Modelling Nucleation and Growth of ZnO Nanoparticles in a Low

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Modelling Nucleation and Growth of ZnO Nanoparticles in a Low Temperature Plasma by Reactive Dynamics Giovanni Barcaro, Susanna Monti, Luca Sementa, and Vincenzo Carravetta J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b01222 • Publication Date (Web): 07 Feb 2019 Downloaded from http://pubs.acs.org on February 7, 2019

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Journal of Chemical Theory and Computation

Modelling Nucleation and Growth of ZnO Nanoparticles in a Low Temperature Plasma by Reactive Dynamics

Giovanni Barcaro,a Susanna Monti,b Luca Sementa,a and Vincenzo Carravetta*,a

a

CNR-IPCF, Institute of Chemical and Physical Processes and bCNR-ICCOM , Institute of Chemistry of Organometallic Compounds, via G. Moruzzi 1, I-56124 Pisa, Italy E-mail: [email protected]

Keywords: DFT, Reactive Force Field, Global Optimization, Nucleation, Growth

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ABSTRACT

The very first stages of nucleation and growth of ZnO nanoparticles in a plasma reactor are studied by means of a multi-scale computational paradigm where the DFT-GGA approach is used to evaluate structure and electronic energy of small (ZnO)N clusters (N ≤ 24) that are employed as a training set (TS) for the optimization of a Reactive Force Field (ReaxFF). Reactive Molecular Dynamics (RMD) simulations based on this tuned ReaxFF are carried out to reproduce nucleation and growth in a realistic environment. Inside the reaction chamber the temperature is around 1200 K and the zinc atoms are oxidized in an oxygen-rich atmosphere at high pressure (about 20 atm), whereas in the quenching chamber where the temperature is lower (about 800 K) the ZnO embryo-nanoclusters are grown. The main processes ruling gas-phase nucleation and growth of ZnO nanoclusters are identified and discussed together with the dependence of the inception time and average stoichiometry of nanoclusters of different size on the composition of precursor material and physical parameters.


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1. Introduction Since the beginning of nanoscience and nanotechnology, zinc oxide has attracted strong interest in the scientific community for a variety of novel properties exhibited at the nanoscale due to quantum confinement effects1–3. In fact, 2D (ultra-thin films)4,5, 1D (nanowires)6,7 and 0D (nanoparticles, NPs)8,9 can find several applications in relevant technological fields like the design of photovoltaic and photocatalytic materials10,11, sensors12–14, piezoelectric devices15,16, just to cite some. Furthermore, non-toxicity, bio-compatibility and low-cost have encouraged medical applications for drug-delivering17, and cancer therapy as ZnO NPs can be used as efficient generators of ROS (Reactive Oxygen Species) able to kill cancer cells18. Regarding the investigation of the structural evolution of ultra-small ZnO NPs in the gas-phase (or supported on a substrate19,20), most works appeared in the literature include some level of theoretical/computational contribution21, that should bridge the gaps between measurements and interpretations of the structural data of very small clusters22–24.. Indirect information can instead come from the investigation of the optical properties of ZnO NP25, as it has been theoretically proven that change in morphology can be correlated to different features in the excitation spectrum of the NP26– 28

or of the bulk polymorph29. A variety of approaches, such as accurate first-principles DFT30–43,

classical and reactive inter-atomic potentials44–48, simplified Hamiltonians49,50 have been applied to study the energy competition between structural motifs as a function of cluster size. It was found that at smaller size low-coordinated motifs are favoured (in the form of rings), whereas, when increasing cluster size, single and then multi-wall (onion-like) cages are preferred49,51. After that, a transition towards bulk structures is encountered, with the possibility of a competition between different bulk polymorphs47,52–54, some of which can be created by assemblies of building blocks made of small “magic” clusters55, as in the case of the sodalite phase56. Among the different synthetic routes which can be followed to produce stable ZnO NPs, plasmabased techniques are very appealing from a technological point of view because they do not resort to chemical solvents (as it currently happens in the wet-chemistry procedures), even though their main ACS Paragon Plus Environment


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drawback is a difficult control of the size distribution and composition of the NPs. However, close control of the morphology (often aiming at producing crystalline depositions) is achieved by using very low pressures of the gas mixture containing the reactive species57,58. When considering NP production on an industrial scale for real technological applications, pressures of the reactive gas are in the order of magnitude of atmospheric pressure, determining a much more complicated scenario of all the events inside the reactor. A detailed knowledge of the main chemical and physical processes in a plasma reactor is fundamental to achieve control on the NP synthesis. Such information is very scarce from the experimental point of view, due to the inherent difficulties of a real-time characterization of the NP formation, especially in the very early stages of NP growth and particularly in the case of a plasma environment. Modelling can be very useful to shed light on the complex and interwoven processes taking place inside the reactor and to suggest efficient strategies to tune the synthesis protocol (in terms of fluxes, pressure, temperature) for the desired optimization of the NP growth. Collecting information on large scales (time and size) is necessary to get reliable estimates of inception time rates, average composition and structural information of the investigated NP. For this purpose, a synergic multi-scale approach integrating computational methods on different scales represents a good strategy. In this paper, we have adopted such an approach by combining: (1) a firstprinciples method (DFT) which is very accurate in describing the electronic structures of the investigated systems, but limited on both length and time scale (to NP of maximum 100-200 atoms in size and few tens of picoseconds in time); (2) a Reactive Force Field (ReaxFF) method, inherently less accurate than DFT, but trained on DFT data and able to investigate the dynamical processes of NP formation on larger scales (of the order of tens of nanoseconds and nanometers). This methodology could be used to develop the parameters for coarse-grained simulations. Thus, the data derived in the present paper have a double purpose: (i) shed light on the dynamical processes taking place in plasma conditions and ruling nucleation and growth of zinc oxide nanoparticles; (ii) derive significant descriptors (like inception times and average stoichiometry) to design a meso-scale computational protocol. The latter scope is the view at the base of the project NanoDome that ACS Paragon Plus Environment

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motivated our group in pursuing the achievements described in the present paper. The manuscript is organized in four sections. Section 2 contains a detailed description of the multiscale methodology adopted. Section 3 reports results and discussion of: (3.1) the refinement, against DFT data, of the ReaxFF proposed by Tainter46; (3.2) an evaluation of the reliability of the refined ReaxFF to investigate the structure of stoichiometric ZnO clusters as a function of their size; (3.3) simulation of the nucleation and growth processes in realistic plasma conditions. Section 4 contains the conclusions of the investigation.

2. Computational details 2.1. Density Functional Theory Calculations First-principles DFT local optimizations were carried out to derive specific structures of small ZnO clusters that can be present during nucleation in a plasma environment both to define a training set (TS) for the optimizations of the ReaxFF and a validation set as discussed hereafter. All the DFT calculations were performed by means of the Quantum Espresso package (version 6.3)59 by using ultra soft pseudo potentials60 for the core electrons of each atom (2 electrons for O, corresponding to the 1s orbital and 18 electrons for Zn, corresponding to the 1s,2s,2p,3s and 3p orbitals) and the GGA-PBE DFT functional61 for the electronic structure of the remaining electrons (6 for O and 12 for Zn). This functional predicts a cohesive energy of the wurtzite bulk of 6.86 eV, an equilibrium lattice constant a=3.28 Å and a c/a ratio of 1.61, which satisfactorily compare with the experimental values of 7.52 eV, 3.25 Å and 1.60 respectively62. The DFT-PBE underestimation of the cohesive energy (about 9%) is relatively small in comparison with the overestimation (about 20%) provided by the commonly applied DFT-LDA approach. Although recent calculations on small (ZnO)N clusters have shown that the use of hybrid meta-GGA xc-functionals can improve the quality of DFT predictions against accurate CCSD(T) calculations63, we decided to employ PBE as the best compromise between cpu-demand and accuracy of the obtained results. Energy optimizations were



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carried out in cubic boxes with an edge length between 20 and 30 Å (depending on cluster size) applying periodic boundary conditions to effectively project the wave function on a set of plane waves with wave-function/electronic density cut-offs of 400/4000 eV, respectively. The Gaussian smearing for the occupation of the Kohn-Sham single-particle states was set to 0.03 eV and the Brillouin zone was explored at the Gamma point. For single local minimizations a threshold of 10-3/10-4 a.u. (atomic units) on energy/forces was employed.

2.2. Optimization of the ReaxFF parameters for the Zn-O interaction (ND-FF parametrization) Starting from a previous parametrization available in the literature for ZnO46, hereafter dubbed TAFF, we re-optimized64 selected parameters of the ReaxFF, by using the serial version of the ReaxFF code65, against a TS of data relevant for describing small ZnO clusters. These parameters were selected: (i) Zn-O bond (13 parameters); (ii) Zn-O off-diagonal terms (4 parameters); (iii) O-Zn-O valence angle terms (5 parameters); (iv) Zn-O-Zn valence angle terms (5 parameters); (v) O-Zn-Zn valence angle terms (5 parameters); (vi) O-O-Zn valence angle terms (5 parameters). The parameters of bond and off diagonal terms related to the O-O and Zn-Zn interactions remained untouched.

2.3. Validation of the ReaxFF parametrization by identification of the energy GM (Global Minima) In order to test the structural reliability of the presently optimized force field (ND-FF) outside the TS, we identified a number of low-energy structures of (ZnO)N clusters (N from 8 to 48) by means of the protocol described in Ref. 66 where the scheme was applied to the structural investigation of Si clusters grown in a plasma environment67. The algorithm (RMD-BH) consists of a joint reactive molecular dynamics (RMD) simulation at high temperature and a basin hopping (BH) search at T= 0 K. Both calculations are carried out by using the LAMMPS code (2017 version)68 for a fast evaluation of energies and forces. Each step of the RMD-BH protocol consists of: (i) 500000 steps of RMD run at 1000 K with a time step of 0.50 fs and Nosé-Hoover chain thermostat (default choice in Lammps ACS Paragon Plus Environment

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when using canonical ensemble)69; (ii) 200 moves of BH, starting from the last cluster geometry of the dynamics, with an acceptance criterion between 23 and 69 Kcal/mol. The procedure is usually repeated for a number of times between 20 and 50 for each investigated system, according to the criterion that the putative GM has to be found in the exploration of the Potential Energy Surface (PES) several times. However, as there always exists a margin of uncertainty about the exhaustiveness of the search method, the identified GM have to be considered as putative GM. Each identified structure is then used as starting point of a DFT optimization to establish the degree of agreement between the ReaxFF and the first-principles approach in terms of structure predictivity. A simple structural analysis of the ReaxFF generated configurations was based on R and  descriptors65. The first one refers to an average value of the interatomic distances: 𝑛

𝑟𝑖 =

𝑖 𝑟 ∑𝑗=1 𝑖,𝑗

𝑛𝑖

𝑅=

∑𝑁 𝑗=1 𝑟𝑗 𝑁

where N is the number of atoms in the cluster, each atom i has ni first-neighbours, and ri,j is the distance between atoms i and j, whereas the second one refers to an average value of the molecular angles:

𝜃𝑖 =

∑𝑗 ∑𝑘 𝜃𝑖,𝑗,𝑘 𝑛𝑖′

𝜃=

∑𝑁 𝑗=1 𝜃𝑗 𝑁

Considering that each atom i is involved in ni’ angles.

2.4. Simulation of nucleation and growth processes To collect information on the nucleation and growth processes, we performed several classical reactive molecular dynamics simulations by using the LAMMPS code and both ND-FF and TA-FF force fields in order to compare the predicted growth rates. All the simulations were carried out in the NVT ensemble with the Berendsen thermostat69 and a time step of 0.50 fs. This last value was chosen as the largest one and then the most convenient one, that could provide, for long simulations at high ACS Paragon Plus Environment


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temperature, stable results. In fact, by a series of test microcanonical simulations with a time step in the range between 0.1 and 1 fs, it turned out to be the maximum value leading to a satisfactory energy conservation and no instability of the motion of the atoms. Our simulations ran at different temperatures and compositions to mimic possible scenarios inside a thermal plasma reactor employed for industrial large-scale production of ZnO nanoparticles. Each simulation was separately interrupted when the system property of interest reached “convergence”, that is a flat, constant trend

3. Results and discussion 3.1. Optimization of the ReaxFF parameters for Zn-O clusters The reactive force field TA-FF available in the literature for ZnO materials was derived to reproduce the correct behaviour of both Zn extraction from EZE (di-ethyl zinc) and bond dissociation of the molecular Zn-O bond. This choice determined a poor accuracy of TA-FF with regard to the zinc oxide crystal properties. To improve TA-FF for simulating ZnO nanoclusters, we performed a partial reoptimization of the force field parameters starting from the generation of a TS including structure and energy data obtained through first-principles calculations on a number of small (ZnO)N clusters (Figure 1). The structures displayed in Figure 1 were selected from a rich set of energy optimized ZnO clusters already studied in the literature70. The selected geometries were re-optimized at the DFT level through the aforementioned protocol to derive parameters consistent with the first-principles approach. The main purpose of this choice was to quantitatively reproduce the competition between planar, ring and compact structures at the very first stages of the formation of (ZnO)N units. It turned out that rings are the most stable motifs up to a size of 7: the energy difference per ZnO unit between planar and ring motifs is 3.7 Kcal/mol at N=4, 2.4 Kcal/mol for N=5, 0.9 Kcal/mol for N=6 and 0.7 Kcal/mol for N=7. At N=8 there is a crossover and the most stable structure is the compact motif included in the TS. The GM structure at N=12 is the basic building block of the sodalite motif, which can be also ACS Paragon Plus Environment

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stabilized in a bulk form39. Its geometry could be described as the arrangement of six (ZnO)2 lozenges at the vertexes of an octahedron. The motif of the (ZnO)2 lozenge can be identified also in the structure of other 2D-motifs, as the structure at N=24. Here, we can notice that there are not internal atoms and the cluster surface is formed by two types of building blocks, namely the aforementioned lozenge (ZnO)2 and a (ZnO)3 motifs, where a central zinc atom and the three oxygens coordinated to it (at angles of about 120°) are organized as a flatter block. An extended plane of ZnO could be created by crosslinking (ZnO)3 motifs resulting in a graphene-like structure. The last configuration added to the TS is the wurtzite crystal, where each atom is characterized by a tetrahedral coordination.

Figure 1: Structures included in the ND-FF training set. Oxygen and zinc atoms are displayed in red and yellow, respectively.



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In summary, we prepared the TS considering three types of coordination that can be found in ZnO small clusters: coordination 2 (rings), coordination 3 ((ZnO)2 and (ZnO)3 motifs) and coordination 4 (wurtzite). The data included in the TS are cohesive energies (per ZnO unit) and z-matrices (interatomic distances, valence angles and dihedral angles) of the geometries shown in Fig 1, for a total of 350 descriptors. The cohesive energy (per ZnO unit) of a (ZnO)N cluster is calculated according to the following expression:

𝐸𝑐𝑜ℎ (𝑁) =

𝑁 𝑁 𝐸𝑡𝑜𝑡 − ( 2 ) 𝐸𝑍𝑛 − ( 2 ) 𝐸𝑂 𝑁

For each property f of the TS, computed at the ReaxFF level, it is defined a deviation from the benchmark value that contributes to the following error function EF: 𝑓𝑅𝐹𝐹,𝑖 − 𝑓𝑄𝐶,𝑖 2 𝐸𝐹 = ∑ { } 𝑤(𝑖) 𝑖

where fRFF;i and fQC;i are the running ReaxFF and the benchmark DFT values of the ith TS entry and w(i) is its weight, that should be intended as an estimation of its accuracy. The sum is extended to all the data of the training set. In the sequential optimization routine of the ReaxFF program, at each step a single parameter is considered and its starting value varied by adding and subtracting a given quantity. For these three values of the parameter, the total EF is computed and a parabolic interpolation/extrapolation is adopted for estimating, at the minimum of the parabolic expression, the optimal value. As the force field parameters are strongly entangled, several sequential optimization cycles are carried out in order to achieve an effective reduction of the EF against the reference data. The starting (TA-FF) and final (ND-FF) values of the chosen parameters (37 in all) and the cohesive energies of all the structures of the TS are reported in Table 1 and 2, respectively. Examination of Table 2 confirms that TA-FF largely overestimates the cohesive energy of both bulk and cluster structures and stabilizes compact structures with respect to the low-coordinated ones, as the crossover takes place between size 4 and size 5. On the other hand, the ND-FF shifts forward this crossover, which takes place at size 7, where the two structures (the compact and the ring) are almost degenerate. ACS Paragon Plus Environment

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Apart from the overestimation of the stability of the (ZnO)7-b motif, the agreement between DFT and ND-FF cohesive energies is quite satisfactory.

Parameter

TA value

ND value

Parameter

TA value

ND value

Zn-O Edis1

193.7071

169.7190

O-Zn-O Theta0

10.8790

5.6260

Zn-O Edis2

107.4583

98.9420

O-Zn-O ka

38.9915

43.7278

Zn-O Edis3

23.3136

26.8305

O-Zn-O kb

0.7072

1.0324

Zn-O pbe1

-0.5983

-0.7360

O-Zn-O pv2

2.0000

4.7231

Zn-O pbo5

-0.1743

0.0567

O-Zn-O pv3

2.6162

3.6052

Zn-O 13corr

1.0000

1.0000

Zn-O-Zn Theta0

37.5284

39.4234

Zn-O pbo6

10.8209

13.4913

Zn-O-Zn ka

32.3525

35.0400

Zn-O kov

0.0375

0.0343

Zn-O-Zn kb

0.2657

0.2230

Zn-O pbe2

1.7527

2.1396

Zn-O-Zn pv2

0.4403

0.9120

Zn-O pbo3

-0.3113

-0.2249

Zn-O-Zn pv3

1.1000

1.3179

Zn-O pbo4

7.0000

5.3741

O-Zn-Zn Theta0

16.9624

13.1467

Zn-O pbo1

-0.3421

-0.3673

O-Zn-Zn ka

30.3241

45.0979

Zn-O pbo2

5.4933

5.2095

O-Zn-Zn kb

0.2697

1.3975

O-Zn-Zn pv2

2.0000

2.5771

Zn-O Ediss

0.2744

0.2760

O-Zn-Zn pv3

3.0708

2.3771

Zn-O Rvdw

2.1414

2.1219

O-O-Zn Theta0

60.0000

57.5803

Zn-O alfa

9.7703

9.7288

O-O-Zn ka

20.0000

18.3690

Zn-O cov.r

1.9804

1.9721

O-O-Zn kb

0.5000

0.8863

O-O-Zn pv2

1.0000

1.9291



O-O-Zn pv3

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2.0000

0.8320

Table 1. parameters characterizing the difference between TA-FF and ND-FF.

Structure

DFT Coh. En.

TA-FF Coh. En.

ND-FF Coh. En.

(ZnO)2-a

-85.0

-150.0

-84.5

(ZnO)3-a

-114.1

-173.5

-112.9

(ZnO)4-a

-124.2

-180.5

-122.0

(ZnO)4-b

-109.0

-171.6

-108.6

(ZnO)5-a

-127.4

-182.1

-126.4

(ZnO)5-b

-115.6

-184.7

-119.3

(ZnO)6-a

-128.0

-182.7

-128.1

(ZnO)6-b

-122.2

-190.6

-123.6

(ZnO)7-a

-128.8

-182.8

-128.7

(ZnO)7-b

-123.6

-201.7

-128.8

(ZnO)8-a

-129.4

-195.6

-129.9

(ZnO)12-a

-136.4

-209.0

-134.9

(ZnO)24-a

-140.8

-216.1

-140.8

Wurtzite

-158.2

-251.0

-158.3

Table 2. Comparison between the cohesive energies predicted at DFT-GGA level (second column). Energies, per ZnO unit, are in Kcal/mol.

3.2. Identification of the energy GM (Global Minima)


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To check the transferability of TA-FF and ND-FF outside the TS and their structure prediction capability, the joint RMD-BH protocol was applied to identify the most representative low energy structures of (ZnO)N clusters with N=8, 12, 24, 36 and 48. The analysis of the results is focused on: (i) final DFT-energies after DFT-re-optimization of the geometries predicted at the ReaxFF level; (ii) structural characteristics, through R and  classification; (iii) number of “bulk” (wurtzite-like) coordination centres. Even though a (ZnO)8 was explicitly inserted in the TS, we performed a deeper investigation to disclose the motifs predicted for this cluster size by the two ReaxFFs and their energy ordering after DFT re-optimization. All the structures are shown in Figure 2.

Figure 2: The eight most stable structures predicted by the Reactive Molecular Dynamics – Basin Hopping (RMD-BH) calculations for (ZnO)8. Oxygen and zinc atoms are displayed in red and yellow, respectively.



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In this search, the (ZnO)8-d structure was singled out as the GM for ND-FF, whereas (ZnO)8-i was the GM for TA-FF. As expected, TA-FF predicts over-binding energies and a compact structure, whereas ND-FF stabilizes a low-coordination motif almost degenerate in energy with the (ZnO)8-a structure (that is the GM according to DFT-GGA) present in the TS. Re-optimization at the DFT level improves the agreement in the structural prediction between DFT and ND-FF. It should be noted that at the DFT level the (ZnO)8-a and (ZnO)8-d structures are almost degenerate, whereas the compact motif (ZnO)8-i is much higher in energy. From the point of view of the structural descriptors, ND-FF has the tendency to overestimate the average nearest-neighbour distances, which are, instead, well reproduced by TA-FF.

DFT

TA-FF

ND-FF

Structure Coh. Ene

Coh. Ene. Coh. Ene.

DFT

TA-FF

ND-FF

R-

R-

R-

(ZnO)8-b

-128.2

-193.7

-130.0

-

-

-

(ZnO)8-c

-125.0

-187.8

-129.4

-

-

-

(ZnO)8-d

-129.4

-196.1

-130.2

(ZnO)8-e

-123.0

-187.5

-129.1

-

-

-

(ZnO)8-f

-125.0

-187.4

-129.1

-

-

-

(ZnO)8-g

-121.4

-190.1

-128.8

-

-

-

(ZnO)8-h

-128.8

-183.0

-129.0

-

-

-

(ZnO)8-i

-126.7

-197.2

-127.5

-

-

-

(ZnO)12-a

-132.8

-199.1

-134.2

-

-

-

(ZnO)12-b

-132.3

-196.2

-134.0

-

-

-

(ZnO)12-c

-136.4

-209.2

-134.9

(ZnO)24-a

-140.5

-216.5

-140.6

1.87 – 108.3 1.86 – 112.0

1.93 – 108.9 1.91 – 109.8 -


-

1.93 – 106.5

2.01 – 109.8 -

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1.92 – 113.7 1.89 – 114.5

1.99 – 114.3

(ZnO)24-b

-140.8

-216.2

-140.8

(ZnO)24-c

-138.8

-216.3

-139.6

(ZnO)36-a

-142.3

-219.0

-142.8

(ZnO)36-b

-141.9

-220.3

-141.9

-

-

-

(ZnO)48-a

-142.2

-220.6

-144.2

-

-

-

(ZnO)48-b

-142.7

-222.8

-142.9

-

-

-

(ZnO)48-c

-143.7

-221.1

-144.1

-

-

1.91 – 114.7 1.89 – 115.2

1.91 – 115.8 1.88 – 116.2

1.99 – 115.1

1.98 – 116.2

Table 3. Energetical and structural data of the clusters reported in Figure 2-5. Energies, per ZnO unit, are in Kcal/mol. Bold face data refer to the most stable DFT structures of the considered clusters.

This tendency could be ascribed to the weak bias deriving from the present selection of the structures included in the TS in order to stabilize low-coordinated structures with respect to compact ones. As far as angles are concerned, ND-FF is in closer agreement with DFT data even though the structures predicted are slightly expanded.



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Figure 3: The three most stable structures predicted by Reactive Molecular Dynamics – Basin Hopping (RMD-BH) calculations for (ZnO)12. Oxygen and zinc atoms are displayed in red and yellow, respectively.

As it can be observed by inspecting the data in Table 3, in the case of N=12, both ReaxFFs predict the sodalite motif as the GM, well separated in energy from the other structural configurations (two of them are shown in Figure 3). This effect is due to the fact that N=12 is a “magic” size for the sodalite motif39. As far as structural analysis is concerned, ND-FF predicts an elongation of about 5%, whereas TA-FF a slight contraction of about 1%. The (ZnO)12-a motif can be classified as the evolution of (ZnO)8-a: the former can be viewed as the staggered stacking of two Zn6O6 hexagons, whereas the latter as the staggered stacking of two Zn4O4 squares. Both geometries can be thought as the embrions of tubular structures with different curvature radius.


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Figure 4. The three structures predicted by Reactive Molecular Dynamics – Basin Hopping (RMDBH) calculations for (ZnO)N with N=24 and N=36. Oxygen and zinc atoms are displayed in red and yellow, respectively.

For the N=24 size ND-FF identify the (ZnO)24-b configuration as the GM. Instead, the compact motif represented by the (ZnO)24-c configuration, where about 9% of the atoms are “internal” (i.e. characterized by coordination 4), is located at higher energy in agreement with DFT results. The (ZnO)24-a configuration, which is another cage with D2d symmetry, is located at a slightly higher energy with respect to the GM. Moving to TA-FF, it is found that the (ZnO)24-b structure is disfavored in relation to the compact structure, although the (ZnO)24-a cage configuration is stabilized. It could be speculated that the number of “internal” (or bulk) atoms that the structure can accommodate is not large, hence the extra-stability due to overbinding of the wurtzite-like atoms does not compensate the loss in surface energy associated to the creation of the compact structure. From a topologically point of view, the (ZnO)24-b structure is made of 8 (4 at north pole and 4 at south pole in staggered configuration) (ZnO)2 lozenges, whereas the lateral surface of the barrel contains a net of (ZnO)3 motifs. This structure could be viewed as the embryo of a nanotube with a perimeter of eight ZnO units. For N=36 the difference between TA-FF and ND-FF is clearer, as ND-FF stabilizes a low-symmetry cage configuration given by the (ZnO)36-a structure, whereas TA-FF the compact (ZnO)36-b structure, where 25% of the atoms are wurtzite-like, a much higher percentage in comparison to size 24 (see Figure 4 and Table 3). ND-FF is in agreement with DFT in stabilizing the surface motif, although we have to notice that the energy difference between the (ZnO)36-b and the (ZnO)36-a motif at the DFT level is 0.4 Kcal/mol per ZnO unit, which is about one half of the value at the ND-FF level. This is a first indication that the transition to “bulk” motif could be shifted to greater sizes at the ND-FF level with respect to DFT. This hypothesis is confirmed by the results for N=48. According to literature48, ACS Paragon Plus Environment


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a Td-symmetric structure should be the GM for (ZnO)36 , but this isomer was not identified by the search procedure. At size N=48 (structures shown in Figure 5), the DFT level predicted the (ZnO)48-c cage as the GM, in agreement with the literature48. Although at the ReaxFF level, ND-FF stabilizes this cage, it finds a slightly lower-energy structure (about 0.1 Kcal/mol per ZnO unit) represented by the (ZnO)48-a motif, which has some internal trigonally coordinated atoms. This could be viewed as the tendency of the ReaxFF to create a double-layer configuration, which is identified by Chen et al.49 as the lowestenergy structural motif for clusters with diameters between 1.2 and 1.6 nm. On the other hand, TAFF predicts the compact (ZnO)48-b structure as the GM (where the percentage of wurtzite-like atoms is raised to about 32%). Re-optimizing the structures at the DFT level it turned out that (ZnO)48-a has a higher energy than (ZnO)48-b, showing that the presence of some internal low-coordinated atoms found by ND-FF is not energetically convenient at the DFT level for this cluster size. The (ZnO)48-c cage is recognized by TA-FF as a high-energy isomer (about 1.7 Kcal/mol per ZnO unit), confirming that cage motifs are not well described by this parametrization.

Figure 5. The three most stable structures predicted by Reactive Molecular Dynamics – Basin Hopping (RMD-BH) calculations for (ZnO)48. Oxygen and zinc atoms are displayed in red and yellow, respectively.


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3.3. Nucleation and growth in low temperature plasma conditions By means of RMD simulations based on ND-FF we have studied inception time and stoichiometry (O/Zn ratio) of ZnO NPs grown in a plasma conditions. The inception time was defined as the minimum time at which a particle of definite size is found in the simulation box. A number of calculations were performed to analyse the dependence of inception times on: (i) dimension of the simulation box; (ii) force field parametrization; (ii) reactor temperature; (iii) composition of the gasphase; (iv) dimension of the starting building blocks (Zn atoms, ZnO monomer, (ZnO) 2 dimer). The first two points concern only the numerical modelling, whereas the other three are real physical parameters related to the experimental synthesis procedure. All the simulations were performed with ND-FF, except a few cases where also TA-FF was tested for comparison.

3.3.1. High-T reaction zone The simulations conditions, temperature of 1200 K and pressure of 20 atm, were suggested by our experimental partners (Daniel Nurkowski, personal communication, 5 October 2018) on the basis of their experience and are consistent with data found in the literature71,72. A typical composition of the gas inside a plasma reactor is: Zn 461 mol/hour; O2 4014 mol/hour and N2 1067 mol/hour; Zn reaches the reaction chamber in atomic form and becomes oxidized (in a strongly oxidizing environment) giving rise to the formation of ZnO NPs. In order to derive inception time curves and average stoichiometry of the growing particles in the reaction zone, two simulation protocols differing only in the dimension of the unit cell, were used. More specifically: Simulation R1: the model system consists of a cubic cell with an edge length of 320 Angstrom, containing 4000 gas-phase molecular species, namely 320 Zn atoms, 2880 O2 molecules and 800 N2 molecules corresponding to a total pressure of 20 atm at the fixed temperature of 1200 K for the



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sampling of the NVT ensemble. Two simulations were performed with different random starting configurations, in order to statistically reinforce the obtained growth rates. The total simulation time was about 10 ns with a time step of 0.50 fs.


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Figure 6. inception time (left) and average stoichiometry (right) of the ZnO nanoparticles obtained by R1 and R2 Reactive Molecular Dynamics (RMD) simulations; see text for details. Total cluster dimension refers to the total number of atoms that form the cluster. Simulation R2: same conditions as R1, but using a larger cubic cell with an edge length of 434 Å, containing 10000 molecular species, namely 800 Zn atoms, 7200 O2 molecules and 2000 N2 molecules. For this system simulations at 600 K, 800 K, 1000 K, 1200 K and 1400 K were carried out. Apart from mimicking nucleation and growth in the plasma reaction zone, a comparison between the results of R1 and R2 are useful to appreciate the dependence of the estimated growth rate on dimension of the unit cell and temperature of the reactor chamber. As already observed in our previous study on Si nanoparticles growth66, the inception time of a nanoparticle can be affected by large statistical oscillations (especially for large particles), so that averaging on several simulations is a mandatory procedure to obtain smooth curves relating inception time to particle size. The results of R1 and R2, at different temperatures, are shown in the panels of Figure 6. As it can be observed, the curves of the inception times in Figures 6a, 6c and of the average stoichiometry in Figures 6b, 6d are quite independent of the choice of the starting configuration of the gas-phase molecules in the simulation box. Furthermore, the curves obtained employing the smaller (R1, Figures 6a, 6b) and larger (R2, Figures 6c, 6d) cell are not distinguishable (see also the comparison in Figures 6e, 6f), demonstrating that the R1 model is already at convergence with respect to the size of the simulation box. Inspecting Figure 6f we can see that for both R1 and R2 the average stoichiometry initially passes through values around 2.0-2.2, indicating a strong initial tendency of oxygen to molecularly adsorb on bare zinc atoms in the cell; this transient “oxidizing” phase is quickly lost and, already after about 1 ns of simulation, average stoichiometry converges towards values not far from an O/Zn ratio of 1. In order to understand the dependence of the inception time curves and average stoichiometry on the reactor temperature, we performed a screening over 5 different ACS Paragon Plus Environment


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temperatures between 600 K and 1400 K: the results of these simulations are summarized in the plots of Figures 6g-6h and 7a-7b. By looking at the average stoichiometry of the growing particles in Figure 6h, we can see that at T=600 K, its value converges towards about 1.5, due to the high number of undissociated oxygen molecules inside the particles or on their surfaces. By increasing the temperature, the average stoichiometry of the particles decreases and reaches an asymptotic value around 1 in the case of the highest temperature (T=1400 K). This finding is in line with the tendency of an oxide to form more reduced phases73 as the temperature increases, due to the entropic stabilization which accompanies the release of gas-phase molecular oxygen.

. Figure 7. Number of (a) bare Zn atoms and (b) ZnO dimers as a function of time for simulation at different temperatures.

On the other hand, by inspecting Figure 6g, we can observe that the inception time curve, at any temperature, has the same trend: an initial strong steepness (jump) followed by a linear regime, whose slope is roughly proportional to the temperature of the simulation. In the case of ZnO the inception time curves are characterized not only by an initial jump, but also by the change of its height in connection with the temperature (monotonical correlation). We have identified two regions corresponding to: the nucleation regime (region interested by the jump) and to the growth regime (linear relation between size and simulation time). The presence of the jump suggests that, before the on-set of the growth regime, there is a period of latency during which particles do not appreciably ACS Paragon Plus Environment

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grow. For example, in the case of T=1400 K this latency was around 3 ns, whereas for T=800 K was around 1 ns. To understand what happens during the latency period, we plotted the number of unreacted (bare) Zn atoms in the simulation box at different temperatures, see Figure 7a. At lower temperature, T=600 K, 90% of the bare Zn atoms disappear in about 0.5 ns, whereas at T=1400 K, the disappearance of 90% of the bare Zn atoms takes about 5 ns. Reactivity at higher temperature is hindered by the stronger thermal motion of the system, and if we add this information to the inception time curve profiles, we conclude that the on-set of the growth mode takes place only after that the majority of the bare Zn atoms have disappeared from the box. A further confirmation comes from the evolution in the number of ZnO dimers plotted in Figure 7b: at T=1400 K we see that the number of ZnO dimers grows until 3 ns and then slowly decreases (in favour of the larger sizes), suggesting that the growth regime has been activated at about 3 ns, in agreement with the values shown in the curve of Fig 6g. The same analysis applies to the other temperatures proving that the system goes through the oxidization of the bare Zn atoms before the particle grows. If the oxidation step takes more time, the on-set of the growth mode is delayed until the majority of the bare metal atoms have reacted with oxygen. It should be remarked that the present use of terms “nucleation” and “growth” is different from that used within the Classical Nucleation Theory (CNT)74 which distinguishes between a nucleation and a growth regime depending on the balancing, for a growing spherical aggregate, between surface and bulk free energy, having opposite size and different dependence on the aggregate radius. According to CNT a critical size exists, as smaller aggregates (with respect to this critical size) are unable to growth due to an excess of the former quantity over the latter. CNT makes the hypothesis of a system in which a thermodynamic equilibrium between a gas and a liquid phase exists. In the present simulations, which describe the dynamics of a non-equilibrium gas-phase system, the two terms have a different meaning according to our discussion.



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3.3.2. Low-T quenching (or coagulation) zone The average temperature and pressure of the low-T quenching zone of the plasma reactor were fixed at 800 K and 20 atm, following the indications of our experimental partners (Daniel Nurkowski, personal communication, 5 October 2018) . A typical composition of the gas flux present in this region of the reactor can be considered: ZnO about 500 mol/hour and a total of 450000 mol/hour among O2 and N2. In the quenching zone the second step of the synthesis of zinc oxide nanoparticles is realized. In absence of experimental information on the nature and size of the particles in this region, we have assumed that atomic Zn is fully exhausted and considered (ZnO)N units as starting blocks for the simulation. Four different simulation protocols have been adopted, differing for the dimension of the starting building blocks and for the composition of the quenching gas; more specifically: Simulation C1: cubic cell of 434 Å in size, containing 10000 molecular species divided in: 800 ZnO units, 7200 O2 molecules and 2000 N2 molecules, corresponding, at the fixed temperature of 800 K, to a total pressure of 20 atm and a strongly oxidizing environment; four simulations, with a total time of about 5 ns, of the NVT ensemble were performed with different random starting configurations, in order to statistically reinforce the obtained estimation of growth rates. Simulation C2: same conditions as C1, but using the following composition: 800 ZnO units, no O2 molecules and 9200 N2 molecules: this choice represents a non-reactive environment, where the buffer gas has mainly a quenching effect during ZnO particles growth. Simulation C3: same conditions as C1, but using the following composition: 800 (ZnO)2 units (dimers), 7200 O2 molecules and 2000 N2 molecules. Simulation C4: same conditions as C2, but using the following composition: 800 (ZnO)2 units, no O2 molecules and 9200 N2 molecules.


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Inception times and average stoichiometry of the obtained ZnO nanoparticles were derived for the four models here investigated for the quenching zone. The comparison between C1 and C2 aims at investigating growth rates and stoichiometry of the obtained particles in a much oxidative environment (C1) with respect to a non-reactive one (C2). The comparison between C1 and C3 (as between C2 and C4) aims at investigating the effect of the dimension of the starting units on growth rates and stoichiometry. The results of the quenching zone simulations are shown in the panels of Figure 8.



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Figure 8. inception times and average stoichiometry of the quenching region simulations.

The comparison of inception time curves in Figures 6 and 8 show a clear difference between the results of the simulations for the reactive and the quenching region. As previously discussed, the reaction zone is characterized by a nucleation regime, during which priority is given to the oxidation of bare Zn atoms, followed by a growth regime, whereas in the quenching zone only the growth regime is observed. This is not surprising, as, in the quenching zone, the starting building blocks are fully oxidized ZnO particles and the system does not show any latency time to complete the oxidation of the bare metallic species. As a confirmation, we can observe that a cluster of size 100 at T=800 K takes about 4 ns to be formed in the reaction zone and about 3 ns in the quenching zone: we can ascribe this “delay” in the reaction zone to the latency time due to the oxidation of the bare Zn atoms. This interpretation agrees with the curve in Figure 7b: the number of dimers in the simulation of the reaction region at T=800 K, in fact, starts decreasing after 1 ns, indicating that the on-set of the growth mode takes place about after 1 ns. This picture is further confirmed by the small difference, see Figure ACS Paragon Plus Environment

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8a, observed among the inception time curves obtained by the C1 and C2 simulations (reactive vs non-reactive environment). As only a growth regime, driven by the aggregation of ZnO units, is present in the quenching zone and zinc is already oxidized, we can expect that an oxidative environment plays a minor role in particle growth. The difference between the two environments is instead more evident when considering the stoichiometry of the growing particles, as in oxidative environment, nanoparticles result richer in oxygen (see Figure 8b); when molecular oxygen is not present (C2), on the other hand, a very small variation in oxygen content of the particles is observed during the simulation. A remarkable difference in the inception time curves is observed when, instead of starting from ZnO units, we start from (ZnO)2 units, in both reactive and non-reactive environments (see Figures 8c, 8e); in fact, by increasing the dimension of the starting blocks, we boost the growth process and we reduce (by a factor of 2-3) the inception time. An interesting effect on the stoichiometry in reactive environment can be observed in Figure 8d: when starting from ZnO units, an initial enrichment in oxygen content is observed, enhancement which is quickly lost during the particle growth; when we start from (ZnO)2 units this enrichment is not observed, confirming that smaller units are more reactive towards oxygen. Nevertheless, the final plateau values of the average stoichiometry are rather similar in the two cases (differences around 1%), indicating that this “history” effect is quickly lost as growth proceeds. In the case of unreactive environment (see Figure 8f), differences in the stoichiometry evolution are small, confirming that, as could be expected, the nitrogen buffer gas does not play a role in changing particle composition during the growth process. Finally, we show in Figures 8g-8h, a comparison of the results obtained by C4 simulations carried out by employing the two here considered reactive force fields: TA-FF and ND-FF. We can see that the use of TA-FF, although predicting energy overbinding in the growing particles, does not determine a relevant quantitative difference in the inception times (especially looking at the slope in ACS Paragon Plus Environment


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the region of sizes below 40 atoms, where statistical oscillations are smaller). Also the effects on the stoichiometry are very small: the flat line that we observe in the stoichiometry profile during growth associated to the use of TA-FF is probably related to the energy overbinding. In fact, as larger energies (with respect to ND-FF) are requested to break chemical bonds, and no oxygen addition is possible in the unreactive environment, particle growth proceeds via cluster aggregation without any ripening and stoichiometry results unaltered.

4. Conclusions The early stage of nucleation and growth of zinc oxide nanoparticles, in specific conditions related to the industrial production in plasma reactors, have been studied by applying a multi-scale computational approach, joining first-principles DFT-GGA calculations on small (ZnO)N clusters and RMD simulations. Starting from an existent literature parametrization (TA-FF46), a new refined parametrization (ND-FF) of the force field for ZnO has been achieved and applied to single out GMs and, more in general, low-energy structures of (ZnO)N clusters with N in the range from 8 to 48 which have been identified as possible seeds of NP formation. By performing DFT re-optimization on the structures predicted at the ReaxFF level, the prediction power of ND-FF has been tested, confirming an accurate estimate of the cohesive energies of all the considered ZnO clusters. By using RMD, nucleation and growth of ZnO nanoparticles have been investigated by simulating the early steps of the synthesis process in two different regions of a plasma reactor. Inception time and average stoichiometry curves have been derived from all the simulations and discussed in terms of dependence by several variables. These included “computational” parameters: extension and composition of the model system, statistical sampling, parametrization of the force field, as well as “physical” parameters: composition of the gas-phase, dimension of the ZnO building blocks and temperature. The analysis of the dynamics in the reaction and quenching regions have shed light on new mechanisms ruling the nucleation and growth of ZnO NPs: in presence of bare Zn atoms, as it happens ACS Paragon Plus Environment

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in the higher-T reaction zone, priority is given to the oxidation of the latter species, and only after that a large portion of the metallic atoms have been oxidized, the growth regime is activated. The procedures we have developed could be conveniently extended to other ionic oxides and used to derive important information on the gas-phase synthesis of nanoparticles with technological relevance in the fields of oxide-based materials.

ACKNOWLEDGMENTS This work has been developed as part of the European project Nanodome that has received funding from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement number 646121. The authors thank A.C.T Van Duin for providing the serial version of the ReaxFF program.

Supporting Information Parameters of the Reax force field for ZnO clusters.

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For Table of Contents use only

Modelling Nucleation and Growth of ZnO Nanoparticles in a Low Temperature Plasma by Reactive Dynamics Giovanni Barcaro, Susanna Monti, Luca Sementa and Vincenzo Carravetta


Modelling Nucleation and Growth of ZnO Nanoparticles in a Low

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