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

2.4 Steady State Diffusion of a Solute Across a Dense Non-Porous Membrane 43
as chemical potential difference for the same solvent is considered. In calculating
the difference in chemical potential between two locations (i.e., across a membrane
with water on both sides), the reference potential cancels.
The situation is different when we consider chemical potentials in two adjacent
immiscible phases; for instance, water and octanol or water and cuticles. The value
of the chemical potential for a solute in the standard state (µ ∗ j
) depends on the sol-
vent, and in calculating the difference in chemical potential between two different
and immiscible phases the two reference potentials do not cancel. For example, if
a lipophilic solute is added to a vessel containing water and pieces of cuticle and
the vessel is shaken vigorously, the concentrations in the two phases at equilibrium
will not be the same. If the solute is more soluble in the cuticle than in water, the
activity in the cuticle (acuticle) will be higher than in water (awater). Since we are in
equilibrium, the chemical potential of the solute in water and cuticle is the same
(µcuticle = µwater). Hence, the standard chemical potentials must differ, such that
µ ∗ cuticle < µ∗ water.
2.4.1 The Experiment
We want to study diffusion of 2,4-D across an isolated pepper fruit cuticle. This
cuticle (ℓ = 10µm, A = 1cm 2 ) is inserted into an apparatus similar to that shown
in Fig. 2.1. To donor and receiver chambers, 100 ml citric acid buffer of pH2.73
are added. At this pH, 50% of the 2,4-D molecules are ionised, the other 50% are
non-ionised. Donor and receiver solutions are stirred to assure mixing, and once
the apparatus has obtained the desired temperature of 25 ◦ C 2,4-D is added to the
donor solution at a total concentration of 2 × 10 −3 moll −1 ; hence, the concentration
of non-ionised 2,4-D molecules is 1 × 10 −3 moll −1 . The receiver solution is withdrawn
quantitatively every hour and replaced by fresh buffer. The receiver solution
is assayed for 2,4-D.
Results are shown in Fig. 2.8. The amount that diffused into the receiver increased
linearly with time. The extrapolated hold-up time was 0.8 h or 2,880 s. The slope of
the plot is 1 × 10 −8 molcm −2 h −1 , which amounts to 2.78 × 10 −8 molm −2 s −1 . The
linear plot suggests that diffusion was in the steady state. We can check this by
comparing the amount diffused in 5 h (∼5 × 10 −8 mol) with the amount of 2,4-D in
the donor, which is 1 × 10 −4 mol. Indeed, only 0.05% of the amount in the donor
diffused into the receiver, and the concentration of the donor solution practically
remained constant. According to (2.2), the permeance can be calculated
P =
J
Cdonor −Creceiver
= 2.78 × 10−8 molm −2 s −1
1molm −3 = 2.78 × 10 −8 ms −1 . (2.15)
In this calculation we used the concentration of non-ionised 2,4-D in the aqueous
donor, even though we know (Fig. 2.7a) that the concentration difference across the
cuticles was in fact 600 times steeper than that between donor and receiver. Hence