A theory of cuticular penetration of crop protection agents (CPAs) is presented, which incorporates properties of cuticles and cuticular waxes as well as properties of active ingredients and adjuvants. Based on this theory, two models are developed which are analytical in the sense that they help to quantify and understand (i) differences in permeability among cuticles from different species, (ii) effects of properties of CPAs on permeabilities of cuticles and rates of uptake and (iii) the effects of adjuvants on properties of cuticles and rates of uptake of CPAs. The models can be used to predict rates of uptake of CPAs as affected by properties of cuticular waxes, active ingredients and adjuvants. However, before this can be done, a constant, two parameters and at least two variables must be estimated. Properties of cuticles are accounted for by the constant D0/Ax and the parameter p'. The former, the ratio of the mobility of a hypothetical molecule having zero molar volume ( D o ) divided by the path length (Ax) across the cuticle, has the dimension of velocity (m s -' ) and is independent of the solubility of the CPA. The latter is a measure of size selectivity of the cuticle. Differences in permeabilities of cuticles from different species increase with increasing size of active ingredients due to size selectivity (p). Removing cuticular waxes from Citrus cuticles increased D0/Ax by a factor of 2042, while [ Y was not affected. Differential solubility of CPAs is considered part of the driving force and at least two different partition coefficients are needed to account for differences in solubilities in cuticular waxes, cutin, water and the formulation residue on the surface of the cuticles. Adjuvants are solvents in the formulation residue on the leaf surface once the carriers (water and other volatile solvents) have evaporated and certain adjuvants also act as accelerators; they penetrate the cuticle and increase D0/Ax. Thus, accelerators increase rates of uptake and this effect depends on two factors, (i) the intrinsic activity of the accelerator and (ii) rate of penetration into the cuticle, because the active ingredients follow the accelerator front across the cuticle. Since accelerators penetrate from the formulation residue into the cuticle, the volume of the formulation residue decreases with time. This maintains high concentrations of CPAs in the formulation residue and, thus, maximum driving forces and rates of penetration. To utilise fully this dual accelerator effect, it is necessary to match velocities of penetration of accelerators and active ingredients accurately.

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Ptant, Cell and Environment (^997) 20,[982][983][984][985][986][987][988][989][990][991][992][993][994],viv In this range, solute mobilities increased up to 1000-fold, which corresponds to temperature coefficients Qio of 3 (IAA in P. armeniaca) to 14 (cholesterol in fi. hetix). For most species, Arrhenius graphs showed good linearity up to 40 °C, and up to 78 °C for some species, while for others activation energies declined with increasing temperature. However, no distinct phase transitions caused by sudden structural changes in the CM were observed. In three species we examined whether heating to 70 °C changed solute mobility irreversibly by comparing Arrhenius graphs for two successive experiments with the same CM. The two graphs were very similar for P, taurocerasus, while mobilities in the second graph were somewhat reduced for C. aurantium and greatly increased (at 25 and 35 °C) for H. helix. This indicates rearrangements of at least some wax constituents when heated to high temperatures. The activation energies of diffusion (/i|,) ranged from 75 to 189 k. F moP' depending on .species and .solute size. Size selectivity and variability between cuticles decreased witb increasing temperature, and this is caused by differences in li|,. An excellent correlation between the pre-exponential factor of the Arrhenius equation and /i,, was observed, which is evidence that organic solutes differing greatly in molecular size (130-349 cm' moP') and cuticle/water partition coefficient (25-10*") use similar diffusion paths in the CM of all 12 plant species tested. Diffusion occurs in regions with identical phy.sicochemical properties and differs only in magnitude.

Abstract. Solute mobilities of 28 compounds in isolated cuticular membranes (CM) from Capsicum annuum L. fruit, Citrus aurantium L. and Pyrus communis L. leaves were studied using unilateral desorption from the outer surface. First-order rate constants of desorption (k*), which are directly proportional to the diffusion coefficient in the waxy outer limiting skins of cuticles were measured. When log k* was plotted vs. molar volumes of test compounds linear graphs were obtained. The y-intercepts of these graphs (k *~ represent the mobility of a hypothetical molecule having zero molar volume and the slopes of the graphs (13') represent the size selectivity of the barrier and are related to the free volume available for diffusion. Thus, solute mobilities in cuticles are composed of two independent terms which are subtractive. If k *~ and 13' are known, k* can be estimated for any solute from its molar volume (Vx) using the equation log k*= log k *~ 13'Vx. These parameters were used to analyse the effects of plant species, extraction of cuticular waxes and molecular structure of solutes on solute mobilities in plant cuticles. For aliphatic solutes, k *~ was a factor of 10 smaller than for cyclic compounds, while 13' was 0.011 and 0.012, respectively. The k*-values for CM of the three species were very similar, but 13' was higher for bitter-orange CM (0.012) than for those 9 f pepper fruits and pear leaves (0.009). This has the consequence that differences in solute mobilities (k *~ among cuticles from different plan species increase with increasing molar volumes of solutes. Our data and our analysis provide evidence that constituents of cuticular waxes are mobile, at least in the solid amorphous wax fraction, but mobility decreases rapidly with increasing molar volume. For instance, if 13' amounts to 0.01, mobilities of wax monomers decrease by a factor of 10 for every increase in molar volume of 100 cm 3. mol-1. Thus, hexaAbbreviations: CM = cuticular membrane(s); 2,4-D = 2,4-dichlorophenoxyacetic acid; LAB = lactic acid buffer; MX = polymer matrix membranes; UDOS = unilateral desorption from the outer surface Correspondence to: P. Baur; FAX: 49 (5066) 82 61 1 l decanoic acid is quite mobile in the amorphous wax fraction of Citrus (k* = 1.5 x 10 -6. s-l), but for dotriacontane having twice the molar volume, k* was only 2.5 x 10-9. s-a, which is almost three orders of magnitude smaller. Wax esters have even higher molar volumes and their mobilities will be even smaller (about 4 x 10-12. s-1 for a C4s-ester). Since low chain mobilities are a prerequisite for low mobilities and permeabilities, the selective advantage of high-molecular-weight wax monomers in plant cuticular waxes becomes obvious. Extracting cuticular waxes from pear leaf CM increased solute mobilities by a factor of 182, but it had no effect on size selectivity. We interpret this result as evidence to the effect that cuticular waxes reduce mobility by increasing tortuosity of the diffusion path, rather than by decreasing the mean free path of diffusiona...

It is shown that water permeabilities and organic solute mobilities in plant cuticles have a lognormal distribution. Seven-hundred and fifty values for rate constants of desorption (^mobility) of 2,4-D from isolated Citrus aurantium L. cuticles from a population of leaves were pooled and analysed. A histogram of the rate constants of individual cuticles showed a skew distribution with a strong tail to higher values. Cuticular membranes with high values did not differ from others in visual appearance and were not leaky. After log-transformation of original data an almost perfect normal distribution was obtained. Statistical tests showed that a normal distribution of original values is not acceptable. Inspection of older data for water permeability in the same species and experiments using large samples of cuticles from leaves of Pyrus communis L. and Stephanotis floribunda Brongn. and from fruits of Capsicum annuum L. showed a similar distribution, as did inspection of data for experiments with organic solutes. A lognormal distribution was found for cuticles of plants from growth chambers, glasshouses and outdoors as well as for water permeability of intact leaves of Hedera helix L. For small samples the overestimation from using the arithmetic mean of original data can be high, but use of the geometric mean or the median leads to smaller deviations. Removing cuticular waxes from cuticles produced normally distributed samples. A normal distribution was also obtained when organic compounds which increase solute mobility were sorbed into cuticles.