Modulus enhancement

To clarify whether the modulus enhancement of the nanocomposite foams was reasonable, Equation (9.7) proposed earlier by Kumar [66] was applied to estimate the relative moduli with various foam densities ... 

Tahir and Birley24 have considered the tangent modulus at intervals on the stress relaxation curve and compared it to the modulus of the initial loading curve to derive what they termed the Modulus Enhancement Factor, hence adding to the information which can be gained from a stress relaxation test. 

There is, however, a limit to the amount of stretch that can be given to a polymer because the phenomenon of necking can intervene and cause rupture of the fiber. In other words, in a polymeric fiber there is a limit to the modulus enhancement that can be obtained by subjecting it to an ever higher draw ratio. As we shall see in Chapter 4, this led to other means of obtaining high stiffness polymeric fibers such as aramid and polyethylene. 

Rowe, R.C. Modulus enhancement in pigmented tablet film coating formulations. Int. J. Pharm. 1983, 14, 355-359. 

Two questions remain, however why is the modulus enhancement, attributed primarily to these Interlocking loops, greater for the Ca and Sr lonomers than for the Ni, Zn, and Cd telechelics, and why is the stress-hardening behavior exhibited only by the telechelics neutralized with Ca and Ni Small-angle x-ray scattering (SAXS) and extended x-ray absorption fine structure (EXAFS) spectroscopy were employed to address these questions. 

Figures 20.4 and 20.6 show that both O and Af are important in determining the amount of reinforcement. The curves in Figure 20.4 are roughly S-shaped. Relatively little stiffening is expected for [E(filler)/E(matrix)]=50 at 0<0<0.05 for l

In order to elaborate the relationship between stoichiometric imbalance of the epoxy-amine system and its resulting elastic properties, a series of reference samples of well-defined concentration ratios r was investigated using dynamic mechanical analysis (DMA). A clear increase in the glassy epoxy modulus (as measured at 20 °C) with an increasing excess of epoxy (r< 1) was observed [32]. Notably, the observation of modulus enhancement with increasing excess of epoxy is consistent with the concentration and modulus maps of the PVP/epoxy IP. 

R Sukananta and S. Bualek-Limcharoen. In situ modulus enhancement of polypropylene monofilament through blending with a liquid-crystalline copolyester. J. Appl. Polym. Sci., 90 1337-1346, 2003. 

Spherical particles showed the smallest modulus enhancement and platelets the largest. For microparticles the shape at a constant filler content of 5 wt% showed a trend similar to that seen for nanoparticles (except that at high temperatures, where glass fibers were more effective than flakes). The test results confirmed that microparticles are significantly less effective than nanoparticles. 

Liu et al reinforced PVA with hydroxyl-functionalised SWNT. The idea was that the hydroxy groups would be linked by hydrogen bonding with the hydroxyl functionalities of the PVA. A reasonably good modulus enhancement was observed with an increase from 2.4 to 4.3 GPa on the addition of 0.8 wt% nanotubes, corresponding to a reinforcement value of 305 GPa, whereas the strength increases from 74 to 107 MPa was also observed. These results were explained by the observation of good load transfer by Raman spectroscopy. 

The protein, ferritin, was successfully grafted on to CVD-MWNT. This material was mixed with PVA. The authors claimed that the ferritin was expected to form bonds with the PVA. Indeed, a significant modulus enhancement from 3.4 to 7.2 GPa was observed corresponding to a reinforcement of 380 GPa. 

Coleman et also fabricated PVA-based composites using commercial low diameter (D 15 nm) MWNT as a filler. They observed significant reinforcement with modulus enhancement from 1.92 GPa to 7.04 GPa at 0.6% nanotube volume fraction. This represents a reinforcement of d T/d Ff = 754 GPa. Also, strength enhancement from 81 MPa to 348 MPa was... 

Figure 2.2 Modulus enhancement factor for reinforced thermoplastics as a function of fiber volume fraction, orientation angle, and aspect ratio. (Adapted from Ref. [18].)...

Polymer sample Test direction Maximum modulus (GPa) Maximum strength (MPa) Modulus enhancement factor Strength enhancement factor... 

As for the PET based blends, apparently opposite results have been obtained. In fact, whereas the addition of a semi-aromatic LCP, such as SBH or SBHN, leads to a remarkable modulus enhancement, the effect of the addition of an intrinsically much suffer wholly aromatic LCP, such as VA, is surprisingly negligible. This is even more unexpected because, for compression molded specimens, the modulus improvement was found to be higher for PET/VA blends than for, e.g., PET/SBH blends (8). 

Introductory paragraphs similar to the above can be found in hundreds of nanocomposite papers. With the exception of reinforced elastomers, nanocomposites have not lived up to expectations. Although claims of modulus enhancement by factors of 10 exist, these claims are offset by measurements that show little or no improvement... The lackluster performance of nanocomposites has been attributed to a number of factors including poor dispersion, poor interfacial load transfer, process-related deficiencies, poor alignment, poor load transfer to the interior of filler bundles, and the fractal nature of filler clusters [5]. 

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