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

4.5 Diffusion and Viscous Transport of Water 83
infinity
Pviscous = Pmaximum
viscous
θPmaximum viscous
× rsolute
. (4.14)
Data can also be analysed assuming that Pviscous varies linearly with the reciprocal of
the solute radius. Dependence was in fact linear, as the coefficients of determination
were 0.99 or better at all three pH values. The following regression equations were
obtained:
−7 1
at pH 3: Pviscous = −1.34 × 10 + 1.87 × 10
rsolute
−6 (r 2 = 0.997),
−7 1
at pH 6: Pviscous = −1.21 × 10 + 1.27 × 10
rsolute
−6 (r 2 = 0.985),
−8 1
at pH 9: Pviscous = −6.05 × 10 + 7.38 × 10
rsolute
−7 (r 2 = 0.999).
(4.15)
The constants on the right hand side of the equations are the maximum values of
Pviscous when rsolute approaches infinity, that is, when 1/rsolute is zero. These equations
were used to calculate Pviscous for selected solute radii and results (empty
symbols) were plotted in Fig. 4.9b. Experimental data are included as filled symbols.
Pviscous increased in the order urea < glucose < sucrose, showing that these
solutes penetrated the MX membranes to some degree (Fig. 4.9). Inspection of
the figure might suggest that membranes were impermeable to raffinose, but the
Pmaximum viscous
values obtained from the hyperbola and inverse functions were slightly
larger than the experimental values (Table 4.3). The difference is smallest at
pH 3 (0.06 × 10 −6 ), but at pH 6 and 9 the difference amounts to 0.27 × 10 −6
and 0.12 × 10 −6 respectively. This indicates that MX membranes were not totally
impermeable to raffinose.
According to our hypothesis, water and polar solutes can penetrate the membrane
only in aqueous pores. This is confirmed by the fact that viscous flow increased with
solute size. Solutes which dissolve in the polymer matrix, that is, solutes having a
high partition coefficient (2.17) would not have induced viscous water flux. Clearly,
large polar solutes are discriminated, and membranes should be impermeable to
solutes larger than the size of the pores (Fig. 4.9).
This was tested by measuring permeability at pH 9 of MX membranes to radiolabelled
water, urea and glucose (Schönherr 1976a). Sucrose, raffinose or larger
Table 4.3 Values of P experimental
viscous (ms−1 ) obtained experimentally with raffinose, and values calculated
by regression analysis (Pmaximum viscous ) based on a hyperbola or an inverse function. In the last
column, the means of the fitted values are given
pH P experimental
viscous
Pmaximum viscous hyperbola Pmaximum viscous inv. function Pmaximum viscous mean
3.0 0.68 × 10 −6 0.80 × 10 −6 0.68 × 10 −6 0.74 × 10 −6
6.0 1.08 × 10 −6 1.43 × 10 −6 1.27 × 10 −6 1.35 × 10 −6
9.0 1.80 × 10 −6 1.97 × 10 −6 1.87 × 10 −6 1.92 × 10 −6