One long chain among shorter chains

We discuss the end to end distance RN of one long chain, with N monomers, immersed in a solution of shorter chains, each with P monomers, in a good solvent. When P increases, RN crosses over an excluded volume behavior (RN ∼ N3/5) to an ideal behavior (RN → R1n ∼ N1/2). The relevant crossover parameter Z is constructed here from an improved version of the Edwards screening idea, incorporating the correct scaling laws. The result is where ϕp is the volume fraction of the P chains in the solution. The N chain will be ideal when Z ⪖ > 1, and swollen (non‐Gaussian) when Z ⪖ > 1.