The absorption spectra of drugs depend on pH of the solution due to protonation/deprotonation of nitrogen atom in the drug structure. Figure 1 presents examples of the absorption spectra of three drugs at different pHs.

The calibration curves are included in these figures. The absorption spectra were recorded in the range of 190–350 nm and for the calculation of 2HP-β-CD concentration the change of absorption was measured at 340 nm (pH 7.0), 195 nm (pH 2.0) for MEF; 245 nm (pH 7.0), and 250 nm (pH 2.0) for NIF and 255 nm (pH 7.0), and 225 nm (pH 2.0) for FLU, respectively.

The aqueous solubility of the studied compounds were found to increase almost linearly with 2HP-β-CD concentration. The two exceptions are MEF and NIF at T = 298.15 K and pH = 2, for which the influence of 2HP-β-CD is linear but not very intensive (see Figure 2a and 2b). The solubility dramatically increases with an increase of pH and temperature (see Table 1).

Solubility enhance ratio, R, was calculated as a drug concentration at the highest cyclodextrin concentration with relation to drug concentration in the absence of cyclodextrin. Calculated values have been reported in Table 1. Solubility enhance ratio increases with an increase of temperature for MEF at pH = 2, 7, for NIF at pH = 2, and for FLU at pH = 2, 7 and slightly decreases with an increase of temperature for NIF at pH = 7. R decreases with an increase of pH for MEF and FLU, which demonstrates effects in drug release in the basic environment of intestinal part of the alimentary tract. The opposite effect is observed for NIF. The highest solubility enhance ratio, R is observed for FLU at pH = 2 (R = 31.0 at T = 298.15 K and R = 19.0 at T = 310.15 K) and MEF at pH = 2 (R = 17.3 at T = 310.15 K). In general, when the solubility of the drug is very low, the solubility enhance ratio, R is high. Substitution of hydroxyl groups surrounding the 2HP-β-CD rim by the hydroxypropyl group promotes the complex formation process for drug derivatives of anthranilic acid with polar carboxylic substituent. Perhaps the aromatic rings increase the 2HP-β-CD cavity dimensions and the carboxylic group stabilizing the outside hydrophilic groups and the binding of drug with 2HP-β-CD becomes more effective.

It was shown for MEF that the phenyl moieties were located outside the β-CD cavity, and the N atom that links the two phenyl rings is situated at the secondary face of the CD macrocycle with a hydrogen bond to the G4 glucose unit of the neighboring β-CD molecule [25].

Measurements of cyclodextrin-drug complex stability constants K_s and dissociation constants K_d are very important since these values indicate changes in physicochemical properties of a compound upon inclusion. Linear dependence of drug concentration to cyclodextrin concentration, with slope ratio below one usually assumes 1:1 ratio of complex.

The stability constant, K_s, for complexes with 1:1 ratio is represented by: (1) K s = [ CD ] [ D ] ⋅ [ C ]Where: [D] is pure drug concentration, [C] is pure cyclodextrin concentration, and [CD] is concentration of drug-cyclodextrin complexes in solution. Complex dissociation constant, K_d, is represented by: (2) K d = 1 K s

For such systems, stability constant can be obtained by the following equation, investigated previously by Higuchi and Connors, 1965 [25]: (3) K s = K 1 : 1 = slope c 0 ⋅ ( 1 − slope )

Calculated values are reported in Table 1. The solubility data indicate that the largest enhancement of the solubility and the highest stability constant values were obtained for FLU at pH = 2 (K_s = 3055 M⁻¹, T = 298.15 K; K_s = 1850 M⁻¹, T = 310.15 K) and for MEF at pH = 2 (K_s = 1627 M⁻¹, T = 310.15 K). These values suggest a relatively stable complex. The cavity of cyclodextrin exhibits a hydrophobic character, whereas the exterior is strongly hydrophilic. The process of complexation of MEF by 2HP-β-CD is high at two pHs and two temperatures, which can be connected with the association between the guest molecule and cyclodextrin molecule in solution via the two methyl groups of the MEF molecule stabilized by the carboxylic group outside the cyclodextrin. The structure of the three investigated compounds is similar. Two methyl groups in the molecule of MEF decrease the solubility in water in comparison with fluorine atoms of NIF and FLU and increase the complexation. The only difference between the NIF and FLU is the nitrogen atom in one of the aromatic rings in NIF. For these two substances, the molar mass is close to the same, and as a consequence of the additional nitrogen atom in NIF molecule, the stability constants, Ks are lower than those for FLU at two pH and two temperatures. The significant differences in the stability constants for different drugs at various pHs and temperatures are connected to a different drug ionization degree, which increases with lowering pH, and with consequently less affinity for neutral 2HP-β-CD cavity. Data listed in Table 1 shows that at pH = 2, the FLU is almost fully ionized. A similar effect was observed for ketoconazole and flutamide with different CDs [13].

2HP-β-CD was found to be a more suitable complexating agent between four cyclodextrins for NIF, which was confirm by ¹H NMR, UV-vis spectroscopy, densimetry and calorimetry (at pH = 7.4 and T = 298.15 K) [26]. The 1:1 stoichiometry of the 2HP-β-CD/NIF complexes was determined by Terekhova et al. [27], Zielenkiewicz et al. [26] and Bogdan et al. [28].

The phase solubility diagrams and stability constant was presented for FLU at pH = 6.75 and T = 298.15 K by Mura et al. [29].

Our value of stability constant for NIF at pH = 7 is log K_s = 1.98, whereas from the calorimetric, densimetry, UV-vis, and ¹H NMR measurements at pH = 7.4 it is log K_s = 2.2, log K_s = 2.8, log K_s = 3.09 and log K_s = 2.3, respectively (T = 298.15 K) [26]. The literature value at pH = 12 is log K_s = 2.53 [28] and at pH = 7 log K_s = 2.72 [30] (T = 298.15 K). For FLU our value of stability constant at pH = 7 is log K_s = 2.30 and the literature value, obtained also from the phase-solubility diagrams at similar pH = 6.75 is log K_s = 2.36 [29] (T = 298.15 K). We can conclude at this moment that not only the temperature and pH but also the method of developing the stability constant is important.

Thermodynamic parameters of reactions i.e. the free energy change (ΔG), the enthalpy change (ΔH) and the entropy change (ΔS), can be obtained from the temperature dependence of stability constant [2]. Calculated values are reported in Table 2.

The thermodynamic parameters of the inclusion process estimated from the temperature dependence of the stability constants using van’t Hoff relation show different values of enthalpy, which is complexation parameter control. The highest value of enthalpy was observed for FLU (−4.9 kJ·mol⁻¹) in comparison with the two other drugs (−10.0 kJ·mol⁻¹ and −24.6 kJ·mol⁻¹ for NIF and MEF, respectively). Negative values of ΔH and ΔS indicate that the van der Waals forces are responsible for the complexation process (observed only for MEF). In contrast, a huge hydrophobic interaction appears to contribute to the association of 2HP-β-CD and FLU, for which the entropy is high and positive (50.2 J·mol⁻¹·K⁻¹). The lower value of positive entropy for NIF indicates also hydrophobic interactions. The only difference between those two structures is aromatic nitrogen in the NIF structure, which increases hydrophobic interactions with 2HP-β-CD.

For the sake of comparison, only the free energy change (ΔG) of the reaction of complexation for NIF is similar to the literature value: ours is ΔG = −11.3 kJ·mol⁻¹ (T = 298.15 K and pH = 7); the literature value is ΔG = −12.3 kJ·mol⁻¹ (T = 298.15 K and pH = 7.4) [26]. The high negative value of enthalpy was obtained in previous work (−20.1 kJ·mol⁻¹) and negative entropy [26]. These results were concluded from the densimetry and ¹H NMR measurements.

Studied drugs were obtained from Sigma Aldrich, i.e., mefenamic acid (CAS Registry No. 61-68-7; ≥0.99 mass fraction purity), niflumic acid (CAS Registry No. 4394-00-7; ≥0.99 mass fraction purity), flufenamic acid (CAS Registry No. 530-78-9; ≥0.99 mass fraction purity). The drugs were used without purification and were used as powder or small crystals. 2-Hydroxypropyl-β-cyclodextrin (2HP-β-CD) was delivered by ACROS Organics (CAS Registry No.128446-35-5; ≥0.97 mass fraction purity). Water used as a solvent was twice distilled, degassed and filtered with Milipore Elix 3. The buffers solution, were prepared from substances delivered by POCH, i.e., potassium dihydrogen phosphate (CAS Registry No. 7758-11-4; ≥99.5% mass fraction purity), disodium hydrogen phosphate CAS Registry No. 7558-80-7; ≥99.5% mass fraction purity), hydrochloric acid (CAS Registry No. 7647-01-0; ≥35% mass fraction purity). All drugs were filtrated twice with Schott funnel with 4 μm pores. The names, abbreviations, structures and molar masses of the drugs and 2HP-β-CD are given in Table 3.

The UV-Vis spectrophotometer (Perkin–Elmer Life and Analytical Sciences, Shelton, USA) was used to determine the 2HP-β-CD influence on drug solubility. Maximum drug concentration was measured at different cyclodextrins concentrations, temperatures and pHs. Samples contained buffer solution with pH 7 or 2, 2HP-β-CD in different concentrations, i.e., 0, 1, 2, 4, 7 or 10 mmol·dm⁻³ and drug in excess. Samples were thermostated and mixed for 20 hours and then left for 4 hours for separation. The uncertainties of the temperature measurements were judged to be 0.1 K. Absorbance of each sample was measured with the UV-vis spectrophotometer.

The stability constants were determined by the measurements of the concentration of the drug in the sample as a function of the cyclodextrin concentration. Such a method is usually called “Phase solubility study” [31]. In this method complex stability constants are calculated from the obtained solubility data using a spectophotometric method. As a reference sample, the buffer + 2HP-β-CD solutions were used. Two buffers were prepared (mol concentration) i.e., potassium dihydrogen phosphate (0.008), disodium hydrogen phosphate (0.008; buffer, pH = 7.0), potassium dihydrogen phosphate (0.05), hydrochloric acid (0.05, buffer, pH = 2.0). Samples were scanned with a scan step of 1 nm from 650 to 190 nm. Measurements at pH = 10 were not performed in all systems, because of the necessity of using too high drug concentrations and because of problems with separation of two phases.