Fillers fraction effect

By extending the works of Guth, Gold, and Simha on viscosity-filler fraction effects, one can express the effect of CB loading on modulus with a similar expression, but using an appropriate anisometry factor to somewhat take into account the nonspherical shape of CB aggregates, i.e. ... 

This equation shows that debonding stress increases with adhesion and filler fraction and decreases with particle size. Figure 7.27 shows the effect of particle size on prediction of yield stress based on the debonding simulated by an equation derived from Eq 7.27. Decreasing particle size increases the stress required for debonding. 

Tensile strength (Fig. 6), and strain (Fig. 7), continuously decrease with the increase in 0. This is a well known effect premature fracture occurs due to the amount of defects (flaws) which is directly related to the filler fraction. 

Figure 13.7b shows the imaginary part of the dielectric modulus, M", versus/of a PA-11/BT 700-nm nanocomposite at 72°C for volume fractions / = 0.03,0.1, and 0.2. The maximum of M" decreases when the filler content increases, due to the increase in permittivity e. The filler content does not affect the frequency dependence of the three relaxations. However, the ratio between the maximum value of the a -mode versus the maximum value of the a-mode increases with increasing filler content, indicating the interphase effects between the polymer and the nanoparticles. The low-frequency relaxation associated with the MWS phenomena become more pronounced with increasing volume filler fraction compared to the other relaxations. This evolution is attributed to the increase in interfacial effects around the particles. 

K.A. Schulze, A. A. Zaman, K. Soderhohn, Effect of filler fraction on strength, viscosity and porosity of experimental compomer materials, J. Dent. 31 (2003) 373-382. 

However, the calculation according to the Eqs. (15.11) and (15.12) does not give a good correspondence to the experiment, espeeially for the temperature range ofT= 373 13 K in PC case. As it is known [38], in empirical modifications of Kemer equation it is usually supposed, that nominal concentration scale differs from mechanically effective filler fraction, which can be written accounting for the designations used above for natural nanocomposites as follows [41]. 

The use of a homogeneous matrix material leads, in the ideal case, to the preparation of random percolated filler networks. More complex matrix systems have been addressed in an attempt to direct or manipulate the formation of such percolated networks. The use of immiscible polymer blends to create restricted percolation networks has been applied to many types of fillers. To effectively manipulate the network formation in a selected volume fraction of the blend, a phase-separated system must be achieved and, preferably, a distribution of the filler within either of the phases or at the interface must be favored. Using conductive fillers the "directed" network could be electrically connected at a lower overall concentration of filler, - which is favorable for economic reasons and processability. 

Anmnes, P.V., Ramalho, A., Carrilho, E.V.P., 2014. Mechanical and wear behaviours of nano and microfilled polymeric composite effect of filler fraction and size. Materials Design 61, 50-60. 

As we have seen, hydrodynamic effects can somewhat be understood with respect to the works of Einstein, Guth, Gold, Simha, and others, but most of e technologically significant effects are due to rubber-CB interactions. BdR is the most significant evidence for rubber-carbon interactions, which is readily considered through the effective filler fraction, i.e. ... 

PDMS-silica systems variation of the low strain (y = 0.001) dynamic properties with filler fraction the dash curve in the right graph is the Guth and Gold term for mere hydrodynamic effects. 

Block copolymer chemistry and architecture is well described in polymer textbooks and monographs [40]. The block copolymers of PSA interest consist of anionically polymerized styrene-isoprene or styrene-butadiene diblocks usually terminating with a second styrene block to form an SIS or SBS triblock, or terminating at a central nucleus to form a radial or star polymer (SI) . Representative structures are shown in Fig. 5. For most PSA formulations the softer SIS is preferred over SBS. In many respects, SIS may be treated as a thermoplastic, thermoprocessible natural rubber with a somewhat higher modulus due to filler effect of the polystyrene fraction. Two longer reviews [41,42] of styrenic block copolymer PSAs have been published. 

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