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

58 3 Permeance, Diffusion and Partition Coefficients: Units and Their Conversion
3.2 Diffusion Coefficients
No problems arise with D when calculated from the extrapolated hold-up time (te)
using (2.5) or from sorption data (2.33) or (2.34). The dimension is always m 2 s −1
or cm 2 s −1 .
3.3 Partition Coefficients
In Chap. 2, we defined the partition coefficient as ratio of molal concentration in the
membrane and in the surrounding solution (2.12). In the polymer literature dealing
with gas or vapour permeability across homogeneous membranes, another variable
is used which is related to the partition coefficient. The vapour sorption coefficient
(S ) can be calculated from PHg and the diffusion coefficient
S = PHg
. (3.12)
D
For the PETP membrane shown in Fig. 3.2, PHg was 1.77 × 10 −8 cm 3 (STP) cm per
cm 2 scmHg, and D amounted to 3.94 × 10 −9 cm 2 s −1 (Yasuda and Stannett 1962).
With these data we obtain
S = PHg
D =
1.77 × 10−8cm3 (STP)cm
cm2 scmHg(3.94 × 10−9 cm2 s−1 )
= 4.49 cm3 vapour (STP)
(cm 3 polymer)cmHg .
(3.13)
This is the amount of water vapour sorbed in PETP at a vapour pressure of
1 cmHg or at a partial pressure of 0.421. When the sorption isotherm is linear, the
amount sorbed is proportional to vapour pressure. Thus, sorption at 100% humidity
(2.375 cmHg) is 10.66cm 3 (STP) water vapour per cm 3 polymer. The partition
coefficient KHg is
KHg = S
=
p/p0
4.49cm3 (STP)
(cm 3 polymer)0.421 = 10.66 cm3 (STP)
cm3 . (3.14)
polymer
Multiplying KHg by the density of water vapour at STP results in a new partition
coefficient Kw which is on the basis mass per volume:
Kw = KHg × δwv(STP)
�
= 10.66 cm3 vapor(STP)
cm3 ��
8.03 × 10
polymer
−4 gwater
cm3 �
vapour
= 8.56 × 10 −3 gwater
cm3 polymer .
(3.15)