Size-and phase-dependent structure of copper(II) oxide nanoparticles

Abstract

Copper(II) oxide (CuO) nanoparticles (NPs) have found numerous applications in electronics, optics, catalysis, energy storage, health, and water purification. Controlled synthesis of CuO NPs requires information on their nanoscale structure, which is expected to vary depending on the size, shape, phase, and most importantly, on the surface morphology. In this work, we report a detailed analysis of the structure of solid and melted CuO nanoparticles as functions of size and temperature at global and local scales, using molecular dynamics simulations. Comparisons of simulated X-ray diffraction profiles, mean bond lengths, average coordination numbers, and melting points with available experimental data support the modeling results. Melting points of CuO NPs vary linearly with the reciprocal of the diameters of NPs. The long-range order seen in solid nanoparticles with diameters greater than 6 nm gradually vanishes as size decreases, indicating the loss of translational symmetry of the lattice structure and the emergence of amorphous-like structure even below the melting point. Melted nanoparticles show liquid-like characteristics with only a short-range order. Mean bond lengths and average Cu–O coordination numbers of both solid and melted NPs indicate weakening of the structural stabilization for smaller NPs that leads to an increased deformation in the local atomic arrangement because of the lack of long-range interactions. For the cases studied, most of the structural features are independent of temperature, with the notable exception of the number of oxygen atoms coordinated to Cu. This latter quantity is indeed indicative of melting phase transition and can be used to compute the melting point accurately. Atoms on the surface of solid NPs show amorphous-like behavior even at temperatures well below the melting point of the NPs due to the limited coordination environment. This study represents a useful step towards the establishment of a structure–property relationship for CuO nanoparticles.

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Introduction

Many of the fascinating features of nanoparticles (NPs) are due to their large surface volume ratio, structure and morphology that dictate surface-mediated reactions, nucleation, and growth mechanisms.^1–4 Copper(II) oxide NPs have found a multitude of applications^5–10 in the fields of catalysis,^11,12 semiconducting and superconducting materials, lubricants, electronics, optics, sensors,¹³ spintronics, and health.¹⁴ Examples of cutting-edge utilizations of CuO NPs include arsenic removal from water,¹⁵ fabrication of lithium ion battery,¹⁶ rocket propellant combustion, and antimicrobial.¹⁷ Despite the remarkable technological importance of this material, the literature on atomic scale investigations of CuO NPs is very limited as compared with other metal oxide nanoparticles, such as TiO₂,^18–20 Al₂O₃,²¹ SiO₂,^22,23 CeO₂, and ZnO.

Recently, Rodrigo²⁴ has observed different XANES (X-ray absorption near edge structure) spectra between solid and bulk phases of CuO, and he attributed this feature to the different coordination geometry of Cu atoms during the synthesis process. Zhang et al. have highlighted the importance of surface characteristics, consisting of under-coordinated²⁵ atoms of dissimilar ionic radii and dangling bonds, in catalysis and surface mediated reactions for CuO NPs.¹³

The nature of the atomic interactions at the nanoscale,^26,27 however, depends on the environment and thermophysical conditions.²⁸ This information is hard to obtain experimentally, not only because of the length and timescales involved, but mostly because the synthesis of monodisperse nanoparticles is difficult to realize and hence the structure, thermodynamics, and dynamics measures become complicated by polydispersity, impurities, and defects.

Atomistic simulations represent a powerful tool that can provide insights on the molecular mechanisms that drive and control the interactions at the nanoscale. Furthermore, atomic scale data of NPs via molecular simulations are also important for understanding and interpreting the experimental information obtained from X-ray diffraction (XRD), neutron scattering, EXFAS (extended X-ray fine absorption structure), XANES, WAXS (wide-angle X-ray scattering), XAS (X-ray absorption spectroscopy).^1,18,19,29 For these reasons, a considerable effort has been devoted to understand the structures of solid, amorphous, and liquid nanoparticles, including a few metal oxides,^18,19,30 using molecular simulation techniques.^{18,19,22,23,31,32} For CuO, however, there is still a limited understanding of its growth mechanisms as well as its physicochemical properties as a function of size, shape, and temperature.

In this paper, we report a comprehensive analysis of the atomic scale properties of solid and melted CuO NPs and their dependence on size and temperature using molecular dynamics simulation techniques. We examine structural properties using simulated XRD profiles, mean bond length, and coordination numbers.

Methodology

Force field

Although, a number of force fields (FFs) are available for pure metals or for specific metal oxides (e.g., TiO₂, Al₂O₃), the number of FFs for CuO is limited. On one side the use of fixed charge ionic potentials has shortcomings, as indicated by Zhou et al.³³ and Stolbov and Rahman,³⁴ on the other hand, the application of first principles methods to simulate nanoparticles is prohibitively expensive in terms of computational resources due to the number of atoms involved. A new version of the ReaxFF variable charge force field,^35,36 optimized for CuO and applicable to a wide range of temperatures,^36–38 was employed in this study. This force field was evaluated previously for bulk CuO by computing heat of formation and comparing it with DFT prediction which were −43.2 kcal mol⁻¹ and −37.3 kcal mol⁻¹, respectively.^36,39,40 Our choice was also motivated by the ability of ReaxFF to perform dynamic charge equilibrations dependent on local geometries at each time step.

ReaxFF force field computes the energy of a system considering the following partial contributions:

E_system = E_bond + E_lp + E_over + E_under + E_val + E_pen + E_3conj + E_tors + E_4conj + E_H-bond + E_vdWaals + E_Coulomb (1)

where from first to the last symbolic terms represent energies due to bond, lone pair, over-coordination, under-coordination, valence angle (3-body), penalty, 3-body conjugated, torsion angle (4-body), 4-body conjugation, hydrogen bond interactions, van der Waals interactions, and Coulomb interactions, respectively. Details of each energy contributions including complete functional forms can be found in the work by van Duin et al.^41,42 In contrast to fixed charge force fields, ReaxFF uses variable charges computed on the fly using electron equilibrium method⁴³ and considering charge transfer and polarization. Also, instead of fixed connectivity between atoms, ReaxFF computes bond order from instantaneous interatomic distances, which allows bond breaking and formation. The pairwise van der Waals interactions and electrostatic interactions are modeled using distance corrected (to limit excessive repulsive interactions between bonded atoms and atoms shearing a valence angle) Morse-potential and Coulomb potential, respectively. ReaxFF also applies a Taper correction (7th order polynomial function) to avoid energy discontinuities when charged species move in and out of the non-bonded cutoff radius. The parameters for CuO relevant to the energy terms in eqn (1) can be found in the ESI of the literature by van Duin.³⁶

Simulation details

Molecular dynamics simulations were carried out for four spherical CuO nanoparticles with diameters of 2 nm, 3 nm, 4 nm, and 6 nm consisting of 416, 1404, 3362, and 11 326 atoms, respectively. The initial configurations were obtained via a spherical cut of a superlattice generated from monoclinic CuO lattice parameters, using Accelrys Materials Studio software. To maintain charge balance, excess ions were removed from the surface. All the nanoparticles considered were spherical, as reported from different synthesis routes,⁴⁴ as well as by the size range chosen for our work.

Molecular dynamics simulations were carried out in vacuum using the LAMMPS package.⁴⁵ The simulations were run at constant temperature employing the Berendsen thermostat^46,47 without periodic boundary conditions and with an integration step of 0.01 fs. All the systems were equilibrated for up to 250 ps depending on the system size, temperature and the analysis performed.

X-ray diffraction (XRD) profiles at a wavelength of 1.5418 Å were computed using Debye scattering formula:^48–50

where I(Q) is the scattering intensity, r_ij = |r_i − r_j| is the distance between atoms i and j and Q is the atomic scattering vector which is a momentum transfer vector defined bywhere θ is the diffraction half-angle and λ is the radiation wavelength.

Results and discussion

The effect of structural properties on melting point is an important information and as first step we investigated the size dependence of the melting points. Empirical models^51–53 for different metal oxides can be found in the literature, but none of them is specific for CuO. To determine the melting points of NPs of various sizes, we carried out simulations at intervals of 100 K. We monitored the potential energy profile, isochoric heat capacity, and radial distribution function to locate the melting point. Fig. 1 shows the computed potential energy profile, isochoric heat capacities, and radial distribution functions at melting point (1100 ± 50 K) for a 4 nm CuO NP.

Fig. 1 Computed (a) potential energy profile, (b) isochoric heat capacity profile, and (c) radial distributions as functions of temperature for a 4 nm CuO NP.

Fig. 2 shows the comparison between our MD simulations (filled circles) and the values obtained from the empirical model proposed by Zhang et al.⁵³ The latter bases its prediction on the bulk properties of the materials and has been used for other metal oxides.^54,55 We extended the empirical model to include the physical properties of CuO; further details can be found in the ESI.†

Fig. 2 Melting temperatures of spherical CuO NPs as a function of the inverse of diameters computed with MD (solid circles) and predicted by the model of Zhang et al. Solid and dashed lines show the linear fits of the results. The bulk melting temperature as determined with MD is 1657 ± 132 K. Dotted line shows the melting temperature for the bulk (1600 K) as determined experimentally.⁵⁷

Molecular dynamics results show the expected decrease in melting temperatures as the diameter of the NP increases, a phenomenon commonly observed for other nanomaterials, including metals and metal oxides.^51–53,56 An important point is the ability of MD simulations to reproduce the experimental value of the bulk melting point: despite the limited number of simulated NPs, the extrapolation of the bulk melting point (1657 ± 132 K) is in agreement with the experimental value of 1600 K.⁵⁷

While both the MD simulations and the empirical model predict the same trend, the difference between them increases rapidly as the diameters of NPs are reduced. Without an experimental measure of the melting point of the nanoparticles is hard to conclude the relative quality of these two methods. However, the MD method shows consistency and applicability to a broad range of sizes. It can predict the bulk melting point using information on the computed melting temperatures of nanoparticles. In addition, the empirical model is applicable only to nanoparticles as small as 4 nm in diameter.^53,58,59

Based on these results, we simulated solid NPs at 300 K and melted NPs at 1700 K. To examine their structures, we computed their XRD profiles and compared with the experimental XRD patterns of bulk CuO. Fig. 3 shows the simulated XRD profiles and the experimental pattern (ICSD: 67850).^60,61 XRD data clearly differentiates between the two states (solid and melted), except for very small NPs (2 nm in diameter). Peaks in the XRD plots of solid NPs (Fig. 3a) indicate the presence of a CuO monoclinic phase. The match between the XRD profiles of the solid NPs and the bulk increases with the diameters of NPs, transitioning from the amorphous-like spectrum of the smallest (2 nm) NP to the biggest NP (6 nm). NP melts are characterized by a disordered structure (so called “X-ray amorphous”¹⁸) that results in flattened characteristic peaks as reported in Fig. 3b.

Fig. 3 Simulated X-ray diffraction (XRD) profiles for (a) solid (300 K) and (b) melted (1700 K) CuO nanoparticles of different diameters. The positions of the peaks of the experimental^60,61 XRD profile of bulk CuO are shown as dashed vertical lines.

While XRD diffraction profiles describe the global structure, the average Cu–O and Cu–Cu first nearest neighbor distances can provide information on the short range atom arrangement. These values are computed as the first moment of the distribution of the Cu–O and Cu–Cu minimum distances.

For solid NPs, the Cu–O bond length slightly decreases with the size of NPs (Fig. 4a). Linear fit of the mean bond lengths as a function of the reciprocal diameters predicts bulk Cu–O bond length of 0.194 nm that is in great agreement with the experimental value of 0.1954 ± 0.0005 nm,^62,63 obtained from XRD at low temperature and the value of 0.1944 ± 0.0010 nm (ref. 63) measured with EXAFS for the bulk crystal. This value is higher than the theoretical value of 0.181 nm (ref. 64) obtained from density functional theory calculation using B3LYP/LANL2DZ and experimental value of 0.1704 nm (ref. 65) obtained for a single CuO molecule at 0 K. This discrepancy is unsurprising as single molecules are expected to have a different bond length than NPs or bulk systems. Similar size-dependent bond lengths of solid NPs were reported earlier⁶⁶ for metal and metal oxide NPs.

Fig. 4 Mean Cu–O and Cu–Cu first neighbor distances of (a) solid (300 K) and (b) melted (1700 K) CuO NPs as a function of the inverse diameter. Dashed lines show the linear fits.

Differently from solid NPs, the mean bond lengths of melted NPs (Fig. 4b) are slightly shorter and marginally vary with the system size between 0.191 ± 0.004 nm (2 nm NP) and 0.193 ± 0.004 (6 nm NP). A similar shortening of metal–oxygen bond length has been previously reported for amorphous TiO₂ nanoparticles compared to bulk anatase,¹⁸ once again confirming the amorphous nature of CuO NP melts.

The results for the Cu–Cu nearest neighbor distances indicate opposite phase trends. Solid phase Cu–Cu nearest neighbor distances are more sensitive to the size of the system than to those of the melted phase, even though the predicted bulk values are the same (0.275 nm). In fact, the Cu–Cu nearest neighbor distances for melted NPs is all within their standard errors. In contrast, for solid NPs Cu–Cu nearest neighbor distances vary between 0.270 ± 0.003 nm (for 2 nm NP) and 0.274 ± 0.003 nm (for 6 nm NP).

To augment the information on local structure given by the average first neighbor distances, we analyzed the local environment of the atoms by computing the average number of oxygen coordinated to Cu in the melt and solid states. The coordination number (CN) was obtained by computing the ensemble average of the RDF integral up to the minimum after the first significant peak. The computed coordination numbers as a function of the inverse of NP diameter (Fig. 5) show that the CNs are smaller in the melt than the solid state, as expected due to the change in entropy associated with melting. For both solid and melted NPs, however, the CN has strong size dependence, increasing with decreasing NP size. Extrapolated CNs of solid NPs are in reasonable agreement with the standard bulk value of 4 for the Cu–O coordination.^63,67 Cu–O coordination of a solid nanoparticle with a diameter of 2 nm is mostly pentahedral (CN = 5) instead of tetrahedral. This increased CN is a consequence of the reduced stabilization of surface atoms from long range interactions compensated by an increase of short-range interactions. This increased “effective surface pressure”¹⁸ is reflected in the deformation of monoclinic crystallographic planes observed in smaller CuO NPs. The same effect is visible in the melted NPs, even though in this case the extrapolated bulk CN value is 3.7. Similar reduction in CN of oxide melts (Y₂O₃, Ho₂O₃, La₂O₃, ZrO₂, and Al₂O₃) has been very recently reported using both experiments (combining aerodynamic levitation, neutron and X-ray diffraction) and MD simulations.^68–70

Fig. 5 Coordination numbers as a function of the inverse of diameter of nanoparticles. Dashed lines show the linear fit of the data.

The understanding of the phase transition mechanism in CuO NPs requires a different approach, as it involves exploring a first order phase transition (see Fig. 1). However, information can be inferred by looking at the thermal dependence of structural data. Therefore, we studied a CuO NP with a diameter of 4 nm in two temperature intervals: 300–600 K for the solid state and 1500–1800 K for the melted phase (Fig. S2 in the ESI†). We chose a size of 4 nm, since it is the smallest size for which we can still observe a clearly distinct behavior between solid and melted phases.

Fig. 6 shows the mean Cu–O bond lengths at different temperatures in both solid and melted NPs. Unsurprisingly, the bonding distance depends on the phase with a slight contraction observed in the melted NP. Similar contraction of bond distances has been recently reported for the melted Cu and for other pure metal nanoparticles using both experiments (XRD and/or EXAFS) and molecular dynamics techniques.^71,72 Moreover, a similar behavior was previously found for the melts of other pure metals^72–74 and alloys.^75,76 Both in the solid and melted phases Cu–O bond distances are independent of temperature, in agreement with previous results for CuO NPs and bulk, obtained respectively, from XRD and EXAFS⁶³ measurements. The temperature dependence of the CN of oxygen atoms around Cu atoms (Fig. 7) is striking.

Fig. 6 Mean Cu–O bond lengths as a function of temperature in the solid and melted phases.

Fig. 7 Temperature dependence of the numbers of oxygen atoms coordinated around Cu in a 4 nm (diameter) CuO NP.

In both phases the CN decreases with increasing temperature, and while the effect is almost negligible in the solid phase, it is very pronounced for the melted NPs. This result is in agreement with the CNs' trends shown above and a consequence of the balance between enthalpic and entropic contributions. Interestingly, the temperature dependence is linear within the limit of the error and therefore CN can be used to estimate the melting temperature. For example for the 4 nm NP, extrapolation of the CN predicts a melting temperature of 1160 ± 50 K in great agreement with the 1100 ± 50 K value obtained from Fig. 1.

Due to the high surface to volume ratio typical of NPs, many properties are potentially affected by surface behavior, which is normally negligible in bulk. Therefore, we decided to investigate to which extent outer and inner layers of the CuO NPs differ. Since for small NPs it is hard to distinguish between surface and core atoms, we studied NPs with a diameter of 4 nm. Our previous results show that this is the smallest size where “bulk” behavior begins to appear and therefore we expect this NP to show the strongest surface effects. We defined the surface as the NP's outermost layer having a thickness of 0.36 nm (approximately twice Cu–O bond length), as a compromise between statistical error (from the small number of atoms) and error due to averaging of the surface and core properties.

A comparison of the core and surface XRD profiles for solid NP (see Fig. 8) suggests that surface structure does not have the monoclinic features present in the core structure as shown in Fig. 9.

Fig. 8 Simulated X-ray diffraction (XRD) profiles of the surface (blue) and core (black) of a CuO NP of 4 nm in diameter at 300 K. The positions of the peaks of the experimental XRD profile of bulk CuO are shown as dashed vertical lines.

Fig. 9 Structures of core and surface of a CuO NP. Red and blue represent oxygen and copper(II) ions, respectively.

The XRD profile shows an amorphous-like organization for the surface of a solid 4 nm NP even at room temperature, far below the melting point. This effect is probably caused by the truncation of crystal plane at the surface due to the high curvature of the NP. Similar distorted surface was previously observed experimentally for nearly spherical CuO nanoparticles using transmission electron microscopy (TEM).¹³ Based on these results, we expected the surface and core of a melted NP to produce similar XRD profile.

While this is generally true, as shown in Fig. 10, there are slight differences. In both cases here is no indication of long-range order in either the core or the surface plot, which confirms the amorphous structure. However, the XRD plot of the core shows a characteristic¹⁸ broad and weak hump at 35° whereas the surface profile is flattened, although slightly noisy. This difference suggests amorphous structures of different stoichiometry for the surface and core.

Fig. 10 Simulated X-ray diffraction (XRD) profiles of the surface (blue) and core (black) of a CuO NP of 4 nm in diameter at 1700 K. The positions of the peaks of the experimental XRD profile of bulk CuO are shown as dashed vertical lines.

Conclusions

In this paper, we reported a detailed analysis of the nanoscale structure of CuO nanoparticles using molecular dynamics simulations, and compared the results with available experimental data. We investigated the properties of different phases as function of size and temperatures. As for other inorganic NPs, we found that the melting temperature is inversely proportional to the particle diameter, with a linear fit that predicted the experimental bulk melting temperature very well (1657 K versus 1600 K), and it estimated NP melting point better than generic empirical models. The comparison between predicted and experimental XRD profiles showed a remarkable agreement indicating monoclinic crystal structure for solid particles, as small as for particles of 4 nm in diameter. Global structural information was integrated with data on local geometries, such as first neighbors mean distance and Cu average coordination number. The results suggest distinct nanoscale structural features for the solid and melted NPs. Differently, particles with diameters of 2 nm do not show any clear core–surface or phase dependent distinction. These simulations results were confirmed by experimental observations of amorphous-like structures for NPs of 2 nm or less in diameter. Like other transition metal oxides, the Cu–O bond length in NPs is smaller than that of the bulk, with negligible temperature dependence, again in accordance with experimental data.

For nanoparticles with diameters of 4 nm, we observed key differences in properties depending on spatial position (surface vs. core) and thermodynamic phase (melt vs. solid). The local geometry of CuO NPs at different temperatures is modified not by virtue of bond change, which is only minimally dependent on NP size and phase, but by the atomic arrangement (quantified as coordination number, or CN). Since the phase dependence of the CNs is significant, CN can be used as an indicator of the phase transformation. Atoms on the surface of a solid NP form an amorphous-like layer (or distorted outer shell) at temperatures well below the melting point. This phenomenon explains the existence of a rough spherical surface of CuO nanoparticles observed in TEM images. Notably, even the surface of melted NPs displays differences, from the core.

This study is a useful step towards the establishment of a structure–property relationship for CuO nanoparticles that is important for the understanding of nucleation, melting/freezing transition, sintering, aggregation, nanocomposite, and the growth of nanoparticles on other nanostructures (e.g., multi-walled carbon nanotube, nanoelectrode devices). These results will provide guidance for understanding the phase diagrams of mixed metal oxides and surface mediated reaction mechanisms in catalysis.

Acknowledgements

This research has been funded by NSF through DMR1105361. This research was supported in part through computational resources and services provided by Advanced Research Computing at the University of Michigan, Ann Arbor.

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Footnote

† Electronic supplementary information (ESI) available: Potential energy profiles versus time to demonstrate convergence; details about the empirical model to determine melting point; and temperature dependence of X-ray diffraction (XRD) profiles are given. See DOI: 10.1039/c5ra04276c

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