CRITICAL PHENOMENA IN POLYMER-SOLUTIONS - SCALING OF THE FREE-ENERGY

The thermodynamics of monodisperse solutions of polymers in the neighb orhood of the phase separation temperature is studied by means of Wils on's recursion relation approach, starting from an effective phi4 Hami ltonian derived from a continuum model of a many-chain system in poor solvents. Details of the chain statistics are contained in the coeffic ients of the field variables phi, so that the parameter space of the H amiltonian includes the temperature, coupling constant, molecular weig ht, and excluded volume interaction. The recursion relations are solve d under a series of simplifying assumptions, providing the scaling for ms of the relevant parameters, which are then used to determine the sc aling form of the free energy. The free energy, in turn, is used to ca lculate the other singular thermodynamic properties of the solution. T hese are characteristically power laws in the reduced temperature and molecular weight, with the temperature exponents being the same as tho se of the 3d Ising model. The molecular weight exponents are unique to polymer solutions, and the calculated values compare well with the av ailable experimental data.