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9.4 Distribution of Water and Solute Permeability 263 total permeance may be acceptable. But holes larger than that, and more numerous ones, may contribute significantly to Ptotal, and this may go unnoticed if hold-up times are not determined. This is the case when foliar penetration is measured with only one time point. In some studies, k ∗ was determined using UDOS (Sect. 6.3), and with many species k ∗ was as low as 10 −7 and 10 −8 s −1 (Fig. 6.21). These rate constants can be converted to permeances P ∗ by multiplying k ∗ by membrane thickness ℓ (6.16). If k ∗ is 1 × 10 −8 s −1 and ℓ is 3µm, P ∗ is 3 × 10 −14 m s −1 . P can be obtained by multiplying P ∗ by the partition coefficient (6.17). For bifenox log K is 4.4, and we obtain P equal to 7.5 × 10 −10 m s −1 . This calculation shows that with lipophilic chemicals small holes in the CM result in few problems, as long as the partition coefficient is very high. With polar non-electrolytes or with ionic solutes having a K < 1, P values as small as 10 −15 m s −1 or lower are obtained. Such CM are essentially impermeable to these solutes when penetration is restricted to the waxy pathway. From the data of Table 6.8 and (6.21), k ∗ for Pyrus communis can be calculated. When the molar volume is 100cm 3 mol −1 we obtain 3.5 × 10 −6 s −1 , and a calculation similar to that above yields a permeance P ∗ of 1.05 × 10 −11 m s −1 if ℓ is 3µm. For ionic solutes K is at least 0.01 or smaller, and this results in a P of 1.05 × 10 −13 m s −1 . A hole in this CM having a permeance of 7 × 10 −12 m s −1 would be a disaster, as the flux across the hole would be 67 times larger than the flux across the CM. This calculation assumes that aqueous pores are absent from this CM. In this case, almost the total ionic flux observed would be the flux across the hole. With pear CM, ionic solutes penetrate across the aqueous pathway, having rate constants in the range of 1 × 10 −5 −1 × 10 −6 s −1 (Fig. 5.7). Hence, P ranges from 3 ×10 −11 to 3 ×10 −12 m s −1 . This is of the order of the permeance of the hole of 7 × 10 −12 m s −1 , and by no means negligible. Extremely low diffusion coefficients (Chap. 6) in the range from 10 −15 to 10 −20 m 2 s −1 or even lower are typical for CM. As a consequence [cf. (2.5)], very long hold-up times in the order of hours or even days are observed (Fig. 6.2). If plots amount diffused vs time intersect the origin or even the positive part of the ordinate, this is an indication for membrane defects, resulting in water–water continuity between donor and receiver. D of water in water is about 2.5 × 10 −9 m 2 s −1 , and with a 3µm-thick CM the hold-up time for a water layer of this thickness would be 6 × 10 −4 s. If cuticular or foliar penetration is studied using only one sampling interval, the hold-up time is not known and cannot be used as an integrity criterion. 9.4 Distribution of Water and Solute Permeability The tremendous variability of permeance and rate constants among individual CM of a given species poses the question as to the appropriate statistics for characterising populations. This was studied by Baur (1997),who investigated distribution of permeance and rate constants of CM, MX and leaf discs for water and lipophilic solutes.
264 9 General Methods, Sources of Errors, and Limitations in Data Analysis Population size ranged from 50 to 750 CM. With MX membranes distribution were normal, and arithmetic means, standard deviations or confidence intervals can be used to characterise these MX membranes. With CM from all species, histograms of frequency distributions of k ∗ or P were always skewed and had a pronounced tail at high values. Skewness tended to be more pronounced with small populations. After log transformation, symmetrical histograms with normal distributions were obtained. If populations are skewed, arithmetic means are higher than geometric means obtained by log transformation of the data. For this reason, it is a good practise to use large sample sizes of 50–100 CM and to subject data to log transformation for calculating geometric means and confidence intervals. Log transformation of normal distributions presents no problems, as in this case arithmetic and geometric means are numerically identical. 9.5 Very High or Very Low Partition Coefficients Determination of partition coefficients, although technically easy and straightforward, can cause serious experimental problems with highly lipophilic (Kcw > 10 4 ) or very polar (Kcw < 1) compounds. These problems have been dealt with in detail in Sect. 6.1.6. Possible solutions when working with highly lipophilic and polar compounds, insurmountable difficulties, and problems in data interpretation have been presented and discussed. It is very difficult or impossible to determine Kow for emulsifiers, because in their presence oil in water emulsions can be formed and phase separation may not be possible. No such problems arise with MX or CM, and reliable partition coefficients have been determined (Riederer et al. 1995). As there is an excellent correlation between Kow and KCM at low solute concentrations, the problem of emulsification can be circumvented by using pieces of MX rather than octanol as lipid phase. 9.6 Cutin and Wax Analysis and Preparation of Reconstituted Cuticular Wax Gas chromatography with flame ionisation detection (GC-FID) was used for the quantification of cuticular waxes (Riederer and Schneider 1989) and cutin monomers after depolymerisation (Hauke and Schreiber 1998). Identification of constituents by gas chromatography coupled to mass spectrometry is the method of choice. Experimental problems arise when cutan occurs in the polymer matrix (incomplete depolymerisation) or when high molecular weight oligomers occur in wax. They have been discussed in Sect. 1.3. Solute sorption and diffusion in wax was studied using reconstituted wax preparations (Sects. 6.1.3 and 6.5). The experimental setup is shown in (Fig. 9.1).
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Water and Solute Permeability of Pl
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Professor Dr. Lukas Schreiber Ecoph
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vi Preface This is not a review abo
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Contents 1 Chemistry and Structure
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Contents xi 4.6.3 Diffusion Coeffic
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Contents xiii 7.4.2 Effects of Plas
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2 1 Chemistry and Structure of Cuti
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10 1 Chemistry and Structure of Cut
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Chapter 2 Quantitative Description
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2.1 Models for Analysing Mass Trans
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2.3 Steady State Diffusion Across a
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2.4 Steady State Diffusion of a Sol
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2.4 Steady State Diffusion of a Sol
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2.5 Diffusion Across a Membrane wit
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2.5 Diffusion Across a Membrane wit
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2.6 Determination of the Diffusion
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Solutions 51 2.7 Summary In this ch
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Chapter 3 Permeance, Diffusion and
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3.1 Units of Permeability 55 3.1.1
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3.1 Units of Permeability 57 identi
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3.3 Partition Coefficients 59 The d
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Chapter 4 Water Permeability All te
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4.1 Water Permeability of Synthetic
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4.2 Isoelectric Points of Polymer M
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4.2 Isoelectric Points of Polymer M
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4.3 Ion Exchange Capacity 69 The hi
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4.3 Ion Exchange Capacity 71 has an
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4.3 Ion Exchange Capacity 73 Counte
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4.4 Water Vapour Sorption and Perme
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4.4 Water Vapour Sorption and Perme
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4.5 Diffusion and Viscous Transport
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4.6 Water Permeability of Isolated
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Problems 121 Our present knowledge
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Solutions 123 5. Ca 2+ , because se
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126 5 Penetration of Ionic Solutes
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146 6 Diffusion of Non-Electrolytes
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206 7 Accelerators Increase Solute
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Page 248 and 249: 8.2 Solute Mobility in Cuticles 239
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Page 266 and 267: Problems 257 E D (kJ/mol) DH S (kJ/
Page 268 and 269: Chapter 9 General Methods, Sources
Page 270 and 271: 9.2 Testing Integrity of Isolated C
Page 274 and 275: 9.6 Cutin and Wax Analysis and Prep
Page 276 and 277: 9.7 Measuring Water Permeability 26
Page 278 and 279: 9.8 Measuring Solute Permeability 2
Page 284 and 285: 276 Appendix A Abbreviations (conti
Page 286 and 287: 278 Appendix A Symbols (continued)
Page 288 and 289: 280 Appendix B Physico-chemical pro
Page 290 and 291: Appendix C Index of Plants Botanica
Page 292 and 293: References Abraham MH, McGowan JC (
Page 294 and 295: References 287 Doty PM, Aiken WH, M
Page 296 and 297: References 289 Kolattukudy P (2004)
Page 298 and 299: References 291 Sabljic A, Güsten H
Page 300 and 301: References 293 Schreiber L, Schönh
Page 302 and 303: Index 2,4-D, 46 2,4-Dichlorophenoxy
Page 304 and 305: Index 297 leaf disks, 130 leaf surf
Page 306: Index 299 water molar volume, 110 p
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