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Development and modeling of an ultra-robust TPU-MWCNT foam with high flexibility and compressibility

  • Pardis Ghahramani , Kamran Behdinan EMAIL logo , Rasool Moradi-Dastjerdi and Hani E. Naguib EMAIL logo
Published/Copyright: April 9, 2024
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 13 Issue 1

Abstract

Developing a cost-effective industrially scalable manufacturing method that can improve the mechanical properties of nanocomposite foams with higher flexibility, compressibility, and, at the same time, mechanically robustness is of significant interest. In this study, porous thermoplastic polyurethane (TPU)/multiwalled carbon nanotube (MWCNT) was fabricated with the chemical blowing agent (CBA) by a combination of compounding-compression molding methods. The effects of CBA and MWCNT contents on the foam morphology, porosity, foam cell size, Young’s modulus, and compressibility of fabricated samples were investigated. Through conducting cyclic compressive tests, it was observed that nanocomposite foams exhibited consistent mechanical responses across multiple compressive cycles and demonstrated notable characteristics, including high compressibility (up to 76.4% compressive strain) and high elastic modulus (up to 8.8 ± 2.6 MPa). Moreover, theoretical approaches were employed to predict the elastic modulus of solid and foam TPU/MWCNT. For solid MWCNT/TPU, a specific micromechanical model based on different modifications of the Halpin-Tsai (HT) approach was used, which showed a good agreement with experimental data at different MWCNT contents. Furthermore, the constant parameters of Gibson and Ashby’s method were found to successfully predict the elastic modulus of foam TPU/MWCNT at different MWCNT and CBA percentages.

Keywords: chemical blowing agent; experimental characterization; theoretical modeling; elastic modulus; TPU/MWCNT nanocomposite

1 Introduction and background

In recent years, flexible strain sensors with their potential prospects have attracted great attention [1,2,3,4,5] in many fields. These fields include wearable electronics such as stretchable materials for electronic devices [6,7], wearable sensors [8], energy harvesters [9,10], and micropumps with active diaphragms [11]; field of human movement monitoring [12,13], soft robotics for elastomer actuators [14] or self-healing actuators [15], sensitive electronic skin [16], and prosthetics [17,18]. Piezoresistive nanocomposite foams consisting of conductive nanoparticles and a flexible polymeric matrix are one of the significant types of flexible strain sensors [19,20,21]. This type of sensor provides tremendous advantages, such as high electrical conductivity, high flexibility, compressibility, and lightweight [22]. The sensing mechanism of piezoresistive foam nanocomposites is based on the electrical resistance variation in response to applied external stress [23,24].

Foaming the nanocomposites can enhance their electrical properties [25] and tailor their mechanical properties, including flexibility [26,27], compressibility [28], and mechanical strength [29,30]. The mechanical properties of nanocomposite foam sensors are crucial for their design and development, in addition to the electrical properties. Pressure-detecting sensors must be both flexible and compressible when subjected to high-pressure loads, without compromising their morphology, durability, and mechanical strength. While the addition of conductive reinforcements can aid in the formation of conductive paths in the insulating polymer matrix, excessive filler content can harm the mechanical properties of the nanocomposite foam, reducing its processability and limiting its potential applications [31]. Despite successful demonstrations of nanocomposite foam sensors reported in the literature, they still have some limitations [32]. These sensors have low Young’s modulus, limited recoverability, weak compressive strength, and a restricted pressure detection range of up to 900 kPa [1,33,34,35,36,37]. Yao et al. [38] showed that the detection range of polyurethane–graphene sponges was as low as 10 kPa, indicating its poor mechanical strength. Some nanocomposite foams are insensitive to large strain levels (more than 30%) due to conductive network saturation [39]. Additionally, fabricating a piezoresistive nanocomposite foam with a controlled elastic modulus that can operate within a broad loading range at a limited thickness is challenging [40,41].

Moreover, developing a cost-effective and scalable fabrication technique to create nanocomposite foams with uniformly distributed conductive fillers and controlled porosity, cell wall thickness, and foam morphology for achieving superior mechanical properties in the foam structure is a critical objective. Many foaming fabrication methods such as the particulate leaching method [42,43] are not cost-effective and scalable to the industrial manufacturing process. Supercritical gas foaming is an environmentally friendly industrial-scale technique that creates porous structures in thermoplastic polymeric (TPU) matrixes. However, in the nanocomposites with high loadings of nanoparticles, the gas diffusion is decreased, which adversely affects the physical foaming process and reduces the expansion ratio of the foamed product [26,44]. Also, the physical blowing agent (PBA) requires high pressure to be dissolved in the polymeric phase, which limits some types of foaming processes that are not practical at high pressures [45]. Hence, to broaden the nanocomposite foam applications, a new strategy that is able to enhance its mechanical properties with high controllability via an industrially scalable method is of great interest. One possible alternative foaming technique is implementing chemical blowing agent (CBA) particles, which promise highly controllable foaming with a uniform close-cell structure [1,46]. When subjected to heat, CBA thermally decomposes and produces gas, which can be trapped inside the polymeric matrix and create a foam structure [47]. CBA content and decomposition rate have a significant role in the foaming process of polymeric mixtures [48]. Unlike PBA, CBA particles operate at the pressure-free operating condition and undergo the chemical reaction at the decomposition temperature, which makes them a proper candidate to be utilized in pressure-free foaming processes such as rotational foam molding [45]. Therefore, compared to PBAs, CBAs are easier to handle and have more engineering and economic efficiency [47].

The design parameters including the polymer matrix, porous structure, characteristics of conductive filler, and manufacturing technique significantly impact the electrical and mechanical properties of nanocomposite foams. Despite existing literature on the topic, currently, a comprehensive study investigating the impact of foam porosity and morphology, filler contents, and sample fabrication methods on piezoresistivity, repeatability, and mechanical properties of nanocomposite foam sensors is missing [35,49]. Therefore, more research in this field is necessary to consider all these factors. In the current study, TPU was used as the polymeric phase due to its beneficial properties, which expand its application in a variety of fields. TPU is a flexible material that suits our target for compressibility in this study [41,50]. Moreover, it has abrasion resistance, chemical resistance, and ease of processing due to being melt-processable and recyclable [26,51]. Having high mechanical and electrical properties including high conductivity, large aspect ratio, and high elastic modulus, multiwalled carbon nanotube (MWCNT) was chosen as the nanofiller in this study [52,53,54,55].

In this work, TPU/MWCNT foam nanocomposites with varying contents of MWCNT and CBA were fabricated, and their flexibility, compressibility, and mechanical properties were analyzed. Moreover, the effects of nanofiller and blowing agent contents on the foam porosity, morphology, and mechanical properties of TPU/MWCNT nanocomposites were investigated. The potential application of fabricated TPU/MWCNT nanocomposite foams is in pressure-detecting systems to help the rehabilitation of people with artificial joints and suffering from osteoarthritis [56,57]. Unbalanced pressure distribution applied to the artificial knee over time can cause the wear of the tibial insert and result in further problems [58]. Pressure-detecting sensors embedded in artificial knees can detect plantar pressure map which shows the pressure distribution applied to the knee. The recorded results from the pressure sensors will be used to detect the accuracy and further adjustment of the designed biomechanical system.

Due to the limitations and costs associated with experimental tests, theoretical models are also used in our research to predict Young’s modulus of solid and foam nanocomposites. This approach offers a better understanding of material properties and helps identify the ideal conductive reinforcement content, which can meet the desired mechanical property requirements [59]. Therefore, in this study, Young’s modulus of solid TPU/MWCNT nanocomposites was predicted by micromechanical models based on several modified HS approaches. Also, based on experimental results, the constant parameters of Gibson and Ashby’s method for evaluating Young’s modulus of foams made of pure TPU or MWCNT/TPU nanocomposites were proposed.

2 Experimental section

2.1 Experimental materials

TPU (Estane 58202, an 85A polyether-type thermoplastic polyurethane) was purchased from the Lubrizol Corporation. The CBA, azodicarbonamide (AC or ADCA) (CELLCOM-AC3000FD, decomposition temperature of 201–205°C), was ordered from Kum Yang Company Limited. The MWCNT (NC7000TM series, average length of 1.5 mm, average diameter of 9.5 nm) was purchased from Nanocyl Company. All materials were used in the sample fabrication as received without further modifications.

2.2 Manufacturing process of TPU nanocomposites and their foams

Fabrication of TPU/MWCNT foams involved two different stages. One stage was blending the materials with the micro-compounder (DSM Xplore, MICRO 15, The Netherlands) to create homogeneous filaments. The second stage involved using the hot press compression molding (Carver Model 4386, USA) to reshape the filaments and create the samples with the desired shape, which was suitable for characterization. Since the CBAs are temperature sensitive, these particles should not be activated during the blending process. Otherwise, during the compression molding process, due to the extra heat and high pressure, their structure will be damaged, and porous morphology will not be achieved. Therefore, during the blending stage, the operating temperature was selected far from the CBA decomposition temperature (higher than TPU’s melting point [155°C]) to just create solid TPU/CBA/MWCNT filaments. Later, in the compression molding stage, by increasing the working temperature, CBAs could decompose and create a porous structure.

Figure 1 shows the manufacturing process of TPU/MWCNT foams. At the beginning of this process, the specified weight ratios of TPU pellets and CBAs were fed to the micro-compounder through the conical forced feeding part. At this stage (the first step of compounding), materials were blended for 2.5 min with a speed of 200 rpm and a working temperature of 160°C. Then, the obtained filament was cut into small pieces for step 2 of compounding, and at this time, different weight ratios of MWCNTs were added to TPU/CBA pieces. It is worth mentioning that blending the MWCNTs at the same time with the TPU pellets and CBAs hindered the CBAs from being activated completely by heat in the compression molding stage. The reason for this phenomenon could be the entanglement of MWCNTs with TPU, which caused improper mixing of CBAs with TPU. Therefore, two-step compounding was conducted to create TPU/CBA/MWCNT solid filaments. In compounding step 2 similar operating condition as the first step was used. In the next stage, obtained TPU/CBA/MWCNT solid filaments were cut into small pieces and were filled into an aluminum mold with rectangular cuboid cavities (25.0 mm [L] × 12.5 mm [W] × 2.0 mm [T]). Then, the mold was transferred into the hot press compression molding with a preset temperature of 195°C. Once the mold was in contact with both heating platens of the device, it was heated up for 5 min without external pressure. After 5 min, the mold was pressurized to 1,000 psi for 2.5 min. Then, in order to provide space for the expansion of CBAs, the external pressure was released to zero while the mold was in contact with two heating plates for an additional 2.5 min. Afterward, the mold was removed from the hot press compression molding and instantly cooled with cold water. Once the samples were removed from the mold cavities, they were placed in an oven to dry at 70°C for 24 h. TPU foam samples were fabricated with the manufacturing process shown in Figure 1 with the only difference of excluding step 2 of compounding since MWCNTs were not used for this type of sample. Also, the fabrication process of solid TPU/MWCNT nanocomposite followed the same procedure as TPU/MWCNT foams, excluding the first step of compounding. The final products with various MWCNT and CBA contents are named as summarized in Table 1. In this table, Nn-Fm indicates a sample that has n wt% MWCNT content and m wt% CBA content.

Figure 1 Schematic of foam TPU/MWCNT manufacturing process.
Figure 1

Schematic of foam TPU/MWCNT manufacturing process.

Table 1

Composition of fabricated samples

Sample identification MWCNT content (wt%) CBA content (wt%)
N0-F0, N0-F3, N0-F5 0 0, 3, 5
N1-F0, N1-F3, N1-F5 1 0, 3, 5
N3-F0, N3-F3, N3-F5 3 0, 3, 5
N5-F0, N5-F3, N5-F5 5 0, 3, 5

2.3 Characterization methods

Cyclic compression tests were carried out on an Instron 5944 machine (Instron, Norwood, USA-2kN load cell) with a displacement rate of 1 mm/min and a maximum allowable force of 1.9 kN in ten continuous loading–unloading cycles [41,60,61,62]. The average sample geometry was 25.0 mm (L) × 12.5 mm (W) × 2.0 mm (T). Young’s modulus of the samples was determined through a linear regression analysis of the compressive stress versus compressive strain curves, focusing on the initial 5% of the compressive strain in the first loading cycle. The slope of the resulting trendline was used as the calculated value for Young’s modulus.

A scanning electron microscope (SEM, JSM-IT100, InTouch Scope™, JOEL Inc, Tokyo, Japan) at 10 kV was used to observe the morphologies of the fabricated foams. For SEM sample preparation, foams were submerged in liquid nitrogen to be cryo-fractured. Then, the fractured cross-sectional surface was subjected to the sputter-coating device (DII-29010SCTR Smart Coater, JOEL Inc, Tokyo, Japan) for 4 min.

The average cell diameter of nanocomposite foams was assessed through the analysis of SEM micrographs using ImageJ software [63,64,65].

3 Theoretical approaches

To estimate the elastic modulus of the fabricated TPU/MWCNT foams at any MWCNT or porosity percentages, a theoretical approach has been developed. In this approach, in the first step, the elastic modulus of solid TPU/MWCNT nanocomposites is calculated at various MWCNT contents using micromechanical models based on the Halpin-Tsai (HT) approach. Then, using the results of the previous step, the elastic modulus of foams made of pure TPU or TPU/MWCNT nanocomposites is evaluated. In the second step, a method introduced by Gibson and Ashby [66] is used to calculate the elastic modulus ratio of foams to their solid material at any porosity percentage.

3.1 Solid TPU/MWCNT

To utilize this heavily employed approach for nanocomposite materials, various modifications to the original HT have been performed. In MWCNT-reinforced nanocomposites, there are a few parameters that affect the mechanical properties of the resulting nanocomposites such as the aspect ratio, agglomeration, orientation, and waviness of CNTs [67,68,69]. To capture the effect of MWCNT aspect ratio (AR) when they are dispersed with random orientations, the elastic modulus of such nanocomposites E nc can be estimated as a function of longitudinal E L and transverse E T components of the elastic modulus as follows [70,71]:

(1) E nc = 3 8 E L + 5 8 E T ,

where the definition of E L and E T are given as follows [70,71]:

(2) E L = 1 + AR ⋅ η L . f r 1 − η L . f r E m , E T = 1 + 2 η T . f r 1 − η T . f r E m ,

where f r is MWCNT volume fraction and

(3) AR = l CNT d CNT , η L = ( E r / E m ) − 1 ( E r / E m ) + AR , η T = ( E r / E m ) − 1 ( E r / E m ) + 2 ,

where l CNT , d CNT , E r , E m are MWCNT length, MWCNT diameter, elastic modulus of the reinforcement (i.e., MWCNT), and elastic modulus of the matrix (i.e., TPU), respectively.

Considering the geometrical shape of the reinforcement components, the coefficients of E L and E T in equation (1) are also suggested to be as follows [72]:

(4) E nc = 2 10 E L + 8 10 E T .

To further involve the effect of reinforcement waviness and distribution states, another modified HT approach has been introduced, as mentioned in the following equation [73,74]:

(5) E nc = 1 + 2 AR ⋅ η . f r 1 − η . f r E m ,

where

(6) η = ( F O ⋅ F W ⋅ F A ⋅ E r / E m ) − 1 ( F O ⋅ F W ⋅ F A ⋅ E r / E m ) + 2 AR .

F O , F W , and F A represent orientation, waviness, and agglomeration factors of MWCNTs, respectively.

The orientation factor is applied to consider the effect of random orientations of MWCNTs, as F O = 1 assumes that all MWCNTs are oriented in the same direction. The use of F O = 1 / 3 and F O = 1 / 6 has been recommended for two-dimensional and three-dimensional random orientations, respectively [73,74,75]. As 3D distribution for MWCNTs has been considered, in this work, F O = 1 / 6 was selected for the orientation factor.

Due to MWCNT’s high aspect ratio, they are usually bent when they are added to their matrix material. Therefore, a waviness factor, which is defined based on an assumed wave shape of long MWCNTs, has also been considered to capture the effect of MWCNT’s bending in the HT approach. As suggested in previous studies [73,76,77], F W = 0.6 is selected to modify the HT model introduced in equation (5).

Moreover, to better modify the evaluation of the elastic modulus of the nanocomposite, an agglomeration factor is suggested to modify the utilized HT approach in equation (7) as follows [73,74]:

(7) F A = exp ( − α f r β ) ,

where α and β are two coefficients that define various agglomeration states of MWCNTs.

Finally, to bridge MWCNT content from weight fraction wt to volume fraction, the following equation can be employed:

(8) f r = wt wt + ρ r ρ m − ρ r ρ m wt ,

where ρ r and ρ m are the mass density of MWCNT and TPU.

3.2 TPU and TPU/MWCNT foams

According to Gibson and Ashby’s method [66], the elastic modulus of foam is a function of density ratio λ = ρ f / ρ s where the subscripts of f and s indicate a property attributed to foam and solid (non-porous) made of the same material, respectively. They suggested the following equation to estimate the relative elastic modulus of foams based on density ratio [66,78]:

(9) E f / E s = C λ n ,

where C and n are two constants that can be defined by performing regression analysis on the experimental data. These constants are changed by void geometry, foam material, cell type, etc.

It is worth mentioning that the following equation shows the relation between density ratio and porosity percentage γ , which is usually utilized to identify the amount of porosity in foams [62,63]:

(10) γ = ( 1 − λ ) × 100 % .

Accordingly, for example, γ = 0 % and γ = 40 % represent a non-porous material ( λ = 1 ) and a foam in which 40% of its volume fraction is occupied with porosities ( λ = 0.6 ) .

4 Results and discussion

Figure 2 presents the cyclic compression test curves (ten cycles) for the fabricated samples with different contents of MWCNTs and CBAs. Furthermore, this figure presents a focused area of an initial 5% of the compressive strain in the first loading cycle for each sample. Young’s modulus of the samples is calculated based on linear regression analysis of the compressive stress versus compressive strain curves of this section. The curves in Figure 2 indicate that all the samples follow a repeatable mechanical behavior in different compression cycles. Moreover, this figure shows that the inclusion of CBAs in the polymer matrix increased the sample's flexibility and elevated their strain range under compression test. Based on the data plotted in Figure 2, it is evident that the inclusion of MWCNTs in the foam structures has a significant impact on their compressibility and maximum strain capacity. Table 2 presents a concise overview of the maximum strain capacity exhibited by different categories of nanocomposite foams when subjected to a uniform force range. As per Table 2, in comparison with the pristine foams (N0-F3 and N0-F5), the inclusion of 1 wt% MWCNT in N1-F3 and N1-F5 samples reduced their maximum strain by 13.3 and 21.1%, respectively. Also, increasing the MWCNT content to 3 wt% in N3-F3 and N3-F5 had a similar impact on their compressibility and the maximum strain that they could undergo. The maximum strain in N3-F3 and N3-F5 was further reduced by 25.4 and 36.8% compared to their pristine foams.

Figure 2 10 cyclic compression test curves. (a) solid TPU and TPU/MWCNT, (b) foam TPU and TPU/MWCNT with 3 wt.% CBA, and (c) foam TPU and TPU/MWCNT with 5 wt.% CBA.
Figure 2

10 cyclic compression test curves. (a) solid TPU and TPU/MWCNT, (b) foam TPU and TPU/MWCNT with 3 wt.% CBA, and (c) foam TPU and TPU/MWCNT with 5 wt.% CBA.

Table 2

Maximum strain levels under force of 1,900 N

MWCNT (wt%) 0 wt% CBA 3 wt% CBA 5 wt% CBA
0 27.8 64.3 76.4
1 24.2 51.0 55.3
3 20.4 38.9 39.6
5 21.2 34.9 41.4

Figure 3(a) presents Young’s modulus of solid TPU, solid TPU/MWCNT with different MWCNT weight ratios, TPU foams with different CBA contents, and TPU/MWCNT foams with different MWCNT and CBA contents. This figure demonstrates that the foam TPU and TPU/MWCNT have considerably lower Young’s modulus compared to the solid TPU and TPU/MWCNT. This reduction in Young’s modulus is attributed to the inclusion of CBAs in the polymer matrix, which introduces a porous structure to the morphology of the samples, resulting in increased flexibility but decreased mechanical strength [61]. However, it is noteworthy that the foams fabricated in this study exhibit significantly enhanced mechanical strength compared to similar foams reported in the literature [39]. Moreover, Figure 3(a) shows that increasing the MWCNT content, increased Young’s modulus of both foam and solid samples in a similar trend. The high elastic modulus of MWCNTs contributes to the enhancement of mechanical strength observed in nanocomposite structures [42,43]. Moreover, the results revealed that N0-F3 demonstrated a higher Young’s modulus of 527 ± 80 kPa in comparison to N0-F5 with a Young’s modulus of 430 ± 78 kPa. Figure 3(b) illustrates the porosity characteristics of both foamed TPU and TPU/MWCNT samples. As depicted in this figure, an increase in the content of CBAs in nanocomposite foams with 5 wt% CBA resulted in higher porosity compared to the ones containing 3 wt% CBA. This increase in porosity resulted in enhanced flexibility and softness, consequently leading to reduced mechanical strength and Young’s modulus [63,64].

Figure 3 (a) Young’s modulus of TPU, TPU/MWCNT solid, and foamed nanocomposites, (b) porosity of foamed TPU and TPU/MWCNT at different CBA and MWCNT contents.
Figure 3

(a) Young’s modulus of TPU, TPU/MWCNT solid, and foamed nanocomposites, (b) porosity of foamed TPU and TPU/MWCNT at different CBA and MWCNT contents.

As depicted in Figure 3(b), the introduction of MWCNTs into the polymer matrix resulted in a reduction in the foam porosity of the nanocomposite foams containing both 3 and 5 wt% CBAs, as the MWCNT content was increased up to 3 wt%. This phenomenon could be attributed to the entanglement of MWCNTs with CBAs, which hindered the proper dispersion of CBAs within the polymer matrix and limited cell formation.

However, the porosity change was found to be negligible when the MWCNT content was further increased from 3 to 5 wt%, as per the obtained results. SEM micrographs with uniformly porous structures in Figure 4 confirm the results of porosity measurements. According to these micrographs, N0-F3 and N0-F5 samples had a larger number of voids with larger cell sizes in their structure. This revealed that increasing the CBAs weight ratio resulted in the growth of porosity in the N0-F5 sample due to the higher gas production during blowing agent decomposition. Moreover, the SEM micrographs show that as MWCNT content increased in the foam structures, smaller cells appeared in their morphology. Figure 5 summarizes the average cell size of different types of foams. The presence of MWCNTs with their fine dimensions and large surface area in the nanocomposite structure created more challenges for bubble growth within the polymer matrix, which led to reduced cell sizes. However, at large MWCNT contents, the average cell sizes in TPU/MWCNT foams with 3 and 5 wt% MWCNT were statistically equal [79]. Considering the results of Figures 3 and 5, it can be comprehended that, alongside the higher MWCNT content and reduced porosity, smaller foam cell sizes could contribute to the sample's stiffness, thereby resulting in an elevated value of Young’s modulus.

Figure 4 Cellular morphology of foamed TPU and TPU/MWCNT at different CBA and MWCNT contents.
Figure 4

Cellular morphology of foamed TPU and TPU/MWCNT at different CBA and MWCNT contents.

Figure 5 Foams average cell size.
Figure 5

Foams average cell size.

4.1 Theoretical characterization

As already mentioned in Section 3, the developed theoretical method starts with the characterization of solid TPU/MWCNT nanocomposites. The comparison between the average experimental results performed in this article and HT approaches presented in equations (1), (4), and (5) indicates which HT approach has the best level of accuracy in the elastic modulus estimation of such solid nanocomposites. As shown in Figure 6, equation (1) offers better estimations in comparison with equation (4). However, at a higher amount of MWCNT contents, they both fail in the estimation of the elastic modulus of solid TPU/MWCNT nanocomposites as they consider a steady increase of elastic modulus with the increase of CNT volume fraction, which cannot practically happen.

Figure 6 Comparison of the elastic modulus of solid TPU/MWCNT nanocomposites obtained from theoretical approaches with the results obtained from experimental tests with their standard deviations at various MWCNT weight percentages.
Figure 6

Comparison of the elastic modulus of solid TPU/MWCNT nanocomposites obtained from theoretical approaches with the results obtained from experimental tests with their standard deviations at various MWCNT weight percentages.

Due to the involvement of more MWCNT parameters in the estimation of elastic modulus, it can be seen that equation (5) offers the best estimations when the coefficients of the agglomeration factor (i.e., α and β ) are properly selected. It is shown that equation (5) with F O = 1 / 6 , F W = 0.6 , α = 7 , and β = 0.085 successfully estimates the elastic modulus such that this estimation either crosses the average values of experimental data or it is within the standard deviation experimental values. Moreover, it is shown that this approach is relied on the correct selection of α and β such that the selection of other combination values of α and β results in a significant error.

According to equation (9), first, the nondimensional form of elastic modulus ratio ( E f / E s ) versus density ratio ( λ = ρ f / ρ s ) was plotted. Then, based on the average values of experimental elastic modulus, regression analysis was performed to calculate the best values of the two constants (C and n) in equation (9). Figure 7 shows the elastic modulus ratio versus density ratio of porous TPU/MWCNT nanocomposites obtained from experimental tests and regression analysis for 0, 1, 3, and 5 wt% of MWCNT. The regression analysis shows that by selecting C = 1.001 and n = 2.805, equation (9) can successfully predict the elastic modulus of such nanocomposite foams regardless of how much MWCNT is involved. The comparison illustrates that except for highly porous pure polymeric materials, which have the lowest elastic modulus, the elastic modulus predictions are properly within the standard deviation values of experimental data. It is worth mentioning that the R-squared value for this regression analysis is R 2 = 0.9766. Moreover, it can be concluded that higher amounts of MWCNTs lead to the formation of foams with lower porosities, which is helpful in improving elastic modulus.

Figure 7 Comparison of the elastic modulus ratio of porous TPU/MWCNT nanocomposites obtained from the theoretical approach with the results obtained from experimental tests at various density ratios.
Figure 7

Comparison of the elastic modulus ratio of porous TPU/MWCNT nanocomposites obtained from the theoretical approach with the results obtained from experimental tests at various density ratios.

5 Conclusion

This study aimed to fabricate foam TPU/MWCNT nanocomposites with varying MWCNT and CBA contents, using an industrially scalable foaming method, to enhance their mechanical properties. In conclusion, the results indicated that:

  • Increasing the MWCNT content improved the elastic moduli of both the foams and solid TPU/MWCNT.

  • The pristine foams and nanocomposite foams demonstrated higher void fraction values in samples with higher CBA content.

  • Introduction of MWCNTs into the polymer matrix resulted in a reduction in foam porosity and cell sizes of the nanocomposite foams containing both 3 and 5 wt% chemical CBAs, up to a MWCNT content of 3 wt%.

  • The modified HT model successfully estimated Young’s modulus of solid nanocomposites by including more MWCNT parameters such as aspect ratio, agglomeration state, waviness, and orientation.

  • Gibson and Ashby’s method was utilized to determine the best equation for estimating the elastic modulus of pure and nanocomposite TPU foams at a wide range of MWCNT and CBA contents.

Acknowledgments

The work described in this article was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC under grant no. RGPIN-217525). The authors are grateful for their support.

  1. Funding information: This work was supported and funded by the Natural Sciences and Engineering Research Council of Canada (NSERC under grant no. RGPIN-217525).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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Received: 2022-12-10
Revised: 2024-02-12
Accepted: 2024-02-21
Published Online: 2024-04-09

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  99. Advances in the synthesis of gold nanoclusters (AuNCs) of proteins extracted from nature
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  124. Future prospects of gold nanoclusters in hydrogen storage systems and sustainable environmental treatment applications
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  126. Microstructural, mechanical, and corrosion characteristics of Mg–Gd–x systems: A review of recent advancements
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  147. Synthesis, characterization, thermal stability, and application of microporous hyper cross-linked polyphosphazenes with naphthylamine group for CO2 uptake
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  153. An environmentally greener and reusability approach for bioenergy production using Mallotus philippensis (Kamala) seed oil feedstock via phytonanotechnology
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  164. Poly-3,4-dihydroxybenzylidenhydrazine, a different analogue of polydopamine
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  168. Special Issue on Implementing Nanotechnology for Smart Healthcare System
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  171. Tracking success of interaction of green-synthesized Carbopol nanoemulgel (neomycin-decorated Ag/ZnO nanocomposite) with wound-based MDR bacteria
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  174. Metal oxides on the frontlines: Antimicrobial activity in plant-derived biometallic nanoparticles
  175. Controlling pore size during the synthesis of hydroxyapatite nanoparticles using CTAB by the sol–gel hydrothermal method and their biological activities
  176. Special Issue on State-of-Art Advanced Nanotechnology for Healthcare
  177. Applications of nanomedicine-integrated phototherapeutic agents in cancer theranostics: A comprehensive review of the current state of research
  178. Smart bionanomaterials for treatment and diagnosis of inflammatory bowel disease
  179. Beyond conventional therapy: Synthesis of multifunctional nanoparticles for rheumatoid arthritis therapy
https://doi.org/10.1515/ntrev-2023-0219
Keywords for this article
chemical blowing agent; experimental characterization; theoretical modeling; elastic modulus; TPU/MWCNT nanocomposite
Creative Commons
BY 4.0

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  146. Incorporating GO in PI matrix to advance nanocomposite coating: An enhancing strategy to prevent corrosion
  147. Synthesis, characterization, thermal stability, and application of microporous hyper cross-linked polyphosphazenes with naphthylamine group for CO2 uptake
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  168. Special Issue on Implementing Nanotechnology for Smart Healthcare System
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  174. Metal oxides on the frontlines: Antimicrobial activity in plant-derived biometallic nanoparticles
  175. Controlling pore size during the synthesis of hydroxyapatite nanoparticles using CTAB by the sol–gel hydrothermal method and their biological activities
  176. Special Issue on State-of-Art Advanced Nanotechnology for Healthcare
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  178. Smart bionanomaterials for treatment and diagnosis of inflammatory bowel disease
  179. Beyond conventional therapy: Synthesis of multifunctional nanoparticles for rheumatoid arthritis therapy
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