Paradox in phase transitions with volume change

Abstract

In gels, a critical point at which swelling transition becomes continuous, is characterized by vanishing of the bulk modulus K. At this point, however, an instability is triggered by a single mode representing homogeneous expansion while fluctuations with finite wave numbers are still suppressed by the finite shear modulus μ. Critical divergence of the fluctuation spectrum is expected not at this critical point but only in an unstable region. This unusual feature has been overlooked because of small values of μ in previous experiments.