The velocity sedimentation and isothermal translational diffusion studies were made separately in three different solvents: water, dimethylformamide (DMF) and dimethylsulfoxide (DMSO). The solubility of the CDs studied in these solvents increases in the following order: H2O < DMF < DMSO. The velocity sedimentation experiments were run overnight (12–14 h), at a solute concentration c ≅ 4 mg/mL. Figure 1 represents the sedimentation interference profiles of α-cyclodextrin in DMF and in DMSO as well as the calculated distribution of the sedimentation coefficients, c(s), as obtained by the use of the Sedfit program. Figure 2 shows the comparison of the normalized differential distributions for γ-CD, obtained in the different solvents. The density increment (Δρ/Δc), which is also required for the quantitative interpretation of the sedimentation data, allows the determination of the partial specific volume  The value remained the same for different CDs in the same solvent and was found to be 0.667, 0.632, and 0.649 cm3/g in H2O, DMF, and DMSO, respectively. The refractive index increment (Δn/Δc) also remained virtually the same for different CDs in the same solvent: 0.148, 0.104, and 0.07 cm3/g in H2O, DMF, and DMSO, respectively. The translational diffusion was studied at an average solute concentration c of ≅1–2 mg/mL (Fig. 3).
Fig. 1 Velocity sedimentation of CDs: experimental data and evaluations obtained with the Sedfit program. a α-CD with c = 4.2 × 10−3 g/cm3 in DMF, b the same solute with c = 4.8 × 10−3 g/cm3 in DMSO. Panels at the top show the superposition of some interference profiles on the whole range of sedimentation time (12 h), those at the middle the corresponding residual plots. The panels at the bottom represent the distribution of sedimentation coefficients, c(s), obtained with a regularization procedure with a confidence level of 0.70
Fig. 2 Comparison of the normalized differential distributions of sedimentation coefficients, c N(s), of γ-CD in H2O (1), DMF (2), and DMSO (3), as obtained with the Sedfit program. For clearness each distribution is normalized on the maximal value of c max(s) such as c N(s) ≡ c(s)/c max(s) to eliminate the influence of different increments of refractive indexes
Fig. 3 Time dependence of dispersion of the diffusion boundary 2σ2 versus time t of diffusion in H2O (a) and DMF (b), for α-CD (1), β-CD (2), and γ-CD (3)