Crystal size spread

Crystal Size Spread. Figure 3 shows that the size range of the crystals increases as the crystals grow. In Figure 7 the standard deviation of the distribution, cr is plotted against the mean size, L, for run 5. This plot is approximately linear, giving a slope q. 

The complete characterization of a particulate material requires development of a functional relationship between crystal size and population or mass. The functional relationship may assume an analytical form (7), but more frequentiy it is necessary to work with data that do not fit such expressions. As such detail may be cumbersome or unavailable for a crystalline product, the material may be more simply (and less completely) described in terms of a single crystal size and a spread of the distribution about that specified dimension. 

Figure 15 shows how the population density function changes with the addition of classified-fines removal. It is apparent from the figure that fines removal increases the dominant crystal size, but it also increases the spread of the distribution. 

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

No nucleatlon occurs provided the supersaturation is kept below a value equivalent to 35 C of subcooling. There Is a size spread effect, but it decreases with high ethanol contents. The results Indicate that a practical process Is feasible to grow large fructose crystals by the addition of ethanol to aqueous fructose solutions. 

Figure 8. Size spread coefficient, q vs E/W for fructose crystallization from aqueous ethanol solutions.

The melting point is also somewhat dependent on the crystal size, in particular, when the crystals are very small, Tm is lower. This is, i.a., caused by the restrictions in chain conformations near the crystal surface. A spread in crystal size, therefore, also contributes to the presence of a melting region. This is clearly demonstrated by the (new) PE grades with very low density (copolymers of ethylene with e.g. 1-octene) the crystallites are so small that for a grade with d =.86 the melting point is only 30 °C ... 

Crystal size distributions may be characterized usefully (though only partially) by a single crystal size and the spread of the distribution about that size. For example, the dominant crystal size represents the size about which the mass in the distribution is clustered. It is defined as the size, Ld, at which a unimodal mass density function is a maximum, as shown in Fig. 11 in other words, the dominant crystal size LD is found where dm /dL is zero. (The data used to construct Fig. 11 are from Table II.) As the mass density is related to the population density by ... 

Recrystallization is generally evidenced by an increase in the mean size and spread in the width of a crystal size distribution (Hartel 1998a), as seen for ice crystals in ice cream in Figure 13.12. In this case, it is also accompanied by a decrease in the number of crystals so that the total phase volume of crystalline matter remains the same. However, recrystallization also may result in a... 

When a crystalline polymer is oriented, the random circular film pattern (random orientation) transforms to a collection of defined reflection arcs that are correlated with particular (hkl) planes that can be identified based on the crystal structure and Bragg relationship (see Fig. 12a-b). It follows that the magnitude of the azimuthal spread (x/2) of these reflections is indicative of the degree of orientation. (The breadth, k, of the reflection is related to crystal size and imperfection—see Ref. 32.) Also, the location of the reflection with respect to the sample axes indicates the orientation of the crystallographic planes. For example Fig. 5(a) and (b) show two X-ray photographs of polyethylene that had been cold rolled. From the (200) reflection in sample (a) one sees that the a-axis is aligned preferentially normal to Z whereas in (b) there are two distinct orientations of the a-axis—one along Z and one normal to this. 

The coefficient of variation of the mass density function, which is a measure of the spread of the distribution about the dominant crystal size, is 50%. Such a distribution may be too broad to be acceptable for certain crystalline products, such as sugar. 

The developed image from a given crystal, however, may be significantly larger (frequently 2-10 times) than the crystal itself. The spread of crystal sizes is typically of the same order as the mean size. A highsensitivity emulsion is typically about 7 jj-va thick, and it may contain roughly 5x10 crystals per cm. ... 

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