Demixing potential

Van den Dries and Vromans41 studied three different particle sizes of lactose with a low-dose formulation containing micronized estradiol at a drug load of 0.1%. A demixing potential was calculated which related to the nonuniform distribution of the dmg in the different sized granules. It was found that a large demixing potential... 

In 1970 Widom and Rowlinson (WR) introduced an ingeniously simple model for the study of phase transitions in fluids [185]. It consists of two species of particles, A and B, in which the only interaction is a hard core between particles of unlike species i.e., the pair potential v jsir) is inflnite if a P and r < and is zero otherwise. WR assumed an A-B demixing phase transition to occur in dimensions D >2 when the fugacity... 

The segregation or demixing is a purely kinetic effect and the magnitude depends on the cation mobility and sample thickness, and is not directly related to the thermodynamics of the system. In some specific cases, a material like a spinel may even decompose when placed in a potential gradient, although both potentials are chosen to fall inside the stability field of the spinel phase. This was first observed for Co2Si04 [39]. Formal treatments can be found in references [37] and [38],... 

In principle, the molar ratio of different thiols in a mixed SAM is the same as their original molar ratio in the solution which was used for the formation. In other words, for a mixture of two thiol compounds which does not show demixing tendencies (phase segregation), a random attachment of both compounds onto the surface can be assumed [16]. This observation offers the potential to mix a cw-substituted alkane thiol with short-chain nonsubstituted thiols. As the result, anchor molecules are available for which steric hindrance is minimized (cf. Fig. 3). 

Equation (8.14) demonstrates once more that the cation flux caused by the oxygen potential gradient consists of two terms 1) the well known diffusional term, and 2) a drift term which is induced by the vacancy flux and weighted by the cation transference number. We note the equivalence of the formulations which led to Eqns. (8.2) and (8.14). Since vb = jv - Vm, we may express the drift term by the shift velocity vb of the crystal. Let us finally point out that this segregation and demixing effect is purely kinetic. Its magnitude depends on ft = bB/bA, the cation mobility ratio. It is in no way related to the thermodynamic stability (AC 0, AG go) of the component oxides AO and BO. This will become even clearer in the next section when we discuss the kinetic decomposition of stoichiometric compounds. 

Figure 8-3. a) Experimental and calculated demixing profiles for (Mg.Co)O under steady state conditions in an oxygen potential gradient (t = 126 h at T = I439°C p /p 0 = 3) and b) its steady state reaction path. 

Kinetic demixing stems from activity differences established between the opposite surfaces. These differences can be produced in various ways. In this section, we applied buffers with different chemical potentials. Other possibilities are activity changes through temperature gradients and activity changes through stress gradients. These situations will be discussed in Sections 8.5 and 8.6. 

For ideal solid solutions which demix in an oxygen potential gradient we obtain from Eqn. (8.21)... 

If we identify jy in Eqn. (8.66) with j° in Eqn. (8.3), we can use Eqn. (8.3) to calculate the (steady state) demixing when a stress driven vacancy flux flows across the solid solution (A,B)0. At a fixed oxygen potential, we obtain from the steady state condition... 

Olivine and other orthosilicates have been exposed to oxygen potential gradients in order to investigate the demixing of solid solutions and internal reactions (oxidation, decomposition). The corresponding formalism was outlined in Chapters 8 and... 

S02) easily reacts with the same membrane components, and need therefore to be removed before the separation unit. The material designer must also consider possible evaporation of membrane components. The high temperature in combination with steam can lead to increased evaporation by metal-hydroxy components. Kinetic demixing seems to be an unavoidable phenomena originating from difference in diffusivity of the metal components in thermodynamic potential gradients... 

It is important to note that demixing may not occur for all formulations. However, the potential of a blend to demix should always be investigated during formulation and... 

Aside from this, a comparison with the equilibrated mixture results shows that we are now dealing with a situation in which the partial quenching alters the behavior of the chemical potential, and to a much lesser extent the internal energy. As the dipolar density is increased, the HNC equation of the electrolyte breaks down. This is very likely due to a demixing transition, as we could conclude from the stability analysis carried out following the prescriptions of Chen and Forstmann [24, 28], According to them, it is possible to analyze the stability of the grand potential functional for the case of a ion-dipole mixture with equal size particles. The fluctuations in this quantity for the present case can be cast in the form [24],... 

Using the hard sphere adhesive state equation proposed by Baxter (16), it is possible to calculate the demixing line due to interactions. This state equation corresponds to the exact solution of the Percus-Yevick equation in the case of an hard sphere potential with an infinitively thin attractive square well. In our calculation we assum that the range of the potential is short in comparison to the size of the particles (in fact less than 10 %). 

For the water, AOT and decane system, light scattering experiments are in progress in view to apply the proposed interaction potential to ternary systems. As expected the first results clearly indicate that interactions increase as the system approaches the critical point. Besides preliminary calculations confirm that a liquid-gas type transition must occur very close to the experimental demixing line. 

K. Vedula, Modelling of transient and steady-state demixing of oxide solid solutions in an oxygen chamical potential gradients. Oxid. Met., 28 (1987) 99-108. 

For higher ab = 0-5, the phase diagram differs qualitatively from the previous one. This can be seen from Fig. 4.14(b) where a bifurcation appears (i.e., at a triple point) for ptr — —2.25 and Tjr 1.075 at which a gas phase coexists simultaneously with both a mixed and a demixed fluid phase. Consequently a critical point exists (peb — -2.25, Tcb — 1.15) at which the line of first-order transitions between mixed liquid and gas states ends. The line of first-order transitions involving mixed and demixed liquid states ends at a higher temperatinre and chemical potential of ptri — —2.00 and Ttri — 118, and the A-line is shifted toward lower temperatures as one can see from the plot in Fig. 4.14(b). This type of phase diagram comports with the one shown in Fig. 1(b) of Wilding et al. [87]. 

A further slight increase of eab to 0.56 does not cause the phase diagram to change qualitatively but quantitatively firom the previously discussed case. This can be seen in Fig. 4.14(c) where for sab = 0.56 the triple point is shifted to a lower temperature and chemical potential compared with ab = 0.50. Likewise, the line of first-order tran.sit.ions between gas and mixed liquid appears at lower chemical potential but is somew hat longer because the critical point is elevated to a higher Tcb — 118. The opposite is true for the coexistence between mixed and demixed liquid phases as one can see from Figs. 4.14(b) and 4.14(c). 

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