Elastocaloric effect of shape memory polymers in elastic response regime

Tetra-branched (4b) PCL was synthesized by ring opening polymerization of -caprolactone (CL) with the tetravalent initiator, pentaerythritol [31, 34]. The PCL with various degrees of polymerization (x= 10–70) (abbreviated as 4bxPCL) was designed by adjusting the ratio of pentaerythritol to CL during the polymerization. Thereafter, hydroxyl end groups of 4bxPCL were modified using acryloyl chloride to introduce polymerizable acrylate groups onto the branch ends. The 4bxPCL modified with acrylate groups were cross-linked by thermal polymerization with benzoyl peroxide (BPO) and Michael addition reaction with dithiothreitol (DTT) (figure 1). The acrylated 4bxPCL was dissolved at 45 wt.% in xylene containing 2-fold molar excess BPO to the end-group of the polymer. The solution was injected between glass slides with a ∼0.2 mm thick Teflon spacer. Subsequent thermal polymerization was conducted at 353 K for 16 h to obtain the cross-linked 4bxPCL (4bxPCL-BPO). In cross-linking with DTT, N,N-dimethylformamide was used as a solvent instead of xylene, and a solution was prepared by adding 0.5-fold molar amount of DTT against end-groups of polymer and a catalytic amount of triethylamine, and cross-linked 4bxPCL (4bxPCL-DTT) was obtained in the same manner as described above. The actual values of x were estimated at x = 11, 21, 32, 52, and 67 (x = 11, 21, 32, and 52) for 4bxPCL-BPO (4bxPCL-DTT) sheets by proton nuclear magnetic resonance spectroscopy. The thickness t of the 4bxPCL-BPO and -DTT samples is in the range of 0.1–0.2 mm. After fabrication, all the 4bxPCL SMP sheets are cut out into a strip with the width w of 6 mm. For comparison, we prepared five commercial plastic sheets: PS, polypropylene, polyvinyl-chloride, high density polyethylene (HDPE), and polyethylene-terephthalate with t = 1.0 mm and w = 6 mm, which are available from NaRiKa Corp., Japan. For the lock-in thermography (LIT) measurements (see section 2.3), the surface of the samples was coated with insulating black ink with an emissivity of >0.94 (JSC-3, JAPANSENSOR Corporation) to endure high and uniform thermal radiation.

The crystallinity ratio X_c and the melting temperature T_m, corresponding to the crystal-amorphous transition of SMPs, of the 4bxPCL-BPO and -DTT samples were estimated using the differential scanning calorimetry (DSC). All samples were first equilibrated at 353 K and then cooled to 253 K, followed by performing the measurements during the heating process to 353 K at a rate of 5 K min⁻¹ under nitrogen atmosphere. The value of X_c was calculated from the enthalpy change quantified by DSC thermograms and the melting enthalpy of 100% crystalline PCL and that of T_m was defined as the temperature at the peak top of DSC thermograms [35, 36]. To check the reproducibility and estimate the magnitude of errors, the DSC measurements were conducted three times for each sample.

The temperature modulation generated by the elastocaloric effect was measured using the LIT technique [37]. In the LIT measurement, we recorded thermal images of a sample surface by applying a periodic oscillation of the input signal using an infrared camera and extracted a temperature change oscillating with the same frequency f as the input frequency [25, 38–42] (figure 2). Since the LIT method enables contact-free temperature measurements with high temperature and spatial resolutions and separation of the temperature change due to a target effect and a background signal, it is suitable to measure the elastocaloric temperature change in the small strain regime, compared with other methods for measuring the caloric effects [39]. The procedure of the LIT measurement for this study is as follows (see also figure 2). First, the samples were clamped at the distance L₀ = 15 mm on a motor-driven tensile machine with a load cell and a linear encoder, where the center between the two clamps was adjusted to the center of the viewing area of the infrared camera by using a custom-made ball screw. Second, a sinusoidal strain with the amplitude Δ, offset ₀, and f = 1 Hz was applied to the sample along its longitudinal direction, where Δ = Δl/L₀ and ₀ = Δ + 0.5% with Δl being the amplitude of the sinusoidal elongation. Finally, the thermal images recorded were transformed into the lock-in amplitude A (>0) and phase φ (0° ⩽ φ < 360°) images through Fourier analysis, in which A informs the magnitude of the elastocaloric temperature modulation and φ the sign of the temperature modulation as well as the time delay due to the thermal diffusion. In previous study, it was shown that the value of φ due to the elastocaloric effect in unpatterned plastic sheets at 1 Hz is nearly 180° and the contribution of thermal diffusion is negligible [25]. Unless otherwise specified, the integration time of each LIT measurement t_int is 60 s. The performance of the elastocaloric temperature modulation was thus quantified by |ΔT|/Δσ, where ΔT is the elastocaloric temperature change calculated as ΔT = Acosφ and Δσ is the stress for stretching the sample, calculated as Δσ= ΔF/wt with ΔF being the change in the load monitored using the load cell. All the LIT measurements were conducted at room temperature and under air atmosphere.

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Figures 3(a) and (b) show the x dependence of X_c (T_m) for 4bxPCL-BPO and -DTT samples. In both SMPs, the decreasing trend of X_c and T_m was observed with a decrease in x. When comparing the two SMPs with same x, the value of X_c of 4bxPCL-DTT and 4bxPCL-BPO was almost the same except for the sample with x = 11, while T_m of 4bxPCL-DTT was larger than that of 4bxPCL-BPO. Figure 3(c) shows the absolute value of DSC heat flow per unit mass |j_H|, proportional to specific heat of each SMP, at 300 K. The magnitude of j_H of 4bxPCL-BPO was larger than that of 4bxPCL-DTT and, in both 4bxPCL SMPs, the maximum |j_H| was obtained in the sample with a minimum x (i.e., x = 21 for 4bxPCL-BPO and x = 11 for 4bxPCL-DTT).

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In figure 4(a), we show the A and φ images of the 4b11PCL-DTT sheet at Δ = 1.5% as an example of the result of the LIT measurement. The temperature modulation signal with uniform A and φ of ∼180° was clearly observed in the sample. As shown in figure 4(b), the magnitudes of A and φ are independent of t_int, confirming the reversible temperature modulation during the LIT measurement. Figure 4(c) shows the Δ dependence of A and Δσ for the 4b11PCL-DTT sheet. These linear relationships indicate that the elastocaloric effect obtained here is dominantly attributed to the mechanism (i), similar to the conventional plastic sheets [25]. In all of the samples used in this study, we obtained φ∼ 180°, indicating that heat is absorbed (ΔT < 0) when stretching the sample. We confirmed the linear Δ dependence of A and Δσ below Δ < 3%. To check endurance of the elastocaloric material, we performed repetitive LIT measurements in the 4b11PCL-DTT sheet. In figure 4(d), A and Δσ at Δ = 2.0% are plotted against the repetitive stretching number N_rep up to 10 000, where the LIT measurements with the accumulation time of 60 s and interval of 40 s were repeated by N_LIT = 100 times. The magnitudes of A and Δσ were found to be independent of N_rep, confirming the durability of our elastocaloric material up to 10 000-repeated strains of 2.0%. Figure 4(e) depicts the relationship between |ΔT| and Δσ at Δ = 1.0% for the 4bxPCL SMP and plastic sheets. Since the data at upper (larger |ΔT|) and left (smaller Δσ) positions in this graph correspond to higher performance of the elastocaloric temperature modulation, we found that 4bxPCL SMPs are better elastocaloric materials than the conventional plastics. Note that |ΔT|/Δσ of the PS sheet with t = 1.0 mm is 1.4 × 10⁻⁸ K Pa⁻¹, which is comparable to that of the PS sheets with t = 0.2 and 0.3 mm [25], showing that the difference in t is irrelevant to the present results. Figure 4(f) shows the x dependence of |ΔT|/Δσ for the 4bxPCL-BPO and -DTT samples. The |ΔT|/Δσ values of the PCL-based SMP sheets were larger than that of the HDPE sheet (∼2.0 × 10⁻⁸ K Pa⁻¹), the maximum among five conventional plastic sheets. In both SMP sheets, the values of |ΔT|/Δσ were almost the same in the range of x ⩾ 32, but below x = 32, the value of |ΔT|/Δσ increased with decreasing x. The maximum |ΔT|/Δσ observed here was estimated to be ∼3.0 × 10⁻⁸ K Pa⁻¹ in the 4b11PCL-DTT sheet, which leads to ΔS_iso ∼ 7 × 10⁻⁴ J g⁻¹K⁻¹. To compare the performance of elastocaloric materials, we can use the material-level dimensionless elastocaloric efficiency ζ [43, 44], defined as the ratio between the useful cooling/heating (=ρc_p|ΔT|) and the work input, i.e., the area between the Δσ-Δ curve and horizontal axis [13]: ΔΔσ/2 in an elastic response. Here, we note that the material-level coefficient of performance COP_mat is also widely used for comparing elastocaloric materials but inappropriate for our samples; since the work input in COP_mat is defined by the area of the Δσ-Δ curve enclosed by loading and unloading curves (=${\mathop \oint \nolimits}\sigma d\varepsilon$), it is almost zero in the reversible elastic regime, leading to the divergence of COP_mat. Although the magnitude of |ΔT| and |ΔT|/Δσ of the PCL-based SMP sheets are still smaller than those of SMAs, ζ is estimated to be ∼5 for our samples when ρ= 1.1 × 10⁶g m⁻³ and c_p = 1.8 J g⁻¹K⁻¹ are used [45, 46]. This ζ value is comparable to that of SMAs [13, 47]. Moreover, assuming that the 4b11PCL-DTT sheet is patterned into the same kirigami structure as shown in the PS sheets in [25] and the similar increase ratio of focused stress is obtained within the linear elastic response regime, the local |ΔT|/Δσ value will be enhanced around 4 × 10⁻⁷ K Pa⁻¹. This value is nearly an order of magnitude larger than that of SMAs, corresponding the local |ΔT| of over 1.0 K only at Δ = 2.0% (note that the total |ΔT|/Δσ averaged over the kirigami-patterned sample is not enhanced).

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Here, we discuss the origin of the x dependence of |ΔT|/Δσ in 4bxPCL SMPs. When we consider only the mechanism (i), equation (1) is simply reformulated as |ΔT_ad|/Δσ = |T₀ α/c|, where α and c are the linear expansion coefficient and volumetric heat capacity, respectively [9]. According to the results of the DSC measurements (see section 3.1), c should increase with decreasing x. Thus, the dominant contribution of the enhancement of |ΔT|/Δσ with decreasing x is the increase in α. In the vicinity of T_m, the thermomechanical properties including α may be modulated as well as the mechanical properties [48, 49]. However, the decrease in T_m also causes the reduction of X_c and durability. The combination of small x and large X_c are crucial for enhancing |ΔT_ad|/Δσ at room temperature. Owing to the DTT cross-linking, the high rate of ordered crystal structure can be kept even at room temperature in the 4bxPCL SMPs with small x, resulting in the large |ΔT_ad|/Δσ.

To further investigate the elastocaloric properties of SMPs, we performed the same measurements on the SMP sheets uniaxially deformed by the shape memory effect. Figure 5(a) shows the images of the PCL-based SMP sheets before and after deformation of which the procedure is as follows. First, the sheet clamped on the tensile machine was heated up to T_m using a blow-dryer. Then, while heating, the sheet was quickly stretched by a uniaxial deformation strain η, which was controlled by moving the clamps of the tensile machine. Finally, by cooling down the sheet to RT while holding the elongated sheet, the deformation was persistently fixed.

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Figure 5(b) shows the A images of the 4b52PCL-BPO sheet at several η values. Even after the deformation, the distribution of the A signal in the SMP sheets is uniform. Importantly, the magnitude of the A signal depended on η. The upper panel of figure 5(c) shows the A signal as a function of η at Δ = 1.0% in the 4b52PCL-BPO sheet. The magnitude of A was enhanced with increasing η below η = 150%, where A at η = 100%–150% were about 1.4 times larger than that at η = 0%, but was decreased toward zero with further increasing η above 150%. However, the η dependence of Δσ at Δ = 1.0% was quite different from A: the clear increase in Δσ was obtained only around η = 150% as shown in the bottom panel of figure 5(c). Such individual η dependences enhanced the |ΔT|/Δσ factor (light blue circle data points in figure 5(d)) to ∼3.0 × 10⁻⁸ K Pa⁻¹ at η = 100%, a similar value obtained in the 4b11PCL-DTT sheet with η = 0%. Although the enhancement of |ΔT|/Δσ around η = 100% was also observed in the 4b67PCL-BPO sheet, the |ΔT|/Δσ of the 4b21PCL-BPO sheet monotonically decreased with the increase in η (figure 5(d)). In the 4bxPCL-DTT samples, as shown in figures 5(e) and (f), the significant enhancement of A was not obtained and only the decrease in |ΔT|/Δσ with η increase was confirmed even in the sample with x =52, whereas the Δσ-η relation showed the similar behavior.

Finally, we discuss the origin of the modulation of the elastocaloric properties induced by the shape memory effect. The dominant contribution is expected to be different from the mechanisms discussed in section 3.2, because uniaxial deformation via the shape memory effect induces the orientation of polymer chains and the change in the order from isotropic to anisotropic network with almost no change in crystallinity of PCL [50]. Previous reports show that the orientation of polymer chains monotonically reduces α in other polymers [51–53]. If this scenario is applicable to PCL-based SMPs, the dramatic reduction of A at large η can be explained, while the enhancement of A around η = 100%–150% is still unclear. Thus, additional ΔS_iso induced by the mechanism (iii) corresponding to the conformation of polymer chains may exist. To clarify the microscopic mechanism and optimize |ΔT|/Δσ in SMPs, detailed analyses of their structures are necessary.