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External Magnetic Field Induced Percolation in Polyvinylidene Fluoride and Nickel Composites Weiping Li,* Lijia Yu, Yuejin Zhu, and Dayin Hua Department of Physics, Ningbo UniVersity, Ningbo, 315211, People’s Republic of China ReceiVed: April 23, 2010; ReVised Manuscript ReceiVed: July 19, 2010
The dielectric properties of polyvinylidene fluoride (PVDF) and nickel (Ni) composites annealed under external magnetic fields were studied here. It was found that a similar percolation effect could be induced by an external longitudinal magnetic field in low filler PVDF/Ni composites. The permittivity of PVDF/Ni (95/5) composites showed a 4 times improvement at low frequency, and the dielectric loss was kept in the range of 0.1-0.4. In comparison to the traditional percolation effect caused by the involvement of conductive particles, field-induced anisotropic percolation may be another type of percolation effect, which can be used to improve the dielectric properties of polymer-based composites. Introduction Polymeric dielectric materials are currently of considerable interest as solution-processable high permittivity materials for electronic applications, such as high-performance capacitors, gate dielectrics, and power storage devices.1-4 On the basis of the percolation theory, a great deal of work has been carried out to get high permittivity composites by embedding different conductive particles into dielectric polymers.5-9 The high dielectric constant can be obtained when the volume fraction of the conductive filler is very close to, but does not exceed, the percolation threshold. At the proper filler loading, percolative composites can exhibit very high dielectric constants. However, these composites also exhibit a relatively high dielectric loss due to the insulator-conductor transition near the percolation threshold. Simultaneously, to prepare high electric constant polymer composites for electromechanical devices, the agglomeration of the filler should be avoided and the flexibility of the polymer should be retained, both of which requires a low volume fraction of filled particles.10 Therefore, how to prepare a percolative composite with low filler is an open question. On the other hand, extensive external fields (electric, magnetic, thermal, and force) play an important part in the properties of materials. The structure and final macroscopic performance of composites not only is related to the chemical composition but also is affected by the preparation process. As for a polymerbased dielectric percolative system, the molecular arrangement of the polymer and the distribution of conductive particles in the host polymer may be changed after the application of external fields, such as shear flow, magnetic, or electric forces.11-14 Considering the nature of the percolation phenomenon is the random formation of a conducting network in the polymer/metal composites due to the increasing percentage of conductive particles, we expect to prepare an anisotropic percolative composite with low filler and promote the occurrence of the percolation effect in one special direction by external fields. In our present work, nickel particles had been chosen to fill into polyvinylidene fluoride (PVDF) matrix, owing to good conductivity and ferromagnetism, and the samples were treated * To whom correspondence should be addressed. E-mail: liweiping@ nbu.edu.cn. Fax: 86-574-87600744. Tel: 86-574-87600953.
under a constant magnetic field during the annealing process. It is found that the composites with a Ni volume fraction of 5% (far below the percolation threshold of 17%) exhibit high permittivity and low loss when the applied magnetic field is perpendicular to the plane of the sample. We contribute it to the percolation effect induced by the external field. Experimental Section Sample Preparation. The PVDF and Ni particles (200 nm in diameter) were purchased from 3F New Materials Co., Ltd. (Shanghai, China) and Guangbo Nanomaterials Co., Ltd. (Ningbo, China), respectively. After sufficient blending, the mixtures of PVDF and Ni powders were molded by hot pressing at about 200 °C under 10 MPa. Samples in a sheet shape with a diameter of 12 mm and a thickness of 1 mm were produced. The samples were then treated at 200 °C under a constant magnetic field with a magnetic induction density of 0.2 T for 3 h, and they continued to be annealed at 120 °C for another 12 h without a magnetic field before being cooled to room temperature at a 2 °C/min cooling rate. To investigate the effect of the direction of the magnetic field, two kinds of samples were prepared under the longitudinal and parallel magnetic fields. Measurements. The up and bottom electrodes were painted with silver paste to conduct electronic measurements. The longitudinal dielectric properties and conductivity of the samples were measured at room temperature by use of an Agilent precision impedance analyzer 4294A with the 16451B fixture. SEM images were obtained by a field emission scanning electron microscope (Hitachi S-4800). Results and Discussion At first, the effect of the longitudinal magnetic field on the dielectric properties of PVDF/Ni (95/5) composites was studied. Figure 1 shows the dependence of the effective conductivity (σeff) and dielectric constant (εeff) at 40 Hz on the action time (τ) of an external longitudinal magnetic field. The εeff and σeff increase gradually with τ and enhance greatly when τ > 120. With τ ) 180, the maximum of the εeff reaches to 120, which is 4 times that of the sample without the application of a magnetic field. Compared with theoretical values, the experimental results are in good agreement with the power law of percolation theory1 as follows
10.1021/jp103086y 2010 American Chemical Society Published on Web 07/29/2010
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Figure 1. Dependence of the conductivity and dielectric constant of PVDF/Ni (95/5) composite films on the action time of the longitudinal magnetic field at 40 Hz.
Figure 2. Dependence of the conductivity and dielectric constant of PVDF/Ni (95/5) composite films on the action time of the parallel magnetic field at 40 Hz.
σeff ∝ (τ - τc)t, for τ > τc
(1a)
σeff ∝ (τc - τ)-s, for τ < τc
(1b)
εeff ∝ (τc - τ)-δ, for τ < τc
(2)
where τc is the percolation time, t is the critical exponent in the conducting region, and s and δ are the critical exponents in the insulating region. From Figure 1, it can be seen that the conductivity of PVDF/Ni (95/5) composites clearly exhibit the typical insulator-conductor transition after application of an external longitudinal magnetic field and the experimental values of the εeff and σeff agree with eqs 1a, 1b, and 2 very well, with τ ≈ 125, t ≈ 1.36, s ≈ 0.73, and δ ≈ 0.14. It proves that the percolation phenomenon can be induced by a magnetic field in the lower Ni volume fraction PVDF/Ni composites. The longitudinal conductivity and dielectric constant exhibit a sudden increase after the application of a magnetic field for a certain time. It is similar to the typical percolation phenomenon due to the conductive filler, although here, the transition is a function of the action time of the magnetic field instead of a function of the Ni filler loading in a typical percolation transition. Thus, we name this magnetic field induced percolation (MFIP) here.
Figure 3. SEM images of freeze-fractured cross sections of the PVDF/ Ni (95/5) composites: (a) annealed without a magnetic field, (b) annealed under a longitudinal magnetic field, (c) annealed under a parallel magnetic field.
Note that the values of the critical exponents (t, s, and δ) are not in accordance with the universality of percolation theory in common percolative systems.7,15-18 MFIP has its own percolative direction on account of the external field, rather than randomly producing the percolative network. It is then an anisotropic percolation behavior induced by the external field, different from the traditional percolation effect. Also, the critical exponents here may be affected by the magnitude of the magnetic field and annealing temperature. To further investigate the direction of MFIP, another magnetic field was applied parallel to the plane of films. Figure 2 shows
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Figure 4. Schematic drawings of the distribution of Ni particles in the PVDF polymer under an external magnetic field: (a) longitudinal, (b) parallel.
the dependence of the σeff and εeff at 40 Hz on the action time of a parallel magnetic field. It can be observed that the σeff decreases from 2.3 × 10-8 to 1.5 × 10-9 with time and the εeff reduces from 35 to 20. Therefore, it indicates that the direction of the magnetic field has a great effect on the dielectric properties of composites. To show the effect of a magnetic field on the distribution of the Ni particles in the PVDF matrix, SEM images of freezefractured cross sections of PVDF/Ni (95/5) composites are presented in Figure 3a-c. It can be seen that the Ni particles are randomly distributed in the PVDF matrix without obvious agglomeration before annealing under a magnetic field. As shown in Figure 3b,c, some Ni particles come in contact with each other and become big clusters along the direction of the magnetic field. We interpret this to mean that magnetic fields have changed the distribution of the Ni filler in the PVDF polymer and the accumulating direction of the Ni particles are influenced by the direction of magnetic fields. The schematic drawings of the distribution of Ni particles in the PVDF polymer are presented in Figure 4 to interpret the anisotropic percolation behavior induced by a magnetic field. It can be supposed that Ni particles are able to move easily and touch together to form clusters in a melting state of the polymer matrix (at 200 °C) and these clusters may array in parallel with an ellipsoid shape along the direction of the external magnetic field. Therefore, when a longitudinal magnetic field is applied, the oriented distribution of Ni clusters is helpful for formation of a conductive network in this direction, as shown in Figures 3b and 4a. It is the reason for the enhancement in conductivity, just like MFIP discussed above. The Ni cluster arrays also can be regarded as a great amount of parallel-connected minicapacitors,19 resulting in a great increase of the effective dielectric constant. However, when the external magnetic field is a parallel one, the orientation of Ni clusters in parallel to the plane of the film may hinder the formation of a longitudinal conductive network, which reduces the longitudinal conductivity. Simultaneously, now the cluster arrays are corresponding to the series
Figure 5. Dependence of the dielectric properties of PVDF/Ni (95/5) composite films on frequency under a longitudinal magnetic field: (a) conductivity, (b) dielectric constant, (c) dielectric loss.
of combined minicapacitors, which is responsible for the decrease of the dielectric constant. The dependence of the εeff, σeff, and dielectric loss (tan θ) on the frequency of PVDF/Ni (95/5) composites after application of a longitudinal magnetic field are shown in Figure 5. The εeff, σeff, and tan θ of samples annealed under a magnetic field show obvious changes in the frequency range from 40 to 105 Hz. The enhancement of the σeff indicates the transition tendency from insulator to conductor induced by the magnetic field, and the increase of the εeff results from improvement of interface polarization during the annealing process. When the frequency
Percolation in PVDF and Ni Composites is above 105 Hz, the εeff begins to reduce, but the tan θ increases with frequency, which is the typical relaxation behavior of dielectric materials. Generally speaking, the dielectric loss is attributed to the conductive loss of motion of the charge carrier and the dipole loss of the dipole orientation polarization.20 Here, the peaks of loss in the range from 106 to 107 Hz correspond to the dipole orientation polarization of the polymer.2,21 When τ > τc, the loss is dominated by the conductive loss for the formation of a conductive pathway during the insulator-conductor transition. A small increase can be found in dielectric loss in the range of 40 to 105 Hz. But, after all, the values of loss are in the range of 0.1-0.4, which are low enough to match the requirement of the application of electric devices. Conclusions In summary, we have studied the dielectric properties of PVDF and Ni particles composites after treatment under a magnetic field. It is found that a time-dependent percolation effect can be induced by a longitudinal magnetic field in a low Ni volume fraction composite, accompanied with the increase of the dielectric constant and conductivity in the range of 40 to 105 Hz. Differing from the traditional percolation effect, it is an anisotropic percolation behavior, corresponding to a formation of a conductive path in the direction of a magnetic field. Although the existence of the universality in the external field induced percolation needs to be further studied in the future, it indeed offers a good way to obtain high permittivity and low loss dielectric material. The time-dependent alignment of Ni particles in polymer composites and the magnetic field induced percolation behavior helps one to understand the influence of external fields on the microstructure and properties of composites. Acknowledgment. This work was supported by the Natural Science Foundation of China (Grant Nos. 10575055 and 10774079), the Natural Science Foundation of Zhejiang Province (Grant Nos. Y7080401 and Y4090429), and the Natural Science
J. Phys. Chem. C, Vol. 114, No. 33, 2010 14007 Foundation of Ningbo (Grant Nos. 2008A610055, 2009A610056, 2009A610103, and 2009A610036). This work was also sponsored by the K. C. Wong Magna Fund in Ningbo University. References and Notes (1) Nan, C. W. Prog. Mater. Sci. 1993, 37, 1. (2) Dang, Z. M.; Lin, Y. H.; Nan, C. W. AdV. Mater. 2003, 15, 1625– 1629. (3) Bai, Y.; Cheng, Z. Y.; Bharti, V.; Xu, H. S.; Zhang, Q. M. Appl. Phys. Lett. 2000, 76, 3804–3806. (4) Wang, C. C.; Shen, Q. D.; Tang, S. C.; Wu, Q.; Bao, H. M.; Yang, C. Z.; Jiang, X. Q. Macromol. Rapid Commun. 2008, 29, 724–728. (5) Kota, A. K.; Cipriano, B. H.; Duesterberg, M. K.; Gershon, A. L.; Powell, D.; Raghavan, S. R.; Bruck, H. A. Macromolecules 2007, 40, 7400– 7406. (6) He, F.; Lau, S.; Chan, H. L.; Fan, J. AdV. Mater. 2008, 20, 1–6. (7) Lonjon, A.; Laffont, L.; Demont, P.; Dantras, E.; Lacabanne, C. J. Phys. Chem. C 2009, 113, 12002–12006. (8) Li, J.; Seok, S.; Chu, B.; Dogan, F.; Zhang, Q.; Wang, Q. AdV. Mater. 2009, 21, 217–221. (9) Han, M.; Zhao, K. S. J. Phys. Chem. C 2008, 112, 19412–19422. (10) Wang, C. C.; Song, J. F.; Bao, H. M.; Shen, Q. D.; Yang, C. Z. AdV. Funct. Mater. 2008, 18, 1299–1306. (11) Zhu, Y. J.; Ma, Y. Q. J. Chem. Phys. 2003, 118, 9023–9029. (12) Xu, J.; Florkowski, W.; Gerhardt, R.; Moon, K.; Wong, C. P. J. Phys. Chem. B 2006, 110, 12289–12292. (13) Obrzut, J.; Douglas, J. F.; Kharchenko, S. B.; Migler, K. B. Phys. ReV. B 2007, 76, 195420. (14) Fang, F.; Yang, W.; Jia, C.; Luo, X. P. Appl. Phys. Lett. 2008, 92, 222906–222908. (15) Levon, K.; Margolina, A.; Patashinsky, A. Z. Macromolecules 1993, 26, 4061–4063. (16) Huang, X.; Jiang, P.; Xie, L. Appl. Phys. Lett. 2009, 95, 242901– 242903. (17) Forsyth, M.; Shriver, D. F.; Ratner, M. A.; DeGroot, D. C.; Kannewurf, C. R. Chem. Mater. 1993, 5, 1073–1077. (18) Dang, Z. M.; Wang, L.; Yin, Y.; Zhang, Q.; Lei, Q. Q. AdV. Mater. 2007, 19, 852–857. (19) Yao, S. H.; Dang, Z. M.; Xu, H. P.; Jiang, M. J.; Bai, J. Appl. Phys. Lett. 2008, 92, 82902–82904. (20) Zhu, C. S. Structural Analysis of Polymer; Science Publishing House: Beijing, 2004; pp 257-264. (21) Dang, Z. M.; Shen, Y.; Nan, C. W. Appl. Phys. Lett. 2002, 81, 4814–4816.
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