Interparticle interference

The first tenn, P(q), represents the interferences within particles and its contribution is proportional to the number of particle, N. The second tenn, Q(q), involves interparticle interferences and is proportional to the... 

Following the intrusion branch with increasing pressure (Fig. 1.16A), the steep initial rise at low pressures is caused by the filling of interparticle spaces. The breakthrough pressure, i.e. the pressure when the voids between the particles are filled, follows in principle the theory of Mayer and Stowe [94], and is inversely proportional to the particle size [95]. The demarcation between interparticle spaces and actual intraparticle pores may be unclear for microparticles, but in the case of polymer beads from suspension polymerization having particle sizes between 50-500 pm, usually no interference occurs. The second rise of the intrusion branch is caused by pores inside the particles. Shown in Fig. 1.16A is a porous material of rather narrow pore size distribution. 

The structure factor accounts for interparticle interferences. It relates to the so-called pair distribution function, g(r), of particles through ... 

Van der Waals forces There has been some success in relating these forces to micellar stability. However, the steric stabilization has been found to be also of some importance. Especially, the hairy layer interferes with the interparticle approach. There are several factors that will affect the stability of the casein micelle system ... 

It is important to understand admixture-cement and also admixture- admixture interactions so that optimum use of these materials can be made, admixture-cement incompatibility can be prevented, better troubleshooting of field problems is enabled, and the prediction of concrete properties is made possible. In the following pages some examples of problems that arise from admixture-cement and admixture-admixture interactions are cited, and an outline of the physicochemical concepts involved in the interference with cement hydration and interparticle interactions that limit admixture performance, and cause incompatibility and field problems is presented. 

We have so far focused our attention on dilute systems so that we could avoid dealing with interference of scattering from different particles. The interference effects considered until now are restricted to interference due to scattering centers from within the same particle. When we have a fairly concentrated dispersion or even a dilute dispersion of charged particles that influence the position of each other through their interactions, the scattering data may have to be corrected for interparticle interference effects. Extending the previous discussion to mte/particle interference is not difficult, but the subsequent analysis of the information obtained is not trivial. We shall not go into the details of these here, but just make some brief remarks to establish the connection between interparticle effects and what we have described so far for dilute systems. 

Even in the case of monodisperse systems, the observed decay rate of gi(s,td) (and hence the diffusion coefficient) in general depends on the angle at which the decay is measured if interparticle interference effects exist. In the case of dilute dispersions, in which interactions... 

The parameters used in the simulation are those derived from the observed pattern (H). No allowance has been made for interparticle interference effects which are responsible for the sampling of the particle imensity transform along the equator in the observed specimen intensity transform. 

Although not illustrated in these examples the extension of the method to include interparticle interference effects is straightforward. The principles involved and the necessary formulae are given by James (10). Similarly the effects of specimen absorption and finite beam size can readily be incorporated if required. 

Wax Emulsions. The final component in most particleboard is a sizing agent to reduce the absorption of liquid water. This is normally a paraffin wax emulsion which is supplied to the particleboard manufacturers at approximately a 50 percent wax solids in water. Less than 1 percent wax solids based on the ovendry wood weight is used in most particleboard levels above 1 percent tend to interfere with interparticle bonding while levels below 0.75 percent do not offer maximum water resistance. 

Equations (16) and (18) discriminate between intraparticle and interparticle interference effects embodied in bj(q. t) and exp rq- ry(/)—r/(/) ), respectively. The amplitude function bj(q.t) contains information on the internal structure, shape, orientation, and composition of individual particles. Variations of bj(q.t) across the particle population reflect the polydispersity of particle size, shape, orientation, and composition. The phase function expjrq (ry (r) — r/(/)]( carries information on the random motion of individual particles, the collective motion of many particles, and the equilibrium arrangement of particles in the suspension medium. 

The viscosity of some fluids (particle solutions or suspensions) measured at a fixed shear rate that places the fluid in the non-Newtonian regime increases with time as schematically shown by curve C of Figure 13.39. This behavior can be explained by assuming that in the Newtonian region the particles pack in an orderly manner, so flow can proceed with minimum interference between particles. However, high shear rates facilitate a more random arrangement for the particles, which leads to interparticle interference and thus to an increase in viscosity. Models that illustrate the thixotropic and rheopectic behavior of structural liquids can be found elsewhere (58,59). 

A molecular interpretation of scattering data is model dependent, and several models for the distribution of salt groups in ionomers have been proposed to explain the ionic peak. They consist mainly of two approaches (1) that the peak arises from structure within the scattering entity, 1.e., from intraparticle Interference, and (2) that the peak arises from interparticle interference. 

Figure 8. Two models describing the spatial organization of the ionic sites, a Two-phase model composed of ionic clusters (ion-rich regions) dispersed in a matrix of the intermediate ionic phase, which is composed of fluorocarbon chains and nonclustered ions. The ionic scattering maximum arises from an interparticle interference effect, reflecting an average intercluster distance S. b Core-shell model in which the ion-rich core is surrounded by an ion-poor shell composed mostly of perfluorocarbon chains. The core-shell particles are dispersed in the intermediate ionic phase. The scattering maximum arises from an interparticle interference effect, reflecting a short-range order distance S of the core-shell particle. Note that the crystalline region was not drawn in the model for the sake of simplification and that the shape of the core-shell particle may not necessarily be spherical.

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