Thermodynamics of Platelet Formation

The Alexander de Gennes [52,53] brush model considers the entropic situation in a brush. It is derived from an analogy to semi-dilute polymer solutions. There the screening of the excluded volume interactions leads to a blob structure with swollen chain sections inside the blobs [87]. In this approach each hair may be considered as a string of blobs reaching out from the surface. The blob size describes the screening of the excluded volume interactions due to the neighboring chains. Its size relates to the surface density of the blobs where  

The hair surface density directly relates to the core thickness d and the chain length NpE of the polyethylene subchain  

We now turn to the free energy of the aggregate [88]. Two contributions need to be considered. The chain stretching within the brush leads to a loss of conformational entropy that can be estimated by the munber of blobs ( b) per chain. Each blob contributes k T to the free energy. Since Wb = f-p/l) with Eqs. 47,48, and 50 we obtain  

The enthalpic part of the free energy contains two contributions. The first results from the chain folding and is simply given by the number of chain folds f times the fold energy of If = 170 meV [89]  

Minimization of the total free energy with respect to leads to the following scahng relations  

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