Sorting by shape

The sequence of the areas presented to panelists was random. The results were sorted by shape and size for this table. Twenty two panelists were used for this exercise. 

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Another common method is sorting by density in a float-sink tank or hydrocyclone. This method is, however, difficult for polyolefins as these have very similar density. Air classification uses a combination of density and shape to achieve the separation, e.g. for separating plastic films and paper residues. 

Molten lead passed as drops through a card or colander perforated with numerous holes— 1448 for the smallest shot — and fell into water which usually contained a little sodium sulphide. This coated the shot with a thin layer of sulphide of a lustrous black metallic colour which remained permanent in moist air. The size of the shot depended not only on the diameter of the holes in the colander, but also on the initial temperature and composition of the molten metal. The shot was sorted by sieves and by rolling down an inclined plane, the imperfectly shaped pellets remaining behind. Finally the shot was polished by rolling with plumbago in a barrel or rumble. 

Mechanical separation. Certain optically active compounds form crystals with distinct left- and right-handed shapes. The crystals can be sorted by hand. 

Now let s look at a -strand. The monomers deep inside it can arrange themselves in any sort of shape. Therefore, they do not contribute to the entropy (since they do not reduce the choice of possible conformations of the chain). On the other hand, the ends of the -strand must be near the walls, even though they cannot leave the cavity. This restricts the munber of possible conformations, so that each end loses a bit of entropy, of order (To see this suppose the number of conformations fi of a monomer segment in (7.2) drops by half. Then the entropy decreases by ks In 2 0.76 ks)-... 

What sort of shapes arise from these plots Admittance-plane curves for several different circuits have been presented by Bauerle, and complex dielectric constant and complex conductivity-plane curves given for several other circuits by Grant. For the N = 2 circuit, it turns out that VY and Z plots lead to two connected but well distinguishable semicircles... 

Table IV. Representative Red Glass Bead Data Sorted by Bead Shape...

The frequency range of devices of this sort is of the order of 10 to 5000 Hz. Since neither the frequency response curve nor the logarithmic decrement requires an absolute measurement of amplitude, the relative amplitudes are rather easily measured by optical or electrical elements or even by observation with a microscope. The limited choice of frequencies is a serious drawback, however. Usually only a few harmonics can be applied, and, in contrast to the flexibility of the compound resonance devices in Chapter 6, whose frequencies can be adjusted by changing the mass or moment of inertia of the apparatus, a new set of values can be obtained only by shaping a new sample. Temperature control can be satisfactorily arranged, since the mechanical system can easily be isolated in a thermostat, and in fact measurements have been made at temperatures down to 4.2 K. 

Principal component analysis Is a powerful technique for studying the variance within a sample, but It Is Important to remember that It can t describe particle shape as such, only the variation In shape. The method can yield different trends and patterns for the same material sorted by different methods or for different materials sorted by the same method It Is capable of reducing a huge volume of data to a few coefficients. 

To carry out the technique, protein molecules are denatured and move through a polyacrylamide gel by electrophoresis to be sorted by molecular mass. Proteins with the highest molecular mass move through the gel more slowly under the influence of the applied electric field, but because different proteins have a variety of different shapes and charge distributions, the experiment must be carefully designed so that these factors do not affect the rate of displacement, and that mass is really the only parameter influencing migration rate. 

Fig. 14.22 First y-axis shows the fine particle fraction (FPF) of interactive mixtures with mannitol and SBS as mean of three measurements standard deviation. The second y-axis shows the particle shape in categories from 1 (spherical) to 5 (indented) as mean of 20 relative SD. The x-axis gives the six different mannitol batches. The plot is sorted by the particle shape [11]...

The technique just described requires the porous medium to be sealed in a cell, so It cannot be used with pellets of irregular shape or granular material. For such materials an alternative technique Introduced by Eberly [64] is attractive. In Eberly s method the porous pellets or granules are packed into a tube through which the carrier gas flows steadily. A sharp pulse of tracer gas is then injected at the entry to the tube, and Its transit time through the tube and spreading at the exit are observed. A "chromatographic" system of this sort is very attractive to the experimenter,... 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

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