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J. Phys. Chem. C 2008, 112, 2404-2411
Growth Kinetics of ZnO Nanorods: Capping-Dependent Mechanism and Other Interesting Features Kanishka Biswas, Barun Das, and C. N. R. Rao* Chemistry and Physics of Materials Unit, DST nanoscience unit and CSIR Centre of Excellence in Chemistry, Jawaharlal Nehru Centre for AdVanced Scientific Research, Jakkur P. O., Bangalore-560064, India, and Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India ReceiVed: September 18, 2007; In Final Form: NoVember 6, 2007
Although the growth of nanocrystals has been investigated by several workers, investigations of the growth of 1-D nanostructures have been limited. We have investigated the growth kinetics of both uncapped and poly(vinyl pyrollidone) (PVP)-capped ZnO nanorods carefully by a combined use of transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) which provide direct information on size and shape and compensate for the deficiency of each other. Values of average length and diameter of the ZnO nanorods obtained by TEM and SAXS are comparable. In the presence of the capping agent, the length of the nanorods grows faster while the diameter becomes narrower. The length distribution shows periodic changes in the width in the case of the uncapped nanorods, a feature absent in the case of the capped nanorods. In the absence of the capping agent, we observe the presence of small nanocrystals next to the nanorods after a lapse of time. The occurrence of small nanocrystals as well as the periodic focusing and defocusing of the width of the length distribution lend support to the diffusion-limited growth model for the growth of uncapped ZnO nanorods. Accordingly, the time dependence of the length of uncapped nanorods follows the L3 law as required for diffusion-limited Ostwald ripening, while the PVP-capped nanorods show a time dependence which is best described by a combination of diffusion and surface reaction with a L3 + L2 type behavior. Collapse of all distribution curves obtained at different times of the reaction into a single universal Gaussian in the case of the PVP-capped nanorods also shows that the growth mechanism is more complex than Ostwald ripening.
Introduction Nanorods and nanowires constitute an important class of nanomaterials1,2 and chemical routes have proved to be more useful for the synthesis of these one-dimensional materials, just as in the case of nanocrystals.3,4 The growth mechanism of nanocrystals has attracted the attention of a few workers recently. One of the popular mechanisms employed to explain the growth kinetics of nanocrystals is the diffusion-limited Ostwald ripening process following the Lifshitz-Slyozov-Wagner (LSW) theory.5,6 An early study of the growth kinetics of ZnO nanocrystals in the absence of capping agents revealed the diffusion-limited growth mechanism to be valid.7 A more recent study of ZnO nanocrystals in the absence of NaOH has also shown that the variation of particle size follows the LSW model for diffusionlimited coarsening.8 Alivisatos and co-workers9 examined the growth of CdSe and InAs nanocrystals by employing UVvisible absorption spectroscopy to determine the size of nanocrystals and by employing the band widths of the photoluminescence spectra to determine their size distribution. These workers observed a focusing and defocusing effect of the size distribution similar to that expected in Ostwald ripening. Qu et al.10 have shown that the growth of CdSe nanocrystals involves a prolonged formation of relatively small particles (nucleation) followed by focusing and then defocusing of the size distribution because of the growth of the bigger particles and disappearance of the small ones. These workers also found the particle size * To whom correspondence should be addressed. E-mail: cnrrao@ jncasr.ac.in. Fax: +91 80 22082760.
distribution to be asymmetric, indicating a diffusion-limited mechanism in the last stage of the growth. In the case of TiO2 nanocrystals, the average particle radius cubed is reported to increase linearly with time consistent with the LSW model of coarsening.11 On the basis of an in situ transmission electron microscope (TEM) investigation, El-Sayed and co-workers12 report a diffusion-controlled growth of small gold nanoclusters. There are a few reports in the literature where the growth kinetics of nanocrystals are found to deviate from the simple diffusion-limited Ostwald ripening model. Thus, Seshadri et al.13 propose the growth of gold nanoparticles to be essentially stochastic wherein the nucleation and growth steps are wellseparated. Furthermore, these workers observe that the average diameter and the standard deviation of the size distribution exhibit the same time dependence. Theoretical considerations suggest that the growth of the nanocrystals could be either controlled by the diffusion of particles, by the reaction at the surface, or by both factors.14 Thus, Viswanatha et al.15 observe the growth of the ZnO nanocrystals in water to follow a growth mechanism intermediate between diffusion-control and surface reaction-control. These workers also report the growth kinetics of the ZnO nanocrystals in the absence of any capping agent to be slower than that predicted by diffusion-controlled Ostwald ripening and to be dependent on the concentration of OH- in a nonmonotonic manner as well as on the temperature.16 Growth kinetics of nanocrystals in the presence of capping agents is determined by several complex factors, and signatures of either the diffusion or the reaction-controlled regimes are
10.1021/jp077506p CCC: $40.75 © 2008 American Chemical Society Published on Web 01/29/2008
Growth Kinetics of ZnO Nanorods seen. The effect of capping agents on the growth of nanocrystals have been examined by a few workers.9,10,17-23 For example, the growth of ZnO nanocrystals in the presence of poly(vinyl pyrollidone) (PVP) is reported to show deviations from Ostwald ripening.17 To our knowledge, information of the mechanism of the growth of nanorods, especially in the presence of capping agents, is limited. A useful study in this context is that of Peng and Peng24,25 who examined the growth kinetics of CdSe nanorods by UV-vis spectroscopy and TEM images and found the diffusion-controlled model to be valid when the monomer concentration was sufficiently high. At low monomer concentrations, the aspect ratio of the rod decreases because of intraparticle diffusion on the surface of the nanocrystal. Thoma et al.26 have observed anisotropic growth of CdSe in the presence of a surfactant. On the basis of TEM studies, Pascholski et al.27 proposed that small ZnO nanoparticles are converted to rods by the oriented attachment mechanism assisted by Ostwald ripening. On the basis of the estimation of nanorod lengths from XRD peak broadening, Zhu et al.28 have found the growth kinetics of oleic acid-capped ZnO nanorods to deviate from Ostwald ripening. In the present study, we have carried out a detailed investigation of the growth of ZnO nanorods prepared solvothermally in the presence and absence of a capping agent by employing TEM and SAXS. Employing two such independent techniques is important because of the limitations of the techniques themselves. While TEM is the most direct probe to observe the size, shape, and the size distribution of nanostructures, it is not possible to carry out in situ measurements. Furthermore, the sampling size in TEM is rather small. SAXS, on the other hand, provides a direct probe to determine the size and shape of nanomaterials, and the sampling size is much larger than what can be used in TEM. The determination of size and shape in SAXS, however, is dependent on the model employed for fitting the data. A combined use of TEM and SAXS provides a satisfactory means to study the growth of one-dimensional (1D) nanorods. We should note that UV-vis, photoluminescence, and such spectroscopic methods are indirect and are strongly affected by the change in the electronic structure of the nanomaterials. Furthermore, the spectroscopic methods are not as suitable for the study of nanorods as for nanocrystals, since the size of the former is determined both by length and by radius. Widths of X-ray diffraction peaks provide only average values of size which are not reliable in the case of nanorods. The present study of the growth of ZnO nanorods in the presence and absence of a capping agent (PVP) has enabled us not only to determine the growth mechanism of ZnO nanorods but also to determine the effect of the capping agent. The length of the nanorods increases preferentially in the presence of PVP. We find that the growth mechanism of the ZnO nanorods in the absence of PVP follows the diffusion-limited Ostwald ripening mechanism, with evidence of focusing and defocusing of the length distribution. In the presence of PVP, the growth mechanism deviates from the diffusion-limited LSW model requiring an additional contribution from a surface process. Experimental Section Synthesis of ZnO Nanorods. In order to carry out the growth study in the absence of any capping agent, ZnO nanorods were prepared by the reaction of zinc acetate dihydrate (Zn(CH3COO)2‚2H2O) and sodium hydroxide in ethanol at 100 °C under solvothermal conditions. The reaction was stopped at different times (1, 2, 3, 6, 12, 18, and 24 h), and the products were analyzed by TEM and SAXS. In a typical synthesis, Zn(CH3-
J. Phys. Chem. C, Vol. 112, No. 7, 2008 2405 COO)2‚2H2O (0.05 g. 0.23 mmol) was dissolved in 12 mL ethanol, and NaOH (0.228 g, 5.69 mmol) was added under stirring. The reaction mixture was sealed in a Teflon-lined autoclave of 20 mL capacity (60% filling fraction) and maintained at 100 °C in a hot air oven. The solid products obtained at different times after the reaction were thoroughly washed with ethanol and distilled water. To study the effect of the capping agent on the growth process, we prepared the ZnO nanorods in the presence of PVP (0.25 g, MW ∼ 55 000) by maintaining the other reaction parameters the same as in the synthesis of the uncapped ZnO nanorods. The samples were taken out after different reaction times (1, 2, 3, 6, 12, 18, and 24 h) for investigation. TEM Characterization. The solid products obtained after different reaction periods were dispersed in ethanol by sonication, and the dispersions were taken on holey carbon-coated Cu grids for TEM investigations with a JEOL (JEM3010) microscope operating with an accelerating voltage of 300 kV. The length and diameter distribution were obtained from magnified micrographs by using DigitalMicrograph 3.4 software. Typically, 150-200 well-separated nanorods from three or four micrographs of the same sample were used to arrive at the size distribution. SAXS Characterization. The average length and diameter of the ZnO nanorods could be readily obtained by SAXS.29-31 We performed SAXS experiments with a Bruker-AXS NanoSTAR instrument modified and optimized for solution scattering. The instrument is equipped with a X-ray tube (Cu KR radiation, operated at 45 kV/35 mA), cross-coupled Go¨bel mirrors, threepinhole collimation, evacuated beam path, and a two-dimentional (2D) gas-detector (HI-STAR).31 The modulus of the scattering vector is q ) 4π sin θ/λ, where 2θ is the scattering angle and λ is the X-ray wavelength. We recorded the SAXS data in the q ) 0.007 to 2.2 Å-1 range, that is, 2θ ) 0.1 to 3°. Solutions of the ZnO nanorods in ethanol (approximately 0.1 w/v % concentration) obtained after lapse of different reaction times were used for SAXS measurements. The ethanol solutions of nanorods were taken in quartz capillaries (diameter of about 2 mm) for the measurements. A capillary filled with only ethanol was used for background correction. The concentration of the nanorods was sufficiently low to neglect interparticle interference effects. The experimental SAXS data were fitted by Bruker-AXS DIFFRACplus NANOFIT software by using a solid cylinder model. The form factor of the cylinder used in this software is given by Fournet.32,33 Results and Discussion In order to prepare the ZnO nanorods, we employed a high monomer concentration with a Zn2+/OH- ratio of 1:25. High monomer concentrations favor the growth of the ZnO nanorods27,34 because the chemical potential of an elongated structure is generally higher than a dot-shaped nanocrystal because of the lower surface energy of anisotropic structure.25 As a result, the growth of such an anisotropic structure requires a relatively high chemical potential environment, that is, high monomer concentration in the solution. We could obtain sufficient concentrations of the nanorods with the reactant concentrations and the reaction conditions employed by us. In what follows, we discuss the results of TEM and SAXS studies of the nanorods obtain after different reaction times. Figure 1a,b shows typical TEM images of the uncapped product after 3 and 12 h of reaction. The inset in Figure 1a indicates the presence of a small nanocrystal on the side wall of an uncapped nanorod in the process of dissolution. The inset
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Figure 1. (a,b) TEM images of uncapped ZnO nanorods obtained after 3 and 12 h of reaction. The inset in (a) shows how a small ZnO nanoparticle attached to the side wall of an uncapped ZnO nanorod. The inset in (b) is a TEM image of uncapped ZnO nanorods obtained after 18 h of reaction. The arrow indicates the existence of small nanocrystal along with the nanorods. Several such nanocrystals can be seen in the image. (c,d) TEM images of PVP-capped ZnO nanorods obtained after 3 and 12 h of reaction. Note the absence of nanocrystals sticking to the nanorods.
in Figure 1b shows a TEM image of the uncapped ZnO nanorods after 18 h of reaction. The presence of small nanocrystals with the nanorods is indicated by black arrows in Figure 1b. The existence of small nanocrystals along with the uncapped nanorods after a sufficiently long period of reaction (e.g., 12 or 18 h) suggests that the diffusion-limited Ostwald ripening may be operative, wherein large particles grow at the cost of smaller ones. At the early stage of the growth, the monomer concentration is sufficiently high for the nanorods to grow, and the growth process is fast. After longer times, the monomer concentration gets depleted below a certain critical level, rendering the smaller nanocrystals to dissolve. El-Sayed and co-workers12 have reported the existence of smaller gold nanocrystals located near gold nanorods and observed shrinkage of the nanocrystals with increasing temperature. From the TEM studies, we have estimated the distributions of the length as well as the diameter of the ZnO nanorods after different times of the reaction. Figure 2 shows the time evolution of the length distribution of the uncapped ZnO nanorods (in blue). We have fitted each distribution curve by a Gaussian distribution function (solid blue curve). We see from Figure 2, length distribution becomes sharper and broader in a periodic fashion. Such focusing and defocusing of the diameter distribution is a phenomenon noticed earlier in the case of CdSe nanoparticles growth.9 Since the monomer concentration is high at the beginning of the reaction, focusing of the length distribution (e.g., t ) 3 h) occurs because of a faster growth rate of the small nanorods. When the monomer concentration gets depleted because of the faster growth of the nanorods, the smaller nanorods start to shrink while the longer ones keep
growing. The size distribution, therefore, becomes broader (e.g., t ) 6 h). Dissolution of the small nanorods again enriches the monomer concentration in the solution, with the growth of the longer rods continuing through the diffusion of the monomer from solution to the nanorod surface, giving rise to focusing of the length distribution (e.g., t ) 9, 12 h). Periodic focusing and defocusing of the length distribution is thus dependent on the periodic variation of the monomer concentration in the solution. Focusing and defocusing of the length distribution gives a clean qualitative indication of diffusion-limited growth of uncapped ZnO nanorods. In Figure 1c,d, we show typical TEM images of PVP-capped ZnO nanorods after 3 and 12 h of reaction. We do not see the presence of small nanocrystals along with the nanorods as found earlier in the case of the uncapped nanorods. We have estimated the length distribution of the PVP-capped ZnO nanorods from the TEM images. In Figure 2, we show the histograms (in black) with Gaussian distribution fittings (solid black curve). In the presence of PVP, we do not observe periodic changes in the width of the distribution curves. Instead, we find the width of the length distribution to become broader continuously with reaction time. This reflects the growth of ZnO nanorods in the presence of PVP to be more complex than simple diffusionlimited growth. Seshadri et al.13 had observed a similar increase in the width of the distribution with time in the case of gold nanocrystals. We now examine the results of SAXS measurements at the same reaction time intervals as in the case of TEM studies. Figure 3a,b shows typical plots of intensity versus scattering vector in the logarithmic scale for different times of the reaction
Growth Kinetics of ZnO Nanorods
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Figure 2. Time evolution of the length distributions of the uncapped (blue) and the PVP-capped (black) ZnO nanorods obtained from TEM images.
in the case of uncapped and PVP-capped ZnO respectively. Under the reaction conditions employed, the length of the nanorods varies significantly with time, while the diameter varies only slightly. On the basis of this observation, we assume the cylindrical shape for the nanorods to analyze the SAXS data. A cylinder is a close approximation of a hexagonal rod. To date, the hexagonal rod model has not been employed in the literature to analyze SAXS data. In order to estimate the average length and diameter of ZnO nanorods, we have fitted the experimental SAXS data to the cylinder model of Bruker-AXS DIFFRACplus NANOFIT software. The form factor of the cylinder is that due to Fournet:32,33
P(q,R,L) )
∫0
π/2
[
]
2J1(qR sin R) sin(qL cos R/2) 2 sin R dR qR sin R qL cos R/2
Here, q is the scattering vector, R is the radius of the cylinder, L is the length of the cylinder, R is the orientation dependent parameter (angle between scattering vector and cylinder long axis), and J1(x) is the first-order Bessel function of the first kind. We have not introduced the length and diameter distribution in the scattering cross-section equation because the form factor amplitude of a cylinder is a more complicated function of length, diameter, and the orientation of the cylinder than the form factor amplitude of a spherical model where the diameter is the only variable. Such a cylindrical model fitting of simulated SAXS data have been reported in the literature.33,35 The solid lines in Figure 3 are the cylinder model fits of the experimental SAXS data. In the case of the uncapped ZnO nanorods, the theoretical fits are good, but the fits are not as good in the case of PVP-
Figure 3. SAXS data of (a) uncapped and (b) PVP-capped ZnO nanorods obtained after different times of reaction. Solid lines are the model fits to the experimental data.
capped ZnO nanorods. We have constructed our model only considering the cylindrical ZnO nanorods present in the solution. The PVP molecules present on the side walls of the nanorods, may be responsible for not obtaining very good fits of the experimental data. Figure 4a,b shows the time evolution of the average length calculated from TEM images (filled circles) and SAXS (open circle) of uncapped and PVP-capped ZnO nanorods, respectively. In the absence of PVP, the length of the nanorods increases from 19 to 52 nm after 24 h of reaction. In the presence of PVP, the growth is greater, and the length increases up to 77 nm after 24 h of reaction. In Figure 5a,b, we show the time evolution of the average diameter and aspect ratio calculated from TEM (filled circles) and SAXS (open circles) of uncapped ZnO nanorods, respectively. The diameter of the uncapped nanorods increases slightly starting from 8.3 to 12.3 nm. The aspect ratio increases from 2.3 to 4.3 after 24 h of reaction. Figure 6a,b shows the time evolution of the average diameter and aspect ratio obtained from TEM images (filled circles) and SAXS (open circles) of PVP-capped ZnO nanorods, respectively. In the presence of PVP, we observe an even smaller variation in the diameter (9.1 to 10.4 nm) compared with the capped ones. The aspect ratio, therefore, increases from 1.8 to 7.4 after 24 h of reaction. It is noteworthy that the estimates of lengths and diameters from TEM and SAXS agree closely.
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Figure 6. Time evolution of the (a) average diameter (〈D〉) and (b) aspect ratio of the PVP-capped ZnO nanorods obtained from TEM and SAXS. Figure 4. Time evolution of the average length (〈L〉) of (a) uncapped and (b) PVP-capped ZnO nanorods obtained from TEM and SAXS.
Figure 5. Time evolution of the (a) average diameter (〈D〉) and (b) aspect ratio of the uncapped ZnO nanorods obtained from TEM and SAXS.
ZnO with a polar hexagonal wurzite structure can be described as being due to the hexagonal close packing of the
oxygen and zinc atoms, in point group 3m and space group P63mc, the zinc atoms being present in the tetrahedral sites. Thus, the crystal habit of wurzite ZnO exhibits well-defined crystallographic faces; that is, polar-terminated (0001) planes and six side facet are generally bound by the (101h0) family of planes. The growth rates of different family of planes follow the sequence (0001) > (101h1) > (101h0).36 ZnO anisotropic structures are normally bound by six (101h0) facets grown along the (0001) direction, that is, along the c axis of the rods. Powder X-ray diffraction patterns of PVP-capped and uncapped ZnO nanorods could be indexed on the hexagonal space group P63mc of ZnO. High-resolution electron microscope (HREM) images along with electron diffraction patterns also support the hexagonal crystal structure as well as the preferential c-directional growth of nanorods. Electron diffraction patterns confirm the single crystallinity of nanorods. PVP appears to selectively cap the side facet of the ZnO nanorods, allowing the growth to occur selectively along the c direction compared with the uncapped ZnO nanorods. As a result, we find the length to grow to a greater extent in the presence of PVP compared with the uncapped situation. When PVP is not present in the solution, there is a possibility of diffusion of the monomer to the side walls of the nanorods, rendering the nanorods thicker compared with the capped ones. The inset in Figure 1a gives a typical TEM image showing the presence of a small nanocrystal on the side wall of an uncapped nanorod in the process of dissolution which supports the proposed mechanism. We do not observe the presence of such small nanocrystal on the side of PVP-capped nanorods in the TEM images. Figure 7a,b shows the time evolution of the standard deviation, σ, of the length calculated from TEM images for uncapped and PVP-capped ZnO nanorods, respectively. In the lower insets of Figure 7, we show the time evolution of the σ of the diameter obtained from TEM images for uncapped and
Growth Kinetics of ZnO Nanorods
Figure 7. Time evolution of the standard deviation of the length (σL) of (a) uncapped and (b) PVP-capped ZnO nanorods. Lower insets in (a) and (b) show the time evolution of the standard deviation of the diameter (σD). Upper inset in (b) shows the plot of mean rod length, 〈L〉, against the σL.
PVP-capped ZnO nanorods, respectively. We observe that σ of the length (σL) and the diameter (σD) vary periodically with time in the absence of PVP as in Figure 7a. This indicates periodic fluctuation of the monomer concentration in the solution during the growth process of uncapped ZnO nanorods. In the presence of PVP, both σL and σD increase continuously with time. By plotting the average length as a function of σL for different times in the case of PVP-capped ZnO nanorods, we find that the mean and the σL bear a linear relationship, with a correlation coefficient (R) of 0.996. This means that both σL and average length have the same time dependence (see upper inset in Figure 7b). We have observed the same linear relationship (R ) 0.988) between σD and the average diameter of the PVP-capped ZnO nanorods for different times. This observation suggests that it should be possible to represent the length or the diameter distribution by means of a variable scaled by the mean length or diameter. We do not observe such a relationship between σ and average length or average diameter in the case of uncapped ZnO nanorods. Figure 8a,b shows plots of normalized frequency (normalized by the maximum counts) against L/〈L〉 in the case of uncapped and PVP-capped nanorods, respectively. In the insets in Figure 8a,b, we show the plots of normalized frequency (normalized by the maximum counts) against D/〈D〉 in the case of uncapped and PVP-capped nanorods, respectively. In the case of the uncapped nanorods (Figure 8a), the distribution is somewhat asymmetric, and we do not obtain as good a universal curve. The asymmetric nature of universal length as well as diameter distribution curves supports a diffusion-limited Ostwald ripening growth mechanism in the case of the uncapped ZnO nanorods. In the case of PVP-capped nanorods, however, all of the data
J. Phys. Chem. C, Vol. 112, No. 7, 2008 2409
Figure 8. Universal length distribution curves of (a) uncapped and (b) PVP-capped ZnO nanorods obtained by scaling mean lengths at different times. Insets in (a) and (b) show the universal diameter distribution curves of (a) uncapped and (b) PVP-capped ZnO nanorods. (Nf ) normalized frequency).
collapse to a single curve that can be represented by the Gaussian distribution function (solid line) as shown in Figure 8b. Ostwald ripening does not appear to be the sole factor determining growth in the case of the PVP-capped nanorods. We have attempted to obtain information regarding the growth mechanisms of ZnO nanorods in the presence and the absence of the capping agent based on the time evolution of the average length of nanorods. If the diffusion-limited Ostwald ripening according to LSW theory5,6 were to be the sole contributor of the growth mechanism, then the rate law would be given by
L3 - L30 ) Kt where, L is the average length at time t and L0 is average initial length of the nanorods. The rate constant K is given by K ) 8γDVm2C∞/9RT, where D is the diffusion constant at temperature T, Vm is the molar volume, γ is the surface energy, and CR is the equilibrium concentration at flat surface. We have tried to fit the L(t) data obtained from TEM and SAXS to the Ostwald ripening model in the case of the uncapped (solid curve in Figure 9a) and the PVP-capped ZnO nanorods (broken curve in Figure 9b). The fit is reasonably good for the uncapped nanorods (reduced χ2 of the fit ) 0.71 and coefficient of determination, R2 ) 0.996) as can be seen from Figure 9a. We have not found it possible to fit the experimental L(t) data of the PVP-capped ZnO nanorods to the diffusion-limited model (χ2 ) 58.59 and R2 ) 0.903). The growth process appears to deviate from diffusion-limited Ostwald ripening. We have also tried to fit the L(t) data of the PVP-capped nanorods to the surface-limited reaction model (i.e., L2 ∝ t) or by varying the value of the
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Biswas et al. barrier present to limit the diffusion process in the case of uncapped nanorods. Conclusions
Figure 9. (a) Fits of L(t) data (solid circles from TEM and open circles from SAXS) of uncapped ZnO nanorods to the Ostwald ripening (L3) model (solid curve). (b) Fits of L(t) data (solid circles from TEM and open circles from SAXS) of PVP-capped ZnO nanorods to the Ostwald ripening (L3) model (broken curve) and mixed diffusion-surface control growth (L3 + L2) model (solid curve).
exponent (n in Ln ∝ t,). We have found the fit of the data either to the surface reaction model (χ2 ) 16.97 and R2 ) 0.972) or to a variable n model to be unsatisfactory. In order to fit the experimental L(t) data of the PVP-capped ZnO nanorods, we have, therefore, used a model which contains both the diffusionlimited and surface-limited growth,15
BL3 + CL2 + const ) t where, B ) AT/exp(-Ea/kBT), A ∝ 1/(D0γVm2C∞), C ∝ T/(kdγVm2C∞), and kd is the rate constant of surface reaction. The remarkable goodness of fits (χ2 ) 0.95 and R2 ) 0.989) over the entire range of experimental data by the mixed diffusion-reaction control model is shown by a thick solid curve in Figure 9b. Thus, the growth of the PVP-capped ZnO nanorods deviates sufficiently from the diffusion-limited Ostwald ripening model and follows a mechanism involving both diffusion-control and surface reaction control. The growth of the nanorods mainly occurs by the diffusion of monomers from solution to the nanorod surface or by the reaction at the surface where units of the diffusing particles get assimilated into the growing nanorods. Diffusion and surface reaction are two limiting cases in the growth of nanorods. In the absence of a capping agent, the nanorod growth is essentially controlled by diffusion as suggested by TEM, as well as the goodness of fits of L(t) data to diffusion-limited growth model. Presence of PVP gives rise to a barrier to diffusion. As a result, the contribution of the surface reaction becomes more prominent. The growth of PVP-capped nanorods occurs through a combination of diffusion and surface reaction processes. There is no
Several major conclusions can be drawn of the growth mechanism of ZnO nanorods based on the present study. The values of the average length and diameter of the nanorods obtained by TEM and SAXS techniques are close to each other in the cases of both uncapped and PVP-capped ZnO nanorods. The average length of the PVP-capped ZnO nanorods grows at a higher rate compared with the uncapped ones, while the average diameter of the capped nanorods grows at a slower rate. PVP appears to selectively cap the side walls of the ZnO nanorods giving rise to such a preferential increase in the aspect ratio. The observation of small nanocrystals along with the nanorods in TEM images lends support to a growth mechanism based on the diffusion-limited Ostwald ripening process in the case of the uncapped nanorods. The uncapped nanorods exhibit periodic changes in the width of the length distribution curves because of changes in the monomer concentration. The periodic focusing and defocusing as well as the somewhat asymmetric nature of the distribution curves (Figure 8) are also the consequence of the diffusion-limited growth of uncapped ZnO nanorods. Good fits of the L(t) data of uncapped ZnO nanorods with L3 model confirms the growth mechanism to be mainly diffusion-controlled. In the presence of PVP, however, the nonexistence of small nanocrystals with the nanorods in the TEM images and the continuous broadening of the width of the size distributions with time reveal the growth mechanism to be more complex than a diffusion-limited process. Fits of the L(t) data to L3 + L2 model suggest that the growth mechanism of the PVP-capped ZnO nanorods involves both diffusion and surface reactions. A similar time dependence of standard deviation σL (or σD) and the average length (or diameter) as well as the collapse of all distributions onto a single Gaussian also suggest that the basic process contributing to the growth of PVP-capped nanorods to be distinct from Ostwald ripening alone. References and Notes (1) Rao, C. N. R.; Govindaraj, A. Nanotubes and Nanowires, RSC series on Nanoscience, Royal Society of Chemistry, London, 2006. (2) Rao, C. N. R., Muller, A., Cheetham, A. K., Eds. The Chemistry of Nanomaterials; Wiley-VCH: Weinheim, 2004; Vols. 1,2. (3) Rao, C. N. R.; Thomas P. J.; Kulkarni, G. U. Nanocrystals: Synthesis, Properties and Applications; Springer: New York, 2007. (4) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025. (5) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (6) Wagner, C. Z. Elektrochem. 1961, 65, 581. (7) Wong, E. M.; Bonevich, J. E.; Searson, P. C. J. Phys. Chem. B 1998, 102, 7770. (8) Hu, Z.; Ramı´rez, D. J. E.; Cervera, B. E. H.; Oskam, G.; and Searson, P. C. J. Phys. Chem. B 2005, 109, 11209. (9) Peng, X.; Wickham, J.; Alivisatos, A. P. J. Am. Chem. Soc. 1998, 120, 5343. (10) Qu, L.; Yu, W. W.; Peng, X. Nano Lett. 2004, 4, 465. (11) Oskam, G.; Nellore, A.; Penn, R. L.; Searson, P. C. J. Phys. Chem. B 2003, 107, 1734. (12) Mohamed, M. B.; Wang, Z. L.; El-Sayed, M. A. J. Phys. Chem. A 1999, 103, 10255. (13) Seshadri, R.; Subbanna, G. N.; Vijayakrishnan, V.; Kulkarni, G. U.; Ananthakrishna, G.; Rao, C. N. R. J. Phys. Chem. 1995, 99, 5639. (14) Talapin, D. V.; Rogach, A. L.; Haase, M.; Weller, H. J. Phys. Chem. 2001, 105, 12278. (15) Viswanatha, R.; Santra, P. K.; Dasgupta, C.; Sarma, D. D. Phys. ReV. Lett. 2007, 98, 255501. (16) Viswanatha, R.; Amenitsch, H.; Sarma, D. D. J. Am. Chem. Soc. 2007, 129, 4470. (17) Viswanatha, R.; Sarma, D. D. Chem. Eur. J. 2006, 12, 180.
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