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P at or below 0.85, while IPs that have Log P at or above 1.86 successfully form precipitates. 

[0087] Ion pairs that are the least hydrophobic and least acidic failed the first screening test, while ion pairs with intermediate hydrophobicity and acidity failed during the first and third screening tests (FIG. 4). Successful IP agents had hydrophobicities represented by log P>2. 

[0088] Increasing difficulty in deprotonation, represented by increased pKa, requires greater hydrophobicity for suc› cessful NC formation. The first ionization of polymyxin occurs at pH=l0.23. Therefore, the li.pKa gap between oleic acid and polymyxin is over 5 units. In a previous study of hydrophobic APis, li.pKa>2 values were required for stable NC formation. For the very strongly basic polymyxin B and gentamicin, that criteria li.pKa>2 is satisfied by all of the IP counterions. These results provided general experimental insight on candidate IP selection for hydrophobic ion pair› ing. 

Model of IP Complex Equilibria 

[0089] Without being bound by theory, in order to gain additional insight on IP selection and complexation forma› tion procedures, a quantitative model of complexation and precipitation for basic and acidic APis and IPs was devel› oped and compared with experimental results. The goal was to have rules that can predict the properties of successful IP agents, and determine concentration ratios for successful FNP NC formation. For the complexation of an ionized basic API and acidic IP: 

[0090] Concentrations in square brackets are given in equivalents of anionic or cationic charge, so [ API+] indicates API in the units of molarity, with the compound having a single cationic charge. At or above saturation of ion paired complex, the concentration of aqueous API:IP is equal to the aqueous saturation concentration of API:IP. 

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Correspondingly, at or above saturation, the concentrations of aqueous API, IP, and API:IP complex are described by the equilibrium relationship of Ks and that of [ API:IPL,. While this equation is commonly reduced by combining the satu› ration concentrations and Ks terms to provide a solubility product, it is useful to separate these terms when assessing precipitation yields. 

For strongly disassociating and fully ionizedAPI and IP, the starting concentrations of ionized compounds would be equal to the initial concentrations of the salt forms added. 

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After exceeding the solubility of the API:IP complex, pre› cipitates form. The amount of precipitate formed is denoted as Vx[API:IPLM where Vis the volume of the system and [API:IPJs$_{1}$ d is the concentration of API:IP complex above its saturation concentration prior to precipitation. This relation› ship would hold, if the volume of the precipitated solid phase is much lower than that of the initial volume of reaction such that the volume of the solution phase is essentially constant. By mass balance and combining equa› tions (7-8), the concentration of aqueous soluble ionized API and IP are as follows: 

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Substitution of (9-10) into (6), yields a general expression that relates the starting concentrations of aqueous API and IP with the moles of solid precipitated API:IP complex. 

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Solving for the precipitated API:IP complex, the expression for the solid precipitate is obtained. 

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[0091] This expression holds for concentrations above the API:IP saturation concentrations. For the complexation of the strongly basic polymyxin B and gentamicin at neutral pH -7, and at concentrations where precipitates had formed, these conditions are satisfied. Thus, under these assumptions and conditions, the bulk concentration of precipitatedAPI:IP is a function of the starting concentrations of API and IP, the equilibrium constant K,, and aqueous saturation solubility [API:IPLa,-all of which are readily determined. Whereas the Ks [API:IPLa, term is typically simplified to a Ksp solubility product, separation of these two terms provides mechanistic insight on precipitation yields. Ksp is a function of complexation strength and molecular actions between the API and IP (the charged groups between the API and IP), while the [ API:IPLa, is a function of the hydrophobicity of the IP complex, e.g., a function of the complex hydropho› bicity and interactions with water due to the hydrophobic tail group on the IP. 

[0092] Inspection of Eq. 12 provides insight on how to design precipitation reactions for NC processing, as shown in FIGS. SA and SB. For a system with Ks and initialAPI and IP concentrations, the fraction of initial API that precipitates increases as the [API:IPLa, values decrease, as shown in FIG. SA. The following conditions were used to generate FIG. SA: [API]$_{0}$=l M; [IP]$_{0}$=l M; 10-$^{6 }$M<[API:IPLa,<l M; and 10- 2 M-$^{1}$<Ks<l0 4 M- 1 . If the complex is below a critical [ API:IPL, value, no solids are formed. Highly hydrophobic IPs result in the formation of API:IP complexes with lower saturation solubilities-which is in agreement with our experiment results that higher Log P complexes are 

