Elastocaloric Performance of Natural Rubber in Solid State Cooling: Evaluation of the Effect of Crosslinking Density

Abstract

Elastocaloric cooling is recognized as a promising alternative to modern vapor-compression cooling systems, which often rely on environmentally hazardous refrigerants. Natural rubber (NR), a well-known renewable resource, stands out among elastomers exhibiting elastocaloric behavior due to a peculiar combination of nontoxicity, low cost, softness, long-life fatigue and high caloric power. Despite these properties, research on the refrigeration potential of NR is still in its early stages, and several aspects require attention. This work investigates, for the first time, the effect of crosslinking density on the elastocaloric properties of NR. Samples with three different crosslinking densities (2.9, 4.0 and 5.2 mol·10⁻⁴/cm³) were produced by internal compounding and hot pressing, and thermo-mechanically characterized. The assessment of the elastocaloric effect of the produced samples revealed that reducing the crosslinking degree significantly enhanced the elastocaloric properties. To compare the cooling capacity of the samples, a qualitative coefficient of performance (COP_mat) was evaluated as the ratio between extracted thermal energy and deformational work per unit volume. The results highlight that the least crosslinked sample achieved the higher COP_mat, equal to 2.4. These results underscore the significance of crosslinking density as one of the primary factors to be considered to enhance the refrigeration potential of NR.

1. Introduction

It is widely recognized that the global temperature has increased by 1.1 °C compared to the commencement of the Industrial Revolution. Despite the ostensibly modest nature of this temperature increase, it has engendered a heightened frequency of severe weather phenomena, notably flooding, heat waves, and tornadoes [1,2,3]. The scientific community expects the warming trend to worsen in the future, rendering parts of the world unlivable. In response to the escalating frequency of heat waves, cooling, and particularly air conditioning, have become essential for the survival of billions of people around the world, as well as for the safeguarding of vital resources such as food and medicine [4]. According to the data from the International Energy Agency, 2 billion Air Conditioner (AC) units are in use worldwide, and the number is thought to increase to 5.6 billion by 2050 [5]. This underlines the critical role that air conditioning plays in ensuring the survival and comfort of vast populations in the face of escalating temperatures and the associated challenges posed by climate change.

Despite the countless benefits, ACs based on vapor-compression technology consume a large amount of electricity (approx. 15% of the total amount) and use refrigerant fluids, such as hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs), characterized by an elevated Global Warming Potential (GWP) [6,7]. Over time, AC devices can be exposed to refrigerant fluid leaks with a significant probability. This can occur for many reasons, including the improper installation or maintenance and ageing of the equipment. In addition, if air conditioners at the end of their life are not disposed of properly or are illegally dismantled, refrigerant fluids can flow out during the dismantling process. When the coolants are released into the environment, they have a severe environmental impact and contribute in a significant way to greenhouse gas emissions. The paradox is evident: global warming leads to increased demand for air conditioners, which in turn contributes to further global warming. In consideration of the dangerous effects of refrigerant fluids, the Kyoto Protocol (1997) set a timeline for the phase-out of HCFCs by 2020–2030 and HFCs by 2025–2040. However, as these deadlines are approaching, many countries are displaying insolence, reluctance, and a lack of awareness or financial resources to meet these commitments [8].

Solid-state cooling technologies based on caloric effects present a novel alternative to conventional refrigerant-based cooling systems, specifically in household ACs. These caloric effects encompass magnetocaloric, electrocaloric, barocaloric, and elastocaloric phenomena. They pertain to the alteration in isothermal entropy or adiabatic temperature upon the application or removal of a magnetic field, an electrical field, hydrostatic pressure, and uniaxial stress, respectively [8]. The elastocaloric effect is investigated in two categories of materials: shape memory alloys (SMAs) and elastomers. In elastomers, the elastocaloric effect refers to the reversible change in temperature the material undergoes when subjected to the rapid application and removal of mechanical stress, and it is the consequence of a coupling between mechanical stress and macromolecule rearrangement [9]. When an elastomer is rapidly stretched, it experiences a negative entropy variation due to macromolecule orientation, and it heats up. Maintaining the deformation, the heat is released into the environment and the material returns to room temperature. Finally, when the elastomer is unloaded, the material returns to the initial high entropy state and cools down, absorbing heat from the environment. Such a relation between thermal and elastic behavior is referred to as the thermoelastic effect. If this behavior is properly exploited, a refrigeration cycle alternative to the ones currently used may be developed.

Among elastocaloric polymers, natural rubber (cis 1,4 polyisoprene, NR) seems to be among the most promising ones. The elastocaloric effect of NR was discovered by John Gough, a natural philosopher in the early nineteenth century, and was then reported for the first time by Joule in 1859 [9]. However, only very recently, the elastocaloric properties of NR have been considered for developing a solid-state cooling technology. NR is a biobased non-toxic material, and its good fatigue properties make it ideal for a future solid-state cooling application [10]. Furthermore, recent research works have brought to light its optimum elastocaloric performance in comparison to other elastomers. Bennacer et al. studied the elastocaloric properties of five types of rubbers, including natural rubber, cis-butadiene rubber, chlorosulfonated polyethylene, silicon rubber and styrene–butadiene rubber [11]. They observed that natural rubber presented the best cooling performance among the studied elastomers, showing a coefficient of performance (COP), evaluated as the ratio between thermal energy extracted during the stress release phase and the mechanical energy needed to deform it, of more than 2, and a correspondent temperature decrease of 3.5 °C. However, they observed that the temperature difference (ΔT) of the material during the stretching phase was higher than that in the recovery stage, meaning that undesired dissipative phenomena occurred. Coativy et al. examined the elastocaloric effect of thermoplastic polyurethane (TPU), noting that while its elastocaloric performance was promising, it was slightly lower than that of natural rubber. Additionally, TPU’s inelastic behavior and limited fatigue resistance posed challenges for its use in solid-state cooling applications [12].

Differently from other elastomers, the elastocaloric effect of NR is attributed to two contributions. The first is related to the reversible orientation/disorientation of macromolecules in the strain direction, as described before. The second contribution comes from the phenomenon of strain-induced crystallization (SIC), i.e., a partial crystallization of the elastomer as a result of deformation. When NR is stretched, the molecular orientation in the rubber network favors the nucleation and growth of crystallites, which melt once the NR returns to the initial unstretched state. Since crystallization and melting are exothermic and endothermic phenomena, respectively, the heat developed/released in the stretching/release phases is added to the thermoelastic heat contribution. In the literature, it has been extensively evidenced that the SIC of NR occurs at a strain of approx. 300% [9,13,14,15,16]. Consequently, to enhance the cooling performance of this material, it should be deformed at a strain level close to or higher than 300%.

Recent works have explored the effects of temperature, strain rate, maximum deformation and filler addition on the elastocaloric properties of NR. The temperature dependence was the objective of the study of Xie et al. [17]. They observed that NR exhibited interesting elastocaloric properties over a broad temperature range between 0 and 49 °C. The maximum temperature change (12 °C) was observed at 10 °C and a strain of 600%. In the temperature range 10–49 °C, the ΔT decreased from 12 to 5.8 °C, while in the range 0–10 °C, it dropped to 4 °C. These results suggest that working at a temperature of 10–30 °C is needed to take full advantage of the cooling performance of NR. The elastocaloric properties of natural rubber and natural/waste rubber blends were also investigated by Candau et al, who discriminated between the contributions of thermoelastic effects and strain-induced crystallization/melting by using a thermodynamic frame [18]. They observed that the elastocaloric properties of the blends increase with a waste rubber content of 20 wt. %. In particular, they found an increase in both thermoelastic effects and crystallization abilities, and attributed these observations to a strain amplification effect owing to the presence of non-deformable carbon black aggregates in the waste particles. COP values of 4.0 and 3.8 were estimated for natural rubber and the blends, respectively. The same authors also explored the influence of sample thickness on the elastocaloric effect of the same NR/waste rubber blends [19]. They pointed out that by reducing the sample thickness, the crosslinking density of the rubber chains became more homogeneous, leading to an increased SIC ability, which ultimately resulted in an enhancement of the elastocaloric effect. Yukihiro observed the effect of strain level on the cooling performance of NR. He deformed the NR sample by 100, 300, 400 and 600%, and found that ΔT increases, during both the stretching and releasing phase, with increasing strain level [20].

Despite all these findings, the research on the refrigeration potential of NR is still in its early stages. A deep research campaign is required to explore and understand which material properties affect the elastocaloric effect. This will help enhance its cooling capabilities and make it competitive with existing cooling technologies. An aspect as important as the relationship between the crosslinking density (produced by the vulcanization process) and the elastocaloric effect has, to the best of the authors’ knowledge, never been systematically investigated. Hence, the focus of this research is to examine the potential impact of crosslinking density on the elastocaloric performance of natural rubber (NR) and, if present, to elucidate the nature of this influence.

2. Materials and Methods

2.1. Material

The natural rubber used in this work was a TSR (Technically Specified Rubber) grade SMR 10 (Standard Malaysian Rubber), kindly provided by Marangoni S.p.a (Rovereto (TN), Italy). Zinc oxide (curing activator), sulfur (vulcanizing agent) and stearic acid (curing activator) were supplied by Rhein Chemie (Cologne, Germany). The accelerator zinc dibutyldithiocarbamate (ZDBC) was obtained from Vibiplast S.r.l. (Castano Prino (MI), Italy).

Toluene, acetone and methanol were acquired from Carlo Erba Reagents S.r.l, (Cornaredo MI, Italy) and were used for the determination of the crosslinking density of the produced NR samples. All the materials were used as received.

2.2. Sample Preparation

With the aim of producing natural rubber sheets with varying degrees of crosslinking density, three distinct natural rubber compounds were considered. The only differing factor in the formulation of these compounds was the level of sulfur present. The composition of the other rubber chemicals was defined after preliminary analysis. The composition in parts per hundred rubber (phr) of the prepared NR sheets along with their codes is reported in

Table 1. The nominal composition of the produced samples (phr = parts per hundred rubber, i.e., grams of component every 100 g of rubber polymer).

Sample	SMR 10 (phr)	Sulfur (phr)	ZnO (phr)	Stearic Acid (phr)	ZDBC (phr)
NR_1.5S	100	1.5	5.0	2.0	0.7
NR_2.5S	100	2.5	5.0	2.0	0.7
NR_3.5S	100	3.5	5.0	2.0	0.7

. A conventional cure system, i.e., rubber formulations characterized by a sulfur-to-accelerator ratio ranging between 0.1 and 0.6, was selected for the NR formulations. This choice was dictated by the fact that physical properties such as tensile strength, fatigue resistance and elongation at break are superior in this type of system [21]. The code of the natural rubber samples is constituted by the term NR followed by the letter S, which stands for sulfur, and a number referring to the sulfur content (in phr) in the sample.

The rubber compound’s production process referred to ASTM 3182 standard [22], with the mixing stages summarized in

Table 2. Procedure used for mixing natural rubber compounds.

Stage	Process/Ingredients	Time
I	Mastication of NR	5
II	ZnO	1
III	Stearic Acid	1
IV	ZDBC	1
V	Sulfur	1
VI	Mixing for homogenization	2

. First, natural rubber underwent a mastication process lasting five minutes in an internal mixer (Thermo Haake Rheomix 600, Thermo Fisher Scientific, Waltham, MA, USA), equipped with counter-rotating rotors, at a temperature of 50 °C and a rotation speed of 60 rpm. Subsequently, the rubber chemicals were sequentially added to natural rubber. The order of addition was as follows: ZnO, stearic acid, ZDBC and, lastly, sulfur. Upon the introduction of these rubber compound chemicals, the mixture was blended and homogenized for two minutes.

The resulting natural rubber compounds were then subjected to vulcanization using a Carver hydraulic hot press (Carver, Wabash, IN, USA). The vulcanization process occurred at a temperature of 120 °C and a pressure of 2 bar. The dimensions of the mold were 120 × 120 × 1 mm³.

2.3. Characterization

2.3.1. Physical Properties

In accordance with the standard ASTM D792 [23], the density of the vulcanized NR samples was measured by Archimedes’ principle. The tests were performed at ambient temperature and employing a Mettler kit ME-33340 (Mettler Toledo, Columbus, OH, USA). The specimens were weighed in air and submerged in methanol. The density was calculated using Equation (1):

$$\rho ={\displaystyle \frac{a}{a-b}}\times P$$

(1)

where a is the weight of the sample in air, b is the weight of the material submerged in methanol, and P is the density of methanol at the testing temperature (0.791 g/cm³ determined by using the Mettler kit ME-33340 (Mettler Toledo, Columbus, OH, USA)). For each NR formulation, three specimens were tested.

In accordance with the standard ASTM D6814 [24], the determination of the crosslinking density (υ) of the NR samples was conducted through equilibrium swelling measurements in toluene. NR specimens, weighing approximately 0.10 g each, were first immersed in acetone for three days to remove the acetone-soluble fraction. The rubbers were then dried for 24 h in a ventilated oven and cooled to room temperature. After that, the specimens were immersed in toluene for 4 days until an equilibrium state was achieved. Subsequently, the specimens were taken out, the swollen masses were weighted (w_s) and subjected to drying to eliminate excess solvent in a ventilated oven at 60 °C until constant weight (i.e., approx. 24 h). Finally, the dried masses were recorded (w_d). Then, the crosslinked density (υ) was determined through Equation (2), developed by Flory-Rehner [24]:

$$\upsilon ={\displaystyle \frac{-\ln \left(1-V_r\right)+V_r+{\rm X}x{V}_r^2}{V_{1}x(V_r^{\frac{1}{3}}-V_r)/2}}$$

(2)

where Χ is the polymer–solvent interaction parameter, V₁ is the molecular volume of solvent, and V_r is volume fraction of polymer in a swollen network in equilibrium with pure solvent, calculated according to ASTM D6814 standard, as reported in Equation (3):

$$V_r={\displaystyle \frac{\frac{w_d}{{\rho }_d}}{\frac{w_d}{{\rho }_d}+\frac{w_{so}}{{\rho }_s}}}$$

(3)

where w_d is the weight of dry rubber, ρ_d is the density of dry rubber, w_so is the solvent absorbed by the sample evaluated as difference between w_s and w_d, and ρ_s is the density of the solvent.

The values used for the molar volume of toluene (V₁), the Flory–Huggins interaction parameter (Χ) and the toluene density were 106.288 cm³ mol⁻¹, 0.391 and 0.867 g/cm³, respectively [24]. The density of dry natural rubber was determined by Archimedes’ principle in methanol according to Equation (1). For each NR formulation, six specimens were tested.

Shore A hardness measurements were conducted using a Hilderbrand Durometer (Prüf-und Meßtechnik GmbH, Wendlingen am Neckar, Germany) in compliance with the ASTM D2240 standard [25]. Square specimens measuring 15 mm in width and 3 mm in thickness were tested by pressing an indenter against the specimen for 10 s. The load was set at 488 g, and tests were performed at a temperature of 25 °C.

2.3.2. Thermal Properties

Differential scanning calorimetry (DSC) tests were performed on the NR samples by means of a Mettler DSC30 calorimeter (Mettler Toledo, Switzerland). One specimen was tested for each composition, with a mass of approximately 10 mg. The specimens were subjected to the following thermal sequence: (I) first heating scan from −100 °C to 150 °C at 10 °C/min, (II) cooling scan from 150 °C to −100 °C at −10 °C/min, (III) final heating scan from −100 °C to 150 °C at 10 °C/min. Nitrogen was used as the purge gas at a flow rate of 100 mL/min. DSC analysis allowed the determination of the glass transition temperature of the samples and allowed us to study the effect of sulfur content on the thermal properties of the NR formulations.

The material’s ability to release/absorb heat to the environment and the kinetics of such heat exchanges depend on the thermal properties of the material. For this reason, the specific heat capacity (c_p), thermal conductivity (λ) and thermal diffusivity (α) of the NR samples were measured through Laser Flash Analysis (LFA) with a Netzsch LFA 447 instrument (NETZSCH-Gerätebau GmbH, Selb, Germany). Cylindrical samples (diameter 12.7 mm, thickness 1 mm) were die-cut from the produced NR sheets. The tests were carried out at 20 °C, and for each specimen five pulses were performed. To compute the thermal diffusivity (α), the Cowan method with numerical pulse correction was employed (Proteus^® Software Version 8.0.3, NETZSCH Analyzing & Testing, NETZSCH-Gerätebau GmbH, Selb, Germany). For the determination of the heat capacity, the reference material Pyroceram 9606 was employed, according to the standard ASTM-E 1461 [26]. The thermal conductivity was calculated according to Equation (4),

$$\lambda =\alpha \rho c_P$$

(4)

where ρ is the density of the sample (g/cm³) determined by Archimedes’ method, while α and c_p are the data provided by the LFA measurements. For each NR formulation, three specimens were tested.

2.3.3. Mechanical Properties

Room-temperature uniaxial tensile tests were performed on a universal testing machine Instron 5969 (Instron, Pianezza, Torino, Italy) equipped with a load cell of 10 kN (load accuracy: ±0.5% of the reading) and operating at a crosshead speed of 500 mm/min. The strain was measured with a resistance extensometer Instron 2603 (Instron, Pianezza, Torino, Italy; extension accuracy (μm)—0.75% of extension, extension resolution (μm)—100) with a gauge length of 25 mm. The tests were carried out on ASTM D412 specimens [27]. From the tests, the stress corresponding to strain levels of 200 and 400 was determined (σ₂₀₀, σ₄₀₀), together with the stress at break (σ_b) and the corresponding strain (ε_b). The Young’s modulus (E) was measured as the initial slope of the stress–strain curve. Five specimens were tested for each composition.

To ensure that the mechanical properties of NR samples remain constant under long-term use, it is necessary to account for and evaluate the Mullins effect. The Mullins effect is commonly observed in elastomers subjected to cyclic deformations. It manifests as a softening phenomenon that leads to an appreciable change in the rubber’s mechanical properties resulting from the first extension. In particular, the stress during unloading or second loading is considerably lower than the first loading stress [28,29,30]. Understanding after how many cycles the mechanical response of the material stabilizes is crucial from an application standpoint. Once the mechanical response is stabilized, the material must be used immediately after since, with time, the Mullins effect is recovered. To investigate the effect of crosslinking density on the Mullins effect, NR samples were subjected to uniaxial cyclic tensile tests ten times using an Instron 5969 testing machine (Instron, Pianezza, Torino, Italy) equipped with a load cell of 10 kN and operating at a crosshead speed of 125 mm/min. The strain was measured with a resistance extensometer Instron 2603 ((Instron, Pianezza, Torino, Italy. Gauge length of 25 mm). Specimens having dimensions of 25 × 10 × 3 mm³ were used. For each NR formulation, the samples were cyclically stretched up to 200%, 300% and 400%. One specimen was tested for each degree of crosslinking and strain level. The energy dissipated and the stress corresponding to the maximum strain applied (σ_M200, σ_M300, σ_M400) were determined for each cycle. To accurately assess the residual deformation of the samples, two lines spaced 1 cm apart were marked on the surfaces of the specimens. Following the completion of 10 cycles, the distance between the lines was measured immediately after the sample was dismounted from the instrument, and the residual deformation was then calculated.

2.3.4. Evaluation of the Elastocaloric Effect

To evaluate the effect of crosslinking density on the elastocaloric performance of the prepared materials, a high-speed tensile testing machine, STEP Lab XUD05 (STEP Lab S.r.l, Resana TV, Italy), equipped with a 1 kN load cell was used. The tests were carried out at room temperature (approx. 22 °C) and rectangular specimens 1 mm thick and 15 mm wide were used. The distance between the specimen grips was set at 25 mm (tested volume of the specimens of about approx. 0.4 cm³). The following procedure was adopted to evaluate the elastocaloric performance: At first, the specimens were rapidly stretched up to the desired deformation level, setting the crosshead speed at 0.5 m/s. After that, they were maintained in traction for 250 s, to allow the materials to return to room temperature. In this work, the cooling of natural rubber occurred by natural convection. The NR samples were then unloaded, at the same crosshead speed of the stretching phase, followed by a relaxation step of 250 s. For each formulation, three strain levels (i.e., 300%, 400% and 500%) were considered and two specimens were tested per each strain level.

The surface temperature variation of the samples was recorded by using an infrared thermal imaging camera IRtech Fotric 348A (E Instrument Group s.r.l., Lesmo MB, Italy), placed at a fixed distance of 50 cm from the surface of the NR strips, having a thermal sensitivity of 0.04 °C. The acquisition frequency was set at 16 fps and the emissivity parameter employed was 0.9. The AnalyzIR software Version 5.0.7.117 (E Instrument Group s.r.l., Lesmo MB, Italy) was used to measure punctual temperature values along the specimen’s longitudinal axis. As the thickness of the samples was 1 mm and the Biot number (i.e., the ratio between the thermal resistance for conduction inside the body and the resistance for convection at the surface of the body [31,32]) was found to be less than 0.1, the temperature difference between the surface and the core of the specimens could be considered negligible. Thus, the temperature could be deemed uniform throughout the material.

During both the stretching and retraction phases, the temperature of the samples was represented as a function of time. The temperature variation of NR_1.5S, deformed during the test at 500%, is reported as an example in Figure 1.

For each specimen and strain level, the temperature increase during the stretching phase (ΔT_heat) and the temperature reduction during the retraction phase (ΔT_cool) were registered. In addition, the characteristic time of temperature dampening (τ_c), the heat absorbed from the environment per unit volume during the retraction phase (Q_ab), the work to deform the sample per unit volume (W) and the coefficient of performance of the material (COP_mat) were determined.

The ΔT_heat and ΔT_cool, represented in Figure 1, were, respectively, evaluated as the difference between the temperatures of the NR samples just after the stretching and releasing phase (points 2 and 4 in Figure 1) and the temperature assumed by the material before the mechanical action (points 1 and 3 in Figure 1, assuming the material to be in thermal equilibrium with the environment).

The characteristic time of temperature dampening, i.e., the time in which the temperature difference between the NR samples and the air drops, in absolute value, at a fraction equal to 1/e (≈37%) of the initial value, was calculated for both the stretching and retraction phases. This parameter is of fundamental importance since it provides information about the kinetics of the heat exchange process [32]. The thermal analysis adopted to determine τ_c, and to describe how the temperature of the NR sample evolved over time due to the convective heat transfer with the surrounding fluid, is described below.

Assuming that the NR samples during the elastocaloric test were immersed in a fluid at constant temperature T_f, and on their surfaces touched by the fluid there was a uniform and constant convective heat transfer coefficient h (W/(m²K)), the temperature variation of the material, initially at a temperature T₀, was estimated with the temporal law reported in Equation (5) [32]:

$$T\left(t\right)=T_f+\left(T_0-T_f\right)e^{{\displaystyle \raisebox{1ex}{$-hA$}\!\left/ \!\raisebox{-1ex}{$\rho V{c}_p$}\right.}t}=T_f+\left(T_0-T_f\right)e^{{\displaystyle \raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{${\tau }_c$}\right.}}$$

(5)

where A is the area of heat exchange (m²), T is the temperature of the sample assumed at time t, V is the volume of the material (m³), ρ is the density (g/m³) and c_p is the specific heat capacity of the material (J/(g·K)). The initial temperature of the sample (T₀) refers to the temperature assumed immediately after the stretching/releasing phase (points 2 and 4 in Figure 1).

Considering a negligible radiative heat transfer phenomena, the characteristic time of heat exchange was determined by fitting the experimental temperature variation curves, related to the stretching and retraction phase, by using Equation (5). Figure 2 shows an example of the fitting procedure.

Once we had determined the characteristic time of temperature dampening, the heat transfer coefficient was evaluated by using a reverse procedure. From Equation (5), τ_c could be expressed as

$${\tau }_c={\displaystyle \raisebox{1ex}{$\rho V{c}_p$}\!\left/ \!\raisebox{-1ex}{$hA$}\right.}$$

(6)

Consequently, as all the other parameters are known, the heat transfer coefficient (h) could be determined via Equation (7) as

$$h={\displaystyle \raisebox{1ex}{$\rho V{c}_p$}\!\left/ \!\raisebox{-1ex}{$A{\tau }_c$}\right.}$$

(7)

and the heat extracted from the environment per unit volume of material was calculated via Equation (8) as

$$Q_{ab}=(h\ast A\ast {\int }_{t1}^{t2}T\left(t\right)dt)/V$$

(8)

where h is the heat transfer coefficient of natural rubber determined experimentally, as previously explained; A is the surface of the sample between the specimen grips; t₁ and t₂ define the time interval in which the heat absorption from the environment occurred (see Figure 3), while T(t) is the experimental temperature variation of the samples.

Finally, the COP_mat value was calculated as the ratio between the heat absorbed during the retraction phase (Q_ab) and the mechanical work per unit volume of material (W) employed to deform the samples during the elastocaloric tests (integral of the stress–strain curves normalized by the volume of tested rubber), as reported in Equation (9),

$${COP}_{mat}={\displaystyle \frac{Q_{ab}}{W}}$$

(9)

The COP_mat parameter is qualitative and was introduced solely to compare the performances of the produced samples and to identify the most promising formulation [19]. Once a prototype is developed, all energy consumption terms will be taken into account, as well as fluid temperature and humidity.

3. Results

3.1. Physical Properties

The crosslinking densities obtained by the swelling method, the density values resulting from the application of Archimedes’ principle and the Shore A values are reported in

Table 3. Experimental crosslinking density, density and Shore A values of the prepared NR samples.

Sample	Crosslinking Density (mol·10−4/cm3)	Density (g/cm3)	Shore A
NR_1.5S	2.94 ± 0.21	0.958 ± 0.006	35.9 ± 1.1
NR_2.5S	4.04 ± 0.22	0.968 ± 0.005	41.3 ± 0.7
NR_3.5S	5.24 ± 0.51	0.981 ± 0.007	43.9 ± 1.3

.

The results of the crosslinking density reported in Table 3 confirm that the selected rubber formulations lead to three distinct degrees of crosslinking. As expected, with increasing sulfur content and keeping the other additives constant, the crosslinking density of NR increases. It can be noticed that the data dispersion increases with the sulfur content. The crosslinking density distribution observed in NR_3.5S is wider with respect to NR_1.5S and NR_2.5S. This experimental evidence highlights a lower material homogeneity and could be related to difficulties in obtaining a good dispersion of the vulcanizing agent when increasing the sulfur content in the NR formulation.

Considering the density measurements, the experimental results are in good agreement with the values in the literature [33]. The density increases with increasing sulfur content and hence the crosslinking degree.

Shore A hardness increases, moving from NR_1.5S to NR_3.5S, confirming the increase in crosslinking density.

3.2. Thermal Properties

To investigate the thermal properties of the produced rubbers, DSC analyses have been carried out. The glass transition temperature (T_g) values of NR_1.5S, NR_2.5S and NR_3.5S samples are reported in

Table 4. Results of the DSC tests on the prepared rubber samples.

	1st Heating Scan	Cooling Scan	2nd Heating Scan
Sample	Tg (°C)	Tg (°C)	Tg (°C)
NR_1.5S	−67.7	−73.3	−67.4
NR_2.5S	−66.6	−73.5	−66.9
NR_3.5S	−65.9	−72.0	−65.4

.

As can be seen in Table 4, the T_g remains practically unchanged for all rubber formulations when moving from the first to the second heating scan. This indicates that the curing process was completed for all the formulations. Moreover, a slight increase in T_g can be observed moving from NR_1.5S (−67.7 °C) to NR_3.5S (−65.9 °C). This further confirms that different crosslinked samples were produced and the degree of crosslinking increases with increasing sulfur content.

The values of specific heat, thermal diffusivity and thermal conductivity obtained from the LFA analysis are reported as a function of the crosslinking density in

Table 5. Specific heat capacity, thermal diffusivity and thermal conductivity as a function of crosslinking density obtained from LFA analysis on the prepared NR samples.

Sample	Crosslinking Density (mol·10−4/cm3)	Specific Heat Capacity (J/g·K)	Thermal Diffusivity (mm2/s)	Thermal Conductivity (W/m·k)
NR_1.5S	2.94 ± 0.21	1.704 ± 0.049	0.081 ± 0.001	0.132 ± 0.003
NR_2.5S	4.04 ± 0.22	1.822 ± 0.063	0.081 ± 0.002	0.143 ± 0.006
NR_3.5S	5.24 ± 0.51	1.775 ± 0.044	0.082 ± 0.001	0.143 ± 0.004

.

The values of thermal diffusivity, thermal conductivity and specific heat capacity obtained from the LFA analysis are in agreement with those reported in the literature [33]. No significant differences are observed within the prepared samples, leading to the conclusion that the crosslinking density, in the range studied, does not influence the thermal properties of the samples. Consequently, the origin of any difference in the elastocaloric performance of the NR samples is not attributable to differences in the heat transfer behavior of the materials.

3.3. Mechanical Properties

Representative stress–strain curves obtained in the uniaxial tensile tests are shown in Figure 4, while the main results are summarized in

Table 6. Results of uniaxial tensile tests at 25 °C on NR_1.5S, NR_2.5S and NR_3.5S samples.

Sample	E (MPa)	σ200% (MPa)	σ400% (MPa)	σb (MPa)	εb (%)
NR_1.5S	2.94 ± 0.21	1.704 ± 0.049	0.081 ± 0.001	0.132 ± 0.003	730 ± 14
NR_2.5S	4.04 ± 0.22	1.822 ± 0.063	0.081 ± 0.002	0.143 ± 0.006	573 ± 79
NR_3.5S	5.24 ± 0.51	1.775 ± 0.044	0.082 ± 0.001	0.143 ± 0.004	523 ± 47

.

The stress–strain curves shown in Figure 4 present the typical hyperelastic behavior, characterized by an initial “toe region” in which small deformation results in a linear increase in stress, followed by a “plateau region”, where stress remains relatively constant despite further increases in strain, and, finally, a stiffening region in which the material experiences a significant increase in stress as a result of material stiffening. According to the literature [34], rubber stiffening can be attributed to two phenomena: the first is related to the achievement of the maximum extensibility of the polymeric chains during stretching, while the second mechanism regards the occurrence of strain-induced crystallization.

As the crosslinking density of natural rubber increases, the stress–strain curves in Figure 4 show a progressive stiffening of the samples. This can also be noted when comparing the stress required to deform the materials by 200% and 400% (see Table 6), the values of which increase, moving from NR_1.5S to NR_3.5S. For example, σ_400% is equal to 2.1 MPa in NR_1.5S and 8.0 MPa in NR_3.5S. This is a reasonable result considering that the chain length between crosslinks is reduced as the degree of crosslinking increases and, consequently, the limit of chain extensibility is reached earlier [35,36]. Focusing on the stress and strain at break, it is possible to observe that while σ_b is comparable among the samples, ε_b undergoes a reduction, even if not dramatic, with an increasing degree of crosslinking.

To evaluate the elastocaloric properties, the NR samples were deformed up to 500%. It is interesting to note that the stress required to achieve this deformation ranges between 3 MPa (NR_1.5S) and 15 MPa (NR_3.5S), and is close to the stress required to compress a refrigerant fluid in the current air conditioning systems, i.e., approx. 1 MPa [37]. This is a positive aspect that must be underlined since other caloric materials under study for developing solid-state refrigeration systems, such as shape memory alloys or ferroelectric materials, require stresses of at least one or two orders of magnitude higher. For example, for shape memory alloys, several hundreds of MPa are required to exhibit elastocaloric performance [8]. This makes the behavior of NR interesting and of great potential for solid-state cooling applications.

An elastocaloric cooling device requires the repetitive stretching and releasing of rubber. Consequently, it becomes crucial to thoroughly examine the mechanical response of the samples under cyclic loading conditions, particularly considering their susceptibility to the Mullins effect. Figure 5a–c shows the stress–strain response of the NR samples under cyclic tensile loading when maximum strain levels of 200%, 300% and 400% are applied.

Analyzing Figure 5a–c, the Mullins effect can be observed in all the samples, particularly in those subjected to a deformation of 300% and 400%. Progressing from the first to subsequent cycles, a noteworthy stress-softening phenomenon becomes evident, together with a reduction in the hysteresis loop, which is representative of the dissipated energy. As the deformation level increases, the prominence of the Mullins effect becomes increasingly apparent. This empirical observation aligns with existing literature on the subject [30]. However, to derive a more precise comparison among the cyclic behaviors of the samples, the stress at the maximum deformation per each cycle (peak stress) and the energy dissipated in the 1st, 2nd, 5th and 10th cycles have been determined, with the results shown in Figure 6a–c and Figure 7a–c, respectively, while the residual deformation at the end of the 10th cycle is reported in Figure 8.

Several considerations can be made. As can be seen from Figure 6, the stress-softening is more pronounced moving from the first to the second cycle. After the second cycle, the maximum stress only slightly decreases, suggesting the mechanical response of the material has stabilized. With increasing strain levels, the difference between the peak stress of the first and second cycles increases as well. The same consideration can be made also for the energy dissipated. The variation of the hysteresis loop from the first and successive cycles is even more pronounced than the stress-softening. For example, NR_2.5S experiences a reduction of dissipated energy from 0.8 J/cm³ to 0.4 J/cm³ moving from the first to the second cycle. For maximum deformation levels of 200% and 300%, the samples show quite similar dissipated energy values. In contrast, significant differences can be noticed for a deformation of 400%, in which NR_1.5S presents the highest value, followed by NR_3.5S and NR_2.5S. A larger number of dangling chains and trapped entanglements compared to the other crosslinking levels may explain the higher hysteresis found for the NR_1.5S sample [38]. Similar results were found by Quian et al. [39], who investigated the influence of filler size and crosslinking degree on the Mullins effect in filled NR/butadiene rubber (BR) blends. They observed that by keeping the filler content constant, the dissipated energy increased when reducing crosslinking density. Such a clear trend is not observable in Figure 7c, but still, NR_1.5S was shown to be the sample with the most important hysteresis. However, in the future, it will be essential to conduct further analysis to validate this hypothesis.

Finally, the residual deformation values at the end of the 10th cycle are shown in Figure 8. The values range from 2% to 6% depending on crosslinking degree and applied strain. When holding the degree of crosslinking constant, there is a rise in residual deformation with increasing strain levels. Conversely, maintaining a constant strain level, the residual deformation increases with the crosslinking density, specifically at 200% and 300% strain levels, while at 400%, the values are close to each other. Since the residual deformation was evaluated at the end of the 10th cycle, its trend as a function of cycle number is not known. However, since both dissipated energy and peak stress show the same behaviors, it could be reasonable to assume that the residual deformation does so as well. Consequently, it may be hypothesized that most of the residual deformation results from the first cycle.

These results highlight the need to pre-stretch the rubber just before its application, especially when its use involves deformation of more than 200%. It is evident that the extent of strain plays a pivotal role in the Mullins effect, whereas the impact of crosslinking density remains not entirely understood. In the assessment of the elastocaloric effect, the NR samples underwent a single pre-stretching procedure and were promptly subjected to testing thereafter. This strategic pre-stretching approach serves as a practical means to mitigate the impact of the Mullins effect, ensuring more reliable and consistent results, particularly in scenarios requiring significant deformation. Future works will focus on determining how long it takes for the material at rest to fully recover the Mullins effect. This is of fundamental importance from a practical point of view, since if a solid-state AC device is not used for a long period of time, the Mullins effect of NR should be removed before its use.

3.4. Evaluation of the Elastocaloric Properties

Figure 9a–c shows the temperature variation of the surface of the NR samples during the stretching and retraction phases as a function of time and deformation, while Figure 10a–e reports the most important results.

For all the samples, in all testing conditions, the elastocaloric effect is evident. The fast stretching of the material induces a positive temperature variation caused by the orientation of the macromolecules in the impact direction. When the samples are maintained in traction, the temperature progressively drops, returning to ambient temperature and reaching thermal equilibrium. In the retraction phase, the return of the material to the undeformed state, characterized by a high entropy state, causes the rubber to cool down. The deformation strongly affects the surface temperature evolution of the samples, as in all the cases the increase in strain results in a more significant temperature variation, during both the stretching and retraction phases. The higher orientation of the macromolecules achieved with increasing strain levels probably favors strain-induced crystallization phenomena. Such an effect of deformation on temperature variation is in line with the results reported by Yukihiro et al. [20,40]. The increased thermoelastic and SIC contributions are probably at the basis of this experimental observation. However, in the future, XRD analysis should be performed in situ to confirm this hypothesis.

By comparing the temperature responses of the samples in Figure 9a–c and Figure 10a–b, it is clear that the crosslinking density is another parameter that influences the thermal response of NR. Moving from Figure 9a to Figure 9c, a decreasing trend in the temperature variation of the samples can be observed. This experimental observation is probably the result of two contributions. The first is related to the limit of chain extensibility. As was previously explained, when the degree of crosslinking increases, the chain length between crosslinks is reduced and the limit of chain extensibility is reached earlier. Intuitively, this means that the entropy variation from the random coil configuration to the limit of chain extensibility is more pronounced for the rubber showing the lower crosslinking degree, since macromolecular mobility is less restricted. The second aspect concerns strain-induced crystallization. As reported in the literature, by reducing crosslinking density, the ability of natural rubber to crystallize under strain improves [34]. Thus, at a given deformation, the higher strain-induced crystallization phenomena and thermoelastic contribution make NR_1.5S the samples with the higher ΔT, during both the stretching and retraction phases. From Figure 10b, it is possible to see that NR_1.5S shows a ΔT_cool of 2.9 °C at 300% and 11.0 °C at 500%. In the literature, the highest ΔT_cool registered for NR is 12 °C [9].

For a given deformation and crosslinking degree, ΔT_cool is similar to or even larger than ΔT_heat (Figure 10a,b) in almost all the cases. Only for NR_2.5S deformed at 200% and NR_3.5S deformed at 200% and 300%, the temperature increase during stretching is larger than the temperature reduction during unloading. This is an interesting result since, in the literature, ΔT_heat is very often larger than ΔT_cool [11], suggesting non-negligible dissipative phenomena such as friction. In this work, it is plausible that during the maintenance of the samples in traction, crystalline domains progressively develop. As the crystallization of these domains is not instantaneous, the heat generated during their formation may not have been considered in ΔT_heat. Conversely, during unloading, if all crystalline domains, regardless of their formation time, melt, they could contribute to ΔT_cool, potentially resulting in ΔT_cool values greater than ΔT_heat. However, it is crucial to emphasize that this is still a hypothesis and demands further experimental investigation.

Following further analysis, it can be noted that the width of the temperature peaks in Figure 9a–c (i.e., the time required to the sample to return to ambient temperature) is wider in the retraction phase with respect to the stretching stage. The characteristic time of temperature dampening, determined during both heating (stretching phase) and cooling (retraction phase) reported in

Table 7. Characteristic time of temperature dampening (τ_c) and heat transfer coefficient (h) calculated in the stretching and retraction phases of the samples.

Physical Parameter	Sample	Maximum Deformation
		300%	400%	500%
τc stretching phase (s)	NR_1.5S	18.3	20.4	17.2
	NR_2.5S	21.1	21.1	17.1
	NR_3.5S	22.3	20.7	23.9
τc stretching phase (s)	NR_1.5S	51.8	57.8	57.1
	NR_2.5S	39.8	56.6	62.3
	NR_3.5S	58.6	53.6	62.1
h stretching phase (W/(m2K))	NR_1.5S	12.6	11.3	13.4
	NR_2.5S	21.1	21.1	17.1
	NR_3.5S	22.3	20.7	23.9
h retraction phase (W/(m2K))	NR_1.5S	17.8	15.9	16.1
	NR_2.5S	24.9	17.5	15.9
	NR_3.5S	17.0	18.6	16.1

, confirms this observation.

For a given degree of crosslinking and deformation, the τ_c calculated in the retraction phase is always higher than the one calculated in the stretching phase. More specifically, the ratio between τ_c determined in the retraction phase and τ_c determined in the stretching stage ranges between 1.8 and 3.6. During stretching, the specimen becomes thinner, favoring a more rapid heat transfer. For the heat transfer coefficient, values ranging from 11 to 24 W/(m²·K) are obtained. According to the literature, typical ranges of h are 3–20 W/(m²·K) under the condition of free convection, and 10–100 W/(m²·K) under forced convection [41]. The rapid stretching and unloading of the samples might have triggered air movements, inducing a slight forced convection. Thus, it can be stated the values obtained are in line with data from the literature.

Going into details on the elastocaloric effect, Figure 10c–e show Q_ab and the COP_mat values of the samples as a function of deformation and degree of crosslinking. Since the elastocaloric effect of natural rubber is being studied for solid-state cooling applications, it is fundamental to quantify the capability of the material to extract thermal energy from the environment. For a given crosslinking density, Q_ab increases with increasing deformation, whereas, if the deformation is fixed, Q_ab decreases with the degree of crosslinking. NR_1.5S is the sample able to extract a higher amount of thermal energy during the unloading phase. In particular, at a deformation of 500% and in one loading/unloading cycle, NR_1.5S absorbs approx. 16.4 J/cm³. However, to evaluate the performance of the materials, the attention should be focused on the Coefficient of Performance, evaluated by the ratio between the extracted thermal energy and the mechanical work required to deform the samples (W, Figure 10d). The findings clearly show that NR_1.5S is the best formulation among the ones prepared, exhibiting a COP_mat ranging from 1.8 to 2.4. The optimal compromise appears to be reached by deforming NR_1.5S at 400%. This not only allows for the highest COP_mat value, but also ensures a safer operational condition, as it is further from the strain at break. The COP_mat values obtained were found to be higher than those reported by Bennacer et al., who used the same expression for calculating COP [11].

To conclude, it is worth making some remarks. From a practical point of view, the time required by the sample to return to room temperature, both during the stretching and retraction phases, proves to be rather long. Consequently, the time of the entire refrigeration cycle was set at 480 s to ensure the return of the materials at room temperature in each step and that the same time interval of waiting is applied in the two phases. One possible solution to reduce the heat exchange time and increase the cooling power could be to work in forced convection, using a fan. Future works are in progress to explore this possibility.

Finally, it can be interesting to make a comparison between the elastocaloric performance of shape memory alloys reported in the literature [9] and NR_1.5S, the most promising NR formulation among the ones tested. Three parameters are considered for the comparison reported in

Table 8. Comparison of the elastocaloric properties in NR_1.5S and shape memory alloys [9].

Caloric Material	Δε (mm/mm)	ΔTcool/Δσ (°C/MPa)	ΔT/Δε (°C)
NR_1.5S	5	3.2	2.1
Shape memory alloys (SMAs)	0.03–0.05	0.013–0.045	300

: the deformation imposed during the elastocaloric tests (Δε), ΔT_cool/Δσ where Δσ the maximum stress needed to deform the material, and ΔT/Δε.

NR exhibits a strain two orders of magnitude higher than that of shape memory alloys. NR needs to be stretched several times its original length to demonstrate noteworthy elastocaloric performance, presenting a drawback in the context of designing compact air conditioners. Consequently, the elastocaloric strength ΔT/Δε in natural rubber is two orders of magnitude lower. In the literature, a suggested approach to address this challenge is to work with pre-strained natural rubber [9]. On the other hand, the parameter ΔT_cool/Δσ is two orders of magnitude higher compared to shape memory alloys, which is an important advantage as the stress required to deform natural rubber is well below that required for metal alloys and quite close to the stresses involved in current air conditioners.

4. Conclusions

In this work, the influence of the crosslinking density on the elastocaloric properties of NR has been investigated for the first time. Samples with varying degrees of crosslinking—2.9, 4.0 and 5.2 mol·10⁻⁴/cm³—were produced by melt compounding and hot-pressing, and thermo-mechanically characterized. The assessment of the elastocaloric effect revealed that both the imposed deformation and the crosslinking density played a crucial role in the elastocaloric properties of NR. In particular, reducing the crosslinking degree and increasing the deformation led to enhancing the capability of the material to extract thermal energy from the environment. The NR sample characterized by a crosslinking density of 2.9 mol·10⁻⁴/cm³ (the least crosslinked sample) was found to be capable of extracting 16.4 J/cm³ of thermal energy in one single refrigeration cycle when stretched at 500%. The evaluation of the Coefficient of Performance of the material (COP_mat) confirmed the least crosslinked sample to be the best formulation among the ones prepared, exhibiting a COP_mat ranging from 1.2 to 2.4.

The investigation of the Mullins effect of the prepared sample highlighted the need to pre-stretch the rubber before its application, to ensure more reliable and consistent results, particularly in scenarios requiring significant deformations. It was found that the extent of strain played a pivotal role in the Mullins effect, whereas the impact of crosslinking density remained not entirely elucidated.

In conclusion, the results underscore the significance of crosslinking density as one of the primary factors to be considered in enhancing the refrigeration potential of NR. It could be interesting to explore even lower crosslinking density and investigate if the elastocaloric properties could be even more improved. It is important to emphasize that the cooling performance of NR is far from that of conventional air conditioners. To improve the cooling power of natural rubber, a comprehensive research campaign is needed to investigate all material properties that could positively impact its elastocaloric performance. With the aim of enhancing the cooling power, future works will be focused on trying to reduce as much as possible the time of the refrigeration cycle; for example, working under forced convection conditions.