Water and Solute Permeability of Plant Cuticles: Measurement and ...

158 6 Diffusion of Non-Electrolytes
concentrations of non-ionised molecules. The partition coefficients CM/water for
the non-ionised species varied from 83 (4-nitrophenol) to 7.24 × 10 7 (diethylhexyl
phthalate), which is a factor of almost one million. It is not trivial to measure
extremely high partition coefficients (Sect. 6.1) and permeances. With hexachlorobenzene
(HCB), perylene and diethylhexyl phthalate (DEHP), Kerler and Schönherr
(1988b) measured steady state diffusion using solid residues of the solutes in the
donor to prevent rapid depletion in the donor solutions.
When log P was plotted vs log Kcw, a positive dependence could be seen (red
circles). From 4-nitrophenol to DEHP, permeance increased by a factor of nearly
2,000. This is considerably less than the difference in partition coefficients. One
of the reasons for this is the fact that molecular weights of the compounds were not
constant but ranged from 139 (4-nitrophenol) to 390g mol −1 (DEHP), and diffusion
coefficients in CM and waxes greatly depend on size of solutes. This will be dealt
with quantitatively in Sect. 6.3. There are various ways to estimate the volumes of
molecules. With liquids it is not difficult to determine the volume of one mole of
substance, but these figures greatly depend on temperature, and it is not possible to
obtain good estimates for solids. We have been using the method of Abraham and
McGowan (1987) to characterise size of solutes. Molar volumes (in cm 3 mol −1 ) are
obtained by adding the volumes of the atoms and correcting for the influence of
bonds on molar volumes. Volumes of all relevant atoms have been tabulated, and
the molar volumes (Vx) calculated are characteristic volumes at zero Kelvin. For
this reason characteristic volumes are smaller than molecular weights, but for the
purpose of comparing permeances or diffusion coefficients of compounds having
different molecular weights, Vx turned out to be well-suited.
Dividing log Kcw by Vx corrects for differences in size of solutes, and a good
correlation with log Pcw/Vx is obtained (green squares in Fig. 6.3) if data for DEHP
and HCB were disregarded. The fact that permeances for DEHP and HCB are much
higher than predicted by the regression line is probably related to their plasticising
activity (Chap. 7). Plasticisers render solid polymers more flexible and increase
solute mobility (Buchholz 2006). DEHP is a typical plasticiser used commercially
in synthetic polymers. Some ethoxylated alcohols are very effective plasticisers
(Schönherr 1993a, b). Pentafluorophenol is also a very effective plasticiser (Schönherr
and Baur 1996). Plasticising activities of PCP and HCB seem not to have been
studied, but in view of structural similarity with pentafluorophenol it is likely that
they are plasticisers as well. The effect of plasticisers is concentration-dependent,
but concentration of solutes in the CM cannot be calculated, as donor concentrations
were not given in the original publication. Their concentration in the CM probably
differed, and their intrinsic activity probably as well. It should be realised that
plasticiser activity of solutes would have gone unnoticed had penetration been measured
using only one time interval, and results would have been expressed as percent
penetration in an arbitrary time interval.
Prediction of permeances of Citrus CM at 25 ◦ C to other solutes is possible using
the equation
logP = 192 logKcw
Vx
− 13.2. (6.7)