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.
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