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

44 2 Quantitative Description of Mass Transfer
Amount diffused (mol/cm 2 )
6e-8
5e-8
4e-8
3e-8
2e-8
1e-8
t e = 0.8 h
slope: 1 x 10 -8 mol cm -2 h -1
0
0 1 2 3 4 5 6 7
Time (h)
Fig. 2.8 Steady state diffusion of 2,4-D across a pepper fruit CM. Membrane area was 1cm 2 and
donor concentration was 1molm −3
the real driving force was much greater than assumed in our calculation. This could
be accounted for by including the partition coefficient K in (2.2):
J = P(KCdonor − KCreceiver) = PK(Cdonor −Creceiver). (2.16)
If we decide to use model 2 for analysing the data, (2.3) assumes the form
J = DK
ℓ (Cdonor −Creceiver), (2.17)
which shows that permeance P is a mixed parameter which includes the diffusion
and partition coefficient and membrane thickness:
P = DK
. (2.18)
ℓ
It is a general convention not to include K as part of the driving force, because
it is not always known, while concentrations are known or can be measured. If P
and K are measured and ℓ is known, D can be calculated as Pℓ/K. For pepper fruit
cuticles we get 4.63 × 10 −16 m 2 s −1 . Alternatively, we can use (2.5) and calculate
D from the hold-up time, and we obtain 5.79 × 10 −15 m 2 s −1 , which is 12.5 times
larger. The reason for this discrepancy is the heterogeneity of cuticles. In deriving
the above equations, it was assumed that membranes are homogeneous in chemistry
and structure. Heterogeneity of cuticles is a major obstacle in analysing permeability
of cuticles in terms of structure–property relationships (Chaps. 4–6).