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Giant reversible barocaloric effects in Nitrile Butadiene Rubber around room temperature

Elastomers have shown to be promising barocaloric materials, being suitable candidates for solid-state cooling devices. Moreover, this family of polymers presents additional advantages, such as their low cost and long fatigue life. In this context, we investigated the barocaloric effects in Nitrile Butadiene Rubber (NBR) in a large range around room temperature. Moderated applied pressures on NBR yield giant temperature change ({\Delta}TS) and entropy change ({\Delta}ST), reaching the maximum values of 16.4(2) K at 323 K and 59(6) J kg-1K-1 at 314 K, respectively, for a pressure change of 390 MPa. Besides, both {\Delta}TS and {\Delta}ST have shown to be rather reversible. An influence of the glass transition on the barocaloric effects was verified: the glassy state tends to diminish the entropy and temperature changes in comparison with the rubbery state. Furthermore, we calculated the pressure coefficient of glass transition (dTg/dP) obtained from different processes. Our study evidences the potential of NBR for cooling applications based on barocaloric effect, but also points out the glass transition must be avoided for a better barocaloric performance.


INTRODUCTION
The Nitrile Butadiene Rubber (NBR) is a well-known polymer from the family of elastomers with remarkable mechanical and chemical properties. NBR is an unsaturated copolymer formed by chains composed of butadiene (C4H6) and acrylonitrile (C3H3N). The rubber-like behavior (elasticity), the resistance to chemical agents (e.g. oils and acids) and low-cost make the NBR an interesting material for applications in many fields, such as automotive and aeronautic industry, as well as for making disposable equipment [1]. In recent years, elastomers have been found to be promising materials for applications in solid-state cooling [2][3][4][5]. Despite the favorable properties of NBR, this elastomer has not been explored in view of its cooling potential to date.
Current refrigeration technology is based in vapor-compression cycles, which brings environmental and energetic issues. Aiming to solve these problems, solid-state cooling devices appear as promising options [6][7][8]. This technology is based in materials which present i-caloric effects, in other words, materials exhibiting a thermal response when exposed to an external field change (i stands for intensive thermodynamic variablesdenoting the external fields). The nature of the external field can be magnetic (H), electric (E) or mechanical (σ). Therefore, we can categorize the i-caloric effects as: magnetocaloric (h-CE), electrocaloric (e-CE) and mechanocaloric effects (σ-CE). The later can be subdivided in barocaloric (σb-CE) and elastocaloric effect (σe-CE). Over the past two decades, the research on caloric materials have seen a fast growth due to the discoveries of the giant h-CE in Gd5Si2Ge2 compound in 1997 [9], the giant e-CE in PbZr0.95Ti0.05O3 in 2006 [10] and the giant σb-CE in Ni-Mn-In shape-memory alloy in 2010 [11]. However, the studies on i-caloric materials date from 1805, when J. Gough reported a temperature change in natural rubber under rapid stretching (σe-CE) [12]. Decades later, W. Thomson predicted the σ-CE, h-CE and e-CE using thermodynamic considerations [13,14].
In this context, NBR appears as a new option of barocaloric material for application. Here, we investigate the σb-CE in NBR in a large range around room temperature at moderate pressures (up to 390 MPa). Direct measurements of temperature change (ΔTS) yielded giant values. Strain (ε) versus temperature (T) data allowed us to calculate the isothermal entropy change (ΔST). Moreover, we observed both ΔTS and ΔST results are clearly hindered by the glass transition, which shifts to higher temperature with the applied pressure.

II.
EXPERIMENT We used a commercial vulcanized NBR sample reinforced with carbon black fillers provided by Elastim company. The material was supplied in a long cylindrical shape with a diameter of 12 mm. The sample with 8 mm in diameter and 20 mm in length was formed from the supplied material. The density of the sample, measured with a pycnometer, is 1390(10) kg m -3 . We characterized the NBR sample via Fourier transform infrared spectroscopy (see Fig. 1 in the Supplemental Material [28]) using a PerkinElmer spectrometer (model spectrum Two).
The experimental setup and procedures used in the present work are described in detail elsewhere [2][3][4]29]. Strain vs. temperature experiments were performed through isobaric processes, i.e., the temperature was varied, in a rate of 4 K/min, between 213-333 K under constant pressures within the 4 -390 MPa range.
Direct ΔTS measurements were performed by applying/releasing pressure (maximum values within the range of 26 -390 MPa) in a quasi-adiabatic condition. When the temperature in the sample is stable at the set point, a compressive stress is rapidly applied, resulting in a sharp increase in temperature. The load is kept constant until the temperature downs to the initial value. Finally, the stress is fastly released, causing an abrupt decrease in the sample's temperature.

RESULTS AND DISCUSSION
ΔTS data as a function of the initial temperature for compression and decompression processes are shown in Fig. 1(a). Both processes present very close results in the compared temperature range (293 -324 K). At 390 MPa, we observe a maximum ΔTS value of 16.4(2) K (at 323 K) for decompression. This giant barocaloric ΔTS surpasses or it is comparable to the best barocaloric intermetallics reported so far [30]. Normalizing this result by the applied pressure (|ΔTS/ Δσ|) we have a huge value of 42(2) K GPa -1 . For the two lowest pressures, the ΔTS curves present a slight ascending behavior as the temperatures increases. On the other hand, for 86 MPa and above, we observe a stronger dependence of the ΔTS with temperature: the curves show a smooth increase of the ΔTS values, tending to saturate at higher temperatures (plateau). This behavior can be attributed to the influence of the glass transition of the NBR, since the mobility of the chains is significantly reduced as the material changes from the rubbery state (plateau) to the glassy state (steep region and below). Therefore, ΔTS values tend to decrease below the glass transition temperature (Tg). Corroborating this hypothesis, a similar behavior was reported by Bom et al in vulcanized natural rubber [3]. In Fig. 1(b), the temperature and pressure are shown as a function of time for sequential adiabatic compression-decompression cycles. Note that the procedure is different from the measurements of ΔTS. Here, the sample does not return to the initial temperature after the pressure is applied. The behavior of the temperature change shows a rather reversible process, since the temperature change in compression is very close to the temperature change in decompression, with a difference less than 3%. Furthermore, the magnitude of the temperature change (~10 K) remains the same for repeated applications of pressure, also showing the reproducibility of these cycles.
It is a known fact that Tg is sensitive to pressure [3,[30][31][32][33][34][35], so it is expected that Tg shifts to higher values as pressure increases. This behavior is shown in Fig. 2, where Tg was calculated from ΔTS and ε vs T. data for pressures within the range of 0 -390 MPa. We defined Tg as the point where the third derivative is zero in the curves of Fig. 1 and Strain-Temperature data (See Fig. 2 and Fig. 3 in Supplemental Material [28]). Values from strain data exhibit distinct slopes for cooling and heating processes. This discrepancy occurs due to the different kinects involving glass transformation on cooling and heating processes, which may shift the Tg to higher or lower values [34,37]. In the cooling process, Tg values are lower than those in the heating process, which is expected for polymers, since the material is coming from an equilibrium state (above Tg) to a non-equilibrium one (below Tg).
For Tg obtained from ΔTS data, we observe the curve is in between the cooling and heating curves. This is possibly explained by the differences in the processes [38]. On one hand, the ε vs. T was performed at isobaric process. On the other hand, ΔTS is measured when pressure is applied very quickly increasing the sample's temperature; then, the material cools down to the initial temperature and the pressure is released. These two distinct experimental procedures may yield different results. Still, there is a good agreement between the data from both methods considering the estimated errors. The pressure coefficient of the glass transition temperature (dTg/dP) for the heating, cooling and ΔTS curves are 0.186(4), 0.14(2) and 0.11(4) K MPa -1 , respectively. The entropy change was indirectly obtained by taking the derivative (dε/dT)σ from strain vs. T curves (See Fig. 2 and Fig. 3 in Supplemental Material [28]) and using Maxwell's relation to reach the following expression [39,40]: where and 0 are the compressive stress and the density of the sample at atmospheric pressure and room temperature, respectively. is the strain, defined as ≡ ∆ 0 ⁄ , where ∆ is the length change of the sample and 0 is the initial length, a constant measured at ambient pressure and room temperature. We have obtained giant values of ΔST for the heating process, as shown in Fig. 3. At 314 K and Δσ = 390 MPa, a maximum ΔST of 59(6) J kg -1 K -1 was found. This leads to a normalized entropy change (|ΔST/ Δσ|) of 0.15(2) kJ kg -1 K -1 GPa -1 . A clear influence of Tg is also observed in the profile of ΔST vs. T curve in Fig. 3: the plateau indicates the rubbery state, while the steep region is due to the glassy state.
At low temperatures (T ≤ 240 K) we observe positive ΔST values, trend associated with the inverse thermal expansion observed in the ε vs. T data on heating (see Fig. 2 in Supplemental Material [28]), which is pronounced for the higher pressures. This inverse entropy change is probably related to the molecular rearrangements taking place in, since the movement of polymer chains slows down drastically in the glassy state. Therefore, the system requires a longer time-scale to reach the thermodynamic equilibrium when compared with the rubbery state [34]. As consequence of this mechanism, we suppose the structure is retained while the temperature cools down in such a way that, on heating, the structure is relaxed and contracts (inverse thermal expansion).
Envisaging the application of NBR in solid-state cooling, it is interesting to assess its performance under cyclic conditions. As we can see in ε vs. T data (see Fig. 4 in Supplemental Material [28]), NBR presents thermal hysteresis under cooling/heating cycles. Thermal hysteresis may be a drawback when considering the efficiency of refrigeration devices [41]. According to previous works [23,41], we calculated the reversible entropy changes (ΔSrev), defined as the intersection of the heating and cooling curves. This is represented by the shaded region in Fig. 4.
ΔSrev fills a wide temperature range and slightly narrows as the pressure increases. Taking the 86 MPa curve [ Fig. 4(a)], the temperature range goes from ~ 230 K to 314 K (range of 84 K). On the other hand, for 390 MPa [ Fig. 4(c)], ΔSrev was observed between 241 K and 314 K (range of 73 K), only 13% smaller than that for 86 MPa. Moreover, the losses in ΔST values in the reversible range are minimum due to the hysteresis and are mostly located at the left borders of the shaded region, especially considering the lower pressure variations (87 and 173 MPa). For the highest pressure change, (390 MPa), ΔSrev is reduced by 15% (compared to the maximum ΔST in cooling process), but still maintaining its giant value of 56 J kg -1 K -1 [ Fig. 4(c)].
Another interesting aspect of ΔSrev region is its direct dependency on pressure. A good way to tackle this aspect is calculating the reversible refrigerant capacity (RCrev) for several applied pressures. We can calculate RCrev by integrating ΔSrev over the reversible temperature range. In Fig. 5(a), we observe a linear increment of RCrev values, which start to saturate at 234 MPa. The maximum RCrev of 2.7 kJ kg -1 is achieved at 390 MPa, although at 234 MPa we already have a close value of 2.5 kJ kg -1 . To compare the barocaloric performance of different materials, the normalized refrigerant capacity (NRC) is a useful parameter, which has been used before [3,4]: where ΔTh-c ≡ Thot -Tcold is the temperature difference between the hot (Thot) and cold (Tcold) reservoirs, Δσ is the pressure change. NRC as function of ΔTh-c is shown in Fig. 5(b). For NBR, Thot was fixed at 315 K and Tcold was varied between 310 K and 240 K for Δσ = 173 MPa. NRC values for NBR on the cooling process are similar to those obtained for heating process up to ΔTh-c = 55 K. Above that point, the cooling process results in slightly higher values of NRC. Nevertheless, both heating and cooling present huge values of NRC, with a clear trend to increase. When comparing NRC results of NBR with other materials, it is significantly higher than intermetallics Mn3GaN [42] and Fe49Rh51 [23], which both presenting a curve profile that tend to saturate at ΔTh-c = 15 K. Comparing with PDMS, the values for NBR are higher for ΔTh-c up to 20 K. Lastly, NBR presents lower NRC values when comparing with V-NR due to the higher ΔST values of the later material in the compared range. But for ΔTh-c up to 10 K, both materials have similar values of NRC.  [42]; Fe49Rh51 (Thot = 325 K, |Δσ| = 160 MPa) [23].