Star Polymer Conformation in a Dilute Solution

According to the blob model, a flexible neutral star polymer can be envisioned as an array of concentric shells of closely packed blobs. For a visualization of the blobs, see Fig. la. The chain ends are assumed to be localized at the edge (i.e., within the outermost blobs), and each chain contributes one blob to each shell. The chain segment inside a blob remains unperturbed by the interactions with other branches and, therefore, exhibits Gaussian or excluded-volume statistics under theta- or good solvent conditions, respectively. For transparency, we consider first athermal, u = a, and theta-solvent, i = 0, conditions. The blob size at distance r from the star center is equal to the average interchain separation = which 

V = jl under good and theta-solvent conditions, respectively). Hence, the blob picture enables one to derive the power law for the radial decay in polymer density  

Here and below, the sign implies that a numerical coefficient on the order of unity, is omitted. 

The radial decay in polymer density corresponds to a radial decrease in local stretching of the arms, dr/dn = p/[r Cp(r)] = At the same 

---