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. 2025 Apr 17;3(7):372–379. doi: 10.1021/prechem.5c00004

Nonequilibrium Process for Doping Under Continuous-Flow Hydrothermal Synthesis of Cerium Oxide-Based Nanoparticles

Akira Yoko †,‡,*, Chunli Han ‡, Ayame Sakonaka §, Gimyeong Seong ∥, Takaaki Tomai ⊥,#, Satoshi Ohara ○, Tadafumi Adschiri ‡,○,*
PMCID: PMC12308591  PMID: 40746582

Abstract

The nonequilibrium composition and its formation process are critical aspects of nanoparticle production technology. Understanding the dynamics of nanoparticle formation under nonequilibrium conditions is essential. In this study, Cr-doped CeO2 nanoparticles are synthesized via continuous-flow hydrothermal synthesis at various temperatures (300, 350, 400 °C) with reaction times precisely controlled on the order of seconds. At the initial stage of particle formation, Cr-rich CeO2 particles form due to a low surface energy. Over time, the Cr content decreases as the particles relax toward the equilibrium structure. This process yields an unusual nonequilibrium composition through rapid heating and short residence times. Similar nonequilibrium compositions are also observed for other dopants, such as Fe and Eu. Continuous-flow hydrothermal synthesis thus presents an efficient method for fabricating nanomaterials with unique compositions that are unattainable using conventional batch methods.

Keywords: continuous-flow reactors, Cr-doped CeO2 , nonequilibrium processes, supercritical hydrothermal synthesis, dopant release mechanism, composition changes in nanoparticles, surface stabilization by doping

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1. Introduction

The development of new materials that leverage the unique properties of nanomaterials is being actively pursued. Structural differences between nanoparticles and their bulk counterparts contribute to their extraordinarily high performance. − Therefore, elucidating the structural effects of the nanoparticle size is crucial for exploiting these novel functions. Earlier studies from various perspectives have assessed the structural effects of nanosizing on materials, focusing on crystal lattice distortion, , electronic states, and crystal structure transitions. − Moreover, it has been reported that size effects govern the composition of the composite nanoparticles. Some studies have shown that reducing particle size to the nanometer scale enables the synthesis of solid-solution nanoalloys from metals that are typically immiscible in the bulk state over the entire compositional range. −

In addition to nanoscale effects, nonequilibrium processing is also critical in determining the unusual composition of nanoparticles. Among various synthetic methods, finely controlled metal oxide nanoparticles can be synthesized via supercritical hydrothermal processes, which involve the rapid heating of a metal salt aqueous solution to the supercritical state. − A homogeneous supercritical reaction field can be achieved using a flow reactor for the rapid mixing and heating of fluids in the supercritical region. , In this region, the solubility of metal oxides decreases drastically, leading to a significant increase in the reaction kinetics. This sharp contrast induces an extremely high degree of supersaturation and nonequilibrium conditions.

During the synthesis of composite oxide nanoparticles containing multiple metals, complex phenomena arise owing to the differing solubilities of the metal-ion components. − For instance, in the synthesis of Ba–Fe complex oxide nanoparticles, the particle composition and crystal phase reportedly evolve over time. A gradual change from BaO­(Fe2O3)6 to BaO­(Fe2O3)2 has been observed between 10 and 240 min. This finding suggests that the materials initially form with nonequilibrium compositions and compositional changes toward the equilibrium state occur via the Ostwald stepwise ripening mechanism. In other cases, nonstoichiometric phases form during the initial stages of the synthesis. Their composition evolves over time: a deficient nonequilibrium structure forms for a short time at the early stage, followed by compositional adjustments toward equilibrium through the incorporation of ions into the deficient sites. Such behavior has been observed during the continuous-flow hydrothermal synthesis of perovskite-type complex oxides (BaTiO3, BaZrO3, , and Ba1–x Sr x ZrO3 , ) and spinel-type complex oxides (NiFe2O4 and CoGa2O4 , ).

A previous study on the hydrothermal synthesis of Cr-doped CeO2 nanoparticles provided insights into another type of nonequilibrium composition and processing. During hydrothermal synthesis, the Cr concentration in the CeO2 lattice was 22.7 mol % using a flow reactor, compared to 5.1 mol % using a batch reactor. This significant difference in Cr concentration may result from variations in heating rates (owing to products forming at low temperatures) or reaction times between the flow and batch reactors. If the difference arises from lower temperatures during heating, then the heating rate primarily determines the nanoparticle composition. Conversely, if the reaction time controls the dopant concentration, the highly Cr-doped CeO2 exhibits a nonequilibrium composition. Recently, unusual dopant release from organic-modified Mn-doped CeO2 nanoparticles synthesized hydrothermally has been reported. Composition changes during ripening were attributed to metal–organic complexes. To generalize the effects of rapid processing, it is essential to investigate the formation of composite particles in systems without organic modifications. Additionally, the effects of nanoscale size on the composition must be considered alongside processing effects.

In this study, the formation mechanism of CeO2-based nanoparticles was investigated, with a focus on the dopant behavior in nonequilibrium states. The nanoparticle compositions were analyzed to determine how reaction time, on the order of seconds, influences dopant concentration. High-concentration metal-doped CeO2 is a promising catalyst and oxygen carrier for various chemical reactions. Therefore, controlling the dopant concentration in CeO2 nanoparticles is essential for producing nanomaterials with desired catalytic properties.

2. Results and Discussion

2.1. Cr Dopant Behavior under Particle Formation

Figure a,b displays TEM images of pure CeO2 nanoparticles synthesized at 300 °C with residence times of 1.0 and 7.0 s, respectively. Most particles were octahedral, with this morphology becoming more pronounced as the residence time increased. The particles grew from approximately 10 nm obtained at 1.0 s to approximately 60–80 nm at 7.0 s. Figure c,d presents TEM images of Cr-CeO2 nanoparticles synthesized at 300 °C with residence times of 1.0 and 7.0 s, respectively. The Cr-doped CeO2 nanoparticles exhibited irregular shapes and smaller particle sizes compared to those of the undoped samples under the same temperature and time conditions (Figure a,c). Aggregated secondary structures were also observed in the Cr-CeO2 samples. These differences in the particle size and morphology are attributed to the effects of Cr doping on the structural formation of nanoparticles.

1.

1

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TEM images of undoped CeO2 and Cr-CeO2 nanoparticles synthesized at 300 °C with different residence times: (a, b) undoped CeO2 at residence times of 1.0 and 7.0 s, respectively; (c, d) Cr-doped CeO2 at residence times of 1.0 and 7.0 s, respectively.

The XRD patterns of undoped CeO2 and Cr-CeO2 nanoparticles (Figure ) correspond to the cubic fluorite-type CeO2 structure (Fm3̅m, S.G. 225). No byproducts, such as chromium oxides or hydroxides, were detected under any synthesis conditions.

2.

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XRD patterns of the undoped CeO2 and Cr-CeO2 nanoparticles synthesized at 300 °C with residence times of (a) 1.0 and (b) 7.0 s. Insets show the 111 peak positions.

As shown in Figure a, the XRD peaks of Cr-CeO2 nanoparticles synthesized at 300 °C with a residence time of 1.0 s shifted to higher angles compared to those of undoped CeO2, indicating a reduced lattice constant. This suggests lattice contraction occurs due to the incorporation of smaller Cr3+ ions (0.0615 nm) into CeO2 crystal lattice, replacing Ce4+ ions (0.097 nm). However, at a residence time of 7.0 s under the same conditions (Figure b), the degree of lattice contraction was reduced, indicating that the incorporation of Cr into the lattice was less pronounced at longer reaction times. Lattice constants were analyzed to quantify the incorporation of Cr into the CeO2 lattice. As shown in Figure , the lattice constant of the Cr-CeO2 nanoparticles increased with the residence time. Higher reaction temperatures resulted in larger lattice constants for the same residence time.

3.

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Effect of residence time on the lattice constant of Cr-CeO2 based on XRD data at various reaction temperatures.

The Cr content of Cr-CeO2 nanoparticles was determined using scanning electron microscopy–energy-dispersive X-ray spectroscopy (SEM–EDS). A decrease in Cr content was observed with increasing residence time, from 18.7% at 1.0 s to 15.5% at 7.0 s at 300 °C (Table ). ICP-AES confirmed nearly 100% conversion of Ce under all of the tested conditions.

1. Dopant Concentrations of Samples Synthesized in a Flow Reactor and after Re-hydrothermal Treatment in a Batch Reactor .

Sample Reactor Temperature (°C) Reaction Time (s) Dopant Concentration (mol %)
Cr-doped CeO2 Flow 300 7.0 15.5
Cr-doped CeO2 Flow 400 0.5 11.3
Batch (re-hydrothermal treatment of above) 400 300 3.6
Cr-doped CeO2 Flow 350 0.8 15.8
Batch (re-hydrothermal treatment of above) 350 300 9.9
Cr-doped CeO2 Flow 300 1.0 18.7
Batch (re-hydrothermal treatment of above) 300 300 10.8
Fe-doped CeO2 Flow 300 3.8 12.9
Batch (re-hydrothermal treatment of above) 300 300 8.6
Eu-doped CeO2 Flow 300 3.8 23.7
Batch (re-hydrothermal treatment of above) 300 300 7.1
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a

Measurements were performed by using SEM-EDX.

These findings indicate that significant Cr incorporation into the CeO2 lattice occurs in the early stages of the reaction. Over time, Cr is released from the CeO2 lattice into a hydrothermal solution. The Cr release rate is higher at higher reaction temperatures, as can be seen in Figure . High-concentration Cr doping is achievable only through flow-type hydrothermal processes with short reaction times, whereas batch-type hydrothermal processes with extended reaction times yield lower Cr concentrations. Notably, the slower heating rates in batch synthesis do not negatively affect high-concentration doping, as the Cr content is higher at lower temperatures. Instead, the reaction time is the primary factor governing the final composition. Consequently, the highly concentrated Cr-doped CeO2 is a nonequilibrium product formed during the initial stages.

2.2. Stability of Dopant

To examine the long-term behavior of Cr in the hydrothermal environment, Cr-CeO2 nanoparticles synthesized with the shortest residence time at each temperature in a flow reactor were subjected to re-hydrothermal treatment in a batch reactor. The treatment time was 5 min, which is significantly longer than reaction time in a continuous flow reactor (of the order of seconds), with pressure, reaction temperature, and nitric acid concentration in the aqueous solution being identical with those in the flow synthesis. After re-hydrothermal treatment of Cr-CeO2 nanoparticles at 300, 350, and 400 °C, Cr content, as determined by ICP-AES, decreased from 19.9% (1.0 s), 17.2% (0.8 s), and 13.6% (0.5 s) to 12.9%, 11.3%, and 4.5%, respectively (300 s). SEM-EDX results corroborated this trend (Table ). Crystallite sizes, ranging from 8.6 to 11.3 nm, showed no clear correlation with Cr doping levels, confirming that Cr content decreased over time, approaching equilibrium during the longer time duration in hydrothermal environment (re-hydrothermal treatment). High dopant concentrations were significantly influenced by process conditions, consistent with previous observations for other materials. In the case of the previous synthesis of Cr-doped CeO2 using a batch reactor for 10–120 min reactions, only low doping concentrations, e.g., 5.1%, were reported. ,

Similar doping behavior was observed for the Fe and Eu dopants. Fe-CeO2 and Eu-CeO2 nanoparticles were synthesized in a flow reactor under 300 °C and subsequently treated hydrothermally in a batch reactor at 300 °C for 5 min. Re-hydrothermal treatment reduced dopant content, mirroring the Cr-CeO2 results (Table ). Fe and Eu dopants were initially incorporated into the CeO2 lattice but were subsequently released in high-temperature compressed water, following a pattern similar to that observed for Cr doping.

The release of dopants over extended reaction times likely results from differences in the chemical potential of the dopant ions. Cr-doped CeO2 is less stable than pure CeO2 owing to the lower chemical potential of Cr in water, driving the composition change. The formation of this unstable state during the initial reaction stage is attributed to surface energy effects during nucleation. The surface energy of the (111) facet of Cr-doped CeO2 is lower than that of undoped CeO2 as discussed in the next section. This difference may result from surface reconstruction caused by the flexible valence states of Ce and Cr in highly doped systems. This suggests that Cr-doped CeO2 formation is kinetically favorable with reduced nucleation energy barriers and higher nucleation rates. Structural disorder in the nuclei at the initial stage likely affects dopant stability, leading to differences between the crystalline state and the nuclei. The observed particle (approximately 10 nm size) was not the primary determinant of composition; rather, the reaction temperature and dopant leaching rate played critical roles in determining the final product composition. The correlation between crystallite size and Cr doped concentration/lattice constant is shown in the Supporting Information.

2.3. Mechanism of Dopant

The crystallite size of the Cr-CeO2 nanoparticles was less than that of the undoped CeO2 nanoparticles, suggesting that Cr doping into the CeO2 phase reduced the surface energy, which is a key factor in the nucleation barrier. Therefore, density functional theory (DFT) simulations were conducted to evaluate surface stabilization by Cr doping. Figure A,B, respectively, portray the structures of pure CeO2 and 25 mol % Cr-doped CeO2. In the Cr-doped CeO2 structure, an oxygen vacancy was introduced near Cr. By introducing an oxygen vacancy, Cr3+ and Ce3+ ions were formed, which is consistent with earlier simulations conducted for 3 mol % Cr-doped CeO2. For 25 mol % Cr-doping, one-third of the Ce ions had a valence of 3+, whereas two-thirds had a valence of 4+.

4.

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Density functional theory simulation results: (A) pure CeO2 perfect crystal, (B) 25 mol % Cr-doped CeO2 structure, (C) slab model for pure CeO2(111) surface, and (D) slab model for 25 mol % Cr-doped CeO2(111) surface. (E) Diagram of the nucleation energy barrier, which includes cohesive and surface energies for CeO2 and 25 mol % Cr-doped CeO2.

Figures C,D show slab models of the CeO2 structure with exposed (111) faces. The surface energy is defined as shown below by using the total energies of the slab and bulk models:

Esur=ET_slab−ET_bulkS 1

Therein, E sur represents the surface energy. Also E T_slab and E T_bulk, respectively, denote the total energies of the slab and bulk obtained from DFT calculations. S stands for the surface area of the slab structure (S = 2l x l y , where l x and l y , respectively, represent the cell length in the x and y axes). From this equation, surface energies of 0.78 and 0.59 J/m2 were calculated, respectively, for pure CeO2 and 25 mol % Cr-doped CeO2. It is particularly interesting that more Ce3+ ions were found at the surface of the first layer than in the inner layer through the valence changes from Cr3+ to Cr4+, as shown in Figure D. The marked differences in the surface energy between the Cr-doped and undoped CeO2 might derive from surface reconstruction because of the flexible surface structure, including the valence states of both Ce and Cr, in the case of a high-concentration doping system.

In addition to the surface calculation, the cohesive energies of the undoped and Cr-doped CeO2 structures (E coh_CeO2 and E coh_Cr–CeO2 , respectively) were calculated using isolated monomer calculations, as shown below.

Ecoh_CeO2=ET_bulkCeO2−μCe(OH)4−2μH2O 2
Ecoh_Cr‐CeO2=ET_bulkCr0.25Ce0.75O2−0.25μCr(OH)3−0.25μCe(OH)3−0.5μCe(OH)4−1.75μH2O 3

Therein, μ denotes the chemical potential of the subscript molecule. The nucleation barrier was simulated for pure CeO2 and 25 mol % Cr-doped CeO2 using the cohesive and surface energies, as shown in Figure E. The Cr-doped state was energetically favorable at the initial stage with a lower nucleation barrier because of the lower surface energy for the doped surface, which is relaxed greatly, including the appearance of Cr4+ ions as discussed above. In contrast, pure CeO2 became more stable after growth, because the contribution of the surface energy is small at larger particle sizes. In the bulk state, Cr-doped CeO2 is unstable compared to the pure CeO2. Leaching occurred with the growth. The absolute values of the simulated nuclei size must be studied further, with differences in stability with particle growth between pure CeO2 and Cr-CeO2 clarified qualitatively through simulations.

3. Conclusions

The continuous-flow hydrothermal synthesis of Cr-CeO2 nanoparticles was performed at temperatures ranging from 300 to 400 °C, with reaction times precisely controlled to fractions of a second. A high concentration of Cr doping was observed within a short reaction time. However, the Cr content in CeO2 decreased with increasing residence time owing to Cr leaching from the CeO2 lattice under the reaction conditions. Initially, a high Cr concentration was incorporated into the CeO2 lattice because the doped structure’s low surface energy kinetically favored this process. The incorporation and subsequent release of Cr were further validated using other dopants such as Fe and Eu. These findings expand the potential for synthesizing nanoparticles with unconventional nonequilibrium compositions via continuous-flow hydrothermal methods. The observed release of dopant from host nanoparticles may lead to unequal dopant distribution, such as surface enrichment or interior depletion. Future studies that innovate strategies for controlling nanoparticle composition by leveraging these phenomena and apply nonequilibrium products based on the understanding of the stability are encouraged.

4. Methods

4.1. Materials

Precursor solutions of Ce, Cr, Fe, and Eu ions were prepared by separately dissolving cerium­(III) nitrate hexahydrate (Ce­(NO3)3·6H2O, purity >98.0%; Fujifilm Wako Pure Chemical Corp.), chromium­(III) nitrate nonahydrate (Cr­(NO3)3·9H2O, purity >98.5%; Alfa Aesar), iron­(III) nitrate nonahydrate (Fe­(NO3)3·9H2O, purity >99.0%; Fujifilm Wako Pure Chemical Corp.), and europium­(III) nitrate n-hydrate (Eu­(NO3)3·nH2O, purity >75.0%; Fujifilm Wako Pure Chemical Corp.) in distilled water produced using an auto still (WG250; Yamato Scientific Co. Ltd.). All chemicals were used without further purification.

4.2. Experimental Procedure

A schematic of the continuous-flow supercritical hydrothermal synthesis system is shown in Figure . Reactors made of stainless-steel tubes (SUS316; Swagelok Co., US) with outer diameters of 1/8 and 1/16 in. (inner diameters of 1.8 and 0.8 mm, respectively) were used. An aqueous metal precursor solution (molar concentration: 5 mM) and distilled water were fed into the reactor using high-pressure pumps P-A and P-B (LC-20AD; Shimadzu Corp.) (Figure ) at flow rates of 1 mL/min and 10 mL/min, respectively. The solutions were mixed in a T-mixer (union tee of 1/8 in., i.d. = 2.3 mm; Swagelok Co.). To prepare the Cr-CeO2 nanoparticles, Ce and Cr precursor solutions with a Ce:Cr molar ratio of 7:3 were used. Four reactors with different volumes (0.075, 0.201, 0.754, and 1.508 cm3) were employed to vary the residence time of the reactants in the range of 0.5–7 s. The pressure was maintained at 30 MPa at the reactor outlet using a back-pressure regulator (27-1764-22; Tescom Co., Ltd.). Reaction temperatures of 300 °C, 350 °C, and 400 °C were used. The temperature was kept constant from the T-mixer to the reactor outlet by external heating. Fluid temperatures were measured by using thermocouples (T1, T2, and T3 in Figure ). Immediately before mixing, the precursor solution was cooled externally to prevent precipitation owing to heat transfer from the reactor to the preheated section. The hydrothermal reaction was rapidly terminated using a cooling water jacket at the reactor outlet. The product slurry was recovered, and particles were separated by filtration under reduced pressure using a membrane filter with 0.025 μm pore size. The obtained particles were freeze-dried before further characterization. For comparison, Fe and Eu precursors were used instead of Cr, following the same procedure to synthesize and characterize Fe-CeO2 and Eu-CeO2 nanoparticles.

5.

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Schematic of the supercritical hydrothermal-flow synthesis method for fabricating metal-doped CeO2 nanoparticles. Symbols T1–T3 denote thermocouples (T1: precursor temperature; T2: preheated water temperature; T3: hydrothermal reaction temperature). Symbol P represents the pressure gauge.

4.3. Characterization

Powder X-ray diffraction (XRD) patterns were recorded on a Rigaku SmartLab diffractometer using Cu Kα radiation (λ = 0.15418 nm) at a 45 kV operating voltage and 200 mA current. Crystal structure data were obtained by Rietveld refinement of the XRD patterns. The Williamson–Hall method was used to separate the effects of size and strain on peak broadening according to the following equation:

βcos⁡θ=2εsin⁡θ+KλD 4

Here, β and θ represent the integral breadth and Bragg angle of the peaks, respectively; ε denotes the lattice strain; K is a shape factor (for spherical particles, K = 3π/8); λ is the wavelength of the X-ray; D is the average crystallite size. The values of D and ε were obtained by fitting the diffraction data to eq .

The particle morphologies of the as-synthesized Cr-CeO2 nanoparticles were observed using transmission electron microscopy (TEM, H-7650; Hitachi, Ltd.) at an accelerating voltage of 100 kV and emission current of 20 μA. The elemental compositions of the nanoparticles were measured using scanning electron microscopy (SEM; JSM-7800F; JEOL) with energy-dispersive X-ray spectroscopy (EDS; X-Max SDD Detector, Oxford Instruments plc.) operated at a 15.0 kV accelerating voltage. Characteristic X-rays of CeLα1 = 4.839 keV and CrKα1 = 5.411 keV were used for elemental analyses. The concentrations of Ce, Cr, Fe, and Eu in the precursor solutions and in metal-doped CeO2 nanoparticles were analyzed by using inductively coupled plasma atomic emission spectroscopy (ICP-AES; Spectro Arcos).

4.4. Computational Method

First-principles simulations were conducted based on plane-wave basis density functional theory (DFT). Perdew–Burke–Ernzerhof generalized gradient approximation was employed as the exchange-correlation energy functional. The DFT+U method introduced by Dudarev et al. was used to treat electron localization. The U–J parameter was set as 5.0, 5.0, and 5.5 eV, respectively, for the Cr3d, Ce4f, and O2p states based on earlier computational studies for Cr2O3 and CeO2 . The valence configurations of the pseudopotentials were 3s23p63d54s1, 5s25p64f15d16s2, and 2s22p4, respectively, for Cr, Ce, and O. The energy cutoff for the plane-wave basis was set as 500 eV, which provided convergence of the total energy in the CeO2 unit cell. Bulk calculations were conducted using a Monkhorst–Pack k-point mesh of 4 × 4 × 4. The atomic positions were relaxed within a cubic cell. Forces acting on the atoms converged to 0.02 eV/Å in all calculations. Slab model calculations were conducted for the (111) facet of the CeO2 structure using a Monkhorst–Pack k-point mesh of 2 × 4 × 1. The quantities of atoms used for the slab model were 144 for CeO2 and 132 for 25 mol % Cr-doped CeO2. Four atomic layers from the surface were relaxed, whereas the atomic positions of the two internal layers of the slab model were fixed. The vacuum layer thickness of the slab model was approximately 2 nm. Dipole correction implemented in VASP was applied to the depth direction. The isolated molecules were calculated with the Γ point in a cell in a framework with periodic boundary conditions, keeping distances between molecules greater than 10 Å. The VASP code , was used for simulations. The calculated crystallographic structure models were visualized using the VESTA code.

Supplementary Material

pc5c00004_si_001.pdf (98.3KB, pdf)

Acknowledgments

The authors gratefully acknowledge support from the Japan Science and Technology Agency (JST) [MIRAI, Grant No. JPMJMI17E4, and CREST, Grant No. JPMJCR16P3]; the New Energy and Industrial Technology Development Organization of Japan (NEDO); JSPS KAKENHI (Grant Numbers JP16H06367, JP20K20548, and JP21H05010); and the Materials Processing Science Project (Materealize; Grant No. JPMXP0219192801). Additional support was provided by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Professional Development Consortium for Computational Materials Scientists (PCoMS), and the World Premier International Research Center Initiative (WPI), MEXT, Japan.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/prechem.5c00004.

  • Correlation between crystallite size and Cr doped concentration/lattice constant evaluated by XRD and SEM-EDX (PDF)

The authors declare no competing financial interest.

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