In the current work, a size-effect
model was developed to describe
the particle size-dependence of adsorption at solid/liquid interfaces.
A parameter, ΔQ
ad, was introduced,
defined as the change of the product of the solid/liquid interfacial
tension and the molar volume of solid surface components caused by
adsorption. The model predicts that with a decrease in particle radius
(r), the saturation adsorption amount per unit area
(Γm, mol/m2) decreases, while the change
of the adsorption equilibrium constant (K
ad) is determined by the ΔQ
ad, namely,
it decreases if ΔQ
ad > 0 but
increases
if ΔQ
ad < 0. There exists a critical r at which the saturation adsorption amount per unit mass
(Γm
g,
mol/g) attains a maximum. In addition, the adsorption of cetylpyridinium
chloride (CPyCl), a cationic surfactant, on silica nanoparticles with
different r (ca. 6–61 nm) values was determined
at 298 K and pH 9, showing an obvious size-dependence. With a decrease
in r, K
ad and Γm decrease, indicating a decrease in the affinity of silica
particles toward CPyCl. The size-dependent adsorption data can be
well described using our model. Adsorption can affect the molar volume
of the solid surface phase, which plays an important role in the size-dependence
of adsorption. This work provides a better understanding of the size-dependent
adsorption phenomenon at solid/liquid interfaces.