Experimental section

Materials

All substances were Sigma-Aldrich products. In all calorimetric measurements, the concentration of QCT was between 1.5 x 10^-4 and 2.0 x 10^-4 mol kg^-1, while the concentration range for the for HPCD was between 2.2 x 10^-3 and 2.5 x 10^-2 mol kg^-1. The average degree of substitution of the HPCD employed was 4.2. Solutions were prepared just before measurements employing phosphate and citrate buffers, at pH = 8.0 and 3.6, respectively.

Preparation and characterization of QCT-HPCD complex

QCT and HPCD were dissolved in each buffer solution at a 1:1 molar ratio and placed in a thermostatic bath under mild agitation (100 rpm) at 37 °C for 72 h. During mixing, each flask was covered with aluminum foil to prevent QCT photodegradation. The obtained QCT-HPCD inclusion complexes were characterized by phase solubility experiments, differential scanning calorimetry curves and isothermal microcalorimetry tests, as described in the following.

Phase solubility experiments

Prior to phase solubility tests, citrate and phosphate buffer were prepared. Citrate buffer was prepared by dissolving 1.93 g of sodium citrate and 2.41 g of citric acid in 500 mL of double-distilled water (DDW). The solution was magnetically stirred for 30 min at room temperature and diluted with further DDW to a final 1 L volume. The resulting liquid was filtered through a 0.45-m membrane filter, and the pH was adjusted to 3.6. For phosphate buffer, 0.201 g of KCl, 7 g of NaCl, 1.42 g of Na2HPO4 were solubilized and the same procedure employed. The pH was adjusted to 8.0.

To verify the formation of QCT-HPCD inclusion complexes, phase solubility experiments were carried out as follows. An excess amount of QCT was suspended in 10 mL of citrate or phosphate buffers containing HPCD in the 3–15 mM concentration range. The suspensions were poured in capped vials, vortexed for 5 min and mixed in the dark at 37 °C in a thermostatic bath for 72 h under continuous agitation at 100 rpm. Thereafter, the solutions were filtered through a 0.45-m membrane and the filtered solution was analyzed by spectrophotometric assay to quantify the solubilized QCT (UV-1800, Shimadzu Laboratory World, Japan; k = 370

41

and 382 nm in citrate and phosphate buffer, respectively). The phase diagram was obtained by plotting the molar concentration of solubilized QCT against HPCD molar concentration.

The stability constant of the QCT-HPCD complex was calculated from the slope of the phase solubility diagram, with the equation:

𝐾_𝑐 = _𝑆 ^{𝑠𝑙𝑜𝑝𝑒}

0(1−𝑠𝑙𝑜𝑝𝑒) (19) where S0 is QCT solubility in the absence of HPCD.

Differential Scanning Calorimetry

The formation of the complex between QCT and HPCD has been qualitatively investigated by performing thermo-analytical tests on the lyophilized solutions (24 h, 0.01 atm, -60 °C;

Modulyo, Edwards, UK) obtained from phase solubility. Particularly, the heats involved in the melting of QCT, HPCD, the inclusion complex and the recovered precipitate from phase solubility tests were determined by a differential scanning calorimeter (DSC Q20, TA Instruments, USA), preliminarily calibrated with a pure indium standard. Weighted solid samples (approximately 3–4 mg) were placed in aluminum pans and scanned from 40 to 400

°C at a constant heating rate of 10 °C min^-1, under an inert nitrogen atmosphere purged at a constant 50.0 mL min^-1 flow rate. The melting temperature (Tm) was obtained from the fusion peak.

Isothermal Calorimetry

Measurements of the experimental heats of dilution or mixing of two binary solutions containing any one of the solutes were determined at 298 K using a thermal activity monitor (TAM) from Thermometric, equipped with a flow mixing vessel. A P3 peristaltic pump from Pharmacia envoys the solutions into the calorimeter through Teflon tubes.

The values of the experimental heats (of dilution or mixing) can be obtained from the equation:

∆𝐻 =^{𝑑𝑄/𝑑𝑡}_𝑃

𝑊 (20)

42

where dQ/dt (W) is the heat flux, PW (kg^-1) is the total mass flow rate of the solvent through the calorimeter, and H is given in J kg^-1 of solvent in the final solution.

The following two kinds of experiments were arranged:

1. The determination of the heat of dilution, Hdil (𝑚^𝑖 → 𝑚^𝑓), from the initial, mⁱ, to the final, m^f, molality of binary aqueous solutions of HPCD or QCT, at the different concentrations employed.

2. The determination of the heat of mixing, HMIX [(𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑖 )(𝑚_𝑄𝐶𝑇^𝑖 ) → 𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑓 , 𝑚_𝑄𝐶𝑇^𝑓 ] of binary aqueous solutions of QCT, with binary aqueous solutions of HPCD.

Dilution and mixing experiments were carried out using PBS buffer as solvent. The enthalpy of mixing two binary solutions, HMIX, is related to the enthalpy of formation of a complex, or in general to the enthalpy of interaction between solutes, H*, and to the heats of dilution experienced by the two solutes, Hdil, by the following equation:

∆𝐻𝑀𝐼𝑋 [(𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑖 )(𝑚_𝑄𝐶𝑇^𝑖 ) → 𝑚_{𝐻𝑃𝛽𝐶𝐷,}^𝑓 𝑚_𝑄𝐶𝑇 ^𝑓 = ∆𝐻^∗+ ∆𝐻𝑑𝑖𝑙(𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑖 → 𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑓 ) +

∆𝐻_𝑑𝑖𝑙(𝑚_𝑄𝐶𝑇^𝑖 → 𝑚_𝑄𝐶𝑇^𝑓 )] (21)

Treatment of the data

Assuming that a 1:1 complex is formed when mixing two binary solutions, the association process can be represented as follows:

𝐻𝑃𝛽𝐶𝐷 + 𝑄𝐶𝑇 ↔ 𝐻𝑃𝛽𝐶𝐷 ∙ 𝑄𝐶𝑇 (22)

H*, normalized to the total molality of the guest, 𝑚𝑄𝐶𝑇 can be related to the actual molality of the cyclodextrin host molecule, 𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑓 , to the standard molar enthalpy of association, 𝐻_𝑎^° , and to the apparent affinity constant, 𝐾𝑎′, as follows (Liu et al., 2013):

𝑚_𝑄𝐶𝑇

∆𝐻^∗ = _∆𝐻¹

𝑎° +_∆𝐻 ¹

𝑎°𝐾_𝑎^′𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑓 (23) For each value of H*, the actual concentration of the host molecule is given by:

43 𝑚_{𝐻𝑃𝛽𝐶𝐷}^𝑓 = 𝑚_{𝐻𝑃𝛽𝐶𝐷}−_∆𝐻^∆𝐻∗

𝑆𝐴𝑇∗ ∗ 𝑚_𝑄𝐶𝑇 (24) where 𝑚𝑄𝐶𝑇 is the total stoichiometric molality of the host molecule. The standard enthalpy and the constant are obtained from Eqs. (23) and (24) by an iterative least-squares fitting. The iterations are continued until two successive values of H° a differ by less than 2%. The values of the free energy and entropy are obtained through the usual thermodynamic relations. The absence of any information about the activity coefficients leads to the evaluation of association parameters thermodynamically not exactly defined. Only an apparent constant, 𝐾𝑎′, can be determined, and consequently the standard free energy and entropy suffer of the same limitations.

3.2 Thermodynamic studies of complex formation between hydroxypropyl--cyclodextrin and quercetin in water–ethanol solvents at T = 298.15 K (Paper II)