Fillers spherical

Organic spheres are predominantly polymeric, consisting of synthetic or natural polymers. The field of polymeric nano- and microparticles is vast, comprising, for instance, latex particles for coatings, hollow particles for syntactic foams, and microcapsules for foaming and additive release. In addition, there are core-shell microbeads and coated polymeric particles, where the particles can exhibit multiple functionalities, thanks to the individual features of their different layers 1]. As fillers in thermosets and thermoplastics, hollow microspheres and expandable microcapsules are among the most frequently used in commercial applications. 

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Spheres. HoUow spherical fillers have become extremely useflil for the plastics industry and others. A wide range of hoUow spherical fillers are currently available, including inorganic hoUow spheres made from glass, carbon, fly ash, alumina, and 2h conia and organic hoUow spheres made from epoxy, polystyrene, urea—formaldehyde, and phenol—formaldehyde. Although phenol—formaldehyde hoUow spheres are not the largest-volume product, they serve in some important appHcations and show potential for future use. 

Fig. 4. Distribution of difference between local (cp) and average (

Other spherical fillers include carbon black. This has several roles particularly in combination with elastomers, e.g., black pigment, anti-oxidant and UV stabiliser, reinforcing filler, and an electrical conductor when used at 60% concentration. Wood flour is particularly effective in phenol/formaldehyde and melamine or urea/formaldehyde thermoset resins because the phenolic lignin component in the wood reacts with the methylol groups (-CH2OH) in the growing polymer. 

Non-spherical filler particles are also of considerable interest [50,69]. Prolate (needle-shaped) particles can be thought of as a bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently... 

Figure 10 Deformation of spherical filler particles into prolate (needle-shaped) ellipsoids see text for details. 

Sphere, flow across, 15 72 It Sphere-of-influence (SOI), 19 355-356, 358 Spherical bubbles, in foams, 12 7-8 Spherical fillers, phenolic resin,... 

Wollastonite is a preferred filler in some instances due to its fibrous form. While not as effective in improving the mechanical properties as glass fibers, it will give more strength than spherical fillers and less anisotropy than longer glass fibers. 

Many other empirical modifications of the Einstein equation have been made to predict actual viscosities. Since the modulus (M) is related to viscosity, these empirical equations, such as the Einstein-Guth-Gold (EGG) equation (8.3), have been used to predict changes in modulus when spherical fillers are added. 

Analogous to the spherical filler of radius R in the Kraus model, Bhattacharya and Bhowmick [31] consider an elliptical filler represented by R(1 + e cos 0), in the polar coordinate. The swelling is completely restricted at the surface and the restriction diminishes radially outwards (Fig. 40 where, qt and q, are the tangential and the radial components of the linear expansion coefficient, q0). This restriction is experienced till the hypothetical sphere of influence of the restraining filler is existent. One can designate rapp [> R( 1 + e cos 0)] as a certain distance away from the center of the particle where the restriction is still being felt. As the distance approaches infinity, the swelling assumes normality, as in a gum compound. This distance, rapp, however, is not a fixed or well-defined point in space and in fact is variable and is conceived to extend to the outer surface of the hypothetical sphere of influence. 

Consider spherical filler particles (phase f) in a matrix (phase m). The probability of a positron hitting a filler particle is proportional to the volume fraction of filler vr. The probability of the positron thermalizing and annihilating in this filler particle can be written [21] as... 

The main technological advantage of microspheres is that the viscosity of systems with spherical fillers is always less than that of a system with fillers of any other shape, because a sphere has the smallest surface. Moreover the isotropic materials with the best strength properties are those with spherical gas inclusions10). 

In the case of non-spherical filler particles, it has been possible to simulate the anisotropic reinforcement obtained, for various types of particle orientation.68-70 127 135 Different types and degrees of particle agglomeration can also be investigated. 

Different concentration limits of the filler arise from the CCA concept [22]. With increasing filler concentration first an aggregation limit O is reached. For >+, the distance of neighboring filler particles becomes sufficiently small for the onset of flocculation and clusters with solid fraction A are formed. Dependent on the concentration of filler particles, this flocculation process leads to spatially separated clusters or, for 0>0, a through going filler network that can be considered as a space-filling configuration of fractal CCA-clusters. The different cases for spherical filler particles are shown schematically in Fig. 1. 

Here, Va is the solid volume and NA is the number of particles or primary aggregates of size d in the clusters of size . p is the solid fraction of primary aggregates considered in Sect. 3.2.2. For spherical filler particles it equals... 

The central point of the present survey is an attempt to show a complete analogy between the free volume of suspensions and that of molecular systems. It is characteristic that the limiting volume fraction of spherical filler particles leaves in the system another 25-40% of unoccupied volume. Precisely the same unoccupied volume exists in molecular systems if we liken them to a volume filled with spheres whose radii are calculated taking into account the Lennard-Jones potential. 

The shape factor ( d/hg) reflects the boundary condition s constraint on rubber flow during deformation, and can be considered as a measure of tightness for a junction. The shape factor, or the ratio d/hg, can be used to calculate the stored energy with a junction rubber between two spherical filler particles [86,87] ... 

The mechanical action of the immobilized rubber layer on spherical filler particles, that are assumed to form a CCA-filler network in a rubber matrix for

cp, is obtained if the mechanically effective solid fraction q>A (Eq. (71)), is applied in Eq. (69) instead of cpA and the space-filling condition [Pg.35]

Figure 2.26 shows one of the reasons why spherical fillers give good performance in compounded materials. The birefringence patterns show stress distribution in the vicinity of various shapes of inclusions - only with a spherical shape and a good adhesion to the matrix, uniform stress distribution is observed. Stress distribution is an essential element of material design. 

Fibers and other non-spherical fillers change their orientation during thermoforming. Small strains are sufficient to orient fibers. Experiments have demonstrated that particles of talc orient themselves parallel to the surface of thermoformed parts.The crystallites are oriented in a direction perpendicular to the either the talc or the mold surface. This is because the mechanism of crystallite growth begins on the surface of talc and grows outwards. 

F Mitsui Building 2-1-1 Nishi-shijuku Shinjuku-ku, Tokyo 163-04, Japan tel 81 3 3347 9689 fax 81 3 3344 2335 polymeric spherical fillers 123... 

Vacuole dilatation information itself is not simply interpreted. The data instead are best understood through models of microstruetural failure (1). Assuming a single size of spherical filler particles encompassed by elliptically shaped voids that form arbitrarily in strain, and once formed grow at a constant rate with further deformation, then one can readily separate vacuole growth from vacuole formation. Models such as the one described above have been substantiated by microscopic studies. The solution of such models (1) indicates that the first derivative of vacuole dilatation with respect to strain c, is directly proportional to the cumulative number of vacuoles per unit volume,n, that exist at any strain. The second derivative is then directly proportional to the instantaneous frequency distribution of vacuole formation. These two results can be expressed mathematically... 

Fig. 10. Modulus-concentration relationships for spherical filler particles...

In these equations, fa is the volume fraction of filler, and subscripts / and 0 refer to the filled and unfilled elastomers respectively. Note that equations (6-95) and (6-96) introduce a parameter m that accounts for the maximum packing fraction of the filler. For randomly placed spherical filler particles, m = 0.637. 

Basu, D. Banerjee, A.N. Misra, A. (1992). Comparative Rheological Studies on Jute-Fibre-and Glass-Fibre-Filled Polypropylene Composite Melts. Journal of Applied Polymer Science, Vol.46, No.ll, pp. 1999-2009 ISSN 0021-8995 Bigg, D.M (1982). Rheological Analysis of Highly Loaded Polymeric Composites Filled with Non-Agglomerating Spherical Filler Particles. Polymer Engineering and Science, Vol.22, No.8, p>p. 512-518 ISSN 0032-3888... 

Mooney (17) developed relations based on Einstein s theory (18) for elastomers having a Poisson s ratio of 0.5 and filled with rigid spherical fillers. 

Extrapolation of the SANS data in [4] to the isotropic state confirms, indirectly, the presence of a diffuse PS-PI transition layer between filler and rubbery matrix with thickness A 0.5 nm around the PS domain with a mean filler radius of about 84 A. Excellent agreement between measured reinforcing factor and corresponding model predictions could be realized within a very recent approach of Huber and Vilgis [5] for the hydrodynamic reinforcement of rubbers filled with spherical fillers of core-shell structures [6]. 

Hence this equation is a natural generalization of the Einstein-Smallwood reinforcement law. For rigid and spherical filler particles at low volume firaction, the Einstein-Smallwood formula is recovered, since in this case the intrinsic modulus [/a] = 5/2 (the intrinsic modulus [/a] follows from the solution of a single-particle problem). Exact analytical results can be obtained for the most relevant cases, such as uniform soft spheres, which describe the softening of the material in a proper way, as well as in the case of soft cores and hard shells [5]. 

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