Interparticle percolation

Savage SB (1987) Interparticle percolation and segragation in granular materials A review. In Selvadurai APS ed. Developments in Engineering Mechanics. Elsevier Science Publishers BV, Amsterdam, pp 347-363... 

Comparing the type of information obtained on suspensions with that obtained on composites gives useful insight into the types of mechanisms that control creep of ceramic matrix composites. The very large increase in creep resistance of dense particulate composites, i.e., more than 65vol.% particles, suggests that the particle packing density is above the percolation threshold. Creep of particulate composites is, therefore, controlled by direct interparticle contract, as modified by the presence of relatively inviscid matrices. Mechanisms that control such super-threshold creep are discussed in Section 4.5. 

A fluid passing through a bed of particles at a relatively low velocity merely percolates through the interparticle voids. The particles in this case retain their spatial entity and the bed is in the fixed bed state. As the flow velocity increases further, the drag exerted on the particles just counterbalances the weight of the bed. At this point the bed is in incipient fluidization and the corresponding velocity is called the minimum, fluidization velocity Umf. As the fluid velocity increases beyond Um, the bed is in a completely fluidized state. 

Previous explanations of the impact modification effect and its phase transition like the brittle-to-tough transition have assumed a basically statistical distribution of the dispersed rubber phase in the continuous polymer matrix [139], From there the critical interparticle distance model originated [139b], which is essentially a percolation-type theoretical interpretation. Experimental results like those reported by Bucknall [139a], but also many crack surfaces published in the literature, show that more rubber phase is present in the visible area of the crack surface than would be expected from a statistical distribution, SEM evaluations are consistent with our findings of a non-statistical distribution, but a phase separation of the dispersed material into some kind of layer. 

SnOi) are isolated and the interparticle distance varies from 5 to 100 nm (Fig. 5). Slightly above the percolation threshold the metal particles (Sn) form continuous filaments of varying diameter, but the maximal diameter never exceeds that of the single metal nanoparticle. Beyond the percolation threshold, the nanoparticles form aggregates located on the boundaries between the polymer globules. 

The threshold volume fraction of percolation (( >,) is guided by the amphiphile shell length and the overall volume fraction of the dispersed phase. For zero shell length and no interparticle attractive interaction, according to the randomly close-packed hard sphere model, 4, = 0.65 systems with strong attractive interactions end up with (f), being lowered from 0.65 to 0.10. 

Percolation Behavior When the Interparticle Conduction Is by Tunneling... 

Most probably, the best known approach to the conduction by tunneling in random systems is the one used in the theories of hopping [6, 30]. However, as discussed below, this approach does not predict a percolation-like behavior as given by Eq. (5.6) with which we were concerned above. One starts the consideration of the hopping model by recalling the exponential decrease of the interparticle conductance g with the distance r, so that... 

As Balberg notes in a review The electrical data were explained for many years within the framework of interparticle tunneling conduction and/or the framework of classical percolation theory. However, these two basic ingredients for the understanding of the system are not compatible with each other conceptually, and their simple combination does not provide an explanation for the diversity of experimental results [17]. He proposes a model to explain the apparent dependence of percolation threshold critical resistivity exponent on structure of various carbon black composites. This model is testable against predictions of electrical noise spectra for various formulations of CB in polymers and gives a satisfactory fit [16]. 

Electrical properties Electrical properties of polymers include several electrical characteristics that are commonly associated with dielectric and conductivity properties. Electrical properties of nanofilled polymers are expected to be different when the fillers get to the nanoscale for several reasons. First, quantum effects begin to become important because the electrical properties of nanoparticles can change compared with the bulk. Second, as the particle size decreases, the interparticle spacing decreases for the same volume fraction. Therefore percolation can occur at lower volume fractions. In addition, the rate of resistivity decrease is lower than in micrometer-scale fillers. This is probably due to the large interfacial area and high interfacial resistance. 

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