Particles aspect ratio

As far as conducting fillers are concerned, we have rather a wide range of choice. In addition to the traditional and long used fillers, such as carbon black and metal powders [13] fiber and flaky fillers on organic or metal bases, conducting textures, etc recently appeared and came into use. The shape of the filler particles varies widely, but only the particle aspect ratio, the main parameter which determines the probability... 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

MIO is nontoxic, it is more environmentally acceptable than the lead and chromate based paints which are used to provide chemical protection in other anticorrosion paints and primers (Etzrodt, 1933). The highest quality (with respect to the flatness of the particles, aspect ratio, etc.) MIO comes from the mine at Waldenstein in Austria (Producer Karntner Montanindustrie), but there are also mines in Spain, South Africa and Western Australia. The supply of highest quality MIO, which used to be mined in Devon in England, was exhausted during the 1970s. This was one of the factors which prompted the U.K. workers to seek a method of making synthetic MIO (Carter, 1988 see Chapter 20). 

Particle morphology Particle aspect ratio Characteristics... 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

According to the Einstein theory, the intrinsic viscosity of a spherical particle suspension is 2.5. However, for a colloidal suspension of nonspherical particles, [r ] > 2.5. Jeffery [112] obtained the viscosity of an ellipsoidal particle suspension under shear. Incorporating Jeffery s results of velocity fields around the particle, Simha [113] obtained expressions for two explicit limiting cases of ellipsoids. Kuhn and Kuhn [114] also obtained an expression for intrinsic viscosity for the full range of particle aspect ratio (p) by taking an approach similar to Simha s method. 

It is evident that it is more difficult to define particle size if the particle shape is not spherical or cubic. With some other simple geometric forms, a single linear dimension, d may be used to calculate the surface area. In particular, when the particle aspect ratio is sufficiently large, dx is taken as the minimum dimension. Thus, if the particles are thin or long (i.e. plates or rods), it is the thickness which mainly determines the magnitude of the specific surface area (Gregg and Sing, 1982). 

Cell (or particle) aspect ratios are conventionally divided into volume ratios (Oy) and surface ratios... 

Eor anisometric particles it is useful to use the particle aspect ratio, p, defined as a ratio of two orthogonal axes. For prolate ellipsoids (fibers) p > 1 is the length-to-diameter ratio, whereas for oblate ellipsoids (plates) p < 1 is the thickness divided by the largest dimension of the plate. It was observed that both, the intrinsic viscosity, [T ], and the inverse of the maximum packing... 

In the absence of interlayer slip, addition of a second phase leads to an increase of viscosity. The simplest way to treat the system is to consider that the relative viscosity as a function of the solids volume fraction, particle aspect ratio and orientation. There is no difference between the flow of suspensions in Newtonian liquids and that of polymeric composites, when the focus is on the Newtonian behavior. The non-Newtonian behavior of suspensions originates either from the non-Newtonian behavior of the medium or from the presence of filler particles. The problems associated with this behavior can originate in inter-particle interactions (viz. yield stress), and orientation in flow [Leonov, 1990 Mutel and Kamal, 1991 Vincent and Agassant, 1991 Shi-kata and Pearson, 1994]. 

Figure 3. Equation (5.1) plotted as a function of scattering angle 0 for a variety of particle aspect ratios r. Note that spheres do not produce any depolarization.

Figure 7. The mean intensity in the two detectors for the linear polarization configiwation, shown for a particle aspect ratio r =2.

Figure 8. The mean square error for a recovered aspect ratio as a function of scattering angle for a section of particle aspect ratios.

Figure 9. The field correlation function for the circular polarization configuration of the instrument, shown for a range of particle aspect ratios.

Tj), hence the labeled values are in units of. These contours are displayed as functions of particle aspect ratio r along the ordinate and the effective or spherical volume radius a along the abscissa. The contours have been evaluated for the configuration with illumination and detection in linearly polarized states, hence the detection is assumed to take place at the optimum... 

The concentration of metal particles required to achieve pc has been reported over a wide range, from less than 1 to more than 40 vol %. This range of values occurs due to several factors, including processing techniques [3,30,31], particle size in relatively mono-disperse systems [32], particle size distribution [27], and particle aspect ratio. In many of the systems reported [23,25,33,34] random dispersions were assumed even when dense metal particles were employed. Recent work has demonstrated, however, that dense metal particles can settle, especially when the viscosity of the polymer matrix is low [27]. 

Fig. 4.4 Dependences of the normalized shear moduli of epoxy resin filled with glass heterogeneities on the volume fraction of filler f. curves 1 and 5 are for particle aspect ratio...

The particle aspect ratio not only has an influence on the electrode performance, but also on the DBF absorption (DBPA), which affects the electrode manufacturing process. The DBPA gives the amount of dibutyl phthalate (DBP) oil in gram which is absorbed by 100-g carbon (ASTM 281). In contrast, the oil absorption number (OAN) is based on a modified method giving the volume of DBP, which is absorbed by 100-g carbon (ASTM D2414). The OAN, which is commonly used to compare... 

Following from the same considerations, it can be demonstrated that a fiber-like shape, instead of a platelet-like, can minimize the sharp increase of viscosity due to the addition of nanoclays to polymer melts, and therefore improve the processability of the nanocomposite. Different factors contribute to the viscosity of a nanocomposite (a) the polymer-polymer network, (b) the clay-clay network, and (c) the polymer-clay interaction. Supposing that the chemistry of the system is fixed, the first contribution is invariant and the second depends only on the particle aspect ratio, according to percolation theory [7] the higher the aspect ratio, the higher the viscosity of the composite. Comparing the effect of two nanoclay particles with the same aspect ratio, one with a rod-like shape and the other with... 

In the absence of interlayer slip, addition of a second phase leads to an increase of viscosity. The simplest way to treat the system is to consider the relative viscosity as a function volume fraction of the solids, < ), particle aspect ratio and orientation. 

Fig. 17.10 The effect of elastomer MFI on MMT particle aspect ratio of PP/PP-g-MA/MMT/EOR nanocomposite prepared from various molecular weight PP. Gray- and black- filled symbol represents nanocomposites containing elastomers having 39 and 28 wt% octene content, respectively. The EOR and MMT content is based on the total nanocomposite weight (Tiwari and Paul 2011b)...

Anisometric particle aspect ratio and its generalized value Pascal (pressure)... 

As the performance of the composite is profoxmdly dominated by the micromechanical deformation process, its knowledge and control are critical for the improvement of composite properties. The effect of particle characteristics and interfacial adhesion on the micromechanical deformation processes in PP-wood composites was investigated by Renner et al. [7]. They proposed a failure map as well as the practical results and considered the influence of matrix characteristics on deformation and failure in PP-natural fiber composites in other research [24]. Hietala et al. [78] studied the effect of chemical pre-treatment and moisture content of wood chips on the wood particle aspect ratio during the processing and mechanical properties of WPCs. The use of pretreated wood chips enhanced the flexural properties of the wood chip-PP composites. Moreover, the use of undried wood chips compared to dried one can improve and reduce the flexural strength and flexural modulus, respectively. On the other hand, they concluded that the use of pretreated and undried wood chips lead to the highest aspect ratio after compounding. The effect of composition and the incorporation... 

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