Platelet-Like Aggregates with Internal Structure

Platelet-Like Aggregates with Internal Structure 

The novel commercially used wax crystal modifier is based on diblock copolymers with a crystalhzable and an amorphous component. These diblock copolymers form platelet-like aggregates in oil solution. Therefore, here we will present in some detail the scattering from such hairy platelets in order to make the later reasoning more transparent. It is easy to write down the scattering from a homogeneous rectangular tile with the dimensions L and d  

The reciprocal space intensity is displayed in Fig. 7. It has the shape of a rod along the Qz axis. Any modulation of the platelet density profile along the z axis yields a form factor  

For an isotropic ensemble of platelets, the detection of scattering takes place on a sphere of radius Q in the platelet-associated coordinate system shown in Fig. 7 [7]. Only if the Q sphere intersects the rod, will intensity contributions be expected. Thus, the detection element is diluted on the Q surface by a factor of (47rQ ) For small enough Q, this immediately yields the Q behavior of the scattering behavior from thin plates as invoked from the fractal considerations above. Such a behavior implies a divergence at Q equal zero. For finite plates this is avoided, however, by the total immersion of the very small Q sphere within the rod. There the finite inner intensity contribution of the rod is accumulated completely for all orientations. This then yields a scattering intensity proportional to the size of the aggregates. This situation is depicted in Fig. 8. 

The disappearance of the Q divergence may also be seen if we consider a finite disc with a lateral extension R much larger than the sheet thickness. The orientationally averaged intensity from such a disc is given by  

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Platelet-Like Aggregates with Internal Structure... 

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