Particle length

The observed molecular weight suggests that this polymer associates into a dimer in CHCI3, but that this aggregation is effectively blocked by small amounts of DMF. The particle lengths are not quite in the 2 1 ratio indicative of end-to-end association, but the increase in length is sufficiently large to make such a mechanism worthy of additional study. 

Particulate systems composed of identical particles are extremely rare. It is therefore usefiil to represent a polydispersion of particles as sets of successive size intervals, containing information on the number of particle, length, surface area, or mass. The entire size range, which can span up to several orders of magnitude, can be covered with a relatively small number of intervals. This data set is usually tabulated and transformed into a graphical representation. 

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

There is a relationship that accommodates the wide range of fiber sizes and is independent of the composition or constitution of the fiber or fibrous material. The aspect ratio, or the relationship of the length to the thickness of the particle (length/thickness), can be calculated or estimated with relative ease. 

Field of application Pigment type Approximate particle length, pm Specific surface area, m2/g Coercive field strength 7/c, kA/m Saturation magnetization, Ms, pT m3/kg MJMS... 

Pigments with a higher coercive field strength (ca. 70 kA/m) and smaller particle size (particle length ca. 0.15-0.2 pm) are used for super VHS cassettes. 

Field of application Mean particle length, nm Specific surface area, m2/g Coercivity, kA/m Specific saturation magnetization, Am2/kg... 

The effects of finite particle length are approximated by supposing that the layer lines have a Gaussian profile in the Z direction (9) so that ... 

As indicated previously, moisture was measured by oven-drying at 103°C for 24 h (8). Three samples from each of the five silages were taken for moisture measurement. Mean particle length (MPL) was measured by the standard separator method using five screens and a pan (11). Three samples of about 2 kg each were taken to measure MPL for each of the five silages. 

ZA is the charge number of the diffusing ion F is the Faraday constant S is the particle surface area r is the particle length. 

The measurement of Es and E, during a constant current step of time xs leads to the determination of the diffusion constant DGITT of an ion in a solid electrode with a particle length of r. 

The average particle length vas calculated by dividing the length of a 260 mm long ruler by the number of pellets, counted for each fraction, vhich vere lined up against the ruler. The data is summarized in the following table. 

The units on the population ijoiL) sire number of particles per unit volume per particle length, L. The population can be decomposed into... 

Both the macro and micro population balances just derived conserve the number of particles. In some cases, it is appropriate to perform balances where the particles length, area, or volume (or mass) is conserved. For example, length conservation is critical in grinding fibers and volume conservation is critical in grinding other particle shapes. Such conservation equations can also be developed under the umbrella of a population balance, but this population balance must be different than those previously derived, where particle number is conserved. The way to make them different is to couple to the population balance an appropriate conservation equation. The population based on length, area, md volume (or mass) can be derived from the population based on number as shown in Table 3.1. Let us illustrate this idea of property conservation with an example showing conservation of length. 

The maximum particle length in each preparation may correspond with the length of the molecular clusters formed in an electromagnetic field, and the following idea is held concerning the size of the molecular cluster (29) ... 

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