Tensile modulus of polymer nanocomposites

Abstract

Based on Takayanagi's two‐phase model, a three‐phase model including the matrix, interfacial region, and fillers is proposed to calculate the tensile modulus of polymer nanocomposites (Ec). In this model, fillers (sphere‐, cylinder‐ or plateshape) are randomly distributed in a matrix. If the particulate size is in the range of nanometers, the interfacial region will play an important role in the modulus of the composites. Important system parameters include the dispersed particle size (t), shape, thickness of the interfacial region (τ), particulate‐to‐matrix modulus ratio (Ed/Em), and a parameter (k) describing a linear gradient change in modulus between the matrix and the surface of particle on the modulus of nanocomposites (Ec). The effects of these parameters are discussed using theoretical calculation and nylon 6/montmorillonite nanocomposite experiments. The former three factors exhibit dominant influence on Ec. At a fixed volume fraction of the dispersed phase, smaller particles provide an increasing modulus for the resulting composite, as compared to the larger one because the interfacial region greatly affects Ec. Moreover, since the size of fillers is in the scale of micrometers, the influence of interfacial region is neglected and the deduced equation is reduced to Takayanagi's model. The curves predicted by the three‐phase model are in good agreement with experimental results. The percolation concept and theory are also applied to analyze and interpret the experimental results.

A review on the role of interface in mechanical, thermal, and electrical properties of polymer composites

“…However, Ji et al have theoretically proved that there is a critical size for fillers in nylon 6/montmorillonite nanocomposites, below which the filler size can affect the stiffness (Fig. 2) [41]. This phenomenon has been experimentally proved in separate studies [42,43].…”

Melt compounding of different grades polystyrene with organoclay. Part 3: Mechanical properties

“…For PNC the controlling parameters are: the size of dispersed particles (t c and c ), thickness of the interfacial region , filler-to-matrix modulus ratio E f /E m , and the parameter k. The parameter k represents the ultimate modulus ratio of the interphase to matrix, assuming a linear gradient change in modulus between the matrix and the surface of particle -the value k ϭ 12 has been arbitrarily chosen [32].…”

“…Ji et al [32] adopted the Takayanagi et al [29] two-phase model, expanding it into three phases: matrix, interphase, and filler particles randomly distributed in the matrix. These may be of any shape, viz.…”

“…The following values of equation parameters were used: E f ϭ 170 GPa [33], E m ϭ 3.4 GPa, t c ϭ 1 nm [34], and k ϭ 12 [32]. The volume fraction of clay in PNC was calculated assuming the matrix polymer and clay density equal 1040 and 2860 kg/m 3 , respectively.…”

Investigação da influência do processamento na dinâmica molecular de nanocompósitos de policarbonato e argila organofílica obtidos via intercalação por fusão

“…A desordem causada na organização cristalina da argila, devido à entrada das cadeias poliméricas em sua estrutura, aumenta ainda mais este espaçamento, podendo levar à esfoliação das lamelas (Figura 3) [1,2] . organofílica advêm da íntima interface polímero-carga proporcionada pela forte interação em escala nanométrica [8,[13][14][15][16][17] . O emprego de quantidades reduzidas dessas nanocargas sugere preservação das propriedades da matriz polimérica aliada ao ganho em certas características do nanomaterial sobre o polímero puro.…”