BRANCHED POLYMERS IN RESTRICTED GEOMETRY - FLORY THEORY, SCALING AND BLOBS

This paper discusses the behavior of polymers with arbitrary connectiv ity in restricted geometries, such as pores and slaps. The use of Flor y theories, blob models and scaling theories for linear chains is well -known and does not lead to any problems, i.e. all three approaches ag ree 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 sc aling theories may lead to contradictions, when applied to branched ob jects and polymeric fractals without further information. In this pape r we will suggest a strategy, how to use both in combined form. The su ch obtained results are sensible scaling forms for the radius of gyrat ion and the filling fraction. It turns out that a blob model can be co nstructed 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 linea r chains, i.e. polymers with one-dimensional connectivity and predicts new scaling laws for the case of two-dimensional tethered surfaces.