Page 34 - Nanotechnology an introduction

Figure 3.7 Drops of rainfall on the leaves of the lupin showing the superhydrophobicity.
A similar approach has been used to derive the Cassie–Baxter law for surfaces chemically inhomogeneous (on the nanoscale). Suppose that such
a surface is constituted from fractions f of N different materials, which individually in pure form yield contact angles θ with the liquid under test.
i
i
Then,

(3.27)
†
where θ is the effective contact angle. The advent of nanofabrication has yielded intriguing situations of drops resting on the tops of arrays of
nano- or micropillars, let us suppose with a height r and covering a fraction f of the surface. If the drop remains on the top of the pillars (a situation
that has been called the fakir effect), the surface would presumably be sensed as smooth (with the air–liquid interface between the pillars remaining
parallel to the mean plane of the substrate), but chemically heterogeneous, and the Cassie–Baxter law would be applicable, simplifying to
. If on the other hand the drop completely wets both the horizontal and vertical surfaces, the surface is sensed as rough and
the Wentzel law would be applicable. As the “intrinsic” contact angle varies, the drop can minimize its energy by either obeying the Wentzel law (for
a hydrophilic material) or the Cassie–Baxter law (i.e., displaying the fakir effect, for hydrophobic surfaces). The crossover point between the two
regimes is given by .

3.4.2. Three-Body Interactions

The main structural unit of proteins is the alpha helix. Simple polyamino acids such as polyalanine will fold up spontaneously in water into a single
alpha helix. Many proteins, such as the paradigmatical myoglobin, can be adequately described as a bundle of alpha helical cylinders joined
together by short connecting loops. The alpha helix is held together by hydrogen bonds between the ith and i+4th amino acid backbones.
Denatured myoglobin has no difficulty in refolding itself spontaneously in water, correctly reforming the alpha helices, but one might wonder why the
process is so robust when the denatured polypeptide chain is surrounded by water molecules, each of which is able to donate and accept two
hydrogen bonds (albeit that at room temperature, 80–90% of the possible hydrogen bonds between water molecules are already present—see
Section 3.8). The paradox is that although refolding is an intramolecular process, the overwhelming molar excess of water should predominate,
ensuring that the backbone hydrogen bonds are always fully solvated by the surrounding water and hence ineffectual for creating protein structure.
One of the intriguing features of natural amino acid sequences of proteins is their blend of polar and apolar residues. It was formerly believed that
the protein folding problem involved simply trying to pack as many of the apolar residues into the protein interior as possible, in order to minimize
the unfavorable free energy of interaction between water and the apolar residues. Nevertheless, a significant number (of the order of 50% of the
total, for a folded globular protein of moderate size) of apolar residues remains on the folded protein surface.
The presence of an apolar residue in the vicinity of a hydrogen bond is a highly effective way of desolvating it. Folding success actually involves the
juxtaposition of appropriate apolar residues with backbone hydrogen bonds. The effectiveness of desolvation of a hydrogen bond can be
computed by simply counting the number of apolar residues within a sphere of about 7 Å radius centered midway between the hydrogen bond
donor and the hydrogen bond acceptor [54]. This approach, which can be carried out automatically using the atomic coordinates in the protein data
bank (PDB), reveals the presence of dehydrons, underdesolvated (or “underwrapped”) hydrogen bonds. Clusters of dehydrons are especially
effective “sticky patches” on proteins.
3.5. Weak Competing Interactions

In any assembly process starting from a random arrangement, it is very likely that some of the initial connexions between the objects being
assembled are merely opportunistic and at a certain later stage will need to be broken in order to allow the overall process to continue. For this
reason, it is preferable for the connexions to be weak (i.e., the types considered in Section 3.2; e.g., hydrogen bonds) in order to enable them to be
broken if necessary. The impetus for breakage comes from the multiplicity of competing potential connexions that is inevitable in any even
moderately large system.

One example is provided by superspheres (see Section 8.2.9). Another is biological self-assembly (e.g., of compact RNA structures, Section
8.2.11)—bonds must be broken and reformed before the final structure is achieved. This is particularly apparent because these molecules are
synthesized as a linear polymer, which already starts to spontaneously fold (which means forming connexions between parts of the polymer that are
distant from each other along the linear chain) as soon as a few tens of monomers have been connected. As the chain becomes longer, some of