A BINARY MIXTURE OF MONODISPERSE POLYMERS OF FIXED ARCHITECTURES, ANDTHE CRITICAL AND THE THETA-STATES

We study the complete phase diagram for a model of a binary mixture of two interacting polymer species A and A', each of fixed architecture (dendrimer, star, linear, or regularly branched polymer, brush, etc.) and size given by the number hi (or M') of monomers in it, on a lattic e of coordination number q. For M' = 1, the model describes a solution . Branchings, if any, are regular in these architectures. This feature alone makes these polymers different from polymers with random branch ings studied in the preceding paper [J. Chem. Phys. 108, 5089 (1998)]. Then exists a theta point regardless of the fixed architecture, which is not the case for random branchings. We identify this point as a tr icritical point T at which one of the two sizes M and M' diverges. Two critical lines C and C' meet at T. The criticality along C correspond s to the criticality of an infinitely large polymer of any fixed archi tecture, not necessarily linear. This polymer is a fractal object. We identify the relevant order parameter and calculate all the exponents along C. The criticality along C' is that of the Ising model. Connecte d to T is a line t of triple points. The above results are well-known for a solution of linear polymers which we have now extended to a bina ry mixture of polymers of any arbitrary but fixed architecture. Our re sults show that regular branchings have no effects on the topology of the phase diagram and, in particular, on the existence of a theta stat e. The critical properties are also unaffected which is a surprising r esult. We point out the same subtle difference between polymers at the theta point and random walks as was found for a very special class of randomly branched polymers in the preceding paper (see the text). The behavior of a blend of a fixed aspect ratio a=M/M', M-->infinity, is singular, as discussed in the text. (C) 1998 American Institute of Phy sics.