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

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2.4 Steady State Diffusion of a Solute Across a Dense Non-Porous Membrane 41 rather than molar concentrations (moll −1 ) are used K = concentration in cuticle (molkg−1 ) concentration in water (molkg−1 . (2.12) ) K is dimensionless, and depending on type of solute it can vary by more than 10 orders of magnitude. If K = 1 the solute is equally soluble in the cuticle and in water. If K < 1 we consider the solute as hydrophilic. The solute is lipophilic when K > 1. 2,4-Dichlorophenoxyacetic acid (2,4-D) is an important substance in research and agriculture. It is an artificial auxin (growth regulator), and can be used as a selective herbicide. It is a weak acid having a pKa of 2.73 and a molecular weight of 221gmol −1 . The cuticle/water partition coefficient K of non-ionised, protonated 2,4-D varies among plant species, and for pepper fruit cuticle it is about 600 (Sect. 6.1). In an experiment to determine K, a piece of isolated pepper fruit cuticle is dropped into an aqueous solution of 2,4-D. Since it is a weak acid, the solution must be buffered to maintain a constant pH and known concentrations of ionised and nonionised 2,4-D molecules. We decide to use a buffer having pH2.73 which provides us with 50% ionised and non-ionised molecules each [cf. (6.5a)]. The dissociated form is negatively charged, and it is not lipid-soluble because the ionised carboxyl group is surrounded by water molecules. Only the non-ionised 2,4-D molecules dissolve in cuticles and can diffuse in it (Riederer and Schönherr 1984). Initially the cuticle is free of 2,4-D, but as time progresses 2,4-D accumulates in the cuticle until equilibrium is established. At equilibrium, the concentration of non-ionised species in the cuticle is 600 times higher than in the surrounding solution. This appears to be a transport from lower to higher concentration. How can this enigma be explained? Equilibrium means that the chemical potentials in the cuticle and the buffer are equal, not the concentrations. We shall explain this by considering steady state diffusion of a solute across a non-porous homogeneous membrane inserted between two aqueous solutions. Differential solubility in solutions and in the membrane results in a discontinuity in the concentration–distance profile (Fig. 2.7). If K > 1, the concentration in the membrane at the solution–membrane interface is K × Cdonor. This is higher than the concentration of the donor, and the concentration gradient across the membrane (which is linear since we are in the steady state) is steeper by the factor K than that between the solutions (Fig. 2.7a). When the chemical potential is plotted no discontinuity is seen, and the gradient in the membrane is no longer linear, because chemical potential varies with the logarithm of concentration (2.13). The chemical potential (µ) of a neutral species ( j) is (Nobel 1983) µ j = µ ∗ j + RT · lna j + ¯Vj p+m jgh. (2.13) For diffusion across cuticles this equation can be simplified, as not all of the terms make significant contributions. The gravitational term m jgh accounts for the work required to raise an object of mass m j per mole to a vertical height h, where g is the
42 2 Quantitative Description of Mass Transfer Fig. 2.7 Concentration profiles across a lipophilic membrane. (a) Linear profile obtained with a lipophilic solute having a partition coefficient K > 1. The concentration in the membrane at the solution/membrane interface is higher by the factor K than concentration of donor and receiver respectively. (b) Linear profile with a solute having K < 1. (c) Profile of the chemical potential (µ) across a membrane. The profile is not linear, and there are no discontinuities at the solution/membrane interface on either side gravitational acceleration. This term can be omitted since ∆h is extremely small in diffusion across cuticles. The effect of pressure (p) on chemical potential can also be neglected, even though a significant pressure gradient exists across cuticles due to the turgor pressure of the leaf cells. However, at 20 ◦ C the pressure term in (2.13) amounts to only 200Jmol −1 if the partial molar volume of a molecule ( ¯Vj) is 0.2 L and the pressure is 10 bar. By comparison, the term RT is 2.44kJmol −1 at the same temperature. The effect of solute activity (a j) on chemical potential is contained in the second term on the right side of the equation. The activity of a species in a solution or a membrane is usually not known precisely and the concentration (Cj) is used instead, assuming the activity coefficient to be 1.0. Multiplying ln a j with RT (where R is the gas constant in Jmol −1 K −1 and T the temperature in Kelvin) gives the term RT ln a j with the units of energy per mole of solute. With these simplifications, the chemical potential of a non-electrolyte (or a non-ionised weak acid) is µ j = µ ∗ j + RT lnCj. (2.14) Chemical potential, like electrical potential, has no absolute zero. It is a relative quantity, and it must be expressed relative to an arbitrary level. Electrical potential is measured against ground, and in the equation for the chemical potential an unknown additive constant, the reference potential µ ∗ j is added. The absolute value for the chemical potential is therefore never known, but this has little consequence as long
Page 2 and 3: Water and Solute Permeability of Pl
Page 4 and 5: Professor Dr. Lukas Schreiber Ecoph
Page 6 and 7: vi Preface This is not a review abo
Page 8 and 9: Contents 1 Chemistry and Structure
Page 10 and 11: Contents xi 4.6.3 Diffusion Coeffic
Page 12 and 13: Contents xiii 7.4.2 Effects of Plas
Page 14 and 15: 2 1 Chemistry and Structure of Cuti
Page 22 and 23: 10 1 Chemistry and Structure of Cut
Page 42 and 43: Chapter 2 Quantitative Description
Page 44 and 45: 2.1 Models for Analysing Mass Trans
Page 50 and 51: 2.3 Steady State Diffusion Across a
Page 54 and 55: 2.4 Steady State Diffusion of a Sol
Page 56 and 57: 2.5 Diffusion Across a Membrane wit
Page 58 and 59: 2.5 Diffusion Across a Membrane wit
Page 60 and 61: 2.6 Determination of the Diffusion
Page 62 and 63: Solutions 51 2.7 Summary In this ch
Page 64 and 65: Chapter 3 Permeance, Diffusion and
Page 66 and 67: 3.1 Units of Permeability 55 3.1.1
Page 68 and 69: 3.1 Units of Permeability 57 identi
Page 70 and 71: 3.3 Partition Coefficients 59 The d
Page 72 and 73: Chapter 4 Water Permeability All te
Page 74 and 75: 4.1 Water Permeability of Synthetic
Page 76 and 77: 4.2 Isoelectric Points of Polymer M
Page 78 and 79: 4.2 Isoelectric Points of Polymer M
Page 80 and 81: 4.3 Ion Exchange Capacity 69 The hi
Page 82 and 83: 4.3 Ion Exchange Capacity 71 has an
Page 84 and 85: 4.3 Ion Exchange Capacity 73 Counte
Page 86 and 87: 4.4 Water Vapour Sorption and Perme
Page 88 and 89: 4.4 Water Vapour Sorption and Perme
Page 90 and 91: 4.5 Diffusion and Viscous Transport
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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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Chapter 8 Effects of Temperature on
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8.1 Sorption from Aqueous Solutions
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8.1 Sorption from Aqueous Solutions
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8.2 Solute Mobility in Cuticles 239
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8.3 Water Permeability in CM and MX
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8.3 Water Permeability in CM and MX
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8.4 Thermal Expansion of CM, MX, Cu
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8.5 Water Permeability of Synthetic
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8.5 Water Permeability of Synthetic
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Problems 257 E D (kJ/mol) DH S (kJ/
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Chapter 9 General Methods, Sources
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9.2 Testing Integrity of Isolated C
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9.4 Distribution of Water and Solut
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9.6 Cutin and Wax Analysis and Prep
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9.7 Measuring Water Permeability 26
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9.8 Measuring Solute Permeability 2
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276 Appendix A Abbreviations (conti
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278 Appendix A Symbols (continued)
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280 Appendix B Physico-chemical pro
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Appendix C Index of Plants Botanica
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References Abraham MH, McGowan JC (
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References 287 Doty PM, Aiken WH, M
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References 289 Kolattukudy P (2004)
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References 291 Sabljic A, Güsten H
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References 293 Schreiber L, Schönh
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Index 2,4-D, 46 2,4-Dichlorophenoxy
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Index 297 leaf disks, 130 leaf surf
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Index 299 water molar volume, 110 p
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