Interparticle distance particle diameter

The aim of this work is to study the influence of particle size, interparticle distance, particle volume content, and local stress state on the toughening mechanism in several dispersed systems. The systems consist of a matrix of an amorphous or semicrystalline thermoplastic (see Figure 1). It is necessary to determine whether the particle diameter or the interparticle distance is of primary importance. But it is difficult to check the influence of both parameters because there is an interrelation between D, the average minimum value of A, and the particle volume content, t>P ... 

In order to obtain a finely sized dispersed phase in the PET matrix, the use of reactive compatibilization has been found to be important. Small dispersed rubber particles and a small interparticle distance are necessary to induce high toughness. For effective rubber toughening of PET, it is important that the rubber domains be less than 3 im in diameter (and preferably less than 1 xm) and that the interparticle distance be between 50-300 nm. 

A convenient particle size is required for cavitation (Dompass and Groeninckx, 1994). In an epoxy matrix cured with dicyan-diamine, the maximum toughness was obtained using CSR particles with a diameter of 450 nm, which corresponds to an optimum interparticle distance of 500 nm (Becu-Longuet et al., 1999). 

It is recognized that within the range where drag reduction occurs, the solids concentration is so dilute that the averaged distance between particles is usually 10 or more particle diameters. Therefore, under this flow condition, interparticle effects can be neglected. Consider the case of a fully developed horizontal pipe flow with negligible electrostatic effects. From Eq. (11.6), the pressure drop depends only on the wall friction, as given by... 

EBL was used to fabricate uniform platinum nanoparticle arrays on Si02 (mean platinum particle diameter 30-1000 nm 52,53,106,107,398)), and evaporation techniques were used to prepare smaller particles and a continuous platinum film. The EBL microfabrication technique allows the production of model catalysts consisting of supported metal nanoparticles of uniform size, shape, and interparticle distance. Apart from allowing investigations of the effects of particle size, morphology, and surface structure (roughness) on catalytic activity and selectivity, these model catalysts are particularly well suited to examination of diffusion effects by systematic variations of the particle separation (interparticle distance) or particle size. The preparation process (see Fig. 1 in Reference 106)) is described only briefly here, and detailed descriptions can be found in References 53,106,399). 

FIGURE 15.5 Diagram illustrating the relationship between average interparticle surface-to-surface separation distance, and other system dimensions, for a particle diameter = 20 nm and O = 13.2%. 

Two parameters are of particular interest the diameter, D, of modifier particles and the distance, A, between particles (interparticle distance). Until now, the literature has given conflicting accounts of the influence of these parameters on different systems. HIPS and ABS have often served as model systems for producing new materials, but the fact that the morphologies as well as the micromechanical mechanisms of toughness enhancement can be different has not always been considered. 

D particle diameter A interparticle distance ctc stress concentration at particles o stress field superposition... 

Figure 2. Variation of interparticle distance, A, with particle volume content, vP, and particle diameter D.

The deformation behavior of toughened PA is compared for larger and smaller particles in reference 26. In large particles with an average diameter, D, of about 1 xm and an average minimum interparticle distance, A, of about 0.5 xm, an intense plastic deformation appears in only a few bands. In the case... 

Figure 16. Modified PA with small particles of diameter D (D = 0.15 pm) and small interparticle distances A (A = 0.08 mm), showing beginning plastic deformation (HVEM image). The deformation direction is horizontal.

Figure 18. Effect of interparticle distance, A, on plastic deformation of matrix strands between particles (a) definitions of the size parameters D = particle diameter, vP = particle volume content, aQ = applied stress, and aK = stress concentration (b) with a small interparticle distance, a uniaxial stress state is dominant between the particles and microvoids after cracking of the particles, and plastic yielding can be obtained and (c) with a large interparticle distance, thick matrix strands favor a triaxial stress state between the particles and microvoids, and plastic yielding is hindered.

The section Toughening by the Multiple-Crazing Mechanism mentioned the effect of superposition of the local fields of stress concentration, which must also be considered. As shown in Figure 8, there is a remarkable increase of the local stress between particles by superposition if the interparticle distance is smaller than the particle diameter (A/D < 1, which corresponds to particle volume contents above 5%). 

Thus, both the transmission and reflection properties of thin gold films can be easily controlled by means of an adjustment of the thickness of the silica shell surrounding each NC, so that dipole-dipole interparticle interactions are effectively screened. Detailed studies using different metal core sizes have not been carried out yet, but it is expected that the distance at which interactions are effectively screened will scale up with particle size, being of the order of one particle diameter. 

Particle-Particle Interaction and Hindered Settling. At solids concentrations of <0.5% by volume, the individual particles are on average so far apart they do not affect each other (i.e., no particle-particle interaction) as they move through the fluid (i.e., laminar flow). For practical purposes, there is no particle-particle interaction in suspensions where the ratio of particle diameter to interparticle distance is <0.1. 

Figure 7 illustrates the total interparticle potential, E, for colloidally stable systems and flocculated systems, where d is the particle diameter and r is the distance between the centers of two approaching particles. A colloidally stable suspension is characterized by a repulsive interaction (positive potential) when two particles approach each other (Figure 7a). Such a repulsion varies with distance, and hence it is termed soft repulsion. In the extreme, owing to the short range of the repulsive...

Particle Crowding" Effect. The growth of a crystal in a suspension can be influenced by the presence of other crystals when the crystal number concentration (number/volume) exceeds a certain level so that the interparticle distance becomes smaller than 20 particle diameters. For most precipitation systems, the crystal number concentration is typically higher than lO" per cm, and the interparticle distances are normally less than 15 times the crystal size. In such a crowded system, the diffusion fields around the individual crystals begin to influence one another and one may expect some interparticle effects on crystal growth. 

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