Branched polymers in restricted geometry : Flory theory, scaling and blobs

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Abstract
This paper discusses the behavior of polymers with arbitrary connectivity in restricted geometries, such as pores and slaps. The use of Flory theories, blob models and scaling theories for linear chains is well-known and does not lead to any problems, i.e. all three approaches agree with each other. In the case of branched molecules this is not the case and e.g. no blob model exists. Indeed Flory free energies and scaling theories may lead to contradictions, when applied to branched objects and polymeric fractals without further information. In this paper we will suggest a strategy, how to use both in combined form. The such obtained results are sensible scaling forms for the radius of gyration and the filling fraction. It turns out that a blob model can be constructed for branched polymers. This will be demonstrated in the case of randomly branched polymers. It is also shown that the new results for arbitrary connectivity extrapolate to the well-known case of linear chains, i.e. polymers with one-dimensional connectivity and predicts new scaling laws for the case of two-dimensional tethered surfaces

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