Considering Electrospun Nanofibers as a Filler Network in Electrospun Nanofiber-Reinforced Composites to Predict the Tensile Strength and Young’s Modulus of Nanocomposites: A Modeling Study

In this study, a simple approach was described to investigate the theoretical models for electrospun polymer nanofiber-reinforced nanocomposites. For predicting the tensile strength of the electrospun nylon 6 nanofiber-reinforced polyurethane acrylate composites, conventional Pukanszky, Nicolais–Narkis, Halpin–Tsai, and Neilson models were used, while for Young’s modulus, Halpin–Tsai, modified Halpin–Tsai, and Hui–Shia models were used. As per the Pukanszky model, composite films showed better interaction since the values of the interaction parameter, B, were more than 3. Similarly, the value of an interfacial parameter, K, was less than 1.21 (K = −5, for the curve fitting) as per the Nicolais–Narkis model, which indicated better interfacial interaction. For composite films, the modified Halpin–Tsai model was revised again by introducing the orientation factor, α, which was 0.333 for the randomly oriented continuous nanofiber-reinforced composites, and the exponential shape factor, ξ = (2l/d)e−avf−b, which showed the best agreement with the experimental Young’s modulus results. Based on mentioned remarks, these models would be applicable for estimating the tensile strength and Young’s modulus of electrospun nanofiber-reinforced polymer composite films.


Introduction
Polymer nanocomposites reveal significant high-performance properties using small fractions of nanofillers in the polymer matrices. The excellent properties of nanocomposites have attracted extensive attention in distinct technologies such as automobiles, energy, sensors, fuel cells, agriculture, and biotechnology [1][2][3][4][5]. One of the attractive characteristics of polymer nanocomposites is their mechanical properties. However, the mechanical characteristics of composites cannot be predicted properly due to the small fractions and novel characteristics of the polymer nanocomposites, compared to traditional composites. The mechanical characteristics of polymer nanocomposites have been estimated with many proposed models [6][7][8].
During the last few decades, the electrospinning technique experienced substantial progress and attracted researchers from various fields, such as biomedical, sensors, energy, and environmental applications [9][10][11]. Many nanofiber fabrication techniques, such as drawing, template synthesis, temperature-induced phase separation, and molecular selfassembly, are not scalable, are limited to specific polymers, and are tricky to control the fiber dimensions for [12]. In the case of electrospinning, it offers distinct advantages, such as control over morphology, porosity, and ease of fiber functionalization and material combination; a wide variety of polymers and materials have been used to form nanofibers The notable properties of nanofiber-reinforced polymer nanocomposites were qualified to the robust interfacial adhesion between the polymer matrix and electrospun nanofibers, which properly transferred the load from the matrix to continuous nanofibers. The strong adhesion between the polymer and nanofibers from the interphase around the nanofibers was quite different from both matrix and nanofibers [24]. Our team has investigated the mechanical characteristics of the electrospun nylon 6 nanofiber-reinforced polyurethane acrylate nanocomposites [16]. In this regard, some wholesome models were proposed, which provide a possible means to determine mechanical properties in nanofiber-reinforced composites. The mechanical characteristics of the polymer nanocomposites depend on various parameters such as reinforcement, the aspect ratio of the nanofibers, the dispersion feature, and the filler volume fraction [27][28][29].
In this study, the ultimate tensile strength and Young's modulus (E c ) of the nylon 6 nanofiber-reinforced polyurethane acrylate nanocomposites (N6/PUA) were evaluated from experimental and theoretical views. The Pukanszky, Nicolais-Narkis, Halpin-Tsai, and Neilson models for the ultimate yield strength, and the Halpin-Tsai, modified Halpin-Tsai, and Hui−Shia model were used, assuming randomly oriented continuous nanofibers. Moreover, the assumptions of these models showed good agreement with the experimental results.

Method
The UV-curable polyurethane acrylate (PUA) matrix system was formulated with 50% difunctional polyurethane acrylate oligomer, 45% isobornyl acrylate monomer (as a diluent), and 5% of Irgacure 184D. Nylon 6 nanofiber-reinforced polyurethane acrylate nanocomposite films were fabricated by over-coating the nanofibers on the PUA matrix system, which consisted of casting, electrospinning, and UV curing. The formulated UV-curable PUA matrix system was cast on the glass substrate, and nylon 6 nanofibers were electrospun on the PUA-coated glass substrate for different deposition times (N15: 15 min, N30: 30 min, N60: 60 min, N2 h: 120 min, and N4 h: 240 min) without any break. Afterward, the nanocomposite was cured in a conveyor-belt-type UV-curing machine LZ-U101 (Make-Lichtzen Co. Ltd., Gunpo-si, Korea) fixed with a gallium lamp (160 w/cm, main wavelength: 365 nm, UV-A: 1100 mJ/cm 2 , Arc system). The detailed procedures of the electrospinning of nylon 6, fabrication of N6/PUA nanocomposites, and characterizations were reported in our earlier research [16]. The density of the nanofibers, PUA films, and N6/PUA nanocomposite films were calculated using ASTM D 792, with the help of a weighing balance using Archimedes principle.

Theoretical Models
There are three kinds of modeling concepts employed for polymer nanocomposites according to different size effects, such as molecular-scaled, micro-scaled, and meso-/macroscaled models [6,30]. For the nanofiber-reinforced polymer composites, an applied force could be transferred from the polymer matrix to the polymeric nanofibers through shear stress at the nanofiber/polymer matrix interface.

Models for Tensile Strength
The Pukanszky model [28] explained the composition dependency of tensile strength in the nanocomposites, accepting the spontaneous formation of interphase as shown in the following: where σ c is the tensile strength of the composite, σ m is the tensile strength of the matrix, and ∅ f is the volume fraction of polymer nanofibers. B is an interaction parameter denoting the load-bearing capacity of the filler, which depends on the interfacial interactions. The represents the effective load-bearing cross-section of the matrix. At zero interactions, the complete load is transferred by the matrix, and the load-bearing crosssection drops with an increase in the nanofiber content. If B = 0, the fillers act as voids, and due to this, the composite evidences inferior interfacial bonding, excepting adhesion and load transfer at the matrix-filler interface. However, if the value of B ≤ 3, the filler matrix interface is poor, apart from the reinforcing effect; from Equation (1), parameter B can be calculated with Equation (2): For the Nicolais-Narkis model, the ratio of the tensile yield stress of the composite (σ c ) and tensile yield stress of a polymer matrix (σ m ) deviates as a two-thirds power law function, with K as an interfacial parameter for filler matrix adhesion. Equation (3) is stated as follows: The mechanical characteristics of the nanocomposites rely on the volume fraction (φ f ), filler properties, structure, and interfacial interaction. If the adhesion between the filler and matrix polymer is not established, then the filler cannot bear the applied load, and the whole load is transferred to the matrix phase. In this equation, the parameter K counts for the adhesion between the reinforcement (filler) and matrix. The lower the K value, the stronger the adhesion. For an extreme case of weak adhesion, the theoretical value of K is 1.21 [27,29].
Conforming to this model, the tensile strength is stated, as in Equations (4) and (5), as follows: with, where φ f is the volume fraction of the nanofibers, and σ m and σ c are the tensile strength of the matrix and composite, respectively. Parameter A can be determined from the Einstein coefficient K [31], as stated below (Equations (6) and (7)): with Polymers 2022, 14, 5425

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Similarly, the Neilson model is termed the modified Halpin-Tsai model, as Neilson revised the original equation by introducing ϕ as a filler packing factor. According to the Neilson model, the tensile strength is given as the following Equations (8) and (9): where ϕ max is the maximum packing fraction constant, and it is 0.82 for randomly oriented fibers.

Models for Young's Modulus
The Halpin-Tsai Model anticipates the E c of several nanocomposites, where the reinforcement is in the form of nanofibers, nanotubes, nanorods, and nanoparticles with capricious aspect ratios [32][33][34][35]. The model can be illustrated as follows (Equations (10) and (11)): with where E f , E c , and E m are the Young's modulus of the fiber, composite, and matrix, respectively. φ f is the nanofiber volume fraction, and η is the shape factor relating to the reinforcement geometry. τ is the aspect ratio τ = 2(l/d) for the tubular geometry. The length of the nanofiber was assumed to be l = 100,000 nm, and the diameter of the nanofiber was approximately 100 nm. The Halpin-Tsai model (Equations (10) and (11)) correlates the modulus of the unidirectional fiber composites to the fiber volume fraction. This model cannot authentically predict the modulus of nanofiber-reinforced polymer nanocomposites, since it does not deliberate definite features of the nanofibers such as their high surface area, very high aspect ratio of nanofibers, dispersion of the nanofibers, and exceptional Young's modulus of the nanofibers. However, nanofiber-reinforced polymer nanocomposites have a random alignment of the nanofibers in the matrix. Much research explored anticipating the modulus of randomly aligned fiber-reinforced composites by modifying the Halpin-Tsai model [33,36,37]. In some research, an orientation factor, α, accounted for the randomly oriented fiber. Likewise, in this case, the orientation factor, α, accounted for the randomly oriented fibers. If the length of the fiber is larger than the thickness of the samples, the fibers are assumed to be randomly oriented, and the value of the parameter is considered to be 0.333 (α = 1/3). If the length of the fiber is much smaller than the thickness of the specimen in randomly oriented fiber composites, then α = 1/6 is used [26,36,38,39]. However, the Halpin-Tsai model (Equations (12) and (13)) was modified as follows: Here, they further tailored the model by altering the shape factor, τ, to the ξ = (2l/d)e −av f −b , which is an exponential relation, with a and b being constants that are affiliated to the degree of fiber agglomeration, and by varying the values of a and b, the best fit to the experimentally determined E c [36,38].
The Hui-Shia model equation broadens the estimation of E c for unidirectional aligned composites with fiber-or flake-like fillers [31]. The Hui-Shia model eases the orientation of fibers, following the perfect interfacial bonding amongst matrix systems and nanofillers with similar Poisson's ratios. The affiliated E c model Equations (14)- (20) are stated as follows: where α' is the converse of the aspect ratio (i.e., d/l), and g is assumed to be a geometric parameter of composites, which is expressed in Equations (18) and (19). Equation (18) refers to the incorporation of fiber-shaped fillers, while Equation (19) is applicable to the incorporation of flake-or plate-like nanofillers. Additionally, for a flawless interface, g would be stated in Equation (20). Table 1 shows the physical properties of the N6/PUA nanocomposites. Due to ultralow loading (below 1%) of nylon 6 nanofibers in the PUA matrix, the practical and theoretical density of the nanocomposites did not show significant differences. Figure 1 shows the experimental stress-strain curves of the nylon 6 nanofiber-reinforced PUA nanocomposites. E c , tensile strengths, and % elongation were collected according to the average six sample estimates for an individual case. The mechanical characteristics of N6/PUA nanocomposites are noted in Table 2. The tensile strength and E c of the nanocomposites were enhanced with the introduction of nylon 6 nanofibers. There were no significant variations observed in % strains compared to the reference samples for each composite.

Results and Discussion
The discrepancy is much more familiar in modeling nanocomposite properties by the conventional rule of mixture or micromechanics models. In this section, we implemented the different models, and compared model predictions with the same set of available experimental data compiled in the previous study [16]. The material parameters required in the calculation process can be found in Tables 1 and 2.  The discrepancy is much more familiar in modeling nanocomposite properties by the conventional rule of mixture or micromechanics models. In this section, we implemented the different models, and compared model predictions with the same set of available experimental data compiled in the previous study [16]. The material parameters required in the calculation process can be found in Tables 1 and 2.

Tensile Strength of the Nanofiber-Reinforced Composites
The theoretical values of tensile strength were estimated with the Pukanszky model using Equations (1) and (2), and compared to the experimental values of nylon 6 nanofiberreinforced PUA polymer nanocomposites. The constant B was determined by befitting experimental values with the mathematical values, and derived from the minimum sum of squares of variance more than from experimental values of composite strength. Pukanszky's model underestimated the experimental data with the tensile strength of nanofiber-reinforced nanocomposites, when constant B = 0. It means that the nanofiberreinforced nanocomposites dominated with better interfacial adhesion amongst the polymer nanofibers and matrices, and thus amelioration in tensile properties was depicted with the embodiment of reinforcement of the nanofibers. For the curve fitting, the constant B values were calculated by employing Equation (2), constant B values were 6.82, 5.75, 5.05, 4.27, and 4.04 for the N-15, N-30, N-60, N-2 h, and N-4 h N6/PUA nanocomposites, respectively, which indicated that nanofiber-reinforced nanocomposites at a nanofiber content from 0.004 to 0.066 vol%, revealed better interfacial bonding, resulting in more effective filler-matrix load transfer.
The theoretical predictions of tensile strength were compared employing the Nicolais-Narkis model Equation (3) and compared to the experimental values, as depicted in Figure 2. For modeling nylon 6/PUA matrix composites, the values of K were considered as 1, −1, −2, and −5 for the Nicolais-Narkis model. Using values of K, the tensile strength was estimated for the composites using Equation (1). As shown in Figure 2a, the experimental K values were approximately −5 for the N6/PUA matrix composites.
ting experimental values with the mathematical values, and derived from the minimum sum of squares of variance more than from experimental values of composite strength. Pukanszky's model underestimated the experimental data with the tensile strength of nanofiber-reinforced nanocomposites, when constant B = 0. It means that the nanofiber-reinforced nanocomposites dominated with better interfacial adhesion amongst the polymer nanofibers and matrices, and thus amelioration in tensile properties was depicted with the embodiment of reinforcement of the nanofibers. For the curve fitting, the constant B values were calculated by employing Equation (2), constant B values were 6.82, 5.75, 5.05, 4.27, and 4.04 for the N-15, N-30, N-60, N-2 h, and N-4 h N6/PUA nanocomposites, respectively, which indicated that nanofiber-reinforced nanocomposites at a nanofiber content from 0.004 to 0.066 vol%, revealed better interfacial bonding, resulting in more effective filler-matrix load transfer.
The theoretical predictions of tensile strength were compared employing the Nicolais-Narkis model Equation (3) and compared to the experimental values, as depicted in Figure 2. For modeling nylon 6/PUA matrix composites, the values of K were considered as 1, −1, −2, and −5 for the Nicolais-Narkis model. Using values of K, the tensile strength was estimated for the composites using Equation (1). As shown in Figure 2a, the experimental K values were approximately −5 for the N6/PUA matrix composites.

Young's Modulus of the Nanofiber-Reinforced Composites
The deviations of Ec of the N6/PUA nanocomposites with the different volume fractions are plotted in Figure 3. To further determine the effectiveness of reinforcement, we implemented the conventional Halpin-Tsai model for N6/PUA nanocomposites. The Halpin-Tsai model is apparently effective in predicting Ec of not merely unidirectional aligned fiber-reinforced composites, but also of several nanocomposites where the rein-

Young's Modulus of the Nanofiber-Reinforced Composites
The deviations of E c of the N6/PUA nanocomposites with the different volume fractions are plotted in Figure 3. To further determine the effectiveness of reinforcement, we implemented the conventional Halpin-Tsai model for N6/PUA nanocomposites. The Halpin-Tsai model is apparently effective in predicting E c of not merely unidirectional aligned fiber-reinforced composites, but also of several nanocomposites where the reinforcement phase has functionality relating to the aspect ratio in regards to CNF, CNTs, and cellulose nanofibers. As shown in Figure 3, the illustrated calculations show increments in E c as the volume fraction of nanofibers is enhanced. The experimental data of relative strength and the predictions of the model did not properly follow the experimental data at numerous nanofibers concentrations because of the absence of some parameters, such as an alignment of the nanofibers, shape factor, and aggregation in the composites. aggregation/agglomeration coefficients a and b on the Ec of the nanofiber-reinforced composites were estimated using the modified Halpin-Tsai equation. As depicted in Figure 4, no substantial changes were observed in the Ec of the composites, and because of that, the values of aggregation/agglomeration coefficients predicted less than 200 to fit with the experimental Ec of the composites.  For the Halpin-Tsai equation, shape factor ξ and orientation factor α were introduced, and modified the model as shown in Equations (12) and (13). In this research, ξ values were assumed and the graph was plotted for nanofiber-reinforced composites, as shown in Figure 4. However, this model usually unpredicted the E c of nanofiber-reinforced nanocomposites, and it was clearly found that the calculations were above the experimental data as volume fractions of the nanofibers increased in the composites. There was no significant difference observed for ξ > 200. Furthermore, the ξ (exponential shape factor) had the form of ξ = (2l/d)e −av f −b .  The effect of aggregation-related coefficient a nurtured to relent the fitted curves of Ec of the nanofiber-reinforced composites at a high % of nanofibers, which demonstrated more aggregation established with multiplying nanofiber content. The aggregation-related coefficient b on the model curve for Ec of the nanofiber-reinforced composites is depicted in Figure 5. The Ec of composites was further adapted to tend lower for higher values of b at a high-volume fraction of nylon 6 nanofibers. In this study, the E m of the PUA matrix and nylon 6 nanofibers were 196 MPa and 30 GPa, respectively. The orientation factor α was appropriated as 0.333. The effects of the aggregation/agglomeration coefficients a and b on the E c of the nanofiber-reinforced composites were estimated using the modified Halpin-Tsai equation. As depicted in Figure 4, no substantial changes were observed in the E c of the composites, and because of that, the values of aggregation/agglomeration coefficients predicted less than 200 to fit with the experimental E c of the composites.
The effect of aggregation-related coefficient a nurtured to relent the fitted curves of E c of the nanofiber-reinforced composites at a high % of nanofibers, which demonstrated more aggregation established with multiplying nanofiber content. The aggregation-related coefficient b on the model curve for E c of the nanofiber-reinforced composites is depicted in Figure 5. The E c of composites was further adapted to tend lower for higher values of b at a high-volume fraction of nylon 6 nanofibers. The effect of aggregation-related coefficient a nurtured to relent the fitted curves of Ec of the nanofiber-reinforced composites at a high % of nanofibers, which demonstrated more aggregation established with multiplying nanofiber content. The aggregation-related coefficient b on the model curve for Ec of the nanofiber-reinforced composites is depicted in Figure 5. The Ec of composites was further adapted to tend lower for higher values of b at a high-volume fraction of nylon 6 nanofibers. After periodically modifying the coefficients of aggregation a and b, complete adequacy to the experimentally achieved Ec of the nylon 6 nanofiber-reinforced PUA com- After periodically modifying the coefficients of aggregation a and b, complete adequacy to the experimentally achieved E c of the nylon 6 nanofiber-reinforced PUA composites was found when a = 30 and b = 3, and it could be modeled by Equations (12) and (13) with the following exponential shape factor: However, model Equations (12) and (13), associated with Equation (21), are termed the modified Halpin-Tsai equation for nanofiber-reinforced composites. Figure 6 depicts the comparison of experimental data with theoretical values of the nanocomposites adapted by the modified Halpin-Tsai equation model with exponential shape factor ξ. In this study, the shape factor ξ was picked to conceal the randomly aligned nanofibers with different volume fractions, and it underrated the value of E c of the nanofibers loading to a little below 0.008% volume fraction. Moreover, the mechanical characteristics of the composites at marginally higher wt% of nanofibers were a little overestimated using this modified model by reasonably extrapolating results. this study, the shape factor ξ was picked to conceal the randomly aligned nanofibers with different volume fractions, and it underrated the value of Ec of the nanofibers loading to a little below 0.008% volume fraction. Moreover, the mechanical characteristics of the composites at marginally higher wt% of nanofibers were a little overestimated using this modified model by reasonably extrapolating results. Hui-Shia model Equations (14) and (15) demonstrated higher aspect ratio estimation with the presence of randomly oriented fillers in matrix systems, and an increasing degree of fiber aggregation with increasing fiber content. For predicting the Ec of the nanofiber-reinforced composites, α', an inverse of the aspect ratio was correlated with the perfect interface geometric parameter g [31,40,41]. The inverse of the aspect ratio was smaller than 1 (α' = 0.001). Therefore, for calculating the geometric parameter g, Equation (19) was used, and it perfectly matched with the values from Equation (20). It is well known that the orientation of the dispersed phase has a substantial effect on the composite Ec. It was evidenced from their geometry that disk-or plate-like fillers can contribute equal reinforcement in two directions if proportionately oriented, while fibers contribute primary reinforcement in one direction. In this case, the nanofibers were randomly oriented, and if the longitudinal modulus and transverse modulus were known, the effective modulus of the composite in all orthogonal directions [31] could be derived by the following equation: where Ec, E11, and E22 are effective, longitudinal, and transverse Young's moduli of the composite, respectively. x is the constant to govern the stress transfer amongst the fibers Hui-Shia model Equations (14) and (15) demonstrated higher aspect ratio estimation with the presence of randomly oriented fillers in matrix systems, and an increasing degree of fiber aggregation with increasing fiber content. For predicting the E c of the nanofiberreinforced composites, α', an inverse of the aspect ratio was correlated with the perfect interface geometric parameter g [31,40,41]. The inverse of the aspect ratio was smaller than 1 (α' = 0.001). Therefore, for calculating the geometric parameter g, Equation (19) was used, and it perfectly matched with the values from Equation (20). It is well known that the orientation of the dispersed phase has a substantial effect on the composite E c . It was evidenced from their geometry that disk-or plate-like fillers can contribute equal reinforcement in two directions if proportionately oriented, while fibers contribute primary reinforcement in one direction. In this case, the nanofibers were randomly oriented, and if the longitudinal modulus and transverse modulus were known, the effective modulus of the composite in all orthogonal directions [31] could be derived by the following equation: (22) where E c, E 11 , and E 22 are effective, longitudinal, and transverse Young's moduli of the composite, respectively. x is the constant to govern the stress transfer amongst the fibers and matrix systems in the composites, which is based on the curve fitting with experimental data (0 < x < 1). As shown in Figure 7, from Equations (14) and (15), longitudinal and inverse modulus predictions were obtained. The curve fitting with experimental results showed that factor x was calculated to be about 0.9, but it could only provide a rough estimation for E c of randomly oriented nanofiber-reinforced composites. The percentage errors of E c prediction for nanofiber-reinforced composites became much less than the experimental result data, and theoretical predictions appeared to overestimate experimental result data at higher volume fractions. The overestimated results could be based on the geometric constants engaged in the equation.
and inverse modulus predictions were obtained. The curve fitting with experimental results showed that factor x was calculated to be about 0.9, but it could only provide a rough estimation for Ec of randomly oriented nanofiber-reinforced composites. The percentage errors of Ec prediction for nanofiber-reinforced composites became much less than the experimental result data, and theoretical predictions appeared to overestimate experimental result data at higher volume fractions. The overestimated results could be based on the geometric constants engaged in the equation. From the above analysis, we can identify that in order to obtain more precise predictions of the tensile properties of nanofiber-reinforced polymer nanocomposites, nanofiber aspect ratio, distribution of nanofibers, and volume fraction of the nanofibers are fundamentally important. These models simultaneously review these parameters and ensure a simple approach to predict the mechanical characteristics of the nanofiber-reinforced polymer nanocomposites. However, it is a significant challenge to establish a more comprehensive model capable of considering the nanofiber geometry, agglomeration, critical nanofiber length, and so on, which is the subject of future research.

Conclusions
A comparative study among the experimental results and several theoretical models of filler reinforcement was implemented to predict the mechanical characteristics of electrospun nylon 6 nanofiber-reinforced PUA nanocomposites. Our findings suggested that the theoretical results predicted employing the Pukanszky model and Nicolais-Narkis model are in close agreement with the tensile strength experimental values of the nanofiber-reinforced nanocomposites. Meanwhile, the Neilson and Halpin-Tsai models of tensile strength showed higher bound values than the experimental values for the high-volume fraction of the nanofibers in composites (for 0.033 and 0.066 Vf). Additionally, theoretical values predicted using the modified Halpin-Tsai model showed close agreement with the available experimental values of Young's modulus, due to the introduction of exponential shape factor ξ in the form of ξ = (2 ) ⁄ . Young's modulus values evaluated using the Hui-Shia model and Halpin-Tsai were in the least agreement with the experimental values. The theoretical prediction applicable for a polymer nanocomposite with randomly dispersed high-aspect-ratio nanofibers has its From the above analysis, we can identify that in order to obtain more precise predictions of the tensile properties of nanofiber-reinforced polymer nanocomposites, nanofiber aspect ratio, distribution of nanofibers, and volume fraction of the nanofibers are fundamentally important. These models simultaneously review these parameters and ensure a simple approach to predict the mechanical characteristics of the nanofiber-reinforced polymer nanocomposites. However, it is a significant challenge to establish a more comprehensive model capable of considering the nanofiber geometry, agglomeration, critical nanofiber length, and so on, which is the subject of future research.

Conclusions
A comparative study among the experimental results and several theoretical models of filler reinforcement was implemented to predict the mechanical characteristics of electrospun nylon 6 nanofiber-reinforced PUA nanocomposites. Our findings suggested that the theoretical results predicted employing the Pukanszky model and Nicolais-Narkis model are in close agreement with the tensile strength experimental values of the nanofiberreinforced nanocomposites. Meanwhile, the Neilson and Halpin-Tsai models of tensile strength showed higher bound values than the experimental values for the high-volume fraction of the nanofibers in composites (for 0.033 and 0.066 V f ). Additionally, theoretical values predicted using the modified Halpin-Tsai model showed close agreement with the available experimental values of Young's modulus, due to the introduction of exponential shape factor ξ in the form of ξ = (2l/d)e −av f −b . Young's modulus values evaluated using the Hui-Shia model and Halpin -Tsai were in the least agreement with the experimental values. The theoretical prediction applicable for a polymer nanocomposite with randomly dispersed high-aspect-ratio nanofibers has its advantages, since polymer nanofiber-reinforced nanocomposites are extensively used in human motion detection, self-healing electronic skins, sensors, fuel cells, epidermal electronics, microfluidic devices, and so on. It would be advantageous to estimate the mechanical properties of these composites using these modified models, before designing the final experiment.