content_image/346928.jpg content_image/346927.jpg
uniform phase is stable against macroscopic phase separation as long as λ 2 $_{1}$λ 2 < 0. The model can describe phase separation into two uniform phases only when the boundary of stability of the uniform phase is associated with k = 0, i.e., when upon decreasing temperature ( λ 2 1 + k $^{2}$)( λ 2 + k $^{2}$) changes sign first at k = 0. In our case this means that λ 2 $_{1}$λ 2 > ( λ 2 1 + k 2 $_{max}$)( λ 2 + k 2 $_{max}$); the necessary condition for the above is λ 2 1 + λ 2 < 0. This condition can only be satisfied when T r M < 0, since in this case λ 2 1 < 0 and λ 2 → 0 $^{+}$; hence, 1 /ξ$_{b}$ = λ$_{2}$ . Our model permits an instability at 0 < k ≤ k$_{max}$ , which will lead to the modulated phase, for a set of parameters satisfying J < 0 and T r M > 0, since in this case λ 2 1 → 0 − and λ 2 > 0. We will not consider such parameters in the current paper. 

For a given composition, the spinodal surface T$_{s}$ (¯ s, ¯ ρ$_{c}$ ) is determined by the higher tem- perature satisfying the condition (36). The explicit relation between the temperature and the composition of the mixture that satisfies the first condition in Eq. (36), reads 

<img src='content_image/346928.jpg'>

For ¯ ρ$_{c}$ = 0 we have simply k$_{B}$T$_{c}$ = 6 J$_{ss}$ and ¯ s$_{c}$ = 0 in this model. For a very small amount of ions the shift of the critical temperature can be estimated from the derivative of T$_{s}$ with respect to ¯ ρ$_{c}$ at ¯ s = ¯ ρ$_{c}$ = 0. The derivative at that point is 

<img src='content_image/346927.jpg'>

while the derivative at ¯ s = ¯ ρ$_{c}$ = 0 of k$_{B}$T satisfying ˜ C$_{ss}$ (0) = 0 is − 6 J$_{ss}$ . Hence, Eq. (37) describes the actual instability at least for small amount of the solute. The critical temperature increases upon addition of ions when J$_{sρ}$ − J$_{ss}$ > 0. Experimentally addition of some salt leads to the increase of the temperature of the upper critical point [10, 11]. Thus, if we require that this model describes the experimental situation on the MF level, we should assume that J$_{sρ}$ − J$_{ss}$ > 0. This condition, together with the earlier assumption J$_{ss}$ > J$_{ρρ}$ , leads to J < J 2 ss − J 2 sρ < 0. On the other hand, for J > 0 the critical point decreases upon addition of salt, which is not consistent with the experimental observation. However, the present study is limited to MF approximation, and the effect of fluctuations on the critical point should be taken into account to draw definite conclusions. We shall consider both cases, J > 0 and J < 0, bearing in mind that in the latter case the parameters must satisfy the condition T r M < 0. 

