured using a Lambda 1050 ultraviolet/visible/near-infrared spectrometer from PerkinElmer and an integrating sphere with a diameter of 150 mm. The content of various elements was measured by an ICP-MS (Aurora M90, Jenoptik). An infrared thermal (IR) imaging camera (Fotric 226s#L28) was used to record photothermal imaging and photothermal temperatures. X-ray absorption fine spectra (XAFS) measurements were performed on the B11 station in the Shanghai Synchrotron Radiation Facility (SSRF).