Size-Activity Relationship of TiO₂-Supported Pt Nanoparticles in Hydrogenation Reactions

Abstract

Quantitative assessments of the geometric influence on catalytic activity are crucial for catalyst design and understanding reaction mechanisms. In this study, we synthesized a series of catalysts comprising TiO₂-supported Pt nanoparticles with varying particle sizes, which were systematically evaluated in representative hydrogenation reactions. A consistent size–activity relationship is established, wherein overall turnover frequency (TOF) values (TOF_overall: calculated as moles of reactant converted per mole of Pt per hour) are modeled as functions of the average diameter of the supported Pt particles, yielding slope values consistently near −1 across a variety of common substrates. This finding underscores that catalytic activity predominantly originates from surface sites on the Pt nanoparticles rather than from interfacial, edge, or corner active sites.

1. Introduction

Hydrogenation is among the central themes of the petrochemical, coal chemical, and fine chemical industries. For example, in the petrochemical industry, processes like hydro-reforming and hydro-isomerization are pivotal for enhancing the octane value of gasoline, while the hydrogenation of benzene to cyclohexane is a critical step in the production of nylon intermediates. Noble metals are extensively employed in these hydrogenation reactions due to their exceptional catalytic activity. However, given the high cost and limited availability of noble metals, there is an urgent need to develop highly active and efficient catalysts for hydrogenation reactions. In past research, a widely accepted yet simplified notion is that smaller noble metal nanoparticles yield higher overall activity per unit of noble metal loading [1,2]. Consequently, researchers have shown great interest in strategies to reduce the size of supported noble metal nanoparticles and to elucidate the catalytic performance differences arising from size variation, emphasizing the essential need to understand the structure–activity relationship [3,4,5].

Current studies on the structure–activity relationship in the hydrogenation of supported noble metal catalysts primarily focus on the selectivity of nanoparticles of different sizes or provide nonquantitative insights into how nanoparticle diameter affects catalytic activity [2,4,6]. Notable examples include hydrogenation reactions such as cinnamyl aldehyde hydrogenation [7,8,9], ethene semi-hydrogenation [10,11,12,13], and nitroaromatic hydrogenation [5,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. However, detailed quantitative investigations into the relationship between nanoparticle size and catalytic activity remain scarce. Given the frequent comparisons of catalytic performance across nanoparticles of varying sizes in heterogeneous hydrogenation catalysis, we highlight the urgent need for rigorous quantitative evaluations to clarify the geometric influence on catalytic activity.

Quantitatively described size–activity relationships in catalytic reactions, such as CO oxidation and low-temperature water–gas shift (LWGS), have been elegantly demonstrated by the groups of M. Cargnello and M. Shekhar [28,29,30,31], respectively. By theoretical simulation and CO oxidation catalyzed by CeO₂-supported metal, the groups of M. Cargnello correlated the ceria–metal interface sites with slope of overall turnover frequency (TOF) and the size of supported metal particles (unless otherwise specified, all TOF values refer to the overall TOF, calculated as moles of reactant converted per mole of Pt per hour). Concretely speaking, the overall TOF calculated based on all metal located on support and catalyst dispersion was put aside. Then, the slope value of the linear fitting equation of l n (overall TOF) and l n (metal size) should correspond with which part active catalytic sites are located. Inspired by these pioneering studies, we sought to adopt analogous analytical paradigms to elucidate the geometric influence on catalytic activity in representative hydrogenation reactions. Herein, we synthesized a series of TiO₂₂-supported Pt nanoparticles with systematically varied particle sizes and rigorously evaluated their performance across representative hydrogenation reactions. A robust size–activity relationship was observed, with turnover frequency (TOF) values modeled as functions of the average diameter of the Pt nanoparticles, consistently yielding slope values near −1 across a range of common substrates. These findings highlight that catalytic activity is predominantly derived from surface sites on the Pt nanoparticles rather than from interfacial, edge, or corner sites, offering new insights into the fundamental structure–activity relationship in these systems.

2. Results

In this work, a series of catalysts consisting of TiO₂-supported Pt nanoparticles with average sizes of approximately 2.32 nm, 4.38 nm, 9.63 nm, 14.64 nm, and 40.98 nm were synthesized (details provided in the Supporting Information). Inductively coupled plasma optical emission spectrometry (ICP-OES) analysis indicated Pt loading rates of approximately 1 wt% for all prepared Pt/TiO₂ catalysts (detailed data provided in Table S1). These average sizes were determined from transmission electron microscopy (TEM) images, with representative TEM images shown in Figure 1 (additional images are available in Figure S1). Each size variant was supported on TiO₂ and labeled accordingly: 2-Pt/TiO₂, 4-Pt/TiO₂, 10-Pt/TiO₂, 15-Pt/TiO₂, and 41-Pt/TiO₂. In addition, the TEM images revealed similar sub-globular shapes for the supported Pt nanoparticles across the series. In addition, attempts to further determine the particle sizes by X-ray diffraction (XRD) (Figure 2) were unsuccessful owing to the low Pt loading. All five nanoparticle size fractions, each displaying sub-spherical Pt morphology, were prepared by the same polyol colloidal route under identical surfactant and reduction conditions, and TEM and XRD confirm the absence of sintering necks or irregular aggregates in every sample.

Nitrobenzene hydrogenation is a fundamental catalytic reaction with broad applications in fine chemical production. Numerous studies have explored Pt-based catalysts for this transformation, underscoring their efficacy and versatility [27,32,33,34]. In this work, we evaluated the performance of the synthesized Pt/TiO₂ catalysts in nitrobenzene hydrogenation using H₂.

Hydrogenation experiments were systematically conducted under varying reaction conditions using 4-Pt/TiO₂ as the initial catalyst. Initial control experiments using TiO₂ as the catalyst confirmed its inactivity for the reaction, as no conversion was observed even after 6 h (

Table 1. Performance of 4-Pt/TiO₂ at various reaction conditions for nitrobenzene hydrogenation.

Entry [a]	Temp. (°C)	Time (h)	Conv. (%)	TOF (h−1)
1 [b]	25	6	0	/
2	25	1	20.7	669.8
3	30	1	30.6	1012.8
4	35	1	34.2	1044.0
5	40	1	35.2	1145.5
6	25	3	59.8	644.1

^[a] Reaction conditions: nitrobenzene, 1 mmol; 10 mL ethanol; 5 mg 4-Pt/TiO₂ catalyst; H₂ pressure, 0.1 MPa. ^[b] 5 mg TiO₂ support was used. TOF values refer to the overall TOF, calculated as moles of reactant converted per mole of Pt per hour.

, entry 1). In sharp contrast, the introduction of Pt nanoparticles onto the TiO₂ support markedly enhanced catalytic activity, achieving approximately 21% conversion within just 1 h (Table 1, entry 2). Interestingly, a moderate increase in reaction temperature to 30 °C (Table 1, entry 3) further boosted the conversion to 31%, with a concomitant rise in the turnover frequency (TOF) from 669.8 h⁻¹ (Table 1, entry 1) to 1012.8 h⁻¹. However, as the reaction temperature was increased further (Table 1, entries 4 and 5), the incremental improvements in TOF became less pronounced, suggesting a saturation effect at higher temperatures. Prolonging the reaction time to enhance the conversion (Table 1, entry 6) led to a significant decrease in TOF. This decline is likely attributed to kinetic limitations arising from substrate depletion during the later stages of the reaction.

Based on the above findings, a reaction temperature of 25 °C was selected for further studies. At this temperature, the conversion of nitrobenzene remains sufficiently low, minimizing the impact of substrate depletion on the reaction rate. Additionally, the mild conditions are expected to enhance the stability of the supported Pt catalyst, ensuring prolonged performance with high reliability. Reusability tests were conducted with the 4-Pt/TiO₂ catalyst, and no significant loss in overall TOF was observed after five consecutive cycles, as illustrated in Figure 3. These results demonstrate the robustness and stability of the catalyst under the chosen reaction conditions.

A qualitative relationship between the apparent reaction rate and Pt nanoparticle size was observed, indicating that the overall TOF decreased as the average Pt particle diameter increased, the trend shown in

Table 2. Performance of NPs Pt with different average sizes supported by TiO₂ for hydrogenation of nitrobenzene ^[a].

Entry	Catalyst	Time (h)	Conv. (%)	TOF (h−1)
1	2-Pt/TiO2	1	22.7	718.3
2	4-Pt/TiO2	1	20.7	669.8
3	10-Pt/TiO2	2	10.7	184.1
4	15-Pt/TiO2	5	16.2	108.1
5	41-Pt/TiO2	5	9.0	62.2

^[a] Reaction conditions: nitrobenzene, 1 mmol; solvent, 10 mL ethanol, 5 mg catalyst; temperature, 25 °C; H₂ pressure, 0.1 MPa. TOF values refer to the overall TOF, calculated as moles of reactant converted per mole of Pt per hour.

. To ensure the nitrobenzene conversion remained sufficiently low and comparable across all entries in Table 2, thereby equalizing the impact of reaction kinetics on TOF calculations, the reaction times were adjusted accordingly. Therefore, the reaction times of 2-Pt/TiO₂ and 4-Pt/TiO₂, 10-Pt/TiO₂, 15-Pt/TiO₂ and 41-Pt/TiO₂ are increased with the overall TOF reduced.

Building on the model proposed by Matteo Cargnello, which establishes a quantitative relationship between overall TOF and different supported crystalline metal grains with uniform packing structures, we developed a simplified version to create a highly generalized reference framework that facilitates direct comparison. In this generalized model, logical deduction (details provided in the Supporting Information) demonstrates that the natural logarithm of the overall TOF and the natural logarithm of the supported metal particle diameter form a linear relationship. The slope of this linear function is directly linked to the distribution of active sites on the supported metal particles. Specifically, slope values of −1, −2, and −3 correspond to surface active sites, interfacial/edge active sites, and corner active sites, respectively. Using this simplified model, we applied logarithmic transformations to the TOF data from Table 2, treating TOF as the dependent variable and the average Pt particle diameter as the independent variable. Employing linear regression to plot the experimental data, the slope was determined to be approximately −1, as shown in Figure 4. This result suggests that the active sites on Pt particles are predominantly located on their surface.

It should be noted that this inference is based on necessary but reasonable assumptions, which are crucial for the generalized model we proposed before. Supported crystalline metal grains should present similar figures and uniform packing structures even if the size changes. In addition, active sites that are located in the same kind of areas on Pt particles, to be more specific, including surface parts, interfacial/edge parts, or corner parts, should perform uniform or approximate activity, respectively. However, the assumption about uniform activity might correspond to all cases. Here is a typical counterexample reported that for CH₄ reactions with CO₂ or H₂O over supported Pt clusters, CH₄ turnover rates over surface Pt sites are different on Pt clusters with different sizes [3]. These two hypotheses may narrow the range of applicability but significantly enhance reliability. Fortunately, the CO-DRIFTS results shown in Figure 5 indicate that the Pt nanoparticles in this study exhibit relatively uniform adsorption behavior, supporting the rationale and necessity for the assumptions of uniform shape and activity. Linear CO adsorption signals were observed between 2000 and 2100 cm⁻¹, with peaks around 2088 cm⁻¹ and 2065 cm⁻¹ corresponding to CO adsorption on Pt^δ+ and Pt⁰ sites, respectively. Similar adsorption signals have been reported for other Pt-based catalysts [35,36], further validating these findings.

XPS analyses were also carried out, and peak–deconvolution of the Pt 4f region (Figure 6) shows virtually identical binding energies for both metallic Pt⁰ (4f7/₂ ≈ 71.2 eV) and the slightly oxidized Pt^δ+ component (4f7/₂ ≈ 72.0 eV) across all Pt/TiO₂ catalysts. This uniform valence–state distribution further substantiates our assumption of consistent particle morphology and comparable per-site activity.

3. Discussion

To delve deeper, we propose that the dominant factor influencing catalyst performance in this work is the activation of H₂ or substrates on the surface sites of Pt nanoparticles rather than the spillover of H₂ or H atoms from Pt to TiO₂. Literature reports suggest two common hydrogenation mechanisms for heterogeneous catalytic processes: direct hydrogenation and hydrogen spillover [37,38,39,40,41,42,43]. While it is challenging to exclude the coexistence of these two mechanisms in the hydrogenation reactions catalyzed by Pt/TiO₂, certain inferences can be made. Hydrogen spillover involves the migration of hydrogen atom equivalents from metal nanoparticles to the support, implying that the interfacial sites between the Pt surface and TiO₂ would serve as the active sites if spillover were the dominant mechanism. In such a case, the slope value of the linear relationship between TOF and Pt particle diameter would be expected to be −2. However, this is inconsistent with the experimental results for nitrobenzene hydrogenation. Instead, the observed slope value, approximately −1, suggests that surface sites on the Pt nanoparticles are the primary active sites (Figure 4). Thus, we conclude that the dominant parameter governing catalyst performance in this work is the activation of H₂ or substrates on these surface sites rather than hydrogen spillover.

Considering the universality of the slope description for the size–activity relationship of Pt nanoparticles supported on TiO₂, we extended the study to other typical unsaturated substrates, including cyclohexene, cyclohexanone, and styrene, under similar reaction conditions. Typical results are collected and shown in

Table 3. Performance of 4-Pt/TiO₂ for various substrate hydrogenations. ^[a].

Entry	Reaction	Conv. (%)	TOF (h−1)
1		20.7	669.8
2		23.5	508.3
3		26.1	372.1
4		17.4	1071.4

^[a] Reaction conditions details in Tables S2–S4. TOF values refer to the overall TOF, calculated as moles of reactant converted per mole of Pt per hour.

. Following logarithmic transformation and linear regression analysis of the experimental data (raw data provided in Tables S1–S4), the results, shown in Figure 7, revealed slope values close to −1, −0.87, −1.18, and −0.85 for cyclohexene, cyclohexanone, and styrene, respectively. These findings indicate that, for the hydrogenation of these typical unsaturated substrates, the active sites are located on the surface of the supported Pt nanoparticles, consistent with our inference for nitrobenzene hydrogenation.

4. Materials and Methods

4.1. Preparation of the H₂PtCl₆ Aqueous Solution

Dissolve the purchased H₂PtCl₆ in deionized water (DIW) to obtain H₂PtCl₆ aqueous solution.

4.2. Preparation of the 2-Pt/TiO₂ Catalyst

Measure 600 µL DIW and 600 µL H₂PtCl₆ aqueous solution into a test tube. Add 1 g TiO₂ after fully mixing the solution into the test tube. Ultrasound for 0.5 h, quiet for 6 h, then dry the test tube in an oven. After the solid is dried, burn it in a muffle furnace at 400 °C for 5 h. Then, place the solid in a reaction vessel and add 10 mL ethanol, fill with 1.0 MPa hydrogen, and reduce it for 1 h at 200 °C. Obtain a 2-Pt/TiO₂ catalyst after centrifugation and vacuum drying.

4.3. Preparation of the 4-Pt/TiO₂ Catalyst

Add 1 g TiO₂ and 100 mL DIW to the beaker. Add 100 mL DIW, 1 g of PVP, and 600 µL H₂PtCl₆ aqueous solution to the other beaker. Put the beaker into a water bath at 20 °C, turn on the magnetic stirring, and add 20 mL of aqueous solution containing 0.0102 g NaBH₄ slowly. Then, pour the suspension from the previous beaker into this beaker. Stir for 12 h. After filtration, washing, and drying, burn the solid in a muffle furnace at 400 °C for 5 h. Then, place the solid in a reaction vessel and add 10 mL of ethanol, fill with 1 Mpa hydrogen, and reduce it for 1 h at 200 °C. Obtain 4-Pt/TiO₂ catalyst after centrifugation and vacuum drying.

4.4. Preparation of the 10-Pt/TiO₂ Catalyst

Add 1 g TiO₂, 600 µL H₂PtCl₆ aqueous solution, 600 µL formaldehyde, and 100 mL DIW to the flask. Put the flask into oil bath at 120 °C, and stir for 12 h. After filtration, washing, and drying, burn the solid in a muffle furnace at 400 °C for 5 h. Then, place the solid in a reaction vessel and add 10 mL ethanol, fill with 1.0 MPa hydrogen, and reduce it for 1 h at 200 °C. Obtain 10-Pt/TiO₂ catalyst after centrifugation and vacuum drying.

4.5. Preparation of the 15-Pt/TiO₂ Catalyst

Add 1 g TiO₂, 600 µL H₂PtCl₆ aqueous solution, 600 µL formaldehyde, and 100 mL DIW to the flask. Put the flask into oil bath at 120 °C, and stir for 24 h. After filtration, washing, and drying, burn the solid in a muffle furnace at 400 °C for 5 h. Then, place the solid in a reaction vessel and add 10 mL of ethanol, fill with 1.0 MPa hydrogen, and reduce it for 1 h at 200 °C. Obtain 15-Pt/TiO₂ catalyst after centrifugation and vacuum drying.

4.6. Preparation of the 41-Pt/TiO₂ Catalyst

Add 1 g TiO₂, 600 µL H₂PtCl₆ aqueous solution, and 10 mL ethanol to the reaction kettle, fill with 1 Mpa hydrogen and reduce it for 1 h at 200 °C. After filtration, washing, and drying, burn the solid in a muffle furnace at 400 °C for 5 h. Then, place the solid in a reaction vessel and add 10 mL of ethanol, fill with 1 Mpa hydrogen, and reduce it for 1 h at 200 °C. Obtain 41-Pt/TiO₂ catalyst after centrifugation and vacuum drying.

4.7. Catalytic Performance

The nitrobenzene hydrogenation was conducted in a branched reaction tube equipped with a magnetic bar. In a typical procedure, 5 mg catalyst, 1 mmol nitrobenzene, and 10 mL ethanol were subjected to the branched reaction, which was then flushed with 1 atm H₂ five times and charged successively with 0.1 MPa H₂. After the branched reaction was sealed, it was placed in water bath at 25 °C. After reaction, 150 µL anisole was added to 5 mL the reaction liquid as inner standard. The product was qualitatively analyzed by gas chromatography (GC) and quantitatively analyzed on an Agilent 6890B instrument equipped with an on-column injector (250 °C), an FID detector (250 °C), and an HP-5 capillary column (30 m × 0.32 mm × 0.25 mm). The conversion was calculated by gas chromatography.

The cyclohexene hydrogenation was conducted in a branched reaction tube equipped with a magnetic bar. In a typical procedure, 5 mg catalyst, 1 mmol cyclohexene, and 10 mL ethanol were subjected to the branched reaction, which was then flushed with 1 atm H₂ five times and charged successively with 0.1 MPa H₂. After the branched reaction was sealed, it was placed in water bath at 25 °C. After reaction, 150 µL anisole was added to 5 mL the reaction liquid as inner standard. The product was qualitatively analyzed by gas chromatography (GC) and quantitatively analyzed on an Agilent 6890B instrument equipped with an on-column injector (250 °C), an FID detector (250 °C), and an HP-5 capillary column (30 m × 0.32 mm × 0.25 mm). The conversion was calculated by gas chromatography.

The cyclohexanone hydrogenation was conducted in an autoclave equipped with a magnetic bar. In a typical procedure, 5 mg catalyst, 1 mmol cyclohexene, and 10 mL ethyl acetate were subjected to the autoclave, which was then flushed with 1 MPa H₂ five times and charged successively with 1 MPa H₂. After the autoclave was sealed, it was heated to 120 °C. After reaction, 150 µL benzaldehyde was added to 5 mL the reaction liquid as inner standard. The product was qualitatively analyzed by gas chromatography (GC) and quantitatively analyzed on an Agilent 6890B instrument equipped with an on-column injector (250 °C), an FID detector (250 °C), and an HP-5 capillary column (30 m × 0.32 mm × 0.25 mm). The conversion was calculated by gas chromatography.

The styrene hydrogenation was conducted in a branched reaction tube equipped with a magnetic bar. In a typical procedure, 5 mg catalyst, 1 mmol styrene, and 10 mL ethanol were subjected to the branched reaction, which was then flushed with 1 atm H₂ five times and charged successively with 0.1 MPa H₂. After the branched reaction was sealed, it was placed in water bath at 25 °C. After reaction, 150 µL anisole was added to 5 mL the reaction liquid as inner standard. The product was qualitatively analyzed by gas chromatography (GC) and quantitatively analyzed on an Agilent 6890B instrument equipped with an on-column injector (250 °C), an FID detector (250 °C) and an HP-5 capillary column (30 m × 0.32 mm × 0.25 mm). The conversion was calculated by gas chromatography.

The conversion of nitrobenzene was calculated as follows:

$$\mathrm{C}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{a}\mathrm{n}}}{{\mathrm{N}}_{\mathrm{n}\mathrm{i}}}}\times \mathrm{100\%}$$

The conversion of cyclohexene was calculated as follows:

$$\mathrm{C}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{c}\mathrm{a}}}{{\mathrm{N}}_{\mathrm{c}\mathrm{e}}}}\times \mathrm{100\%}$$

The conversion of cyclohexanone was calculated as follows:

$$\mathrm{C}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{c}\mathrm{l}}}{{\mathrm{N}}_{\mathrm{c}\mathrm{o}}}}\times \mathrm{100\%}$$

The conversion of styrene was calculated as follows:

$$\mathrm{C}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{e}\mathrm{t}}}{{\mathrm{N}}_{\mathrm{s}\mathrm{t}}}}\times \mathrm{100\%}$$

where N_an, N_ni, N_ca, N_ce, N_cl, N_co, N_et, and N_st represent mole amounts of aniline, nitrobenzene, cyclohexane, cyclohexene, cyclohexanol, acyclohexanone, ethylbenzene, and styrene, respectively.

The TOF refers to the overall TOF, calculated as moles of reactant converted per mole of Pt per hour was calculated as follows:

$$\mathrm{TOF}={\displaystyle \frac{\mathrm{Conversion} \mathrm{of} \mathrm{reaction} \mathrm{substrate}}{\mathrm{time}\times \mathrm{Mole} \mathrm{ratio} \mathrm{of} \mathrm{Pt}/\mathrm{substrate}}}\times \mathrm{100\%}$$

(6) Logical deduction about l n (TOF)-l n (size of NP Pt):

There are several premise assumptions:

I. Supported crystalline metal grains should present similar figures and uniform packing structure even if size changes.

II. Active sites that are located in the same kind of areas on Pt particles, to be more specific, including surface parts, interfacial/edge parts, or corner parts, should perform uniform or approximate activity, respectively.

For a certain Pt particle,

N_V = λ_V × V_Pt = λ_V’ × R³

Ns = λ_S × S_Pt = λ_S’ × R²

N_I = λ_I × P_Pt = λ_I’ × R

N_C = λ_C = λ_I’ × R⁰

If active sites located at surface part,

then TOF_real = TOF_overall × N_V/ Ns = λ_’V/S × TOF_overall × R,

lnTOF_overall = ln (TOF_real/λ_V/S/R) = λ_S0−lnR,

so the slope about l n(TOF)−l n (size of NP Pt) is −1.

If active sites located at interfacial/edge part,

then TOF_real = TOF_overall × N_V/N_I = λ_’V/I × TOF_overall × R²,

lnTOF_overall = l n (TOF_real/λ_V/I/R) = λ_I0−2lnR,

so the slope about l n (TOF)−l n (size of NP Pt) is −2.

If active sites located at corner part,

then TOF_real = TOF_overall × N_V/N_C = λ_’V/C × TOF_overall × R³,

lnTOF_overall = l n (TOF_real/λ_V/C/R) = λ_C0−3lnR,

so the slope about l n (TOF)−l n (size of NP Pt) is −3.

N_V, Ns, N_I, and N_C are Pt atom numbers counted for volume of Pt particle, surface part of Pt particle, interfacial/edge part of Pt particle, and corner part of Pt particle, respectively. V_Pt is volume of supported Pt particle. S_Pt is surface area of supported Pt particle. P_Pt is perimeter part contacted with support of supported Pt particle. λ_XX^X are constants related to figures of Pt particles and size of a single Pt atom.

5. Conclusions

In conclusion, uniform, size-controlled Pt NPs from 2 to 40 nm were synthesized, and corresponding supported catalysts were used in certain typical hydrogenations. A consistent size–activity relationship can be summarized when overall TOF was modeled as a function of supported metal particles’ average diameter; the slope value of these functions is close to −1 consistently for a variety of common substrates. This size–activity relationship suggests that active sites are located at the surface part of supported Pt particles. A further inference is that the parameter that dominates the performance of the catalyst should not be hydrogen spillover from Pt nanoparticles to TiO₂ support for these typical hydrogenations. This study briefly but fittingly demonstrates the quantitative size–activity relationship of nanoparticle Pt supported by TiO₂ in certain typical hydrogenations, which might contribute to the design of related catalysts and research on other size–activity relationships of supported nanoparticle metals in heterogeneous catalysis.