Apparent exponents for the chain length dependence of the volume fraction in critical polymer solutions

The dependence of the critical volume fraction at constant pressure as a function of the chain length of a polymer/solvent system can be described by a power law. The exponent of this power law is investigated based on an equation of state model and experimental data for various chain-molecule solutions here. The results are compared to recent molecular simulation data taken from the literature and analytical models. The theoretical models, simulation, and experimental data show that the exponent depends on the chain length of the dissolved chain molecules. The power law with a constant exponent is therefore not a universal relationship for this dependence. Based on the investigation of the chain length dependence a correlation for the critical volume fraction is proposed here. This function generalizes the Flory and a renormalization group model and is applied to the correlation of the experimental data. This more general relationship includes the power law with the exponent obtained from the Flory theory as limiting behavior. Some additional experimental data for oligomer solutions which are necessary for an investigation of the short chain length limit have been measured.