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

8.2 Solute Mobility in Cuticles 241
This shows that Do is proportional to the square of the jump distances, temperature
and of some physical constants. The entropy enters as an exponent.
Temperature dependence of diffusion is usually described using (8.6). D is measured
at various temperatures, and ln D is plotted versus T −1 . If the slope is a
straight line ED can be calculated from the slope, and the y-intercept is equivalent
to ln Do. With Do and activation energy known, D can be calculated for any other
temperature (8.6).
These equations can be used to investigate dependence on temperature of solute
mobility in CM and MX. Using the UDOS method (Sect. 6.3), rate constants k ∗
are obtained which are proportional to diffusion coefficients. In CM, their magnitude
depends on properties of the waxy barrier. Temperatures studied, ranged from
15 to 70 ◦ C, and internal solute concentrations were in the order of mg kg −1 . At
these concentrations, solute–membrane interactions predominate and solute–solute
interactions in cuticles are improbable.
8.2.1 Effect of Temperature on Rate Constants k ∗
Rate constants were measured at various temperatures, and k ∗ was calculated using
(6.3). Temperature dependence was analysed based on the Arrhenius equation:
k ∗ = k ∗ infinite exp(−ED/RT) (8.12)
where k ∗ infinite is the pre-exponential factor and ED is the activation energy of diffusion.
This equation is similar to (8.6), except that D was replaced by the UDOS
rate constant k ∗ . In the original publications by Baur et al. (1997a), Buchholz and
Schönherr (2000) and Buchholz 2006, the symbol for pre-exponential factor was k ∗ o
similarly as for Do in (8.6). However, k ∗ o was previously used for rate constants for
solutes having zero molar volume (Buchholz et al. 1998, Sects. 6.3.2.2 and 6.3.2.3);
we now define the symbol k ∗ infinite for the y-intercept of Arrhenius plots. This
y-intercept k ∗ infinite is the solute mobility at infinite temperature. By plotting log k∗
vs the reciprocal of the Kelvin temperature, a straight line is obtained and ED can
be calculated from the slope:
ED = −2.3 × slope× R (8.13)
The factor 2.3 is included in the above equation because published Arrhenius plots
are on log scale, rather than ln scale as in (8.6) and (8.12).
Figure 8.3a shows Arrhenius plots for seven individual Citrus CM/2,4-D combinations.
Slopes are linear, and log k ∗ increases with decreasing values of T −1 . With
increasing temperature, solute mobility k ∗ increases by almost two orders of magnitude.
Regression equations for the CM having highest and lowest rate constants are
shown in the graph, and it can be seen that plots tend to converge at higher temperatures.
CM having high k ∗ values have lower y-intercepts and smaller slopes than CM
having low k ∗ values. Differences in k ∗ among membranes decrease as temperature