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Nanoscale contact optimizes adhesion
Optimal adhesion of geckos and insects based on shape
optimization
and contact surface size reduction,
report Max Planck researchers in Stuttgart, Germany

The
nanometer size of hairs (spatulae) on the feet of geckos
and many insects may have evolved to optimize adhesion
strength, according to new research conducted at the
Max Planck Institute for Metals Research in Stuttgart.
The scientists discovered that there exists an optimal
shape of the contact surface of the tip of such hairs
which gives rise to optimal adhesion to a substrate
via molecular interaction forces. For macroscopic objects,
such optimal shape design tends to be unreliable because
the adhesion strength is sensitive to small geometrical
variations. It is shown that this limitation can be
remedied via size reduction. The key finding of this
research is that there exists a critical contact size
around 100 nanometers below which optimal adhesion can
be reliably achieved independent of small variations
in the shape of the contact surface. In general, optimal
adhesion can be achieved by a combination of size reduction
and shape optimization. The smaller the size, the less
important the shape. This result provides a plausible
explanation why the characteristic size of hairy attachment
systems in biology fall in a narrow range between a
few hundred nanometer and a few micrometers and suggests
a few useful guidelines for designing adhesive structures
in engineering. (PNAS, Early Edition, 17 May 2004)
Welding, sintering, diffusion bonding and wafer bonding
are some of the widely used engineering strategies of
joining different structural components or objects together.
Normally, if two objects are joined together by adhesion
and then subject to an externally applied load, stress
concentration is expected to occur near the edge of
the joint. As the load increases, the stress intensity
ultimately reaches a critical level to drive a small
crack to propagate and break the joint. Under these
circumstance, the material in the joint is not being
used most efficiently because only a small fraction
of material is highly stressed at any instant in time.
The failure occurs by incremental propagation of cracklike
flaws. How to achieve robust and reliable optimal adhesion
between different structural components has so eluded
engineers.
Biological adhesion
mechanisms that have been tested and improved through
evolution are of interest not only to biologists but
also to engineers. Geckos and many insects have adopted
nanoscale hairy structures on their feet as adhesion
devices. The density of surface hairs increases with
the body weight of animals, and the gecko has the
highest density among all animal species that have
so far been studied. Different mechanisms, such as
capillary forces, have been proposed in the past to
explain adhesion mechanisms in biology. However, there
is now strong evidence that molecular adhesion via
van der Waals interaction plays a dominant role in
the attachment of geckos. This may appear somewhat
surprising because it takes a much greater force to
pull a gecko away from a ceiling than removing a human
hand off a table, even though the same van der Waals
force is expected to exist in both situations. A question
thus arises: What determines the adhesion strength?
The chemical nature of materials cannot explain why
the same van der Waals force results in strong adhesion
in gecko but not in human.
Apparently, nature has evolved mechanisms to utilize
weak van der Waals forces in animal species for which
adhesion is crucial for survival.

Fig.
1: The nanoscale fibrillar structures in
the hairy attachment pads of beetle, fly, spider
and gecko. The density of surface hairs increases
with the body weight of animal, and the gecko has
the highest density among all animal species.
Image: Max Planck Institute for Metals Research/Gorb

The
scientists (H. Gao and H. Yao) of Max Planck Institute
for Metals Research in Stuttgart developed a model for
adhesion between a single fiber and a substrate via
van der Waals interaction. According to their model,
the shape of the tip of the fiber strongly affects the
adhesion strength. It is shown that there exists a specific
shape, called the optimal shape, for which the adhesive
strength reaches the theoretical strength of the van
der Waals interaction. For the optimal shape, the adhesive
force is uniformly distributed over the contact area
at the instant of pulloff, corresponding to the optimal
use of material against detachment 
Fig.
2: The optimal shape of adhesion for two
objects in contact over a prescribed surface area
is defined as such that the stress distribution
is uniform and equal to the theoretical adhesion
strength of molecular (e.g., van der Waals) interaction
at pulloff. Robust optimal adhesion is achieved
when the contact size is reduced to around 100 nanometers.
At this critical size scale, the adhesion strength
becomes insensitive to small deviations from the
optimal shape.
Image: Max Planck Institute for Metals Research

Why
hasn’t such an optimal shape been used in engineering?
One problem is that the adhesion strength is found to
be highly sensitive to small variations in geometry.
For example, for a fiber with radius equal to 1 mm,
the pulloff force is found to drop by more than two
orders of magnitude with only 12% deviation from the
optimal shape. Interestingly, this hypersensitivity
in shape can be eliminated by size reduction. As the
fiber size is reduced to a critical size estimated to
be 100 nanometers, the adhesion strength remains at
the theoretical strength independent of small variations
in shape.
Therefore,
in nature and in engineering, optimal adhesion could
be achieved by a combination of size reduction and
shape optimization. The smaller the size, the less
important the shape becomes. At large contact sizes,
optimal adhesion could still be achieved if the shape
can be manufactured to a sufficiently high precision.
From a practical point of view, it is necessary to
reduce the contact size to achieve robust optimal
adhesion. These principles could be of great value
to artificial materials design.
Original work:
H.
Gao, H. Yao
Shape insensitive optimal adhesion of nanoscale fibrillar
structures
Proceedings of the National Academy of Sciences of
the USA, 2004, Vol. 101, no. 21, pp. 78517856, Early
Edition, published May 17, 2004, 10.1073/pnas.0400757101

Contact:
Prof.
Huajian Gao
MaxPlanckInstitute of Metals Research, Stuttgart/Germany
Tel.: +49 711 6893510
Fax: +49 711 6893512
Email: hjgao@mf.mpg.de



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