Filler relative fractions

The mechanical behaviour of a two-phase composite system depends partly on the filler characteristics, such as the geometry of inclusions, their size, the size distribution, the orientation of inclusions, the filler volume-fraction, the relative positions between the inclusions, the physical state of the filler, etc. and partly on the matrix characteristics, which are related to the physico-chemical state of the matrix, the degree of its polymerization, the crystallinity, the degree of cross-linking, etc. 

It was shown 15,161 that, as the filler-volume fraction is increased, the proportion of macromolecules, participating in this boundary layers with reduced mobilities, is also increased, so that the number of macromolecules participating in the Tg-process is reduced. This is equivalent to a relative increase of ur... 

Using silicon nitride powder in a polypropylene/microcrystalline wax/stearic acid binder formulation, the effect of filler volume fraction (V) (over the range 50 to 70%) on relative viscosity (rjj.) was predicted from Eq. 5 ... 

Figure 20.9. Predicted gas permeability of composites containing perfectly aligned disk-like filler particles, relative to that of the matrix polymer. The number in each curve label denotes the filler volume fraction d>. Results obtained by using the analytical equation of Fredrickson and Bicerano [60] are compared with results obtained by the numerical simulations of Gusev and Lusti which suggest that relative penneability is a function of the product 0-Af [61].

Equation (6.60) was used to determine the effects on the bulk modulus of the relative polymer-filler interactions, r = the filler volume fraction, 4>2-... 

Relative oxygen permeability of nanocomposites with imidazolium modified montmorillonite as a function of filler volume fraction. The permeation behavior is compared with composites containing dioctadecyldimethylammo-nium ions [22] ( ) Ammonium and (a) Imidazolium composites. The dotted lines only serve as guides. (Reproduced from Mittal, V., Eur. Polym. /., 43, 3727, 2007. With permission from Elsevier.)... 

FIGURE 36.1. Filler particles with hard core relative increase of the elastic modulus as a function of filler volume fraction for different values of the ratio shell modulus to matrix modulus The ratio between shell (total) and core radius is taken as 4/3. 

With emerging nanoscale fillers where the particle sizes are in the l(X)s of nanometers, the specific snrface area of filler particles can be orders of magnitude larger than that for conventional fillers. As fractional volume of matrix-filler interphase determines the level of reinforcement achieved in the composite, nanofillers can achieve superior properties at relatively low volume fractions, provided they are adequately dispersed in the base polymer. 

Figure 6.9 Effect of filler volume fraction on relative strain energy release rate. O, Upper limit no adhesion , lower limit perfect adhesion. (From Ref. 63, courtesy of SPE.)...

Figure 8.16 Relative oxygen permeation and water vapor transmission through the epoxy nanocomposites (montmorillonite filler) as a function of filler volume fraction [13].

It is also seen in Figure 6.5 that the data at three different temperatures superimpose on a single curve for each shear rate considered. This is in contrast to the findings of Saini et al. [63] who also prepared plots of relative viscosity with filler volume fraction for four different polymer matrices at three levels of loading as shown in... 

Figure 6.5 Variation of relative viscosity at constant shear rate with filler volume fraction. (Reprinted from Ref. 95 with kind permission from Elsevier Science-NL, Sara Burgerhartstraat 25,1055 KV Amsterdam, The Netherlands.)...

Figure 6.4. Relative storage modulus dependence on filler volume fraction for nauofilled amorphous polymers below HA depicts the hydroxyapatite nano-filler...

Figure 6.5. Relative storage modulus vs. filler volume fraction dependence for nano-filled amorphous polymers above T. The PEA and PEO depict cross-linked poly(ethyl acrylate) and poly(ethylene oxide) matrix, respectively...

In Figure 9.32 the dependence of the thermal expansion linear coefficient a p on the relative fraction of nanoclnsters, which are considered as nanofiller, for epoxy polymers is addnced. As has been expected [35], an increase in results in a reduction in ttpp, comparable with that observed for polymer composites with the introduction of particnlate fillers. So, an increase in (p from 0 to 0.60 reduces a p by about 1.50 times (Figure 9.32) and with the introduction of calcium carbonate or aluminium powder with volume contents (p = 0.60 in the epoxy polymer the thermal expansion linear coefficient value decreases by 1.70-2.0 times [35]. The dependence a p(expressed analytically by the following empirical equation [62] ... 

For such ideal systems as suspensions of spheres of equal diameter, many equations, either theoretical or empirical have been proposed for the relative viscosity as a function of the filler volume fraction. Such a subject is obviously of tremendous importance in many fields. A thorough discussion of suspensions of rigid particles in Newtonian fluids was made by Jeffrey and Acrivos and some models available up to 1985 were discussed in detail by Metzner.59 We will consider below only the most referred equations that explicitly consider the maximum packing fraction. One of the oldest proposal was likely made by Filers in order to model the behavior of highly viscous suspensions, i.e. ... 

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