Molecular Simulation, 2018 https://doi.org/10.1080/08927022.2018.1469751
Molecular dynamics simulation of the size-dependent morphological stability of cubic shape silver nanoparticles Margaret M. Blazhynska, Alexander Kyrychenko
and Oleg N. Kalugin
School of Chemistry, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
ABSTRACT
The morphological stability of sharp-edged silver nanoparticles is examined by the classical molecular dynamics (MD) simulations. The crystalline structure and the perfect fcc atom packing of a series of silver nanocubes (AgNC) of different sizes varying from 63 up to 1099 atoms are compared against quasi-spherical nanoparticles of the same sizes at temperature 303 K. Our MD simulations demonstrate that starting from the preformed perfect crystalline structures the cubic shape is preserved for AgNCs composed of 365–1099 atoms. Surprisingly, the rapid loss of the cubic shape morphology and transformation into the non-fcc-structure are found for smaller AgNCs composed of less than ~256 atoms. No such loss of the preformed crystalline structure is seen for quasi-spherical nanoparticles composed of 38–1007 atoms. The analysis of the temperature dependence and the binding energy of outermost Ag surface atoms suggests that the loss of the perfect cubic shape, rounding and smoothing of sharp edges and corners are driven by the tendency towards the increase in their coordination number. In addition, we revealed that AgNC1099 partially loses its sharp edges and corners in the aqueous environment; however, the polymer coating with poly(vinyl alcohol) (PVA) was able to preserve the well-defined cubic morphology. Finally, these results help improve the understanding of the role of surface capping agents in solution phase synthesis of Ag nanocubes.
1. Introduction For over a decade, silver nanoparticles (AgNPs) have been a subject of the intensive research owing to their great performance in a broad range of applications involving localised surface plasmon resonance (LSPR), surface-enhanced Raman scattering (SERS), metal-enhanced fluorescence, sensing, in vivo imaging, catalysis and antimicrobial technology [1,2]. It has been well established that the physicochemical properties of Ag nanoparticles are strongly modulated by their size, shape and morphology [3]. Among various Ag nanostructures, nanocubes with sharp corners and edges (Figure 1) have attracted particular attention owning to their superb performance in applications involving LSPR and SERS [4]. Exposed to light, AgNPs excite strong resonant fields in the visible and infrared ranges due to the effect of LSPR. The interesting feature of Ag nanostructures is their ability to behave similar to optical antennae by supporting the excitation of LSPR, where conduction electrons of the metal oscillate in resonance with the incident light wave to produce intense electromagnetic fields localised at the metal surface [5]. Therefore, the use of anisotropic or non-spherically shaped Ag nanostructures with high aspect ratios or sharp edges, such as cubes, rods and stars, has been shown to have promising perspectives in tuning of a peak position and intensity of LSPR [3,6–9]. Molecular dynamics (MD) simulation has become a powerful tool for facilitating the investigation of the growth, phase
CONTACT Alexander Kyrychenko
[email protected]
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ARTICLE HISTORY
Received 14 August 2017 Accepted 16 April 2018 KEYWORDS
Silver nanoparticle; nanocube; sharp-edged; Lennard-Jones potential; molecular dynamics simulations; PVA
transitions and self-assembling of metal nanoparticles at the atomic level [10]. Atomic-scale theoretical methods can provide important insight to solution-phase synthesis of silver nanostructures that involves the seeded growth [11,12], aggregation of silver clusters, as well as adsorption of stabilising agents and solvent molecules onto the exposed facets of inorganic metal nanocrystals [13,14]. Numerous MD simulation studies of quasi-spherical metal nanoparticles protected by organic ligand monolayers [15–17], polymers [18–24], dendrimers [25] and peptides [26] have been conducted. However, the reliability of classical MD simulations of non-spherical nanoparticles with sharp edges and corners, such as cubes, pyramids, octahedrons and rods, is still poorly understood [11,27–31]. The main goal of our study is to benchmark the macroscopic morphological stability, the local crystalline structure and the perfect face-centred cubic (fcc) atom packing in the sharp-edged silver nanocubes by means of classical MD simulations. From the computational point of view, several functional forms of interatomic potentials for simulations of non-bonded interactions between Ag atoms in a solid phase have already been suggested [34–40], among which are the many-body potentials, such as the tight-binding potential [34,39,41], the embedded atom method (EAM) potential [27,37,42–45], the Gupta model [35,46], the quantum Sutton–Chen (QSC) potential [40,46–48], as well as the pairwise Lennard-Jones (LJ) 12-9 and 12-6 potentials [18,49–52]. Recently, the parameters of the LJ 12-6 pair potential for Ag-Ag
2
M. M. BLAZHYNSKA ET AL.
Figure 1. (Colour online) Examples of scanning electron microscopy (SEM) images of Ag nanocubes (adopted from ref [2] (a), [32] (b) and [33] (c)). The insert shows schematic structure of a perfect cubic silver nanocrystal (d).
have been adopted for MD simulations of bulk fcc-crystalline silver [53]. Their scope has further been validated for quasi-spherical Ag nanoparticles [18,53–55]; however, the performance of these LJ parameters has never been evaluated in modelling sharp-edged Ag nanostructures. Therefore, another goal is to study the scope and limitations of the LJ 12-6 parameters for MD simulations of AgNCs. The obvious advantage of the use of the well-documented LJ 12-6 parameters for Ag-Ag interactions is that these parameters should easily be transferable between various popular biomolecular force fields, such as OPLS, GROMOS, CHARMM and AMBER, which leaves open the possibility for MD simulations of a broad range of hybrid organic/inorganic nanomaterials. Recently, such an approach has been validated in the CHARMM-INTERFACE force field [55,56]. The understanding of the shape control mechanism of sharpedged silver nanoparticles is very important for technological application and is crucial to obtain reproducible results [57]. The polyol synthetic strategy is commonly used for the seed-mediated growth of colloidal Ag nanocrystals [58,59]. In this method, a precursor solution of AgNO3 is injected into a solution already containing a mixture of reductant, a capping agent and colloidal stabiliser [59,60]. The AgNO3 precursor is reduced (or decomposed) leading to zero-valent Ag atoms, which then heterogeneously nucleate on the surface of the Ag seeds. In a typical synthesis procedure, silver nanocrystals are in general prepared as having equilibrium quasi-spherical and polyhedral shapes, in which the facets correspond to low index planes. However, it has been suggested that altering the synthetic procedure and the use of proper capping agent could lead to the formation of non-equilibrium sharp-edged cubic shapes of AgNPs, which may primarily be driven by kinetic factors [12,22,61]. Kinetically controlled
growth of the seeds, through one of the many possible pathways, results finally in the formation of well-defined nanocrystals, such as cubes (Figure 1) and other octahedrons [57]. Therefore, to understand the interplay between thermodynamic versus kinetic factors in the shape control of AgNCs we carried out preliminary MD simulations to examine a role of the environment on the morphological stability of cubic shape silver nanoparticles in bulk water and in the presence of an organic stabilising agent. Our MD simulations suggested that the morphological stability of the unprotected Ag nanocube (AgNC1099) was strongly affected by surrounding water molecules, which facilitated the loss of sharp edges and corners. These results are in accord with known experimental observations that bare Ag nanocubes are readily degraded to polyhedral quasi-spherical NPs in solution [62,63]. However, our atomistic modelling also provide some evidences that these environment-induced structural rearrangements of Ag nanocubes could be slowed down by the polymeric coating of AgNC1099 by poly(vinyl alcohol), which further support a kinetic rather than thermodynamic origin for the formation of various sharp-edged Ag nanostructures in solution.
2. Computational methods 2.1. Molecular dynamics simulation setup The preformed silver nanocubes (AgNCs) were approximated by the perfect face-centred cubic (fcc) crystalline structure (Figure 2) composed of six (001) facets. AgNCs consist of neutral, non-polarisable silver atoms with the zero charge. The repulsion and dispersion terms of non-bonded interactions between silver atoms were computed using the Lennard-Jones 12-6 potential
MOLECULAR SIMULATION
3
Figure 2. (Colour online) Structure of perfect fcc silver nanocubes (AgNCs), composed of the number of silver atoms N varying from 1099 to 63.
energy function (Eq. 1), which describes the dependence of the potential interaction energy VLJ(rij) of two silver atoms as a function of the interatomic distance. The non-bonded interaction parameters Ag-Ag σ = 0.2955 nm and ε = 19.05865 kJ/mol were taken from our recent works [18,54]. No any rigid bonds and restraints were applied between silver atoms, so that the silver core crystalline structure was maintained by the Ag-Ag nonbonded LJ interactions. Each AgNC was simulated in vacuum according to the following procedure: (1) Steepest descent energy minimisation was performed for 500 steps. (2) Initial atomic velocities were generated with the Maxwellian distribution at T = 220 K. Then, MD sampling was carried out at the reference temperature of T = 303 K, which was kept constant using the Berendsen weak coupling scheme with the temperature coupling constant of τT = 0.1 ps [64]. The cut-off distance of 0.8 nm was used for Lennard-Jones interactions.
�
⎛ 𝜎 ij VLJ (rij ) = 4 𝜀ij ⎜ ⎜ rij ⎝
�
�12 −
𝜎ij rij
�6
⎞ ⎟ ⎟ ⎠
(1)
In addition, for better understanding of a role of the environment in the morphological stability of the cubic nanoparticles, additional MD simulations of AgNC1099 were also carried out in water in the absence and in the presence of poly(vinyl alcohol) PVA. The PVA model and interaction parameters, based on the GROMOS G45a4 united atom FF [65], in which CH, CH2 and CH3 moieties are treated as a single united interacting site, were taken from our recent work [54]. Water molecules were simulated with the Simple Point Charge (SPC) model [66]. The Lorentz–Berthelot combination rules (Eq. 2-3) were used for mixed non-bonded interactions between Ag and PVA, and water atoms [67]. ) ( 1 𝜎ii + 𝜎jj 𝜎ij = (2) 2
( ) 12 𝜀ij = 𝜀ii × 𝜀jj
(3)
Periodic boundary conditions were applied to all three directions of the simulated box. Electrostatic interactions were simulated with the particle mesh Ewald (PME) approach [68] using the long-range cut-off of 0.8 nm. All bond lengths in PVA were kept constant using the LINCS routine [69,70]. The MD simulation time step was 2 fs with the neighbour list updates every 10 fs. The MD simulations were carried out using the GROMACS set of programs, version 4.6.5 [67]. Molecular graphics and visualisation were performed using VMD 1.9.1 [71].
Table 1. Structural parameters of the studied AgNCs.
System AgNC63 AgNC108 AgNC172 AgNC256 AgNC365 AgNC500 AgNC666 AgNC864 AgNC1099
Ncorea 9 28 62 108 171 176 364 500 665
Nsurfa 54 80 110 148 194 324 302 364 434
Edge length (nm) 0.91 1.04 1.23 1.44 1.63 1.85 2.04 2.30 2.70
Fcore (%) 14.3 25.9 36.1 42.2 46.9 35.2 54.7 57.9 60.5
Fsurf (%) 85.7 74.1 63.9 57.8 53.1 64.8 45.3 42.1 39.5
Surface area (nm2) 4.97 6.74 9.08 12.44 15.94 20.54 24.96 31.74 43.74
RMSD (nm)b 0.332 0.218 0.163 0.103 0.055 0.052 0.050 0.046 0.042
a
Ncore and Nsurf are the number of Ag atoms that belong to the nanoparticle core and those located at the outermost surface layer. Fcore and Fsurf are the fractions of the core and surface atoms in percent. b The root mean squared displacements were averaged over the last 3 ns of MD sampling.
2.2. DFT Calculation The electronic structure calculations were done at the density functional theory (DFT) level using the Gaussian program, version 09 [72]. The geometry optimisation of silver nanoparticles were carried out with the exchange correlation B3PW91 functional [73] and the dispersion corrected M06–2X functional by Truhlar and Zhaol [74]. The Lanl2dz basis set [75] and effective core potential was used for Ag. Geometry optimisation of AgNC to a local minimum was carried out with the Berny algorithm [76]. No symmetry restriction was applied during geometry optimisation.
3. Results and discussion A series of MD simulations of the nine AgNCs of varying sizes N = 1099–63 and edge lengths of 2.70–0.91 nm were performed to study their cubic shape morphological stability. In each case, the initial structure was approximated by the preformed perfect fcc cubic nanocrystal (Figure 2). Structural parameters of the studied AgNCs are summarised in Table 1. 3.1. Validation of Ag-Ag Lennard-Jones potential by DFT calculations To validate the scope and the limitations of the used LJ potential for Ag-Ag we first compared the structure of the smallest AgNC63 obtained by classical MD simulations carried out in vacuum at 0 K and those optimised by DFT calculations. MD simulations demonstrated that, at these conditions, the thermal fluctuations of the Ag atoms are negligible, so that the perfect cubic shape of AgNC63 was preserved. To characterise the atom packing and the long-range order of the Ag atoms in AgNC63, the pair radial distribution function (RDF) g(r) was calculated between all silver
4
M. M. BLAZHYNSKA ET AL.
Figure 3. (Colour online) Comparison of the structure of AgNC63 estimated by MD simulation in vacuum at 0 K with those optimised by the DFT methods.
atoms, as shown in Figure 3. As can be seen, g(r) calculated for AgNC63 is characterised by narrow and sharp peaks. The structure optimisation of AgNC63 was done at the density functional theory (DFT) level using two different functionals. First, the dispersion-corrected functional M06–2X [74] was used, which showed a good performance to study structural, energetic and optical properties of small- and middle-sized Ag clusters [77,78]. In order to examine the quality of the DFT optimisation results, we also benchmarked the popular exchange correlation B3PW91 functional [73], which is commonly used for global structural investigations of Ag clusters with N as large as a few hundred particles [77]. The Lanl2dz basis set [75] and effective core potential on Ag was used. The DFT geometry optimisations of AgNC63, performed at the M06–2X/Lanl2dz and B3PW91/Lanl2dz theory level and
starting from the initial cubic shape, converged to a nearly perfect cubic geometry (not shown). The atom packing within the DFT-optimised AgNC63 was further examined by their RDF profile. Figure 3 shows the comparison between the RDF profiles calculated using the MD simulated geometry and those of the DFT-optimised structures. As can be seen, the MD simulated and the M06-2X optimised structures revealed a good agreement of the RDF profile patterns, so that the positions and the amplitudes of the peaks corresponds to the RDF profile of the fcc crystalline structure of bulk silver [39,79]. The B3PW91 functional, although providing the very good agreement in the first RDF peak position of 0.292 nm, as compared to the MD value of 0.291 nm, seems to somewhat lose long-range Ag atom ordering. Therefore, these findings point out that classical force fields based on the LJ pair potential can be employed as a simpler computational alternative to semi-empirical embedded atom models [27,37,42–45] and other many-body potentials [34,39,41], which are commonly used for local minimisation investigations of metal nanostructures composed of several thousand particles. The LJ-based geometry optimisation of low-energy isomers for smalland medium-sized Ag clusters can be fruitful in providing candidate structures to be further optimised at a higher level of theory. 3.2. MD simulation benchmarking of macroscopic morphological stability Our MD simulations reveal that at 303 K the morphological stability of the preformed silver cubic-shaped fcc-nanocrystals is size dependent. We found out that the structures of AgNCs with size N varying from 1099 up to 365 were characterised by the well-defined crystalline structure with the sharp edges and corners. As can be seen in Figure 4 top, in the case of AgNC365, all the Ag atoms were found at their well-defined equilibrium positions in the fcc lattice and only small thermally driven oscillations around the vicinity of these equilibrium positions
Figure 4. (Colour online) MD snapshots of the side view of instantaneous configurations of AgNCs taken at different simulation times, which demonstrate different sizedependent morphological stability of the cubic shape Ag nanoparticles.
MOLECULAR SIMULATION
5
Figure 5. (Colour online) A radial distribution function g(r) averaged over pairs of Ag-Ag atoms in AgNCs. The RDF plots of AgNC1099 to AgNC365 show the narrow peaks, which are characteristic for the fcc ordering of bulk crystalline silver. The loss of the perfect fcc structure is observed upon the decrease in the size from AgNC108 up to AgNC63.
occurred. The cubic shape of the nanoparticle was easily determined from instantaneous MD configurations (Figure 4 top). For AgNC172, outermost Ag atoms become more mobile, so that some structural disorder and the loss of the perfect atom packing were observed (Figure 4 middle). Surprisingly, the rapid crossover from fcc-nanocubes into disordered amorphous structures occurs for AgNCs with N
