Table 1.
Morphological parametrs of ns-TiO2 samples measured by AFM.
Table 2.
IEP of colloidal AFM probe and reference flat substrates.
Figure 1.
Top and 3-dimensional views of AFM topographic maps of ns-TiO2 films.
Thickness of ns-TiO2 films is (A, D) 8 nm; (B, E) 50 nm; (C, F) 200 nm. Representative topographic profiles are superimposed to top-view maps.
Figure 2.
Double layer force-distance curves at ns-TiO2 surfaces.
(A) Average force curves at pH∼5.4 and [NaCl] = 1 mM between the colloidal borosilicate glass probe and ns-TiO2 films with different roughness. (B) The net surface charge density σS of ns-TiO2 versus roughness Rq, extracted from the best fit of average force curves by Eq. 6. For comparison, the net surface charge density of the reference <100> rutile TiO2 surface is also shown. (C) Debye lengths λD as a function of the surface roughness Rq of ns-TiO2 films extracted from the best fit of force curves by Eq. 6.
Figure 3.
Schematic representation of the interaction geometry of a colloidal probe with a nano-rough surface.
Red upper line: plane of first-contact, defined by the protruding asperities; orange bottom line: mid-plane, or average plane of charges. The distance between the two planes is approximately equal to Rq.
Figure 4.
Double layer force-distance curves at ns-TiO2 surfaces with corrected distance axis.
(A) Average force curves at pH∼5.4 and [NaCl] = 1 mM between the colloidal borosilicate glass probe and ns-TiO2 films with different roughness with corrected distance axis (i.e. positively shifted by Rq, see main text for details). (B) The net surface charge density σS of ns-TiO2 versus Rq, extracted from the best fit of force curves by Eq. 6 after correction of distance axes. For comparison, the net charge density of the reference <100> rutile TiO2 is also shown.
Figure 5.
The net surface charge density σS of ns-TiO2 films.
Evolution of the net surface charge density σS with pH for ns-TiO2 films with increasing roughness (Rq ≥ 20 nm; all films have similar IEP, see Table 3 and Figure 6).
Figure 6.
pHIEP of ns-TiO2 samples with different rms roughness Rq.
For comparison, pHIEP of flat single-crystal <100> and polycrystalline rutile TiO2 samples are shown.
Table 3.
IEP of ns-TiO2 samples.
Figure 7.
Schematic representation of the self-overlap of electrical double layers at corrugated interfaces.
A simplified double layer extending to a distance λD into the bulk of the electrolyte is shown. Surface pores are characterized by half-width ξ, height 2Rq, and slope 2Rq/ξ. (A,B) Two pores with same height 2Rq, same double layer depth λD, but markedly different slope. (C) A “real” surface pore of a cluster-assembled nanostructured surface in aqueous electrolyte: pore structure is statistically scale-invariant, replicating itself at small scales.