## 2 Methods for Determination of Lipophilicity
### Indirect Experimental Determination of Lipophilicity
#### 2.3.2 Reversed-Phase High-Performance Liquid Chromatography
The retention factor k is easily calculated using the retention time (t\({}_{r}\)), according to Equation (5) [27; 30]:  
\[\log\mathrm{k}=\log\biggl{(}\frac{\mathrm{t}_{r}-\mathrm{t}_{0}}{\mathrm{t}_{0}} \biggr{)} \tag{5}\]  
where t\({}_{0}\) is the dead retention time (the retention time of an unretained solute) and t\({}_{r}\) is the retention time of the solute. The major factors that influence the retention time are the nature, length, and diameter of the stationary phase and the composition and flow rate of the mobile phase [57]. Compounds that are either unretained or too retained may have to be assessed using different column lengths or eluent compositions [77]. Under suitable isocratic conditions, the \(\log\mathrm{P}\) of the compound under study is obtained by measuring its retention factor and then inputting the k values into the Collander equation:  
\[\log\mathrm{P}=\mathrm{a}\ \times\log\mathrm{k}+\mathrm{b} \tag{6}\]  
where a and b are regression constants for the slope and intercept obtained by linear regression of the \(\log\mathrm{P}\) of reference substances against the \(\log\mathrm{k}\) of the reference substances. In these conditions, the k-value of a given solute and stationary phase depends on the composition of the mobile phase [77]. To address this problem, pure aqueous eluent (log k\({}_{w}\)) should be used as it is not affected by the organic modifier and reflects the partitioning behavior that occurred in a shake-flask measurement [77; 85]. As under most conditions pure water cannot be used as mobile phase, \(\log\mathrm{k}_{w}\) is obtained by extrapolation to 100%  
\begin{table} \begin{tabular}{c c c c} \hline \hline
**Analytes** & **Aim** & **Chromatographic Method** & **Chromatographic Conditions** & **Ref.** \\ \hline Quinolone drugs & Estimate lipophilicity and correlate it with pharmacokinetic & MLC/UV-Vis (270 nm) & Column: Kromasil C18 column (150 \(\times\) 4.6 mm, 5 \(\upmu\)m); MP: 0.05 M phosphate buffer at pH 7.4 with Brij35 and with NaCl (9.20 g/L); FR: 1 mL/min \\ \hline \(\beta\)-Hydroxy-\(\beta\)-aryalkanoic acids analogues & Estimate lipophilicity and correlate it with absorption & MLC/DAD & Column: Zorbax Extend-C18 (150 mm \(\times\) 4.6 mm, 5 \(\upmu\)m); MP: 40 mM solution of Brij35 in a mixture of ACN (20\%) and 0.07 M phosphate buffer at pH 5.50 & [202] \\ \hline Structurally diverse drugs & Study the influence of pH, temperature, and ionic strength in MLC and compare it with IAM & Column: High Stability C18 Supelco (150 \(\times\) 4.6 mm, 5 \(\upmu\)m); MP: 0.05 M phosphate buffer at pH 5.5 and (220 nm) & [203] \\ \hline \hline \end{tabular}   
* [213  
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water [19; 78; 114]. The Snyder-Soczewinski equation (Equation (7)) is the most common approach to estimate \(\log\mathrm{k_{w}}\)[19]:  
\[\log\mathrm{k}=\log\mathrm{k_{w}}-\mathrm{S}\varphi \tag{7}\]  
where \(\varphi\) is the volume fraction of the organic modifier in the mobile phase and \(\mathrm{S}\) is a constant derived by linear regression analysis. The extrapolation for \(\log\mathrm{k_{w}}\) is performed by determining the \(\log\mathrm{k}\) values using different percentages of organic solvent in the mobile phases (at least four isocratic \(\log\mathrm{k}\) values) and then extrapolating to 100% of pure water eluent [19; 81; 204]. Triplicates should be made [30] and they should fall within a range of \(\pm 0.1\log\) units [30]. The classical method for the determination of \(\log\mathrm{P}\) by RP-HPLC employs isocratic conditions. For compounds with high retention factors, the determination may be challenging due to band broadening. Although it requires a more complex mathematical treatment, elution in gradient mode can be used for the determination of \(\log\mathrm{P}\) and offers faster analysis time and resolution with constant peak width [166]. In gradient methods, the lipophilicity index is expressed by a different chromatographic parameter--the chromatographic hydrophobicity index (CHI).