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

86 4 Water Permeability
Only about 2–3 water molecules fit into the diameter of these pores and since
pore walls are made of permanent dipoles and ionised groups, many of these water
molecules represent hydration water. Water molecules bound to permanent dipoles
or to ions are not completely immobilised. They exchange with bulk water, and
at room temperature the mean residence time of water in the primary hydration
shell of monovalent cations is about 10 −9 s −1 , and with hydrogen-bonded water
residence time is shorter (10 −11 s −1 ) (Israelachvili 1991). This means that many
water molecules jump from one dipole to the next. Thus, viscosity of water in the
pores is much higher than in bulk. Fortunately, in calculating pore radii the product
Dη enters rather than D alone (4.11). For diffusion in liquids, the Stokes–Einstein
relationship states that Dsolute is proportional to the Boltzmann constant (κ) and temperature
(T) and inversely proportional to viscosity (η) and the radius of the solute:
Dsolute =
κT
. (4.16)
6πη × rsolute
This implies that at constant temperature (T in Kelvin) the product of the diffusion
coefficient and viscosity is constant. It is reasonable to assume this to hold
also for aqueous pores, and deviation of D and η from bulk properties should not
greatly affect pore size estimates. However, it could account in part for the fact
that estimated pore size is somewhat smaller than pore size expected from viscous
permeance (Fig. 4.9). Another factor might also have contributed. For a solute to
enter the pore by a diffusional jump it must find the opening and not hit the pore
wall, from which it would be reflected. This steric hindrance increases as the solute
approaches the size of the pore opening and may be estimated. Empirical corrections
are discussed by Lakshminarayanaiah (1969).
Since we have data on sorption of water in MX membranes in H + form (Fig. 4.7),
which were measured gravimetrically, we can compare them with fractional volume
of water at pH 3 calculated from diffusion of THO (Table 4.4). At pH 3, most carboxyl
groups are not ionised and fractional water content was about 2.8 × 10 −4 .
At 100% humidity (p/p0 = 1.0) the weight fraction of water in Citrus MX was
about 0.08 (Chamel et al. 1991), which can be taken to be the volume fraction, since
specific gravity of water and the MX do not differ much (Schreiber and Schönherr
1990). This figure is 285 times larger than fractional volumes of water derived
from diffusion of water. In calculating fractional pore area and number of pores, the
diffusion coefficient of water in bulk was used and the tortuosity was disregarded.
Absolute values of the fractional pore areas given in Fig. 4.8 could be multiplied by
285, which is the factor by which ℓ/D is larger in the pore liquid than in bulk. Such
a calculation results in a fractional pore area and a fractional pore volume of 0.0385
for the MX in Ca 2+ form. Thus, the average volume of water in the MX would be
3.85% of its total volume. As total water content is about 8% (Chamel et al. 1991),
48% of the total water would be located in aqueous pores, while 52% should be
sorbed in other compartments, possibly in cutin. In tomato fruit, cutin water sorption
amounted to 19gkg −1 , which is 1.9% by weight. Data for Citrus cutin are not
available.