Root-Mean-Square Thickness of Loops

4 Root-Mean-Square Thicknesses of Loops and Tails B.3.4.1 Root-Mean-Square Thickness of Loops 

Experimentally, the root-mean-square thicknesses of loops and tails can be measured by ellipsometry. It is thus necessary to relate them to the average numbers of segments in loops and tails for deducing the conformation of an adsorbed polymer. 

Hesselink39,40 derived relations between the root-mean-square thickness and the loop or tail size. For the case in which no intrasegment interaction exists, he derived the segment distribution p4(z) for a single loop of size i by considering all posable configurations of the chain that starts at the interface and returns at its end to the interface. His expression for p4(z) reads 

The mean-square thickness of loops for Hesselink s distribution function is thus given by 00 

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