The interpenetration of two chain polymers in a good solvent

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Abstract
The interpenetration of two excluded‐volume chain molecules of different size in dilute solution is studied via scaling and renormalization methods. The chains are found to interpenetrate much more strongly than smoothed‐density models suggest, in accordance with recent work by Khokhlov. The pair correlation funtion g(r) goes to zero at the origin only as a weak power of r. This power is related to Des Cloizeaux’s exponents ϑi describing intrachain correlations. The power is also related to the scaling exponents of star polymers. The mutual excluded volume MSL of two chains with greatly different length is proportional to the volume of the smaller chain and to the mass of the larger. Thus MSL is much smaller than a smoothed density model would predict. We discuss which chain correlations give rise to this small MSL. The universal coefficient relating MSL to the radius of gyration of the smaller chain is strongly dependent on the dimension d of space, according to our second‐order expansion in 4‐d. The interpenetration behavior predicted here affects measurable thermodynamic, scattering, and physical–chemical properties of the solution