Water potential

The water potential is a term which in the plant physiology is used to the availability of water in a system (for. Example, plant tissue , soil or air ) to characterize. It is used to describe the absorption and transport of water in plants and is designated with or ( Greek letter Psi ). Differences or gradients of the water potential drive the water transport , whereby the water flows from the place with the higher to the place with the lower potential (e.g. soil  -  roots , leaf  - air). ${\displaystyle \psi }$ ${\displaystyle \Psi }$

From a physical point of view, the water potential is the chemical potential of the water, scaled to units of pressure . It is a measure of the work that has to be done in order to supply a unit volume of water from a reference state to the system (at constant pressure and constant temperature ) . Since water potentials in nature usually take on negative values, the higher potential (in the sense of the larger number including the sign ) has the smaller numerical value, and vice versa. For example, water will flow from one place with a water potential of (fully saturated) to another place with a water potential of . ${\displaystyle 0\,\mathrm {MPa} }$ ${\displaystyle -0{,}5\,\mathrm {MPa} }$

In older literature the term suction force is occasionally used as a driving force for water transport in plants. This term is less precise, not uniformly defined and, clearly speaking, is the opposite of water potential: the lower the water potential, the higher the suction force and vice versa. A related concept is the hydraulic potential in soil science . In contrast to the water potential, osmotic effects are ignored, so that it is suitable for describing transport processes in which dissolved substances are transported unhindered with the water (e.g. seepage).

definition

The water potential is defined by the chemical potential of water: ${\displaystyle \mu }$

${\displaystyle \psi :={\frac {\mu -\mu _{0}}{\bar {V}}}}$.

Here, the chemical potential is in a standard state , usually pure water at atmospheric pressure at a specified reference altitude, and the molar volume of pure liquid water. The size of the water potential is therefore the energy per volume , which is synonymous with pressure . The most common unit of measurement is the megapascal ( ). ${\displaystyle \mu _{0}}$ ${\displaystyle {\bar {V}}\approx 18\,\mathrm {cm^{3}\,mol^{-1}} }$ ${\displaystyle \mathrm {MPa} }$

Breakdown into partial potentials

Water potential in the liquid phase

The water potential is often broken down into a sum of partial potentials, which describe different physical effects. In the liquid phase (or in porous media filled with aqueous solution ) the following applies: ${\displaystyle \psi }$

${\displaystyle \psi =\psi _{\text{s}}+\psi _{\text{p}}+\psi _{\text{m}}+\psi _{\text{g}}}$

with the osmotic potential , the pressure potential , the matrix potential and the gravitational potential . ${\displaystyle \psi _{\text{s}}}$ ${\displaystyle \psi _{\text{p}}}$ ${\displaystyle \psi _{\text{m}}}$ ${\displaystyle \psi _{\text{g}}}$

The osmotic potential (also: solution potential ) is the molar concentration of dissolved substances, in particular salts , depending. It is equal to the negative of the osmotic pressure ; H. . Van-'t-Hoff's law applies in sufficiently dilute solutions : ${\displaystyle \psi _{\text{s}}}$ ${\displaystyle \Pi }$ ${\displaystyle \psi _{\text{s}}=-\Pi }$

${\displaystyle \psi _{\text{s}}=-\Pi =-c\,R\,T\;,}$

where is the total solute concentration, the universal gas constant, and the absolute temperature . The osmotic potential is a colligative property in dilute solutions . In soils in arid areas and in marshes , the osmotic potential can be particularly negative. ${\displaystyle c}$ ${\displaystyle R\approx 8{,}314\,\mathrm {J\,mol^{-1}\,K^{-1}} }$ ${\displaystyle T}$

The pressure potential takes into account the effect of the pressure within the observed system. Atmospheric pressure ( ) is usually used as the reference pressure . Because of the turgor , this term is particularly relevant in the protoplast or symplast of plant cells . For example, negative values ​​occur in the xylem . The hydrostatic pressure plays a role in soil science below the groundwater surface. ${\displaystyle \psi _{\text{p}}=p-p_{0}}$ ${\displaystyle p}$ ${\displaystyle p_{0}}$ ${\displaystyle \approx 0.10\,\mathrm {MPa} }$

Water tension curves for sand (Ss), silt (Uu), silty loam (Lu) and clay (Tt). The figure shows the amount of the matrix potential ( logarithmic ) as a function of the volume fraction of water in the soil. ${\displaystyle \psi _{\mathrm {m} }}$ ${\displaystyle \theta }$

The matric potential (also: capillary potential ) includes all the surface effects with which water of a porous media (soil or cell wall or apoplast is retained), and colloidal effects. The matrix potential is more negative, the finer the pores are (in the soil: the finer-grained it is structured). If the pores slowly dry out, the amount of the matrix potential increases until only the dead water that cannot be mobilized is present in the finest pores. In soil science, the matrix potential corresponds to the soil water tension with the opposite sign : . The relationship between the matrix potential and the relative water content in the soil is represented as a water tension curve and is often empirically described by the Van Genuchten equation: ${\displaystyle \psi _{\text{m}}}$ ${\displaystyle \tau }$ ${\displaystyle \psi _{\text{m}}=-\tau }$ ${\displaystyle \theta }$

${\displaystyle \theta =\theta _{r}+{\frac {\theta _{s}-\theta _{r}}{\left(1+\left(\alpha \,{\frac {\left|\Psi _{\mathrm {m} }\right|}{\mathrm {hPa} }}\right)^{n}\right)^{m}}}\;,}$

wherein , , , and are empirically determined parameters. ${\displaystyle \theta _{r}}$ ${\displaystyle \theta _{s}}$ ${\displaystyle \alpha }$ ${\displaystyle n}$ ${\displaystyle m}$

The gravitational potential describes the influence of the positional energy on the water. With the density of liquid water , the acceleration due to gravity and the altitude relative to the reference state applies . The gravitational potential is relevant when water is transported over great heights (several meters), for example in trees . ${\displaystyle \psi _{\text{g}}}$ ${\displaystyle \rho _{\mathrm {H_{2}O} }\approx 998\,\mathrm {kg\,m^{-3}} }$ ${\displaystyle g\approx 9{,}81\,\mathrm {m\,s^{-2}} }$ ${\displaystyle h}$ ${\displaystyle \psi _{\text{g}}=\rho _{\mathrm {H_{2}O} }\,g\,h}$

Inserted results in:

${\displaystyle \psi =-\Pi +\left(p-p_{0}\right)-\tau +\rho _{\mathrm {H_{2}O} }\,g\,h\;.}$

Water potential in the gas phase

The following applies to the water potential in the gas phase , especially in air :

${\displaystyle \psi ={\frac {R\,T}{\bar {V}}}\,\ln \left({\frac {p_{\mathrm {H_{2}O} }}{p_{\mathrm {H_{2}O} }^{0}}}\right)\;.}$

Here again is the universal gas constant , the absolute temperature and the molar volume of liquid water; is the partial pressure of water vapor and the saturation vapor pressure of water at the given temperature. Since the quotient is equal to the relative humidity , this can also be written as: ${\displaystyle R\approx 8{,}314\,\mathrm {J\,mol^{-1}\,K^{-1}} }$ ${\displaystyle T}$ ${\displaystyle {\bar {V}}}$ ${\displaystyle p_{\mathrm {H_{2}O} }}$ ${\displaystyle p_{\mathrm {H_{2}O} }^{0}}$ ${\displaystyle p_{\mathrm {H_{2}O} }/p_{\mathrm {H_{2}O} }^{0}}$ ${\displaystyle \varphi }$

${\displaystyle \psi ={\frac {R\,T}{\bar {V}}}\,\ln \left(\varphi \right)\;.}$

Typical values

By definition, pure water at reference altitude and at atmospheric pressure has the water potential . Well-irrigated, salty soils have a slightly negative water potential of around . At the permanent wilting point , a soil has a water potential in the range to . In the well-watered state, the roots have a water potential of up to . In leaves of herbaceous plants the water potential is usually between and , in trees and shrubs the values ​​can be more negative, up to about . In the leaves of plants that are adapted to a strongly arid climate , values ​​below are even possible. The ambient air has a water potential of at and a humidity of according to the above formula for the gas phase . Due to the osmotic effects of the dissolved salts, sea ​​water has a water potential of approx . ${\displaystyle 0\,\mathrm {MPa} }$ ${\displaystyle -0{,}1\,\mathrm {MPa} }$ ${\displaystyle -2{,}0\,\mathrm {MPa} }$ ${\displaystyle -1{,}5\,\mathrm {MPa} }$ ${\displaystyle -0{,}4\,\mathrm {MPa} }$ ${\displaystyle -0{,}2\,\mathrm {MPa} }$ ${\displaystyle -1{,}0\,\mathrm {MPa} }$ ${\displaystyle -0{,}2\,\mathrm {MPa} }$ ${\displaystyle -2{,}5\,\mathrm {MPa} }$ ${\displaystyle -10\,\mathrm {MPa} }$ ${\displaystyle 20\,\mathrm {^{\circ }C} }$ ${\displaystyle 50\,\mathrm {\%} }$ ${\displaystyle -94\,\mathrm {MPa} }$ ${\displaystyle -2\,\mathrm {MPa} }$

Flow of water through a membrane

The water potential difference represents the driving force for the water flow through an ideal, i.e. H. represents a completely impermeable membrane (or other interface ) for dissolved substances . The flow velocity or volumetric water flux density (in ) can in this case be expressed as ${\displaystyle J_{v}}$ ${\displaystyle \mathrm {m\,s^{-1}} =\mathrm {m^{3}\,m^{-2}\,s^{-1}} }$

${\displaystyle J_{v}=Lp\,\Delta \psi \;,}$

where is the difference in water potentials between the two sides of the membrane and the hydraulic conductivity (in ). Aquaporins are crucial for the good water conductivity of many biomembranes . ${\displaystyle \Delta \psi }$ ${\displaystyle Lp}$ ${\displaystyle \mathrm {m\,s^{-1}\,MPa^{-1}} }$

For real membranes that are partially permeable to dissolved substances, the contribution of the osmotic potential to water transport is reduced. One can retain the ability of a membrane or interface solutes in a reflection coefficient (with summarize) to give ${\displaystyle \sigma }$ ${\displaystyle 0\leq \sigma \leq 1}$

${\displaystyle {\begin{aligned}J_{v}&=Lp\,\left(\Delta \psi -\left(1-\sigma \right)\,\Delta \psi _{\mathrm {s} }\right)\\&=Lp\,\left(\Delta \psi _{\mathrm {h} }+\sigma \,\Delta \psi _{\mathrm {s} }\right)\;,\end{aligned}}}$

where denotes the hydraulic potential . In the borderline case of an ideal reflective membrane ( ), the above equation results with the water potential difference as the driving force. In the borderline case of a membrane that allows dissolved substances to pass through unhindered with the water ( ), the difference in the hydraulic potential as the driving force results instead of that of the water potential. The reflection coefficient depends on the type of dissolved substances (size, electrical charge , polarity ) and the type and condition of the membrane. ${\displaystyle \psi _{\mathrm {h} }:=\psi -\psi _{\mathrm {s} }}$ ${\displaystyle \sigma =1}$ ${\displaystyle \sigma =0}$

Experimental determination

Measurement in plant tissues

Different measurement methods are used depending on the plant tissue to be examined. Usually individual partial potentials are measured separately and then the sum is calculated.

The water potential in the xylem sap of a leaf (or shoot) can, for example, be measured by clamping it in a so-called Scholander bomb . This is a chamber from which only the severed stem of the leaf protrudes. If the air pressure in the chamber is increased from atmospheric pressure until xylem sap begins to emerge at the cut surface, this pressure difference is a measure of the (negative) pressure potential previously prevailing in the xylem . If the volume of the exiting juice is measured as a function of the pressure with a further increase in pressure, the osmotic potential can also be determined from the resulting pressure-volume curve . Since the matrix potential in the xylem does not play a major role ( ) and the gravitational potential can easily be calculated from the height of the leaf if necessary ( ), the water potential in the xylem can be determined by adding . ${\displaystyle \psi _{\mathrm {p} }}$ ${\displaystyle \psi _{\mathrm {s} }}$ ${\displaystyle \psi _{\text{m}}\approx 0}$ ${\displaystyle \psi _{\text{g}}=\rho _{\mathrm {H_{2}O} }\,g\,h}$ ${\displaystyle \psi }$

• 

  How the Scholander bomb works

• 

  Scholander bomb

• 

  At a certain pressure in the chamber, the xylem sap emerges on the cut surface.

The hydraulic properties of an individual cell can be shown in the so-called Höfler diagram . For this purpose, the water potential of the cell wall is successively varied by soaking it in a solution with known osmotic properties and the cell volume which is established in equilibrium is measured. The lowering of the freezing point can be used for the experimental determination of the osmotic potential , since both are colligative properties . In addition, the pressure potential of some cells can be measured directly by piercing the vacuole with a pressure probe . ${\displaystyle \psi _{\mathrm {s} }}$ ${\displaystyle \psi _{\mathrm {p} }}$

Measurement in the ground

The water potential of a soil can be measured directly with the help of gypsum block electrodes . A block of plaster is built into the floor and the electrical conductivity within the block is measured:

• At a high water content of the soil (low amount of water potential) are many of the pores of the block filled with water and lead the current better.
• If the water content of the soil is low (high value of the water potential, i.e., however, a more negative number), few of the pores of the block are filled with water and conduct the current less well.

Tensiometer with (1) porous ceramic cell, (2) water-filled sight glass, (3) electronics, (4) pressure sensor

Using a tensiometer that can matric potential can be determined. In soils with little salt, this corresponds essentially to the water potential , since the osmotic potential is negligible here .

Historical development

Research into water transport in plants

Pfeffer's cell as an analogue to plant cells: Fig. 1 from Osmotic studies: Studies on cell mechanics . Manometer  (m), porous cup (z), nested glass pieces (v) (t), glass ring (r).

Until the 19th century in which was water transport in plants , like many other processes in the living world, in the tradition of Aristotle ' De anima with the creatures own soul justified. Fundamental to the modern understanding of water transport in plants and the development of the concept of water potential , the findings on were diffusion and osmosis in the second half of the 19th century by Adolf Fick , Moritz Traube , Hugo de Vries and Wilhelm Pfeffer (see. Pfeffersche cell ). Pfeffer is said to have used potential concepts occasionally around 1900. After it became clear that the osmotic pressure alone is not sufficient to describe all transport processes, different, competing terms ( suction force , hydration , ...) emerged up to the middle of the 20th century , with which an attempt was made to summarize the relevant driving forces. From the middle of the 20th century, in the course of improved measurement methods, the term water potential has established itself as a fundamental concept.

In 1941, Tang and Wang criticized the vague and inconsistent formation of terms and suggested describing the water status of plant and animal cells using terms from thermodynamics , especially chemical potential . The concept of water potential is said to have been coined by Schofield. This concept spread to Owen in 1952 when he proved that wheat seed even under extremely dry conditions for water absorption and germination able are and this tried to explain. The notion of water potential was eventually spread by Slatyer and Taylor:

“An alternative method of expression is in terms of the chemical potential of water, which is identical with the partial molal free energy. This procedure was adopted by Day (1942) who referred to it as 'moisture potential.' Schofield, cited by Owen (1952), suggested the term 'water potential' for the same function, and more recently the 1959 UNESCO conference on plant water relations in arid regions favorably considered a terminology based on an evaluation of this function. ”

“An alternative way of expressing this is to start from the chemical potential of water, which is identical to the partial molal free energy. This approach was used by Day (1942), who termed it 'moisture potential'. Schofield, whom Owen (1952) cited, suggested the term 'water potential' for the same function, and only recently, in 1959, the UNESCO Conference on Plant Water Issues in Arid Regions advocated terminology based on consideration of this function. "

- Slatyer : Absorption of water by plants. 1960, p. 335 above.

However, in this article Slatyer still uses the magnitude of the chemical potential for the water potential and argues against the use of the magnitude of the pressure.

In the Strasburger textbook of botany , the water potential is used for the first time in the 31st edition from 1978. Up to and including the 30th edition of 1971, the older, less sharply defined term suction force was used. While the definition of the water potential as the chemical potential of water in relation to its molar volume is common in modern textbooks, this can also be expressed in an equivalent way verbally based on the free enthalpy (for example in Richter). Different conventions regarding the notation are still in use for the various partial potentials.

Related terms in related sciences

The terms free enthalpy (sometimes also called Gibbs potential ) and chemical potential were introduced to thermodynamics by Josiah Willard Gibbs in the 1870s . Edgar Buckingham , who had already written a thermodynamics textbook in 1900, introduced related potential concepts in soil science in his 1907 work Studies on the Movement of Soil Moisture , starting from a definition of the work to be done . Water transport processes in the soil, in which dissolved substances are transported unhindered with the water, are described today with the hydraulic potential , which, compared to the water potential, disregards the osmotic potential.

There are both historical and practical reasons for the fact that related potentials in different sciences are related to different sizes and are thus given in different types of sizes . In chemical thermodynamics, the mole is the natural reference, which is why the chemical potential is measured in. For plant physiology, pressure is a sensible type of quantity, because the pressure component (turgor) in plant cells makes a considerable contribution to the potential and osmotic properties are traditionally given as osmotic pressures . Therefore, the volume is selected here as reference, indicating the water potential in units of pressure ( of batteries also , , or ) causes. Various reference values ​​are used in soil science, where the height of a water column is a particularly clear measure that corresponds directly to measurements in the water level tube. ${\displaystyle \mathrm {J\,mol^{-1}} }$ ${\displaystyle \mathrm {Pa} }$ ${\displaystyle \mathrm {bar} }$ ${\displaystyle \mathrm {atm} }$ ${\displaystyle \mathrm {dyn\,cm^{-2}} }$ ${\displaystyle \mathrm {mmHg} }$

See also

• Water balance of plants
• Root pressure
• Perspiration suction
• pF value
• Soil water tension

literature

• Lincoln Taiz, Eduardo Zeiger, Ian Max Møller, Angus Murphy (Eds.): Plant Physiology and Development . 6th edition. Sinauer Associates, Sunderland, Massachusetts, USA 2014, ISBN 978-1-60535-255-8 , Chapter 3 Water and Plant Cells and Chapter 4 Water Balance of Plants , pp. 83–118 (Original English edition, Chapters 3 & 4 author: N. Michele Holbrook). Or. German translation: Lincoln Taiz, Eduardo Zeiger (Hrsg.): Physiologie der Pflanzen . 1st edition. Spektrum Akademischer Verlag, Heidelberg / Berlin 2000, ISBN 3-8274-0537-8 , Chapter 3 The water balance of plant cells and Chapter 4 The water balance of plants , p.
  
   59-100 .
• Peter Schopfer, Axel Brennecke: Plant Physiology . Founded by Hans Mohr . 6th edition. Elsevier, Spektrum Akademischer Verlag, Munich 2006, ISBN 3-8274-1561-6 , Chapter 3 The cell as an energetic system and Chapter 13 Long-distance transport of water and inorganic ions , p. 47-70, 311-331 .
• Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 .
• Park S. Nobel: Physicochemical and environmental plant physiology . 4th edition. Elsevier Academic Press, Amsterdam / London 2009, ISBN 978-0-12-374143-1 , Chapter 2 Water , Chapter 8 Leaves and Fluxes , Chapter 9 Plants and Fluxes , pp. 45-100, 365-506 .

Web links

• Plant Physiology and Development, Sixth Edition - Companion Website. Web Topics and Essays. Lincoln Taiz, Eduardo Zeiger, Ian Max Møller, Angus Murphy, 2015, accessed on July 23, 2015 (English, web-based additional material to the textbook of the same name, Sinauer Associates, freely accessible). In particular:  
  
  • N. Michele Holbrook et al. a .: Web Topics for Chapter 3: Water and Plant Cells. 2015, accessed on July 20, 2015 . 
  • N. Michele Holbrook et al. a .: Web Topics and Essays on Chapter 4: Water Balance of Plants. 2015, accessed on July 20, 2015 . 

Individual evidence

1. ↑ ^{a b c d e f g h} N. Michele Holbrook (Chapter 3 & 4): Plant Physiology . Eduardo: Lincoln Taiz, Eduardo Zeiger. 6th edition. Sinauer Associates, Sunderland, Massachusetts, USA 2014, ISBN 978-1-60535-255-8 , Chapter 3, Sections Water Potential , Water Potential of Plant Cells , Cell Wall and Membrane Properties , Plant Water Status , and Summary , pp. 89-98 .
2. ↑ ^{a b c d e f g h i} Peter Schopfer, Axel Brennecke: Plant Physiology . Founded by Hans Mohr . 6th edition. Elsevier, Spektrum Akademischer Verlag, Munich 2006, ISBN 3-8274-1561-6 , Section 3.5: Chemical potential of water and 3.6 Applications of the water potential concept on the water status of the cell , p. 51-61 .
3. ^ ^{A b c d} Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 2: Functions and Properties of Water , Subsection Chemical Potential of Water , pp. 35-37 .
4. ↑ ^{a b c d} Gerhard Richter: Metabolic physiology of plants . Physiology and biochemistry of primary and secondary metabolism. 5th edition. Georg Thieme Verlag, Stuttgart 1988, ISBN 3-13-442005-8 , Chapter 2, Section 1 Water Management , p. 31-51 .
5. ↑ ^{a b} Dietrich von Denffer u. a .: Textbook of botany for universities . Founded by Eduard Strasburger u. a. 30th edition. Gustav Fischer Verlag, Stuttgart 1971, ISBN 3-437-20050-X , Part Two: Physiology , Section One: Physiology of Metabolism , II. The Water , p. 205–223 (From the following 31st edition from 1978 onwards, water transport is no longer described in terms of suction power , but rather with water potential . The term "suction power" is only used figuratively in the running text "Suction power" no longer suggests (full text search in PDF, doi: 10.1007 / 978-3-642-54435-4 ).).
6. ↑ Ulrich Kutschera : Short textbook of plant physiology . Quelle and Meyer, Wiesbaden 1995, ISBN 3-8252-1861-9 , Chapter 4: Water balance of the plant cell: diffusion, osmosis, water potential , p. 60 .
7. ↑ ^{a b c} Peter Sitte : Textbook of botany for universities . Founded by Eduard Strasburger . 33rd edition. G. Fischer, Stuttgart / Jena / New York 1991, ISBN 978-3-437-20447-0 , second part physiology , IV  nutrients and their turnover in plants , B  water balance , p. 321–337 (This definition of water potential via chemical potential is first found in the 31st edition from 1978. In older editions, specifically in the 29th edition from 1967 and the 30th edition from 1971, “water potential” does not appear; instead the term “suction power” is used. In more recent editions, specifically in the 36th edition from 2008 and the 37th edition from 2014, calculations are made with the “water potential”, but a definition is missing.).
8. ^ Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 3: Cell Water Relations , Section Water Status , pp. 49-53 .
9. ^ ^{A b} Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 4: Soil and Water , Section Soil water terminology , pp. 89-93 .
10. ^ Gerd Wedler, Hans-Joachim Freund: Physical chemistry . 6., completely revised and updated edition. Wiley-VCH Verlag, Weinheim 2012, ISBN 978-3-527-32909-0 , section Osmotic pressure in 2.5.6 Phase equilibria in two-component systems between a mixed phase and a pure phase , p. 348-352 (equation (2.5-79)).
11. ↑ ^{a b} Ad-hoc-AG Boden: Linkage rule 1.18 - parameters for the model of a continuous function of the θ (ψ) relationship. (PDF, 242 kB) (No longer available online.) State Geological Services and BGR, September 17, 2004, archived from the original on March 4, 2016 ; Retrieved July 29, 2015 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
12. ^ Karl-Heinrich Hartge , Rainer Horn: Introduction to soil physics . 3. Edition. Ferdinand Enke Verlag, Stuttgart 1999, ISBN 3-432-89683-2 , Section 4.6 Water tension and water content , in particular subsection 4.6.5 Mathematical description of the water tension curve , p. 130-137 .
13. ↑ ^{a b c d} Peter Schopfer, Axel Brennecke: Plant Physiology . Founded by Hans Mohr . 6th edition. Elsevier, Spektrum Akademischer Verlag, Munich 2006, ISBN 3-8274-1561-6 , Chapter 13: Long-distance transport of water and inorganic ions , p. 311–331 (especially Fig. 13.2 on p. 313).
14. ^ Joachim W. Kadereit, Christian Körner, Benedikt Kost, Uwe Sonnewald: Strasburger - Textbook of Plant Sciences . Founded by E. Strasburger, F. Noll, H. Schenk, AFW Schimper. 37th edition. Springer Spectrum, Berlin / Heidelberg 2014, ISBN 978-3-642-54435-4 , subsection 19.1.2.4 Mineral salts as location factors , p. 345 , doi : 10.1007 / 978-3-642-54435-4 .
15. ^ N. Michele Holbrook: Web Topic 3.9: Understanding Hydraulic Conductivity. Plant Physiology and Development, Sixth Edition. Lincoln Taiz, Eduardo Zeiger, 2015, accessed on July 21, 2015 (English, web-based additional material to the textbook of the same name, Sinauer Associates, freely accessible). 
16. ^ Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 3: Cell Water Relations, Section Water Transport , pp. 63-68 .
17. ↑ ^{a b} N. Michele Holbrook: Web Topic 3.6: Measuring Water Potential. Plant Physiology and Development, Sixth Edition. Lincoln Taiz, Eduardo Zeiger, 2015, accessed on July 20, 2015 (English, web-based additional material to the textbook of the same name, Sinauer Associates, freely accessible). 
18. ↑ ^{a b c} Hans-Peter Blume u. a .: Textbook of Soil Science . Founded by Fritz Scheffer and Paul Schachtschabel . 16th edition. Spectrum Akademischer Verlag, Heidelberg 2010, ISBN 978-3-8274-2251-4 , Section 6.4 Soil water (especially subsection 6.4.2.1 Potentials ) and Subsections 4.2.2 Water and atmosphere , 9.2.2 Water movements in the soil – plant – atmosphere system and 9.2.3 Water consumption and crop yield , p. 220-249, 103, 384-388 , doi : 10.1007 / 978-3-8274-2251-4 .
19. ^ Wilhelm Pfeffer : Osmotic investigations . Cell mechanics studies. 2nd Edition. Wilh. Engelmann, Leipzig 1921, p. 5 (unchanged edition of the first print from 1877).
20. ^ Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 1: Historical Review , pp. 1-15 .
21. ^ PS Tang, JS Wang: A Thermodynamic Formulation of the Water Relations in an Isolated Living Cell . In: The Journal of Physical Chemistry . tape 45 , no. 3 , 1941, pp. 443-453 , doi : 10.1021 / j150408a010 .
22. ↑ ^{a b c} R. O. Slatyer: Absorption of water by plants . In: The Botanical Review . tape 26 , no. 3 . Springer-Verlag, 1960, ISSN  0006-8101 , p. 331-392 , doi : 10.1007 / BF02860807 .
23. ↑ PC Owen: The Relation of Germination of Wheat to Water Potential . In: Journal of Experimental Botany . tape 3 , no. 2 , 1952, pp. 188-203 , doi : 10.1093 / jxb / 3.2.188 . PC Owen: The Relation of Water Absorption by Wheat Seeds to Water Potential . In: Journal of Experimental Botany . tape
     3 , no. 9 . Oxford University Press, 1952, ISSN  0022-0957 , pp. 276-290 .
24. ^ N. Michele Holbrook: Web Topic 3.3: Alternative Conventions for Components of Water Potential. Plant Physiology and Development, Sixth Edition. Lincoln Taiz, Eduardo Zeiger, 2015, accessed on July 22, 2015 (English, web-based additional material to the textbook of the same name, Sinauer Associates, freely accessible). 
25. ^ Gerd Wedler, Hans-Joachim Freund: Physical chemistry . 6., completely revised and updated edition. Wiley-VCH Verlag, Weinheim 2012, ISBN 978-3-527-32909-0 , time table in the front cover and section 2.3, p. 301-324 .
26. ^ TN Narasimhan: Central Ideas of Buckingham (1907): A Century Later . In: Vadose Zone Journal . tape 6 , no. 4 , 2007, ISSN  1539-1663 , pp. 687-693 , doi : 10.2136 / vzj2007.0080 .
27. ^ ^{A b} Karl-Heinrich Hartge , Rainer Horn: Introduction to soil physics . 3. Edition. Ferdinand Enke Verlag, Stuttgart 1999, ISBN 3-432-89683-2 , Section 4.4 Potential of Soil Water , in particular Table 4.1, p. 119-128 .

Remarks

1. ↑ The saturation vapor pressure also depends to a much lesser extent on the total pressure. This is negligible for biological applications, since this dependency is weak and the pressure in the gas phase is usually close to atmospheric pressure.
2. ↑ Values ​​of in plants are in the range (Paul J. Kramer, John S. Boyer: Water relations in plant and soil . Academic Press, San Diego 1995, ISBN 0-12-425060-2 , Chapter 3: Cell Water Relations , Table 3.1, p. ${\displaystyle Lp}$ ${\displaystyle 10^{-8}~\ldots ~2\times 10^{-5}\,\mathrm {m\,s^{-1}\,MPa^{-1}} }$ 66-67 . ). Expressed
   in SI base units , the following applies ${\displaystyle 1\,\mathrm {m\,s^{-1}\,MPa^{-1}} =10^{-6}\,\mathrm {m^{2}\,s\,kg^{-1}} .}$
3. ↑ The gravitational potential, if it is relevant at all for the respective question, can always be easily calculated from the height difference.
4. ↑ To the formulas for the "water potential" by Hans-Peter Blume u. a .: Textbook of Soil Science . Founded by Fritz Scheffer and Paul Schachtschabel . 16th edition. Spektrum Akademischer Verlag, Heidelberg 2010, ISBN 978-3-8274-2251-4 , doi : 10.1007 / 978-3-8274-2251-4 (equation (Eq. 6.4.7) on p. 225). and Karl-Heinrich Hartge , Rainer Horn: Introduction to Soil Physics . 3. Edition. Ferdinand Enke Verlag, Stuttgart 1999, ISBN 3-432-89683-2 (p. 126 center). It should be noted that these represent neither a definition nor a general basis for calculation, but are only to be understood as a calculation guide for the water potential in the soil in the immediate vicinity of the roots. Rather, the water potential of the plant physiological literature corresponds to what Scheffer / Schachtschabel / Blume ((Eq. 6.4.5) on p. 224) and Hartge / Horn (p. 122 above) call the “total potential” . ${\displaystyle \psi _{\mathrm {w} }}$
   
   
   ${\displaystyle \psi }$