Modified Halpin-Tsai Equation for Clay-Reinforced Polymer Nanofiber

Abstract

In this paper, two sets of electrospun fibers—nylon-6 and montmorillonite (MMT)-reinforced nylon-6—are being investigated for their tensile modulus. Results show that a reduction of fiber diameter close to nano-scale range reveals increasing modulus due to greater alignment of polymeric molecules and increased influence of surface stresses as a result of increased surface-to-volume ratio. However, addition of MMT caused a reduction of modulus in spite its very high modulus. This anomalous phenomenon may well be attributed to the effect of small fiber radius for containing the MMT platelet's width. By expressing the matrix modulus as a function of fiber diameter and by introducing a proportionality constant, we obtained a semi-empirical micromechanical model within the framework of the Halpin-Tsai equation—hence the modified Halpin-Tsai model. The result suggests that the fibers be shrunk for increasing its modulus without reinforcement. However, for cases where fillers are required to fulfill non-mechanical purposes (such as medical purposes), the modified Halpin-Tsai model is useful for informing the designer of the threshold weight or volume fraction of the inclusion to maintain the modulus above the required level.