First-order volume phase transition hysteresis

Certain polyelectrolyte hydrogels display first-order volume phase transitions, with hysteresis, in response to external stimuli 2,7). Hydrophobic polyelectrolyte hydrogels, in particular, may undergo discrete transitions in response to changes in external pH. Such hydrogels have been considered as chemically-sensitive mechanical switches 8). 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

The oscillatory behavior of the system is a consequence of the first order phase transition, with hysteresis, in the relationship between the pH in Cell II and the hydrogel membrane s volume. Understanding the pH-swelling behavior of the membrane will provide clues as to the influence of membrane parameters on... 

One can see that, as illustrated in Fig. 10.1a, the practical Tc is always lower than The volume-temperature curves for crystallization/melting are roughly the same results. Such a hysteresis loop is an important feature of first-order phase transitions. If we make a reference to the melting point of infinitely large crystals, we can define the... 

---