Materials and methods
The CDs studied, α-, β- and γ-cyclodextrin, were obtained commercially from Sigma (purity ≥ 98%) (Table 1). Velocity sedimentation, the translational diffusion, and viscosity as well as the increment of density were measured in three different solvents: water, dimethylformamide, and dimethylsulfoxide.
Table 1 Images of modeling structures, calculated molecular mass (M calc), inner (d ii) and outer (d 0i) diameters and the values of molecular mass obtained with MALDI-TOF MS of cyclodextrin molecules
CD Images of modeling structures  M calc (g/mol)  d iia (108 cm)  d 0ia (108 cm)  M (MALDI) (g/mol)
α-CD (C6H10O5)6 972.9 5.0–4.7 14.6 972.4
β-CD (C6H10O5)7 1,135.0 6.5–6.0 15.4 1,134.5
γ-CD (C6H10O5)8 1,297.1 8.3–7.5 17.5 1,296.6
aAs measured on space-filling or CPK models (Saenger 1980; Corey and Pauling 1953)
Sedimentation velocity experiments were performed on a Beckman XLI analytical ultracentrifuge at a rotor speed of 55,000 rpm and at 20°C in Al-double-sector cells of optical path 12 mm using interference optics. The evaluation program Sedfit for continuous particle size distributions (Schuck 2000) was used for data analysis. The regularization method used was the Tikhonov-Philips 2nd derivative, and the confidence level (F ratio) chosen was 0.8–0.9. By fitting for (f/f sph) in a nonlinear regression, an estimate of the weight-average frictional ratio of all macromolecules in solution is obtained, where f is the frictional ratio of the solute macromolecule and f sph is the frictional ratio of the rigid sphere with the same “anhydrous” volume (free of solvent) as the macromolecule. The final result is the differential distribution (dc(s)/ds) of the sample, which is named c(s). It is scaled such that the area under the c(s) curve between the smallest s value, s 1, and the largest one, s 2, in the distribution will give the loading concentration of macromolecules between these sedimentation coefficients (expressed in number of fringes, J, in the case of interference optics). J, which is proportional to the polymer concentration in solution, was used to calculate the refractive index increment: (Δn/Δc) = Jλ/Kcl (Pavlov et al. 2003), where λ is the wavelength (675 nm), K the magnifying coefficient and l the optical path. With K = 1 and l = 12 mm we obtain: Δn/Δc = 5.625 × 10−5(J/c) and c in g/cm3.
Translational diffusion was studied by the classical method of forming a boundary between the solution and the solvent on Tsvetkov polarizing diffusiometer (Tsvetkov 1989). The diffusion boundary was formed in glass cell of length h = 30 mm along the beam path. The optical system used for recording the solution-solvent boundary in diffusion analysis was a Lebedev’s polarizing interferometer (Lebedev 1930). Translational diffusion coefficients were calculated from the equation: 1 where σ2 is the dispersion of the diffusion boundary calculated from the maximum ordinate and the area under the diffusion curve, σ02 is the zero dispersion characterizing the quality of boundary formation, and t is the diffusion time. Experiments were carried out at 25°C, and the intrinsic diffusion coefficient, which depends only on the macromolecule properties, is calculated as: [D] = D 0η0/T.
Viscosity measurements were conducted using an Ostwald viscometer. The respective flow times, τ0 and t, were measured at 25°C for the solvent and polymer solutions, with relative viscosities ηr = t/τ0. The extrapolation to zero concentration was made by using both the Huggins and Kraemer equations (Cantor and Schimmel 1980; Tsvetkov 1989) and the average values were considered as the value of intrinsic viscosity.
The density measurements were carried out in the density meter DMA 5000 (Anton Paar, Graz, Austria) according to the procedure of Kratky et al. (1973).
The cyclodextrins were investigated also by Matrix-Assisted Laser Desorption/Ionisation Time-Of-Flight Mass Spectrometry (MALDI-TOF MS). MALDI-TOF MS measurements were performed with an Ultraflex III TOF/TOF (Bruker Daltonics, Bremen, Germany) equipped with a Nd:YAG laser and a collision cell. All spectra were measured in the positive reflector mode. For the MS/MS mode, argon was used as collision gas at a pressure of 2 × 10−6 mbar. The instrument was calibrated prior to each measurement with an external PMMA standard from PSS Polymer Standards Services GmbH (Mainz, Germany) in the required measurement range. MS and MS/MS data were processed using PolyTools 1.0 and an isotope pattern calculator.