History effects spheres

History. Wilke [129] considers the case that different orders of a reflection are observed and that the orientation distribution can be analytically described by a Gaussian on the orientation sphere. He shows how the apparent increase of the integral breadth with the order of the reflection can be used to separate misorientation effects from size effects. Ruland [30-34] generalizes this concept. He considers various analytical orientation distribution functions [9,84,124] and deduces that the method can be used if only a single reflection is sufficiently extended in radial direction, as is frequently the case with the streak-shaped reflections of the anisotropic... 

Drops accelerated by an air stream may split, as described in Chapter 12. For drops which do not split, measured drag coefficients are larger than for rigid spheres under steady-state conditions (R2). The difference is probably associated more with shape deformations than with the history and added mass effects discussed above. For micron-size drops where there is no significant deformation, trajectories may be calculated using steady-state drag coefficients (SI). 

Crystals are ubiquitous. They vary enormously in form, size and shape, partly reflecting their internal structure, partly their growth history. Particle size and shape are quantified by use of characteristic dimensions and shape faetors that, in combination, permit calculation of important properties sueh as particle volume (mass) and surface area. Relating them to the shape of ideal particles, e.g. the sphere often approximates real partieles. Similarly, the size of a mass of particles can be expressed in terms of a eharaeteristic mean and spread. The voidage of a mass of particles is influeneed by both these quantities. It will be shown in subsequent ehapters that these particle characteristics can have a determining effect on both their processing behaviour and properties in application. They are therefore very important for the process engineer or scientist to measure, predict and control in a particulate crystallization process system. 

In this section, we present the effect of thermal history on the oscillatory shear rheometry of block copolymers. We will show that the occurrence of a minimum in G in the isochronal dynamic temperature sweep experiment does not necessarily signify OOT for highly asymmetric block copolymers instead, it sometimes reflects imperfect bcc spheres, as determined by SAXS and TEM, due to an insufficient annealing of a specimen. Here, we will show that a minimum in G, observed for an unannealed specimen in the isochronal dynamic temperature sweep experiment, may disappear completely when the specimen is annealed for a sufficiently long time at an elevated temperature below the TmoT of highly symmetric SI diblock copolymer. 

We have shown in the preceding section that the rheological properties of particulate-filled molten thermoplastics and elastomers depend on many factors (1) particle size (t/p), (2) particle shape (a), (3) volume fraction of filler (f)), and (4) applied shear rate (y) or shear stress a). The situation becomes more complicated when interactions exist between the particulates and polymer matrix. There is a long history for the development of a theory to predict the rheological properties of dilute suspensions, concentrated suspensions, and particulate-filled viscoelastic polymeric fluids. As early as 1906, before viscoelastic polymeric fluids were known to the scientific community, Einstein (1906,1911) developed a theory predicting the viscosity of a dilute suspension of rigid spheres and obtained the following expression for the bulk (effective) viscosity of a suspension ... 

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