Particle size, characterization definition

Many emulsion polymerizations can be described by so-called zero-one kinetics. These systems are characterized by particle sizes that are sufficiently small dial entry of a radical into a particle already containing a propagating radical always causes instantaneous termination. Thus, a particle may contain either zero or one propagating radical. The value of n will usually be less than 0.4. In these systems, radical-radical termination is by definition not rate determining. Rates of polymerization are determined by the rates or particle entry and exit rather than by rates of initiation and termination. The main mechanism for exit is thought to be chain transfer to monomer. It follows that radical-radical termination, when it occurs in the particle phase, will usually be between a short species (one that lias just entered) and a long species. 

In order to evaluate the extent of attrition and its impact on the particle size distribution, there is a need of a qualitative and quantitative characterization. This, however, is not as simple as it may seem at first. There are many different properties, parameters and effects that manifest themselves and could be measured. In addition, as will be shown, the choice of the assessment procedure is strongly connected with the definition of attrition which, on its part, depends on the degradation mechanism that is considered to be relevant to the process. Hence there are a lot of procedures and indices to characterize the process of particle attrition. Section 3 deals with those which are relevant to fluidized beds and pneumatic conveying lines. 

Not only quality reasons, but also economic considerations, make it necessary to reduce the particle size. Generally, the development of an economic SSP process is characterized by the trend to a reduced particle size. The commonly used cubic chips size (2-4 mm) is reduced to that of the known small nylon chips ( 1.5 mm diameter, spherical shape). The size of the chips can be defined by the length of the cubes and is easily measured. Due to their irregular shape, however, determination of their average volume is difficult. Therefore, the definition weight (g) of 100 pieces has become popular. 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

An empirical method that is not related to a rigorous treatment of the convolution of a diffraction profile by size and strain is the Williamson-Hall analysis. This method is suitable for substances characterized by a large number of diffraction peaks and for highly defective samples for which analytical procedures bring upon problems with background definition. The method involves plotting of reciprocal breadth ((3 ) (FWHM) in units of the 20 scale versus the reciprocal positions (d ) of all peaks of a phase. The intercept yields the particle size and the slope the "apparent strain" 2r. The required quantities are defined as follows ... 

Particle behavior is a function of particle size, density, surface area, and shape. These interact in a complex manner to give the total particle behavior pattern [28], The shape of a particle is probably the most difficult characteristic to be determined because there is such diversity in relation to particle shape. However, particle shape is a fundamental factor in powder characterization that will influence important properties such as bulk density, permeability, flowability, coatablility, particle packing arrangements, attrition, and cohesion [33-36], Consequently it is pertinent to the successful manipulation of pharmaceutical powders that an accurate definition of particle shape is obtained prior to powder processing. 

The bulk density of a powder is obtained by dividing its mass by the bulk volume it occupies. The volume includes the spaces between particles as well as the envelope volumes of the particles themselves. The true density of a material (i.e., the density of the actual solid material) can be obtained with a gas pycnometer. The bulk density of a powder is not a definite number like true density or specific gravity but an indirect measurement of a number of factors, including particle size and size distribution, particle shape, true density, and especially the method of measurement. Although there is no direct linear relationship between the flowability of a powder and its bulk density, the latter is extremely important in determining the capacity of mixers and hoppers and providing an easily obtained valuable characterization of powders. 

For these reasons, the characterization of hazardous solid materials has changed and, with it, the requirements for pollution control. In addition to its nature, described by certain properties (e.g., radioactive) and compositions (e.g., containing toxic components), legislation often defines the term hazardous material by below a certain particle size . With this definition, totally inert materials, consisting of or containing ultrafine particles, become hazardous by law and require processing. 

Since the 1950s, batch emulsion polymerization has been used to prepare standard latexes which have specific particle sizes, narrow particle size distributions and well-defined particle surfaces, though most of the definitive research activity in this area occurred during the 1960s and 1970s [e.g. consult 35-37], The latexes can either be prepared as required or purchased from ranges which are commercially available. In either case, they invariably are polystyrene latexes which have been cleaned after preparation (by processes such as exhaustive dialysis and ion exchange [38]) and fully characterized. 

Imperfection in the performance of any real separation equipment can be characterized by the separation efficiency. In this chapter basic definitions are given together with the relationships between the efficiency and particle size distributions of various combinations of the feed, underflow or overflow product streams. Practical considerations for grade efficiency testing and total efficiency prediction are given, together with worked examples. 

The dispersion model takes into account diffusion. In modelling, the Peclet number Pe is used as a ratio of the convective transport to diffusive transport. Here we can define two different Peclet numbers one for the overall flow in the cake Pec and another. Pep, for the flow in the vicinity of a particle of an average size characterizing the particles in the cake. The definitions are as follows ... 

In most applications, the systems and processes contain large amounts of particles with size distribution each size may also possess a distinguished shape. To describe properly these systems and processes for design and analysis, they need to be adequately characterized to reflect their physical and chemical potentials. In the following sections, different average particle diameter definitions are introduced along with statistical descriptions of particle size distribution. Depending on applications, one definition may be more suitable than others. Thus care must be exercised to select the proper characterization for each process. 

As mentioned earlier, naturally occurring particles are usually irregular in shape and also different in size. Different definitions of average particle diameter have been used to characterize an assemblage of particles. Some may be hypothetical while others may have physical significance. They are summarized here. 

In situ thermal transitions were also described by Taylor et al., who examined the isothermal dehydration behavior of trehalose dihydrate [29]. For small particle size fractions (<45 fjLm), heating at 80°C caused loss of peak definition until, at 210 min, amorphous material was present. In contrast, a larger particle size fraction (>425 fim) converted to the crystalline anhydrous form of the material. The kinetics of this conversion was probed from the Raman data using peak height ratios with time a two-stage rearrangement was indicated. A broader consideration of pharmaceutical hydrates, including their characterization by several techniques (NMR, Raman spectroscopy, and isothermal calorimetry) can be found in the literature [30] as can a review of the use of spectroscopic techniques for the characterization of polymorphs and hydrates [31]. 

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