Page 36 - Nanotechnology an introduction

Writing this as a polynomial in p using equation (3.34), it will be noticed that for p < p the value of the series converges, but for p > p the value of
c
c
the series diverges. The “critical” value p = p corresponds to the formation of the “infinite” cluster. For site percolation on a square lattice, p = p =
c
c
0.5; the universal Galam–Mauger formula [59]
(3.37)
with a= 1.2868 and b = 0.6160 predicts p , with less than 1% error, for all known lattices of connectivity q embedded in a space of dimension d.
c
The larger the lattice, the sharper the transition from not percolating to percolating. For a 3 × 3 lattice there can be no percolation for two particles
or less, but the probability of randomly placing three particles in a straight line from edge to edge is evidently one third.
3.8. The Structure of Water

So much nanotechnology takes place in water, including microfluidic-enabled reactors, many self-assembly processes, as well as
nanobiotechnology and bionanotechnology, that it is important to recall some of the salient features of this remarkable liquid.
Water—H–O–H—can participate in four hydrogen bonds (HB). The two electron lone pairs (LP) on the oxygen atom are electron donors, hence HB
acceptors. The two hydrogens at the ends of the hydroxyl groups (OH) are HB donors, hence electron acceptors. The equilibrium

(3.38)
is balanced such that at room temperature about 10% of the OHs and LPs are nonbonded, i.e. free. It is especially noteworthy that the
+
concentrations of these two free species are 7–8 orders of magnitude greater than the concentrations of the perhaps more familiar entities H and
−
OH , and their chemical significance is correspondingly greater.
The OH moiety has a unique infrared absorption spectrum, different according to whether it is hydrogen-bonded or free, which can therefore be
used to investigate reaction (3.38). A striking example of how the equilibrium can be controlled is given by the spectroscopic consequences of the
−
+
addition of cosolutes. If sodium chloride is added to water, the Na and Cl ions can respectively accept and donate electron density to form
quasihydrogen bonds to appropriate donors and acceptors in roughly equal measure, and the intensity of the OH band in the infrared spectrum
does not change. If sodium tetraphenylborate is added, the borate ion is prevented by its bulky phenyl ligands from interacting with the water,
resulting in fewer bonded OH groups; hence in order to maintain the equilibrium (3.38) the concentration of free lone pairs must diminish.
Conversely, if tetrabutylammonium chloride is added, there will be an excess of bonded OH.
On the basis of extensive experiments on hydrogels, Philippa Wiggins has proposed that two kinds of water, low and high density with respectively
more and less hydrogen bonding, can be created by surfaces in contact with aqueous solutions. Although the theoretical interpretation of the
phenomenology is as yet incomplete, whatever its origins it must inevitably have profound effects on nanoscale fluidic circuits, in which essentially
all of the fluid phase is in the vicinity of solid surfaces.

3.9. Summary
The large ratio of surface to volume characteristic of nanoscale objects and devices places interfacial forces in a prominent position in governing
their behavior. Although subject to criticism, the surface tension formalism allows the magnitudes of these forces between objects made from
different materials in the presence of different liquids to be quickly estimated from tables of experimentally derived “single substance surface
tensions”.
In aqueous systems, Lewis acid/base interactions, most notably hydrogen bonding, typically dominate the interfacial forces.

Real, that is morphologically and chemically heterogeneous, surfaces require some modification to the basic theory. In some cases a simple mean-
field correction may be adequate; in others nanostructure must explicitly be taken into account. This is especially strikingly shown in protein
interactions, which are actually three-body in nature and depend on the subtle interplay of solvation and desolvation.
Multiple forces of different strength and range may be operating simultaneously. This provides the basis for programmability. The assembly of
objects into constructions of definite size and shape is only possible if programmability is incorporated, and in the nanoscale this can typically only
be achieved by judicious design at the level of the constituent atoms and groups of atoms of the objects.
Multibody connexions provide the basis for cooperativity, an essential attribute of many “smart” devices. Another collective phenomenon is
percolation, which is a paradigm for the assembly process known as gelation.
3.10 Further Reading
Binns, C., Prodding the cosmic fabric with nanotechnology, Nanotechnol. Percept. 3 (2007) 97–105.
Cacace, M.G.; Landau, E.M.; Ramsden, J.J., The Hofmeister series: salt and solvent effects on interfacial phenomena, Q. Rev. Biophys. 30 (1997)
241–278.
de Gennes, P.G., Wetting: statics and dynamics, Rev. Mod. Phys. 57 (1985) 827–863.
Rowlinson, J.S.; Widom, B., Molecular Theory of Capillarity. (1982) Clarendon Press, Oxford.