Cu₂S Nanocrystals and Their Superlattices

Abstract

We report the successful synthesis of monodispersed Cu₂S nanocrystals and the subsequent formation of highly ordered nanocrystal superlattices. The synthesis is performed under ambient air conditions using simple experimental setups, making the process both accessible and scalable. By systematically tuning the reaction temperature and duration, we demonstrate precise control over the nanocrystal size, which is crucial in achieving uniformity and monodispersity. Furthermore, we uncover a previously unidentified nanocrystal growth mechanism that plays a key role in producing highly monodisperse Cu₂S nanocrystals. This insight into the growth process enhances our fundamental understanding of nanocrystal formation and could be extended to the synthesis of other semiconductor nanomaterials. The self-assembly of these nanocrystals into superlattices is carefully examined using electron diffraction techniques, revealing the presence of pseudo-crystalline structures. The ordered arrangement of nanocrystals within these superlattices suggests strong interparticle interactions and opens up new possibilities to tailor their collective optical, electronic, and mechanical properties for potential applications in optoelectronics, nanomedicine, and energy storage.

1. Introduction

Copper sulfide (Cu_2−xS) nanoparticles have garnered significant attention over the past two decades due to their promising applications in solar cells [1,2,3], batteries [4,5], sensors [3], biomedical imaging, and therapy [6,7,8,9,10,11]. The Cu-S system encompasses a series of compounds with varying stoichiometries and crystal structures, ranging from Cu-rich chalcocite (Cu₂S) to Cu-deficient covellite (CuS). These compounds are generally represented by the formula Cu_2−xS, where x varies between 0 and 1. The bonding nature within Cu_2−xS compounds is influenced by the relatively small electronegativity difference between Cu (1.9) and S (2.5). This results in a predominantly covalent Cu-S bond, where each Cu atom donates a 4s electron, and each S atom contributes six electrons to bonding. As a result, Cu cations are generally considered to have a +1 oxidation state, while S anions adopt a −2 oxidation state.

Cu₂S is the fully stoichiometric form of copper sulfide, which exhibits semiconducting properties with a bandgap of approximately 1.21 eV. This energy range places it within the near-infrared region of the electromagnetic spectrum, making Cu₂S particularly attractive for a wide range of optoelectronic and energy conversion applications due to its ability to efficiently absorb and interact with solar and thermal radiation. Historically, Cu₂S has garnered significant attention in the field of photovoltaics, especially when used in combination with cadmium sulfide (CdS) to form heterojunction solar cells [1,2,3]. The Cu₂S/CdS heterojunction was among the earliest examples of thin-film solar cells and served as a foundational system in understanding photovoltaic interfaces. In this configuration, CdS acts as the n-type semiconductor (electron conductor), while Cu₂S serves as the p-type one (hole conductor). During the 1970s and 1980s, considerable research efforts were devoted to optimizing this material pair due to its low cost, abundance, and ease of fabrication. While limitations such as poor long-term stability and interfacial degradation eventually limited its commercial viability, the Cu₂S/CdS system continues to be studied as a model for low-cost, earth-abundant photovoltaic materials. Cu₂S has also found widespread application as a counter electrode material in quantum dot-sensitized solar cells (QDSSCs) [1]. In these systems, semiconductor quantum dots such as CdSe or PbS are used as light-absorbing layers, and Cu₂S serves as a low-cost alternative to platinum in the counter electrode. Cu₂S offers good electrical conductivity and suitable electrocatalytic activity for the redox reactions required in QDSSCs, particularly for sulfide/polysulfide electrolytes. The use of Cu₂S in this role not only reduces the overall cost of solar cell fabrication but also helps to improve device performance by enhancing the rate of electron transfer and the regeneration of redox species at the electrode surface. Cu₂S has also been explored as a promising thermoelectric material [12]. Cu₂S exhibits several properties that are favorable for thermoelectric applications: low thermal conductivity, moderate electrical conductivity, and a high Seebeck coefficient. Moreover, Cu₂S undergoes a phase transition near room temperature, transitioning from a low-temperature monoclinic phase to a high-temperature cubic or tetragonal phase, which exhibits superionic conductivity—a state in which copper ions become highly mobile within the sulfide lattice. This superionic behavior results in ultralow thermal conductivity due to phonon scattering, thereby enhancing its thermoelectric figure of merit (ZT). Recent research has demonstrated that doped or nanostructured Cu₂S materials can achieve ZT values close to or exceeding 1, making them competitive with other state-of-the-art thermoelectrics.

Furthermore, Cu₂S nanoparticles and nanocrystals have attracted growing interest for next-generation biomedical applications [6,7,8,9,10,11]. Due to the presence of Cu vacancies in nonstoichiometric Cu_2−xS phases, hole carriers are introduced into the system to maintain electrostatic neutrality. Consequently, Cu_2−xS compounds behave as p-type (hole-doped) semiconductors. The hole concentration can reach 10²² cm⁻³ in CuS, the most Cu-deficient phase, imparting it with metallic-like conductivity. When Cu_2−xS nanoparticles are irradiated with light, the oscillation of hole carriers leads to the strong absorption and scattering of incident light, a phenomenon known as localized surface plasmon resonance (LSPR). It is well established that the LSPR frequency is directly correlated with the carrier density—as the hole concentration increases, the LSPR frequency undergoes a blue shift (higher energy absorption). Unlike metals such as gold (Au) and silver (Ag), which have extremely high free electron densities, Cu_2−xS has a hole density that is at least one order of magnitude lower. As a result, the LSPR frequency of Cu_2−xS lies in the near-infrared (NIR) region, making these nanoparticles highly suitable for biomedical applications. The absorbed light energy is efficiently converted into heat, elevating the temperatures of both the nanoparticles and their surrounding environment. This photo-induced heating has enabled the extensive exploration of Cu_2−xS nanoparticles for use in photoacoustic imaging (PAI) and photothermal therapy (PTT), particularly in cancer treatment. Both techniques rely on externally applied light: PAI utilizes localized heating to generate acoustic waves, which are then detected to create high-resolution images of tissues; PTT exploits photothermal conversion to raise temperatures sufficiently to induce hyperthermic cell destruction, effectively eliminating cancer cells. Since NIR light penetrates biological tissue (e.g., skin, blood) more effectively than visible light due to reduced scattering and absorption at longer wavelengths, it is the preferred choice for biomedical applications. The NIR spectrum is divided into two primary biological transparency windows: NIR-I (650–950 nm) and NIR-II (1000–1700 nm) (offers deeper tissue penetration due to further reduced scattering and background interference). Among the various Cu_2−xS compositions, CuS covellite nanoparticles have been extensively studied for PAI and PTT due to their high hole concentrations, which give them an intense LSPR peak in the NIR-I region. However, shifting the LSPR peak into the NIR-II region is often desirable for deeper tissue penetration. Increasing the nanoparticle size can redshift the LSPR peak to longer wavelengths, but this also enhances scattering, which reduces the heat generation efficiency—an undesirable effect for PAI and PTT. Although pure Cu₂S bulk material lacks Cu vacancies, in Cu₂S nanoparticles, when exposed to oxygen such as during suspension in water, Cu atoms undergo oxidation and leave the crystal lattice, creating Cu vacancies. For small Cu₂S nanoparticles, the resulting hole density can reach 10²¹ cm⁻³, which is sufficient to induce an LSPR peak in the NIR-II region. This makes oxidized Cu₂S nanoparticles highly attractive for deep-tissue biomedical applications.

In the last two decades, more than a dozen of reports have described synthesis methods to fabricate monodispersed Cu₂S nanoparticles [2,13,14,15,16,17,18,19,20,21,22,23,24]. These methods can be categorized into three groups: hot-injection synthesis, solventless synthesis, and thermolysis synthesis. These published papers are usually based on the following original reports. Yin and co-workers [14] reported the synthesis of monodispersed Cu₂S nanocrystals by injecting dodecanethiol (C₁₂H₂₅SH) into a hot mixture of cuprous acetate (CuOAc), tri-n-octylphosphine oxide (TOPO), and 1-octadecene (ODE), where dodecanethiol (as a S source) and CuOAc (as a Cu(I) source) reacted at a high temperature to produce Cu₂S nanocrystals capped with TOPO. By varying the reaction temperatures from 160 °C to 190 °C and the reaction time from 60 min to 540 min, Cu₂S nanocrystals with different sizes and different shapes were produced, ranging from spherical nanoparticles with a diameter of ~3.1 nm to nanodisks with a diameter of ~13 nm and a thickness of ~7.9 nm. Korgel et al. [20] first reported the solvent-less synthesis of Cu₂S nanorods, nanodisks, and nanoplatelets. In such synthesis, Cu²⁺ ions (copper (II) nitrate) in an aqueous solution were first transferred to chloroform (CHCl₃) using sodium octanoate as a catalyst. Dodecanethiol was added to the Cu(II) chloroform solution, followed by the evaporation of chloroform, resulting in a waxy solid precursor material. The solid precursor was heated in air at temperatures ranging from 140 to 200 °C for times ranging from 10 to 180 min. After heating, the solid consisting of Cu₂S nanocrystals was redispersed in chloroform. The sizes and shapes of the Cu₂S nanocrystals were controlled by the reaction temperature and time. The synthesized nanocrystals ranged from spheres with a 3.2 nm diameter to nanodisks with a ~20 diameter and a ~5 nm thickness. The yield for this method is typically only 10–20%. In thermolysis synthesis, first reported by Hyeon and co-workers [24], a solid Cu–oleate complex precursor was first prepared. Copper chloride and sodium oleate were added in a solvent mixture of ethanol, water, and hexane, followed by heating at 70 °C for 4 h, resulting in the formation of a Cu–oleate complex in hexane. The evaporation of hexane yielded the Cu–oleate complex in solid form. Then, the Cu–oleate complex was dissolved in a mixture containing oleylamine and dodecanethiol, and the resulting mixture was heated to high temperatures ranging from 215 to 230 °C under an argon flow for times ranging from 20 min to 17 h. The sizes of the Cu₂S nanocrystals could be controlled by varying the reaction temperature and time and the molar ratio of oleylamine and dodecanethiol, ranging from 7 nm to 19 nm.

Here, we report a novel, facile, and scalable synthesis strategy for the production of monodisperse Cu₂S nanocrystals with exceptional uniformity in size and shape. The entire synthesis is conducted under ambient air conditions and utilizes simple and cost-effective experimental setups that are easily adaptable for large-scale production. The high degree of monodispersity achieved through this method enables the self-assembly of the nanocrystals into highly ordered 2D and 3D superlattices.

2. Materials and Methods

2.1. Materials

The chemicals used in this study were purchased from Sigma-Aldrich (St. Louis, MO, USA) and included the following: copper(II) chloride dihydrate (CuCl₂ · 2H₂O, ≥99.0%), sodium oleate, 1-octadecene (ODE), ethanol, 1-dodecanethiol, acetone, toluene, lipoic acid, sodium borohydride, and sodium bicarbonate.

All aqueous solutions were prepared using ultra-pure Millipore Milli-Q deionized (DI) water with resistivity of 18 MΩ·cm, which was obtained from a Millipore Gradient Milli-Q water purification system (Billerica, MA, USA).

2.2. Methods

2.2.1. Synthesis of Cu–Oleate Precursor

To prepare the Cu–oleate precursor, 15 mg of CuCl₂ · 2H₂O was first dissolved in a mixture containing 150 µL of deionized (DI) water and 200 µL of ethanol. Upon dissolution, the solution exhibited a characteristic light blue color, indicating the presence of Cu²⁺ions in the aqueous phase. In parallel, 75 mg of sodium oleate was dissolved in 200 µL of ODE. Sodium oleate acted as a capping ligand, playing a crucial role in stabilizing the copper precursor and facilitating its phase transfer from the aqueous phase into the organic phase. Once both solutions were prepared, they were combined in a single reaction vessel and continuously stirred at 200 rpm while being heated to 70 °C. The reaction proceeded for 1 h, during which the color of the organic phase (ODE) progressively changed from clear to dark blue, signifying the formation of Cu–oleate complexes. This transformation indicated the successful transfer of Cu²⁺ ions from the aqueous phase into the organic phase, resulting in a stable Cu–oleate precursor solution. This organic phase was labeled as the “Cu–oleate precursor”.

2.2.2. Nanocrystal Synthesis

The synthesis of Cu₂S nanocrystals was conducted by heating the Cu–oleate precursor to a target reaction temperature ranging from 140 °C to 220 °C, depending on the desired particle size. Once the precursor solution reached the designated temperature, 1-dodecanethiol was rapidly injected into the heated mixture while vigorous stirring was maintained. The rapid introduction of dodecanethiol provided a sulfur source, initiating the formation of copper sulfide nanocrystals. The reaction was allowed to proceed for a predetermined duration, typically ranging from 20 min to 3 h. During the course of the reaction, distinct color changes were observed in the solution, which provided visual cues about the nanocrystal formation process. Initially, the reactant solution appeared dark blue due to the presence of Cu–oleate complexes. As the reaction progressed, the solution color shifted to yellow and then to orange/brown, indicating the nucleation and growth of Cu₂S nanocrystals. Upon completion of the reaction, the solution was rapidly cooled in an ice bath to quench further growth and stabilize the synthesized nanocrystals. The cooled solution exhibited a highly viscous consistency, necessitating the addition of extra ODE to achieve a uniform suspension of the nanocrystals and other reactants.

To purify the nanocrystals and remove excess unreacted precursors and byproducts, an extensive washing and precipitation process was conducted. The crude reaction mixture was treated with excess acetone, which facilitated the precipitation of Cu₂S nanocrystals while leaving residual oleate and unreacted sulfur species in the supernatant. The precipitated nanocrystals were separated by centrifugation and then washed three consecutive times with acetone to ensure thorough purification. Finally, the purified Cu₂S nanocrystals were resuspended in toluene, providing a stable colloidal dispersion.

2.2.3. High-Resolution Transmission Electron Microscopy (HRTEM), Selected Area Electron Diffraction (SAED), and Nanocrystal Size Distribution Analysis

High-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) analyses were performed using a Hitachi H-9500 HRTEM operating at an accelerating voltage of 300 kV.

To prepare samples for HRTEM analysis, a dilute suspension of the synthesized nanocrystals was carefully deposited onto a 300-mesh copper TEM grid coated with a lacey carbon film. After deposition, the samples were left to dry overnight under ambient conditions to ensure the complete removal of residual solvent and to prevent the aggregation of nanocrystals during imaging.

The size distribution of the synthesized nanocrystals was quantitatively analyzed by processing the TEM micrographs using the Nanoparticle Size Distribution Analysis module in ImageJ (1.54i), an open-source image analysis software program. To obtain statistically reliable results, multiple TEM images were captured from different regions of the sample to account for any potential variations in the size distribution. From these micrographs, approximately 100 individual nanocrystals were randomly selected and manually outlined to measure their diameters. ImageJ was then used to calculate the mean particle diameter and standard deviation, providing a comprehensive statistical assessment of the size uniformity.

3. Results

3.1. Synthesis of Cu₂S Nanocrystals

The synthesis of copper(I) sulfide (Cu₂S) nanocrystals was achieved via a simple and efficient hot injection method, where 1-dodecanethiol (DDT) was rapidly injected into a hot 1-octadecene (ODE) solution containing a copper–oleate complex. In this reaction system, dodecanethiol serves as both the sulfur precursor and the reducing agent, facilitating the formation of Cu₂S nanocrystals. Copper–oleate acts as the metal precursor, providing Cu²⁺ ions for the reaction. Oleate ions function as capping agents, preventing the uncontrolled aggregation of nanocrystals and ensuring the synthesis of monodispersed particles. ODE is used as a high-boiling-point solvent (~315 °C), enabling precise control over the reaction temperature, which plays a critical role in determining the nanocrystal size and uniformity.

Upon the injection of dodecanethiol into the hot Cu–oleate solution, the reaction mixture undergoes a rapid color change, transitioning to a dark brown, highly viscous solution. This observation suggests the initial formation of a Cu–thiol polymer network, likely involving Cu–thiolate species. As the reaction progresses, the viscosity gradually decreases, indicating the breakdown of polymeric chains and the subsequent nucleation and growth of Cu₂S nanocrystals. This transformation plays a crucial role in ensuring the formation of well-dispersed and uniform nanocrystals.

Figure 1 shows the HRTEM images and SAED patterns of the nanocrystals obtained at 190 °C after 1 h of reaction. The SAED pattern shown in Figure 1b reveals the hexagonal Cu₂S crystal structure (P6₃/mmc, a = 3.89 Å, c = 6.88 Å, PDF# 04-007-2394) with the following specific interplanar spacings: 1. 3.36 Å ((100) plane), 2. 3.05 Å ((101) plane), 3. 2.38 Å ((102) plane), 4. 1.97 Å ((110) plane), and 5. 1.86 Å ((103) plane). These values are in good agreement with the expected lattice parameters for hexagonal Cu₂S, confirming the formation of phase-pure Cu₂S nanocrystals. The HRTEM micrographs of Cu₂S nanocrystals in Figure 1c clearly show lattice fringes of (110) planes in several nanocrystals, indicating high crystallinity. The estimated average particle size is approximately 7 nm, as determined from the TEM imaging analysis.

3.2. Formation of Superlattices

A striking feature of the synthesized Cu₂S nanocrystals is their ability to self-assemble into highly ordered superlattices, as shown in Figure 2a–c, demonstrating the great monodispersity of the nanocrystals. The formation of such long-range ordered superlattices suggests a strong interparticle interaction, likely mediated by van der Waals forces and oleate-capped surfaces.

Further analysis of the SAED pattern in Figure 2d reveals distinct superlattice diffraction spots surrounding the transmitted beam. The observed diffraction pattern exhibits a pseudo-single-crystal structure with six-fold symmetry, characteristic of well-ordered nanocrystal assemblies. The calculated superlattice diffraction spacing (labeled as ‘S’) is approximately 4.4 nm, which corresponds to the interparticle distance within the superlattice. The spacing between two adjacent nanocrystals can be estimated as √3 × 4.4 = 7.6 nm. Given that the individual nanocrystal size is 7.0 nm, the gap between adjacent nanocrystals is approximately 0.6 nm, which is consistent with the presence of a thin capping ligand layer (oleate).

3.3. Formation of Large-Area Nanocrystal Monolayers

In addition to superlattice formation, the Cu₂S nanocrystals could also spontaneously organize into mono- and bilayered structures, covering an entire TEM grid, as demonstrated in Figure 3. Such highly uniform monolayers are promising for applications requiring controlled thin-film deposition, including nanoelectronics, sensing, and optoelectronic devices. It also suggests that the dip-coating technique can be an effective method for the assembly of large-area monolayers of Cu₂S nanocrystals, highlighting their potential for scalable fabrication.

3.4. Temperature Dependence

Figure 4 presents a series of TEM images illustrating the morphological evolution of Cu₂S nanocrystals synthesized at various reaction temperatures, each held for a duration of 120 min, unless otherwise noted. These images highlight the significant impact of the temperature on the size, shape, and uniformity of the resulting nanocrystals.

As shown in Figure 4a, a reaction temperature of 180 °C yields highly monodisperse, ultrasmall Cu₂S nanocrystals with an average diameter of approximately 5 nm. These nanocrystals exhibit a uniform spherical morphology and tight size distribution.

When the reaction temperature is increased to 190 °C, as shown in Figure 4b, the average particle size increases to approximately 8 nm, while the nanocrystals remain relatively monodisperse.

However, when the reaction temperature is further increased to 200 °C, a drastic change in both morphology and size distribution is observed, as shown in Figure 3. Instead of spherical particles, large and irregularly shaped nanodisks begin to form, accompanied by a much broader size distribution.

To better understand the kinetics at this elevated temperature, a short-term experiment was conducted, holding the reaction at 200 °C for only 20 min. As shown in Figure 4d, even within this brief timeframe, the nanocrystals quickly grow to an average diameter of about 8 nm, demonstrating the significantly accelerated growth rate at 200 °C.

3.5. Time Dependence

The growth process of Cu₂S nanocrystals was systematically investigated by collecting samples at different reaction times and then characterizing them using TEM. This study was focused on the synthesis conducted at a reaction temperature of 180 °C. The corresponding TEM images are shown in Figure 5.

At the 60 min time point, the TEM analysis revealed the formation of ultrasmall nanocrystals with an average diameter of approximately 3.0 nm (min: 2.0 nm, max: 4.2 nm) (see Figure 5a,b). These particles displayed excellent monodispersity, although their shape was not yet well defined, suggesting that the nanocrystals were still in the early stages of growth.

By 120 min, the nanocrystals had grown significantly in size, reaching an average diameter of approximately 6.5 nm (min: 5.0 nm, max: 7.8 nm) (see Figure 5e,f). Interestingly, the size distribution had become even narrower compared to that at 60 min. The nanocrystals at this stage also exhibited more defined shapes.

However, the most intriguing observations occurred at the intermediate time point of 90 min. TEM imaging, as shown in Figure 5c showed a clear bimodal size distribution—two distinct populations of nanocrystals coexisting within the same sample. One group of nanocrystals had sizes closely resembling those observed at 60 min (approximately 3 nm), while the second group exhibited sizes and shapes that matched the nanocrystals seen at 120 min (around 6.5 nm). This unexpected dual-population phenomenon was not an isolated occurrence; it has been consistently reproduced in at least three independent synthesis batches under identical conditions.

3.6. Synthesis Efficiency Based on Cu Incorporation

The synthesis efficiency—specifically the incorporation of copper—was quantitatively evaluated using the radioactive isotope ⁶⁴Cu. The transfer of ⁶⁴Cu radioactivity was tracked at each stage of the synthesis, providing a direct measure of copper incorporation (as detailed in

Table 1. Radioactivity retention rate after each synthesis step.

Step	Incorporation Rate (%)
Cu–oleate precursor synthesis	80
Nanocrystal synthesis	99
Washing (3 repetitions)	90
Water transfer	88
Overall	62

, where percentages represent the radioactivity carried over to the subsequent step). Our measurements indicate an overall copper incorporation rate of approximately 62%. Notably, a significant portion of the observed losses can be attributed to the high viscosity of the Cu precursor and the final nanocrystal solution in toluene, leading to substantial residue adhering to the reaction containers and pipette tips. This suggests that the actual chemical incorporation efficiency within each reaction step is likely higher, and, with meticulous handling, the overall incorporation rate could be substantially improved. The most significant handling-related loss occurs during the collection of the Cu–oleate precursor in ODE using a separatory funnel. Trace amounts of a water–ethanol phase within the precursor can induce violent bubbling when the mixture is heated above 170 °C in the subsequent synthesis step, causing the Cu precursor to spill out from the reaction flask.

4. Discussion

The synthesis method that we developed represents a classic colloidal approach that is widely used in the preparation of nanocrystals, relying on the fundamental components of precursors, surfactants, and an organic solvent as the reaction medium. In this particular case, the copper and sulfur sources are provided by copper oleate (Cu–oleate) and 1-dodecanethiol, respectively. Copper oleate serves as the Cu precursor, while thiol acts as the sulfur donor. Oleate, in addition to being a ligand for copper, functions as a surfactant that helps to control nanocrystal growth and prevents agglomeration. The entire reaction is carried out in 1-octadecene (ODE), a high-boiling-point, non-coordinating organic solvent that provides a stable thermal environment for the controlled synthesis of nanocrystals.

When the reaction mixture is heated to a temperature exceeding 180 °C, a key ligand exchange process is initiated. At elevated temperatures, the thiol molecules displace the oleate ligands surrounding the Cu ions through a thermally driven ligand exchange reaction. This exchange leads to the formation of reactive Cu–thiol complexes, which serve as the primary monomer units for subsequent nanocrystal formation. As the concentration of these monomers builds up in the solvent (1-octadecene, or ODE), the solution becomes supersaturated. Once the supersaturation crosses a critical threshold, the rapid and sudden formation of nanocrystal “seeds” or nuclei occurs—a process often described as an “explosion of nucleation”. During this brief but intense burst, a large number of very small Cu₂S nanocrystals are formed almost simultaneously. Following nucleation, the remaining monomers in the solution continue to attach to the surfaces of the newly formed nuclei, allowing the nanocrystals to grow. This growth phase is heavily influenced by the presence of surfactant molecules, primarily oleates, which were introduced as part of the Cu–oleate precursor. Oleates serve a dual function during this stage: they bind selectively to specific crystal facets of the growing nanocrystals, which helps to regulate both the rate of monomer attachment and the final shape of the particles. They also prevent aggregation by creating a steric barrier around each nanocrystal. Crucially, this surfactant binding is not static; rather, it must be a dynamic process at the reaction temperature. Oleate molecules constantly adsorb and desorb from the nanocrystal surfaces. This transient desorption allows localized regions of the nanocrystal surface to remain accessible to incoming monomers, facilitating controlled growth. Meanwhile, the average presence of surfactants on the surface maintains colloidal stability, preventing the nanocrystals from clumping together in the reaction medium. The balance between surfactant-mediated stabilization and monomer accessibility is key. If surfactants bind too strongly or fail to exchange dynamically, growth slows or halts. Conversely, insufficient surface coverage could result in uncontrolled growth or aggregation.

Our findings, consistent with the existing literature [14], strongly suggest that the use of thiols as a sulfur source in the synthesis of copper sulfide nanocrystals, as employed in our method, consistently yields a copper-rich chalcocite (Cu₂S) crystal structure. This outcome appears to be independent of the synthesis parameters that we explored, including the ratio of copper precursor to thiol, the reaction temperature, and the duration. This consistent formation of Cu₂S likely stems from the initial formation of a stable copper–thiol complex, whose subsequent decomposition preferentially leads to the chalcocite phase. In contrast, alternative synthetic routes utilizing elemental sulfur [25] or mercapto-propionic acid (MPA) [13] as sulfur sources offer greater control over the final stoichiometry, enabling the production of a range of copper sulfide nanocrystals—from chalcocite (Cu₂S), djurleite (Cu_1.97S), and digenite (Cu_1.8S) to covellite (CuS)—by manipulating the reaction conditions.

Classical Gibbs homogeneous nucleation theory effectively describes this nanocrystal nucleation and growth. It posits that the total free energy change (ΔG) of nucleus formation arises from competing volume (ΔG_v) and surface (γ) energy contributions. ΔG_v, favoring nucleation, is negative and scales with r³ (nucleus volume), becoming more so with higher supersaturation. Conversely, γ, a positive energy penalty from the new solid–liquid interface, scales with r² (surface area). Therefore, ΔG as a function of the size of a spherical nucleus, r, is written as

$$∆G \left(r\right)={\displaystyle \frac{4}{3}}\pi r^3∆G_v+4\pi r^2\gamma$$

The illustrative plot of this equation is shown in Figure 6. This equation reveals a critical radius (r^∗). Nuclei smaller than r^∗ dissolve, while larger ones grow. A burst of nucleation yields numerous nuclei slightly above r^∗, resulting in nanocrystals with a narrow size distribution.

In the case of Cu₂S nanocrystals synthesized at 180 °C for one hour, the TEM analysis reveals particles with an average size of 3.4 ± 0.4 nm (see Figure 5a). This small size with a narrow size distribution can well be explained using this thermodynamic theoretical model.

However, as the reaction time was extended to 2 h, a notable change in the nanocrystal characteristics was observed: the Cu₂S nanocrystals increased in size to approximately 5.0 nm, and, intriguingly, the size distribution became even narrower (see Figure 5c). This outcome cannot be adequately explained by classical thermodynamic models.

In typical nanocrystal synthesis, once the initial nucleation phase has passed, particle growth generally proceeds via Ostwald ripening. This is a thermodynamically driven process in which smaller, high-energy nanocrystals dissolve, releasing monomers that are then redeposited onto larger, lower-energy crystals. Over time, this leads to an increase in the average particle size, but also a broader size distribution. In contrast, the experimental data for Cu₂S nanocrystals synthesized at 180 °C for 2 h reveal larger nanocrystals with an even more monodisperse population, defying what would be expected from Ostwald ripening. This observation suggests that an alternative growth mechanism must be responsible for the continued development of these particles.

A more suitable explanation might be the size distribution focusing model [26], a kinetic size control theory. This model has successfully been used for quantum dot synthesis, which is based on the above-described thermodynamic Gibbs nucleation theory. Figure 7 shows the dependence of the growth rate on the nanocrystal radius. Nanocrystals with a size below r* have a negative growth rate (they are not stable, as explained in Gibbs nucleation theory), and crystals with a size larger than r* have a positive growth rate. At the critical radius, the growth rate is zero. The growth rate before the peak is thermodynamically controlled by the changing rate of the total free energy, which is zero at the critical size, as shown in Figure 6. The peak is where the growth rate changes from a thermodynamically controlled regime to a kinetically controlled regime. After the peak, the growth rate decreases as the radius increases, simply because increasing the radii of large crystals requires the incorporation of more atoms than increasing the radii of smaller crystals. Because smaller crystals will grow faster than larger ones, the size distribution will spontaneously narrow or “focus”. This “focusing” phenomenon has been experimentally demonstrated.

However, this model also fails to fully explain our findings. As shown in Figure 5c,d, the Cu₂S nanocrystals synthesized at 180 °C for 90 min have a bimodal distribution; there are two distinct groups of nanocrystals, a 3 nm group and a 5 nm group, which are the same size as the nanocrystals obtained with reaction times of 60 min and 120 min, respectively. More importantly, the incorporation experiment using ⁶⁴Cu clearly showed that all Cu ions had been incorporated into the Cu₂S nanocrystals after 60 min, i.e., no monomers were present in the solution. Therefore, the crystal cannot grow by adding monomers, as described in the “size distribution focusing” model.

Therefore, the only possible route for nanocrystals that formed after 60 min to grow larger is through coalescence, which is called “fusion growth” and has been reported in many nanoparticle synthesis studies [27]. In the fusion-based growth mechanism, similarly sized nanocrystals undergo oriented attachment or coalescence to form larger particles without significant broadening of the size distribution. This process differs from Ostwald ripening in that it involves the merging of entire nanocrystal units, rather than the dissolution and re-deposition of monomers. Fusion growth can occur under conditions where the particle mobility is sufficient and surface capping agents (like oleate) are present in the appropriate balance to allow the partial exposure of reactive surfaces while still preventing uncontrolled aggregation. The remarkable consistency in the nanocrystal size after 2 h, along with the reduction in size variability, strongly points toward such a non-classical growth pathway. It appears that approximately five 3 nm Cu₂S nanocrystals fused together to form the observed 5 nm crystals. Such a process would maintain the overall material mass while shifting some of the nanocrystals into a larger size class, without involving additional precursors or monomer feed.

While this fusion hypothesis aligns well with our observations and provides a coherent explanation for the bimodal distribution, it remains tentative, and further experimental validation is required. Techniques such as in situ TEM, time-resolved spectroscopy, or particle tracking during synthesis could offer more definitive insights into whether coalescence is indeed the dominant mechanism driving late-stage growth in this system.

5. Conclusions

A new synthesis method has been developed to produce monodisperse ultrasmall Cu₂S nanoparticles. The synthesis involves three main steps: transferring Cu²⁺ ions from an aqueous CuCl₂ solution into 1-octadecene via the formation of Cu–oleate complexes; injecting 1-dodecanethiol into the heated Cu²⁺ oleate solution to induce Cu₂S nanocrystal formation; and transferring oleate-capped Cu₂S nanoparticles into the aqueous phase with dihydrolipoic acid. The sizes of nanocrystals with a narrow distribution can be controlled by varying the reaction temperature and time. A time dependence study on the synthesis process conducted at 180 °C reveals two mechanisms involved in achieving monodispersity. For the smaller (3 nm) nanocrystals obtained at a reaction time of 1 h, the classic Gibbs nucleation theory can be applied. However, the widely used size distribution focusing model fails to describe the larger (5 nm) nanocrystals obtained at a reaction time of 2 h, and, instead, the fusion growth model has been suggested as the growth mechanism for such nanocrystals.