Relation between molecular size and diffusivity for acid dyes, disperse dyes and their model compounds in aqueous solution.

In order to estimate the diffusivities of dyes (D) in water from their molecular size (MS), the relation between MS and D were examined for acid dyes, non-ionic azo dyes, sulfonic acids, carboxylic acids, alcohols, sugars, amides, ureas, cycloalkanes and benzene derivatives. The molar volume (Vb) at normal boiling point, the van der Waals volume (Vw) and the limiting partial volume (V°) in water were used as measures of the MS.A detailed inspection of the log (Vw, Vb or V°) vs. log (T/Dη) plots results in the following statements, where T is absolute temperature and η is viscosity of water.i) Plots of log Vb or log Vw vs. log (T/Dη) yield straight lines for solutes of a homologous series. The corresponding regression lines render possible an estimation of consistent D value of the respective solute.ii) The Stokes-Einstein equation is unsuited to correlate the parameters characterizing the MS with the diffusion coefficients D of the solutes inspected.iii) The diffusivity of the dyes in water depends on both the solute size and the effect of the solutes on water structure. The values of D for sodium disulfonates with small hydrophobic moiety are far greater than those estimated by the Wilke-Chang's equation, while the values of D for carboxylate anions are smaller than those estimated by Wilke-Chang's. This fact was explained on the facts that carboxylates and sulfonic acid groups act as water structure makers and breakers, respectively.