Solubility in mixed solvents

By itself the solubility parameter can explain the behaviour of only a relatively small group of solvents - those with little or no polarity and those unable to participate in hydrogenbonding interactions. The difference between the solubility parameters expressed as (dj - 2) will give an indication of solubility relationships. 

For solid solutes a hypothetical value of 62 can be calculated from (U/V) where U is in this case the lattice energy of the crystal. In a study of the solubility of ion pairs in organic solvents it has been found that the logarithm of the solubility (log S) correlates well with 6,-62).  

The solubility of small molecules in biological membranes is of importance from pharmacological, physiological and toxicological viewpoints. Biological membranes are not simple 

Solubility parameters of dmgs (d2) have also been correlated with membrane absorption rates in model systems. A reasonable relationship was obtained between d2 and a logarithmic absorption term, thus providing one predictive index of absorption. Scott has said of solubility parameters and equations employing them that the theory offers a useful initial approach to a very wide area of solutions. Like a small-scale map for a very broad long-distance view of a sub-continent they are unlikely to prove highly accurate when a small area is examined carefully, but they are equally unlikely to prove completely absurd.  

The device of using mixed solvents is resorted to when drug solubility in one solvent is limited or perhaps when the stability characteristics of soluble salts forbid the use of single solvents. Many pharmaceutical preparations are complex systems. Common water-miscible solvents used in pharmaceutical formulations include glycerol, propylene glycol, ethyl alcohol and polyoxyethylene glycols. As can be imagined, the addition of another component complicates any system and explanations of the often complex solubility patterns 

Finding an appropriate mixed solvent system should not be done on a strictly trial and error basis. It should be examined systematically based on the binary solubility behavior of the solute in solvents of interest. It is important to remember that the mixed solvent system with the solute present must be miscible at the conditions of interest. The observed maximum in the solubility of solutes in mixtures is predicted by Scatchard-Hildebrand theory. Looking at Eq. (1.50) we see that when the solubility parameter of the solvent is the same as that of the subcooled liquid solute, the activity coefficient will be 1. This is the minimum value of the activity coefficient possible employing this relation. When the activity coefficient is equal to 1, the solubility of the solute is at a maximum. This then tells us that by picking two solvents with solubility parameters that are greater than and less than the solubility parameter of the solute, we can prepare a solvent mixture in which the solubility will be a maximum. As an example, let us look at the solute anthracene. Its solubility parameter is 9.9 (cal/cm ). Looking at Table 1.8, which lists solubility parameters for a number of common solvents, we see that ethanol and toluene have solubility parameters that bracket the value of anthracene. If we define a mean solubility parameter by the relation 

Another useful method is to employ the group contribution methods described in the previous section with data obtained on the binary pairs that make up the system. 

Recently, Frank et al. (1999) presented a good review of these and other calculation-based methods to quickly screen solvents for use in organic solids crystallization processes. 

Accurate solubility data is a crucial part of the design, development, and operation of a crystallization process. When confronted with the need for accurate solubility data, it is often common to find that the data is not available for the solute at the conditions of interest. This is especially true for mixed and nonaqueous solvents, and for systems with more than one solute. In addition, most industrial crystallization processes involve solutions with impurities present. If it is desired to know the solubility of the solute in the actual working solution with all impurities present, it is very unlikely that data will be available in the literature. Methods for the calculation of solubility have been discussed previously. These can be quite useful, but often are not possible because of lack of adequate thermodynamic data. This means that the only method available to determine the needed information is solubility measurement. 

The measurement of solubility appears to be quite simple, however, it is a measurement that can easily be done incorrectly, resulting in very large errors. Solubility should always be measured at a constant controlled temperature (isothermal) with-agitation employed. A procedure for measuring solubility is given below  

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Gas solubility in mixed solvents (and, therefore, Henry s constant) varies with solvent composition. The simplest approximation for this is given in Eq. (16) [23] ... 

Williams, N.A. and Amidon, GL. An excess free energy approach to the estimation of solubility in mixed solvent systemsl, Pharm. Sci.73, 9-12, 1984. 

Additional approaches to understand and predict solubilities in mixed solvents are based on estimation of the activity coefficient, logy, in Eq. (1). Martin, Chertkoff, and Restaino investigated the use of regular solution theory, as developed by Hildebrand and Scott, to predict the solubilities of organic solutes in various solvent mixtures ... 

The aim of the present paper is to develop a theoretical approach for the description of the gas solubility in a solvent containing a salt. To achieve this goal, the Kirkwood—Buff formalism for ternary mixtures will be used. Recently, such a formalism has been used to predict the gas solubility in mixed solvents (mixture of two nonelectrol5rtes) in terms of the solubilities in the individual solvents. A similar approach will be employed here. 

The aqueous mixtures of polymers (PEG and PPG) were selected for comparison with the theory, because accurate data [4,5] regarding the solubility of argon (Ar), methane (CH4), ethane (C2H6) and propane (CsHg) in the individual constituents and the polymer + water mixtures are available. In addition, the above polymers and water are miscible in all proportions and solubility data [4,5] are available for the entire composition range. The theoretical approach regarding the solubility of gases in polymer + water mixed solvents can be extended to the correlation of their solubility in mixed solvents formed of water and pharmaceuticals, proteins, biomolecules, etc. 

Eq. (2) does not contain any adjustable parameter and can be used to predict the gas solubility in mixed solvents in terms of the solubilities in the individual solvents (1 and 3) and their molar volumes. Eq. (2) provided a very good agreement [9] with the experimental gas solubilities in binary aqueous solutions of nonelectrolytes a somewhat modified form correlated well the gas solubilities in aqueous salt solutions [17]. The authors also derived the following rigorous expression for the Henry constant in a binary solvent mixture [9] (Appendix A for the details of the derivation) ... 

It is worth noting that the developed theory provides not only an equation for the protein solubility in mixed solvents, but also provides some insight into the hydration of a protein molecule in aqueous solutions and its connection with the protein solubility. In particular, it was shown [29] that the preferential hydration of a protein molecule (7 2 < 0) is connected with the decrease of the protein solubility (salting-out) and when the water is preferentially excludedfromaproteinsurface(72 > 0), the addition of a small amount of cosolvent increases the protein solubility (salting-in). 

The main difficulty in predicting the solid solubility in a mixed solvent consists in calculating the activity coefficient of a solute in a ternary mixture In this paper, the Kirkwood-Buff (KB) theory of solutions (or fluctuation theory) (Kirkwood and Buff, 1951) is employed to analyze the solid (particularly drug) solubility in mixed (mainly aqueous) solvents. The analysis is based on results obtained previously regarding the composition derivatives of the activity coefficients in ternary solutions (Ruckenstein and Shulgin, 2001). These equations were successfully applied to gas solubilities in mixed solvents (Ruckenstein and Shulgin, 2002 Shulgin and Ruckenstein, 2002). 

Lightly sulfonated polystyrene is soluble in mixed solvent systems, such as xylene containing low levels of alcohols, or in moderately polar solvents. In low polarity solvents the viscosity of such ionomer solutions can be substantially higher than polystyrene of comparable molecular weight due to ion pair association at concentrations >1% as shown in Table I. 

A cosolvent partitioning approach has been developed, based on the solubility in mixed solvents, to account for the effect of DOM and colloidal material that could result in a higher value for Cf.. The distribution of a compound, in this case, benzo[fl]pyrene, is observed as a fiinction of the volume fraction of methanol (Fig. 3.7) The influence of DOM and colloids is overcome when the volume fraction of methanol is >20% and extrapolation to the y axis provides a cosolvent distribution ratio that can be converted to a by multiplying by the molar volume of water. 

There have been two FST approaches to gas solubility in mixed solvents. The first (O Connell 1971a) expressed in terms of collections of DCFI with simple parameterization details of the relations are given in Section 9.33.2. The second (Mathias and O Connell 1979 Campanella, Mathias, and O Connell 1987) used the DCFI model of Equation 9.4 by integrating the DCFI for the solute from one pure solvent, identified as reference solvent, r, to the mixture composition, which for a binary is given by Xr. Then,... 

This method requires values of the pure solute properties. Alternatively, if solute solubilities in mixed solvents are available, these data can be regressed for the parameters simultaneously and the pure solute properties are not needed. Note that the theory demands that parameters for a particular solute-solvent pair be the same for all systems involving the pair, regardless of the additional solvent. In EUegaard, Abildskov, and O Connell (2010), those regressed from ternary data... 

Details regarding the applications of the KB theory of solutions to solubility can be found in a recently published book (Ruckenstein and Shulgin 2009). We also mention here the contribntions of Mazo and Smith (Mazo 2006, 2007 Smith and Mazo 2008) to the application of the KB theory of solntions to the solubility in mixed solvents (see also Section 1.3.5 in Chapter 1 and Chapter 9). 

O Connell, J. P. and J. M. Prausnitz. 1964. Thermodynamics of gas solubility in mixed solvents. Industrial and Engineering Chemistry Fundamentals. 3, 347. 

Smith, P. E. and R. M. Mazo. 2008. On the theory of solute solubility in mixed solvents. Journal of Physical Chemistry B. 112, 7875. 

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