**3.3 Piezoelectric properties**

*Multifunctional Ferroelectric Materials*

**96**

**Figure 7.**

**Figure 6.**

*Ps ~ fBaTiO3 at different electric fields (a) 5 kV/cm (b) 6 kV/cm (c) 7 kV/cm (d) 8 kV/cm.*

*Pr ~ fBaTiO3 at different electric fields (a) 5 kV/cm (b) 6 kV/cm (c) 7 kV/cm (d) 8 kV/cm.*

**Figure 9** gives the explanation of change in piezo- electric coefficient (d33) of the PF as a function of *f*BaTiO3. On increasing the concentration of *n*-BaTiO3, the piezoelectric nature of composite also increases and when the amount of *n*-BaTiO3 filler content increases much, the value of d33 becomes constant. The value of d33 increases from 2.10 pC/N for *f*BaTiO3 = 0.0 up to 2.20 pC/N for *f*BaTiO3 = 0.20 and remains constant, beyond *f*BaTiO3 = 0.20 up to *f*BaTiO3 = 1.0 because of the aggregated filler (*n*-BaTiO3) causes poor improvement in the peizo- electric nature of the PF.

### **3.4 Dielectric properties**

The variation of dielectric properties of the PCC as a function of frequency at 300 K are shown in **Figure 10a** and **b**, respectively. The value of ɛeff at 50 Hz for the 0.0 sample is 16 while this value increases up to 120 linearly up to the PCC with *f*BaTiO3 = 0.5 & after that it raises up to the value of 330 & 420 for the samples with *f*BaTiO3 = 0.55 & *f*BaTiO3 = 0.60 respectively. The higher value of ɛeff for the *f*BaTiO3 = 0.55 & *f*BaTiO3 = 0.60 are attributed to the large interfacial polarization arising due to the occurrence of spherulites and created large interface like structures(during cold pressing), while the spherulites are lost for the hot molded samples (**Figure 11**).

The static dielectric constant (εr) of the cold pressed pure PVDF is ~16 i.e. higher than the εr of hot molded pure PVDF (~10) due to the loss of spherulites (Inset, **Figure 11**) of the polymer. ɛeff decreases with increase of frequency due to the

**Figure 9.** *Variation of the piezoelectric coefficient (d33) as a function of fBaTiO3.*

absence of contribution from interfacial polarization at higher frequencies, where only the involvement from dipolar and atomic polarization exists. A very low Tan δ for the PCC with *f*BaTiO3 = 0.6 (having highest ɛeff = 420 observed at 50 Hz) was approached to 0.9 at 50 Hz and that also decreases with increase of frequency and the tendency of decrement is also observed for all the PCC. Nevertheless, in the cold pressed PMC [33], the Tan δ was reported to be 10 at 50 Hz (Inset, **Figure 10b**) for the percolative sample, with ɛeff ~ 2000. The PMC at *f*c shows 10 times higher value of Tan δ in contrast to the result of PCC, although both type of polymer composites are prepared by the same cold pressing procedure. **Figure 12** shows thebehaviour of ɛeff, σeff and Tan δ of the composites as a function of *f*BaTiO3 at different frequencies. The ɛeff rises linearly from 16 to 120 for *f*BaTiO3 rises from 0.0 to 0.50 at 100 Hz, due to the large interfacial polarization occurring due to the presence of spherulites. The interfaces formed at the PCC, increases ɛeff largely from 120 to 350 & 420 for *f*BaTiO3 = 0.55 & 0.60 respectively. The expression developed by Yamada et al. (which is a model for explaining the sum properties of the composite) was fitted to the dielectric data (**Figure 12(b)**) at 1 kHz frequency. The model is given by

$$\mathcal{E}\_{\text{eff}} = K\_{\text{PVDF}} \left[ 1 + \frac{n f\_{\text{RATO3}} \left( K\_{\text{RATO3}} - K\_{\text{PVDF}} \right)}{n K\_{\text{PVDF}} + \left( K\_{\text{RATO3}} - K\_{\text{PVDF}} \right) \left( 1 + f\_{\text{RATO3}} \right)} \right] \tag{1}$$

**99**

**Figure 10.**

*Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites*

σeff & Tan δ are also found to be increasing with increase of frequency, suggesting conventional hopping conduction in the disordered PCC. Similarly, σeff value was found to be very low i.e. less than 10−4 Ω−1 for all the PCC and that value remains constant over the entire frequency range. The Tan δ raises slowly as a function of

*(color online) the variation of (a) ɛeff and (b) tan* δ *as a function of frequency at 300 K for the PD, inset: Tan* 

The electrical parameters as a function of temperature of the PCC was confirmed by measuring and are given in **Figure 13**. For *f*BaTiO3 = 0.4 (**Figure 13a**) & *f*BaTiO3 = 0.50 (**Figure 13b**), the low frequency (50 Hz) value of ɛeff is sustained at a thermal stabilized value of 90 & 130 (with their corresponding decrement as a function of frequency) as a function of temperature from 40–100°C. The stabilization of ɛeff is ascribed due to the major effective contribution coming from the sum properties of the dielectric constant of both the components. Yet, for the samples with *f*BaTiO3 = 0.55 &0.6, the reached ɛeff ~ 350 & 420 value arises due to the sum properties

*f*BaTiO3 is found to be less than 0.9 even with the PCC having *f*BaTiO3 = 0.6.

δ *~ frequency for some typical percolative PMC samples showing higher tan* δ *[33].*

*DOI: http://dx.doi.org/10.5772/intechopen.96593*

where *eff* ε is the effective dielectric constant of the composite, *KPVDF* and *KBaTiO*<sup>3</sup> are the dielectric constants of the polymer matrix and the ceramic, respectively, *BaTiO f* <sup>3</sup> is the volume fraction of the ceramic and '*n*' is a parameter related to the geometry of ceramic particles [2]. *KPVDF* , *KBaTiO*3 and *n* found from the fitting of Eq. (1) to the dielectric data are 17, 1600 and 10, is in good agreement with the earlier literature [5].

The σeff & Tan δ increases with the increase of *BaTiO f* <sup>3</sup> in the PCC slowly, suggesting the semiconducting nature of the BaTiO3 nano-ceramics. For *BaTiO f* <sup>3</sup> =0.6, the σeff value varies within 10−8 Ω−1 cm−1 to 10−4 Ω−1 cm−1 for frequency varying between 50 Hz to 5 MHz, while the value of Tan δ is maintained in between 0.1 to 0.9. *Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites DOI: http://dx.doi.org/10.5772/intechopen.96593*

**Figure 10.**

*Multifunctional Ferroelectric Materials*

absence of contribution from interfacial polarization at higher frequencies, where only the involvement from dipolar and atomic polarization exists. A very low Tan δ for the PCC with *f*BaTiO3 = 0.6 (having highest ɛeff = 420 observed at 50 Hz) was approached to 0.9 at 50 Hz and that also decreases with increase of frequency and the tendency of decrement is also observed for all the PCC. Nevertheless, in the cold pressed PMC [33], the Tan δ was reported to be 10 at 50 Hz (Inset, **Figure 10b**) for the percolative sample, with ɛeff ~ 2000. The PMC at *f*c shows 10 times higher value of Tan δ in contrast to the result of PCC, although both type of polymer composites are prepared by the same cold pressing procedure. **Figure 12** shows thebehaviour of ɛeff, σeff and Tan δ of the composites as a function of *f*BaTiO3 at different frequencies. The ɛeff rises linearly from 16 to 120 for *f*BaTiO3 rises from 0.0 to 0.50 at 100 Hz, due to the large interfacial polarization occurring due to the presence of spherulites. The interfaces formed at the PCC, increases ɛeff largely from 120 to 350 & 420 for *f*BaTiO3 = 0.55 & 0.60 respectively. The expression developed by Yamada et al. (which is a model for explaining the sum properties of the composite) was fitted to the dielectric data (**Figure 12(b)**) at 1 kHz frequency. The model is given by

> ( ) ( )( )

3 3

<sup>1</sup> (1)

*BaTiO BaTiO PVDF*

*nf K K <sup>K</sup>*

*PVDF BaTiO PVDF BaTiO*

*nK K K f*

+− + 3 3

is the effective dielectric constant of the composite, *KPVDF* and *KBaTiO*<sup>3</sup>

<sup>−</sup> = +

are the dielectric constants of the polymer matrix and the ceramic, respectively, *BaTiO f* <sup>3</sup> is the volume fraction of the ceramic and '*n*' is a parameter related to the geometry of ceramic particles [2]. *KPVDF* , *KBaTiO*3 and *n* found from the fitting of Eq. (1) to the dielectric data are 17, 1600 and 10, is in good agreement with the earlier literature [5]. The σeff & Tan δ increases with the increase of *BaTiO f* <sup>3</sup> in the PCC slowly, suggesting the semiconducting nature of the BaTiO3 nano-ceramics. For *BaTiO f* <sup>3</sup> =0.6, the σeff value varies within 10−8 Ω−1 cm−1 to 10−4 Ω−1 cm−1 for frequency varying between 50 Hz to 5 MHz, while the value of Tan δ is maintained in between 0.1 to 0.9.

**98**

*eff PVDF*

1

*Variation of the piezoelectric coefficient (d33) as a function of fBaTiO3.*

ε

where *eff* ε

**Figure 9.**

*(color online) the variation of (a) ɛeff and (b) tan* δ *as a function of frequency at 300 K for the PD, inset: Tan*  δ *~ frequency for some typical percolative PMC samples showing higher tan* δ *[33].*

σeff & Tan δ are also found to be increasing with increase of frequency, suggesting conventional hopping conduction in the disordered PCC. Similarly, σeff value was found to be very low i.e. less than 10−4 Ω−1 for all the PCC and that value remains constant over the entire frequency range. The Tan δ raises slowly as a function of *f*BaTiO3 is found to be less than 0.9 even with the PCC having *f*BaTiO3 = 0.6.

The electrical parameters as a function of temperature of the PCC was confirmed by measuring and are given in **Figure 13**. For *f*BaTiO3 = 0.4 (**Figure 13a**) & *f*BaTiO3 = 0.50 (**Figure 13b**), the low frequency (50 Hz) value of ɛeff is sustained at a thermal stabilized value of 90 & 130 (with their corresponding decrement as a function of frequency) as a function of temperature from 40–100°C. The stabilization of ɛeff is ascribed due to the major effective contribution coming from the sum properties of the dielectric constant of both the components. Yet, for the samples with *f*BaTiO3 = 0.55 &0.6, the reached ɛeff ~ 350 & 420 value arises due to the sum properties

#### **Figure 11.**

*The variation of dielectric constant (*ε*r) with frequency for both cold and hot press PVDF, inset: The FESEM micrograph of the cold/hot molded PVDF showing the presence/loss of spherulites at temperature higher than the room temperature.*

#### **Figure 12.**

*(color online) the variation of (a) ɛeff experimentally (b) fitting of ɛeff experimental data at 1KHz with Yamada model as a function of fBaTiO3 (c)* σ*eff and (d) tan* δ *as a function of fBaTiO3 for various frequencies at 300 K.*

of the dielectric constant of both the components as well as also due to the major contribution of the spherulites. Hence with the rise of temperature, the ɛeff decreases due to the deteriorating of the spherulites of the PCC (**Figure 13c** and **d**). Hence the spherulites are useful at room temperature in case of PCC for realizing high value of ɛeff with lower Tan δ.

**101**

*Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites*

*DOI: http://dx.doi.org/10.5772/intechopen.96593*

**3.5 Electrical conductivity**

σ ωε ε δ

*for varying fBaTiO3 (a) 0.40 (b) 0.50 (c) 0.55 (d)) 0.60.*

*ac* = <sup>0</sup> *Tan* ) as a function of frequency at different *f*BaTiO3

*ac* = + *dc A* (2)

is shown in **Figure 14**. The σeff as a function of frequency was found to be the ac hoping conduction satisfying the Johnscher's fractional power law. The plot shows dispersion of ac conductivity with frequency corresponding to *f*BaTiO3 ≤ 0.20, be in

*(color online) the variation of ɛeff as a function of frequencies for the temperature varying from 40 ̊C to 100 ̊C* 

σω

( ) *<sup>k</sup>*

with the σdc part becoming zero and the value of *k ~* 1*.* The non-presence of dc conductivity for the samples with *f*BaTiO3 ≤ 0.20, can be understand as the nonpresence of percolating paths (being formed from the semiconducting *BaTiO3* nano-ceramics in the PVDF matrix) due to insufficient fraction of *BaTiO3*. The long rage dc conduction starts to develop for *f*BaTiO3 = 0.3 to 0.5, but a good fit of Eq. (2) could not be resulted for them as the percolating paths were not sufficient. Interestingly, for *f*BaTiO3 ≥ 0.55, a mixed conductivity is found. The plateau due to the appearance of long range dc conductivity. At higher frequency the conductivity becomes more or less with *f*BaTiO3 dependent. This "hopping or critical frequency *ω*H." at which the change in slope takes place can be observed to be increasing with the increase of *f*BaTiO3, since the length of dc plateau increases with increase of *f*BaTiO3 from 0.3 to 0.6. On the other hand, the value of '*k*' lies well within the Johnscher's universal regime [0,1] symptomatic of the validity of

 ω

 σ

Ac conductivity (

**Figure 13.**

agreement with Eq. (2) i.e.

Johnscher's power law universally.

*Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites DOI: http://dx.doi.org/10.5772/intechopen.96593*

**Figure 13.**

*Multifunctional Ferroelectric Materials*

**100**

**Figure 12.**

**Figure 11.**

*the room temperature.*

ɛeff with lower Tan δ.

of the dielectric constant of both the components as well as also due to the major contribution of the spherulites. Hence with the rise of temperature, the ɛeff decreases due to the deteriorating of the spherulites of the PCC (**Figure 13c** and **d**). Hence the spherulites are useful at room temperature in case of PCC for realizing high value of

*(color online) the variation of (a) ɛeff experimentally (b) fitting of ɛeff experimental data at 1KHz with Yamada model as a function of fBaTiO3 (c)* σ*eff and (d) tan* δ *as a function of fBaTiO3 for various frequencies at 300 K.*

*The variation of dielectric constant (*ε*r) with frequency for both cold and hot press PVDF, inset: The FESEM micrograph of the cold/hot molded PVDF showing the presence/loss of spherulites at temperature higher than* 

*(color online) the variation of ɛeff as a function of frequencies for the temperature varying from 40 ̊C to 100 ̊C for varying fBaTiO3 (a) 0.40 (b) 0.50 (c) 0.55 (d)) 0.60.*

#### **3.5 Electrical conductivity**

Ac conductivity (σ ωε ε δ *ac* = <sup>0</sup> *Tan* ) as a function of frequency at different *f*BaTiO3 is shown in **Figure 14**. The σeff as a function of frequency was found to be the ac hoping conduction satisfying the Johnscher's fractional power law. The plot shows dispersion of ac conductivity with frequency corresponding to *f*BaTiO3 ≤ 0.20, be in agreement with Eq. (2) i.e.

$$
\sigma\_{ac} \left( \phi \right) = \sigma\_{dc} + A\phi^k \tag{2}
$$

with the σdc part becoming zero and the value of *k ~* 1*.* The non-presence of dc conductivity for the samples with *f*BaTiO3 ≤ 0.20, can be understand as the nonpresence of percolating paths (being formed from the semiconducting *BaTiO3* nano-ceramics in the PVDF matrix) due to insufficient fraction of *BaTiO3*. The long rage dc conduction starts to develop for *f*BaTiO3 = 0.3 to 0.5, but a good fit of Eq. (2) could not be resulted for them as the percolating paths were not sufficient. Interestingly, for *f*BaTiO3 ≥ 0.55, a mixed conductivity is found. The plateau due to the appearance of long range dc conductivity. At higher frequency the conductivity becomes more or less with *f*BaTiO3 dependent. This "hopping or critical frequency *ω*H." at which the change in slope takes place can be observed to be increasing with the increase of *f*BaTiO3, since the length of dc plateau increases with increase of *f*BaTiO3 from 0.3 to 0.6. On the other hand, the value of '*k*' lies well within the Johnscher's universal regime [0,1] symptomatic of the validity of Johnscher's power law universally.

**Figure 14.**

*(color online) the variation of (a)* σ*eff experimentally and (b)* σ*eff fitted with Johnscher's power law, as a function of frequencies.*

#### **3.6 Conclusions**

The micro-structural, ferroelectric, piezoelectric, dielectric and conductivity properties of the polymer composites have been analyzed and are correlated. The properties strongly depend on the novel cold pressing preparation techniques and the dispersion of *n*-BaTiO3 filler particles into the PVDF matrix and also on the nano-sizes of ceramics. The addition of *n*-BaTiO3 enhances the ferroelectric, piezoelectric and dielectric properties of the composites. It is also found that this cold pressing method is more suitable to the PCC based on PVDF matrix (since very low value of Tanδ is observed). The spherulites present in PVDF matrix are always helpful in maintaining the dielectric constant and increasing the ɛeff of PCC. The enhancement of dielectric results are explained with the help of standard Yamada model. The mixed conductivity appears for the PD/PF and Jonschers universal fractional power law is well satisfied for all composites. The hoping conduction in these disordered materials have been confirmed in all PCC. The dynamics of

**103**

**Author details**

Maheswar Panda

University), Sagar, M.P., India

provided the original work is properly cited.

*Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites*

charge carriers are filler/temperature dependent. These PD/PF should be explored for applications by focusing the research on achieving lowered Tan δ, which will increase the dielectric field strength/high energy density and better ferroelectric/ piezoelectric properties may be expected for various multifunctional applications.

Department of Physics, Dr. Harisingh Gour Vishwavidyalaya (A Central

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: panda.maheswar@gmail.com

*DOI: http://dx.doi.org/10.5772/intechopen.96593*

*Ferroelectric, Piezoelectric and Dielectric Properties of Novel Polymer Nanocomposites DOI: http://dx.doi.org/10.5772/intechopen.96593*

charge carriers are filler/temperature dependent. These PD/PF should be explored for applications by focusing the research on achieving lowered Tan δ, which will increase the dielectric field strength/high energy density and better ferroelectric/ piezoelectric properties may be expected for various multifunctional applications.
