Critical Nature of the Size Exponent of Polymers

On the basis of the thermodynamic theory of the excluded volume effects, we show that the size exponent varies abruptly, depending on the change of the segment concentration. For linear polymers, the exponent changes discontinuously from $\nu=3/5$ for the isolated system ($\bar{\phi}=0$) in good solvents to $\nu=1/2$ in the finite concentration ($0<\bar{\phi}\le1$), while for branched polymers having $\nu_{0}=1/4$, the corresponding exponent varies from $\nu=1/2$ ($\bar{\phi}=0$) to $\nu\cong 1/3$ ($0<\bar{\phi}\le1$).