Size-Dependent Energetics and Thermodynamic Modeling of ZnO Nanoparticles produced by Electrical Wire Explosion Technique

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ScienceDirect Materials Today: Proceedings 5 (2018) 17293–17303

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AMPCO-2017

Size-Dependent Energetics and Thermodynamic Modeling of ZnO Nanoparticles produced by Electrical Wire Explosion Technique Santhosh Kumar Laxmanappaa, Rengaswamy Jayaganthanb,*, Satyanarayanan R Chakravarthya, Ramanujam Sarathic a

National Centre for Combustion Research and Development, Department of Aerospace Engineering, IIT Madras, Chennai-600036, India b Department of Engineering Design, IIT Madras, Chennai-600036, India c High Voltage Laboratory, Department of Electrical Engineering, IIT Madras, Chennai-600036, India

Abstract Zinc Oxide nanoparticles were produced by the electrical wire explosion technique (EWET) by exploding zinc conductor in oxygen ambience and the transmission electron microscopy confirmed that the particle size distribution followed lognormal distribution with both spherical and non-spherical morphology. The mean particle size of the samples skewed to the lower particle size with the increased energy ratio and decreased pressure. The size dependent thermodynamic model was formulated to predict the optimum process conditions in EWET for the production of uniformly distributed ZnO nanoparticles. High energy ratio and high saturation ratio were identified as ideal process conditions for producing ZnO nanoparticles by WEP. The enthalpy of formation of ZnO nanoparticles was found to be size-dependent and decreased with particle size reduction. The reduction in lattice energy observed was because of the increased number of dangling bonds. The computational results proved that the nucleation rate of ZnO nanoparticles increased with the increasing saturation ratio, which is experimentally justified by the reduction in particle size with increased energy deposition. The model predicts that the activation Gibbs free energy of nucleation of ZnO nanoparticles decreases with the increasing temperature and saturation ratio, which is substantiated by the particle size reduction at higher energy ratios. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Advances in Materials & Processing: Challenges & Opportunities (AMPCO-2017). Keywords: Nanoparticles; quantum confinement; wide band-gap; size effect; lattice energy; characterization; thermodynamic modeling; energy ratio; saturation ratio; nucleation rate; activation energy

* Corresponding author. Tel.: +91-44-2257-4735; fax: +91-44-2257-4735. E-mail address: [email protected] 2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Advances in Materials & Processing: Challenges & Opportunities (AMPCO-2017).

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1. Introduction Nanoparticles exhibit the characteristic features that are intermediate between the properties of their atomic constituents and bulk counterparts. The properties of the nanostructured materials can be fine-tuned to the requirements of the application by controlling the particle shape, size, composition and their size distribution. Because of the size-dependent novel properties and applications metal-oxide nanoparticles have gained prominence in the recent years. The beneficial properties of oxide nanopowders are the interest of advanced ceramic industry. ZnO nanoparticles are one among them because of their piezoelectric and dual semiconducting properties. ZnO normally exhibits hexagonal wurtzite, cubic zinc blende and cubic rock-salt structures. Hexagonal wurtzite is the thermodynamically stable crystal structure of ZnO at ambient temperature [1]. ZnO exhibits an exciton binding energy of 60meV and a band-gap of 3.37eV at room temperature [2] which makes it a wide band-gap semiconductor. It has emerged as one of the major photocatalysts in the field of green photocatalysis due to its distinctive photocatalytic activity and near UV-spectrum band-gap [3]. Because of quantum confinement, ZnO experiences a quantum size effect which increases its band-gap energy [4] and the band-gap of ZnO nanoparticles is also size dependent [5]. Based on these significant characteristics, an extensive study has been made to synthesize and characterize ZnO nanostructures. There are various chemical and physical routes that could be used to produce ZnO nanostructures. The direct route of producing ZnO is by heating fine Zn-powder in oxygen [6, 7]. The indirect synthesizing routes are carbothermal method [8] and vapour phase epitaxy [9]. Z.L. Wang's group synthesized ZnO nanorods on a single crystal substrate of ZnO, catalyzed by Sn [10]. Turner et al synthesized highly crystalline ZnO nanoparticles with narrow size distribution using spray pyrolysis [11]. Most of these methods involve expensive precursors, single crystals, high temperature and costly equipment and hence there exists a demand for economically feasible methods for producing ZnO nanostructures. The literature on thermodynamic analysis of process parameters involved in EWET is scarce. Therefore, the present work is focused to produce ZnO nanoparticles by exploding zinc wire in oxygen and characterizing through experimental and thermodynamic analysis. 2. Experimental Studies The basic electrical circuit for the electrical wire exploding setup used for synthesizing ZnO nanoparticles is shown in Figure 1. Sarathi et al., have explained the experimental setup in detail [12]. It is essential to deposit energy on the exploding conductor which is more than vaporization energy of its material. By the electrical wire explosion technique, it is possible to produce nanoparticles of metal, metal-oxides, carbides and nitrides in one step [13].

Fig. 1. Experimental setup of the electrical wire explosion process.

The amount of energy deposited aided by the proper control of ambient pressure dictates the size of the particle in EWET. The process parameter details used for synthesizing ZnO nanoparticles are provided in Table 1. The circuit current and its duration is decided by the inductance and resistance of the explosion circuit. A current probe (Model No-101, Pearson Electronics, USA) and a voltage probe (EP-50k, PEEC. A, Japan) were used to measure the current

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flow and voltage across the thin zinc wire R, respectively. The characteristic current and voltage waveforms during the wire explosion are as shown in the Figure 2.

Fig. 2. Voltage and current waveforms during the explosion. Table 1. Process parameters used in wire explosion. Process Parameters Material Length of the wire Diameter of the wire Charging voltage Capacitance Oxygen pressure

Values Zinc 100 mm 0.5 mm 14, 20, 24 kV 3 F 25, 150 kPa

In the present work, X-ray diffraction analysis was carried out by Bruker D8 diffractometer using Cu-Kα radiation of wavelength of 1.5425Å, at a scan rate of 90/min. Rietveld refinement was applied to analyze the XRD data using PANalytical X'pert High score plus software. The transmission electron microscopy (TEM) was done to analyze the particle morphology and their size distribution using Philips CM12 TEM. Scanning electron microscopy (SEM) was performed by using FEI Quanta FEG 200 attached with an energy dispersive analysis of X-rays (EDAX) module, to determine surface features and the elemental composition. BET analysis is done to calculate the specific surface area of the ZnO-nanopowder produced by explosion, using Micromeritics, ASAP 2020 V3.00 H Porosimeter. 3. Size-Dependent Thermodynamic Model Nanoparticle formation by wire explosion technique is a very complex phenomenon wherein, controlling various process parameters governs tailoring the nanoparticles precisely. Various complex and codependent process parameters that are crucial in controlling the nanoparticle shape, size and size distribution could be understood quite easily by thermodynamic modelling studies, which is one of the important objectives of the present study. In the present study, it is assumed that the reaction takes place in gaseous phase resulting in product-nanoparticles. The sequential phase changes, dissociation, ionization and recombination reactions are explained by using the BornHaber cycle. Also, the influence of dangling bonds and surface area on various thermodynamic parameters is explained. 3.1. Reaction Mechanism The formation reaction mechanism of ZnO nanoparticles can be understood using the Born-Haber cycle. The Born-Haber cycle shows the sequential reactions of phase changes, atomic bond dissociation, ionization, recombination and oxide nanoparticle formation in a closed loop as shown in Figure 3. Hess's law can be applied to this cycle, to calculate the energetics of various reactions occurring in the reaction loop.

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The standard formation reaction of ZnO with Zn and O2 reacting in their standard states is represented as

1 Zn(s)  O2 ( g )  ZnO(s) : H 0f , ZnO  365.46  0.27kJ / mol 2

(1)

Due to explosion, Zn changes its state from solid to vapour or ions depending on the level of energy deposited on the Zn conductor. A completely ionized cloud of Zn-ions will form only when the energy deposited (W) on the Zn wire is very high. In such a condition, the Zn2+ ions react with O2- ions to form homogenized (non-core-shell) ZnO nanoparticles with an enthalpy contribution termed as lattice energy (LE). The ionic reaction is written as

Zn2 ( g )  O 2 ( g )  ZnO(s) : H f , ZnO  LE  4041.5344kJ / mol

(2)

Calculated amount of electrical energy is deposited on a thin Zn conductor of diameter 0.5 mm in an ambience of oxygen, which leads to the vaporization of the Zn wire, consequently forming ZnO nanoparticles upon solidification. Depending on the magnitude of energy deposited on Zn wire, either partially ionized or completely ionized plasma will result. The lattice energy and the cohesive energy involved in the reaction cycle are incorporated in the Figure 3 and graphically elaborated in the Figure 4. The cohesive energy is the energy required in isolating the constituent atoms of a solid whereas the size dependent cohesive energy (SDCE) is the amount of energy required to break the solid into small particles of required size. The energy required to completely isolate the constituent ions from an ionic crystalline solid is the lattice energy. The energy released during the formation of nanoparticles of the ionic solid by the reaction of its constituent ions is called as the size dependent lattice energy (SDLE). The energy deposited (W) on the Zn wire is measured relative to its sublimation energy (Ws) and their ratio is termed as the energy ratio (k=W/Ws). We coin a new term, plasmization ratio (k') which is the ratio of energy deposited and the lattice energy i.e., k'=W/LE. According to the Born-Haber cycle, for a lower energy deposition, the nano-ZnO particle formation reaction takes place in three phases: (i) formation of zinc vapour (ii) reaction of zinc vapour with molecular oxygen to form

Fig. 3. Born-Haber cycle for synthesizing ZnO nanoparticles.

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Fig. 4. Energy diagram showing (a) SDCE of Zn and (b) SDLE of ZnO.

gaseous product and (iii) nucleation and growth of ZnO nanoparticles. When the condition k=1 is met, the Zn vapour reacts stoichiometrically with the molecular oxygen in the chamber to producing the gaseous ZnO and no Zn ions are formed because the energy deposited is only sufficient to sublimate zinc. As a result, the kinetics of the reactions is slower which leads to the production of coarser ZnO nanoparticles. Due to low thermal diffusivity of Zn atoms aided by sluggish kinetics also leads to the formation of Zn nanoparticles along with ZnO nanoparticles. The manner of reaction to synthesize ZnO nanoparticles changes, when the energy deposited increases. When the energy ratio of explosion is increased such that k>1, then the ZnO nanoparticle formation reaction proceeds in the sequence of following phases: (i) formation of partially ionized plasma of Zn and O2 (ii) reaction between partially ionized Zn and O2 to generating product plasma and (iii) condensation, nucleation and growth of ZnO nanoparticles. When the energy deposited is such that, 1
LE  Ws Zn   ZnO

(3) 2

Where,

1 2

2

ZnO  H 0f , ZnO   ( IEi ) Zn  ( BDE)O   ( EAj )O i 1

2

(4)

j 1

Here, IEi is the ionization energy of the ith oxidation state of Zn, EAj is the electron affinity of the jth reduction state of atomic oxygen and BDE is the bond dissociation energy of molecular oxygen. Now, the expressions for energy ratio (k) and plasmization ratio (k') can be written respectively as

k

W W  Ws LE   ZnO

(5)

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and

k' 

W W  LE (Ws ) ZnO   ZnO

(6)

The Hess's diagram shown in Fig. 4 shows the energetics of ZnO nanoparticle formation when k=1. The ZnO vapors tend to decrease the free energy of the system by forming surfaces i.e., by condensing into droplets and eventually as nanoparticles. The equilibrium state of ZnO is dictated by the explosion chamber pressure, quenching rate and agglomeration factor. Applying the Hess's law for the formation of bulk ZnO (reaction path in green), we derive the equation as

H rxn, gas,bulk  H 0f , ZnO  (Ws ) Zn

(7)

where, ΔH0rxn,bulk=ΔH0f,ZnO. By applying Hess's law to the formation of ZnO nanoparticles, the enthalpy equation becomes

H rxn, gas,nano  H 0f , ZnO  SDLEZnO  (Ws ) Zn

(8)

However, considering the size effect and agglomeration factor, additional parameters should be incorporated into this equation. The first compensation parameter termed size ratio (Ψ) which is the ratio of the reactant size and the product size. The second compensation parameter δ signifies the extent of agglomeration. Incorporating the two compensation factors Eq. (8) becomes

H rxn, gas,nano  H rxn, gas,bulk  SDLEZnO  (Ws ) Zn

(9)

3.3. Size-dependent enthalpy of formation of ZnO For a binary nanocompound ZnO, the formation enthalpy is size dependent. The size dependent formation enthalpy for ZnO can be written as [14]

 dcf H 0f ,ZnO (d )  H 0f ,ZnO .1   d d cf 

  2S d cf . exp  f ,ZnO   3R d  d cf  

   

(10)

where, R=8.314 J/(mol-K), Sf,ZnO is the configurational entropy, d is the nanoparticle size and dcf is the half bond length of ZnO molecule which can be written as

S f , ZnO   R( xZn . ln xZn  xO . ln xO ) d cf 

d Zn  d O 4

(11)

(12)

It is lucid from the Eq. (10) that the formation enthalpy decreases with the nanoparticle size. 3.4. Size-dependent cohesive energy Being one of the decisive thermo-physical quantities, cohesive energy signifies the thermal stability parameters such as melting point and enthalpy of fusion of materials. The melting point as a function of cohesive energy also

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Fig. 5. Hess's diagram showing the formation reactions of ZnO nanoparticles.

decreases with the reduction in the particle size. In the present work, we have adopted Nanda's liquid droplet model [15] which is a bond geometry based model. The SDCE (av,d) equation as per which is

1 1 av,d , ZnOnp  av,d , Zn  av,d ,O 2 2

(13)

where, av,d,i is the size dependent lattice energy of the ith species. The simplified expression for SDLE of ZnO nanoparticle is,

  d  dO av , d , ZnOnp  av 1  0.26795 Zn  d  p 

   

(14)

Here, av is the bulk lattice energy of ZnO. It is evident from the Eq. (15) that the SDLE of ZnO decreases with the nanoparticle size. 3.5. Activation energy and nucleation rate of ZnO nanoparticles For a miniscule nucleus the surface free energy dominates the volume free energy resulting in an activation barrier (ΔG*) for nucleation. When the system is supersaturated, the chemical potential becomes negative which drives nucleation and eventually crystallization. The activation energy of the nucleus of critical radius is

4rc2 ZnO G (rc )  3 *

(15)

and the critical size of the nucleus is written as

rc 

2 ZnO RT . ln(S )

(16)

The formation of ZnO nanoparticles begins by homogeneous nucleation followed by growth. The classical nucleation theory is adopted for determining the nucleation rate of ZnO. Assuming the product ZnO gas as an ideal gas, the expression for nucleation rate is written as

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 PZn  PO2 J 0    kT

2

2   16 3 vZnO  2 ZnO  . .vZnO . exp 3 2 M   3kT  ln S  

(17)

where, M is the molecular weight of ZnO and k is the Boltzmann constant. The total pressure of the gaseous product ZnO is the sum of the partial pressures of Zn vapor (PZnO) and oxygen (PO2). It is evident from the equation that the rate of nucleation increases with the increasing supersaturation. 4. Results and Discussion Figure 6a shows the X-ray diffractograms of ZnO nanoparticles produced at different energy levels and pressures. The details of the experimental conditions are provided in Table 2. Table 2. Experimental conditions ZnO Sample code

Pressure (kPa)

Energy ratio (k)

3Zn25 3Zn150 1Zn150

25 150 150

3 3 1

It is clear that, at k= 3 no zinc peaks are present which indicates that purity of ZnO nanoparticles increases with the energy ratio. The inset image in Figure 6a shows broadening of the most intense peak with the increasing energy ratio and decreasing pressure, which can also be attributed to particle size reduction apart from instrumental and strain broadening and the same is substantiated by the reduced mean particle size of the lognormal distribution. Figure 6b, the SEM micrograph of ZnO nanoparticles shows that the particles are not uniformly spherical in shape. The EDAX analysis shows that oxygen content in the sample increases with the increase in energy.

Fig. 6. (a) XRD results of ZnO nanoparticles produced at various pressures and energy ratios and (b) SEM and EDAX results of synthesized ZnO nanoparticles.

Figure 7a shows the TEM micrographs of the ZnO nanoparticles, which confirms the particles possess varied shapes (both spherical and non-spherical). The nanoparticle size distribution follows a lognormal distribution with the mean particle size shifting towards the lower dimensions with the increase in energy ratio, as shown in Figure 7b. It is indicative from Figure 8a that the size dependent heat of reaction decreases with the increase in agglomeration factor and the reason for which is the reduction in the surface area due to agglomeration. Figure 8b illustrates that the exothermicity of the reaction decreases with the decreasing particle. The decrease in the reaction enthalpy is due to the dominance of SDLE of ZnO compared to the SDCE of Zn.

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Fig. 7. (a) TEM images of ZnO nanoparticles synthesized at various pressures and k values and (b) lognormal particle size distribution of ZnO nanoparticles.

Fig. 8. (a) Heat of reaction as a function of particle size and SDLE (b) exothermicity dependence on particle size.

Fig. 9 shows the variation of SDLE of ZnO with the particle size and the size factor. It is clear that the SDLE of ZnO decreases with the decrease in particle size which can be attributed to the increased dangling bonds.

Fig. 9. SDLE as a function of particle size and size factor (ε).

It can be shown from Figure 10a that the nucleation rate of ZnO particles increases with the increasing saturation ratio. Figure 10b infers that, higher the temperature higher is the initial nucleation rate. Figure 11a shows the computational results of activation energy for nucleation at various temperatures and makes evident that the activation energy of nucleation decreases with the increase in reaction temperature and speeds up the nucleation process. Figure 11b illustrates the computational results of activation free energy at various saturation ratios. It can

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be concluded from Figure 11b that the increasing saturation ratio decreases the activation energy barrier and the critical radii of the nuclei which consequently increases the nucleation growth rates

Fig. 10. (a) Nucleation rate of ZnO with varying temperature at saturation ratios 1.25, 2 and 3 (b) 3 dimensional plot of variation nucleation rate of ZnO with temperature and saturation ratio.

Fig. 11. Gibbs free energy of nucleation (a) at different temperatures and (b) at different saturation ratios.

5. Conclusion Both spherical and non-spherical ZnO nanoparticles are successfully synthesized by electrical wire explosion technique by varying the pressure at different levels of energy, which follow a lognormal distribution. The size dependent thermodynamic model has been formulated to predict the optimum process parameters and high energy and saturation ratios are identified as ideal conditions for synthesizing the ZnO nanoparticles by EWET. The computational results prove that the nucleation rate of ZnO nanoparticles increases with the increase in saturation ratio which is experimentally justified by TEM. The model predicted that the activation energy barrier for nucleation decreases with the increasing energy ratios. The mean particle size shifted to the lower particle dimensions with the increase in energy ratio and the decrease in pressure. Acknowledgement This work has been supported by the National Centre for Combustion Research and Development (NCCRD), Department of Aerospace Engineering, Indian Institute of Technology (IIT) Madras, Chennai-600036, India.

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