Particle network formation

At a critical volume fraction, the resistivity of the composite falls sharply to a level at which the composite can readily conduct electricity. Increases in filler concentration above the critical loading do not appreciably reduce the resistivity. The sharp change from insulator to conductor is due to the formation of a network among the filler particles. Network formation has most frequently been treated as a percolation process. The percolation model refers to a means of continuous network formation through a lattice, taking into account the relative amounts of the two materials comprising the network. It is a statistical representation and is most frequently analysed by Monte Carlo techniques. 

In the case of heterogeneous network formation, one can sometimes observe two critical gel points, the first one corresponds to the appearances of the infinite macromolecules in the form of microgel particles of colloid The second macroscopic gel point correlates with the rheological transition from a solution to the state of a gel, when the system as a whole losses the possibility to flow and is converted into a single three-dimension macromolecules. 

Figure 15.3 indicates that for the silica microspheres, the potential and viscosity both follow the expected behavior predicted by the classical DLVO theory. On the other hand, the nanosize fnmed silica exhibits a discrepancy between the expectation of DLVO theory and the experimental results that is, as the of the nanosize fumed silica increases, viscosity sharply increases. Hence factors such as particle crowding, particle ordering, and electroviscous effects will also impact viscosity, in addition to aggregate or network formation. 

With the use of phase diagrams, we are also able to control the temperature and the viscosity at which phase separation occurs. The final morphologies of the three systems based on the same dicyanate monomer and modified with NFBN, ATBN, and PES are quite different and have different interfaces. When the additive can react with the monomer before network formation, a two-level structure is observed a primary structure (dispersed particles), and a substructure inside the dispersed particles. The complex morphology obtained in this case gives the best toughening effect. 

The HMHECs used in these experiments provided good examples of an associative thickener, in that clear evidence of a critical aggregation concentration was seen from the dilute-solution behavior. Although some limited molecular aggregation may occur below this concentration, once this concentration is achieved, a three-dimensional network starts to form. This network formation leads to a significant enhancement of adsorption onto polymer latex particles from which the surfactant has been removed. The adsorption density is high for a cellulosic polymer of the equivalent molecular weight. 

Starting with a statistical distribution of flocculated particles, flocculation to chains, branched chains and the network formation begins with the second iteration (Figure 11 -49(a)). In later iteration steps, clusters of thicker chains and circles are intermediately formed (Figure 11.49(b)), but they are unstable, and always a... 

Another example of network formation is found in PEO (poly(ethylene oxide))-silica systems [58, 59]. At relatively small-particle concentrations, the elastic modulus increases at low frequencies, suggesting that stress relaxation of these hybrids is effectively arrested by the presence of silica nanoparticles. This is indicative of a transition from liquidlike to solidlike behavior. At high frequencies, the effect of particles is weak, indicating that the influence of particles on stress relaxation dynamics is much stronger than their influence on the plateau modulus. 

Twiss and Carpenter (1938) had also proposed that the water soluble polymers induced creaming by a type of cross-linking mechanism. They pointed out that water soluble polymers of the type studied formed a loose network in solution, as witnessed by their exhibition of a high structural viscosity. Twiss and Carpenter argued that if the chains of the water soluble polymer were adsorbed onto the latex particles, then the particles might be interlinked by network formation between polymer chains adsorbed on different particles. 

Fig. 2.14 Formation of particle networks via protolytic cross-linking with bifunctional spacers.

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