Equilibrium volume phase transition

Figure /. Equilibrium volume phase transition diagram for the gel The polymer volume fraction (f> is represented as a function of Flory s interaction parameterX-...

Fig. 6. Equilibrium volume of ionized AJ-isopropylacrylamide (NIPA) gels in water show discontinuous volume phase transition in response to temperature. The values shown in the diagram indicate the amount of ionizable group (sodium acrylate) incorporated in 700 mM NIPA...

FIG. 14 Temperature dependence of normalized equilibrium diameters (d/d0) at pHs 3 (open circles) and 10 (shadowed circles) for four polyelectrolyte gels consisting of NIPA and AAc residues (a) Gel I (b) Gel II (c) Gel III (d) Gel IV. PAAc with Mu = 4.5 X 105 was used for the preparation of Gels II and III. Dashed line indicates a discontinuous volume phase transition at a temperature (7 v) at which we observed a transient pattern in both swelling and shrinking processes and thereby were not able to measure d. Such a transient pattern was not observed in the measurements for Gel III at pH 3, suggesting a continuous transition. (From Ref. 28.)... 

For the example of PNIPAAm, we have demonstrated the two step process of volume phase transition induced by heating of the swollen gel. Figure 25 shows the cross-sections of cylindrical gel samples swollen in D2O at different times. The contrast results of the mobility of the net-chains. If the temperature of the volume phase transition will be exceeded the signals diminish. The net-chains are almost immobile. On a macroscopic level, the modulus increases, but the degree of swelling is not altered. The network is not in equilibrium. It begins to shrink with a typical time constant as discussed in Sect. 2.3. These findings are in accordance with the two-step model in Sect. 2.4. 

The term oilo4> describes the ability of the system to undergo a local volume phase transition upon illumination of light. When the gel is in thermal equilibrium at a fixed gel temperature T, light intensity, /q, beyond a threshold value. When Iq is decreased, (p decreases discontinuously and the gel does not exhibit hysteresis as a functimi of /q. 

The extremely fast volume phase transition from hydrophilic to hydrophobic state of the polymer network is demonstrated in Fig. 15 for cryogels based oti PNIPAAm and hydroxypropylcellulose (HPC). When the temperature changed from 20 to 60 °C, the gel collapsed and reached a near-equilibrium state within 10-12 s. This behavior is attributed to both the existence of a large amount of free water in the pores, which facilitates the heat transfer, and the thin compact cryogel walls, which tend to respond more quickly to temperature changes. The fact that the cryogels preserve their capillary structure above TVpt plays an important role in the rapid transition from hydrophobic to hydrophilic state. As also seen from Fig. 15,... 

From the discussion of swelling equilibrium follows that a volume phase transition of a gel needs further contributions to free energy, resulting, for example, in specific polymer-solvent interactions. The high-temperature collapse of a nonionic single chain and gels in water has been described by using the concentration-dependent interaction parameters x"-... 

Consider how the change of a system from a thennodynamic state a to a thennodynamic state (3 could decrease the temperature. (The change in state a —> f3 could be a chemical reaction, a phase transition, or just a change of volume, pressure, magnetic field, etc). Initially assume that a and (3 are always in complete internal equilibrium, i.e. neither has been cooled so rapidly that any disorder is frozen in. Then the Nemst heat... 

Pressure-induced amorphization of solids has received considerable attention recently in physical and material sciences, although the first reports of the phenomenon appeared in 1963 in the geophysical literature (actually amorphization on reducing the pressure [18]). During isothermal or near isothermal compression, some solids, instead of undergoing an equilibrium transition to a more stable high-pressure polymorph, become amorphous. This is known as pressure-induced amorphization. In some systems the transition is sharp and mimics a first-order phase transition, and a discontinuous drop in the volume of the substance is observed. Occasionally it is strictly not an amorphous phase that is formed, but rather a highly disordered denser nano-crystalline solid. Here we are concerned with the situation where a true amorphous solid is formed. 

Finally, we must be certain we are observing vapor-liquid equilibrium in the column not vapor-solid equilibrium. Braun and Guillet (1976) reported that a discontinuity in a plot of Jin (V°) vs 1/T (where V° is the retention volume at 273.15 K) indicated a phase transition. We calculated V° from the following relationship... 

Figure 3.10. Phase diagrams of attractive monodisperse dispersions. Uc is the contact pair potential and (j) is the particle volume fraction. For udk T = 0, the only accessible one-phase transition is the hard sphere transition. If Uc/hgT 0, two distinct scenarios are possible according to the value of the ratio (range of the pair potential over particle radius). For < 0.3 (a), only fluid-solid equilibrium is predicted. For % > 0.3 (b), in addition to fluid-solid equilibrium, a fluid-fluid (liquid-gas) coexistence is predicted with a critical point (C) and a triple point (T).

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

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