Maximum filler volume fraction

A is the factor depending on the matrix Poisson s ratio, and B is the factor primarily related to the filler/matrix stiffness ratio, G and 6y are moduli of matrix and filler particles, respectively. The factor ip represents a boundary condition and can be expressed using an empirical function taking into account the maximum filler volume fraction, v x-... 

Maximum filler volume fraction at the end of cDBP absorption test ... 

Spatial configuration or fillers in different media Maximum packing volume fraction... 

Table 5.9. Maximum packing volume fraction, ( )m, of some fillers calculated by dividing tamped density by specific density of filler...

Petti (1994) showed the importance of silica-particle shape and maximum packing volume fractions on the chemoviscosity and spiral flow of highly filled epoxy-resin moulding compounds. Ultrahigh concentrations of silica could be used using the correct filler. 

Figure 12.2 Dependence of the maximum radius of aggregates of the filler particles Rmax Qjj filler volume fraction, for 1 PHE-Gr-I and 2 PHE-Gr-II.

The results of measurements of some tensile properties in the small strain range are presented in Fig. 7 in the form of curves of Ep/Ep, epp/eEP Cyp/ YP filler volume fraction. Ep, GeFi YF and Ep, Cpp, Cyp are the moduli, elasticity limits, and elongations and yield of filled and pure polymer samples respectively. The origin of the maximum on the Ep/Ep curve can be explained if we consider... 

The following expression for the j/ term in Eq. (11.6) indicates that there exists a maximum volume fraction, v at which rigid inclusions of a given shape and size distribution can occupy. Similarly, a maximum effective filler volume fraction has to be used in calculating / (119) ... 

Here, q>ja is the maximum packing volume fraction and its value and [jj] have been tabulated (26) for a variety of particles from spheres to glass fibers. It needs to be emphasized that at high filler loading the particle size distribution has a strong effect on viscosity. 

As Vf increases, then Gj passes through a maximum, see Figure 9.7. Note that this statement is not in contradiction to (1) because Gj is related to K c by , which also increases with filler volume fraction, (G = f i/E). Once again, contrary to expectation, the addition of a rigid filler results in a composite that is usually tougher than the thermoset matrix. 

Let us consider a given mass Mcb of a carbon black at the end point of the so-called "crushed" dibutyl phtalate adsorption test (ASTM D-3493 see Section 4.1.3 above). At this stage, all the aggregates of the CB sample are likely exhibiting the most compact arrangement in a DBF matrix and, with respect to the overall volume of the DBF + CB mixture, the filler volume fraction is maximum and can be assessed from ... 

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. ... 

Integrating this equation to any volume fraction, q>, with the boundary conditions that the elasticity is equal to the network value when there are no particles present, and that when the volume fraction reaches packed filler bed), then gives us Equation (2.64). There is an analogous equation describing the viscosity of suspensions of particles and this will be introduced in Chapter 3. When a value of 0.64 is used for the maximum filler concentration, Equation (2.64) becomes... 

Maximum volume fraction of a particulate filler that can be added to a polymer while maintaining the polymer as the continuous phase domains. 

In these Equations, G is the modulus of the syntactic foam, G0 is the modulus of the polymer matrix, v0 is Poisson s ratio of the polymer matrix, and 9 is the maximum packing fraction of the filler phase. For uniform spheres, 9 0.64 (see Sect. 3.6). The volume fraction of spheres in the syntactic foam is 9sph. The slope of the G/G0 vs. 9sph curve depends strongly upon whether or not G/G0 is greater or less than 1.0. The slope is negative if the apparent modulus of the hollow spheres is less than the modulus of the polymer matrix. 

The concept of the free volume of disperse systems can also be correlated with the change in the structure of the composite of the type solid particles — liquid — gas during its compaction. In that case the value of the maximum packing fraction of filler (p in Eq. (80b) remains valid also for systems containing air inclusions, and instead of the value of the volume fraction of filler, characteristic for a solid particles — liquid dispersion-system solid particles — liquid — gas should be substituted. This value can be calculated as follows the ratio of concentrations Cs x g/Cs, to the first approximation can be substituted by the ratio of the densities of uncompacted and compacted composites, i.e. by parameter Kp. Then Eq. (80b) in view of Eq. (88), for uncompacted composites acquires the form ... 

The rabber modulus increases with an increasing volume fraction of Aerosil. The modulus increase can be caused by the elastomer-filler and filler-filler interactions and by an increase of effective filler content. A very sharp peak for the tanZ is observed at 163 K for an unfilled crosslinked sample. This maximum corresponds to the glass transition of the rubber. Furthermore, it is observed that the Tg of the rubber does not change in the presence of filler. However, the second maximum of to 5 can be seen in the vicinity of 200 K for filled samples. The intensity of this maximum becomes more pronounced with increasing Aerosil content. This observation is in agreement with the results of the h and Ty relaxation study, as demonstrated in Fig. 4a and 6, respectively. Therefore, it seems reasonable to assign the maximum for at 200 K to the motion of adsorbed chain units. This maximum is observed at a lower temperature than the H and T, minimum for the adsorbed chain units (at about 280 K) due to difference in frequency of these methods 1.6 Hz and 46-90 MHz, respectively. 

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