A comparison of the experimental and computational results is shown in Fig. 6. As a first approximation, the space-filling models or CPK models data were used to characterize the outer and inner sizes of the CD molecules (Saenger 1980; Szejti 1998). The details of the deviation of the experimental points from the theoretical curves correlate to the above-obtained estimations concerning the hydrodynamic radii of the CD molecules in different solvents. In the plots shown, r 0 is the more crucial parameter since the ordinate directly depends on it whereas the dependence on r i becomes apparent only as a ratio of r i/r 0 in the abscissa. Both plots indicate that, in order to superimpose the experimental data to the computational results, it is necessary to increase the outer sizes of CD molecules. In practice, these sizes could be increased in solution by the absorption of a few solvent molecules to the external surface of the CD molecules, forming an absorbed layer. Thus, in solution the outer size of CD molecules may be characterized by an effective radius r 0eff = r 0 + Δr 0, where Δr 0 is the average thickness of solvent layer. The latter figure probably correlates to the size and the number of the solvent molecules. The size of the solvent molecules can be estimated by the relationship d = (6 M/πρ0 N A)1/3. 3.86, 6.26, and 6.08 × 10−8 cm for H2O, DMF, and DMSO molecules were obtained, respectively. The calculated results could be fitted to the experimental ones by assuming that the thickness of the solvent layer varies depending on the solvent, amounting for Δr 0 ≅ 0.5d solv in water and DMF but Δr 0 ≅ d solv in DMSO. These layers are formed by different numbers of solvent molecules. Qualitatively the number of DMSO molecules must be higher in comparison with both other solvents.
Fig. 6 Comparison of experimental hydrodynamic values (1–3) with the calculated hydrodynamic values for toroidal molecules (4): a characteristic translational diffusion coefficient (1, 1: in H2O, 2, 2′: in DMF, 3, 3′: in DMSO) b intrinsic viscosity (1, 1′: in DMF, 2, 2′: in DMSO) (1–3): The hydrodynamic values are plotted in function of the space-filling (or CPK) models radii r iCPK (average inner) and r 0CPK (outer) of the CD molecules (Table 1). (1′–3′): The hydrodynamic values are plotted in function of effective outer radii r 0eff (see text)