Page 152 - Science at the nanoscale

10:15
RPS: PSP0007 - Science-at-Nanoscale
June 5, 2009
Formation and Self-Assembly at the Nanoscale
142
Top-down
Self -
Assembly
Bottom-up
top-down
showing
bottom-up
Schematic
7.1.
Figure
and
the
approaches coupled with self-assembly in nanomaterials fabrication.
process. Conversely, when heat is released and ∆H is negative, it
is an exothermic process.
Entropy may be simply taken as a measure of the randomness
of objects in a system. An increase in entropy thus indicates the
system has become more disordered. Hence ∆S is positive when ice
melts to liquid water or when water is vaporized to steam, since
the molecules have more freedom to move about in the final state
after both processes. The concept of ∆S will be further illustrated
when we discuss self-assembly in Section 7.3.
All the three parameters G, H and S are state functions, which
mean that ∆G, ∆H and ∆S are only defined by the initial and
final states of the system, regardless of the thermodynamic path
taken. This property allows the values of ∆G, ∆H and ∆S for new
processes to be determined from several known processes as long
as the initial and final states of the substances are the same, i.e.
A → B can be worked out from A → X → Y → Z → B.
The Gibbs energy is often used to assess the direction of a nat-
ural process. At constant pressure and temperature, a chemical ch07
transformation or process will occur spontaneously in the direc-
tion of decreasing G (i.e. ∆G < 0). Thus, it follows from Eq. 7.1
that a spontaneous endothermic reaction, e.g. the boiling of water
at 100 C, occurs only if the increase in ∆S outweighs the increase
◦
in ∆H. When ∆G = 0, the system is in a state of equilibrium, with
the forward and backward processes occurring to the same extent.
7.1.2 Chemical Potential
Besides its dependence on temperature (T) and pressure (P), the
Gibbs energy also depends on the amount of substance present