Segment density distribution Subject

The S parameter is a function of the segment density distribution of the stabilizing chains. The conformation, and hence the segment density distribution function of polymers at interfaces, has been the subject of intensive experimental and theoretical work and is a subject of much debate (1). Since we are only interested in qualitative and not quantitative predictions, we choose the simplest distribution function, namely the constant segment density function, which leads to an S function of the form (11) ... 

Other extensions of the Dolan and Edwards approach Levine et al. (1978) have developed an elegant matrix procedure to evaluate both the segment density distribution functions and the steric interaction for tails, loops and bridges that are subject to excluded volume considerations. 

To calculate the form of the segment density distribution in the depletion layers, it is first necessary to calculate Gw(ri,r), the statistical weight of a chain of N links going from ri to r which is subject to a purely external potential U(r) that acts on each segment. 

Another kind of self-consistent theory used a continuum diffusion representation to describe the distribution of segments.21 23 The segments were assumed to be subjected to an external potential of a mean field. An analytical approximation of the latter self-consistent theory was suggested by Milner et al. (the MWC model)24 on the basis of the observation that at high stretching the partition function of the brush is dominated by the classical path as the most probable distribution. Under this assumption, it was found that the self-consistent field is parabolic and leads to a parabolic distribution of the monomer density. Similar theories for polyelectrolyte brushes25 27 also adopted the parabolic distribution approximation. 

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