Pyroelectric response

The pyroelectric coefficient is a vector 7r, equal to the rate of change of the spontaneous polarization Ps, with temperature T  

from Equation (11.2), the pyroelectric current ip, generated per watt of input power (the current responsivity Rf) is  

The form of this response is simple. At low frequencies (u -c 1 /tt) the response is proportional to us. For frequencies much greater than /tt the response is constant, being  

11 Pyroelectric Ceramics and Thin Films Characterization, Properties and Selection 

This only contains parameters describing properties of the pyroelectric material, and is therefore a figure-of-merit, which can be used to compare different materials for their potential voltage responsivities. If CA Jp CE the voltage response is proportional to  

---

Pyroelectricity of the film is highly dependent on the range of temperature applied to the sample film. The LB film of Compound I showed dull pyroelectric response in the high-temperature range. The signs of pyroelectric coefficients were changed at a temperature characteristic of the film. 

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k (experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF. ... 

The material properties appearing in Eqs. (6)-(9) are defined by the partial derivatives of the dependent variables (P, c, e) with respect to the independent variables. At this point, to maintain consistency with the literature on the P-phase of PVDF, we label c as the 1 axis, a as the 2 axis, and, b as the 3 axis. In evaluating the piezoelectric and pyroelectric responses we consider changes in polarization along the 3 axis only polarization along the 1 and 2 axes remains zero, by symmetry, for all the cases considered here. The direct piezoelectric strain 03 , pC/N) and stress (gaj, C/iiE) coefficients are defined in Eqs. (10) and (11),... 

The total pyroelectric response at constant stress, p , is the sum of the primary pyroelectic response, given by p, and the secondary pyroelectric response, which is the product of the direct piezoelectric stress coefficient gs, and the thermal expansion coefficients ... 

Figure 11.2. Constant stress pyroelectric response as a function of temperature. Open squares, primary pyroelectricity open circles, secondary pyroelectricity filled diamonds, total (reprinted with permission from Carbeek and Rutledge. Copyright 1996, Elsevier Science Ltd).

The total pyroelectric response at constant pressure (or stress) is the sum of two contributions. Primary pyroelectricity, which is due to changes in the magnitude of the dipole oscillation with temperature, accounts for only about 9% of the total response of the crystal at 300 K. The remaining overwhelming contribution is due to secondary pyroelectricity—the coupling of the piezoelectric response and thermal expansion. 

However, it was possible to look at pyroelectric response, that is, the change in polarization as a function of temperature. This is expressed mathematically in Eq. (7) ... 

Fig. 18. Graphical representation of a theoretical pyroelectric response profile.

Fig. 19. Graph showing the pyroelectric response of the stilbazole L-B films as a function of both temperature and number of layers.

There is no direct evidence that in TS-6 individual chains formed in the autocatalytic reaction regime are only a few hundred repeat units long, contrary to what is to be expected from the 200-fold increase of the reaction rate. However, there is a recent estimate based on polarization currents measured during thermal polymerization. Following earlier work on the pyroelectric response of TS Bertault et al. attributed the electric signal to an alignment of non-compensated dipolar defects associated with the chain ends. From the average value of the polarization they concluded that one chain can at most comprise a couple of hundred monomer units. 

The pyroelectric response of ferroelectrics may be exploited to detect tem-peratnre changes with extremely high sensitivity. The most common devices are nncooled infrared (IR) detectors, which may be used for spectroscopic analysis as well as imaging apphcations. Pyroelectric thin films based on perovskite-type complex oxides, including Pb(Sc,Ta)03 have been deposited by CSD for intruder alarms, gas sensors, and IR cameras. It is anticipated that these thin-film devices will be substantially less expensive to manufacture than existing bulk polycrystaUine devices, which require labor-intensive manufacturing procedures. 

However, the exploitation of pyroelectric LB films depends not only on the figures of merit listed in Table 4.1, but also on the ability to deposit such layers successfully on surfaces with low thermal mass. A substrate imposes two constraints on the pyroelectric response of a film. Not only does it provide an undesirable heat sink and reduce the excess temperature of... 

The charge was measured as in the pyroelectric measurement above while the specimen was subjected to square step pressure cycles of amplitude 0-500 psi and duration 10 sec, applied at 1 minute intervals. It was found necessary to apply a correction to d to allow for the pyroelectric response of the sample. This response arose due to the adiabatic heating of the silicone oil on pressurisation. 

A novel research use for this PVDF tube, making use of its pyroelectric response to measure the absorption loss in singlemode optical fibre, has already been reported (18). 

Leister N, Lehmann W, Weber U, Geschke D, Kremer F, Stein P, Fiiikelmann H (2000) Measurement of the pyroelectric response and of the thermal diffusivity of microtomized sections of single crystalline ferroelectric liquid crystalline elastomers. Liq Cryst 27 289... 

Fig. 3 SPEM images cf pcrhydrotripenylene inclusion crystals with a dipolar guest molecule [l-(4-nitrophenyl)piperazine], thinned in three steps. A two-dimensional mapping of the pyroelectric response in the channel direction is shown for a constant modulation frequency of the heating laser source of 415 Hz. Color code red=positive current blue=negative current Low color intensity no current.Moving from the outer to the inner part of the needle-shaped crystal shows that at all depths, there are two main domains of opposite polarization althou somehow interpenetrating. In the middle cf the needle, a cone-shaped structure cf polarity distribution is seen, which is typical for a Markov-type growth in two dimensions. Qualitative agreement with stochastic simulations is obtained. (View this art in color at www.dekker.com.)...

Hilczer, B., Kulek. J., (1998) The Effect of Dielectric Heterogeneity on Pyroelectric Response of PVDF, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 5, No. 1, pp. 45-50, ISSN 1070-9878. 

H. Ohoka, M. Ozaki, L.M. Blinov, Barnik, N.M. Shtykov and K. Yoshino, Polarization measurement in nematic liquid crystal based on the pyroelectric response to laser irradiation. Mol. Cryst. Liq. Cryst. 366(1), 283-293, (2001). doi 10.1080/10587250108023971... 

Strong pyroelectric response under a DC bias field. Solid solutions of relaxors and normal pyroelectrics, which are the subject of much interest, are called relaxor pyroelectrics, such as PMN-PbTiOs and PZN-PbTi03. 

In the first approach the changing temperature can be generated by chopping the incoming radiation source or AC heating (known as the Chynoweth technique) of the sample, and the pyroelectric response current i can be expressed as follows ... 

The surface polarization can be measured by different means. The most straightforward one is based on the pyroelectric technique [15]. To measure P one has to deal only with one surface of a cell with uniform director alignment, either planar or homeotropic at both interfaces. The main idea is to use a spatially dependent temperature increment in order to separate the contributions to the pyroelectric response coming only from the surface under study and not from the opposite one. By definition, the pyroelectric coefficient is y = dPIdT where P is macroscopic polarization of a liquid crystal and T is temperature. If we are interested only in the polarization originated from the orientational order we can subtract the isotropic contribution to y and calculate P in the nematic or SmA phases by integrating the pyroelectric coefficient, starting from a certain temperature T, in the isotropic phase ... 

This highly stereoregular polymer displayed a very high relaxed dipole moment and poled films displayed pyroelectric behaviour with a pyroelectric response figure of merit superior to that of PVF2. By contrast, the Schrock initiator... 

FIGURE 31 Hysteresis of the pyroelectric response from a side-chain siloxane FLCP in the smectic C phase [119) (b) hysteresis of the polarization in the smectic C phase of an LC copolymer [27J. 

The piezoelectric coefficients d, and d, do not cancel each other, as we saw previously with the shear piezoelectric biopolymers, but contribute to a small but finite value of tensile piezoelectricity. The tensile piezoelectric coefficient, d, can be measured with a Berlincourt piezometer [38]. The pyroelectric response can be measured with an apparatus in which the temperature is altered at 0.5°/min by circulating water and the pyroelectric current is measured using a low-impedance current amplifier [39]. 

Figure 7.33 shows the divergence of re times in the vicinity of the S -Sa phase transition. The times were measured by studying the dynamics of the pyroelectric response, arid lie within the range 100 fis-l mS. They do not differ very much from the corresponding times for low-molecular mass analogues of the polymer (7.iv) investigated. It means that the polymer... 

Mauzac et al. measured the pyroelectric properties of their networks compared to the corresponding linear polymer (Figure 13.5) and calculated the spontaneous polarization. Although the chemistry of the linear polymer is similar to the chemistry of the network, the pyroelectric response of the network is lower. The only conclusion for this result is the nonperfect orientation of the network [28]. 

---