Solution properties of branched macromolecules

Dilute and semi-dilute solution properties of several classes of branched m acromolecules are outlined and discussed. The dilute solution properties ar e needed for a control of the chemical synthesis. The molecular parameters also determine the overlap concentration which is an essential quantity for description of the semi-dilute state. This state is represented by a multi -particle, highly entangled ensemble that exhibits certain similarities to the corresponding bulk systems. Because of the rich versatility in branchin g the present contribution made a selection and deals specifically with the two extremes of regularly branched polymers, on the one hand, and the rand omly branched macromolecules on the other. Some properties of hyperbranched chains are included, whereas the many examples of slight deviations from r egularity are mentioned only in passing. The treatment of the two extremes demonstrates the complexity to be expected in the general case of less orga nized but non-randomly branched systems. However, it also discloses certain common features. The dilute solution properties of branched macromolecules are governed by t he higher segment density than found with linear chains. The dimensions app ear to be shrunk when compared with linear chains of the same molar mass an d composition. The apparent shrinking has influence also on the intrinsic v iscosity and the second virial coefficient. Shrinking factors can be define d and used for a quantitative determination of the branching density, i.e., the number of branching points in a macromolecule. A broad molar mass dist ribution has a strong influence on these shrinking factors. Here the branch ing density can be determined only by size exclusion chromatography in on-l ine combination with light scattering and viscosity detectors. The techniqu e and possibilities ape discussed in detail. The discussion of the semi-dilute properties remains confined mainly to the osmotic modulus which in good solvents describes the repulsive interaction among the macromolecules as a function of concentration. After scaling the concentration by the overlap concentration c*(A2) = (A(2)M(W))(-1) and nor malizing the osmotic modulus by the molar mass, universal master curves are obtained. These master curves differ characteristically for the various ma cromolecular architectures. The branched materials form curves which lie, a s expected, in the range between hard spheres and flexible linear chains.