In this study, several simple equations are suggested to investigate the effects of size and density on the number, surface area, stiffening efficiency, and specific surface area of nanoparticles in polymer nanocomposites. In addition, the roles of nanoparticle size and interphase thickness in the interfacial/interphase properties and tensile strength of nanocomposites are explained by various equations. The aggregates/agglomerates of nanoparticles are also assumed as large particles in nanocomposites, and their influences on the nanoparticle characteristics, interface/interphase properties, and tensile strength are discussed. The small size advantageously affects the number, surface area, stiffening efficiency, and specific surface area of nanoparticles. Only 2 g of isolated and well-dispersed nanoparticles with radius of 10 nm (R = 10 nm) and density of 2 g/cm3 produce the significant interfacial area of 250 m2 with polymer matrix. Moreover, only a thick interphase cannot produce high interfacial/interphase parameters and significant mechanical properties in nanocomposites because the filler size and aggregates/agglomerates also control these terms. It is found that a thick interphase (t = 25 nm) surrounding the big nanoparticles (R = 50 nm) only improves the B interphase parameter to about 4, while B = 13 is obtained by the smallest nanoparticles and the thickest interphase.
Response surface method of experimental design was applied to optimize the mechanical properties of polypropylene (PP)/nanoclay/CaCO 3 hybrid ternary nanocomposite using three different levels of melt flow index (MFI) of PP, nanoclay, and CaCO 3 contents. The samples were prepared by melt mixing in a lab scale corotating twin screw extruder. The main effect of each parameter on the tensile modulus, tensile strength, and impact strength was extensively discussed. The structure of obtained nanocomposite was studied using X-ray diffraction (XRD), atomic force microscopy (AFM), and scanning electron microscopy (SEM) techniques. Tensile modulus and impact resistance of prepared ternary nanocomposite were correlated to considered parameters using a second-order polynomial model. Also, the optimum values of studied variables were determined using contour plots. The obtained results show that increasing the nanoclay and CaCO 3 contents improve the tensile modulus up to 45%, whereas the optimum value of impact strength, about 54%, is achieved at low concentrations of nanoclay (2 wt %) and CaCO 3 (8 wt %).
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