Evaluation of viscoelastic properties in polymer nanocomposites for prosthetic applications via microstructural profiling, model-based analysis, and dynamic mechanical thermal analysis

The UHMWPE powder (GUR 1020, Celanese, USA) was used as the base material, while zeolite nanoparticles (Z4A-005-R, Japan) with an average particle size of 50 nm were chosen as the reinforcing agent to enhance the dynamic thermomechanical properties of the composite. The crystalline structure of the zeolite nanoparticles was confirmed by X-ray diffraction (XRD) analysis, as shown in Fig. 1. The diffraction pattern exhibits sharp and well-defined peaks characteristic of crystalline zeolite, indicating high phase purity of the nanofiller. The UHMWPE powder and the respective weight percentages of zeolite were mixed using a twin-screw extruder (Leistritz ZSE 18, Germany) operating at a temperature profile of 180–200 °C and a screw speed of 100 rpm. The extruded strands were pelletized and subsequently compression molded. The final samples were prepared using a Carver hydraulic hot press (Carver Inc., USA) at 200 °C under a pressure of 15 MPa for 10 min. The molded sheets were cooled under controlled conditions to minimize residual stresses. The specimens were then cut into standard dimensions using a high-precision CNC milling machine (Haas Automation, USA) to ensure consistency for DMT testing. The final specimens were polished using SiC abrasive papers (Struers, Denmark) to remove any surface imperfections.

To investigate the viscoelastic response of UHMWPE–zeolite nanocomposites under dynamic loading conditions, DMTA was carried out. Measurements were obtained using a TA Instruments Q800 analyzer (USA) operating in a dual cantilever configuration. E′, E″, and tan δ were recorded as temperature-dependent parameters. The thermal ramp was set at 5 °C/min, spanning from − 150 °C to 100 °C. The selected temperature range (− 150 °C to 100 °C) enables the identification of secondary and primary molecular relaxations of UHMWPE-based nanocomposites and covers both extreme conditions and the physiological temperature range relevant to prosthetic applications. Two excitation frequencies, 1 Hz and 10 Hz, were selected to assess the frequency-sensitivity of nano-composite samples. All test specimens were fabricated with dimensions of 40 × 10 × 3 mm for experimental consistency. DMTA measurements were performed in triplicate for each composition to ensure reproducibility, with average values reported.

Morphological evaluation of the UHMWPE-zeolite nanocomposites was carried out to assess nanoparticle distribution within the polymer matrix and the nature of filler-matrix interfacial bonding. A field-emission SEM (FEI Quanta 250 FEG, Thermo Fisher Scientific, USA) was employed at an accelerating voltage of 15 kV. Specimens were cryo-fractured in liquid nitrogen to expose the fracture surface and then coated with a thin gold layer using a Leica EM ACE600 sputter coater (Leica Microsystems, Germany) to ensure adequate conductivity for imaging.

FTIR was performed using a Bruker Tensor 27 FTIR spectrometer (Bruker Corporation, Germany) to analyze the chemical interactions between the UHMWPE matrix and the zeolite nanoparticles. The spectra were recorded in the range of 4000–400 cm⁻¹ with a resolution of 4 cm⁻¹ using attenuated total reflectance (ATR) method.

In this study, a predictive modeling framework was established to map microstructural and DMTA input variables to the corresponding experimentally measured DMTA outputs, specifically storage modulus (E′), loss modulus (E″), and damping factor (tan δ). A Least-Squares Boosting (LSBoost) regression ensemble, with hyperparameters optimized via Bayesian optimization, was employed to capture the complex, nonlinear relationships between input features and material responses. The trained models enabled extrapolation of property predictions beyond the experimentally tested domain, thereby supporting a more comprehensive understanding of structure–process–property relationships. To further interpret model behavior and assess the influence of individual features, Individual Conditional Expectation (ICE) plots and permutation-based feature importance (PFI) analyses were performed on the optimized models.

Figure 2 shows the impact-fractured surfaces of UHMWPE/NZ nanocomposites containing 1.5, 3, and 4.5 wt% NZ. The yellow arrows in these images indicate nanoparticle agglomerates, which become more noticeable at higher concentrations. One of the main factors influencing nanoparticle dispersion is the processing technique used. Melt mixing with a twin-screw extruder provides high shear forces that help distribute nanoparticles within the polymer matrix. The high shear environment breaks down nanoparticle clusters, allowing for better integration into the matrix. However, at higher nanoparticle concentrations, such as 4.5 wt% NZ (Fig. 2c), the viscosity of the mixture increases significantly. This increased viscosity restricts the free movement of nanoparticles, leading to greater particle-particle interactions, which in turn result in the formation of larger agglomerates. Thermodynamic factors also play a crucial role. At lower nanoparticle loadings (1.5 and 3 wt%), surface energy dynamics favor a more dispersed state due to the optimization of the system’s free energy. However, as the concentration increases to 4.5 wt%, the likelihood of particle-particle interactions rises, causing aggregation. The mechanical implications of nanoparticle dispersion are also significant. Uniform distribution ensures that the applied load is evenly dispersed across the polymer matrix, as mentioned in reference [42]. This even load distribution improves the material’s energy absorption capacity, increasing the energy required for deformation. In contrast, when agglomeration occurs, stress concentrations develop at the aggregation sites, potentially leading to failure under mechanical stress. This even load distribution improves the material’s energy absorption capacity, increasing the energy required for deformation. In contrast, when agglomeration occurs, stress concentrations develop at the aggregation sites, potentially leading to failure under mechanical stress.

FTIR analysis was conducted to investigate the chemical composition and evaluate the interactions between zeolite nanoparticles and the UHMWPE matrix. Figure 3 displays the FTIR spectra of pure UHMWPE and UHMWPE–zeolite nanocomposites, highlighting the relevant absorption bands. The spectrum of pure UHMWPE shows characteristic peaks at 1463 cm⁻¹ and 1361 cm⁻¹, corresponding to the bending vibrations of C-H bonds in methylene (-CH₂-) and methyl (-CH₃) groups, respectively. A prominent peak at 719 cm⁻¹, attributed to the rocking vibration of C–H bonds within the crystalline structure, further confirms the presence of UHMWPE in its crystalline phase.

According to Fig. 3, the incorporation of NZ particles led to noticeable changes in the FTIR spectrum, suggesting the formation of interactions between the nanoparticles and the UHMWPE matrix. One prominent change is the appearance of a new band around 1096 cm⁻¹, attributed to the stretching vibrations of Si–O–Si and Al–O–Si bonds in the zeolite framework, confirming the presence of the inorganic phase within the composite. Another notable change is the emergence of a weak band near 555 cm⁻¹, corresponding to the bending vibrations of Si–O bonds, further supporting the successful integration of zeolite nanoparticles into the polymer matrix.

Furthermore, the increased intensity of common absorption peaks in the zeolite-containing samples indicates the presence of strong interactions between UHMWPE and the zeolite nanoparticles. This enhancement can be attributed to changes in the electron density of functional groups, influenced by the presence of nanoparticles and the higher concentration of active sites within the polymer matrix. The physical interactions between UHMWPE and zeolite led to notable variations in the intensity of characteristic FTIR bands, implying that the nanoparticles were well-dispersed and actively engaged with the polymer chains. These structural alterations are expected to directly influence the mechanical and thermal performance of the resulting nanocomposites.

Nanoparticle size distribution characteristics were obtained using the proposed sequential object detection technique, as detailed in Fig. 4. This technique encompasses noise reduction, clustering-based segmentation, morphological operations, and the final isolation of nanoparticles. Nanoparticle diameters were measured using processed SEM images, and their sizes were further predicted using the RF regression model. The results of the nanoparticle size distribution analysis, summarized in Table 1, reveal that the NZ content significantly influences the distribution characteristics. With increasing NZ concentration, noticeable shifts are observed in the minimum, mean, and maximum particle diameters. These changes are primarily attributed to variations in dispersion behavior at different loading levels. Higher NZ content tends to reduce dispersion uniformity, promoting the formation of larger agglomerates. Consequently, this clustering effect skews the size distribution, leading to increased values for key statistical parameters such as mean and maximum particle diameters. Higher NZ content tends to reduce dispersion uniformity, promoting the formation of larger agglomerates. Consequently, this clustering effect skews the size distribution, leading to increased values for key statistical parameters such as mean and maximum particle diameters.

Figure 4 presents the Weibull distribution analysis of nanoparticle diameter and area at NZ concentrations of 1.5, 3, and 4.5 wt%, illustrating the impact of increasing NZ content on particle size and distribution. As the NZ concentration increases from 1.5% to 4.5%, a noticeable shift toward larger particle sizes is observed. At 1.5 wt%, the highest particle density falls within the 50–70 nm range, with a right-skewed distribution indicating a gradual decline in frequency as particle diameter increases. The corresponding area distribution exhibits an exponential decay, with most particles having areas below 0.01 μm², suggesting a predominance of small, well-dispersed particles. At 3 wt%, the peak of the diameter distribution shifts to 80–100 nm, indicating the formation of larger particles. The extended right tail of the distribution suggests increased variability and the presence of larger aggregates. A similar trend is observed in the area distribution, where the tail broadens, reflecting the emergence of particles with larger surface areas. At the highest concentration (4.5 wt%), the diameter distribution further shifts to 100–120 nm, accompanied by a more pronounced right tail, indicating greater heterogeneity likely due to nanoparticle aggregation or coalescence. The area distribution also extends significantly, with some particles reaching up to 0.2 μm², confirming the formation of substantially larger structures at elevated NZ loadings.

Figure 5 illustrates the Weibull distribution analysis across different NZ concentrations, revealing a clear trend of increasing particle size and area with higher weight percentages. This behavior is primarily attributed to enhanced nanoparticle aggregation and coalescence, driven by the greater availability and proximity of NZ particles at elevated loadings. These observations are particularly significant for material optimization, as particle size distribution critically influences the microstructural uniformity and, consequently, the mechanical and functional performance of the resulting nanocomposites.

The nanoparticle dispersion characteristics were quantitatively evaluated using the NSI, a robust metric that simultaneously characterizes both the polydispersity and distribution asymmetry of nanoparticle sizes. The NSI analysis was performed on the pre-determined size parameters (\(\:{D}_{min}\), \(\:{D}_{ave}\), \(\:{D}_{max}\)), formulated as: 

The first term in Eq. (1) represents a normalized measure of the particle size distribution width, quantifying the relative span of diameters present in the system. The second term serves as an asymmetry correction factor that amplifies the index when the \(\:{D}_{ave}\) deviates from the distribution’s midpoint. This dual-component formulation provides enhanced discrimination between dispersion states compared to conventional metrics, as it simultaneously captures both the breadth and skewness of the size distribution. In the current study, the NSI proved particularly effective at differentiating the dispersion characteristics of UHMWPE composites containing varying nanoparticle loadings (1.5–4.5 NZ), where traditional measures failed to adequately reflect the observed differences in aggregation behavior.

Table 1 presents the NSI quantification of nanoparticle dispersion in UHMWPE composites. The analysis reveals three distinct dispersion regimes: (1) moderate polydispersity in the 1.5 NZ composite (NSI = 5.04), (2) optimized dispersion in the 3 NZ formulation (NSI = 4.13), and (3) significant aggregation in the 4.5 NZ system (NSI = 6.40). The non-linear progression of NSI values suggests a critical nanoparticle loading threshold near 3 NZ, evidenced by the 18% improvement in dispersion quality from 1.5 NZ to 3 NZ compared to the subsequent 55% deterioration at higher loading. This trend indicates that while the 3 NZ loading approaches the optimal stabilization capacity of the polymer matrix, exceeding this concentration leads to predominant nanoparticle aggregation. The NSI quantification thus identifies 3 NZ as the optimal loading for balanced dispersion, whereas the 4.5 NZ composite demonstrates compromised dispersion characteristics due to excessive particle clustering. A lower NSI value indicates a narrower particle size distribution and improved dispersion homogeneity, which is expected to enhance interfacial interactions and contribute positively to the viscoelastic response of the nanocomposites.

Figures 6, 7 and 8 illustrate the dynamic mechanical and thermal behavior of pure UHMWPE and its NZ-reinforced nanocomposites, as characterized by the storage modulus (\(E^{\prime}\)), loss modulus (\(E^{\prime\prime}\)), and damping factor (\(tan\:\delta\)). Figure 6 presents the variation of \(E^{\prime}\) as a function of temperature (− 100 °C to 150 °C) under frequencies of 1 and 10 Hz. Evidently, the inclusion of NZ results in a notable enhancement of \(E^{\prime}\) across the studied temperature range, particularly at sub-ambient temperatures. This improvement is primarily attributed to the stiffening effect imparted by the rigid zeolite nanoparticles, which act as reinforcing agents within the polymer matrix. The nanoparticles restrict the mobility of polymer chains by creating a more constrained molecular environment, thereby reducing segmental motion and enhancing the elastic response of the material. Moreover, the strong interfacial adhesion between the UHMWPE matrix and the NZ particles contributes to effective stress transfer and further limits chain relaxation. The presence of nanoparticles also reduces the free volume within the polymer, hindering molecular rearrangement under mechanical loading. Collectively, these factors result in an overall increase in stiffness, as evidenced by the elevated storage modulus values.

Furthermore, the temperature-dependent trends reveal distinct transition regions within the material. The sharp decline in \(E^{\prime}\) at lower temperatures corresponds to the α-relaxation, typically associated with the glass transition, where molecular mobility increases significantly. At elevated temperatures, a secondary reduction in modulus is observed, likely attributed to segmental motions within the crystalline domains of UHMWPE. Notably, the incorporation of zeolite nanoparticles causes a slight shift in both transitions, indicating their contribution to improved thermal and mechanical stability of the nanocomposite system. The slight shift of these relaxation regions toward higher temperatures in the NZ-filled systems suggests restricted molecular mobility due to polymer–filler interactions, indicating that nano-zeolite acts as an effective thermal stabilizer by delaying chain relaxation processes.

The effect of frequency on \(E^{\prime}\) is evident when comparing Fig. 6a (1 Hz) and Fig. 6b (10 Hz). Across the entire temperature range, the storage modulus at 10 Hz is consistently higher than at 1 Hz. This trend reflects the time-dependent viscoelastic nature of polymers: at higher frequencies, polymer chains have less time to reorient or relax, leading to a stiffer, more elastic response and consequently a higher modulus. The increased stiffness observed at 10 Hz indicates the enhanced rigidity of the UHMWPE matrix under rapid oscillatory loading, further confirming the frequency-dependent mechanical behavior of the nanocomposite system. This frequency-dependent stiffening behavior highlights the ability of the UHMWPE/NZ nanocomposites to sustain higher dynamic loads without significant viscoelastic softening, which is critical for applications involving repetitive or impact-type loading conditions.

The loss modulus reflects the energy dissipated as heat during cyclic deformation and serves as a measure of the material’s viscous behavior or the irreversible energy loss per oscillatory cycle. This parameter is particularly critical for applications requiring energy absorption, damping, and vibration mitigation, such as load-bearing prosthetic components. Figure 7 illustrates the loss modulus of various samples as a function of temperature at frequencies of 1 Hz and 10 Hz. Two distinct peaks are observed across the temperature range: the first, more prominent peak occurs at low temperatures (approximately − 120 °C to − 100 °C), and the second appears at elevated temperatures (around 50 °C to 100 °C). These peaks correspond to molecular relaxation phenomena within the UHMWPE matrix.

According to Fig. 7, the incorporation of NZ significantly influences the loss modulus. At both frequencies, increasing NZ content results in higher peak values, indicating enhanced energy dissipation. This enhancement is attributed to strong interfacial interactions between the UHMWPE matrix and the NZ particles, which increase internal friction at the polymer–nanoparticle boundaries, thereby promoting greater heat generation during deformation. These findings suggest successful integration of NZ into the polymer matrix, as evidenced by increased frictional energy dissipation. The increase in loss modulus reflects not only enhanced internal friction at the polymer–filler interface but also the effective hindrance of segmental chain motions, which collectively improve the material’s capacity for damping and vibration energy dissipation under cyclic loading. As the NZ content increases, the number of local polymer chain restriction sites also rises, leading to higher internal friction and, consequently, greater heat generation within the nanocomposite samples. Overall, NZ alters the viscoelastic response by simultaneously restricting polymer chain mobility—leading to an increase in E′—and elevating internal friction—reflected in the increased E″.

A notable observation in Fig. 7 is the presence of an initial shoulder-like feature in the loss modulus curves within the temperature range of approximately − 150 °C to − 120 °C, particularly evident in the UHMWPE/3NZ and UHMWPE/4.5NZ samples. This feature is more prominent at 1 Hz but becomes less distinct at 10 Hz, suggesting it is associated with a low-temperature molecular relaxation process that is frequency-sensitive. The diminished response at 10 Hz indicates that these localized chain motions cannot effectively respond to the shorter oscillation periods at higher frequencies, resulting in reduced energy dissipation. When comparing the data at 1 Hz and 10 Hz, it is evident that the overall peak intensity of the loss modulus increases with frequency. This behavior is characteristic of viscoelastic materials, where higher frequencies lead to greater energy dissipation due to faster molecular rearrangements. Furthermore, a slight shift of the peak positions toward higher temperatures at 10 Hz is observed, consistent with the time–temperature superposition principle. This indicates that higher thermal energy is required to activate molecular relaxation processes at elevated frequencies.

The dissipation factor (tan δ) represents the ratio of energy lost to energy stored in a material under dynamic loading, reflecting the balance between the segment of the polymer network that undergoes reversible deformation and the part that remains elastic and unchanged. In the context of cyclic or intermittent loading, this energy loss is commonly referred to as damping. Therefore, the damping performance, when considered relative to the material’s stiffness, provides a comprehensive measure of its viscoelastic behavior. The increase in loss modulus reflects not only enhanced internal friction at the polymer–filler interface but also the effective hindrance of segmental chain motions, which collectively improve the material’s capacity for damping and vibration energy dissipation under cyclic loading. Figure 8 illustrates the temperature-dependent variation of tan δ at frequencies of 1 Hz and 10 Hz, highlighting how energy dissipation characteristics evolve with temperature and frequency. According to Fig. 8, the incorporation of nano-zeolite leads to an overall increase in tan δ across the whole temperature range. This enhancement can be attributed to strong interfacial interactions between the polymer matrix and the nanoparticles, which facilitate greater energy dissipation. Additionally, the rigid nature of the nanoparticles restricts polymer chain mobility, resulting in broader and more pronounced relaxation peaks.

A comparison of the damping behavior at 1 Hz and 10 Hz further emphasizes the frequency-dependent viscoelastic response of the nanocomposites. As the frequency increases, the relaxation peaks in the tan δ curves shift toward higher temperatures, in accordance with the time–temperature superposition principle. This shift reflects the need for greater thermal activation to facilitate molecular motion at higher frequencies. Furthermore, the magnitude of tan δ decreases at 10 Hz compared to 1 Hz, due to the limited time available for polymer chain segments to rearrange, resulting in reduced energy dissipation. The shorter deformation time at higher frequencies also contributes to the suppression of tan δ peaks, as evident by the notably diminished relaxation peak around 50 °C at 10 Hz compared to the more pronounced peak observed at 1 Hz. Importantly, the reinforcing effect of nano-zeolite is evident at both frequencies, indicating that the presence of nanoparticles consistently modifies the thermomechanical behavior of the UHMWPE matrix under varying dynamic conditions.

The glass transition temperature (\(\:{T}_{g}\)) can be determined from the tan δ curves, where it is marked by the primary peak, indicating the transition from a glassy to a rubbery state. In pure UHMWPE, \(\:{T}_{g}\) appears at a relatively lower temperature; however, the incorporation of nano-zeolite leads to a noticeable shift of \(\:{T}_{g}\) toward higher temperatures. This upward shift is attributed to enhanced physical interactions between the zeolite nanoparticles and the polymer chains, which restrict the mobility of the amorphous regions. As a result, a higher thermal energy input is needed to activate segmental motion within the matrix. Furthermore, the upward shift in \(\:{T}_{g}\) due to NZ incorporation indicates enhanced thermal and mechanical stability of the nanocomposite, implying that the reinforced matrix can better resist softening and maintain functional integrity under elevated temperature and high-frequency loading conditions. In addition, increasing the frequency from 1 Hz to 10 Hz causes a further elevation in \(\:{T}_{g}\), consistent with the known frequency dependence of the glass transition. At higher frequencies, less time is available for molecular rearrangement, thus requiring greater thermal energy to initiate relaxation processes.

To effectively model the complex relationships between input features and the viscoelastic properties, an ensemble learning model was constructed based on the Least-Squares Boosting (LSBoost) algorithm. This approach iteratively builds a strong regression model by combining a sequence of weak regression learners, where each subsequent learner focuses on minimizing the residual errors of the preceding ensemble. Mathematically, the final model will be a weighted sum of these individual learners [43].

The data for this study was prepared to ensure consistency and reliability in the modeling process. The dataset includes inputs for temperature, weight fraction, NSI, frequency, and corresponding output responses such as the elastic modulus (\(E^{\prime}\)), loss modulus (\(E^{\prime\prime}\)), and dissipation factor (\(\:{tan}\delta\:\)). In this study, the data preparation process included the normalization of input variables to ensure they were on a comparable scale, which is particularly important for improving the performance and convergence of machine learning models. Normalization was applied to each feature independently using the following formulation:

where \(X\) represents the raw value of the input feature, \({\mu}_{X}\) is the mean of the input feature values, \({\sigma}_{X}\) is the standard deviation of the input feature values, and \({X}_{norm}\)​ is the normalized value of the feature. Input normalization standardizes the range of input variables, effectively eliminating scale differences between features. This ensures that no single feature dominates the learning process due to differences in scale, thereby improving model training efficiency. The normalization was applied to all input variables to ensure consistency across the dataset. However, it is important to note that not all temperature data were included in the study. Specifically, only a subset of temperature values, ranging from − 150 °C to 100 °C in 25 °C intervals, was selected for the temperature input variable.

The mechanical and viscoelastic properties of materials used in prosthetic limbs play a crucial role in their performance and user comfort. These parameters are directly related to stiffness, energy absorption capability, and vibration damping in prosthetic limbs, which are critical for improving their functionality. The storage modulus represents the stiffness of the material under dynamic loading. The observed increase in E′ in UHMWPE/NZ nanocomposites indicates enhanced mechanical strength and structural stability. This is essential for prosthetic limbs, as higher stiffness allows for better load-bearing capacity, preventing unwanted deformations and improving durability. Furthermore, the increased storage modulus with higher nanoparticle content provides an opportunity to optimize prosthetic stiffness, ensuring better structural integrity and mechanical reliability.

The loss modulus reflects the amount of energy dissipated during dynamic loading, and its increase in UHMWPE reinforced with NZ suggests improved energy absorption capabilities. This property is particularly important for prosthetic limbs, as it contributes to impact attenuation, reducing shock transmission to the user and enhancing comfort. Specifically, in the body temperature range (25–37 °C), the increased loss modulus in the 3% and 4.5% NZ samples indicates enhanced energy dissipation, which helps minimize the forces transmitted to the user during movement. The damping ratio, which represents the ratio of dissipated to stored energy, plays a significant role in vibration reduction within prosthetics. The higher damping ratio in NZ-reinforced nanocomposites compared to pure UHMWPE demonstrates their superior vibration-damping performance. At body temperature, this characteristic leads to reduced vibration transmission through the prosthetic limb, increasing user comfort. This effect is particularly valuable for daily activities such as walking and running, as it helps decrease user fatigue and long-term mechanical wear.

Increasing the frequency resulted in a decrease in the damping ratio, indicating a reduction in vibration absorption capability under more dynamic conditions such as running. At lower frequencies (1 Hz), which simulate regular walking movements, the damping ratio is higher, showing the ability of these nanocomposites to effectively absorb impact energy when the foot strikes the ground. Conversely, at 10 Hz, the reduced damping ratio suggests a diminished ability to dissipate vibrations during faster movements, likely due to structural changes in the material’s response to higher excitation rates. The results indicate that the addition of NZ to UHMWPE enhances stiffness, energy absorption, and vibration damping simultaneously. These improvements contribute to the increased stability and longevity of prosthetic limbs while enhancing comfort and performance. Therefore, UHMWPE/NZ nanocomposites can be considered a promising material for optimizing prosthetic limb functionality, offering a novel approach to improving their overall mechanical behavior and user experience.