Research ArticleOstwald Ripening of the Platinum Nanoparticles in theFramework of the Modified LSW Theory
R D Vengrenovich B V Ivanskii I I Panko S V YaremaV I Kryvetskyi and M O Stasyk
Yuriy Fedkovych National University of Chernivtsi Ukraine
Correspondence should be addressed to R D Vengrenovich vengrenovichiua
Received 25 February 2014 Accepted 1 June 2014 Published 9 September 2014
Academic Editor Shijun Liao
Copyright copy 2014 R D Vengrenovich et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
An analysis of the experimental data related to themechanism of Pt particles sintering has been carried out using themodified LSWtheory The size distribution for the Pt nanoparticles at the stage of Ostwald ripening fits the generalized Lifshitz-Slyozov-Wagnermodel calculated with the assumption of two parallel mechanisms involved in the nanoparticles growth (dissolution) diffusion andWagnerrsquos (controlled by the chemical reaction rate) Comparison between the experimental histograms and the curves calculatedtheoretically proves the governing role of the Wagnerrsquos mechanism (chemical reaction) in the Pt nanoparticles growth
1 Introduction
Advances in technologies especially in nanotechnologiescause significant interest towards Ostwald ripening (OR) Itis well known that the nanoscaled particles (1ndash100 nm) canreveal new properties different from characteristics of thebulky substances and the potential market of the nanoap-plications in different branches of science and technologysuch as electronics optoelectronics information technologymedicine and pharmacology is very wide [1] On the otherhand OR can take place in some nanosystems because of theGibbs-Thomson effect and this phenomenon results in grad-ual growing of the bigger particles at the expense of smallerones Therefore the smaller nanoclusters or nanocrystals(NC) dissolve while the bigger ones grow This process alsocauses rise in the particles mean size widening of the NCsize distribution and dispersion As a result this processcan worsen specific characteristics and performance of thenanosystemor even cause its complete degradationThusORis an unwanted effect and the investigation of its mechanismand kinetics of the NC growingdissolution through ORcan open new opportunities in controlling this process andminimization of its negative effects
On the other hand there are tight links between OR andthe nanotechnologies The process of a new phase forma-tion always includes three stages regardless of the synthesismethod used or the source phase (liquid solid or gaseous)nucleation independent growing of the new nanoparticlesand their Ostwald ripening The latter stage is governed bythe Gibbs-Thomson effect and many useful characteristics ofnew nanoparticles are formed exactly during this stage [2]
The late OR takes place when oversaturation of thesynthesis solution reduces to the level when new clusters donot appear any more Then the process of the clusters sizeredistribution starts and the process ofOR completes the finalsize range and dispersion [3]
A size distribution function reflecting the most completeinformation related to the structural composition of thenanosystem can be calculated for the given growing mecha-nism and nanoclusters shape using some available theoreticalapproaches [4ndash9]
Themain requirements towards structural characteristicsof the applicable NC can be outlined as follows Regardlessof the synthesis method used NC should have uniform sizeshape composition lattice structure and other technicalparameters Besides the size distribution should be as narrowas possible and the dispersion should be kept low
Hindawi Publishing CorporationJournal of NanomaterialsVolume 2014 Article ID 821584 7 pageshttpdxdoiorg1011552014821584
2 Journal of Nanomaterials
The two separate growing mechanisms were analyzed bythe primary LSW theory the diffusionmechanism controlledby the bulk diffusion coefficient Dv as introduced by Lifshitzand Slyozov [4 5] andWagnerrsquos mechanism controlled by therate of the chemical bonds formation or the surface chemicalreaction rate [6]
Both mechanisms are analyzed simultaneously in theframework of the modified LSW theory A ratio between twosubfluxes of the matter towardsoutwards the NC surfacediffusion 119895V andWagnerrsquos 119895
119894 represents a contribution of each
mechanism into the resulting process of OR [9 10] Thesecontributions depend on many parameters such as nature ofNC temperature and synthesis method
It should be mentioned that many important applicationsin electronics optoelectronics solar energy conversion andother branches are reported [11ndash18] for the semiconductingnanoscaled heterosystems containing quantum dots [19ndash23] The OR stage is known for such systems that wereusually synthesized using the molecular-beam epitaxy in theStranski-Krastanov mode before [24] More advanced andless expensive methods such as dripping liquid phase andelectrophase epitaxy are also used for this synthesis now [25ndash29]
As seen from [30ndash34] significant progress is achieved inthe synthesis of the quantumdots semiconductors using vari-ous chemical and colloidmethods For instance nanocrystalsof ZnO (one of the most universal and multifunctionalsemiconductors) are synthesized usually from oversaturatedsolutions [35ndash45]
As reported in [46ndash49] the modified LSW theory [9 10]proves that the growing of NC in the nanosystems in manycases involves both mechanisms (diffusion and Wagnerrsquos)[46]
This paper is devoted to the investigation of the governingrole of OR in the process of Pt NC sintering that occurs ina nanocomposite material and involves both mechanisms ofgrowing The carbon nanotubes are used in this synthesis asreported in [47]
Evaluation of the sintering process has been performedusing temporal evolution of the particles size distributionduring heating from the initial temperature to 550∘Cand thento 800∘C The size distribution of Pt NC changed from theGauss type to the normal logarithmic type under such heatingmode [47] Since this sintering process runs according toOR mechanism the particles size distribution function isexpected to agree with the theoretical LSW distribution
As a result the experimental histograms [47] should alsobe in agreement with the theoretical distributions calculatedusing the modified LSW theory and the generalized Lifshitz-Slyozov-Wagner distribution
2 The Fundamental of the Modified LSWTheory Applied to the Pt NanoparticlesSintering in a Nanocomposite
The initial average size of the Pt particles in the nanocom-posite was 262 (plusmn06) nm [47] A nanoparticle of such sizeis unstable thermodynamically since its specific surface is
comparatively large which results in high free energy valueAs a system goes to the equilibrium its free energy decreasesand the particles average size grows
It should always be taken into consideration that thenanoparticles are very small and approximate amounts oftheir surface and body atoms are similar which causes higherreactivity of the particles That is why the surface and theinterface processes should be considered together with theregular diffusion transportation in order to analyze growthand dissolution of nanoparticles In other words Wagnerrsquos(kinetic) mechanism of the nanoparticle growthdissolutioncannot be neglected in this case of OR of the Pt NC and bothprocesses diffusion and chemical reaction should be takeninto account for OR in the disperse phase of the nanosystems
Two mechanisms of the nanocrystal (NC) growth areanalyzed by the modified LSW theory [9 10] One of themis the diffusion mechanism (diffusion) introduced by Lifshitzand Slyozov [4 5] while the second mechanism is Wagnerrsquoskinetic growth [6] controlled by the chemical reaction rateAccording to this theory the flux of atoms towardsoutwardsNC 119895 can be represented as a sum of the diffusion 119895V andkinetic 119895
119894subfluxes
119895 = 119895V + 119895119894 (1)
This equation represents the basic idea of the modifiedLSW theory which means two parallel mechanisms (diffu-sion and Wagnerrsquos) of the NC growth
The rate of the NC growth 119903 equiv 119889119903119889119905 should be defined toobtain a function 119891(119903 119905) describing the temporal evolutionof the size distribution for the NCs It is known that thecontinuity equation can be used to couple 119891(119903 119905) and 119903
1minus119909 = 119895119894119895119909(1minus119909) = 119895V119895119894 r is radius of the particle 119903119892 is the
maximal size of NC 119903119896is critical radius of NC which is equal
to the average size ⟨119903⟩ (119903119896equiv ⟨119903⟩) as set by the LSW theory
and 120590 is the specific surface energy 119862infin
is the equilibriumconcentration of the dissolved substance 120592
119898is volume of
atom of the dissolved substance 120573 is the kinetic coefficientdetermining the 119895
119894subflux 119863
120592is the coefficient of bulk
diffusion 119896 is Boltzmannrsquos constant and 119879 is temperature
Journal of Nanomaterials 3
Equation (4) describes the rate of the Pt NC growthgoverned mostly by the kinetic subflux 119895
119894with partial con-
tribution 119909made by the diffusion subflux 119895V On the contrary(5) describes the rate of the Pt NC growth governed mostlyby the diffusion subflux 119895V with partial contribution (1 minus 119909)made by the kinetic subflux Therefore the rates of growth(4) and (5) can be represented in the LSW theory by the ratiobetween subfluxes 119895V and 119895119894
According to [48] 119891(119903 119905) can be represented by theproduct of two functions one depending on time 119905 andanother depending on the relative variable 119906
011990631198921015840(119906)119889119906119872 is total mass of the NCs in the
unit of volume and 120588 is density of the NCrsquos substanceA definition of the relative variable in the form
119906 =119903
119903119892
(8)
instead of the traditional form 120588 = 119903119903119896 was proposed
in [48] and in this way the variation interval of u becameindependent on the growth mechanism of the NC (0 le119906 le 1) Function 119892(119906) in form (7) (or function 1198921015840(119906)(with accuracy to the constantQ)) represents the generalizeddistribution of Lifshitz-Slyozov-Wagner (119866119863119871119878119882) whichinvolves simultaneously twomechanisms of growth diffusionand Wagnerrsquos
The distribution 1198921015840(119906) can be obtained by integrationof (2) with account of (4) or (5) and proceeding fromdifferentiation by 119903 and 119905 to differentiation by 119906 [9 10]
Assuming 119909 = 0 119861 = 5 119863 = minus1 and 119862 = minus3 (9)transforms (with accuracy to the constant Q) into Wagnerrsquosdistribution [6]
1198921015840(119906) = 119906(1 minus 119906)
minus5 exp(minus 3
1 minus 119906) (11)
Assuming 119909 = 1 119861 = 113 119863 = minus73 and 119862 = minus1 (9)matches the Lifshitz-Slyozov distribution [4 5]
1198921015840(119906) = 119906
2(1 minus 119906)
minus113(119906 + 2)
minus73 exp(minus 1
1 minus 119906) (12)
The 119866119863119871119878119882 distribution (7) can represent adequatelythe size distribution for 0 le 119909 le 1 As the average size⟨119903⟩ (or critical size 119903
119896) is growing continuously during OR
the maximum size 119903119892grows as well although the ratio 119903
119892119903119896
remains unchanged According to the modified LSW theory[9 10]
119903119892
119903119896
=2 + 119909
1 + 119909 (13)
ConsideringWagnerrsquosmechanism of the growing and assum-ing 119909 = 0 we obtain 119903
119892119903119896= 2 and for the diffusion
mechanism and 119909 = 1 119903119892119903119896= 32
Since the ratio 119903119892119903119896is a time independent constant
the size distribution 1198921015840(119906) does not depend on the initialdistribution Therefore some generally used characteristicsof 1198921015840(119906) depending on the initial and central moments(dispersion ⟨1199062⟩ minus ⟨119906⟩2 the mean relative radius ⟨119906⟩ areaunder the curve etc) also do not depend on time during OR
The function 119891(119903 119905) (6) describes the temporal evolutionof the size distribution The time dependence of 119903
119892should
be determined in order to define the explicit mode of thisfunction The value 119903
119892can be found from (4) and (5) by
substituting 119903119892for 119903 and a value of the ratio 119903
119892119903119896taken from
(13) for this ratio Integrating (4) for the preliminaryWagnerrsquosmechanism we obtain
1199032
119892= 119861lowast 1
1 minus 1199092119905
1199032
119896= 119861lowast 1 + 119909
(1 minus 119909) (2 + 119909)2119905
(14)
Assuming 119909 = 0 we obtain 1199032119892= 119861lowast119905 1199032
119896= (14)119861lowast119905 and
119903119892119903119896= 2
Alternatively integrating (5) for the preliminary diffusion(diffusion) mechanism we obtain
1199033
119892= 119860lowast 1
119909 (1 + 119909)119905
1199033
119896= 119860lowast (1 + 119909)
2
119909(2 + 119909)3119905
(15)
Assuming 119909 = 1 we obtain 1199033119892= (12)119860lowast119905 1199033
119896= (4
27)119860lowast119905 and 119903119892119903119896= 32
Finally the function 119891(119903 119905) (6) can be defined from thedependence of 119903
119892on 119905
3 Discussion
The distribution (7) is shown in Figure 1(a) as a series ofcurves for various 119909 and Wagnerrsquos distribution (119909 = 0) isshown in the embedment The 119909 = 1 curve corresponds to
4 Journal of Nanomaterials
00 02 04 06 08 10000000
000005
000010
000015
000020
00 02 04 06 08 10
g(u)
8
6
4
2
x = 1
x = 09
x = 08
x = 07
x = 06
x = 05
x = 04x = 03
x = 02x = 01
x = 0
u
times108
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
u
x = 0 x = 1
(b)
Figure 1 The curves corresponding to the GDLSW distribution calculated using the formula (7) with the iteration step Δ119909 = 01 (a) samecurves as in (a) normalized by their maximums (b)
the Lifshitz-Slyozov distribution The same curves normal-ized by theirmaximums are shown in Figure 1(b) Such curvescan be easily compared to the experimental data
The experimental histogram should be presented in thesame normalized mode as the theoretical curves in order toperform their comparison The scale of the horizontal axis(it represents radii 119903 or diameters 119889 of NC in nm) shouldbe transferred to the relative variable (relative diameter) 119906 =119903119903119892= 119889119889
119892 where the maximal diameter 119889
119892is taken from
the histogramThe relative diameter of NC 119906 in the histogramwill be ranged between 0 and 1 after such transformation
All values in the vertical axis corresponding to thenumber of particles in the unit of volume within someinterval Δ119889 are normalized by the maximum of histogramTherefore the histogram is normalized by the unit along allaxes The conformity or inconformity in the theoretical andexperimental data can be evaluated through comparison ofthe experimental histograms and the normalized theoreticalcurves built in the same scaleThe initial and centralmomentscalculated for the experimental and theoretical distributionsshould be compared in order to perform the quantitativecomparison
The comparison between the normalized experimentalhistograms of the Pt NC [47] and the theoretical curves isshown in Figure 2 The histogram (a) shows the initial sizedistribution of the Pt particles and it can be noticed that thishistogram and the GDLSW distribution (7) at x = 02 are ingood agreement
This fact confirms that the OR stage is present even inthe liquid phase synthesis of the Pt NC and that the chemicalreaction running on the Pt NC surface is the governing factorof OR
It should be emphasized that the OR stage has beenidentified and reported using the colloid chemistry methodsin some liquid phase syntheses of NC (including semicon-ducting NC) [32 49ndash51]
Having calculated the ratio 119903119892119903119896(13) and themean radius
of the Pt particles (⟨r⟩= 262 (plusmn06) nm) (in the framework of
the LSW theory this radius corresponds to the critical value119903119896) the maximal radius 119903
119892of the Pt NC can be calculated as
119903119892= 119903119896
2 + 119909
1 + 119909 (16)
where x = 02 as follows from Figure 2(a) Within themeasurement error the maximal size calculated by (16) rg =48 nm is in good agreement with the maximal size of Pt NCrg asymp 43 nm measured experimentally
A mean size of NC rises up to (⟨r⟩ = 858 (plusmn245) nm)[47] and their sphericity becomes more perfect as a result ofthermotreatment of nanocomposites at 550∘CThe histogram(b) in Figure 2 shows size distribution for the particles at550∘C and it is easily noticeable that it fits with the GDLSWdistribution at x = 01 which is very close to WagnerrsquosdistributionThe maximal size 119903
119892according to the histogram
(b) is 165 nm and according to the formula (16) it is about164 nm This agreement seems too good and can be aresult of significant errors committed in the plotting of theexperimental histograms However two conclusions can bedrawn from the results seen in Figure 2(a) first as noticedin [47] the shapes of the histograms (a) and (b) are quiteclose second the rate of the PtNC growthdissolution duringtheir sintering is controlled by the surface chemical reactionrunning on the NC that is Wagnerrsquos mechanism Fasterdiffusion processes (diffusion) do not control OR
Further rise in the NC sizes occurs at rise in temperatureof the nanocomposites thermotreatment and an average sizeof the PtNC reaches (⟨r⟩= 1589 (plusmn523) nm) at 800∘C [47] Ahistogram reflecting sizes distribution for the 800∘C sinteringof Pt NC is shown in Figure 2(c) Similar to the previouscases (a) and (b)Wagnerrsquos distribution or theGDLSWmodelat x = 01 is in good agreement with the (c) histogramThis is another proof of the governing role of the kineticallycontrolled Wagnerrsquos mechanism of the Pt NC sintering at800∘C This process is one of infrequent examples of thedisperse particles growthdissolution involving OR totallycontrolled by the surface chemical reaction
Journal of Nanomaterials 5
00 02 04 06 08 1000
02
04
06
08
10g(u)gmax
u
x = 02
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 01
u
(b)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 0 x = 1
x = 01
u
(c)
Figure 2 Comparison of the experimental Pt NC histograms with the theoretical GDLSW distributions (a) source histogram (b) heatingto 550∘C and (c) heating to 800∘C
Good agreement between the maximal sizes of Pt NC119903119892derived from the experimental histograms and calculated
using the formula (16) also confirms correctness of com-parison between the experimental and the theoretical sizedistributions For example the maximal size calculated using(16) for 800∘C is rg = 318 nm while the experimental value isrg = 339 nm Taking into account the experimental error thisdifference is rather insufficient
Therefore the modified LSW theory is an adequate toolfor the description of the Pt NC sintering according to theORmechanism within the entire temperature range consideredin this paper
4 Conclusion
A theoretical analysis of the Pt NC sintering has been per-formed within some temperature range using the modifiedLSW theory The theoretical GDLSW distribution with the 119909value about the unit can adequately describe the experimentalsize distribution for the Pt NC Therefore only the surface
chemical reaction on the Pt NC (Wagnerrsquos mechanism) gov-erns the processes of growingdissolution of the nanoparticlesat the stage of OR Moreover the same mechanism also con-trols the process of the Pt NC growthdissolution during theirliquid phase synthesis This is one of infrequent examples ofOR for nanoparticles that is totally controlled by the chemicalreaction according to Wagnerrsquos mechanism This conclusioncan be proven by comparison of the source experimentalhistograms and theoretical curves built according to theGDLSW approximation at x = 02
Analysis of the high temperature sintering of PtNC showsgood agreement between the experimental and theoreticalmaximum sizes of the particles 119903
119892and brings another evi-
dence for correctness of the above theory
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
The two separate growing mechanisms were analyzed bythe primary LSW theory the diffusionmechanism controlledby the bulk diffusion coefficient Dv as introduced by Lifshitzand Slyozov [4 5] andWagnerrsquos mechanism controlled by therate of the chemical bonds formation or the surface chemicalreaction rate [6]
Both mechanisms are analyzed simultaneously in theframework of the modified LSW theory A ratio between twosubfluxes of the matter towardsoutwards the NC surfacediffusion 119895V andWagnerrsquos 119895
119894 represents a contribution of each
mechanism into the resulting process of OR [9 10] Thesecontributions depend on many parameters such as nature ofNC temperature and synthesis method
It should be mentioned that many important applicationsin electronics optoelectronics solar energy conversion andother branches are reported [11ndash18] for the semiconductingnanoscaled heterosystems containing quantum dots [19ndash23] The OR stage is known for such systems that wereusually synthesized using the molecular-beam epitaxy in theStranski-Krastanov mode before [24] More advanced andless expensive methods such as dripping liquid phase andelectrophase epitaxy are also used for this synthesis now [25ndash29]
As seen from [30ndash34] significant progress is achieved inthe synthesis of the quantumdots semiconductors using vari-ous chemical and colloidmethods For instance nanocrystalsof ZnO (one of the most universal and multifunctionalsemiconductors) are synthesized usually from oversaturatedsolutions [35ndash45]
As reported in [46ndash49] the modified LSW theory [9 10]proves that the growing of NC in the nanosystems in manycases involves both mechanisms (diffusion and Wagnerrsquos)[46]
This paper is devoted to the investigation of the governingrole of OR in the process of Pt NC sintering that occurs ina nanocomposite material and involves both mechanisms ofgrowing The carbon nanotubes are used in this synthesis asreported in [47]
Evaluation of the sintering process has been performedusing temporal evolution of the particles size distributionduring heating from the initial temperature to 550∘Cand thento 800∘C The size distribution of Pt NC changed from theGauss type to the normal logarithmic type under such heatingmode [47] Since this sintering process runs according toOR mechanism the particles size distribution function isexpected to agree with the theoretical LSW distribution
As a result the experimental histograms [47] should alsobe in agreement with the theoretical distributions calculatedusing the modified LSW theory and the generalized Lifshitz-Slyozov-Wagner distribution
2 The Fundamental of the Modified LSWTheory Applied to the Pt NanoparticlesSintering in a Nanocomposite
The initial average size of the Pt particles in the nanocom-posite was 262 (plusmn06) nm [47] A nanoparticle of such sizeis unstable thermodynamically since its specific surface is
comparatively large which results in high free energy valueAs a system goes to the equilibrium its free energy decreasesand the particles average size grows
It should always be taken into consideration that thenanoparticles are very small and approximate amounts oftheir surface and body atoms are similar which causes higherreactivity of the particles That is why the surface and theinterface processes should be considered together with theregular diffusion transportation in order to analyze growthand dissolution of nanoparticles In other words Wagnerrsquos(kinetic) mechanism of the nanoparticle growthdissolutioncannot be neglected in this case of OR of the Pt NC and bothprocesses diffusion and chemical reaction should be takeninto account for OR in the disperse phase of the nanosystems
Two mechanisms of the nanocrystal (NC) growth areanalyzed by the modified LSW theory [9 10] One of themis the diffusion mechanism (diffusion) introduced by Lifshitzand Slyozov [4 5] while the second mechanism is Wagnerrsquoskinetic growth [6] controlled by the chemical reaction rateAccording to this theory the flux of atoms towardsoutwardsNC 119895 can be represented as a sum of the diffusion 119895V andkinetic 119895
119894subfluxes
119895 = 119895V + 119895119894 (1)
This equation represents the basic idea of the modifiedLSW theory which means two parallel mechanisms (diffu-sion and Wagnerrsquos) of the NC growth
The rate of the NC growth 119903 equiv 119889119903119889119905 should be defined toobtain a function 119891(119903 119905) describing the temporal evolutionof the size distribution for the NCs It is known that thecontinuity equation can be used to couple 119891(119903 119905) and 119903
1minus119909 = 119895119894119895119909(1minus119909) = 119895V119895119894 r is radius of the particle 119903119892 is the
maximal size of NC 119903119896is critical radius of NC which is equal
to the average size ⟨119903⟩ (119903119896equiv ⟨119903⟩) as set by the LSW theory
and 120590 is the specific surface energy 119862infin
is the equilibriumconcentration of the dissolved substance 120592
119898is volume of
atom of the dissolved substance 120573 is the kinetic coefficientdetermining the 119895
119894subflux 119863
120592is the coefficient of bulk
diffusion 119896 is Boltzmannrsquos constant and 119879 is temperature
Journal of Nanomaterials 3
Equation (4) describes the rate of the Pt NC growthgoverned mostly by the kinetic subflux 119895
119894with partial con-
tribution 119909made by the diffusion subflux 119895V On the contrary(5) describes the rate of the Pt NC growth governed mostlyby the diffusion subflux 119895V with partial contribution (1 minus 119909)made by the kinetic subflux Therefore the rates of growth(4) and (5) can be represented in the LSW theory by the ratiobetween subfluxes 119895V and 119895119894
According to [48] 119891(119903 119905) can be represented by theproduct of two functions one depending on time 119905 andanother depending on the relative variable 119906
011990631198921015840(119906)119889119906119872 is total mass of the NCs in the
unit of volume and 120588 is density of the NCrsquos substanceA definition of the relative variable in the form
119906 =119903
119903119892
(8)
instead of the traditional form 120588 = 119903119903119896 was proposed
in [48] and in this way the variation interval of u becameindependent on the growth mechanism of the NC (0 le119906 le 1) Function 119892(119906) in form (7) (or function 1198921015840(119906)(with accuracy to the constantQ)) represents the generalizeddistribution of Lifshitz-Slyozov-Wagner (119866119863119871119878119882) whichinvolves simultaneously twomechanisms of growth diffusionand Wagnerrsquos
The distribution 1198921015840(119906) can be obtained by integrationof (2) with account of (4) or (5) and proceeding fromdifferentiation by 119903 and 119905 to differentiation by 119906 [9 10]
Assuming 119909 = 0 119861 = 5 119863 = minus1 and 119862 = minus3 (9)transforms (with accuracy to the constant Q) into Wagnerrsquosdistribution [6]
1198921015840(119906) = 119906(1 minus 119906)
minus5 exp(minus 3
1 minus 119906) (11)
Assuming 119909 = 1 119861 = 113 119863 = minus73 and 119862 = minus1 (9)matches the Lifshitz-Slyozov distribution [4 5]
1198921015840(119906) = 119906
2(1 minus 119906)
minus113(119906 + 2)
minus73 exp(minus 1
1 minus 119906) (12)
The 119866119863119871119878119882 distribution (7) can represent adequatelythe size distribution for 0 le 119909 le 1 As the average size⟨119903⟩ (or critical size 119903
119896) is growing continuously during OR
the maximum size 119903119892grows as well although the ratio 119903
119892119903119896
remains unchanged According to the modified LSW theory[9 10]
119903119892
119903119896
=2 + 119909
1 + 119909 (13)
ConsideringWagnerrsquosmechanism of the growing and assum-ing 119909 = 0 we obtain 119903
119892119903119896= 2 and for the diffusion
mechanism and 119909 = 1 119903119892119903119896= 32
Since the ratio 119903119892119903119896is a time independent constant
the size distribution 1198921015840(119906) does not depend on the initialdistribution Therefore some generally used characteristicsof 1198921015840(119906) depending on the initial and central moments(dispersion ⟨1199062⟩ minus ⟨119906⟩2 the mean relative radius ⟨119906⟩ areaunder the curve etc) also do not depend on time during OR
The function 119891(119903 119905) (6) describes the temporal evolutionof the size distribution The time dependence of 119903
119892should
be determined in order to define the explicit mode of thisfunction The value 119903
119892can be found from (4) and (5) by
substituting 119903119892for 119903 and a value of the ratio 119903
119892119903119896taken from
(13) for this ratio Integrating (4) for the preliminaryWagnerrsquosmechanism we obtain
1199032
119892= 119861lowast 1
1 minus 1199092119905
1199032
119896= 119861lowast 1 + 119909
(1 minus 119909) (2 + 119909)2119905
(14)
Assuming 119909 = 0 we obtain 1199032119892= 119861lowast119905 1199032
119896= (14)119861lowast119905 and
119903119892119903119896= 2
Alternatively integrating (5) for the preliminary diffusion(diffusion) mechanism we obtain
1199033
119892= 119860lowast 1
119909 (1 + 119909)119905
1199033
119896= 119860lowast (1 + 119909)
2
119909(2 + 119909)3119905
(15)
Assuming 119909 = 1 we obtain 1199033119892= (12)119860lowast119905 1199033
119896= (4
27)119860lowast119905 and 119903119892119903119896= 32
Finally the function 119891(119903 119905) (6) can be defined from thedependence of 119903
119892on 119905
3 Discussion
The distribution (7) is shown in Figure 1(a) as a series ofcurves for various 119909 and Wagnerrsquos distribution (119909 = 0) isshown in the embedment The 119909 = 1 curve corresponds to
4 Journal of Nanomaterials
00 02 04 06 08 10000000
000005
000010
000015
000020
00 02 04 06 08 10
g(u)
8
6
4
2
x = 1
x = 09
x = 08
x = 07
x = 06
x = 05
x = 04x = 03
x = 02x = 01
x = 0
u
times108
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
u
x = 0 x = 1
(b)
Figure 1 The curves corresponding to the GDLSW distribution calculated using the formula (7) with the iteration step Δ119909 = 01 (a) samecurves as in (a) normalized by their maximums (b)
the Lifshitz-Slyozov distribution The same curves normal-ized by theirmaximums are shown in Figure 1(b) Such curvescan be easily compared to the experimental data
The experimental histogram should be presented in thesame normalized mode as the theoretical curves in order toperform their comparison The scale of the horizontal axis(it represents radii 119903 or diameters 119889 of NC in nm) shouldbe transferred to the relative variable (relative diameter) 119906 =119903119903119892= 119889119889
119892 where the maximal diameter 119889
119892is taken from
the histogramThe relative diameter of NC 119906 in the histogramwill be ranged between 0 and 1 after such transformation
All values in the vertical axis corresponding to thenumber of particles in the unit of volume within someinterval Δ119889 are normalized by the maximum of histogramTherefore the histogram is normalized by the unit along allaxes The conformity or inconformity in the theoretical andexperimental data can be evaluated through comparison ofthe experimental histograms and the normalized theoreticalcurves built in the same scaleThe initial and centralmomentscalculated for the experimental and theoretical distributionsshould be compared in order to perform the quantitativecomparison
The comparison between the normalized experimentalhistograms of the Pt NC [47] and the theoretical curves isshown in Figure 2 The histogram (a) shows the initial sizedistribution of the Pt particles and it can be noticed that thishistogram and the GDLSW distribution (7) at x = 02 are ingood agreement
This fact confirms that the OR stage is present even inthe liquid phase synthesis of the Pt NC and that the chemicalreaction running on the Pt NC surface is the governing factorof OR
It should be emphasized that the OR stage has beenidentified and reported using the colloid chemistry methodsin some liquid phase syntheses of NC (including semicon-ducting NC) [32 49ndash51]
Having calculated the ratio 119903119892119903119896(13) and themean radius
of the Pt particles (⟨r⟩= 262 (plusmn06) nm) (in the framework of
the LSW theory this radius corresponds to the critical value119903119896) the maximal radius 119903
119892of the Pt NC can be calculated as
119903119892= 119903119896
2 + 119909
1 + 119909 (16)
where x = 02 as follows from Figure 2(a) Within themeasurement error the maximal size calculated by (16) rg =48 nm is in good agreement with the maximal size of Pt NCrg asymp 43 nm measured experimentally
A mean size of NC rises up to (⟨r⟩ = 858 (plusmn245) nm)[47] and their sphericity becomes more perfect as a result ofthermotreatment of nanocomposites at 550∘CThe histogram(b) in Figure 2 shows size distribution for the particles at550∘C and it is easily noticeable that it fits with the GDLSWdistribution at x = 01 which is very close to WagnerrsquosdistributionThe maximal size 119903
119892according to the histogram
(b) is 165 nm and according to the formula (16) it is about164 nm This agreement seems too good and can be aresult of significant errors committed in the plotting of theexperimental histograms However two conclusions can bedrawn from the results seen in Figure 2(a) first as noticedin [47] the shapes of the histograms (a) and (b) are quiteclose second the rate of the PtNC growthdissolution duringtheir sintering is controlled by the surface chemical reactionrunning on the NC that is Wagnerrsquos mechanism Fasterdiffusion processes (diffusion) do not control OR
Further rise in the NC sizes occurs at rise in temperatureof the nanocomposites thermotreatment and an average sizeof the PtNC reaches (⟨r⟩= 1589 (plusmn523) nm) at 800∘C [47] Ahistogram reflecting sizes distribution for the 800∘C sinteringof Pt NC is shown in Figure 2(c) Similar to the previouscases (a) and (b)Wagnerrsquos distribution or theGDLSWmodelat x = 01 is in good agreement with the (c) histogramThis is another proof of the governing role of the kineticallycontrolled Wagnerrsquos mechanism of the Pt NC sintering at800∘C This process is one of infrequent examples of thedisperse particles growthdissolution involving OR totallycontrolled by the surface chemical reaction
Journal of Nanomaterials 5
00 02 04 06 08 1000
02
04
06
08
10g(u)gmax
u
x = 02
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 01
u
(b)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 0 x = 1
x = 01
u
(c)
Figure 2 Comparison of the experimental Pt NC histograms with the theoretical GDLSW distributions (a) source histogram (b) heatingto 550∘C and (c) heating to 800∘C
Good agreement between the maximal sizes of Pt NC119903119892derived from the experimental histograms and calculated
using the formula (16) also confirms correctness of com-parison between the experimental and the theoretical sizedistributions For example the maximal size calculated using(16) for 800∘C is rg = 318 nm while the experimental value isrg = 339 nm Taking into account the experimental error thisdifference is rather insufficient
Therefore the modified LSW theory is an adequate toolfor the description of the Pt NC sintering according to theORmechanism within the entire temperature range consideredin this paper
4 Conclusion
A theoretical analysis of the Pt NC sintering has been per-formed within some temperature range using the modifiedLSW theory The theoretical GDLSW distribution with the 119909value about the unit can adequately describe the experimentalsize distribution for the Pt NC Therefore only the surface
chemical reaction on the Pt NC (Wagnerrsquos mechanism) gov-erns the processes of growingdissolution of the nanoparticlesat the stage of OR Moreover the same mechanism also con-trols the process of the Pt NC growthdissolution during theirliquid phase synthesis This is one of infrequent examples ofOR for nanoparticles that is totally controlled by the chemicalreaction according to Wagnerrsquos mechanism This conclusioncan be proven by comparison of the source experimentalhistograms and theoretical curves built according to theGDLSW approximation at x = 02
Analysis of the high temperature sintering of PtNC showsgood agreement between the experimental and theoreticalmaximum sizes of the particles 119903
119892and brings another evi-
dence for correctness of the above theory
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
Equation (4) describes the rate of the Pt NC growthgoverned mostly by the kinetic subflux 119895
119894with partial con-
tribution 119909made by the diffusion subflux 119895V On the contrary(5) describes the rate of the Pt NC growth governed mostlyby the diffusion subflux 119895V with partial contribution (1 minus 119909)made by the kinetic subflux Therefore the rates of growth(4) and (5) can be represented in the LSW theory by the ratiobetween subfluxes 119895V and 119895119894
According to [48] 119891(119903 119905) can be represented by theproduct of two functions one depending on time 119905 andanother depending on the relative variable 119906
011990631198921015840(119906)119889119906119872 is total mass of the NCs in the
unit of volume and 120588 is density of the NCrsquos substanceA definition of the relative variable in the form
119906 =119903
119903119892
(8)
instead of the traditional form 120588 = 119903119903119896 was proposed
in [48] and in this way the variation interval of u becameindependent on the growth mechanism of the NC (0 le119906 le 1) Function 119892(119906) in form (7) (or function 1198921015840(119906)(with accuracy to the constantQ)) represents the generalizeddistribution of Lifshitz-Slyozov-Wagner (119866119863119871119878119882) whichinvolves simultaneously twomechanisms of growth diffusionand Wagnerrsquos
The distribution 1198921015840(119906) can be obtained by integrationof (2) with account of (4) or (5) and proceeding fromdifferentiation by 119903 and 119905 to differentiation by 119906 [9 10]
Assuming 119909 = 0 119861 = 5 119863 = minus1 and 119862 = minus3 (9)transforms (with accuracy to the constant Q) into Wagnerrsquosdistribution [6]
1198921015840(119906) = 119906(1 minus 119906)
minus5 exp(minus 3
1 minus 119906) (11)
Assuming 119909 = 1 119861 = 113 119863 = minus73 and 119862 = minus1 (9)matches the Lifshitz-Slyozov distribution [4 5]
1198921015840(119906) = 119906
2(1 minus 119906)
minus113(119906 + 2)
minus73 exp(minus 1
1 minus 119906) (12)
The 119866119863119871119878119882 distribution (7) can represent adequatelythe size distribution for 0 le 119909 le 1 As the average size⟨119903⟩ (or critical size 119903
119896) is growing continuously during OR
the maximum size 119903119892grows as well although the ratio 119903
119892119903119896
remains unchanged According to the modified LSW theory[9 10]
119903119892
119903119896
=2 + 119909
1 + 119909 (13)
ConsideringWagnerrsquosmechanism of the growing and assum-ing 119909 = 0 we obtain 119903
119892119903119896= 2 and for the diffusion
mechanism and 119909 = 1 119903119892119903119896= 32
Since the ratio 119903119892119903119896is a time independent constant
the size distribution 1198921015840(119906) does not depend on the initialdistribution Therefore some generally used characteristicsof 1198921015840(119906) depending on the initial and central moments(dispersion ⟨1199062⟩ minus ⟨119906⟩2 the mean relative radius ⟨119906⟩ areaunder the curve etc) also do not depend on time during OR
The function 119891(119903 119905) (6) describes the temporal evolutionof the size distribution The time dependence of 119903
119892should
be determined in order to define the explicit mode of thisfunction The value 119903
119892can be found from (4) and (5) by
substituting 119903119892for 119903 and a value of the ratio 119903
119892119903119896taken from
(13) for this ratio Integrating (4) for the preliminaryWagnerrsquosmechanism we obtain
1199032
119892= 119861lowast 1
1 minus 1199092119905
1199032
119896= 119861lowast 1 + 119909
(1 minus 119909) (2 + 119909)2119905
(14)
Assuming 119909 = 0 we obtain 1199032119892= 119861lowast119905 1199032
119896= (14)119861lowast119905 and
119903119892119903119896= 2
Alternatively integrating (5) for the preliminary diffusion(diffusion) mechanism we obtain
1199033
119892= 119860lowast 1
119909 (1 + 119909)119905
1199033
119896= 119860lowast (1 + 119909)
2
119909(2 + 119909)3119905
(15)
Assuming 119909 = 1 we obtain 1199033119892= (12)119860lowast119905 1199033
119896= (4
27)119860lowast119905 and 119903119892119903119896= 32
Finally the function 119891(119903 119905) (6) can be defined from thedependence of 119903
119892on 119905
3 Discussion
The distribution (7) is shown in Figure 1(a) as a series ofcurves for various 119909 and Wagnerrsquos distribution (119909 = 0) isshown in the embedment The 119909 = 1 curve corresponds to
4 Journal of Nanomaterials
00 02 04 06 08 10000000
000005
000010
000015
000020
00 02 04 06 08 10
g(u)
8
6
4
2
x = 1
x = 09
x = 08
x = 07
x = 06
x = 05
x = 04x = 03
x = 02x = 01
x = 0
u
times108
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
u
x = 0 x = 1
(b)
Figure 1 The curves corresponding to the GDLSW distribution calculated using the formula (7) with the iteration step Δ119909 = 01 (a) samecurves as in (a) normalized by their maximums (b)
the Lifshitz-Slyozov distribution The same curves normal-ized by theirmaximums are shown in Figure 1(b) Such curvescan be easily compared to the experimental data
The experimental histogram should be presented in thesame normalized mode as the theoretical curves in order toperform their comparison The scale of the horizontal axis(it represents radii 119903 or diameters 119889 of NC in nm) shouldbe transferred to the relative variable (relative diameter) 119906 =119903119903119892= 119889119889
119892 where the maximal diameter 119889
119892is taken from
the histogramThe relative diameter of NC 119906 in the histogramwill be ranged between 0 and 1 after such transformation
All values in the vertical axis corresponding to thenumber of particles in the unit of volume within someinterval Δ119889 are normalized by the maximum of histogramTherefore the histogram is normalized by the unit along allaxes The conformity or inconformity in the theoretical andexperimental data can be evaluated through comparison ofthe experimental histograms and the normalized theoreticalcurves built in the same scaleThe initial and centralmomentscalculated for the experimental and theoretical distributionsshould be compared in order to perform the quantitativecomparison
The comparison between the normalized experimentalhistograms of the Pt NC [47] and the theoretical curves isshown in Figure 2 The histogram (a) shows the initial sizedistribution of the Pt particles and it can be noticed that thishistogram and the GDLSW distribution (7) at x = 02 are ingood agreement
This fact confirms that the OR stage is present even inthe liquid phase synthesis of the Pt NC and that the chemicalreaction running on the Pt NC surface is the governing factorof OR
It should be emphasized that the OR stage has beenidentified and reported using the colloid chemistry methodsin some liquid phase syntheses of NC (including semicon-ducting NC) [32 49ndash51]
Having calculated the ratio 119903119892119903119896(13) and themean radius
of the Pt particles (⟨r⟩= 262 (plusmn06) nm) (in the framework of
the LSW theory this radius corresponds to the critical value119903119896) the maximal radius 119903
119892of the Pt NC can be calculated as
119903119892= 119903119896
2 + 119909
1 + 119909 (16)
where x = 02 as follows from Figure 2(a) Within themeasurement error the maximal size calculated by (16) rg =48 nm is in good agreement with the maximal size of Pt NCrg asymp 43 nm measured experimentally
A mean size of NC rises up to (⟨r⟩ = 858 (plusmn245) nm)[47] and their sphericity becomes more perfect as a result ofthermotreatment of nanocomposites at 550∘CThe histogram(b) in Figure 2 shows size distribution for the particles at550∘C and it is easily noticeable that it fits with the GDLSWdistribution at x = 01 which is very close to WagnerrsquosdistributionThe maximal size 119903
119892according to the histogram
(b) is 165 nm and according to the formula (16) it is about164 nm This agreement seems too good and can be aresult of significant errors committed in the plotting of theexperimental histograms However two conclusions can bedrawn from the results seen in Figure 2(a) first as noticedin [47] the shapes of the histograms (a) and (b) are quiteclose second the rate of the PtNC growthdissolution duringtheir sintering is controlled by the surface chemical reactionrunning on the NC that is Wagnerrsquos mechanism Fasterdiffusion processes (diffusion) do not control OR
Further rise in the NC sizes occurs at rise in temperatureof the nanocomposites thermotreatment and an average sizeof the PtNC reaches (⟨r⟩= 1589 (plusmn523) nm) at 800∘C [47] Ahistogram reflecting sizes distribution for the 800∘C sinteringof Pt NC is shown in Figure 2(c) Similar to the previouscases (a) and (b)Wagnerrsquos distribution or theGDLSWmodelat x = 01 is in good agreement with the (c) histogramThis is another proof of the governing role of the kineticallycontrolled Wagnerrsquos mechanism of the Pt NC sintering at800∘C This process is one of infrequent examples of thedisperse particles growthdissolution involving OR totallycontrolled by the surface chemical reaction
Journal of Nanomaterials 5
00 02 04 06 08 1000
02
04
06
08
10g(u)gmax
u
x = 02
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 01
u
(b)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 0 x = 1
x = 01
u
(c)
Figure 2 Comparison of the experimental Pt NC histograms with the theoretical GDLSW distributions (a) source histogram (b) heatingto 550∘C and (c) heating to 800∘C
Good agreement between the maximal sizes of Pt NC119903119892derived from the experimental histograms and calculated
using the formula (16) also confirms correctness of com-parison between the experimental and the theoretical sizedistributions For example the maximal size calculated using(16) for 800∘C is rg = 318 nm while the experimental value isrg = 339 nm Taking into account the experimental error thisdifference is rather insufficient
Therefore the modified LSW theory is an adequate toolfor the description of the Pt NC sintering according to theORmechanism within the entire temperature range consideredin this paper
4 Conclusion
A theoretical analysis of the Pt NC sintering has been per-formed within some temperature range using the modifiedLSW theory The theoretical GDLSW distribution with the 119909value about the unit can adequately describe the experimentalsize distribution for the Pt NC Therefore only the surface
chemical reaction on the Pt NC (Wagnerrsquos mechanism) gov-erns the processes of growingdissolution of the nanoparticlesat the stage of OR Moreover the same mechanism also con-trols the process of the Pt NC growthdissolution during theirliquid phase synthesis This is one of infrequent examples ofOR for nanoparticles that is totally controlled by the chemicalreaction according to Wagnerrsquos mechanism This conclusioncan be proven by comparison of the source experimentalhistograms and theoretical curves built according to theGDLSW approximation at x = 02
Analysis of the high temperature sintering of PtNC showsgood agreement between the experimental and theoreticalmaximum sizes of the particles 119903
119892and brings another evi-
dence for correctness of the above theory
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
Figure 1 The curves corresponding to the GDLSW distribution calculated using the formula (7) with the iteration step Δ119909 = 01 (a) samecurves as in (a) normalized by their maximums (b)
the Lifshitz-Slyozov distribution The same curves normal-ized by theirmaximums are shown in Figure 1(b) Such curvescan be easily compared to the experimental data
The experimental histogram should be presented in thesame normalized mode as the theoretical curves in order toperform their comparison The scale of the horizontal axis(it represents radii 119903 or diameters 119889 of NC in nm) shouldbe transferred to the relative variable (relative diameter) 119906 =119903119903119892= 119889119889
119892 where the maximal diameter 119889
119892is taken from
the histogramThe relative diameter of NC 119906 in the histogramwill be ranged between 0 and 1 after such transformation
All values in the vertical axis corresponding to thenumber of particles in the unit of volume within someinterval Δ119889 are normalized by the maximum of histogramTherefore the histogram is normalized by the unit along allaxes The conformity or inconformity in the theoretical andexperimental data can be evaluated through comparison ofthe experimental histograms and the normalized theoreticalcurves built in the same scaleThe initial and centralmomentscalculated for the experimental and theoretical distributionsshould be compared in order to perform the quantitativecomparison
The comparison between the normalized experimentalhistograms of the Pt NC [47] and the theoretical curves isshown in Figure 2 The histogram (a) shows the initial sizedistribution of the Pt particles and it can be noticed that thishistogram and the GDLSW distribution (7) at x = 02 are ingood agreement
This fact confirms that the OR stage is present even inthe liquid phase synthesis of the Pt NC and that the chemicalreaction running on the Pt NC surface is the governing factorof OR
It should be emphasized that the OR stage has beenidentified and reported using the colloid chemistry methodsin some liquid phase syntheses of NC (including semicon-ducting NC) [32 49ndash51]
Having calculated the ratio 119903119892119903119896(13) and themean radius
of the Pt particles (⟨r⟩= 262 (plusmn06) nm) (in the framework of
the LSW theory this radius corresponds to the critical value119903119896) the maximal radius 119903
119892of the Pt NC can be calculated as
119903119892= 119903119896
2 + 119909
1 + 119909 (16)
where x = 02 as follows from Figure 2(a) Within themeasurement error the maximal size calculated by (16) rg =48 nm is in good agreement with the maximal size of Pt NCrg asymp 43 nm measured experimentally
A mean size of NC rises up to (⟨r⟩ = 858 (plusmn245) nm)[47] and their sphericity becomes more perfect as a result ofthermotreatment of nanocomposites at 550∘CThe histogram(b) in Figure 2 shows size distribution for the particles at550∘C and it is easily noticeable that it fits with the GDLSWdistribution at x = 01 which is very close to WagnerrsquosdistributionThe maximal size 119903
119892according to the histogram
(b) is 165 nm and according to the formula (16) it is about164 nm This agreement seems too good and can be aresult of significant errors committed in the plotting of theexperimental histograms However two conclusions can bedrawn from the results seen in Figure 2(a) first as noticedin [47] the shapes of the histograms (a) and (b) are quiteclose second the rate of the PtNC growthdissolution duringtheir sintering is controlled by the surface chemical reactionrunning on the NC that is Wagnerrsquos mechanism Fasterdiffusion processes (diffusion) do not control OR
Further rise in the NC sizes occurs at rise in temperatureof the nanocomposites thermotreatment and an average sizeof the PtNC reaches (⟨r⟩= 1589 (plusmn523) nm) at 800∘C [47] Ahistogram reflecting sizes distribution for the 800∘C sinteringof Pt NC is shown in Figure 2(c) Similar to the previouscases (a) and (b)Wagnerrsquos distribution or theGDLSWmodelat x = 01 is in good agreement with the (c) histogramThis is another proof of the governing role of the kineticallycontrolled Wagnerrsquos mechanism of the Pt NC sintering at800∘C This process is one of infrequent examples of thedisperse particles growthdissolution involving OR totallycontrolled by the surface chemical reaction
Journal of Nanomaterials 5
00 02 04 06 08 1000
02
04
06
08
10g(u)gmax
u
x = 02
(a)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 01
u
(b)
00 02 04 06 08 1000
02
04
06
08
10
g(u)gmax
x = 0 x = 1
x = 01
u
(c)
Figure 2 Comparison of the experimental Pt NC histograms with the theoretical GDLSW distributions (a) source histogram (b) heatingto 550∘C and (c) heating to 800∘C
Good agreement between the maximal sizes of Pt NC119903119892derived from the experimental histograms and calculated
using the formula (16) also confirms correctness of com-parison between the experimental and the theoretical sizedistributions For example the maximal size calculated using(16) for 800∘C is rg = 318 nm while the experimental value isrg = 339 nm Taking into account the experimental error thisdifference is rather insufficient
Therefore the modified LSW theory is an adequate toolfor the description of the Pt NC sintering according to theORmechanism within the entire temperature range consideredin this paper
4 Conclusion
A theoretical analysis of the Pt NC sintering has been per-formed within some temperature range using the modifiedLSW theory The theoretical GDLSW distribution with the 119909value about the unit can adequately describe the experimentalsize distribution for the Pt NC Therefore only the surface
chemical reaction on the Pt NC (Wagnerrsquos mechanism) gov-erns the processes of growingdissolution of the nanoparticlesat the stage of OR Moreover the same mechanism also con-trols the process of the Pt NC growthdissolution during theirliquid phase synthesis This is one of infrequent examples ofOR for nanoparticles that is totally controlled by the chemicalreaction according to Wagnerrsquos mechanism This conclusioncan be proven by comparison of the source experimentalhistograms and theoretical curves built according to theGDLSW approximation at x = 02
Analysis of the high temperature sintering of PtNC showsgood agreement between the experimental and theoreticalmaximum sizes of the particles 119903
119892and brings another evi-
dence for correctness of the above theory
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
Figure 2 Comparison of the experimental Pt NC histograms with the theoretical GDLSW distributions (a) source histogram (b) heatingto 550∘C and (c) heating to 800∘C
Good agreement between the maximal sizes of Pt NC119903119892derived from the experimental histograms and calculated
using the formula (16) also confirms correctness of com-parison between the experimental and the theoretical sizedistributions For example the maximal size calculated using(16) for 800∘C is rg = 318 nm while the experimental value isrg = 339 nm Taking into account the experimental error thisdifference is rather insufficient
Therefore the modified LSW theory is an adequate toolfor the description of the Pt NC sintering according to theORmechanism within the entire temperature range consideredin this paper
4 Conclusion
A theoretical analysis of the Pt NC sintering has been per-formed within some temperature range using the modifiedLSW theory The theoretical GDLSW distribution with the 119909value about the unit can adequately describe the experimentalsize distribution for the Pt NC Therefore only the surface
chemical reaction on the Pt NC (Wagnerrsquos mechanism) gov-erns the processes of growingdissolution of the nanoparticlesat the stage of OR Moreover the same mechanism also con-trols the process of the Pt NC growthdissolution during theirliquid phase synthesis This is one of infrequent examples ofOR for nanoparticles that is totally controlled by the chemicalreaction according to Wagnerrsquos mechanism This conclusioncan be proven by comparison of the source experimentalhistograms and theoretical curves built according to theGDLSW approximation at x = 02
Analysis of the high temperature sintering of PtNC showsgood agreement between the experimental and theoreticalmaximum sizes of the particles 119903
119892and brings another evi-
dence for correctness of the above theory
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
[2] W Ostwald ldquoUber die vermeintliche isometric des rotenundgelben quecksilberxyds und die oberflachenspannung fes-ter korperrdquoZeitschrift fur Physikalische Chemie vol 34 pp 495ndash503 1900
[3] R D Vengrenovich Y V Gudyma and S V Yarema ldquoOst-wald ripening of nanostructures with quantum dotsrdquo Fizika iTekhnika Poluprovodnikov vol 35 no 12 pp 1440ndash1444 2001
[4] I M Lifshits and V V Slyozov ldquoOn kinetics of diffusion decayof oversaturated solid solutionsrdquo Journal of Experimental andTheoretical Physics vol 35 pp 479ndash492 1958
[5] I M Lifshitz and V V Slyozov ldquoThe kinetics of precipitationfrom supersaturated solid solutionsrdquo Journal of Physics andChemistry of Solids vol 19 no 1-2 pp 35ndash50 1961
[6] C Wagner ldquoTheorie der alterung von niderschlagen durchumlosen (Ostwald Reifung)rdquo Zeitschrift fur Elektrochemie vol65 pp 581ndash591 1961
[7] V V Slyozov ldquoCoalescence of the supersaturated solid solutionin the case of diffusion block boundaries or dislocation linesrdquoFizika Tverdogo Tela vol 9 no 4 pp 1187ndash1191 1967
[8] V V Slyozov and V V Sagalovich ldquoDiffusive decomposition ofsolid solutionsrdquo Uspekhi Fizicheskikh Nauk vol 151 no 1 pp67ndash104 1987
[9] R D Vengrenovich B V Ivanskii and A V MoskalyukldquoGeneralized Lifshitz-Slyozov-Wagner distributionrdquo Journal ofExperimental and Theoretical Physics vol 131 pp 1040ndash10472007
[10] R D Vengrenovich B V Ivanskyi and A V Moskalyuk ldquoGen-eralized chakraverty-wagner distributionrdquoUkrainian Journal ofPhysics vol 53 no 11 pp 1101ndash1109 2008
[11] M H Huang S Mao H Feick et al ldquoRoom-temperatureultraviolet nanowire nanolasersrdquo Science vol 292 no 5523 pp1897ndash1899 2001
[12] X W Sun J Z Huang J X Wang and Z Xu ldquoA ZnO nanorodinorganicorganic heterostructure light-emitting diode emit-ting at 342 nmrdquo Nano Letters vol 8 no 4 pp 1219ndash1223 2008
[13] Y Jin J Wang B Sun J C Blakesley and N C GreenhamldquoSolution-processed ultraviolet photodetectors based on col-loidal ZnO nanoparticlesrdquo Nano Letters vol 8 no 6 pp 1649ndash1653 2008
[14] C Lizandara-Pueyo S Siroky M R Wagner et al ldquoShapeanisotropy influencing functional properties trigonal prismaticZnO nanoparticles as an examplerdquo Advanced Functional Mate-rials vol 21 no 2 pp 295ndash304 2011
[15] L Spanhel ldquoColloidal ZnO nanostructures and functionalcoatings a surveyrdquo Journal of Sol-Gel Science and Technologyvol 39 no 1 pp 7ndash24 2006
[16] A B Djurisic and Y H Leung ldquoOptical properties of ZnOnanostructuresrdquo Small vol 2 pp 944ndash961 2006
[17] K L Chopra and S R Das EdsThin Film Solar Cells PlenumNew York NY USA 1983
[18] S Hingorani V Pillai P Kumar M S Multani and DO Shah ldquoMicroemulsion mediated synthesis of zinc-oxidenanoparticles for varistor studiesrdquo Materials Research Bulletinvol 28 no 12 pp 1303ndash1310 1993
[19] O P Pchelyakov Y B Nikiforov A I Yakimov and B Foy-htlender ldquoSilicon-germanium nanostructures with quantumdots formation mechanisms and an electric propertiesrdquo Fizikai Tekhnika Poluprovodnikov vol 34 pp 1281ndash1299 2000
[20] O P Pchelyakov Y B Nikiforov A I Yakimov and BFoyhtlender ldquoNucleation of coherent semiconductor islandsduring stranski-krastanow growth induced by elastic stressesrdquoFizika i Tekhnika Poluprovodnikov vol 36 pp 1177ndash1185 2002
[21] V N Nevedomskyi N A Bert V V Chaldyshev V VPreobrazhenskyi M A Putiato and B R Semiahin ldquoGaAsstructures with InAs and As quantum dots produced in asingle process of molecular beam epitaxyrdquo Fizika i TekhnikaPoluprovodnikov vol 43 pp 1662ndash1666 2009
[22] M Burger T Schupp K Lischka and D J As ldquoCathodolu-minescence spectroscopy of zinc-blende GaN quantum dotsrdquoPhysica Status Solidi (C) Current Topics in Solid State Physicsvol 9 no 5 pp 1273ndash1277 2012
[23] P-S Kuo B-C Hsu P-W Chen P S Chen and C W LiuldquoRecessed oxynitride dots on self-assembled Ge quantum dotsgrown by LPDrdquo Electrochemical and Solid-State Letters vol 7no 10 pp G201ndashG203 2004
[24] I N Stranski and L Krastanov ldquoAbhandlungen der mathe-matisch-naturwissenschaftlichen klasse IIbrdquoAkademie derWis-senschaften Wien vol 146 pp 797ndash810 1938
[25] Z R Tian J A Voigt J Liu et al ldquoComplex and oriented ZnOnanostructuresrdquo Nature Materials vol 2 no 12 pp 821ndash8262003
[26] C Pacholski A Kornowski and H Weller ldquoSelf-assemblyof ZnO from nanodots to nanorodsrdquo Angewandte ChemiemdashInternational Edition vol 41 pp 1188ndash1191 2002
[27] C Ribeiro E J H Lee E Longo and E R Leite ldquoA kineticmodel to describe nanocrystal growth by the oriented attach-ment mechanismrdquo ChemPhysChem vol 6 no 4 pp 690ndash6962005
[28] R Bandyopadhyaya R Kumar K S Gandhi and D Ramkr-ishna ldquoModeling of precipitation in reverse micellar systemsrdquoLangmuir vol 13 no 14 pp 3610ndash3620 1997
[29] M Ethayaraja K Dutta and R Bandyopadhyaya ldquoMechanismof nanoparticle formation in self-assembled colloidal templatespopulation balance model and Monte Carlo simulationrdquo Jour-nal of Physical Chemistry B vol 110 no 33 pp 16471ndash164812006
[30] M Ethayaraja and R Bandyopadhyaya ldquoPopulation balancemodels andMonte Carlo simulation for nanoparticle formationin water-in-oil microemulsions Implications for CdS synthe-sisrdquo Journal of the American Chemical Society vol 128 no 51pp 17102ndash17113 2006
[31] R Bandyopadhyaya R Kumar and K S Gandhi ldquoModelling ofCaCO
3nanoparticle formation during overbasing of lubricat-
ing oil additivesrdquo Langmuir vol 17 no 4 pp 1015ndash1029 2001[32] A Layek GMishra A Sharma et al ldquoA generalized three-stage
mechanism of ZnO nanoparticle formation in homogeneousliquid mediumrdquo Journal of Physical Chemistry C vol 116 no46 pp 24757ndash24769 2012
[33] A deKergommeaux J Faure-Vincent A Pron R de BettigniesBMalaman and P Reiss ldquoSurface oxidation of tin chalcogenidenanocrystals revealed by 119Sn-Mossbauer spectroscopyrdquo Jour-nal of the American Chemical Society vol 134 no 28 pp 11659ndash11666 2012
[34] S Sapra and D D Sarma ldquoGrowth kinetics of ZnO nanocrys-tals a few surprisesrdquo Physical Review BmdashCondensedMatter andMaterials Physics vol 69 Article ID 125304 2004
[35] R Viswanatha S Sapra T Saha-Dasgupta and D D SarmaldquoElectronic structure of and quantum size effect in III-V and II-VI semiconducting nanocrystals using a realistic tight binding
Journal of Nanomaterials 7
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
approachrdquo Physical Review BmdashCondensedMatter andMaterialsPhysics vol 72 no 4 Article ID 045333 2005
[36] G Oskam Z Hu R L Penn N Pesika and P C SearsonldquoCoarsening of metal oxide nanoparticlesrdquo Physical Review EmdashStatistical Nonlinear and Soft Matter Physics vol 66 no 1Article ID 011403 4 pages 2002
[37] P E Lippens and M Lannoo ldquoCalculation of the band gap forsmall CdS and ZnS crystallitesrdquo Physical Review BmdashCondensedMatter and Materials Physics vol 39 no 15 pp 10935ndash109421989
[38] S Sapra N Shanthi and D D Sarma ldquoRealistic tight-bindingmodel for the electronic structure of II-VI semiconductorsrdquoPhysical Review BmdashCondensed Matter and Materials Physicsvol 66 no 20 Article ID 205202 8 pages 2002
[39] R Viswanatha H Amenitsch and D D Sarma ldquoGrowthkinetics of ZnO nanocrystals a few surprisesrdquo Journal of theAmericanChemical Society vol 129 no 14 pp 4470ndash4475 2007
[40] S Iijima ldquoHelicalmicrotubules of graphitic carbonrdquoNature vol354 no 6348 pp 56ndash58 1991
[41] A V Eletskii ldquoCarbon nanotubes and their emission proper-tiesrdquo Uspekhi Fizicheskih Nauk vol 172 pp 401ndash438 2002
[42] P N Diachkov ldquoCarbon nanotubes materials for computersXXI centuryrdquo Priroda vol 11 pp 23ndash30 2000
[43] S J Tans M H Devoret H Dai et al ldquoIndividual single-wallcarbon nanotubes as quantumwiresrdquoNature vol 386 no 6624pp 474ndash477 1997
[44] W Choi ldquoCarbon nanotubes for full color field-emissiondisplaysrdquo Japanese Journal of Applied Physics vol 39 no 1 pp2560ndash2564 2000
[45] J-M Bonard T Stockli O Noury and A Chatelain ldquoFieldemission from cylindrical carbon nanotube cathodes possibil-ities for luminescent tubesrdquo Applied Physics Letters vol 78 no18 pp 2775ndash2777 2001
[46] R Vengrenovich B Ivanskii I Panko and M Stasyk ldquoSizedistribution of nanoparticles of ZnO and SnS in the frameof Lifshits-Slezov-Wagner modified theoryrdquo Journal of PhysicalChemistry C vol 117 no 26 pp 13681ndash13687 2013
[47] C Mateo-Mateo C Vazquez-Vazquez M Perez-Lorenzo VSalgueirino and M A Correa-Duarte ldquoOstwald ripening ofplatinum nanoparticles confined in a carbon nanotubesilica-templated cylindrical spacerdquo Journal of Nanomaterials vol2012 Article ID 404159 6 pages 2012
[48] R D Vengrenovich ldquoOn the Ostwald ripening theoryOverview 20rdquo Acta Metallurgica vol 20 pp 1079ndash1086 1982
[49] C Lizandara-Pueyo M W E van den Berg A De Toni TGoes and S Polarz ldquoNucleation and growth of ZnO in organicsolventsmdashan in situ studyrdquo Journal of the American ChemicalSociety vol 130 no 49 pp 16601ndash16610 2008
[50] D Segets L M Tomalino J Gradl and W Peukert ldquoReal-timemonitoring of the nucleation and growth of zno nanoparticlesusing an optical hyper-rayleigh scattering methodrdquo Journal ofPhysical Chemistry C vol 113 no 28 pp 11995ndash12001 2009
[51] A P Thurber G Alanko G L Beausoleil II K N Dodge CB Hanna and A Punnoose ldquoUnusual crystallite growth andmodification of ferromagnetism due to aging in pure and dopedZnO nanoparticlesrdquo Journal of Applied Physics vol 111 no 7Article ID 07C319 2012
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