  The sol-gel transition (SGT), upon which the infinite cluster (IC) of
thermoreversibly bonded particles (gel fraction) appears against a background
of a set of finite clusters (sol fraction), is first quantitatively considered
with due regard for large and complicated (mesoscopic) cycles inevitably
present in the IC. To this end we present a new approach based on a concept of
the monomer identity breaking and density functional description. We strictly
derive, via a proper choice of basic structural units of the gel fraction, all
statements usually supposed to be just Flory (Stockmayer) assumptions. A
further analysis of the IC structure reveals some new IC structural units
(those involved into mesoscopic cycles) overlooked in both Flory and Stockmayer
approaches and to be described by a new order parameter characteristic only of
the gel phase. As a result, the SGT is found to transform from a geometric
phenomenon to a genuine 1st order phase transition always followed by a phase
separation into sol and gel phases. The free energy, total conversion, volume
fractions of the gel fraction and dangling monomers as well as other structural
quantities are calculated as functions of a reduced monomer density and
analyzed for all the existing models. The Flory approach is found to be
superior to the Stockmayer-Tanaka one and satisfactorily describe some of the
dense weak gel properties but fail (even qualitatively) in a quite extended
vicinity of the SGT.
