Fillers structures

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

The effect of strain amplitude is most pronounced in compounds containing reinforcing fillers and can result in a reduction in shear modulus of as much as a factor of 4 when going from a very small strain to about 10%. This is due to breakdown of filler structure which is associated with energy losses that cause a peak in the tan8 value. It was because of this that earlier British and international standards called for tests to be made at 2 and 10% shear strain, a sensible recommendation that has been overlooked in the present version. Turner6 produces an interesting model based on frictional elements to explain this behaviour. 

Another problem encountered in processing of filled composites by the RIM-process is sedimentation of the filler in tanks, transport tubes, etc. In order to overcome this problem the tanks are fitted with stirrers, so that the filled liquid is forced to circulate in the intervals between shots. Finally, it is necessary to consider the possibility of breakdown of the filler structure if this occurs, there is usually an adverse effect on the properties of a final product. 

Since the mechanical properties of the composites are intimately related to the filler structure and especially to the tube surface, techniques able to bring information at a molecular level are required for a further insight into the structure/property correlation. 

Even dynamic measurements have been made on mixtures of carbon black with decane and liquid paraffin [22], carbon black suspensions in ethylene vinylacetate copolymers [23], or on clay/water systems [24,25]. The corresponding results show that the storage modulus decreases with dynamic amplitude in a manner similar to that of conventional rubber (e.g., NR/carbon blacks). This demonstrates the existence and properties of physical carbon black structures in the absence of rubber. Further, these results indicate that structure effects of the filler determine the Payne-effect primarily. The elastomer seems to act merely as a dispersing medium that influences the magnitude of agglomeration and distribution of filler, but does not have visible influence on the overall characteristics of three-dimensional filler networks or filler clusters, respectively. The elastomer matrix allows the filler structure to reform after breakdown with increasing strain amplitude. 

The filler network break-down with increasing deformation amplitude and the decrease of moduli level with increasing temperature at constant deformation amplitude are sometimes referred to as a thixotropic change of the material. In order to represent the thixotropic effects in a continuum mechanical formulation of the material behavior the viscosities are assumed to depend on temperature and the deformation history [31]. The history-dependence is implied by an internal variable which is a measure for the deformation amplitude and has a relaxation property as realized in the constitutive theory of Lion [31]. More qualitatively, this relaxation property is sometimes termed viscous coupling1 [26] which means that the filler structure is viscously coupled to the elastomeric matrix, instead of being elastically coupled. This phenomenological picture has... 

What about monolithics and castables Depending on the type of corn-components (bonding or cementing agents and fillers), structures made of these materials have many of the same characteristics to a lesser or greater degree. 

Applications. Numerous uses of x-ray analysis were reported for filled systems. They include orientation of talc particles in extruded thennoplastics, particle size deteimination in nanocomposites, crystallinity of talc nucleated PP, crystallinity of polymerization filled PE, diffraction pattern of filled PVA, structure of nanocomposites based on montmorillonite, degree of filler mixing, structural characteristics of fillers, structure of carbon black filled rubber, the effect of apatite concentration on the structure of wood pulp, and graphite as template. " This list shows the versatility of the method in applications to filled systems. 

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

Physical and mechanical properties of the filled polymer composite materials (PCM) in dependence on the extent of filling, the rate of deformation were investigated. It was found out that structural properties of the filled composite materials are determined with the nature of polymer matrix, filling degree, nature of the fillers, structural organization of FCM, that is being formed in the process of receiving of the composite materials, and conditions of tests. 

A noteworthy finding has been that all the materials show two distinct relaxation dynamics, a fast and a slow relaxation [60]. The fast mode corresponds to relaxation of bulky polymer molecules, while the slow mode is related to relaxation of the filler structure with much longer time scales. As silica particles are physically connected with adsorbed polymer molecules, the formed polymer-particle network is a temporary physical network. On a long time scale, relaxation of this network occurs when immobilized polymer molecules connecting silica particles become free, via dissociation from silica particles or disentanglement from other immobilized polymer molecules. 

For carbon-black fillers, structure, particle size, particle porosity, and overall physico-chemical nature of particle surface are important factors in deciding cure rate and degree of reinforcement attainable. The pH of the carbon black has a profound influence. Acidic blacks (channel blacks) tend to retard the curing process while alkaline blacks (furnace blacks) produce a rate-enhancing effect in relation to curing, and may even give rise to scorching. 

At present there are several methods of filler structure (distribution) determination in the polymer matrix, both experimental and theoretical. All the indicated methods describe this distribution by a fractal dimension... 

Filler structure can also easily be determined by mercury porosimetry (Pirard et al., 1999 Moscou et al., 1971 Evans and Waddell, 1995). Filler is placed in a smaU chamber and mercury is forced into the voids by increasing pressure. The intrusion curve gives the volume of mercury infiuded in pores for each applied pressure. Usually, intrusion curves present a well-defined... 

Filler structure also has a neat influence on dispersion the higher the structure, the higher the dispersion. This result is well established and likened to the fact that more open aggregate structures develop a lower number of contact with their neighbors in the dry state. 

Occluded rubber and viscosity increases with filler structure and loading on return, specific surface area of the filler has an influence on green mix viscosity. 

At present there are several methods of filler structure (distribution) determination in polymer matrix, both experimental [10, 35] and theoretical [4]. All the indicated methods describe this distribution by fractal dimension of filler particles network. However, correct determination of any object fractal (Hausdorff) dimension includes three obligatory conditions. The first from them is the indicated above determination of fiiactal dimension numerical magnitude, which should not be equal to object topological dimension. As it is known [36], any real (physical) fractal possesses fiiactal properties within a certain scales range. Therefore, the second condition is the evidence of object self-similarity in this scales range [37]. And at last, the third condition is the correct choice of measurement scales range itself As it has been shown in Refs. [38, 39], the minimum range should exceed at any rate one self-similarity iteration. 

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