Page 78 - Partition & Adsorption of Organic Contaminants in Environmental Systems

LIPID–WATER SYSTEMS 69

molecular-size ratios of triglycerides (biological lipids) to common contami-
nants lie in a range of about 3 to 10. Such size disparity offers a rather unique
system relative to the solute–polymer system, in which a huge molecular-size
difference exists, and to the common solute–solvent system, in which the size
difference is relatively small. As such, we have an opportunity to test critically
the relative merits of Raoult’s law and Flory–Huggins theory for the solute
solubility or the solute partition coefficient with a lipid phase. In addition, it
gives us a chance to find out which solvent (e.g., octanol, heptane, or others)
best mimics the partition effects of organic compounds with a biological lipid.
Prior to our discussion of the solute partition in a lipid–water system, it is
instructive to examine first the solubility data of common solutes in a lipid
solvent. This will give us a clear picture on the merits of the Flory–Huggins
model versus Raoult’s law for handling solute solubility in lipids. Triglycerides
are considered to be the lipids of most interest because they are an essential
part of the lipids in animals and plants and because they have very unique
molecular sizes, as mentioned earlier. Triolen (short for glyceryl trioleate,
C 57H 104O 6; MW = 885.4) is selected as a model lipid because of its abundance
and structural similarity to other triglycerides in organisms. It is selected also
because it is a liquid at room temperature that greatly facilitates solubility
measurements for solid compounds (note that most nonpolar liquids are
completely miscible with triolein).
By combining Eqs. (2.5) and (3.25) for the activity of a solid compound,
one obtains on the basis of Raoult’s law the solubility of a solid compound in
a solvent as

o s o -D H fus T m - T
lnx id = lnx g = (5.12)
R TT m
s
where x° id is the ideal mole-fraction solubility of a solid solute, x the solid mole-
fraction solubility if the solution is nonideal, and g° is Raoult’s activity coeffi-
cient to correct for the solution nonideality at saturation. The other terms are
the same as defined earlier. For solutes exhibiting positive deviations from
s
Raoult’s law (i.e., g° > 1), the solid solubility at the point of saturation (x )
cannot exceed x° id if Raoult’s law holds. Thus, if there is no specific
solute–solvent interaction or solute–solute molecular association, the ideal
solubility of a solid compound on a weight-fraction or molar-concentration
basis is expected to decrease with increasing solvent molecular weight (or
solvent molar volume) according to Raoult’s law. This expectation follows
from the reasoning that when the solvent molecular weight increases, the mass
of the dissolved solid solute will have to decrease to maintain a constant solute
mole fraction in solution.
Based on the experimental data shown later, the solid solubility observed
in triolein often exceeds the Raoult’s law ideal solubility limit as defined by
Eq. (5.12), even when the molecular-size disparity between solute and triolein
is only moderately large. To account satisfactorily for the solubility observed