Neutralized gel

The curvature correction can be important when K is small, R is small, and/or a is large. With regard to this aspect, Hirotsu has recently found strong size-dependence of the first-order transition temperature and proposed that a can be much larger in ionized gels than in neutral gels due to the presence of an electric double layer at the interface [31]. 

The right hand side rapidly decreases with increasing a . Hence, if B + 0, first-order changes can occur even in neutral gels (vf = 0) for large enough aj. ... 

Dusek and Patterson examined a phase transition in a constrained neutral gel which has a fixed length in one direction and is allowed to swell in the perpendicular directions [3]. In this case an is a constant and v = 1 / = ( o 1 ) is the order parameter. The calculation to follow is much simplified because FeJ, Eq. (5.2), is composed of terms linear and logarithmic in v [69]. 

Initially, this first order phase transition induced by superposed mechanical force was predicted for neutral gels [1, 30]. However, in the case of polyelectrolyte gels the amplitude of the jump in volume at the point of the transition is larger and the transition itself can be realized for a wider range of network parameters than in the case of the neutral gels. 

In the case of a neutral gel, the values a and Q change smoothly as Qo increases, while in the case of a polyelectrolyte network the jumpwise collapse takes place. Note that the composition of the mixture in the swollen network practically coincides with Q0, whereas a significant difference between solvent compositions in the collapsed network and solution exists. The enrichment of the sample by good solvent can be very considerable. An analysis shows that this redistribution increases with the growth of interaction parameter Xab °f solvent components. The reason for this is the following with an increase of Xab. the tendency to phase separation becomes stronger and preferential solvation of... 

As mentioned above, the discrete collapse of the gels is usually observed for charged networks. In Ref. [46], we showed that it is possible to obtain a jumpwise change of the dimensions for neutral networks by incorporation in a neutral gel of some charged linear macromolecules. In this case, the counter ions situated inside the network create there the same osmotic pressure as in the network, with some chemically connected charged groups. 

It is worthwhile mentioning here some other predictions which follow from the consideration of Sect. 2.3. For the gel, which has charges of one sign, the phase transition induced by elongating force should be sharper than for the neutral network. For a polyampholyte network near the isoelectric point, this transition is always continuous and even less pronounced than for the neutral gel. Finally, for the gel near the transition point, very small values of the applied force can induce a collapse of the gel or a jump-like swelling of the gel sample. 

Fig. la, h. The elastic part (ne) and the negative of the mixing part (— Jtm) of the osmotic pressure as functions of polymer concentration < >. The intercepts of ae and — nm correspond to the equilibrium state of neutral gels. Numbers besides each curve of — represent Xi> which increases with temperature, (a) x2 = 0. Only one root at all temperatures, (b) Xi = 0.56. Three roots appear in the intermediate temperature range (around Xi = 0.465), which correspond to stable, unstable, and metastable states, respectively. (Reproduced with permission from Ref. 20)... 

The critical value of x2 for the three roots to appear is shown [11] to be 1/3 for a gel with infinitely long chains. In actual gels, the critical value must be appreciably larger than 1/3. Thus, a discontinuous transition rarely occurs in neutral gels, because it requires an unusually large concentration dependence of %. An NIPA gel with small crosslinking density is one such rare example. 

We see from the above argument that, within the Flory theory of gels, the concentration dependence of x is the driving force for the transition in neutral gels. Hence, to understand the mechanism of the phase transition of gels on a molecular level, we must identify the microscopic interaction which makes x depend on the concentration. For this purpose, we must specify not only the... 

The value of %2 was deduced from the jump at the transition of and that of calculated %, because these two quantities should be proportional with each other. The value thus obtained was %2 = 0.6 + 0.1. In the actual calculation, the values of Ah, As, and x2 were adjusted within the error limits so that the calculated swelling curve fits the measured one as closely as possible. The results of calculation [21] are shown in Fig. 5a and b, where they should be compared with Fig. 3a and b, respectively. The parameter values used are given in Table 2. Of course the values of Ah, As, and %2 include relatively large arbitrariness, although the fact that we can fit the observed swelling curves using reasonable values of the parameters shows that this theory captures an essential point of the phase transition of neutral gels. 

Swelling curves of NIPA-sodium acrylate (SA) copolymer gels have been measured [7] by the same method as applied to neutral gels using cylindrical samples. The concentration of NIPA (700-572 mM) and SA (0-128 mM) were... 

In neutral gels, in contrast, neither a nor T0 depend on the shape of samples at all, as shown in Fig. 11. Thus, it is certain that the unusual shape-dependent properties shown in Figs. 9 and 10 are due to ions contained in gels. Although the mechanism underlying the shape dependence is not dear at present, one possible mechanism has been proposed [31] on the basis of the surface tension of ionized gels. Denoting the surface tension as y and the radius of curvature of the gel surface as p, an additional contribution to the osmotic pressure due to... 

The preceding comments apply to this technique and it is by far the most used. The experiments can be done in a test tube, where one of the reactants is added to the gel before setting, or in a U-tube using a neutral gel to separate the reactants. The technique giving the better result varies from case to case. The tartrates, for example, produce better results in a test tube. 

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