Single Particle Strength

There is a whole range of tests based on compression between parallel plates54 and two standards exist to define the rate of application of the crushing force and the geometry of the test apparatus. 

There are no standards for single particle impact testing but many different procedures have been used in research they can be classified into those which shoot the particle as a projectile against an impact surface or those where a stationary particle is hit by a surface moving at high velocity (the latter alternative giving a choice of particle orientation on impact). 

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For the determination of the strength of single catalyst particles, the relationship between a and external force F is still not clear. As an approximation, a can be considered proportional to F in the measurement of single-particle strength for a variety of catalysts in common use. That is. 

H tensile strength of a single particle-particle bond N... 

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

In this section, various issues concerning solid particles are presented. The analysis covers the most important particle properties (surface area, particle shape and size distribution, mechanical strength, and density) as well as the behavior of a single particle in suspension (terminal velocity) and of a number of particles in fluidization state. Finally, the diffusion of molecules in a porous particle (diffusion coefficients) is also discussed. 

Fc = the maximum force that can be applied to a single particle without breaking it (particle strength). 

A number of micromanipulation-based techniques have been developed and used to measure the mechanical strength of single particles,... 

Measurement for tablets, spheres, extrudates, monoliths, and so on, is quite simple. A single particle or unit representative of the lot is placed between parallel plates of a device capable of exerting compressive stress, and the force necessary to crush the material is noted. Tablets, extrudates, or monoliths can be placed within the plates so as to measure axial or radial crush strength. Naturally, a sufficient number of particles must be tested to obtain proper statistics. The method cannot be reliably used for granular or other materials with irregular shapes. 

If the particle mobility is known, it is easy to determine the electric force acting on the particle, provided the field strength is also known. However, the field strength may not be constant but may have some spatial or temporal distribution, that is, ft = f[x,y,z,t). In addition, q may vary from particle to particle and may vary on a single particle with time in a discontinuous, stochastic manner. Thus, except for quite simple cases, it is exceedingly difficult to predict particle motion in an electric field with accuracy. 

Therefore, in the frequency range (o> 30 to 40 cm-1) the collective mode contribution to the conductivity becomes negligible compared to the single-particle contribution (see Fig. 30) and the single-particle contribution in the oscillator strength is shifted down to the narrow zero-frequency mode. 

In multidimensional NMR studies of organic compounds, 2H, 13C and 31P are suitable probe nuclei.3,4,6 For these nuclei, the time evolution of the spin system is simple due to 7 1 and the strengths of the quadrupolar or chemical shift interactions exceed the dipole-dipole couplings so that single-particle correlation functions can be measured. On the other hand, the situation is less favorable for applications on solid-ion conductors. Here, the nuclei associated with the mobile ions often exhibit I> 1 and, hence, a complicated evolution of the spin system requires elaborate pulse sequences.197 199 Further, strong dipolar interactions often hamper straightforward analysis of the data. Nevertheless, it was shown that 6Li, 7Li and 9Be are useful to characterize ion dynamics in crystalline ion conductors by means of 2D NMR in frequency and time domain.200 204 For example, small translational diffusion coefficients D 1 O-20 m2/s became accessible in 7Li NMR stimulated-echo studies.201... 

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