Surfactant Effects on Environmental Behavior of Pesticides - Reviews of Environmental Contamination and Toxicology - page 86

K m = X m / X a
where K m is a micelle partition coefficient and X m and X a are the mole fraction of a
substrate in the micellar pseudo-phase and aqueous phase, respectively. When the
concentration of surfactant is above cmc, the aqueous concentration as a monomer
remains constant at cmc. As X m and X a can be expressed by using S mic , S cmc , C s , and
cmc as follows, K m can be rewritten using the MSR value and the molar volume of
water (V w , 0.01805 L/mol):
X m = (S m − S cmc ) / (C s − cmc + S mic − S cmc ) = MSR / (1+MSR)
X a = S cmc . V w , K m = MSR / (S cmc . V w )(1+MSR)
As another approach, the solubilization can be kinetically analyzed for the equili-
brated reaction of [C] + [D N ] « [C . D N ] with a micelle binding constant of K s (M −1 ),
where C, D N , and C . D N are substrate, micelle, and substrate-micelle complex,
respectively. This approach is widely used to kinetically analyze an abiotic hydrolysis
in the micellar pseudo-phase model.
The substrate molecule solubilized in micelles is considered to be distributed in
accordance with a Poisson statistics with a probability as expressed here (Turro
et al. 1980):
P(n) = (<s> n / n!) . exp (-<s>)
P(n) is a probability that the “n” molecule(s) are distributed in a micelle and <s> is
a mean occupancy number defined as bulk concentration of a substrate divided by
that of micelles. When <s> is 0.1, about 90% of micelles are vacant and the remain-
ing 10% is occupied by a single substrate molecule. The solubilized molecule is
considered to spend its time on average with the characteristic region of the micelle,
that is, the micellar core (inner and outer), or Stern or Gouy-Chapman layers (see
Fig. 3). The core region consisting of alkyl chains is a hydrophobic hydrocarbon-
like environment with a higher microviscosity, whereas the Stern layer is rather
hydrophilic, where 50%-70% of the ionic head groups is neutralized by counteri-
ons in the case of ionic surfactants (Cordes and Gitler 1972; Fendler and Fendler
1975). For nonionic surfactants, Raman spectroscopy, fluorescence polarization of
a probe molecule, and the ease of a diffusion-controlled excimer formation, have
shown that the long ethoxylated chain of Brij 35 in the Stern layer generally has a
dihedral helical structure but the shorter one in Triton X-100 has an open coil struc-
ture (Thomas 1980). In the Gouy-Chapman layer, generally with a thickness of
several hundred angstroms, an ionic molecule is less tightly associated. Both elec-
trostatic and hydrophobic factors would play a role in determining the solubiliza-
tion locus of substrate to the micelle, and the various spectroscopic techniques have
been applied to estimate the solubilization locus of a substrate. As the ring current
of an aromatic substrate perturbs the chemical shift and line width of surfactant
protons in the neighborhood of a solubilized site, NMR spectroscopy has been