Mechanical and Thermal Properties of Functionally Graded Polyolefin Elastomer Foams

In this work, uniform and graded polyolefin elastomer (POE) foams were prepared using a single-step technology based on a fixed chemical blowing agent (azodicarbonamide) concentration of 4 phr (parts per hundred rubber). The effect of molding temperature, including the average temperature (Tavg) and temperature difference (ΔT), on the foams’ morphology, mechanical properties (tension, compression and hardness) and thermal conductivity was investigated. Two series of samples were produced by fixing Tavg with different ΔT or setting different ΔT, leading to different Tavg. The morphological analyses showed that two or three regions inside the foams were produced depending on the molding conditions, each region having different cellular structure in terms of cell size, cell density and cell geometry. The results obtained for the conditions tested showed a range of density (0.55–0.72 g/cm3), tensile modulus (0.44–0.70 MPa) and compression elastic modulus (0.35–0.71 MPa), with a thermal conductivity between 0.125 and 0.180 W/m.K. Based on the information provided, it can be concluded that the foam’s properties can be easily controlled by the cellular structure and that graded samples are more interesting than uniform ones, especially for thermal insulation applications, such as packaging, construction, transportation, automotive and aerospace industries.


Introduction
In today's world, with fast economic and social development, human needs for more sources of energy have become more apparent [1,2]. This is why several practical solutions to generate and/or save energy have been proposed to address these requirements. Some options are renewable energy to reduce our dependence on petroleum fuels and their derivatives, but most of these strategies failed to meet the expected results and only a small number has actually yielded beneficial outcomes [3]. As a result, the need for low-weight materials and energy insulation has reduced material usage and energy loss, leading to economic and environmental advantages. This is why polymer foams have attracted more attention due to their ability to decrease emissions, conserve energy and save materials [4][5][6]. Jahani et al. developed polycarbonate (PC) foams with up to eight-fold expansion ratios and 85% open-cell content for sound and thermal insulation [7]. The group of Vahidifar produced sound insulators based on natural rubber (NR)/nanoclay (NC)/nanocarbon black (NCB) foams with high reflection/absorption coefficient ratio (90%) [8]. Peng et al. improved the sound absorption efficiency of silicon rubber (SR) foams in the presence of NaCl (pore forming agent) for the middle frequency range (1000-2000 Hz), which was related to enhanced resonance matching caused by the open-cell morphology [9].
Today, polymeric foams are widely used in numerous practical fields, such as packaging, automobile, transportation, aeronautic, building and construction, due to their low density and high-energy damping ability, as well as their low thermal, sound and electrical conduction [10][11][12]. To this end, the Dileep's group reported that functionally graded

Preparation of POE-ADC Compounds
A laboratory twin-screw extruder was used for melt compounding of the POE with 4 phr of ADC. Compounding was performed using a co-rotating twin-screw extruder ZSE-27 (Leistritz, Allendale, NJ, USA) with an L/D ratio of 40 with D = 27 mm. The feeding rate was kept at 2 kg/h and the diameter of the circular die was 2.7 mm. The screw speed was fixed at 12 rpm with a flat temperature profile of 110 • C. The extrudate was cooled in an ice bath before being pelletized at ambient temperature.

Foam Preparation
A single-step foaming technique was used to produce the uniform and graded POE foams. First, 10 g of the compound was placed in a square mold with dimensions of 8 × 5 × 0.35 cm 3 . The temperature of the bottom (T 1 ) and top (T 2 ) plates of a hot press were preheated to specific temperatures as reported in Table 1 before the filled mold was placed between them for a total of 12 min under a pressure of 8.5 bar. For uniform samples (T205), T 1 was set equal to T 2 , while for graded foams, different temperatures were imposed for both plates (T 1 = T 2 ). In all cases, the highest temperature was set on the top plate. According to Table 1, the first series of graded samples (T210 to T225) had different ∆T and T avg , while the second series (dT10 to dT40) was prepared at fixed T avg and various ∆T. The side of the foam which was in contact with the highest temperature (T 2 ) is referred to as the "Top" side, while the side in contact with the lowest temperature (T 1 ) is called the "Bottom" side. In order to stabilize the cell structure, the mold was cooled to room temperature under pressure before opening for expansion. The unfoamed sample (neat matrix) was coded as PA0 (0 phr of ADC) and used as a reference to determine the effect of the cellular structure.  )   T205  205  205  0  205  T210  205  210  5  207.5  T215  205  215  10  210  T220  205  220  15  212.5  T225  205  225  20  215  dT10  200  210  10  205  dT20  195  215  20  205  dT30  190  220  30  205  dT40  185  225 40 205

Characterization
The foam density was obtained by a gas pycnometer (UltraPyc 1200e, Quantachrome, Boyton Beach, FL, USA) using 3 replicates. Equation (1) was used to calculate the foam expansion ratio where the density of the unfoamed POE is 0.874 g/cm 3 [39]: A scanning electron microscope (SEM) Inspect F50 (FEI, Hillsboro, OR, USA) was used to examine the foam morphology (cell structure) at 15 kV under different magnifications. The samples were first cryo-fractured (liquid nitrogen) and sputter coated with gold before imaging. The BELView software was used to quantify the foam morphology via several parameters, such as the number average cell size (D n ), weight average cell size (D w ), polydispersity index (PDI) and cell density (ρ cell ) as [40][41][42][43]: where n i represents the number of cells with a diameter D i , A is the foam surface analyzed, ρ bulk is the density of the unfoamed matrix and ρ foam is the foam density. A PTC Instrument (ASTM D2240, model 307 L, Boston, MA, USA) was used to determine the foam hardness (Shore A). The average and standard deviation of 5 repetitions were used for each side of every sample. Tensile testing (ASTM D412) was conducted at room temperature (23 • C) on an Instron universal testing machine (USA) model 5565 with a 500 N load cell. The crosshead speed was 10 mm/min and the values (modulus, strength, etc.) were obtained by the average of a minimum of five samples. For the compression tests (ASTM D575), an RSA3 TA Instruments (USA) dynamic mechanical analyzer (DMA) was used with cylindrical samples (2.5 cm in diameter and 3.5 mm in thickness) and compressed at a rate of 0.01 mm/s. The elastic modulus was calculated in the linear zone of strain. All the properties reported represent an average of a minimum of three samples at room temperature. Finally, a home-made thermal conductivity analyzer based on ASTM E1225 was used to calculate the heat flux (Q) and determine the thermal conductivity (k) foams. The specimens were cut (5 × 5 cm 2 ) and a digital caliper was used for measuring the thickness (L = 3.47-3.72 mm). Each sample was placed between two thin aluminum sheets and two plates with controlled temperatures of 33 • C (top plate) and 13 • C (bottom plate) giving an average room temperature of 23 • C and a temperature difference ∆T = 20 • C. Water-cooled Pelletier plates (Model K20, Haake, Vreden, Germany) kept the temperatures constant, while the equilibrium heat flux was measured via a PHFS-01 heat flux sensor (Flux Teq LLC, Blacksburg, VA, USA). The k values reported represent the average of three repetitions with their standard deviations calculated via the Fourier law as: For mechanical compression and thermal conductivity, each sample was tested on both sides to determine any asymmetry due to the density gradation across thickness.  Table 2. Sample T205 has a homogeneous cell structure leading to a narrow PDI (1.022), low average cell size (105 µm) and high cell density (570 cells/mm 3 ). The first series of samples ( Figure 1b) led to the formation of two (top and bottom) regions with different cellular structure in terms of cell size and cell density across the foam thickness. The average cell size and cell density for the top and bottom regions in T210 are 117 and 107 µm, with 750 and 820 cells/mm 3 , respectively. Since the temperature difference in T210 is not very high (∆T = 5 • C), there is limited difference between the cell size/density in both regions. However, the cellular structure difference between both regions is more significant at higher T avg . By increasing T avg from 207.5 • C (T210) to 215 • C (T225), the cell size in the top region increased from 117 to 154 µm (32%), while the values in the bottom region decreased from 107 to 104 µm (3%), respectively. Moreover, increasing T avg from 207.5 to 215 • C resulted in lower cell density in the top (56%) and bottom (3%) regions. The significant decrease in cell density in the top region is due to more gas volume being available with increasing temperature. This condition leads to higher internal cell pressure, enhancing the possibility of cell coalescence and collapse, leading to higher cell size and lower cell density. Furthermore, increasing T avg from 207.5 • C (T210) to 212.5 • C (T220) decreased the PDI in the top region from 1.018 to 1.009, while the values in the bottom region increased from 1.012 to 1.020, respectively. Higher T avg (from 212.5 to 215 • C) resulted in higher PDI in the top region (1.009 to 1.016) with lower values in the bottom region (1.020 to 1.010). To complete the morphological analysis, the foam density and foam expansion ratio are compared in Figure 2. The foam density decreased from 0.669 to 0.546 g/cm 3 as T avg increased from 205 to 215 • C. The larger volume of gas produced at higher T avg is the main reason for this trend. For example, higher gas volume generated from the higher temperature between T205 and T225 led to higher expansion ratios of 24% and 38%, respectively.

Second Series
The second series of samples led to the formation of three regions with different cell shape and cell characteristics: middle (circular cells) as well as top and bottom (elliptical/elongated shape) regions (Figure 1c). Because the top and bottom sections exhibited nearly identical cellular properties, they will be analyzed together. In other words, keeping T avg = 205 • C and increasing ∆T from 10 to 40 • C (dT10 to dT40) increased the cell size in the middle region from 98 to 176 µm, while the cell size in the top and bottom regions increased to 122 and 337 µm, respectively. As a result, the cell density in the middle region decreased by 47%, while it decreased by 52% in the top and bottom regions ( Table 2). As mentioned for the first series, larger cell size and lower cell density are related to higher possibilities of cell coalescence and collapse due to higher generation of gas at elevated temperatures. Furthermore, the cell size difference between the middle region and both top/bottom regions increased with increasing ∆T. For instance, the cell size difference in dT10 between the regions is only 24 µm, while it increases to 161 µm for dT40. In our case, the highest temperature was applied to the top plate, hence, increasing the temperature leading to higher/faster ADC decomposition locally, generating a larger volume of gas. Thus, more gas molecules are available nucleating a higher number of cells with higher internal cell pressure. This can eventually increase the local probability of cell coalescence and collapse [44]. Additionally, the dissolved gas molecules have a stronger plasticizing effect, decreasing the elasticity and viscosity of the matrix, making it easier for the rupture of cell walls during the foaming process, especially as the temperature is high [45]. Further, increasing ∆T from 10 to 20 • C (dT10 to dT20) led to higher PDI in the middle region (from 1.018 to 1.022), as well as in the top and bottom regions (from 1.030 to 1.035), while the values from ∆T = 20 to 40 • C (dT10 to dT20) decreased in the middle region (from 1.022 to 1.016), as well as in the top and bottom regions (from 1.035 to 1.015), respectively. According to Figure 2, the foam density increased from 0.599 to 0.719 g/cm 3 as ∆T increased from 10 to 40 • C, while the expansion ratio decreased from 32 to 18% from dT10 to dT40. This trend is related to the higher probability of cell rupture/coalescence at higher ∆T [46,47].

First Series
The tensile results for the unfoamed, uniform and graded POE foams are shown in Table 3. Two main factors are known to control the foams' behavior: foam density (ρ foam ) and morphology (D n , PDI and ρ cell ). According to the results obtained, it is obvious that higher T avg results in lower mechanical properties (tensile modulus, strength, elongation at break and hardness) due to lower sample density. The uniform foam (T205) has lower modulus (0.7 MPa), strength (2.55 MPa) and elongation at break (939%) compared to the unfoamed matrix. Increasing T avg (205-210 • C) reduced the modulus, strength and elongation at break even more by 17%, 8% and 10%, respectively. This is mostly associated with the presence of a higher volume of gas (bubbles/voids) inside the matrix produced at higher processing temperature (T avg ). The tensile properties of the other graded foams have a similar trend as they decrease with increasing T avg (Table 3). For instance, increasing T avg from 210 to 215 • C decreased the tensile modulus (0.58 to 0.44 MPa) and strength (2.35 to 2.18 MPa), indicating that only a 5 • C difference can have a substantial effect on the mechanical properties. The compression test was carried out on both sides of each sample and the values with typical stress-strain curves (PA0, T205, T225 and dT40) are reported in Figures 3 and 4, respectively. The results show that the compression elastic modulus and compressive strength (at 7% compression) increased by 15% and 16% (top side), but 20% and 26% on the other side (bottom side), respectively, at lower T avg (205-212.5 • C). This is due to the higher T avg leading to the production of more gas molecules inside the matrix. As each cell acts as an inflated balloon, the presence of more gas volume/pressure inside the cells improves their resistance against compressive forces [48]. In addition, foaming the POE led to higher compression properties. For instance, the elastic modulus increased from 0.482 to 0.593 MPa between PA0 and T205, respectively. However, both elastic modulus (34% top and 17% bottom side) and compressive strength (35% top and 22% bottom side) decreased at higher T avg (212.5-215 • C). This behavior is directly related to morphological changes in D n and ρ cell (Table 2), as previously discussed [49]. As reported in Figures 3 and 4, the bottom side of graded foams (having lower cell size and higher cell density) is more resistant to compression force. For example, the bottom side of T225 has higher elastic modulus (33%) and compression strength (31%) compared to its top side.       Finally, the foams' hardness (Shore A) decreased by 36% (60.6 to 38.7) by increasing T avg from 205 to 215 • C (Table 3 and Figure 5). The most significant factor contributing to the loss of hardness is the lower foam rigidity and resistance to needle penetration associated with an increase in expansion ratio (lower density) at higher T avg as less material is available to sustain the applied stresses. Analyzing the hardness for both sides of each foam also showed some differences. This difference was negligible for the foams prepared at lower T avg (205-207.5 • C), but the difference increased from 2% to 7% for higher T avg (210-215 • C), respectively. Nevertheless, the hardness difference could also be associated with differences in the crosslink density of the matrix. This was not determined here but will be investigated in future studies.
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Second Series
The mechanical properties of the second series showed a different trend compared to the first series (Table 3 and Figures 3-5) as all the mechanical properties (tensile, compression and hardness) were improved with increasing ΔT. For example, increasing ΔT from 10 to 40 °C produced higher modulus (14%), strength (26%) and elongation at break (10%). The reason for this trend was discussed above and is related to higher density having more material available to withstand the applied stress.
Similar to the first series' trend, the elastic modulus and compressive strength of the second series increased by 85% and 131% (top side), as well as 65% and 121% (bottom side) from dT10 to dT40, respectively (Figures 3 and 4). According to SEM images ( Figure  1c), increasing ΔT led to the formation of three regions (top, middle and bottom), where the presence of these three regions plays a significant role in resisting against compressive loads. The presence of elliptical cells with large cell sizes (high volume of gas), at the top and bottom regions, prevents the sample from being compressed. Furthermore, the middle region, with homogenous and smaller cells, helps the sample to improve its resistance against compressive loads [50]. Finally, the hardness of the foams increased by 20% by increasing the ΔT from 10 to 40 °C ( Figure 5). The highest hardness difference between both sides of a sample was obtained for dT40. Again, here, the results clearly showed that a graded morphology led to asymmetric mechanical properties. In our case, the maximum difference was 45% for the compression strength of dT20.

First Series
The thermal conductivity of uniform and graded POE foams was carried out on both

Second Series
The mechanical properties of the second series showed a different trend compared to the first series (Table 3 and Figures 3-5) as all the mechanical properties (tensile, compression and hardness) were improved with increasing ∆T. For example, increasing ∆T from 10 to 40 • C produced higher modulus (14%), strength (26%) and elongation at break (10%). The reason for this trend was discussed above and is related to higher density having more material available to withstand the applied stress.
Similar to the first series' trend, the elastic modulus and compressive strength of the second series increased by 85% and 131% (top side), as well as 65% and 121% (bottom side) from dT10 to dT40, respectively (Figures 3 and 4). According to SEM images (Figure 1c), increasing ∆T led to the formation of three regions (top, middle and bottom), where the presence of these three regions plays a significant role in resisting against compressive loads. The presence of elliptical cells with large cell sizes (high volume of gas), at the top and bottom regions, prevents the sample from being compressed. Furthermore, the middle region, with homogenous and smaller cells, helps the sample to improve its resistance against compressive loads [50]. Finally, the hardness of the foams increased by 20% by increasing the ∆T from 10 to 40 • C ( Figure 5). The highest hardness difference between both sides of a sample was obtained for dT40. Again, here, the results clearly showed that a graded morphology led to asymmetric mechanical properties. In our case, the maximum difference was 45% for the compression strength of dT20.

First Series
The thermal conductivity of uniform and graded POE foams was carried out on both sides of each foam and Table 4 reports on the values obtained. As expected, the k value of the uniform foam was the same (0.165 W/m.K) for both sides. In the first series of sample, increasing T avg from 207.5 to 215 • C decreased the k value by 22% (from 0.161 to 0.125 W/m.K). This is mainly related to higher expansion ratio (lower density) as more gas (cells) inside the foam provides better thermal insulation for the foams [51,52]. Furthermore, Table 4 shows that the top side of graded foams has higher k values than the bottom side. This indicates that the bottom side (lower cell size and higher cell density) generates lower thermal conductivity. For example, the bottom side of T220 has 4% higher thermal insulation compared to its top side. It can be concluded that the presence of a higher population of cells (cell density) with lower cell size leads to lower thermal conductivity.

Second Series
The thermal conductivity of the second series showed a different trend compared to the first series. By increasing ∆T from 10 to 40 • C, the k value increased by 7% (0.169 to 0.180 W/m.K). The main reason for this behavior is attributed to lower expansion ratio (lower amount of gas inside the foam). The k values obtained from both sides did not show significant differences for these samples. This can be attributed to the similar morphology of the top and bottom regions (elliptical). A comparison between the thermal insulation performance of the first and second series shows that the cell size and cell density are both critical parameters for heat transfer. For instance, comparing the top and bottom regions of dT40 and T225 shows that the former has larger cell sizes (54% for the top and 69% for the bottom regions) and lower cell density (61% for the top and 290% for the bottom region). This is the origin of the higher thermal insulation of T225 (44%) compared to dT40.

Conclusions
In this work, uniform and density-graded foams were produced using a single-step compression molding process. POE was used as an elastomeric matrix with single blowing agent (ADC) content (4 phr). To control the final morphology of the foams, two series of graded foams with different T avg and ∆T were produced, leading to the formation of different (two or three) regions, respectively, with different cellular morphology (cell size, density and geometry). The results were compared with uniform foam and the neat (unfoamed) polymer matrix.
The cellular structure analysis of the first series indicated that increasing T avg from 207.5 • C to 215 • C resulted in higher cell size in the top region (32%) and lower cell size in the bottom region (3%) combined with lower cell density in the top (56%) and bottom (3%) regions. On the other hand, increasing ∆T from 10 to 40 • C led to larger cell sizes (80%) in the middle region, as well as larger cell sizes in the top and bottom regions (175%).
The tensile properties, such as modulus, strength and elongation at break, of the first series decreased by 33%, 13% and 15%, respectively, with increasing T avg , while they increased for the second series by 14%, 26% and 10%, respectively, with increasing ∆T. For compression, the tests were carried out on both sides of the foams to detect any asymmetry related to the density gradation. Surprisingly, the graded structure of the second series produced a significant improvement in the elastic modulus (85%) and compressive strength (131%) on the top side compared to only 65% and 121% for the bottom side from dT10 to dT40, respectively.
Finally, the thermal conductivity of the first series was decreased by 22%, while it increased by 7% for the second series. Moreover, the thermal insulation analysis of both sides revealed that the side having smaller cell size and higher cell density had better overall thermal insulation performance. This is why the first series of graded foams showed lower thermal conductivity than the second series. The thermal conductivity behavior of the graded POE foams revealed that the amount of thermal damping of the foams depends on two main factors: expansion ratio/foam density (the amount of gas inside the matrix) and the geometry/cellular structure. Therefore, by carefully engineering and tailoring the cellular morphology of the foam, their thermal insulation behavior can be optimized for a fixed amount of materials and be used as high-efficiency thermal insulators in buildings. In addition, since the temperature difference between the inside and outside of buildings in cold and tropical regions can vary over a wide range of temperature differences, we plan to measure the thermal conductivity of graded POE foams at different average temperatures (above and below room temperature). Finally, the real 3D structure of the foams can be simulated via 2D SEM images, which will be applied in finite element techniques (FEM) to simulate the heat transfer behavior of the graded POE foams. Funding: Financial support from both NSERC (Natural science and engineering research council of Canada) and CAMSO-BR was received for this for this project.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.