The effect of activity coefficient on growth control of ZnO nanoparticles

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Phys. Scr. 83 (2011) 015801 (8pp) doi:10.1088/0031-8949/83/01/015801

The effect of activity coefficient ongrowth control of ZnO nanoparticles

AsiehSadat Kazemi1, Seyed Ahmad Ketabi2, Mohamad MehdiBagheri-Mohagheghi2 and Mohamadreza Abadyan3

1 Engineering Department, Islamic Azad University, Bojnourd Branch, Bojnourd, Iran2 School of Physics and Center for Solid State Research, Damghan University, Damghan, Iran3 Mechanical Engineering Group, Islamic Azad University, Ramsar branch, Ramsar, Iran

E-mail: abadyan@yahoo.com

Received 5 August 2010Accepted for publication 9 November 2010Published 8 December 2010Online at stacks.iop.org/PhysScr/83/015801

AbstractIn this paper, the relative importance of effective parameters such as the activity coefficient,thermal decomposition and pH of chemical additives is investigated on the control procedureof ZnO nanoparticle growth. It is found that the activity coefficient is of greater importancecompared with other parameters and should not be neglected in nanosynthesis any longer. Thiseffect of activity coefficient of additives may also improve the fabrication and properties ofother applicable nanostructures.

PACS numbers: 81.07.−b, 78.67.Bf, 78.40.Fy

(Some figures in this article are in colour only in the electronic version.)

1. Introduction

In semiconductors, a change in particle size modifies theband gap value, which is the key factor in determiningoptical properties [1]. ZnO as a semiconductor has promisingpotential for a broad range of high-tech applications suchas field emission, UV light-emitting diodes, photodiodes,surface acoustic wave filters, optical modulator waveguidesand blue region optoelectronic applications [2–4]. It is alsoan important material in pH meters and resonators for micro-electromechanical systems [5]. ZnO can be used as a windowmaterial and a transparent electrode in different types ofsolar cells [6]. The tunability of the properties of ZnOwith the particle size could also be used in formulatingnew composite materials with optimized properties [7].The formation of ZnO nanoparticles proceeds step bystep from crystalline/amorphous seeds to larger particulates.Achieving mono-disperse nanoparticles requires the seedformation/nucleation rate to be higher than the growth rate [8].Therefore, controlling the rate of nucleation and growth rateof particles is of great importance in nanosynthesis. So far,size control of some nanoparticles has been investigated usinga variety of techniques such as supersaturating control andcontrol using dendrimers, co-sputtered materials or polymer

capping agents [9–12]. The polymer blend technique wasused by Saujanya et al [13] to control the nanoparticlesize of fillers. The effect of solvents on ZnO nanoparticlesize was investigated by Kanade et al [14]. The effectsof decomposition temperature, pH and activity coefficientof complexing agents on the control procedure of ZnOnanoparticles were investigated in [15]. But the relativeimportance of the effective parameters on controlling the sizeis not clear so far.

Herein, we have fabricated ZnO nanoparticles usingthe modified hydrolysis method that has the advantagesof simple equipment and large-area fabrication [16]. Wehave investigated the effect of precursors on controlling thesynthesis of nanoparticles. A comparison of the results ofthe present paper with those of [15] gives us an idea of therelative importance of the effective parameters in controllingthe size and shape of ZnO nanoparticles. In [15], the initialsalt was zinc nitrate and the complexing agents were ureaand oxalic acid in compounds (A) and (B), respectively. Here,the complexing agent is oxalic acid and the initial salts arezinc nitrate and zinc acetate in compounds (B) and (C),respectively. The experimental procedure is the same as thatin [15] and compound (B) serves here as a reference withsimilar properties as in [15].

0031-8949/11/015801+08$33.00 Printed in the UK & the USA 1 © 2011 The Royal Swedish Academy of Sciences

Phys. Scr. 83 (2011) 015801 A Kazemi et al

2. Experimental procedure

Zinc nitrate (Zn(NO3)2 · 6H2O), zinc acetate(Zn(CH3COO)2 · 2H2O) and oxalic acid (H2C2O4 · 2H2O),all obtained from Merck, were the materials used.

2.1. Synthesis of compounds

First, 0.01 M zinc nitrate was dissolved in 100 ml of doubledistilled water. Then, 0.015 M oxalic acid was added dropwiseto the zinc nitrate solution at 45 ◦C under vigorous stirring.After 1 h, nanoparticles started to precipitate and the solutionwas transferred to the refluxing system for 6 h at 110 ◦C forpurification. The hot plate was removed and the solution wasdivided into equal parts and centrifuged three times at a lowspeed for 6 min to separate the precipitate from the solvent.The precipitates were kept in an electric furnace at 90 ◦C for4 h. During this time the precipitate was thoroughly dried.The same procedure was carried out for compound (C) exceptthat 0.015 M oxalic acid was added to 0.01 M zinc acetatedehydrate.

Note that compound (A) in [15] was synthesized througha similar route, adding 0.015 M urea as the complexing agentto 0.01 M zinc nitrate.

2.2. Further annealing

The samples of compound (B) were annealed at 400, 450, 500and 550 ◦C and those of compound (C) at 350, 400, 450 and500 ◦C, all for 1 h. The choice of these temperatures and theannealing time was made based on previous experience withsynthesis procedures. Both compounds were synthesized,annealed and characterized at various temperatures threetimes before the principal synthesis in order to find out thebest annealing temperatures. Although the synthesis routewas nearly identical for both, ZnO phases were formed ata temperature lower by 50 ◦C in compound (C). Note that400 and 350 ◦C were the temperatures at which impuritiesand ZnO phases both existed in compounds (B) and (C),respectively. At temperatures below those mentioned above,the structure of both compounds was nearly amorphouswithout any sign of ZnO phases. Note that 550 and500 ◦C were the temperatures at which characterizationsshowed identical properties in compounds (B) and (C),respectively. At the temperature step of 1T = 50 ◦C, thecharacteristics of both compounds demonstrated certaindifferences. Discussions related to the growth mechanism arepresented in the final sections.

2.3. Characterization

Transmission electron microscopy (TEM) and scanningtransmission electron microscopy (STEM) micrographs of theprepared ZnO nanoparticles were taken by a transmissionelectron microscope (model: Leo 912 AB; Zeiss Germany)for compound (B) and a scanning transmission electronmicroscope (model: EM-10 C; Zeiss Germany) for compound(C), for illustrating their morphology. Note that althoughthe imaging principle of STEM is different from that ofTEM, these two microscopic techniques can be consideredas equivalent [17]. X-ray diffraction (XRD) patterns of ZnO

nanoparticles prepared at various annealing temperatureswere recorded by a D8 Advanced Bruker system usingCuKα (λ = 0.154056 nm) radiation to analyze the phaseof the nanoparticles. Optical absorption measurements ofnanoparticles over the range 280–480 nm were made using aUV–visible (UV–vis) spectrophotometer (model: GBC 916)for calculating optical band gap values.

3. Results and discussion

3.1. TEM results

TEM micrographs of ZnO nanoparticles for both compoundshave been demonstrated in figure 1. Small crystallitesembedded in a dark background in figure 1(a) are relatedto compound (B) at 450 ◦C. They are so deeply set in thebackground that we cannot detect their boundaries clearly.Some of them bond with their neighbors to form biggerparticles at 500 ◦C, which are depicted in figure 1(b), andseem to contain overlapping grains. At 400 ◦C in figure 1(c),particles of compound (C) are formed; they are small andclose to each other. They seem to be more homogeneous andexhibit better distribution than those in compound (B). ZnOnanoparticles at 450 ◦C in figure 1(d) have become larger andare still close to each other, but less overlapping in comparisonto particles in figure 1(b).

Four dispersions containing ZnO nanoparticles of meanparticle sizes 8.9 nm (compound (B) at 450 ◦C), 14.6 nm(compound (B) at 500 ◦C), 7.7 nm (compound (C) at 400 ◦C)and 18.2 nm (compound (C) at 450 ◦C) have been utilized.The particle size distributions of these are shown in figure 2.The difference between compounds (B) and (C) is in thedistribution of the crystallites. Otherwise, no significantdifference in size is recognized. In [15], certain differencesin TEM images of compounds (A) and (B) were recognized,such as the faster growth of particles with respect to seedgrowth in a shorter range of temperature in the compoundcontaining urea (compound (A)) than in the compoundcontaining oxalic acid (compound (B)).

3.2. XRD analysis

XRD patterns confirm the hexagonal crystal structure ofZnO where a = b = 0.3249 nm; c = 0.5205 nm for compound(A) and a = b = 0.3242 nm; c = 0.5176 nm for compound(B), with strong reflections from the (1 0 1), (1 0 0) and(0 0 2) planes. Figure 3 depicts XRD patterns for annealingtemperatures related to both compounds. The temperature stepis 1T = 50 ◦C, and as the temperature grows, the particlesbecome more crystallized. The formation of nanocrystallineZnO is reflected by the broadening of corresponding XRDcharacteristic lines. There is no effect of annealing on thecrystalline phase of ZnO as the XRD characteristic lines show.However, annealing has improved the crystallinity of ZnOnanoparticles, which is in agreement with the literature [8].Crystallization reduces the band gap of semi-conductors.Therefore, we expect an increase in the size of nanoparticlesat higher annealing temperatures. By recording the full-widthat half-maximum (FWHM) β of XRD peaks, the average sizeof nanocrystallites has been determined in table 1 using theDebye–Scherrer equation (D = kλ/β cos θ , k = 0.99) [18]

2

Phys. Scr. 83 (2011) 015801 A Kazemi et al

Figure 1. TEM images of the annealed ZnO nanoparticles at (a) 450 ◦C and (b) 500 ◦C for compound (B); STEM images of the annealedZnO nanoparticles at (c) 400 ◦C and (d) 450 ◦C for compound (C). As seen, the size and shape of nanoparticles are slightly better controlledin compound (C).

corresponding to the (1 0 0), (0 0 2) and (1 0 1) planes for bothcompounds. The results of XRD patterns are in agreementwith crystallite mean sizes obtained by TEM micrographs.At 400 and 350 ◦C (related to compounds (B) and (C),respectively), some ZnO phases are formed and some phasesof impurities are still in the system. With 50 ◦C retardation,patterns of compound (B) are nearly identical to those ofcompound (C). No significant difference in size between thetwo compounds is revealed by the XRD results, and theyonly show that the intensities of the peaks in compound (B)grow slightly faster than those of compound (C) at the sametemperature step of 1T = 50 ◦C. However, the differencebetween compounds (A) and (B) was evident from XRDpatterns in [15].

3.3. Crystallite size range variation

It has been shown that the surface effect, i.e. an increaseof the surface-to-volume ratio, has a profound effect onenhancement of emission intensity. The surface-to-volumeratio has been described by the number of Zn–O pairs at thesurface, which can be estimated from

Nsurf

Nvol

∼=S R0

V − S R0=

3R0

R − 3R0, (1)

where Nsurf and Nvol are the numbers of Zn–O pairs at thesurface and in the volume, respectively, S is the surface area,

5 10 15 20 25 30 350

10

20

30

40

50

Particle Size (nm)

Nu

mbe

r (%

)

(B); T= 450oC (B); T= 500oC (C); T= 400oC (C); T= 450oC

Figure 2. Particle size distribution of zinc oxide dispersions due toTEM images. Four dispersions containing ZnO nanoparticles ofmean particle sizes 8.9 nm (compound (B) at 450 ◦C), 14.6 nm(compound (B) at 500 ◦C), 7.7 nm (compound (C) at 400 ◦C) and18.2 nm (compound (C) at 450 ◦C) have been used.

V is the volume, R0 is the Zn–O distance (0.18 nm) and R isthe particle radius [19]. Decreasing the ZnO nanoparticle sizeincreases the surface-to-volume ratio. In addition, the particleshave been presumed to have a spherical shape for equation (1).The surface-to-volume ratio is at a minimum for particles

3

Phys. Scr. 83 (2011) 015801 A Kazemi et al

30 31 32 33 34 35 36 37 38 39 40

Inte

nsi

ty (

a.u

.) (B),T=500oC

(C),T=450oC

(B),T=450oC

(C),T=400oC

(B),T=400oC

(C),T=350oC

2θ (deg.)

Figure 3. XRD patterns of compound (B) at T = 400, 450 and 500 ◦C, and compound (C) at T = 350, 400 and 450 ◦C; the temperaturestep is 1T = 50 ◦C.

Table 1. FWHM β of XRD peaks and the average size of thenanocrystallites determined by the Debye–Scherrer equationcorresponding to the (1 0 0), (0 0 2) and (1 0 1) planes for eachcompound.

Temperature (◦C) hkl FWHM (◦) Crystallite Crystallitesize (nm) mean

size (nm)

Compound (B)400 100 1.489 6.10 6.61

002 1.286 7.11101 1.385 6.63

450 100 1.109 8.19 8.48002 1.003 9.11101 1.128 8.14

500 100 0.434 20.90 20.52002 0.492 18.56101 0.415 22.11

Compound (C)350 100 1.540 5.90 6.35

002 1.419 6.52101 1.402 6.63

400 100 1.159 7.52 7.93002 1.169 7.91101 1.112 8.36

450 100 0.523 17.37 17.70002 0.524 17.45101 0.503 18.28

that are completely spherical. If the particles size decreases,the particles deform to an anisometric shape. Although thesurface effect described by Zn–O pairs at the surface can becontrolled by changing the ZnO nanoparticle size [19]. Thesurface-to-volume ratio versus crystallite size plot for bothcompounds is shown in figure 4, where the graph inclinationof compound (C) is slightly lower than that of compound (B).The surface-to-volume ratio versus crystallite size plot in [15]depicted a major control range in compound (B) which ismissing here. This is because the broadening of XRD patternsfor temperatures below 400 ◦C in compound (C) was nearlyidentical to those of compound (B) at temperatures below450 ◦C.

5 10 15 20 25

0.05

0.10

0.15

0.20.

.

.

.

.

.

N su

rf / N

vol

Crystallite Size (nm)

. (B)

. (C)

Figure 4. Comparison of Nsurf/Nvol values versus crystallite sizebetween compounds (B) and (C). As seen, both compounds arenearly identical in the reducing procedure of Nsurf/Nvol.

3.4. UV–vis spectroscopy and band gap determination

Absorption spectroscopy is a powerful non-destructivetechnique for exploring the optical properties ofsemi-conducting nanoparticles [20]. The absorption spectraof the ZnO/ethanol solution in the UV and visible rangesare presented in figure 5. A blank solution of ethanolis taken as a reference [21]. Absorption curves exhibitabsorption at 310–340 and 305–345 nm for compounds (B)and (C), respectively. As we know, UV–vis spectroscopylooks at electronic transitions. It allows one to determinethe wavelength and maximum absorbance of compounds.Absorption refers to excitations from one electronic band toanother. In the case of an ideal, undoped, direct band gapsemiconductor, energetically favored electron promotion willbe from the highest occupied molecular orbital (HOMO)to the lowest unoccupied molecular orbital (LUMO), i.e.from the highest occupied valence band to the lowestunoccupied conduction band, with the absorption onsetoccurring within a few meV of the energy of the materialband gap. When the sample molecules are exposed to

4

Phys. Scr. 83 (2011) 015801 A Kazemi et al

280 290 300 310 320 330 340 350 360

(C); T=450oC

(C); T=400oC

(B);T=500oC

(B); T=450oC

λ1/2

Wavelength (nm)

Abs

orba

nce

(a.u

.)

Figure 5. UV–vis absorbance spectra of ZnO nanoparticles atvarious annealing temperatures. In samples of compound (C), λ1/2

moves a bit slower toward higher values as temperature increases.

light having an energy that matches a possible electronictransition within the molecule, some of the light energy willbe absorbed as the electron is promoted to a higher energyorbital. Therefore, the wavelengths at which absorptionoccurs and the degree of absorption at each wavelengthare recorded [22]. λ1/2 (wavelength at which absorption is50% of that at the excitonic peak [3]) moves toward highervalues with increasing annealing temperature (figure 6).There is a significant blue shift in the excitonic absorptionfor all nanoparticles compared to that of the bulk ZnO, as theexcitonic absorption for bulk ZnO is at 373 nm [23].

A practical route selected from various methods of bandgap Eg determination [1, 24] consists in equating Eg withλ1/2 through Eg = 1240/λ1/2. The band gap values for allnanoparticles have been calculated. To obtain the size ofnanoparticles by UV–vis analysis, we have used a convenientmethod described by Meulenkamp [24] that involves equatingthe diameter D(Å) with λ1/2 (nm):

1240

λ1/2= A +

B

D2−

C

D, (2)

where A, B and C are constants whose values areA = 3.301, B = 294.0 and C = −1.09 for ZnO nanoparticles.Our results on particle size and band gap energy arecompared in figure 6 with the results obtained by otherresearchers [1, 3, 19, 24, 25]. Good agreement between ourresults and theirs was seen. There is no significant differencebetween compounds (B) and (C) in size and band gap values.Comparing the results with those of [15], it is found that therange of control in compound (B) is much larger than that ofcompound (A).

3.5. Control procedure and thermal decomposition ofcomplexing agents

The decomposition temperature of a substance is thetemperature at which the substance decomposes intosmaller substances or into its constituent atoms. Thermaldecomposition reaction is usually endothermic as heatis required to break chemical bonds in the compoundundergoing decomposition. Along with pH and the activity

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

3.4

3.5

3.6

3.7

3.8

3.9

4.0

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

[24]

[25]

[19]

[3]

[1]

Ban

d G

ap (e

V)

Particle Diameter (nm)

. (B)

. (C)

Figure 6. Size dependence of the optical band gap, defined as λ1/2

(comparison between this work and other references). Bothcompounds are in good agreement with the references.

coefficient of the complexing agents, the decompositiontemperature could have an effective role in the crystallizationof nanoparticles. Oxalic acid crystallizes in prisms, whicheffloresce in air, and is readily soluble in water. The meltingpoint of dehydrate oxalic acid is 101–102 ◦C, i.e. it loses itswater of crystallization at about 100 ◦C and begins to sublimeat about 150–160 ◦C, whereas on heating to a still highertemperature, it partially decomposes into carbon dioxide andformic acid or into carbon dioxide, carbon monoxide andwater [26]. Hexahydrate zinc nitrate decomposes at about125 ◦C. Furthermore, zinc acetate dehydrate loses water at100 ◦C and starts to decompose at 237 ◦C. In brief, zincnitrate, oxalic acid and zinc acetate decompose at 125, 150and 237 ◦C, respectively. The chemical structure of eachsubstance is illustrated in figure 7. As one can see, zinc nitratehas eight bonds: two N O, four N O and two ionic bondsbetween Zn2+ and 2(NO3)

−1, but according to its high contentof water (being a hexahydrate), its melting point is lower thanthat of anhydrous zinc nitrate; therefore, its decompositiontemperature is lower. Zinc acetate also has eight bonds: twoC CH3, two C O, two C O and two bonds between Zn2+

and 2O−1, whereas oxalic acid has five bonds: two C O, aC C and two C OH. At the decomposition temperature,some of these bonds are broken and atoms seek to makenew bonds in their vicinity. Figure 7(a) depicts the mostprobable chemical reactions for compound (B). As seen, eachNO−

3 is replaced by OH− at the first two stages. Whilecarbonate complexes evaporate at temperatures above 200 ◦C,(NO3)2, which is attached to C2O2, has become an unstablesalt and evaporates at the first annealing stage. Positive Znions reach negative OH ions and form Zn(OH)2. This isalso unstable so Zn ions are bonded with oxygen soon afterannealing in the furnace. Impurities in the last stage vanishwith further annealing, but ZnO remains. In figure 7(b), wesee the most probable chemical reactions for compound (C).Two hydrogen ions decompose from oxalic acid, leaving twonegative oxygen ions to attach to Zn2+ at two stages, freeingacetic acid twice. As seen in the third row, Zn2+ (C2O4)

2−

is an unstable structure and easily decomposes throughcompound annealing. Therefore, Zn ions are free and quicklyturn into ZnO through oxidation. Briefly, the materials incompound (B) start to decompose at 125–150 ◦C, whereas the

5

Phys. Scr. 83 (2011) 015801 A Kazemi et al

Figure 7. (a) Chemical reactions for compound (B); each NO−

3 is replaced by OH− at the first two stages. Zn positive ions reach OHnegative ions and form Zn(OH)2. This is unstable and Zn ions are bonded with oxygen soon after annealing in the furnace. (b) Chemicalreactions for compound (C); as seen, two hydrogen ions decompose from oxalic acid, leaving negative oxygens to attach to Zn2+ at twostages, freeing acetic acid twice. As seen in the third row, Zn2+ (C2O4)

2− is an unstable structure and easily decomposes throughcompound annealing. Therefore, Zn ions are free and quickly turn into ZnO through oxidation.

Table 2. The ionic strength, the effective diameter and the Debye–Hückel term for various ions as basic parameters for activity coefficientcalculation.

(NO3)− (CH3COO)− (C2O4)

2− Zn2+ H+

Ionic strength 0.01 0.01 0.02 0.02 0.01Effective diameter (Å) 3 4.45 4. 5 6 9Temperature (◦C) The Debye–Hückel term

25 0.0463 0.0443 0.0595 0.0563 0.039330 0.0467 0.0447 0.0599 0.0567 0.039635 0.0471 0.0451 0.0605 0.0572 0.039940 0.0477 0.0457 0.0613 0.0579 0.040450 0.0485 0.464 0.0623 0.0589 0.041175 0.0512 0.049 0.0656 0.0619 0.0432

100 0.0544 0.0519 0.0696 0.0657 0.0458125 0.0579 0.0553 0.0743 0.0701 0.0487150 0.0624 0.0595 0.0796 0.0751 0.0523175 0.0673 0.0642 0.0858 0.0808 0.0564200 0.073 0.0695 0.0929 0.0874 0.0609250 0.0879 0.0837 0.1139 0.105 0.073300 0.1119 0.106 0.1413 0.1325 0.0923

start of decomposition for compound (C) is at 150–237 ◦C,which means that compound (B) is prepared to form newchemical bonds at a temperature at least 25–87 ◦C lower thancompound (C). Furthermore, greater chances of Zn oxidationwith air exist for Zn in compound (B) at further stages.The thermal decomposition temperature difference here isabout four times what has been mentioned in [15]. Thelower decomposition temperature in compound (B) shouldhave been effective in fastening the chemical reactions andthus in faster crystallization of ZnO nanoparticles. Accordingto XRD, TEM and UV–vis results, the crystallization incompounds (B) and (C) is not very different.

3.6. Control procedure and the complexing agent’s pH

The pH can be affected by the ionic strength of a solution.As the ionic strength of a solution increases, its pH decreasesand therefore its acidity increases [27]. Compound (B) wasprepared at the pH value of 1.92 and compound (C) atpH 2.63. Lepková et al [28] found that a higher pH valueof the aqueous phase ends with lower-sized nanoparticles.ZnO nanorods of different dimensions have been synthesizedthrough appropriate control of the pH by Baruaha and

Dutta [29]. According to the literature, we expected finer ZnOnanocrystallites for compound (C) with higher pH. This hasbeen in agreement with TEM results with regard to crystallitedistribution but not with regard to size. Note that the pHdifference in [15] is nearly one half of the amount reportedhere.

3.7. Control procedure and the complexing agentactivity coefficient

The activity coefficient of a species can be considered asa measure of the effectiveness of that ion in influencingthe equilibrium in which it plays a part. This parameteris dependent on the ionic strengths of a species. As theionic strength increases, the ion becomes less effective inits behavior and the activity coefficient decreases from unityto lower values. There are however some exceptions andcomplexities in calculating the actual value of the activitycoefficient of a species [30]. Several approaches have beendeveloped to estimate the activity coefficient of species inionic liquids using the nonrandom two-liquid segment activitycoefficient model (NRTL-SAC), which is a simple molecularthermodynamic framework that characterizes molecular

6

Phys. Scr. 83 (2011) 015801 A Kazemi et al

Table 3. A brief look at pH, decomposition temperature and mean activity coefficient values of compounds (A), (B) and (C). Note thatcompound (A) differs from the other two compounds in size and shape control. The mean activity coefficient of the initial salt in compounds(A) and (B) are identical due to the similar salt used in their synthesis. Also, the mean activity coefficient of complexing agents incompounds (B) and (C) are identical due to the similar complexing agents used in their synthesis.

pH Decomposition Mean activity coefficient Mean activity coefficienttemperature of the initial salt of the complexing agent

(◦C)

Compound (A) 1.63 125–132 0.731 (25 ◦C)–0.477 (300 ◦C) 1Compound (B) 1.92 125–150 0.731 (25 ◦C)–0.477 (300 ◦C) 0.726 (25 ◦C)–0.468 (300 ◦C)Compound (C) 2.63 150–237 0.716 (25 ◦C)–0.480 (300 ◦C) 0.726 (25 ◦C)–0.468 (300 ◦C)

25 50 75 100 125 150 175 200 225 250 275 300

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Act

ivity

Coe

ffic

ient

T emperature (oC)

U rea [15] (N O

3)-

(A c)-

(C2O

4)2-

Zn 2+

H+

25 50 75 100 125 150 175 200 225 250 275 300

0 .5

0 .6

0 .7

0 .8

0 .9

1 .0

Mea

n A

ctiv

ity

Coe

ffic

ient

Tempera ture (o C)

Ure a [ 15] Zn(N O

3)

2 Zn(C H

3COO )

2

H2C

2O

4

(a)

(b)

Figure 8. (a) Activity coefficient variation with temperature fordifferent ions. The ions with the same charge seem to follow similarprocedures. Oxalic and zinc ions have lower activity value and theymove to even lower values faster than other ions. (b) Mean activitycoefficient variation with temperature for different species. Oxalicacid, zinc nitrate and zinc acetate seem to follow similar procedures.The mean activity coefficient of urea is unity.

interaction in terms of four dimensionless molecular descri-ptors: hydrophobicity, hydrophilicity, polarity and solvationstrength [31–33]. Chemists claim that we shall nearlyalways neglect the activity coefficient and simply use molarconcentrations in all applications of the equilibrium law. Ifthe molar concentrations of two species are identical such asin the work reported here and in [15], the activity coefficientof the additives could not be neglected. To the best ofour knowledge, there is no report available that deals withthe importance of activity coefficients of chemical additivesin controlling the nanoparticle size of ZnO. The influence

of the activity coefficient on the crystallization process ofbarium sulfate has been investigated by Oncul et al [34].They found that the supersaturation ratio, containing theactivity coefficient in its definition, is the driving forcefor the crystallization process and even relatively smallvariations of this coefficient can considerably affect theresults, especially for fast reactions. Here, the specificion interaction model (SIT) is applied to determine theactivity values [35]. The Debye–Hückel term, which is thedominant term in the expression for activity coefficientsin a dilute solution, accounts for electrostatic, non-specificlong-range interactions. At higher concentrations, short-rangenon-electrostatic interactions have to be taken into account.This is usually done by adding ionic strength-dependent termsto the Debye–Hückel expression. Due to the assumptionsmade on the SIT model [35], the ionic strength-dependentterm is neglected and the activity coefficient γ j of an ion j ofcharge z j in the solution of ionic strength Im is simplified to

log γ j = −z2j D, (3)

D =A√

Im

1 + B a j√

Im, (4)

Im =12 {[ j]z2

j + · · ·}, (5)

where D is the Debye–Hückel term, A and B are constantsthat are temperature dependent and a j is the effectivediameter of the hydrated ion j. The values of A and Bas a function of temperature taken from [35] were used.Using equations (3)–(5), the ionic strength, the effectivediameter and the Debye–Hückel term have been determinedfor H+, Zn2+, (C2O4)

2−, (NO3)− and (CH3COO)− and are

summarized in table 2. Also the activity coefficient versustemperature plot has been depicted in figure 8(a). As onesee in this figure, the activity coefficient of (C2O4)

2− haslower values at room temperature (the start of synthesis) anddecreases as the temperature increases. The activity variationprocedures for (NO3)

− and (CH3COO)− are nearly identical.The activity coefficient of urea is unity because its ionicstrength is zero and remains constant during temperaturegrowth.

It should be noted that in a liquid solution, the activitycoefficient of a given ion is not measurable experimentally.Therefore, we introduce the notion of the dimensionless meanionic activity coefficient,

γ j =√

γ+ · γ−, (6)

7

Phys. Scr. 83 (2011) 015801 A Kazemi et al

where γ+ and γ− are the activity coefficients of positiveand negative ions, respectively. Figure 8(b) depicts the meanactivity variation of species with temperature. The valuesare calculated using equation (6) for each ionic structure.The mean activity value of all ions decreases with increasingtemperature except in the case of urea.

When an initial salt is applied once to urea and onceto oxalic acid [15], the corresponding compounds end upwith significant differences and a better control range isobtained for the compound containing oxalic acid with alower activity coefficient. But when oxalic acid is appliedonce to zinc nitrate and once to zinc acetate (two saltswith identical activity coefficient behavior due to identicalcharge and identical ionic strength), no significant differenceis recognized in the controlling procedure. A summary of thepH, decomposition temperature and mean activity coefficientvalues of compounds (A), (B) and (C) is presented intable 3. As can be seen, the pH and thermal decompositionof compound (A) are close to those of compound (B), butdiffer from those of compound (C). Furthermore, the activitycoefficient of compound (A) differs from that of compounds(B) and (C). Note that the control procedure of compound (A)was weak as compared with compounds (B) and (C).

It is found that the activity coefficient is of greaterimportance compared with other effective properties in thecontrol procedure. Wherever a significant difference is seen inthe activity coefficient values of ions, a significant differenceappears in the characterization of ions, and vice versa.Thermal decomposition temperature and pH values could beof secondary importance in controlling the growth of ZnOnanoparticles. It is presumed that the activity coefficient hasa certain role in the nanoparticle growth process and cannotbe neglected in nanometer synthesis.

4. Conclusion

In order to investigate the relative importance of the mosteffective parameter among pH, decomposition temperatureand activity coefficient in controlling the size of ZnOnanoparticles, a compound is used as a reference in threeidentical synthesis routes. The reference shows nearlyidentical characteristics to the compound holding the sameactivity, higher pH and higher decomposition temperature.The comparison of this reference with the compoundholding higher activity, lower pH and lower decompositiontemperature shows more control signals. The most plausibleexplanation for these observations is that they can be due tothe importance of the activity coefficient. However, higherdecomposition temperature and higher pH have a secondaryrole in the control procedure.

Acknowledgments

The authors would like to thank Azadeh Rezakhani for herhelpful advice relating to the chemical aspects of the article.

Furthermore, Majid Sigari Tarkkarde, Mohseni Marangouni,Hosein Abu Zeidabad and Saeid Abu Bath are acknowledgedfor their support of the investigation.

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