Page 79 - Partition & Adsorption of Organic Contaminants in Environmental Systems

70 CONTAMINANT PARTITION AND BIOCONCENTRATION

in triolein, Chiou and Manes (1986) modified the conventional Raoult’s law
by incorporating the Flory–Huggins model [Eq. (2.15) with c= 0] into
Eq. (3.25), which leads to

o Ê
Ê
o
lnf at - f at 1 - V ˆ = -D H fus T m - T - 1 - V ˆ (5.13)
Ë t V ¯ R TT m Ë t V ¯
where f° at is the volume-fraction athermal solubility of a solid solute and V t is
the molar volume of triolein (0.966L/mol). Here the term athermal solubility
is adopted to replace the conventional ideal solubility by Raoult’s law, since
the latter becomes invalid for a macromolecular system.
The suitability of Raoult’s law [Eq. (5.12)] versus the Flory–Huggins model
[Eq. (5.13)] for ordinary solutes with a lipid solvent is here examined against
the measured solubilities of some relatively nonpolar solids in triolein, as
shown in Table 5.4. The size disparity between triolein and the solutes based
on their molar volumes falls into the range /VV t = 3.9 to 8.5. Solubility data
for solids having high melting points (T m) and high heats of fusion (DH fus) are
excluded from consideration because the solid activity calculated is sensitive
to uncertainties in T m and DH fus. Since the solids and triolein selected have
similar compositions and polarities, their solutions are not expected to deviate
greatly from being ideal or athermal.
As shown in Table 5.4, the observed (mole-fraction) solubilities of the solids
in triolein are higher than x° id given by Eq. (5.12) by as much as 100%. On the
other hand,the observed solid solubilities on a volume-fraction basis are either
close to or lower than the respective athermal volume-fraction solubilities
according to Eq. (5.13). The results are therefore in much better agreement
with the Flory–Huggins model than with Raoult’s law. Of particular signifi-
cance are the data with lindane, fluoranthene, and DDT, which exhibit only
moderate size disparities with triolein ( /VV t = 4 to 5). The magnitude of the
negative deviation from Raoult’s law is beyond the uncertainty of observed
and calculated solubilities. Since the experimental data are well reconciled
with the Flory–Huggins model (with c= 0) and since there is no convincing
evidence for the occurrence of any strong specific interaction of these non-
polar solutes with triolein, the negative deviation observed with Raoult’s law
(i.e., g° < 1) is clearly an artifact of the model for which there is no physical
justification.
A contrary finding in favor of Raoult’s law over the Flory–Huggins model
was reported by Shinoda and Hildebrand (1957, 1958) for some binary mix-
tures with molar–volume ratios as high as 9:1. However, these results are for
rare mixtures of globular and compact molecules that do not conform to the
Flory–Huggins postulate for chainlike molecules. As pointed out by Flory
(1970), these rare mixtures do not fulfill the condition of equal accessibility of
the total volume to molecular segments of the solute and solvent. For lipid
triolein, the segments of the hydrocarbon chains are apparently relatively free