Solubility limit theory

The drawback of the solubility limit theory is the difficulty in defining an exact limit for this behavior. Also, if the intercept in eq. 5.9 is very small, although not equal to zero, the binding constants K m and K s can be calculated, but the errors will be very high. Only Psm values can be evaluated for very hydrophobic solutes. It was checked that this partition... 

The solubility limit theory explains the direct transfer of highly hydrophobic solutes from micelles to the stationary phase [6]. The retention factor for these compounds can be expressed as ... 

The implications on selectivity ofthe direct transfer furnishes a new evidence of the solubility limit theory. The retention mechanism of several hydrophobic compounds (i.e., benzene derivatives, polycyclic aromatic hydrocarbons (P AHs), and dihydropyridines) was studied in SDS and CTAB micellar systems, by comparing experimental selectivity coefficients with those theoretically calculated assuming a direct transfer mechanism [7,8]. A mathematical expression was derived by using the three-partition equilibria theory, which explains the tendency of selectivity coefficients to the ratio of P s coefficients of the solutes, when the concentration of surfactant increases. Expressing the equation that relates the retention with the concentration of micelles as a function of Pms and Pwm-... 

Figure 9.5 illustrates plots of k and log k vs. log Pow, for micellar and aqueous-organic mobile phases and a set of 16 aromatic compounds. As shown in Fig. 9.5b, there is a clear curvature in the plot of log k vs. log Pq for the micellar eluent (a quadratic fit provides a better regression than a linear fit). Also, the r data in Table 9.3 indicate that for the micellar mobile phases, k vs. log Pow fits are better than log k vs. log Pow fits. Therefore, the same phenomenon appears in the log k vs. nc and log k vs. log Pow plots, which can be explained by the solubility limit theory proposed by Borgerding et al. [9]. For compounds with low log Pqw values, the solutes are relatively... 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

Complete recovery possible in theory (in practice, recovery dictated by solubility limit of impurities and viscosity of solution). 

It is well known that hydrolyzed polyvalent metal ions are more efficient than unhydrolyzed ions in the destabilization of colloidal dispersions. Monomeric hydrolysis species undergo condensation reactions under certain conditions, which lead to the formation of multi- or polynuclear hydroxo complexes. These reactions take place especially in solutions that are oversaturated with respect to the solubility limit of the metal hydroxide. The observed multimeric hydroxo complexes or isopolycations are assumed to be soluble kinetic intermediates in the transition that oversaturated solutions undergo in the course of precipitation of hydrous metal oxides. Previous work by Matijevic, Janauer, and Kerker (7) Fuerstenau, Somasundaran, and Fuerstenau (I) and O Melia and Stumm (12) has shown that isopolycations adsorb at interfaces. Furthermore, it has been observed that species, adsorbed at the surface, destabilize colloidal suspensions at much lower concentrations than ions that are not specifically adsorbed. Ottewill and Watanabe (13) and Somasundaran, Healy, and Fuerstenau (16) have shown that the theory of the diffuse double layer explains the destabilization of dispersions by small concentrations of surfactant ions that have a charge opposite to... 

As soon as the growing radicals exceed the solubility limit, the oligomers form a second phase which is stabilized by the emulsifier (see Fig. 15). In contrast to the SE theory, the critical emulsifier concentration is unimportant in the... 

Values of 6 for many liquids have been reported, and these have been recorded in extensive Tables [27, 28, 32, 34, 56-59]. The availability of these data provide an easy means of estimating 8. The solubility parameter theory also has serious shortcomings, however, which limits further the reliability of thermodynamic properties computed by the combination of both theories. Nevertheless it does provide useful qualitative, if not quantitative, descriptions of polymer-solvent systems. 

The theories proposed to explain the formation of passivation film are salt-film mechanism and acceptor mechanism [21]. In the salt-film mechanism, the assumption is that during the active dissolution regime, the concentration of metal ions (in this case, copper) in solution exceeds the solubility limit and this results in the precipitation of a salt film on the surface of copper. The formation of the salt film drives the reaction forward, where copper ions diffuse through the salt film into electrolyte solution and the removal rate is determined by the transport rate of ions away from the surface. As the salt-film thickness increases, the removal rate decreases. In the acceptor mechanism, it is assumed that the metal-ion products remain adsorbed onto the electrode surface until they are complexed by an acceptor species like water or anions. The rate-limiting step is therefore the mass transfer of the acceptor to the surface. Recent studies confirmed that water may act as an acceptor species for dissolving copper ions [22]. 

As in the case of hydrophilic (swelling) matrix systems and reservoir (membrane) systems, drug release profiles from insoluble (porous or non porous) systems are most of the time described on a basis of the diffusion theory. This is not true for every situation and we have for example shown that the release from porous matrix systems is dissolution-controlled above the solubility limit of the drug [150]. A simplified equation for the model proposed and for values of kd t > 4, is ... 

With membrane filtration techniques, analytes can be concentrated on the membranes if the molecular diameter is bigger than that of the pores of the membrane. Analytes are dissolved in a buffer containing ions that are smaller than the pores of the membrane. The buffer ions pass through the membrane, and the analytes with sizes bigger than the membrane pores are concentrated at the membrane. In theory, the degree of concentration is only limited by the ratio of the initial sample volume to the surface of the membrane, and the solubility limit of the samples. 

The theory of the electronic energy levels of deep dopants in Si is far more difficult and is not yet fully developed. The electrons are much more tightly bound to these impurities than to shallow impurities, and the Mott transition is not observed. Also, the solubilities of these dopants in Si are generally much lower than those of the shallow dopants, so that solubility limits the concentration of a deep dopant which can be achieved in Si for use as an extrinsic photoconductor. 

Although very convenient, linear isotherms find limited applications in industrial processes. To decrease the diameter of the columns and thus, reduce costs, most industrial separations are done at high concentrations or very close to the solubility limit. Since the isotherms are probably nonlinear and use of linear isotherms can lead to large errors, one needs to use the nonlinear theories in Section 18.6 for concentrated systems. 

For most polymers soluble in organic (nonpolar) solvents, the solubility increases upon heating. For water-soluble polymers, the situation is more delicate the solubility may either increase or decrease as a function of temperature. The solubility limit is often called upper (or lower) critical solubility temperature (UCST or LOST, respectively). For many water-soluble polymers, the LOST is relatively low (from 27-28 C for poly(N-isopropylacry-lamide) (PNIPAM) to about 100 °C for poly(ethylene oxide) (PEO)) and can be reached at normal atmospheric pressure such polymers are often referred to as thermosensitive. In terms of Flory theory of polymer solutions, the UCST or the LCST can be associated with the 6 temperature. Below UCST (above LCST), the polymer solution undergoes macroscopic phase separation into homogenous polymer-rich phase (precipitate) and dilute... 

Solubility parameter theory (Hildebrand ) is not separately considered below but is still widely used in industry. It has led to the construction of comprehensive tables that provide an easy means of estimating thermodynamic quantities of rather limited reliability. Harris and Seymour have edited a collection of papers in several of which solubility parameter theory is used and these offer more details. 

As discussed earlier, many of the basic theories assumed that for effective antifoam action to occur, the antifoaming agent must be in the form of insoluble or undissolved particles or droplets, which transfer to the interface. However, this is not necessarily the case since there is some evidence that some solubilized antifoamers, such as tributyl phosphate and methylisobutyl carbinol (MIBC), can reduce the stability of sodium dodecyl sulfate (SDS) and sodium oleate foam systems. However, in some cases, the oils may exceed the solubility limit. 

When the supersaturated solution is close to the binodal curve (the solubility limit), the transformation occius through the mechanism of nucleation and growth of a minor new phase. This leads to a two-phase material composed of isolated amorphous or crystalline clusters embedded in the homogeneous matrix. The growth of these clusters can be characterized by SAXS, using a model of either a dilute or concentrated set of spherical clusters, as described in the sections Basic theory and Growth of PbTe nanocrystals embedded in a silicate glass . 

Fitch (2) advanced the case of the homogeneous nucleation school which applies to monomers more water-soluble than styrene. This theory teaches that initiation occurs in the aqueous phase to form oligomeric radicals which grow until their solubility limit is reached at which time they collapse to form primary particles. 

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