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J. Phys. Chem. C 2007, 111, 3914-3919
Giant Dielectric Permittivity in Aligned Silver Nanowires Grown within (AgI)(AgPO3) Glasses P. K. Mukherjee,† D. Dutta,‡,§ S. Bhattacharyya,‡,§ A. Ghosh,‡,§ and D. Chakravorty*,‡ Department of Physics, Islampur College, Islampur, West Bengal-733202, India, and DST Unit on Nano Science and Department of Solid State Physics, Indian Association for the CultiVation of Science, JadaVpur, Kolkata 700 032, India ReceiVed: NoVember 4, 2006; In Final Form: January 5, 2007
Silver nanowires of diameters in the range 0.5-3.5 nm have been grown within (AgI)(AgPO3) glasses by subjecting them to an electrodeposition process. Silver nanowires are found to be aligned in the glass containing a high concentration of Ag ions. The electrical resistivity of the composites containing silver nanowires exhibits metallic behavior. The electrical conductivity of the precursor glass shows a frequency variation with an exponent n ∼ 2/3. This indicates a three-dimensional motion of silver ions in the glass when an electric field is applied. The aligned nanowire formation is believed to arise due to an increase in the internal electrical field as a consequence of the aligned dipoles formed by Ag and I ions within the glass matrix. Some of the wires are broken and they give rise to a giant dielectric permittivity (as extracted from the high-frequency value) due to Gorkov-Eliashberg and Rice-Bernasconi mechanisms.
I. Introduction Growth of metallic and elemental nanowires has been an active area of research in recent times because of its importance in the fabrication of nanostructured devices.1-7 Various approaches have been taken for this purpose, both physical and chemical. Some of these are vapor-liquid-solid mechanism, metal surface steps as sites, growth in solution, template growth, growth within transmission electron microscope chamber, etc. We had earlier grown one-dimensional arrays of silver nanoparticles within a silicate glass.8 The approach consisted of first exchanging all the alkali ions within the glass for silver via an ion-exchange reaction. Subsequently the ion-exchanged glass specimen was subjected to an electric field after silver electrodes were applied on the two opposite faces of the specimen. Silver ions moved from the anode to the cathode and, after getting discharged, formed metallic silver at the cathode. This led to the growth of silver nanofilaments and the process stopped when the latter touched the anode. Because of its electrolytic nature, this process was referred to as electrodeposition.9-11 It was shown that some of the specimens exhibited diodelike behavior. The voltage-current characteristics of these specimens showed the asymmetrical nature of a diode. Nanojunctions between large and small particles gave rise to this property. Our earlier work had shown that silver nanoparticles of diameters less than ∼3 nm exhibited a metal-semiconductor transition. A statistical distribution of nanojunctions formed by metal particles with diameters larger than 3 nm and those with diameters less than 3 nm constituted the array of metal semiconductor junctions. This nanostructure thus resulted in a diodelike characteristic. In the present work we have used a fast ion-conducting oxide glass containing silver ions as the template for the growth of * Corresponding author: e-mail
[email protected]. † Islampur College. ‡ DST Unit on Nano Science, Indian Association for the Cultivation of Science. § Department of Solid State Physics, Indian Association for the Cultivation of Science.
silver nanowires. It was found that silver nanowires of diameter ∼0.5-3.5 nm could be grown by this method. The nanowires were aligned parallel with respect to each other in a suitable glass composition. The high-frequency dielectric constant of the samples was very large. The details are reported in this paper. II. Experimental Section The compositions of glasses used were (AgI)x(AgPO3)(1-x) with x having values 0.5 and 0.6. These glasses will be referred to as specimens 1 and 2, respectively in subsequent discussion. AgPO3 glass was first prepared by melting a mixture of weighed quantities of AgNO3 (Aldrich, 99.9%) and NH4H2PO4 (Aldrich, 99%) at 973 K for 6 h in a platinum crucible in an electrically heated furnace. The melt was then poured onto an aluminum mold to quench the same. The AgPO3 glass thus prepared was mixed with an appropriate amount of AgI (Aldrich, 99%) and ground in an agate mortar. The mixture was melted in a platinum crucible at 973 K for 0.5 h and then the melt was quenched in an aluminum mold. Glass formation was confirmed by taking an X-ray diffractogram. The latter did not show any peak, signifying the absence of any crystalline phase. However, electron microscopic investigation of the sample before electrodeposition did show the presence of ultrafine crystals of β-AgI as discussed in the subsequent section. Electrical conductivity variation as a function of frequency was determined by measurements on gold-coated glass samples of diameter ∼10 cm and thickness ∼0.1 cm in the frequency range 10 Hz-2 MHz and temperature range 103-53 K by use of a RLC meter (Quad Tech model 7600). For electrodeposition, specimens of rectangular cross section with area ∼1 cm2 and thickness ∼0.1 cm were coated on both faces with silver paint supplied by Acheson Colloiden BV, Holland. A dc voltage of 10 V was applied across each specimen for a period of 2 h. The resistance of the specimen dropped from ∼1 MΩ to a few kiloohms or less after the electrodeposition run. This indicated the formation of metallic wires. Voltage-current characteristics of the composites of glass and
10.1021/jp067270+ CCC: $37.00 © 2007 American Chemical Society Published on Web 02/17/2007
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Figure 2. (top) Transmission electron micrograph for specimen 1 subjected to electrodeposition and (bottom) its electron diffraction pattern.
TABLE 1: Comparison of Interplanar Spacings Obtained from Specimens 1 and 2 Subjected to Electrodeposition with ASTM Values observed dhkl (nm) specimen 1 specimen 2 0.234 ( 0.001
Figure 1. (a) Transmission electron micrograph for specimen 1. (b) High-resolution electron micrograph of β-AgI nanocrystals within the glass phase. (c) FFT of the crystals in panel b.
metal wires were studied over the temperature range 10-300 K in a closed-cycle cryostat (Zanis, model CCS-450) by use of a Keithley 617 electrometer. Dielectric permittivity as a function of frequency for the composite samples was measured by an impedance meter (Quad Tech model 7600). Microstructural studies of the samples were carried out on a JEM 2010 transmission electron microscope. Specimen preparation details for such investigation have been described earlier.12 III. Results and Discussion Figure 1a is the transmission electron micrograph for specimen 1, showing a two-phase structure (glass-in-glass phase separation), one of them being dispersed in the other. The dispersed phase has dimensions in the range 20-90 nm. Also, this dispersed phase contains β-AgI crystals of dimensions around 20 nm as shown in Figure 1b. The latter gives highresolution images of the lattice planes with spacings 0.167, 0.241, and 0.13 nm of β-AgI crystals. Figure 1c gives the fast Fourier transform (FFT) of the image in panel b, from which dhkl values above were calculated. The micrograph of Figure 1 is typical of specimen 2 also.
0.141 ( 0.001 0.123 ( 0.001 0.082 ( 0.001
0.235 ( 0.001 0.204 ( 0.001 0.144 ( 0.001 0.116 ( 0.001 0.091 ( 0.001 0.083 ( 0.001
ASTM values for silver (nm) 0.2359 0.2044 0.1445 0.1231 0.1179 0.0913 0.0834
Figure 2 (top) shows the transmission electron micrograph for specimen 1 after it was subjected to electrodeposition reaction, and Figure 2 (bottom) is the corresponding electron diffraction pattern. The interplanar spacings dhkl were calculated from the diffraction spot distances from the center of the image. These values are summarized in Table 1. They are compared with ASTM values, and it is evident that the wires consist of metallic silver. It can be seen from Figure 2 (top) that silver nanowires of diameters varying from 0.5 to 3.5 nm are present in the composite system. It must be mentioned here that the β-AgI nanocrystals did not appear to play any role in the growth of the silver nanowires except in contributing to the enhancement of local electric field, which helped in the alignment of the silver nanowires. This has been discussed further in a subsequent section. Figure 3 gives the transmission electron micrograph (top panel) and the corresponding electron diffraction pattern (bottom panel) for specimen 2 after electrodeposition treatment. The interplanar spacings calculated from Figure 3 (bottom) are summarized in Table 1 and compared with ASTM data for metallic silver. These data confirm the presence of silver in the nanowires. The wires found in Figure 3 (top) are aligned parallel
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Figure 3. (top) Transmission electron micrograph for specimen 2 subjected to electrodeposition and (bottom) its electron diffraction pattern.
Figure 5. Variation of resistance as a function of temperature (top panel, O) specimen 1 and (bottom panel, 0) specimen 2.
TABLE 2: Comparison of Interplanar Spacings Obtained after X-ray Diffraction from Specimens 1 and 2 Subjected to Electrodeposition with ASTM Values Figure 4. X-ray diffractograms of glasses in which silver nanowires were grown: (a) specimen 1 and (b) specimen 2.
with respect to each other. Also the diameters of these wires are more uniform than those observed in the case of specimen 1. The diameter has a value ∼1.6 nm. Figure 4 shows the X-ray diffractograms of specimens 1 and 2 in which silver nanowires were grown. The big humps at around 150 are characteristic of the base glass, which was confirmed by taking the X-ray pattern of the precursor glass. Table 2 summarizes the interplanar spacings obtained from the diffraction peaks and compares them with ASTM values of silver. The results confirm the presence of silver nanowires in these specimens. We have examined the voltage-current characteristics of specimens 1 and 2 after electrodeposition treatments over the temperature range 10-280 K. It is seen that the current change is linear with respect to the applied voltage. Also, the behavior is symmetrical with respect to the voltage polarity. The
observed dhkla (nm)
a
specimen 1
specimen 2
dhkl ASTM
0.199 ( 0.001 0.156 ( 0.001 0.121 ( 0.001
0.199 ( 0.001 0.156 ( 0.001 0.121 ( 0.001
0.200 0.159 0.121
From XRD.
resistance of the samples at each temperature was calculated from the slope of the voltage current characteristics. In Figure 5 are shown the variation of resistance as a function of temperature in the range 10-280 K for specimens 1 (top panel) and 2 (bottom panel). It is evident that the conductivity is metallic in nature. The temperature coefficients of resistance as calculated from the data are found to be 170 and 933 ppm/ K, respectively. It should be noted the temperature coefficient of resistance was calculated from the slopes of the linear plots shown in Figure 5. These values for specimens 1 and 2 are 0.2 and 2.8 × 10-3 Ω/K, respectively. It has been shown that the
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Figure 6. Variation of dielectric constant as a function of frequency for treated specimen 2.
resistivity of a metal FL in bulk form arises due to electronphonon scattering and the expression is given by13
FL ) C
( ) ( ) T 5 θD J θD 5 T
(1)
where C is a constant, T is temperature, θD is the Debye temperature, and J5(z) is the Debye integral. It is evident from eq 1 that FL will be inversely proportional to θD5. It has been reported earlier that the Debye temperature decreases when the nanoparticle size of silver is made smaller and the temperature variation of resistance is higher.14 It essentially arises due to a phonon softening effect. In the present case, for specimen 1 the nanowire diameter is on average smaller than that of specimen 2. Hence, we can conclude that the effective value of θD for silver in specimen 1 will be smaller than that of silver in specimen 2. In view of the above discussion, therefore, the slope of R versus T should be higher in the case of specimen 1 than that of specimen 2. This is, in fact, shown by our experimental data in Figure 5. We estimate the expected value of resistance in the case of specimen 2 from the density of silver nanowires as extracted from the electron micrographs. From Figure 3 (top) we deduce the total cross-sectional area of silver nanowires to be 7.6 × 10-3 cm2. Using a value of bulk silver resistivity ∼1.6 × 10-6 Ω‚cm,15 we calculate the expected value of resistance to be 2 × 10-5Ω. This is at variance with the measured resistance of 3 Ω (Figure 5, bottom) by a factor of 10-5. This is, however, to be expected because not all the nanowires are continuous from one electrode to the other. As discussed below, most of the nanowires form interrupted strands and thereby give rise to the giant dielectric permittivity. Also, the electrical resistivity increases drastically as the size of metal particles reaches nanoscale dimensions.16 Figure 6 gives the variation of dielectric constant as a function of frequency for specimen 2 after electrodeposition treatment. It can be seen that the dielectric constant shows an asymptotic value of ∼2.0 × 103 at the high-frequency limit. This is substantiated by the Cole-Cole plot (real and imaginary parts
Figure 7. Cole-Cole diagram for treated specimen 2: electrodeposition time (top) 2 h or (bottom) 1 h.
1 and 2, respectively, of dielectric permittivity plotted in the same plane) shown in Figure 7 (top). The latter indicates a highfrequency dielectric constant of ∼2.0 × 103. Such a giant dielectric permittivity is explained as arising due to quantum mechanical effects as described below. It should be noted that the dielectric constant shows an increasing trend with an increase in temperature at lower frequencies. This is ascribed to a space charge polarization, the mechanism being as follows. Glasses containing mobile charged ions have in most cases a phaseseparated structure, that is, in microscale there are regions that are rich in mobile ions and regions that are deficient in the same. Such a heterostructured system, when subjected to an electric field, will develop space charges at the interfaces of these regions.17 They behave like dipoles and exhibit an increase in the dielectric constant as the temperature is raised. The latter enhances the amount of space charge because of the difference in conductivities of the heterophase regions as described above. In Figure 7 (bottom) is shown the variation of dielectric constant as a function of frequency (by Cole-Cole plot) for specimen 2, which was subjected to electrodeposition treatment
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Figure 8. Variation of logarithm of ac conductivity as a function of logarithm of angular frequency for treated specimen 2. q;1
for a period of 1 h only. It can be seen that the high-frequency dielectric permittivity (∼330) is less than that observed when the electrodeposition time was 2 h. This is ascribed to smaller lengths of silver wires formed in the glass. The silver nanowires of diameter ∼1.6 nm found in the case of specimen 2 is interesting (Figure 3, top). In an earlier investigation, silver nanowires grown within an ion-exchanged silicate glass were found to have a much larger diameter (∼17 nm) and these were randomly oriented.8 Also, silver nanowires grown were found to have a fractal structure in some of the ion-exchanged silicate glasses.18 We have examined the aspect of silver ion migration during the electrodeposition step. Figure 8 shows the variation of logarithm of conductivity as a function of logarithm of frequency in case of specimen 2, before electrodeposition. It should be noted that, while plotting the data, we have substracted the dc conductivity part following the procedure described earlier.19 The variation of conductivity with frequency can be brought out more clearly in this way. It is seen that at the high-frequency region the conductivity σ varies with the angular frequency ω as follows:
σ ∝ ωn
(2)
where n is the frequency exponent. The values of n for the specimen were determined at different temperatures, and these are shown in Figure 9 (the bars indicate the error in the values of n). Because of limitation of the frequency range over which measurements could be carried out, the high-frequency region used was from 1 kHz to 2 MHz for temperatures from 108 to 128 K and from 61 kHz to 2 MHz for temperatures from 133 to 148 K. It can be seen that the value of n remains constant at ∼0.67 ()2/3) in the temperature range 110-140 K. However, there is an indication in this figure of the value of n showing a minimum, though the variation seems to be rather small. This is attributed to arise due to the window effect discussed in the literature earlier.20,21 It has been shown that there is a relationship between the high-frequency limiting slope n and the shape exponent β appearing in the Kohlrausch-Williams-Watts stretched-exponential relaxation function.22-24 The relationship can be written as
n)1-β
(3)
Using the value of n obtained for specimen 2, we obtain a value
Figure 9. Variation of frequency exponent n as a function of temperature for treated specimen 2.
of β ) 1/3. The latter represents the situation in which silver ion migration takes place in three dimensions.23 The reason that we still obtain a one-dimensional motion of silver ions, giving rise to the formation of aligned silver nanowires, is the enhancement of local electric field in the glass system. Since I- ions do not form the glass network, Ag+ and I- ions will be displaced upon application of the external electric field. The finite separation of Ag+ and I- ions will form dipoles within the glass medium. β-AgI nanocrystals will also contribute to formation of dipoles. The local electric field acting on the Ag ions contributing to electrodeposition will therefore be enhanced. This in turn will restrict their movement only in one direction. The mechanism proposed for the growth of silver nanowires is as follows. The electrodeposition takes place by the movement of silver ions within the glass phase by a random walk process.18 A generalized diffusion-limited aggregation mechanism becomes effective by which silver atoms after neutralization get deposited on the cathode and start forming a fractal structure.18 A critical diameter of the latter determined by the silver ion concentration of the original glass and the growth direction controlled by the local electric field ultimately lead to the formation of a nanostructure observed in our experiments. The uniformity of growth and hence the completion of nanowire path formation are dependent on the overall concentration of silver ions in the glass. This model helps explain why, by changing the glass composition and thereby altering the silver ion concentration, one could obtain silver nanowires of different diameters under similar conditions of electrodeposition. For specimen 1 the frequency exponent obtained was ∼0.65 and hence the value of β extracted was ∼1/3. Hence in this sample silver ion migration also takes place in three dimensions. However, the concentrations of silver and iodine ions being lower in this case as compared to the other specimen, local electric field does not get enhanced and hence the nanowire formation leads to a spread of diameters. The giant dielectric permittivity in the electrodeposited glasses is caused by the presence of interrupted silver nanowires. It has been shown earlier that such disjointed metallic nanowires cause an increase of dielectric permittivity due to Gorkov-Eliashberg25 and Rice-Benasconi anomaly.26 The anomaly of high dielectric polarizability arises due to the nanometer size of the
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J. Phys. Chem. C, Vol. 111, No. 10, 2007 3919
metallic species and consequential discretization of the energy levels.25 However, a high aspect ratio in the nanostructure is necessary in order to be able to observe such an effect.26 In the present sample system, some of the silver nanowires get broken or are not fully formed because of the kinetics of the process. We estimate the average length of such nanowires using the simplified equation26
=
1 l 2 2a
()
(4)
where is the dielectric constant, l is the average length of a metallic strand, and a is the interatomic distance of the metallic phase. By substituting the values ∼ 2 × 103 and a ∼ 0.28 nm, we obtain l ∼ 18 nm. From Figure 3 (top) it can be seen that some of the wires have lengths on the order of 17 nm. This is consistent with the prediction of eq 4. In summary, we have been able to grow silver nanowires with diameters in the range 1.6-3.7 nm by subjecting suitably chosen glasses to electrodeposition in the system (AgI)(AgPO3), which have large conductivities due to silver ion migration. For glasses with higher concentrations of silver, the above process leads to the growth of aligned silver nanowires. The voltagecurrent characteristics show symmetric linear behavior. The aligned growth is explained as arising due to an enhancement of internal electric field caused by the effect of dipoles formed by Ag+ and I- ions due to externally applied field. The nanocomposites exhibit ultrahigh dielectric permittivity. This arises due to Gorkov-Eliashberg and Rice-Bernasconi mechanisms. Acknowledgment. This work was supported by Department of Science and Technology, Government of India, New Delhi, under its Nano Science and Technology Initiative Programme. D.C. thanks INSA, New Delhi, for the award of a Senior Scientist position. We thank Supriyo Chakraborty for his help with electron microscopy.
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