4.2. Best performing EC materials

Eq. (20) turns into Eq. (14) describing a thermodynamically reversible process. The COPmat of EC materials (~0.35) is inferior to the ones of MC (~0.86) and elastocaloric materials (~0.65) which both exhibit a much larger latent heat of the corresponding first-order phase transitions [7]. Actually, EC refrigerators benefit much less from the large entropy change induced by driving the material through the phase transition by means of applying of releasing rela-

Eq. (20) includes a device-related parameter—the temperature span ðTl � TsÞ, a thermodynamic parameter ΔS and a physical parameter AEC. For practical use, it would be extremely helpful to implement a refrigerant materials criterion which characterizes the efficiency of the physical cooling process and which is therefore independent on the performance of different

<sup>Φ</sup>mat <sup>¼</sup> <sup>1</sup> � εε0E<sup>2</sup> � tan<sup>δ</sup>

where tanδ is the sum of dielectric and hysteresis losses during E cycling. The temperature difference ΔT� ¼ ΔTEC � ðTl � TsÞ of the heat transfer steps was replaced by its maximum value ΔTEC since we consider the maximum cooling power (cf. Eq. (26)). Then Φmat becomes independent on cycle parameters, and it receives its minimum value. The second term on the right-hand side of Eq. (22) represents the inverse of the EC efficiency, i.e. the ratio between the heat transferred from the load to the heat sink and the dissipated electrical energy, introduced in Ref. [49]. The RC is a measure of how much heat can be transferred between the load and the heat sink

<sup>Δ</sup>SdT <sup>≈</sup>Δ<sup>S</sup> � <sup>δ</sup><sup>T</sup> <sup>¼</sup> <sup>c</sup>ΔTEC

where δT is the full width at half maximum of the ΔS versus T curve. Estimations of δT for different EC materials were given in Ref. [51]. Another physical estimate is the distribution

Complete heat transfer from and to the surroundings requires a Fourier number Fo ¼ αt=d<sup>2</sup> > 1, where α is the thermal diffusivity, t is the time and d is the thickness of the EC material [46]. Since power is the subject of interest, we have to consider the Fourier number per

with κ is the thermal conductivity. The FOM of an ideal EC element proposed in Ref. [37], combines the materials efficiency Φmat, the refrigeration capacity RC and the Fourier number

Fo τc ¼ α <sup>d</sup><sup>2</sup> <sup>¼</sup> <sup>κ</sup>

cΔTEC

COPmat ¼ COPC � Φmat: ð21Þ

, ð22Þ

<sup>T</sup> <sup>δ</sup>T, <sup>ð</sup>23<sup>Þ</sup>

cd<sup>2</sup> , <sup>ð</sup>24<sup>Þ</sup>

thermodynamic cycles. For this purpose, COPmat may be written as [7]

where Φmat is the dimensionless material efficiency:

RC ¼

width of the local Curie temperatures considered in Refs. [22, 37].

ð<sup>T</sup><sup>2</sup> T1

tively small fields (cf. Table 1).

30 Refrigeration

in one ideal refrigeration cycle [50]:

cycle time τ<sup>c</sup>

per cycle time:

The most studied and best performing EC materials are currently polyvinylidene fluoride (-CH2-CF2-)n terpolymers (P(VDF-TrFE-CFE)) and irradiated copolymers (P(VDF-TrFE)) as well as solid solutions of lead magnesium niobate and lead titanate ((1-x)PMN-xPT) [2]. Moreover, lead-free perovskite relaxors BaZrxTi1-xO3 (BZT) provide a ΔTEC value over a broad temperature range sufficient for practical cooling applications [51]. Here, data are available solely for comparably low electric fields (up to 14.5 MV/m). Recently, a large ΔTEC of 45 K was obtained for Pb0.88La0.08Zr0.65Ti0.35O3 thin films on a Pt/TiO2/SiO2/Si substrate at an electric field of 125 V/μm [26].

The general requirements to an EC refrigerant are:


Table 2 compares material characteristics [2, 5, 6, 8, 26, 51, 53], the materials efficiency Φmat, Eq. (22), and the figure of merit, Eq. (25), of promising EC refrigerants. For comparison, a thickness of 100 µm was chosen. To account for the field dependence of the dielectric permittivity ε was estimated by averaging in the given electric field region. The values of Φmat exceed significantly the ones known for Brayton engines (0.6–0.8). The only exception is the MLC due to its comparable low value of ΔTEC. MLCs are still not optimized for EC application. The actual FOM depends on how much of the potential δT will be really used and on the field dependence of ε. The latter problem is absent in ferroelectric polymers.
