041911-3
Kucheyev et al.
Appl. Phys. Lett. 89, 041911 ͑2006͒
only slightly increases E but, at the same time, results in a
slight reduction in H. Finally, the choice of the solvent dur-
ing the sol-gel synthesis ͑which, as discussed above, affects
the average width of the nanoleaflets͒ also affects AG me-
chanical properties ͑compare circles and up triangles in Fig.
3͒. Hence, it would not be appropriate to describe data from
Fig. 3 with scaling law models for mechanical properties of
porous solids12,22 since, in addition to the monolith density,
other important parameters are variable and strongly affect
mechanical characteristics.
The above results demonstrate that both the framework
connectivity and the mechanical properties of individual
nanoligaments in foams with a nanoleaflet morphology can
be improved by thermal processing, which causes dehydra-
tion, phase transformation, and associated curling of leaflets.
FIG. 3. ͑Color online͒ Dependencies of contact pressure ͑H, closed sym-
bols͒ and Young’s modulus ͑E, open symbols͒ on the density of the follow-
ing sets of aerogels: CWE-1 ͑circles͒, CWE-2 ͑stars͒, CE ͑up triangles͒, and
NE ͑down triangles͒. Data for full-density alumina are shown by diamonds.
brittle nanoporous solids than for full-density materials. In-
deed, the hardness for full-density ͑nonviscoelastic͒ solids is
defined by fundamental physical processes such as the gen-
eration and mobility of dislocations, slip, and/or pressure-
induced phase transformations. In contrast, deformation
mechanisms in brittle nanofoams ͑such as alumina AGs͒ are
currently poorly understood6,8–15 but likely involve elastic
bending and brittle fracture of struts, accompanied by the
collapse of pores and foam densification. In this case, hard-
ness is determined by the fracture toughness of struts rather
than by the dislocation and slip activities or phase transfor-
mations as for full-density solids.
It is seen from Fig. 2 that for AGs with the nanoleaflet
morphology, both E and H increase with increasing monolith
density. More importantly, for a given monolith density, AGs
with the nanoleaflet morphology are significantly stiffer and
have larger H than AGs with the string-of-pearls morphol-
ogy. Figure 2͑b͒ also shows that, except for indenter penetra-
tion depths Շ1 m affected by surface roughness, E is es-
sentially independent of depth. However, H increases with
depth for all the samples ͓Fig. 2͑a͔͒, which we attribute to
the effects of strut fracture, associated collapse of pores, and
accumulation of the strut material beneath the indentation
contact with increasing load.
Table I also shows that our alumina AGs have
exceptional mechanical properties. For example, cross-
linked “strong” silica-based AGs with densities of
ϳ250–300 mg cm−3, recently reported by Leventis et al.13,
have E of ϳ5–12 MPa, which are comparable to values for
our alumina AGs with the string-of-pearls morphology of
similar densities, but which are an order of magnitude
smaller than E for our AGs with the nanoleaflet morphology.
The dependence of H and E on material parameters is
more clearly illustrated in Fig. 3. It is seen that both H and E
decrease superlinearly with decreasing relative density of
AGs, with slopes of 2.9 0.3 and 2.8 0.2, respectively.
However, it is clear that data for neither H nor E closely
follow a simple power law scaling with a constant exponent.
Hence, in addition to the monolith density, other parameters
͑in particular, the crystallographic phase and shape of liga-
ments͒ strongly influence the mechanical properties of the
nanofoam. For example, data from Fig. 3 and Table I clearly
show that thermal annealing of AGs with the nanoleaflet
morphology which causes curling of the nanoleaflets, results
in a dramatic improvement of mechanical properties. In con-
trast, annealing of AGs with the string-of-pearls morphology
Work at LLNL was performed under the auspices
of the U.S. DOE by the UC, LLNL under Contract No.
W-7405-Eng-48. Work at the ANU was supported by the
ARC.
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17A skeletal density of alumina of 3.4 g cm−3 was used to estimate the rela-
tive density of AG monoliths since all the three phases of alumina studied
here have densities similar to that ͑3.4, 3.4, and 3.7 g cm−3 for boehmite,
diaspore, and ␥-Al2O3, respectively͒ ͑Ref. 18͒. We are also not aware of
any reports of E and H measurements for full-density boehmite and di-
aspore. In Table I, we use E=200 GPa and H=10 GPa for full-density
alumina since these values are representative of full-density ␥-Al2O3 and
amorphous Al2O3 ͑Ref. 19͒.
18CRC Handbook of Chemistry and Physics, 84th ed., edited by D. R. Lide
͑CRC, New York, 2003͒.
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and CWE-2 in Table I was a different concentration of the precursor in the
starting solution, resulting in different densities of AG monoliths.
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