Nonspherical inclusions

By analogy, the Halpin-Tsai equation type of expression can be used to predict elastic moduli of the composite containing randomly oriented anisometric (nonspherical) inclusions with engineered interphases (30). This is a plausible model of the 3-D randomly oriented Mg(OH)2 platelets or 2-D randomly oriented SGF in the PP matrix. In the first step, the modified Halpin-Tsai equation is used to calculate the longitudinal and transverse moduli of the composites with unidirec-tionally oriented nonspherical inclusions ... 

Nonspherical inclusions are used for modelling elongated pores or fractures mostly with the basic shape of an ellipsoid. The ellipsoid as shape requires the implementation of depolarization exponents La,Lh,Lc along the principal directions a,b,c of the elhpsoid with the condition La + Lf, + Lc =. ... 

Although neglection of the acceleration term for the particle is a reasonable approach, the neglection of the time-dependent term for the Stokes flow is problematic especially for nonspherical particles. Inclusion of the time derivative term for the flow field may result in more rigorous solution. 

The shape or form of the particles is referred to as the particle morphology. Particles may be uniformly spherical, have core-shell morphologies (51, 263), be hemispherical (382), have domains or inclusions (349), be nonspherical or irregular in shape, or may be inverted (in which the core and shell compositions are reversed). Figure 5 illustrates some of the possible particle morphologies. The particular morphology is determined by thermodynamic (equilibrium) (67,101) and kinetic (rate of phase separation versus rate of polymerisahon) considerations. In some cases, latex... 

Another type of inclusion relates to polymers attached covalently to a fraction of the lipids of the bilayer. If these lipid anchors are far apart, the membrane tries to bend away from the polymer in order to increase the volume available to the fluctuating polymer. Therefore, the polymer creates a local spontaneous curvature [42]. If the polymers become denser, the membrane gets effectively thicker which leads to a strong increase of the bending rigidity. If such a decorated membrane forms a nonspherical vesicle, coupling between polymer composition and local curvature will lead to an inhomogeneous distribution of the anchored polymers. 

---