A self-actuated electrocaloric polymer heat pump design exploiting the synergy of electrocaloric effect and electrostriction
一种自驱动的电热聚合物热泵设计，利用电热效应和电致伸缩的协同作用

P(VDF-TrFE-CFE) 63/29.7/7.3 terpolymer was provided by Piezo Technologies, France. FA is induced by an elimination reaction as the same method as indicated in [26]. The FA content was determined by proton nuclear magnetic resonance (1 H NMR) with acetonitrile-d3 as the solvent. In preparation of the unstretched polymer films, 0.4 g polymers were dissolved in 10 ml dimethylformamide (DMF) and stirred overnight at room temperature. The homogeneous solution was then deposited onto a 50 mm × 75 mm clean glass substrate in an oven for 12 h at 60 °C. After drying, the films were placed in deionized (DI) water to be peeled off from the substrate. Afterward, the polymer films were placed in a vacuum oven and annealed at 120 °C for 24 h, followed by a natural cooling in the oven to room temperature. Then the unstretched polymer films were ready for characterization. The thickness of unstretched (US) films were in the range from of 27 μm to 35 μm.
P(VDF-TrFE-CFE) 63/29.7/7.3 三元聚合物由法国 Piezo Technologies 提供。FA 是通过消除反应诱导的，方法与[26]中所示相同。FA 含量通过质子核磁共振（1 H NMR）与氘代乙腈作为溶剂进行测定。在制备未拉伸聚合物薄膜时，将 0.4 克聚合物溶解在 10 毫升二甲基甲酰胺（DMF）中，并在室温下搅拌过夜。然后将均匀的溶液在 60°C 的烘箱中沉积到 50 毫米 × 75 毫米的干净玻璃基板上，放置 12 小时。干燥后，薄膜被放置在去离子水（DI）中，从基板上剥离。随后，聚合物薄膜被放置在真空烘箱中，在 120°C 下退火 24 小时，然后在烘箱中自然冷却至室温。然后，未拉伸的聚合物薄膜准备好进行表征。未拉伸（US）薄膜的厚度范围为 27 μm 到 35 μm。

To prepare stretched samples, a higher concentration of polymer solution was prepared (2 g polymer dissolved in 10 ml DMF). The other processing steps were the same for the unstretched films before annealing. After peeling from the substrate, the polymers films were stretched to 7× initial length through uniaxial zone-stretching. After stretching, the polymer films were annealed at 120 °C for 24 h. Afterward, the films were ready to use. The thickness of stretched films were similar to that of unstretched films. Gold electrodes were sputtered on the polymer films with an EMITECH K550X system, with nominal thickness of 30 nm.
为了制备拉伸样品，准备了更高浓度的聚合物溶液（2 克聚合物溶解在 10 毫升 DMF 中）。在退火之前，其他处理步骤与未拉伸薄膜相同。剥离基材后，聚合物薄膜通过单轴区域拉伸至初始长度的 7×。拉伸后，聚合物薄膜在 120°C 下退火 24 小时。之后，薄膜准备好使用。拉伸薄膜的厚度与未拉伸薄膜相似。金电极通过 EMITECH K550X 系统在聚合物薄膜上溅射，名义厚度为 30 纳米。

The total EC heat flow Q to/from the polymer films when applying/removing electric fields was measured with a heat flux sensor. This yields the isothermal entropy change ΔS of the EC polymers (Q = TΔS). The details of this method were reported in [9].
在施加/去除电场时，通过热流传感器测量了聚合物薄膜的总电致变色热流 Q。这得出了电致变色聚合物的等温熵变 ΔS（Q = TΔS）。该方法的详细信息已在 [9] 中报告。

A thermal imaging infrared (IR) camera (Infratec^® ImageIR 8300) was used to directly measure surface temperature changes of the EUHP device during electric field cycles. A thin layer of carbon-powder-loaded black paint was applied to cover the gold surface to reduce reflections and increase emissivity for thermal imaging measurements.
一种热成像红外（IR）相机（Infratec^® ImageIR 8300）被用来直接测量 EUHP 设备在电场循环过程中的表面温度变化。为了减少反射并提高热成像测量的发射率，涂覆了一层薄薄的碳粉加载黑色涂料以覆盖金表面。

Transverse strain S₁ was measured using a photonic sensor (MTI 2000 FOTONIC SENSOR) connected to a Polarization Loop & Dielectric Breakdown Test System (PolyK Technologies). A 1 Hz triangle wave was applied to the polymer films, and the strain (along the stretching direction for uniaxially stretched films) was recorded. The displacement of the EUHP was measured with a photonic sensor (Polytec OFV 3001S). The electric field was applied via a function generator at 1 Hz sine wave amplified through a Trek (601D) voltage supply.
横向应变 S₁ 是通过连接到极化环和介电击穿测试系统（PolyK Technologies）的光子传感器（MTI 2000 FOTONIC SENSOR）测量的。对聚合物薄膜施加了 1 Hz 的三角波，并记录了应变（沿单轴拉伸薄膜的拉伸方向）。EUHP 的位移是通过光子传感器（Polytec OFV 3001S）测量的。电场通过函数发生器以 1 Hz 的正弦波施加，并通过 Trek（601D）电压源放大。

Polarization-electric field loops of stretched polymer films were characterized with a Polarization Loop & Dielectric Breakdown Test System (PolyK Technologies) at 10 Hz. The Young's modulus was measured with a commercial Dynamic Mechanical Analysis (TA, G2 RSA).
拉伸聚合物薄膜的极化-电场回路使用极化回路和介电击穿测试系统（PolyK Technologies）在 10 Hz 下进行表征。杨氏模量通过商业动态机械分析仪（TA, G2 RSA）进行测量。

First, the dependence of the EC performance of P(VDF-TrFE-CFE-FA) on FA content was studied. The results are presented in figures 1(a) and (b), showing that both the unstretched and stretched films exhibit giant enhancement of ΔS compared to those of neat terpolymers. For example, at 50 MV m⁻¹, the unstretched and stretched terpolymers generate ΔS of about 10 J kg⁻¹ K⁻¹. Tetrapolymers with ∼2 mol% FA generate ΔS of 41.2 J kg⁻¹ K⁻¹ and 43.2 J kg⁻¹ K⁻¹ for unstretched and stretched films, respectively—more than four times than in the terpolymer films. The comparison of ECE in unstretched and stretched films is presented in figure 1(c). It can also be seen that the stretched tetrapolymer films exhibit slightly higher ΔS compared with unstretched films, especially at high electric field such as 70 MV m⁻¹. It has been suggested that the mechanical stretching can facilitate the inclusion of FA in the crystalline phase which makes them more effective in yielding the ferroelectric related responses [26].
首先，研究了 P(VDF-TrFE-CFE-FA)的 EC 性能对 FA 含量的依赖性。结果如图1(a)和(b)所示，未拉伸和拉伸的薄膜相比于纯三元聚合物均表现出ΔS的巨大增强。例如，在 50 MV m⁻¹时，未拉伸和拉伸的三元聚合物产生的ΔS约为 10 J kg⁻¹ K⁻¹。含有∼2 mol% FA 的四元聚合物产生的ΔS分别为未拉伸和拉伸薄膜的 41.2 J kg⁻¹ K⁻¹和 43.2 J kg⁻¹ K⁻¹，是三元聚合物薄膜的四倍多。未拉伸和拉伸薄膜中 ECE 的比较如图1(c)所示。还可以看出，拉伸的四元聚合物薄膜在高电场（如 70 MV m⁻¹）下相比于未拉伸薄膜表现出略高的ΔS。 有研究表明，机械拉伸可以促进 FA 在晶相中的掺入，从而使其在产生与铁电相关的响应方面更有效[26]。

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The polarization-temperature curves under unipolar electric field of 50 MV m⁻¹ for the tetrapolymers with different FA concentrations are presented in figure 1(d). This reveals that the polarization of the tetrapolymer peaks at the terpolymers with 1.9 mol% FA—the same composition of the ECE peak. The peak position of polarization also suggests that 1.9 mol% FA tetrapolymer locates at a composition that close to the end critical point, which is considered as an efficient approach to enhance EM and EC performances of ferroelectric relaxors [28–31]. ΔS and P data were used to determine the phenomenological β coefficient, ΔS = ½ β P² (figure 1(e)). The β coefficient of all the tetrapolymers in the figure is higher than that of the terpolymer. At the EC peak composition (1.9 mol% FA), the β value is more than 2.5 time of that of the terpolymer. This indicates that the polarization processes in the tetrapolymers are much more effective in generating ECE compared with the terpolymer.
在 50 MV m⁻¹的单极电场下，不同 FA 浓度的四聚合物的极化-温度曲线如图1(d)所示。这表明四聚合物的极化在 1.9 mol% FA 的三聚合物处达到峰值——这是 ECE 峰的相同组成。极化的峰值位置还表明 1.9 mol% FA 四聚合物位于接近终点临界点的组成，这被认为是增强铁电弛豫体的电致伸缩（EM 和 EC）性能的有效方法[28–31]。ΔS和P数据用于确定现象学β系数，ΔS = ½ β P²（图1(e)）。图中所有四聚合物的β系数均高于三聚合物。在 EC 峰组成（1.9 mol% FA）处，β值超过三聚合物的 2.5 倍。这表明，与三聚合物相比，四聚合物中的极化过程在产生 ECE 方面更为有效。

As discussed in the section 1, the two polymer layers in an ideal EUHP should possess similar and large ECEs and significantly different EM responses. S₁ is the key parameter governing unimorph actuation, and should be substantially different in the two layers to achieve a large displacement. The transverse strains S₁ were characterized for the tetrapolymers and results are presented in figures 2(a) and (b). Analogous to the ECE and polarization data presented in figure 1, the transverse strains also peak at 1.9% FA concentration. This suggests that the enhancements of both EM and ECE due to FA addition originate from similar mechanisms. The stretched tetrapolymer with 1.9% FA generated a 2% S₁ under 50 MV m⁻¹. In contrast, the unstretched films had much lower S₁. The tetrapolymer with 1.9% FA generated 1% S₁ at the same field—half of that of the stretched film. This large difference in S₁ between the stretched and unstretched films suggests that the tetrapolymers with 1.9% FA are ideal for the proposed EUHPs.
如在章节 1 中讨论的，理想的 EUHP 中的两个聚合物层应具有相似且较大的 ECE，并且 EM 响应显著不同。S₁ 是控制单层驱动的关键参数，并且在两个层中应有显著不同以实现大位移。对四聚合物的横向应变 S₁ 进行了表征，结果如图 2(a) 和 (b) 所示。与图 1 中呈现的 ECE 和极化数据类似，横向应变在 1.9% FA 浓度时也达到了峰值。这表明，由于 FA 添加而导致的 EM 和 ECE 的增强源于类似的机制。拉伸的四聚合物在 50 MV m⁻¹ 下产生了 2% S₁。相比之下，未拉伸的薄膜的 S₁ 要低得多。在相同电场下，含有 1.9% FA 的四聚合物产生了 1% S₁，仅为拉伸薄膜的一半。 这种拉伸和未拉伸薄膜之间的S₁的大差异表明，含有 1.9% FA 的四聚物非常适合所提议的 EUHPs。

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The stretched and unstretched tetrapolymers with 1.9% FA were selected as the base materials for the EUHP. The assembly is illustrated in figure 2(c) and a photograph of the physical specimen is presented in figure 2(d). The thicknesses of epoxy glue layer (<1 µm) and electrodes (∼30 nm) are much smaller than the those of the tetrapolymer films (∼30 µm for each of the two tetrapolymer films). The glue and electrode layers can thus be assumed to have negligible effects on actuation. The measurement of actuation displacement of EUHP is illustrated in figure 2(e), the two ends of the EUHP were fixed at x = ±L/2, where L is 2.0 cm. When an electric field is applied on the device, the actuator moves upward through the mechanism described in [27]. The maximum displacement Z_max occurs at the center of the strip (x = 0), which can be estimated from [27]
拉伸和未拉伸的四聚合物（FA 含量为 1.9%）被选为 EUHP 的基础材料。组装过程如图 2(c) 所示，物理样本的照片呈现在图 2(d) 中。环氧胶层的厚度（<1 id=184>µm）和电极（∼30 nm）远小于四聚合物薄膜的厚度（每个四聚合物薄膜约为 30 µm）。因此，可以假设胶水和电极层对驱动的影响可以忽略不计。EUHP 的驱动位移测量如图 2(e) 所示，EUHP 的两端固定在 x = ±L/2，其中 L 为 2.0 cm。当在设备上施加电场时，驱动器通过[27]中描述的机制向上移动。最大位移 Z_max 发生在条带的中心（x = 0），可以从[27]中估算。

$$\begin{array}{}\text{(1)}& Z_{\text{max}}=a\frac{L^4}{16}.\end{array}$$

Here, a is a parameter determined by the effective strain S_e of the plate under electric field, and L is the distance between the two fixed ends. For a given electric field, the strain of active layer (S-tetrapolymer) is S_a, and the strain of less-active layer (US-tetrapolymer) is S_L. The effective strain S_e can be calculated from a modified form of the classic equation of general unimorph [27],
在这里，a 是由电场下板的有效应变 S_e 决定的参数，而 L 是两个固定端之间的距离。对于给定的电场，活性层（S-四聚物）的应变为 S_a，而低活性层（US-四聚物）的应变为 S_L。有效应变 S_e 可以通过经典通用单层的修正形式计算得出 [27]。

$$\begin{array}{}\text{(2)}& S_{\text{e}}=\frac{S_{\text{a}}-S_{\text{L}}}{1+k}+S_{\text{L}}.\end{array}$$

Here, k = E_L δ_L/E_a δ_a, where E_L and E_a are the Young's moduli of less-active layer and active layer, respectively. δ_L and δ_a are the thicknesses of the less-active layer and active layer, respectively. In the fabricated device, δ_L ≈ δ_a, yielding k ≈ E_L/E_a = 220 MPa/530 MPa = 0.415. S_a and S_L of the tetrapolymer films were shown in figures 2(a) and (b), and can be used to determine S_e as a function of electric field. Using S_e, the coefficient a in equation (1) can be determined as described in [27]. The theoretically predicted Z_max is compared with experimental measurements in figure 2(f). The good agreement between predictions and experimental data supports the proposed mechanism of the EUHP actuators. At 50 MV m⁻¹, the EUHP actuator can switch the device more than 1.5 mm.
在这里，k = E_L δ_L/E_a δ_a，其中 E_L 和 E_a 分别是低活性层和活性层的杨氏模量。δ_L 和 δ_a 分别是低活性层和活性层的厚度。在制造的设备中，δ_L ≈ δ_a，得出 k ≈ E_L/E_a = 220 MPa/530 MPa = 0.415。四聚合物薄膜的 S_a 和 S_L 如图 2(a) 和 (b) 所示，可以用来确定 S_e 作为电场的函数。使用 S_e，方程 (1) 中的系数 a 可以如 [27] 中所述确定。 理论预测的 Z_max 与图 2(f) 中的实验测量结果进行了比较。预测与实验数据之间的良好一致性支持了 EUHP 执行器的提议机制。在 50 MV m⁻¹下，EUHP 执行器可以使设备切换超过 1.5 毫米。

To assess the EC performance of the EUHP, a high-speed thermal imaging IR camera was used to measure the temperature change as the device was switched [18]. As schematically illustrated in figure 3(a), in the IR imaging of the EUHP heat pumping process, the EUHP was hung on two fixed ends and was slightly tilted toward the IR camera to increase the EUHP area facing the IR camera. Eventually, the thickness of EUHP seen in the IR camera is about 3.2 mm, while the actual thickness of the EUHP is ca. 60 μm. Figure 3(b) presents thermal images of the EUHP as electric fields were applied and removed. Upon applying electric field, the EUHP moves upward and the temperature of the EC film increases. When the field is removed, the EUHP returns to its initial position and cools (figure 3(b)). This displacement of the EUHP can be observed in the IR images. For instance, at 53 MV m⁻¹, the displacement between the positions of the EUHP with the field ON and OFF is greater than 1 mm. The temperature changes are summarized in figure 3(c). The asymmetry of EC heating and cooling ΔT is due to the P² dependence of ΔT of the EC polymer. As shown in supporting materials (figure S1), the ΔT measured under a step E field in the heating cycle will be smaller than that in the cooling cycle in short time after the change of E, which is the case in this study. The predicted temperature drops ΔT for S-tetrapolymer and US-tetrapolymer can be calculated from the measured ΔS data (figure 1) as ΔT = TΔS/C_E. Here, C_E is the material specific heat capacity: 1404 J kg⁻¹ K⁻¹ at room temperature. The material-level ΔTs for the S-tetrapolymer and US-tetrapolymers are ∼8.8 K at 50 MV m⁻¹. The measured ΔT for the full EUHP is ∼6.5 K at 53.3 MV m⁻¹. The difference may be due to heat dissipation to the surroundings and the added thermal mass from the glue and carbon-loaded paint layers. The EUHP still exhibits great EC performance considering the low electric field.
为了评估 EUHP 的 EC 性能，使用了一台高速热成像红外相机来测量设备开关时的温度变化[18]。如图3(a)所示，在 EUHP 热泵过程的红外成像中，EUHP 悬挂在两个固定端，并稍微倾斜朝向红外相机，以增加面向红外相机的 EUHP 面积。最终，在红外相机中看到的 EUHP 厚度约为 3.2 毫米，而 EUHP 的实际厚度约为 60μm。图3(b)展示了在施加和移除电场时 EUHP 的热成像。当施加电场时，EUHP 向上移动，EC 薄膜的温度升高。当电场移除时，EUHP 返回到初始位置并冷却（图3(b)）。这种 EUHP 的位移可以在红外图像中观察到。例如，在 53 MV m⁻¹时，EUHP 在电场开启和关闭时的位置位移大于 1 毫米。温度变化总结在图3(c)中。 EC 加热和冷却的非对称性ΔT是由于 EC 聚合物的ΔT对^P2的依赖性。如支持材料（图 S1）所示，在加热循环中，在施加阶跃E场后短时间内测得的ΔT将小于冷却循环中的ΔT，这在本研究中是成立的。S-四聚体和 US-四聚体的预测温度下降ΔT可以从测得的ΔS数据（图1）计算得出，公式为ΔT = TΔS/C_E。这里，C_E是材料的比热容：在室温下为 1404 J kg⁻¹ K⁻¹。S-四聚体和 US-四聚体的材料级ΔTs在 50 MV m⁻¹时约为 8.8 K。全 EUHP 的测得ΔT在 53.3 MV m⁻¹时约为 6.5 K。 差异可能是由于热量向周围环境的散失以及胶水和碳负载涂层所增加的热质量。考虑到低电场，EUHP 仍然表现出良好的电化学性能。

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