POLYDISPERSE SOLUTION OF RANDOMLY BRANCHED HOMOPOLYMERS, INVERSION SYMMETRY AND CRITICAL AND THETA-STATES

We discuss the phase behavior of a model of a binary mixture of random ly branched homopolymers in a solution. The monomer-solvent interactio n is determined by a Boltzmann weight w. The theory has been presented recently and is obtained by approximating the underlying lattice by a Bethe lattice of the same coordination number q. Of special interest is the class of randomly branched polymers with inversion symmetry (se e the text). This class includes linear polymers. The phase diagram fo r the special class of polymers is very simple. There is a line C of c ritical points in the dilute limit on which branched:polymers become a critical object in a good solvent. This is an extension of the result due to de Gennes for linear chains in an athermal solution to the abo ve class of branched polymers in any good solvent. The line C meets wi th another critical Line C' for phase separation in a poor solvent. We identify the theta point as a tricritical point as first suggested by de Gennes for linear chains only. The theta point appears only in the limit of infinite polymers such that the second virial coefficient A( 2) vanishes. We calculate various exponents and identify the order par ameter. We point out a subtle difference between the theta state and t he random walk state. However, the radius of gyration exponent does ha ve its mean-field value of 1/2 in the theta state but only in d greate r than or equal to 3. There does not exist a tricritical point for ran domly branched polymers without inversion symmetry. (C) 1998 American Institute of Physics.