Solubility ideal

The choice of a macromolecular carrier depends on the intended clinical objectives and the nature of the therapeutic agents being used. In general, the properties of an ideal soluble carrier system include the following... 

This expression has been written in terms of concentration if activity coefficients sue known or estimated, then a thermodynamically ideal solubility product may be obtained from the Emalogous product of ionic activities. As the concentration of ions in solutions of lanthanide fluorides is low, the concentration and activity solubility products will not differ markedly, although activity coefficients for these salts of 3 + cations are significantly less than unity even in such dilute solutions (4a). 

As far as we know, the literature contains no quantitative information on the solubility of carbocation salts and the qualitative information available indicated that such salts are relatively insoluble in the solvents of interest. Our first problem was to predict how changes in the structure of the salt would affect the solubility. Although the ideal solubility equation [Equation (1)] cannot be applied rigorously to ionic solutes, our first step was to examine its utility. 

The ideal solubility of a non-dissociating solute, assuming the effects of pressure and specific heat capacity change on melting are negligible is [7,8] ... 

The ideal solubility equation (Eq. 2) is the simplest form of model that is applicable to solvent based crystallization process design. Even though the equation excludes non-ideal interactions in the liquid phase, it is still a useful tool in certain circumstances. 

In systems where the liquid phase interaction between the solute and solvent is close to ideal, then Eq. 2 can be used successfully on it s own to fit and extrapolate solubility data with respect to temperature. The technique is valuable in an industrial setting, where time pressures are always present. Solubility data points are often available without any additional effort, from initial work on the process chemistiy. The relative volume of solvent that is required to dissolve a solute at the highest process temperature in the ciystallization is often known, together with the low temperature solubility by analysis of the filtrates. If these data points fit reasonably well to the ideal solubility equation then it can be used to extrapolate the data and predict the available crystallization yield and productivity. This quickly identifies if the process will be acceptable for long term manufacture, and if further solvent selection is necessary. 

A primary role of crystallization is to purify the desired product and exclude impurities. Such impurities are frequently related in chemical structure to the desired product, through the mechanisms of competitive reaction and decomposition. Where the impurities are similar in structure it is likely that their interactions with the solvent in the liquid phase will also be similar. In this instance the selectivity of crystallization is mainly attributed to the difference between the respective pure solid phases. The ideal solubility equation can be applied to such systems [5, 8] on a solvent free basis to predict the eutectic composition of the product and its related impurities. The eutectic point is a crystallization boundary and fixes the available yield for a single crystallization step. 

The ideal solubility equation has significant value in chiral systems, where a single enantiomer is desired as the product [20]. The behaviour of chiral compounds is very important in biological systems and in drug development, where it is typical for just one enantiomer of an API to be biologically active. The undesired enantiomer may be inert, or possess more serious toxicity effects, as in the case of Thalidomide. Many enantiomeric systems form three discrete solid phases, depending on the solution concentration. Pure crystals of each enantiomer will form at high concentrations of their respective enantiomer. At... 

Comparing Eq. 4 with the ideal solubility equation, Eq. 2 shows that ... 

A predicted solubility curve for Cimetidine in Ethanol is shown in Figure 18. The affect of temperature on solubility occurs through two mechanisms the ideal solubility effect (Eq. 3), and the temperature dependence of the activity coefficient, y. The second affect is not correlated by the NRTL-SAC model, however it is generally accepted that in most phase equilibria problems the affect of temperature on the activity coefficient is relatively small compared to the affect on ideal solubility. A further degree of caution should be applied when extrapolating in this manner, until experimental data are collected. 

A plot of the ideal solubility curves can be used to identify the transition temperatures for the enantiotropic relationships. Form C is the most stable polymorph at high temperature, with a transition to Form B at 20 °C. The Form C to A transition occurs at 11 °C. 

Several different approaches have been made to theoretically determine the solubilities of compounds. Before discussing two of these, a brief review of what is meant by ideal solubility is presented. 

According to Equation (4.5) the ideal solubility of a compound is only dependent upon the heat of fusion, the difference in heat capacity of the solid and supercooled liquid and the melting point of the compound. Since there are no properties of the solvent included in the ideal solubility equation, the solubility of a compound should be the same in all solvents. This equation overlooks all solute-solvent and solvent-solvent interactions. 

The quantity contained in square bracketts represents the ratio between the real solubility and the ideal solubility (the supercritical phase is described by the ideal gas law) it is always greater than 1 and it is also called the enhancement factor (E). E can have values of 10+3 or higher. 

Therefore, the mole fraction ideal solubility of a crystalline solute in a saturated ideal solution is a function of three experimental parameters the melting point, the molar enthalpy of fusion, and the solution temperature. Equation 2.15 can be expressed as a linear relationship with respect to the inverse of the solution temperature ... 

On the basis of these approximations, ideal solubility can then be estimated on the basis of the structure of molecules. Usin n = 13.5 for rigid and nonspherical molecules as described in Equation 3.17, ideal solubility given by Equation 3.14 can be approximated by... 

Other attempts at characterizing the deviation from ideal solubility theory have been made. Anderson et al. [50] showed that solubilities that could not be rationalized from the regular solution theory could be rationalized by assuming the formation of speciLc solute-solvent complexes. Yalkowsky et al. [51,52] showed that the deviation from the ideal solubility equation could be expressed in terms of interfacial tension and surface area. In equation form,... 

Since publication of this work, Japanese researchers have undertaken an effort to demonstrate the feasibility of direct dissolution of U02 from spent nuclear fuels by the TBP-HN03 complex in SC-C02.49 Ultimately, the project is directed at the extraction of both uranium and plutonium from mixed oxide fuels and from irradiated nuclear fuel. Ideally, soluble uranyl and plutonium nitrate complexes will form and dissolve in the C02 phase, leaving the FPs as unwanted solids. As in the conventional... 

Yalkowsky, Myrdal, and co-workers have developed the AQUAFAC group contribution method which predicts the molar activity coefficient ym from which the molar solubility S can be deduced, using supplemental information on the fugacity ratio F (Myrdal et al., 1992,1993,1995). The method exploits the AQUASOL database described by Dannenfelser and Yalkowsky (1991) and Yalkowsky and Dannenfelser (1991). The fugacity ratio (which is termed the "ideal solubility" in their publication) is expressed as... 

Gas Calculated saturation vapor pressure, PiM (atm) Ideal solubility in a liquid at 1 atm (mole fraction) [Equation (2.93)] Ideal solubility in a polymer [10 3 cm3(STP)/cm3 cmHg] [Equation (2.97)]... 

Figure 2.27 Solubilities as a function of critical temperature (Tc) for a typical glassy polymer (polysulfone) and a typical rubbery polymer (silicone rubber) compared with values for the ideal solubility calculated from Equation (2.97)[43]...

Equation (3.6) illustrates that the solubility of a solid in a liquid depends on the enthalpy change at Tm and the melting temperature of the solid. Equation (3.6) is a valid one when T > Tm because the liquid solute in an ideal solution is completely miscible in all proportions. Table 3.1 shows the ideal solubilities of compounds and their heat of fusion. Equation (3.6) is the equation for ideal solubility. The relationship of In x2 (ideal or nonideal solubility) vs. 1/T is shown in Figure 3.1. 

The ratio of the solubility of a crystalline solute to that of its liquid is equal to the ideal solubility and thus, in octanol ... 

For the ideal solubilities of gases in liquids, a similar approach to that taken in Section 3.1 for the ideal solubilities of solids in liquids can be used and thus, Equation (3.69), analogous to Equation (3.8), is obtained ... 

The ideal solubilities of methane and oxygen in water and -heptane are calculated from Equation (3.66), assuming ACp = 0 ... 

The calculated ideal solubilities of the gases in n-heptane are very close to the experimental ones, but the ideal solubilities of the gases in water are too large, giving y > 1. For y > 1, there is a great difference in intermolecular forces between gas and solvent. 

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