Molecular dynamics simulation and experimental study on the mechanical properties of PET nanocomposites filled with CaCO₃, SiO₂, and POE-g-GMA

2.1 Materials

PET with a characteristic viscosity of 0.83 dl·g⁻¹ was purchased from Sanfame Co., Ltd (China). CaCO₃ nanoparticles (CCU-200) were supplied by HUANA New Materials Co., Ltd (China). POE-g-GMA was provided by Fine-Blend Co., Ltd (China). SiO₂ nanoparticles with a specific surface area of 195 m²·g⁻¹ were supplied by Beesley Co., Ltd (China).

2.2 Nanocomposites preparation

PET, CaCO₃, and SiO₂ were placed in a vacuum drying oven and dried at 130°C. Subsequently, both binary composites containing 2 wt% of CaCO₃ and SiO₂, as well as ternary PET nanocomposites containing 10 wt% of POE-g-GMA, respectively, were thoroughly and homogeneously mixed. Afterward, the mixture was melt extruded in a twin-screw extruder at temperatures of 250°C, 255°C, 260°C, and 265°C along the extruder from barrel to head. After the extrusion process, tensile and impact samples were prepared by injection molding, with the barrel temperature of the injection molding machine set at 270°C.

2.3 Characterization

The notched impact strength of PET and its composites was tested using an XBL cantilever beam impact tester (Shanghai, China). The tensile properties of the specimens were measured by a Zwick/Roell Z005 (Germany) material testing machine at a rate of 10 mm·min⁻¹. The bulk modulus, shear modulus, and Young’s modulus of PET and its composites were measured using the universal mechanical testing machine Instron 5982 (USA). Fourier transform infrared spectroscopy (FTIR) was used to characterize the functional groups and interaction properties of materials. The FTIR spectra were recorded using the Thermo Scientific Nicolet iS20 FTIR spectrometer (USA) with 32 scans and a resolution of 4 cm⁻¹. The morphology of the nanoparticles was observed using a transmission electron microscope (TEM) model JEOL JEM-2100Plus (Japan). The morphology of the impact fracture was observed using a Sigma 300 (Germany) scanning electron microscope (SEM), and before testing, a thin layer of gold was sprayed on the samples. X-ray diffraction (XRD) was employed to characterize the crystal structure using Cu Kα radiation (λ _CuKα = 1.5418 Å) on a Rigaku Ultima IV (Tokyo, Japan) X-ray diffractometer, the voltage was set at 40 KV, and the scanning rate was 2°·min⁻¹. The material’s melting and crystallization processes were investigated using differential thermal scanning (DSC) with a TA instruments-Model 25 (USA) differential thermal scanner at a heating rate of 10°C·min⁻¹. The samples were first heated from 25°C to 280°C and then cooled back to 25°C, subsequently, heated up to 280°C and cooled down again.

3.1 MD method

All simulations were performed by the molecular simulation engine Materials Studio 6.0 software (35). During the geometry optimization and MD relaxation phases, the COMPASS force field was employed, which is based on ab initio calculations for condensed phase optimization (18,19). The potential function used in this force field consists of both valence and non-bonding interaction terms. The potential energy of the system is represented by Eq. 1, where the valence terms are composed of E _b , E _θ , E _φ , and E _χ , denoting the bonding (b), angle (θ), torsion (φ), and out-of-plane angle (χ), respectively. Additionally, the cross-coupling terms consist of E _bb′ , E _bθ , E _bφ , E _θθ′ , and E _θθ′φ , and the non-bonding terms include the van der Waals interaction term (E _vdw) (20) and the Coulomb term (E _elec), which accounts for electrostatic interactions (21). These terms are represented by Eqs 2–4.

Verlet’s algorithm (22) is employed to integrate the molecular equations of motion during the simulation. The position of the particle at time t is represented by r _i (t), and the position of the particle at time t + δt is expressed using Eq. 5.

During the equilibrium process of the model, NPT (isothermal and isobaric ensemble) and NVT (canonical ensemble) ensembles were employed. The temperature was controlled using the Nose thermostat (23), and the pressure was controlled using the Berendsen pressure control algorithm (24).

3.2 Simulation details for PET nanocomposites

The initial step involved constructing CaCO₃ and SiO₂ crystal models based on the structures of calcite and quartz crystal cells. The lattice parameters were set as follows: a = b = 4.99 Å, c = 17.061 Å, α = β = 90°, and γ = 120° for CaCO₃, and a = b = 4.91 Å, c = 5.402 Å, α = β = 90°, and γ = 120° for SiO₂ (25,26), as shown in Figure 1(a) and (c). Next geometrically optimized model of spherical CaCO₃ and hydroxylated-silica nanoclusters with a radius of 5 Å were established, as shown in Figure 1(b) and (d). The geometry optimization was conducted using the Smart method, with a maximum iteration of 50,000 and a cutoff radius of 12.5 Å for non-bonded interactions. Subsequent processes involving the construction of packing model and equilibrium utilized an atom-based summation method for electrostatic and van der Waals interaction.

Figure 1

Optimized spherical nanocluster of (a) crystal structure of calcite, (b) CaCO₃, (c) crystal structure of SiO₂, and (d) hydroxylated SiO₂.

The geometrically optimized structural model of PET with a repeat unit of 15 was constructed based on the molecular formula, as depicted in Figure 2(a). To illustrate the molecular structure of POE-g-GMA, the model of POE was built first, comprising two monomers, ethylene, and 1-octene, with the mass fraction of 1-octene accounting for 30%, as displayed in Figure 2(b). The potential chemical reaction pathways for grafting GMA onto the POE molecule are illustrated in Figure 3(a), and the chemical bonds and C atoms at the grafting site were labeled in yellow, as shown in Figure 3(b).

Figure 2

Optimized molecular model of (a) PET chains and (b) POE.

Figure 3

(a) Possible chemical grafting reaction of POE and GMA and (b) optimized molecular model of POE-g-GMA chains.

Subsequently, the polymer molecular chains were packed around the nanoparticles, periodic boxes of PET/CaCO₃ and PET/SiO₂ with a nanoparticle concentration of 2 wt% were constructed, respectively. Additionally, periodic boxes containing 10% POE-g-GMA were also constructed. This step was carried out in the Amorphous Cell Packing module, defining an initial density of 0.1 g·cm⁻³, as shown in Figure 4(a).

Figure 4

(a) Initial structure of PET/POE-g-GMA/SiO₂ nanocomposite and (b) equilibrium structure of PET/POE-g-GMA/SiO₂ nanocomposite.

After geometry optimization, the dynamic relaxation was conducted for 100 ps in the NPT ensemble at a pressure of 0.1 GPa. To enable sufficient movement and relaxation of the polymer chain segments, an annealing process was carried out in the NVT ensemble. The temperature was raised from 298 to 500 K and decreased back to 298 K in steps of 1 fs. Subsequently, a relaxation process was conducted in the NVT ensemble for 100 ps, resulting in a final configuration where both temperature and energy reached an equilibrium state, as illustrated in Figure 4(b).

3.3 Calculation details of mechanical properties

For a classical mechanical system containing a fixed number of atoms N, the equilibrium stress tensor can be obtained from the virial theorem (27), which is expressed as Eq. 6.

in which V represents the volume of the system, m denotes the mass, P _i ^α is the momentum α component of particle i located at position r _i , and F _ij is the interaction force between particle i and particle j. The mechanical properties of the nanocomposites are calculated using the Forcite module. The elastic stiffness constant C _ij is obtained by applying a constant strain. Eqs 7 and 8 express the Lame constant.

For isotropic materials, the mechanical property parameters such as bulk modulus K, shear modulus G, and Young’s modulus E are calculated as shown in Eq. 9.

4.1 Crystallization and melting behavior

The crystalline behavior of PET and its nanocomposites was analyzed using DSC. As shown in Figure 5(a) and Table 1, the addition of SiO₂ and CaCO₃ resulted in an increase in the glass transition temperature (T _g), crystallization temperature (T _c), and crystallinity (X _c) of the nanocomposites compared to pure PET. The increase in T _c and X _c can be attributed to the nanoparticles acting as effective nucleating agents in the PET matrix. The presence of more nucleation sites promoted the growth of PET crystals, and the significant enhancement of the crystallization peaks was also related to this phenomenon. Furthermore, the nanoparticles hindered the free movement of PET molecular chains at lower temperatures, resulting in a higher T _g. However, with the addition of POE-g-GMA, the crystallinity of both nanocomposites decreased, which may be attributed to the generation of an amorphous mixed phase due to the blending of the elastomer and PET. This mixed phase inhibited the crystallization process and interfered with the regular arrangement of the PET chains, resulting in a decrease in the crystallinity of PET.

Figure 5

DSC curves of PET nanocomposites: (a) the first cooling cycle and (b) the second heating run.

For the melting behavior, it can be observed from Figure 5(b) that two melting peaks appeared in all curves except for pure PET. This is a consequence of the material initially forming partially crystallized lamellae with incomplete structures during the cooling process, as the temperature rises over a sufficient duration, these crystals transform into more well-structured crystals (28). Within the blend system, two crystal forms are present: folded-chain crystals and partially elongated-chain crystals (29). Furthermore, the decrease in the melting temperature (T _m) can be explained by the mutual constraints of PET and POE-g-GMA chains. There are reactions occurring between the polymer groups. Additionally, the presence of nanofillers disrupts crystal growth, leading to a reduction in the crystallinity of PET within the blend.

The XRD patterns presented in Figure 6 also explained the crystalline behavior. The diffraction peak of pure PET appeared broad around 2θ = 21.5°, corresponding to a crystallographic index of (−1 1 1). With the addition of CaCO₃, the diffraction peaks in the binary and ternary composite systems were significantly enhanced, appearing at approximately 23.0°, 29.4°, 36°, 39.3°, 43.1°, 47.1°, and 48.5°, corresponding to the crystalline surface indices of (0 1 2), (1 0 4), (1 1 0), (1 1 3), (2 0 2), (0 2 4), and (1 1 6), respectively. However, the diffraction peaks observed in the PET composite system containing only CaCO₃ were sharper than those in the ternary system containing elastomer, indicating that CaCO₃ played a favorable role in promoting PET crystallization. For the composite system containing SiO₂, diffraction peaks corresponding to the crystal surface indices of (1 1 0), (1 0 2), and (2 0 1) were observed at approximately 16.8°, 23.8°, and 26.0°, respectively. The diffraction peaks were not as prominent as those in the system containing CaCO₃, probably because PET/CaCO₃ composites exhibit higher crystallinity. Furthermore, CaCO₃ contains heavier calcium elements with higher atomic scattering factors (30), resulting in relatively higher XRD intensities.

Figure 6

XRD patterns of PET nanocomposites.

4.2 Morphology of nanocomposites

The TEM images of CaCO₃ and SiO₂ nanoparticles are shown in Figure 7, reflecting the morphology and size distribution of the particles. The impact fracture morphology of PET, as well as its binary and ternary blends, was observed by SEM. Figure 8(a) presents the fracture surface of pure PET, which appeared relatively flat and smooth, exhibiting a brittle fracture morphology. With the incorporation of 2 wt% of CaCO₃ and SiO₂, respectively, the nanoparticles were uniformly dispersed within the polymer matrix, resulting in a flat fracture surface with a small number of cracks, which still exhibited brittle fracture characteristics, as shown in Figure 8(b) and (c). However, with the introduction of POE-g-GMA into the PET nano-binary system, the fracture surface became rougher and exhibited deformation. Stacked layer structure and tear-like ripples appeared. The material overcame the crack extension by absorbing a large amount of energy, and the matrix underwent shear yielding. As a result, the fracture morphology transformed from brittle fracture to tough fracture as illustrated in Figure 8(d) and (e) (31). Figure 8(f) shows the magnified POE-g-GMA elastomer morphology, observed to tear but not detach, owing to its strong interfacial bonding with the PET matrix. The elastomer particles effectively absorbed impact energy, reducing stress concentration during the tearing process and significantly enhancing the toughness of the polymer composites.

Figure 7

TEM images of (a) CaCO₃ nanoparticles and (b) SiO₂ nanoparticles.

Figure 8

SEM micrographs of the impact fracture surface of (a) PET and (b) PET/CaCO₃, (c) PET/SiO₂, (d) PET/POE-g-GMA/CaCO₃, (e) PET/POE-g-GMA/SiO₂, and (f) magnified section of (e).

4.3 Analysis of interactions in PET nanocomposites

The curves illustrating the evolution of energy and temperature over time for the initial model in the NPT simulations are depicted in Figure 9. Towards the end of the NPT run, both values exhibited fluctuations around a constant value, indicating that the system had reached an initial equilibrium state. After all simulations were completed, the distribution density of PET molecules near the nanoparticles was analyzed. The radial distribution function (RDF) of the PET/CaCO₃ system is illustrated in Figure 10(a). A higher concentration of PET around the nano-CaCO₃ can be observed, suggesting that PET exhibited a high ligand number density and formed a good interaction with CaCO₃. The RDF showed significant peaks at r = 1.1 Å and r = 1.4 Å. Generally, peaks above 3.5 Å in RDF indicate van der Waals force interactions, while peaks below 3.5 Å primarily consist of hydrogen bonding interactions (26). When PET and nanoparticles were in contact, van der Waals forces and other interactions brought them closer and created interfacial adhesion. Figure 10(b) represents the RDF of CaCO₃ in the composite model around PET molecules, indicating the dispersion state of CaCO₃ particles located at the center of the centroid in the composite system. As the distance between CaCO₃ and the polymer surface increased, the density distribution of PET molecules increased, especially at the peak positions. These peaks indicated a higher presence of PET molecules in these regions, the average distance between nanoparticles and molecules was closer, indicating good dispersion of CaCO₃ particles. Beyond r > 4 Å, no distinct peaks were observed, indicating weak van der Waals interactions between CaCO₃ particles and polymer functional groups, indicating poor dispersion of the particles.

Figure 9

PET/CaCO₃ nanocomposite during NPT dynamics of (a) energy evolution and (b) temperature evolution.

Figure 10

RDF of (a) PET/CaCO₃ nanocomposite and (b) CaCO₃ around PET molecular chains in the composites.

Figure 11 displays the FTIR of PET and its composites, explaining the chemical bonding between nanoparticles and PET. In PET, the stretching vibrations of C═O, C–O, and C–O–C bonds appeared at 1,732, 1,242, and 1,060 cm⁻¹, respectively. The characteristic peak at 3,631 cm⁻¹ corresponded to the O–H stretching between hydroxyl groups in PET chains (5,32). Upon the addition of nano CaCO₃, a stretching vibration of CO₃ ²⁻ appeared at 1,452 cm⁻¹ (33). The enhancement of the peak at 1,712 cm⁻¹ might be related to physical adsorption interactions between CaCO₃ and PET, causing a change in the vibration frequency of C═O. After adding SiO₂ particles, no significant change in peak intensity was observed compared to pure PET. However, an absorption peak at 802 cm⁻¹, corresponded to the stretching vibration of Si–O bonds. The diffraction peak intensity of PET/POE-g-GMA/CaCO₃ and PET/POE-g-GMA/SiO₂ significantly decreased compared to pure PET. This reduction might be due to the disruption of PET molecular chains’ integrity upon the addition of the elastomer, leading to a decrease in crystallinity. Moreover, in PET/POE-g-GMA/SiO₂, strong hydrogen bonding interactions occurred between the free hydroxyl groups on the SiO₂ surface and the carboxyl groups in PET, reducing the hydroxyl content and contributing to the weakened diffraction peak intensity. These interactions contributed to improving the mechanical properties of the composites.

Figure 11

FTIR spectra of PET nanocomposites.

4.4 Mechanical properties

The mechanical properties of PET and its binary and ternary composites obtained from experiments and MD simulations are shown in Table 2 and Figure 12, respectively. The experimental and MD results indicate that compared to pure PET, the tensile strength, bulk modulus (K), shear modulus (G), and Young’s modulus (E) of PET/CaCO₃ and PET/SiO₂ nanocomposites were significantly improved. This improvement can be attributed to the favorable interaction and uniform dispersion of nanoparticles within the PET matrix. The reinforcement of CaCO₃ was more pronounced than that of SiO₂, with a maximal tensile strength reaching 55.1 MPa and a maximal Young’s modulus of 2.51 GPa. This enhancement is likely due to the higher crystallinity with the addition of CaCO₃, which contributed to the improvement of the polymer’s strength and stiffness. Additionally, the elongation at break and notched impact strength of both binary systems was reduced compared to pure PET, mainly due to the constraint imposed on the molecular chain activity of the polymer matrix by the rigid nanofillers (32).

Figure 12

Mechanical properties of PET nanocomposites by MD simulation.

The incorporation of POE-g-GMA into the ternary system exhibited a remarkable increase in both elongation at break and notched impact strength, surpassing those of pure PET and PET nano-binary composites, up to 29.3% and 6.3 kJ·m⁻², respectively. However, the tensile strength decreased compared to that of pure PET, and the elastic modulus was lower than that of the nano-binary system. This behavior can be attributed to the synergistic toughening effect of the soft elastomers within the matrix and the nanoparticles encapsulated around the elastomer (34). The blends underwent a brittle-tough transition from binary to ternary system, allowing the polymer molecular chains to move relatively easily and exhibit higher toughness. Although the rigidity and strength decreased compared to the binary system, the elastic modulus was higher than that of pure PET, and the decrease in tensile strength was not significant, indicating that the rigid nanoparticles served as an advantageous reinforcing phase in the matrix.