Page 28 - Partition & Adsorption of Organic Contaminants in Environmental Systems

FLORY–HUGGINS THEORY 19

For systems involving no specific interaction between components, h i usually
does not deviate greatly from 1, which is analogous to the limiting case of
Raoult’s law that g i approaches 1 as x i approaches 1.
Raoult’s law and Henry’s law have their respective advantages in describ-
ing solution and partition processes, depending on the system involved. If a
substance of interest is either completely miscible with the solvent or has a
very high solubility in the solvent, Henry’s law is preferred to account for the
behavior of the substance in the dilute range, and Raoult’s law is undoubtedly
preferred in the high concentration range; this minimizes the effort to char-
acterize the system over the entire range of concentration. If the substance of
interest has a limited solubility in the solvent, especially if the solubility is very
small, both Raoult’s law and Henry’s law are readily applicable, but Raoult’s
•
law allows for a rapid determination of g i or g i from the solubility data.
In addition to the discussion above, the term Henry’s law has been used in
a broader sense to refer to any linear relation that exists for a dilute substance
between the solution and a neighboring phase, regardless of whether the
process involved with the other phase is a solution or a surface phenomenon.

2.4 FLORY–HUGGINS THEORY

Whereas Raoult’s law accounts for the behavior of solutions of small mole-
cules of comparable size, the Flory–Huggins theory provides a more accurate
treatment for systems where the difference in molecular size between the com-
ponents is considerable, such as for common contaminants in a polymeric or
macromolecular substance. The inability of Raoult’s law to deal with the latter
system has to do with its adoption of the mole fraction as the weighting basis
for the activity of a substance. This criterion gives a satisfactory measure of
the component activity if the components are comparable in molecular size,
in which case the deviation from Raoult’s law as accounted for by the activ-
ity coefficient gives a reasonable assessment of the molecular incompatibility.
Small molecules behave more like rigid bodies because they have more
rigid molecular segments, which prevent the molecules from assuming a large
number of configurations. Large molecules, typically polymers, contain
many relatively flexible repeating units or molecular segments (like a string
of beads) that enable them to take on a large number of spatial orientations.
For this reason, these segments may interact relatively freely with each other
and with other molecular species. In this sense, a macromolecule behaves as
if it consists of many independent small molecules when it interacts with ordi-
nary small molecules. Therefore, the mole fraction concept, as adopted by
Raoult’s law, is not an effective measure of the component activity in a solu-
tion of a macromolecular substance. The Flory–Huggins theory (see Flory,
1953) offers a more accurate and rigorous treatment of the chemical activity
of a component in a macromolecular solution in terms of its volume fraction.