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

54 3 Permeance, Diffusion and Partition Coefficients: Units and Their Conversion
Pressure in receiver (mm Hg)
0.4
0.3
0.2
0.1
t e
slope: 2 x 10 −3 mm Hg/min
0.0
0 50 100 150 200 250 300
Time (min)
Fig. 3.1 Water vapour transport across an ethyl cellulose (EC) membrane at 25 ◦ C. The pressure
increase in the receiver compartment was plotted vs time. (Redrawn from Yasuda and Stannett
1962)
an increase in pressure of the receiver, and this was used to calculate the flux. The
steady state flux was obtained by keeping the pressure difference between donor and
receiver practically constant (steady state). Gas or vapour pressures were measured
in cm mercury (cmHg). Vapour pressure greatly depends on temperature, which
necessitates rigorous temperature control. In this book, we shall deal with permeability
of membranes to water and water vapour. Penetration of permanent gases
(O2, N2, CO2) has been reviewed by Lendzian and Kerstiens (1991). While the following
conversions also apply to permanent gases, we shall simply use the term
vapour. A typical example is steady state diffusion of water vapour at 25 ◦ C across
an ethyl cellulose (EC) membrane, as shown in Fig. 3.1.
After some time the flux becomes steady, and from these data the extrapolated
hold-up time (te) and the steady state flux (amount per unit area and time) can
be calculated. Volumes of gases or vapours greatly depend on temperature, and
fluxes were expressed as volume at standard temperature (273.15 K) and pressure
(101,325 Pa), abbreviated as STP. For calculating permeability (PHg), the volume
of gas or vapour at STP (Jv) was multiplied by membrane thickness (ℓ in cm) and
divided by the pressure in the donor (pdonor in cmHg)
PHg = Jvℓ
pdonor
= cm3 (STP)cm−2s−1cm . (3.1)
cmHg
In words, this permeability coefficient has the dimension cubic centimetres of
vapour at STP passing per second under a gradient of 1 cmHg per centimetre membrane
thickness and square centimetre of membrane area. Before converting this
rather awkward unit to the SI system, we shall present an example taken from
Yasuda and Stannett (1962).