Modulus relative

The above qualitative conclusions made on the basis of the results of [116, 124-127] correlate with the results of [129,130] in which the calculation is based on composite models with nucleus-shell inclusions. The authors illustrate this with the calculation of a system consisting of a hard nucleus and elastomeric shell in a matrix of intermediate properties, and a system where the nucleus and matrix properties are identical whereas the shell is much more rigid. The method may, however, be also applied to systems with inclusions where the nucleus is enclosed in a multi layer shell. Another, rather unexpected, result follows from [129,130] for a fixed inclusions concentration, the relative modulus of the system decreases with increasing nucleus radius/inclusion radius ratio, that is with decreasing shell thickness. 

Figure 9.28 shows the relation of the relative modulus (Ktf Kp) to the relative density (Pf/Pp) of neat PLA and PLA-based nanocomposite foams, taken in the directions parallel (A) and perpendicular (B) to the flow. 

To illustrate how the effect of the adsorption on the modulus of the filled gel may be modelled we consider the interaction of the same HEUR polymer as described above but in this case filled with poly(ethylmetha-crylate) latex particles. In this case the particle surface is not so hydrophobic but adsorption of the poly (ethylene oxide) backbone is possible. Note that if a terminal hydrophobe of a chain is detached from a micellar cluster and is adsorbed onto the surface, there is no net change in the number of network links and hence the only change in modulus would be due to the volume fraction of the filler. It is only if the backbone is adsorbed that an increase in the number density of network links is produced. As the particles are relatively large compared to the chain dimensions, each adsorption site leads to one additional link. The situation is shown schematically in Figure 2.13. If the number density of additional network links is JVL, we may now write the relative modulus Gr — G/Gf as... 

The relative modulus at any temperature is the ratio of the torsional modulus at that temperature to the torsional modulus at 23°C and the results can be expressed as the temperatures at which the relative moduli are 2, 5, 10 and 100 respectively. A table is given in the standard to save calculation. Alternatively, the apparent torsional moduli can be calculated from ... 

The loss in modulus of rupture resulted from acid embrittlement of the fibers. There was no significant difference due to curing with the different catalysts except in the case of the relative modulus of rupture which averaged 0,99 for the specimens... 

It should be noted that an expression similar to (47) was recommended by Budianski [50] and Hill [51] for description of the dependence of the relative modulus of disperse composites on concentration. A more elaborate expression was obtained by Lee [53], who used Vand s concepts of the immobilized liquid for the description of the behavior of dispersions in terms of the mechanics of three bodies ... 

Equations, similar to Hatschek s empirical equation (11) can be found in calculations by Ishai and Cohen [54] or Narkis [55] for describing the dependence of relative modulus on concentration for disperse composites ... 

FIGURE 17.20 The effect of filler particles on gel properties, (a) Relative modulus (Gm/G0) as a function of particle volume fraction (broken lines are calculated for various values of the ratio Gp/Go, indicated near the curves. The drawn lines are average experimental values for acid casein gels (C) and polymer gels (polyvinyl alcohol, P), with emulsion droplets that are either bonded (B) or nonbonded (N) to the gel matrix, (b) Highly schematic pictures of the gel structure. Shaded area denotes primary gel. Particles are nonbonded (1) bonded (2) bonded but with intermediate layer (3) bonded and aggregated (4). (Adapted from T. van Vliet. Colloid Polymer Sci. 266 (1988) 518.)... 

The particle modulus. For bonded particles, the van der Poel theory can be used to predict the relative modulus of the mixed system, i.e., Gm/G0, as a function of

calculated curves are given for four values of Gp/Gq. For Gp = 0, the result applies also to nonbonded particles, whatever their modulus. If the particle is an emulsion droplet or... 

Incarnate and co-workers [2004] reported that at constant clay content the CPNC modulus increases with the extrusion rate. Addition of clay shifted the main E" peak position by about 60 to 70°C. The same authors [2003] also investigated the viscoelastic properties of a PA-6 and its statistical, partially aromatic copolymer, ADS, with 3, 6 and 9wt% C30B. In tensile mode the low-T relative modulus, increased from 1.15 to 1.54 (at 1 Hz and 5°C/min). The influence of clay on Tg might be attributed to the confinement of polymer chains in silicate galleries, which partially hinders the molecular motion [Ash et al., 2002]. It is significant that Tg does not always increase with organoclay content, as the outcome is influenced by the type, quantity, and miscibility of the plasticizing intercalant. 

Relative Modulus of Rupture" Following Sealed Hardening, as Related to Matrix-... 

Figure 12.2. Dependence of relative modulus (composite/polymer) on concentration for (A) the original Kerner equation (B) the modified Kerner equation (C) the Mooney equation. Circles correspond to experimental results. Solid curves are calculated with v = 0.35, Gf/Gp (relative modulus filler/polymer) = 25, and = 0.64.

The previously reported method of kinetics data analysis for DSC data is not readily adaptable to raw data obtained in the integral form of fractional conversion or cure obtained from DMA, TGA or spectroscopic methods such as FT-IR. The basic assumption of the kinetics analysis for DMA is that the change in relative modulus at a given time and temperature during the dynamic temperature scan, divided by the change in relative modulus exhibited by the fully cured system at the same temperature, is proportional to the extent of cure at that point of the reaction. This is then used as the fractional degree of cure in the calculations. This normalization of raw DMA data to fractional degree of cure F(t,T) is defined as... 

Fig, 7. Dynamic relative modulus (DMA) for the uncured (thermoplastic), curing, and fully cured (thermoset) gel coat. 

Fig. 17.5 Comparison of relative modulus as a function of filler content formed from melt mixing with MMT and with talc (Lee et al. 2005)...

Ashby and Gibson (1997) illustrated the model as a cubic array of interconnected beams as shown in Fig. 5.1 with an exponent of 2. Similarly for closed-cell foam, Ashby and Gibson approximated the relative modulus with an additional term accounted for internal gas pressure and membrane stresses on the faces as shown in Table 5.1. 

Figure 11.8 Relative modulus for different types of monomer and various peroxides. Monomer concentration is 2wt% and peroxide concentration is 0.03 wt%.

The effects of the different monomers and peroxides on the relative modulus are shown in Fig. 11.8. The modulus is generally 1-7% lower. 

Maximum damping peak (glass transition of nitrocellulose) 446-451 K (173-178 °C), relative modulus decreases by 2-3 orders of magnitude sub-damping peak (decomposition and cross-linking of nitrocellulose) ca 456-483 K (ca 183-210 °C), relative modulus increases. 

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