Ionic pressure, ionized gels

Tanaka et al. found a critical point at the zero-osmotic pressure condition in ionic gels by varying the degree of ionization and diminishing the volume-discontinuity at first-order changes. At such a critical point, the first three derivatives of F with respect to V should vanish from Eqs. (2.6) and (2.26). On the other hand, the so-called spinodal point is given by K = 0, at which the volume fluctuations diverges as shown by Eq. (2.10). 

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