osmosis

This article covers the process of osmosis; for the French record label of the same name, see article Osmose Productions .

As osmosis ( ancient Greek ὠσμός osmos "penetration", "impact", "push", "drive") is in the science of directed flow of particles through a selectively - or semi-permeable separation layer, respectively. Osmosis is often described as the spontaneous passage of water or another solvent through a semipermeable membrane that is permeable to the solvent, but not to the substances dissolved in it .

Osmosis is of central importance in nature, especially for the regulation of the water balance of living things and their cells . As a separation process , it is used in medicine and process engineering and it is used in osmotic power plants to generate energy . While osmosis is theoretically explained in the context of statistical mechanics and non-equilibrium thermodynamics , the physical processes on the microscopic-molecular level are the subject of scholarly dispute and active research at the beginning of the 21st century.

A clear example of the effect of osmosis is the bursting of ripe cherries after being wetted with rainwater . The water on the outside of the fruit contains very few dissolved particles, so it has a high chemical potential . It penetrates through the outer skin into the fruit, in which the water as a solvent has a low chemical potential due to the high sugar content and other dissolved substances. The influx of water increases the pressure inside the fruit and tears its outer skin. This, along with other substances, is permeable to water, but not to sugar molecules; due to these properties, it acts as a semipermeable membrane. In principle, water molecules can pass through this membrane in both directions, but they are more “held” inside the fruit. The water molecules have to compete with the other dissolved molecules and particles for access to the membrane, so that fewer water molecules penetrate to the outside per unit of time than vice versa.

The driving force behind the spontaneous osmosis is the difference between the chemical potentials of one or more substances in the phases separated by a membrane . These can consist of liquid and gaseous solutions or pure substances . Particles ( atoms , molecules or ions ) of the components to which the membrane is permeable diffuse towards their lower chemical potential. The mixing process resulting from this movement reduces the Gibbs energy (or free enthalpy ) of the entire system; therefore the process takes place without any energy input (see also exergonic and endergonic reactions ). In general, it is a solvent that diffuses towards its lower chemical potential due to the different number of dissolved particles.

In closed systems , the potential differences are balanced by osmosis; the osmotic movement continues until the chemical potential of the diffusing components on both sides of the membrane is balanced; A thermodynamic equilibrium has then been established between the two phases . If the substance flows into a closed volume , the pressure in this volume (the side with the initially lower potential) must inevitably increase; this difference is called the osmotic pressure . The osmotic pressure is a colligative property because it depends on the number of dissolved particles.

History and definitions of the term osmosis

history

Dutrochets endosmometer from Nouvelles recherches

In 1748, Jean-Antoine Nollet , Professor of Experimental Physics at the Collège de Navarre in Paris, described an experiment in which a cylinder was filled with “ alcohol ”, sealed with a defatted pig's bladder and immersed in water upright. Within a few hours, so much water flowed into the cylinder that the bladder bulged outward under great pressure; After piercing with a needle, liquid shot up as a small fountain. While the pig's bladder is permeable to water, alcohol cannot escape through it; With his experiment, Nollet had demonstrated the existence of semipermeable membranes.

The French botanist Henri Dutrochet first used “osmosis” as a word component ; He called the inflow of water into a measuring chamber enclosed with a pig's bladder as endosmosis , the outward movement as exosmosis . With the endosmometer, Dutrochet was the first to construct a device for detecting osmotic pressure and postulated the central importance of osmosis for all life processes. "Osmotically" (English. Osmotic ) as adjective was in 1854 by the Scottish chemist Thomas Graham coined.

In 1864, the chemist and private scholar Moritz Traube succeeded in producing artificial semipermeable membranes that were impermeable to sugar and a number of other organic substances. In 1877 the German botanist Wilhelm Pfeffer first described a method for the quantitative measurement of the osmotic pressure of aqueous solutions. To this end, he developed the Pfeffer's cell named after him , an osmometer made of porous clay , which he coated with the colloidal precipitation membranes discovered by Traube, such as copper (II) hexacyanoferrate (II).

The Pfeffer's method for measuring osmotic pressure was significantly improved around the turn of the century by Harmon Northrop Morse , who applied the membrane material to the walls of the clay cells by means of electrolysis , thereby enabling measurements up to 270 times the atmospheric pressure.

Ten years after Pfeffer, the Dutch chemist Jacobus Henricus van 't Hoff published his pioneering work on the analogy of gas pressure and osmotic pressure of solutions, for which he was awarded the first Nobel Prize in Chemistry in 1901, among other achievements . In 1905 Albert Einstein published his fundamental work on the explanation of osmosis using the "molecular kinetic theory". In 1958, Ora Kedem and Aharon Katchalsky defined the term osmotic flow in the context of Onsager's reciprocity relationships and established the theory of membranes in non-equilibrium systems.

The development of suitable membranes, initially made of cellulose acetate at the end of the 1950s, and a little later synthetic asymmetric membranes, made it possible to use reverse osmosis for drinking water treatment. The first prototype of an osmotic power plant went into operation in Norway in 2009.

Definitions

In the literature, the term osmosis is defined inconsistently, sometimes also contradicting, two examples:

• "Osmosis is understood as the diffusion of particles through a selectively permeable membrane, such as that represented by a biological membrane."
• “The phenomenon of osmosis consists in the effort of a pure solvent to migrate through a semipermeable membrane into a solution. The osmotic pressure Π is the pressure that has to be exerted on the solution in order to prevent the penetration of the solvent particles. "

Originally, osmosis was understood to mean “the partial diffusion of individual components of liquid mixtures through porous walls”, which includes both solvents and dissolved substances. In this context, pepper speaks of the diosmosis of dissolved bodies . Van't Hoff's basic work on osmotic pressure, published in 1887, made the concept of an ideal semipermeable membrane, which is assumed to be permeable only to the solvent, to be the pivotal point for the theoretical representation of osmosis. In contrast, real membranes are always permeable to dissolved substances to a certain extent; to what extent can the substance-dependent reflection coefficient σ be given. For reflection coefficient 1> σ _i  > 0, the membrane is as leaky membrane (English: leaky membrane ), respectively.

For the quantitative description of osmotic systems, a qualitative differentiation between solvent and dissolved substance is not necessary. Phenomena such as the Gibbs-Donnan effect are based on the fact that, in addition to the solvent, dissolved ions also pass through the membrane. The dialysis , besides the solvents other solutes also diffuse through the membrane in which it is often described as a system based on osmosis phenomenon, while other authors, the demarcation between osmosis (only the solvent passes through the membrane) and dialysis stress.

Definitions can often be found that only mention water as a solvent. In fact, with a suitable membrane structure, other liquids and gases (gas osmosis) can also be involved in osmotic processes.

Very often, osmosis is described as a movement caused by diffusion across a semipermeable membrane ; this explanation goes back to a suggestion made in 1855 by the physiologist Adolf Fick . In fact, the osmotic flow through membrane pores is a convective process ( "convective" or "non-diffusional flow" ) that does not obey Fick's laws of diffusion; see also membrane technology # material transport .

From thermal osmosis is when the material flow is due to a difference in temperature. Electroosmosis describes the movement of a liquid along an electrochemical double layer .

Basics

Osmosis: on the left a U-tube with differently concentrated solutions immediately after filling, on the right the same U-tube at a later point in time. Equilibrium is reached when the hydrostatic pressure of the right column of liquid corresponds to the osmotic pressure of the solution.

In the case of osmosis, a difference in concentration between the two sides can only be balanced out by the flow of substances that, due to their properties, can pass through the membrane. In many cases this will be the solvent, e.g. B. Water in biological systems.

As shown in the example on the right, water flows through the membrane from the side with the lower concentration (the left half of the U-tube in the figure); its amount decreases there and leads to a corresponding increase in volume on the other side. The movement of the solvent ends as soon as an equal chemical potential has been established on both sides of the membrane. In the figure, it is the hydrostatic pressure of the right column of liquid that counteracts the continued flow of solvent.

If the water on one side is marked with D ₂ O ( heavy water ) or ³ H ₂ O ( excessively heavy water ) after reaching the state of equilibrium , it can be shown that an exchange of water molecules continues. In equilibrium, however, the amount of inflowing and outflowing molecules is the same on both sides.

Thermodynamic consideration

The spontaneous osmosis involves a mixing process - a substance passes from one phase to the other and mixes there with the existing components. Mixing processes that take place voluntarily lead to a reduction in the free enthalpy (Gibbs energy) and an increase in entropy in closed systems . In the case of osmosis, the selectively permeable membrane acts as a barrier and prevents all concentration differences from disappearing when thermodynamic equilibrium is reached; there are two separate phases at each point in time. (Actually three phases when considering the membrane.)

The total change in free energy in the osmotic cell must therefore be written as the sum of the changes in both phases:

${\displaystyle \mathrm {d} G=\mathrm {d} G^{(1)}+\mathrm {d} G^{(2)}\ }$

where the superscript ^(x) denotes the respective section of the osmotic cell. If only one type of substance (e.g. the solvent) is allowed to pass through the membrane, the relationship between the free enthalpy and the change in the amount of substance can through ${\displaystyle x}$ ${\displaystyle L}$ ${\displaystyle G}$ ${\displaystyle \mathrm {d} n_{L}}$

${\displaystyle \mathrm {d} G^{(1)}=\mu ^{(1)}\mathrm {d} n_{L}}$ and ${\displaystyle \mathrm {d} G^{(2)}=\mu ^{(2)}\mathrm {d} n_{L}}$

are described, wherein referred to the chemical potential and the amount of substance of the substance passing through the membrane. Since the inflow from on side ⁽²⁾ corresponds to the loss on side ⁽¹⁾ (conservation condition), it follows for the entire change in free enthalpy: ${\displaystyle \mu }$ ${\displaystyle n}$ ${\displaystyle L}$

${\displaystyle \ \mu ^{(2)}dn_{L}=-\mu ^{(1)}dn_{L}}$ and thus ${\displaystyle \mathrm {d} G=(\mu ^{(1)}-\mu ^{(2)})\mathrm {d} n_{L}}$

As long as equilibrium has not yet been reached ( ), the following applies to the chemical potentials: ${\displaystyle \mathrm {d} G>0}$

${\displaystyle \mu ^{(1)}>\mu ^{(2)}}$

and in equilibrium ( ): ${\displaystyle \mathrm {d} G=0}$

${\displaystyle \mu ^{(1)}=\mu ^{(2)}}$.

If more than one type of substance takes part in the osmotic process, the above relationships must be expanded to include the chemical potentials of the additional components (see also section The osmotic potential of non-ideal solutions ).

The condition for the osmotic equilibrium is that the chemical potentials of the substances let through the membrane (mostly the solvent) are the same in both phases. As long as there is still a potential difference, particles of the respective component will move in the direction of the lower potential. On the other hand, by increasing the chemical potential, for example by applying pressure or increasing the temperature on one side of the membrane, the direction of movement can be reversed. Osmosis through a membrane, as opposed to diffusion in a single phase system, is a reversible process.

Solution effect as an immediate cause

The solution effect reduces the chemical potential of the solvent in the solution compared to the pure substance, combined with a decrease in the saturation vapor pressure in liquids or the partial pressure in gases. So the dissolving effect is an immediate cause of osmosis.

In contrast, a concentration gradient of the dissolved substances has an indirect effect , since osmosis only takes place if the concentration differences lead to a difference in the chemical potential of the solvent in both solutions. If different substances are dissolved in the same number of particles on both sides of the membrane, the chemical potential of the solvent is the same and therefore no osmosis occurs. This is what the osmolytes , with which cells can protect themselves against osmotic pressure, work.

Molecular kinetic consideration

Albert Einstein provided an approach to explaining osmosis by means of statistical mechanics in 1905 in his work on the movement of particles suspended in stationary solutions required by the molecular kinetic theory of heat . In it he describes that suspended from "dissolved" particles differ only in their size and that, according to the molecular theory of heat, both cause an osmotic pressure. According to Einstein, a force acts on suspended particles which is in dynamic equilibrium with the osmotic pressure forces; The movement can be understood as a superposition of two processes: a movement of the suspended particles due to a force acting on each individual particle, and "a diffusion process as a result of the disordered molecular movement of the heat."

Osmosis and entropy of mixing

The solvent on the left of the membrane, the solution on the right. The flow of solvent into the solution (right picture) increases the number of spatial arrangement options for the solvent as well as for the dissolved molecules. The reverse process of spontaneous segregation is extremely unlikely, but can be forced by applying pressure ( reverse osmosis ).

Osmosis - as the diffusion of the solvent through a membrane into a solution - is a spontaneous mixing process. In general, a mixture of two liquids A and B has a higher entropy than the two separate substances, since in the common and therefore larger volume there are more positions available for each particle A or B to be. This means that there are also a greater number of possible arrangements ( microstates ) for each of the two components than in the partial volumes of the separate substances, so that this large-scale macrostate is most likely. It adjusts itself by the thermal movement of the molecules. The measure for the probability is the entropy and therefore it has its maximum with this distribution. (Entropy is a computational variable that can be used to quantitatively describe macrostates of molecules before and after a process.) The solvent, in many practically important cases water, which diffuses through the selectively permeable membrane, mixes with the dissolved molecules. The entropy of the overall system increases by this entropy of mixing (however, there is no entropy of mixing water / water Gibbs' paradox ). In the calculation example, with 0.001 mol of dissolved substance and 0.1 liter of water that diffuses through the membrane, a mixing entropy of ≈ 0.08 J K ^{−1 is obtained} . This result can be reached in two ways. Firstly via the mole fractions and the mean molar entropy of mixing (Wedler, Textbook of Physical Chemistry) or via the statistical weight of the state of the mixture:

Thermodynamic

Mole quantities and mole fractions : ${\displaystyle n}$ ${\displaystyle x}$

	${\displaystyle n}$	${\displaystyle x}$
(1) solute	0.001 mol	1.80653 · 10 −4
(2) water	5.53446 moles	0.999819

Mean molar entropy of mixing: ${\displaystyle {\overline {\Delta S_{\mathrm {mix} }}}=-R\cdot \left[x_{1}\cdot \ln(x_{1})+x_{2}\cdot \ln(x_{2})\right]=0{,}0144477\;\mathrm {J\,K} ^{-1}\,\mathrm {mol} ^{-1}}$

That gives for 5.53546 mol (i.e. the total molar amount): ${\displaystyle \Delta S_{\mathrm {mix} }=0{,}07997\;\mathrm {J\,K} ^{-1}}$

Statistically

( means the number of molecules) ${\displaystyle N}$

${\displaystyle \Delta S=k_{\mathrm {B} }\cdot \ln W\quad {\text{mit}}\quad W={\frac {(N_{1}+N_{2})!}{N_{1}!\cdot N_{2}!}}\quad {\text{also}}\quad W={\frac {(5{,}53546\cdot 6{,}02205\cdot 10^{23})!}{(0{,}001\cdot 6{,}02205\cdot 10^{23})!\cdot (5{,}53446\cdot 6{,}02205\cdot 10^{23})!}}}$

With the approximation one obtains for the entropy of mixing: ${\displaystyle \ln(N!)\approx N\cdot \ln N}$ ${\displaystyle \Delta S=0{,}07997\;\mathrm {J\,K} ^{-1}}$

Osmotic pressure

Analogy to gas pressure

Fig. 1 Osmotic pressure in equilibrium

Fig. 2 Compensation of the osmotic pressure by means of a piston

If a vessel filled with sugar solution (A) is placed in pure water (B) and its wall is impermeable only to the dissolved sugar molecules, the pressure in the interior will increase due to the inflow of water. The osmotic pressure generated in this way counteracts the influx of water; the movement of the water ends when equilibrium is reached (Fig. 1). The same pressure distribution as in Fig. 1 can be achieved without water inflow if (e.g. via a piston) an equally high pressure acts on the liquid (A). (Fig. 2). By increasing or decreasing the piston pressure, the concentration of the solution (A) changes, since water then flows in or out through the vessel walls accordingly. This principle is used in reverse osmosis (also called anti-osmosis in older writings ); a solution is further concentrated under pressure in order to remove the substances dissolved in it.

This basic analogy between osmotic and gas pressure was first described in 1887 by the Dutch chemist van 't Hoff . He saw the impact of the dissolved particles on the membrane wall ( impermeable to them) as the cause of the osmotic pressure (solute bombardment theory) . The influence of the water molecules, on the other hand, is the same on both sides of the membrane and would therefore cancel each other out. An argument against this interpretation is that no deflection of the membrane is observed if the hydrostatic pressure is the same on both sides.

Application of the gas laws

In dilute liquid solutions, the same laws apply as for ideal gases ( Boyle-Mariotte law , Gay-Lussac law , Avogadro law ). The osmotic pressure

• is proportional to the molar concentration of the solute
• is proportional to the absolute temperature
• of solutions depends only on the number of particles of the dissolved substance (molar concentration) (→ colligative property )
• a solution of 1 mol in 22.4 l solvent is 101.325 kPa ( standard pressure ) at 273.15 K (0 ° C )

These statements are summarized by the van-'t-Hoff law "the osmotic pressure is just as great as the pressure of a gas with the same particle density  and temperature  ": ${\displaystyle n}$ ${\displaystyle T}$

${\displaystyle \Pi ={\frac {n}{V}}\cdot i\cdot R\cdot T=c\cdot i\cdot R\cdot T}$

Here is

• ${\displaystyle \Pi }$ the osmotic pressure
• c = n / V is the molar concentration (molar concentration) of the solution
• i = Van-'t-Hoff factor (number of particles dissociating in water per molecule (e.g. for glucose; for NaCl)) ${\displaystyle i=1}$ ${\displaystyle i=2}$
• ${\displaystyle R}$the universal gas constant
• ${\displaystyle T}$the absolute temperature in K .

In this form, the law only applies to dilute solutions (<0.1 mol / L), just as the ideal gas laws only apply at low pressures (the interaction of the particles with one another is neglected).

Osmotic pressure and vapor pressure

The vapor pressure of a solution is always lower than that of the pure solvent ( solvent or dilution effect). Adding a substance to lowers its chemical potential ${\displaystyle L}$ ${\displaystyle L}$

${\displaystyle \Delta \mu _{L}=RT\ln \left({\frac {P_{L}}{P_{\dot {L}}}}\right)}$.

Here is the vapor pressure of the pure solvent and the solution. The osmotic pressure works in the opposite direction and leads to an increase in ${\displaystyle P_{L}}$ ${\displaystyle P_{\dot {L}}}$ ${\displaystyle \mu _{L}}$

${\displaystyle \Delta \mu _{L}=\int _{0}^{\Pi }V_{L}^{m}\mathrm {d} P}$

For liquids, the partial molar volume can be viewed as independent of pressure. Under this condition, the equation can be derived from both of the above terms: ${\displaystyle V_{L}^{m}}$

${\displaystyle V_{L}^{m}\Pi =RT\ln \left({\frac {P_{\dot {L}}}{P_{L}}}\right)}$

be derived. It states that the osmotic pressure corresponds to the external pressure that would increase the vapor pressure of a solution to the vapor pressure of the pure solvent . The driving force of osmosis is the lowering of the vapor pressure of the solvent caused by the dissolving effect. An osmotic cell is in equilibrium when the osmotic pressure is balanced by an equally large counterforce. ${\displaystyle L}$

Salt solutions (electrolytes)

The osmotic pressure of a saline solution is always higher than it corresponds to van 't Hoff's law in the form Π = c⋅R⋅T, and often twice or three times as high. This effect is based on the fact that salts disintegrate into negatively and positively charged ions during the dissolution process (→ dissociation ) and, when dissolved, have a higher number of particles than the amount of substance in the solid state. For completely dissolved salts (strong electrolytes ) this is an integral multiple of the original amount of substance. By adding a factor to the equation:

${\displaystyle \Pi =i\cdot c\cdot R\cdot T}$

this effect can be taken into account. Here the van't Hoff factor is a dimensionless number. For sodium chloride (NaCl), potassium chloride (KCl) and other binary electrolytes is ; for 1,2-valent electrolytes like sodium sulphate (Na ₂ SO ₄ ) . ${\displaystyle i}$ ${\displaystyle i=2}$ ${\displaystyle i=3}$

For salts that do not completely disintegrate in solution (weak electrolytes), the Van-'t-Hoff factor can be calculated from the degree of dissociation : ${\displaystyle \alpha }$

${\displaystyle i=1-\alpha +\nu \alpha }$

where is the number of ions per salt molecule. Therefore, when specifying the concentration of ions, it can make sense to state them in the units of measurement osmol l ⁻¹ ( osmolarity ) or osmol kg ⁻¹ ( osmolality ), since the dissociation is already taken into account here. ${\displaystyle \nu }$

The osmotic potential of non-ideal solutions

Van 't Hoff's law does not apply to solutions in which the interaction of the molecules can no longer be neglected. Here the chemical potential from Gibbs' fundamental equation must be used. In thermodynamic equilibrium, the free enthalpy ( Gibbs energy ) of an osmotic cell is minimal:

${\displaystyle \mathrm {d} G=V\cdot \mathrm {d} p-S\cdot \mathrm {d} T+\sum _{i=0}^{N}\mu _{i}\cdot \mathrm {d} n_{i}=0}$

At constant temperature the equation simplifies to:

${\displaystyle 0=V\cdot \mathrm {d} p+\sum _{i=0}^{N}\mu _{i}\cdot \mathrm {d} n_{i}}$

At constant ambient pressure, the change in osmotic pressure follows:

${\displaystyle \mathrm {d} \Pi =-\sum _{i=0}^{N}\mu _{i}\cdot \mathrm {d} c_{i}}$.

The osmotic pressure thus results with the molar densities from the change in all chemical potentials . Mixing effects of the substances involved are taken into account in this equation. Usually, however, the mixing effects of the dissolved substances with one another and the concentration of the solvent are neglected: ${\displaystyle \Pi }$ ${\displaystyle c_{i}}$ ${\displaystyle \mu }$

${\displaystyle \Pi =-RT\cdot \sum _{i=1}^{N}\Delta \left(c_{i}\cdot \ln a_{i}\right)}$.

Another approximation would be to neglect the mixing effect of the solute with the solvent. The activity of these substances is assumed to be one, so that a rough approximation results: ${\displaystyle a_{i}}$

${\displaystyle \Pi \approx -RT\cdot \sum _{i=1}^{N}\Delta c_{i}}$.

This rough calculation can be used for dilute solutions, but leads to errors of more than 50% at higher concentrations, especially since the solution effect is not taken into account here.

The negative value of the osmotic pressure is called the osmotic potential . ${\displaystyle \psi _{o}}$

The osmotic coefficient and the ionic strength

There are different definitions of the osmotic coefficient.

The osmotic coefficient is e.g. B. defined as the quotient of the real measured osmotic pressure and the theoretically expected (calculated) osmotic pressure (at this concentration) of a saline solution or non-ionic solution (molecular substances): ${\displaystyle f_{o}}$

${\displaystyle f_{o}={\frac {\Pi _{\text{gemessen}}}{\Pi _{\text{berechnet}}}}}$

Really diluted solutions therefore always have a value less than or equal to one.

The following relationship could be shown empirically:

${\displaystyle f_{o,(c,z,I)}={1-K\cdot {\sqrt {I}}}}$

${\displaystyle K}$is a constant here, the ionic strength . The Debye-Hückel theory led to the following theoretical equation for dilute electrolyte solutions: ${\displaystyle I}$

${\displaystyle f_{o,(c,z,I)}={1-(2{,}303/3)\cdot A\cdot z_{+}\cdot z_{-}{\sqrt {I}}}}$

A is a constant according to the Debye-Hückel theory . The ionic valencies (charge numbers) z are to be used as amounts. This equation confirmed the empirically found first equation.

This osmotic coefficient is used in electrochemistry , among other things . The coefficient says something about the deviation / proximity from / to the ideal state (ideal dilution at c = 0 mol / liter or more precisely ionic strength I = 0 mol / liter) of a solution. Ideally diluted solutions have an osmotic coefficient of the value one - according to this definition. At high concentrations (more precisely: ionic strengths) the value tends towards zero. There are therefore analogies to the degree of dissociation and the conductivity coefficient of the electrolytic conductivity, because these values ​​also run from (theoretically) zero (high concentration c or ionic strength I) to one (ideal dilution, c = 0, I = 0).

The ionic strength I, which was defined by Gilbert N. Lewis and Merle Randall in 1921, is also intended to be a measure of the deviation of an electrolyte solution from the ideal state (apparently what is meant is the comparison with the arithmetic mean of the molar concentrations). For binary electrolytes (one cation and one anion) the ionic strength I is to be regarded as the arithmetic mean of the quadratic weighted concentrations according to the ionic valencies (charge numbers).

Osmometry - measurement of osmotic pressure

Pfeffer's cell - prototype of the membrane osmometer

The osmotic pressure of a solution is determined with membrane osmometers similar to the Pfeffer's cell . The pressure can either be measured statically, after equilibrium has been established, or dynamically by applying an external pressure to the riser manometer , which just interrupts the osmotic flow.

A 1  molal solution of cane sugar ( molar mass 342.30 g · mol ⁻¹ ) in water causes an osmotic pressure of 2.70 MPa (27 bar ) at room temperature  . For significantly higher pressures (several 100 bar), measurement principles such as changing the refractive index of water or the piezoelectric effect can be used.

By measuring the osmotic pressure or potential, it is possible to determine the mean molecular mass of macromolecules ; this process is known as osmometry . Since there is a direct relationship between the osmotic pressure and the other colligative properties of a solution, i.e. the increase in the boiling point and the lowering of the freezing point , the osmotic pressure can be determined indirectly as an osmotic value by measuring it.

While the direct measurement of the osmotic pressure requires the presence of two phases and a specifically permeable membrane, the indirect methods of osmometry only require the solution to be measured. They are therefore particularly suitable for characterizing different solutions with regard to their osmotic properties. Osmolarity and osmolality indicate the concentration of dissolved particles in relation to the volume or the amount of substance. Iso-osmotic are solutions whose osmotic value is the same. Since the osmotic value does not contain any information about the components in the solutions to be compared, iso-osmotic cannot be equated with isotonic.

The selectively permeable membrane

The essential element of osmosis is the selectively permeable membrane; it determines which substances can pass through. This property defines the achievable state of equilibrium of the system. At the same time, it influences the dynamic behavior of the system via the diffusion speed of the substances allowed through.

Grape ash and Pfeffer's cell

→ Main article : Pfeffer's cell

Artificial membranes produced the first private scholar Moritz cluster of Kaliumhexacyanidoferrat (II) (potassium ferrocyanide) , which in dilute copper sulfate solution, a skin Kupfercyanoferrat (II) (also see copper detection ) forms. This is only permeable to water. The water flowing in as a result of osmosis tears the skin, whereby the trapped potassium hexacyanoferrate (II) is released again and osmotic cells form again, which tear again after a while. Salts of alkaline earth and heavy metals behave similarly in alkali silicate solutions . The resulting structures are known as osmotic or chemical gardens .

In 1877 Wilhelm Pfeffer succeeded in applying these mechanically unstable precipitation membranes to the porous wall material of clay cells and thus stabilizing them. He used the Pfeffer's cell as an osmometer and was able to determine the osmotic pressure quantitatively for the first time.

Mechanisms of selectivity

Osmosis through a semipermeable membrane. The larger red particles cannot penetrate the pores of the membrane.

In the membrane model shown in the figure on the right, the selective permeability results from the maximum pore size. The larger red particles cannot pass through the membrane, while the smaller blue particles move freely from one side to the other. The selective permeability , which is decisive for osmosis, can also be based on other mechanisms. In many cases, solution processes play a role, for example with the pig's bladder used by Nollet.

Also catalytic properties of the membrane material may be responsible for the selective permeability. When a mixture of nitrogen (N ₂ ) and hydrogen (H ₂ ) is separated from pure nitrogen by a thin sheet of palladium , osmosis occurs; the hydrogen moves to the lower hydrogen side. The hydrogen molecules are catalytically split into atomic hydrogen on the palladium surface, which then diffuses through the palladium foil.

Ultimately, selective permeability can occur at interfaces that are not membranes in the strict sense. One example of this is electroosmosis .

Osmosis in Biology

Osmosis is of particular importance for biological systems. Each cell is surrounded by a membrane, which represents a barrier for the unhindered transport of substances, but is permeable to the solvent water. At the same time, it has several cell organelles with selectively permeable membranes. Many cells are in exchange with water, especially plant cells that are responsible for absorbing, transporting and releasing water. Vertebrate cells are surrounded by blood and lymph .

Biomembranes

→ Main article : biomembrane

Osmosis in a colored cell

Biomembranes are selectively permeable to numerous substances. The carrier substance of a biomembrane is the lipid bilayer ; it is almost impermeable to water and substances dissolved in it. Embedded in the lipid layer are numerous transmembrane proteins which, in different ways , enable the transport of water and dissolved particles through the membrane. In addition to pore-forming proteins such as ion channels and aquaporins (water channels), the passive ones include so-called cotransporters . Actively working transport proteins such as proton pumps transport substances while consuming energy (mostly obtained from the hydrolysis of adenosine triphosphate ) against an existing concentration gradient. The activity of these proteins can actively influence the chemical potential of the solvent water inside and outside the cell or its organelles.

The permeability or transport rate of numerous passive membrane proteins can be regulated by cellular mechanisms (for example the gating of ion channels); This enables the cell to react to changes in the surrounding environment and thus to influence the osmotic transport of substances.

Water potential

→ Main article : water potential

The concept of water potential has proven useful for describing the water balance of biological systems . It describes the suction value of a solution for water. Only potential differences are considered, the water potential of pure water has the value 0 under standard conditions. The following applies to the water potential of a solution:

${\displaystyle \Psi =p-\Pi +g\cdot h\cdot \rho _{\mathrm {H_{2}O} }}$

${\displaystyle \Psi }$has the dimension energy · volume ⁻¹ or force · area ⁻¹ and is given in the unit Pascal .

In the above equation, the hydrostatic pressure, the osmotic potential and the expression is the gravitational potential , which can be neglected when considering individual cells. ${\displaystyle p}$ ${\displaystyle -\Pi }$ ${\displaystyle g\cdot h\cdot \rho _{\mathrm {H_{2}O} }}$

The water potential of a solution is therefore the sum of several partial potentials. The osmotic potential describes the proportion of the osmotic pressure in the suction value of the solution. ${\displaystyle \psi _{o}=-\Pi }$

Water transport in plants

Plants transport fluids from the root area to the tips. The so-called root pressure is built up through osmosis , which together with the perspiration suction and the capillary forces provides the pressure difference required for water transport against gravity . According to the widely accepted cohesion theory, this transport process is dominated by the perspiration suction, since it reaches significantly higher pressures than the root pressure. Osmosis or the osmotic pressure, i.e. the gradient of the water potential, is sufficient for water transport over large differences in height. In shows that the transpiration thesis for water transport in plants is not consistent over large differences in height.

Osmoregulation

Effect of osmotic pressure on erythrocytes

Osmotic states of a plant cell ( plasmolysis )

→ Main article : Osmoregulation

If the osmotic resistance of red blood cells is exceeded by placing them in distilled water (strongly hypotonic medium), they absorb water in an uncontrolled manner until they finally burst. Your cell membranes can only withstand a lower pressure. Plant cells, on the other hand, are surrounded by a supporting cell wall, which means they can withstand considerably higher internal pressures (→ turgor ).

Numerous organisms such as salt plants , halophiles and freshwater inhabitants live in environments whose osmotic value differs greatly from that in the interior of the body or cells. Without effective osmoregulation, the organism would either dry out or absorb water in an uncontrolled manner.

Protozoa living in freshwater have a contractile vacuole , which first absorbs water from the cytoplasm and then sluices it out of the cell. Halophiles (salt dwellers) have developed a number of strategies to deal with the excess salt. This includes the development of special organs such as salt glands or kidneys for salt excretion, mechanisms for salt storage or the accumulation of osmotically active substances ( osmolytes ) in the cells.

Kidneys are also found in all vertebrates. They are used to excrete so-called urinary substances , including excess electrolytes and glucose , which would otherwise lead to an increase in the osmotic value in the body.

The protein NFAT5 , (a transcription factor , also known as the Tonicity-Responsive Enhancer Binding Protein , TonEBP) has been found in mammalian cells, which is expressed (synthesized) to an increased extent when the osmotic pressure increases. It sets in motion a number of counter-regulatory mechanisms to protect the cell from hypertonic stress. This includes the accumulation of osmolytes in the cell. Examples of such substances are myo-inositol , betaine and taurine , each of which has its own transport protein .

Chloroplasts can store large amounts of glucose within plant cells without bursting due to osmotic stress by condensing many glucose molecules into starch molecules.

Osmotic work

In the experiment with the U-tube (see section Basics ) the right column of liquid was raised against gravity. This clearly shows that work can be done in an osmotic cell.

The concept of generating energy through osmotic work is known as an osmotic power plant , see also section Applications and Examples .

In the life sciences and medicine is under osmotic work (engl. Osmotic work ) times the energy difference between the osmotic potential of a system (for example, a cell understood). In this sense, the cell performs osmotic work when substances are actively transported against a concentration gradient while consuming energy . On the other hand, the osmotic energy resulting from the difference in osmotic potentials can be used by the cell for energy-consuming processes, for example in chemiosmotic coupling .

Applications and examples

Osmolarity measurement, isoosmolar buffers and solutions

The determination of the osmolarity of solutions using osmometric methods is part of everyday laboratory work in many areas of the life sciences. When working with living cells, an isotonic buffer solution (such as Ringer's ) is often indispensable in order to avoid undesirable reactions of the cells due to osmotic stress. Especially in the isolation of protoplasts one would hypoosmolarer buffer to pop by any cell wall more protected cells. When preparing such solutions in the laboratory, the actual osmolarity can be measured as a control and compared with the expected value.

In medicine, an isotonic saline solution is used for infusions in order to avoid damage to the body cells by osmotic pressure. It is a mixture of water with 0.9% ( mass percent ) common salt, the osmolarity of this solution with 308 mosmol / l approximately corresponds to that of the blood plasma , this corresponds to an osmotic pressure of 0.7 MPascal. If pure water were used for infusions instead of an isotonic solution, such a pressure difference could cause the blood cells to burst.

dialysis

→ Main article : Dialysis  and dialysis (chemistry)

In dialysis, membranes are used that let through molecules and ions below a certain size or molecular mass and hold back macromolecules such as proteins or nucleic acids . With this method, low molecular weight substances and ions can be specifically removed from a solution or their concentration can be adjusted to the value of a given solution. For this purpose, depending on the application, the solution to be dialyzed is filled into a suitable vessel (the dialysis tube) and dipped into the external dialysis solution, in which it remains for a longer period of time. Or, as with hemodialysis , the liquid to be cleaned is in contact with a rinsing solution via a semipermeable membrane. Dialysis processes are used in medicine, among other things, for blood purification, as well as in chemistry and process engineering (for example in the production of alcohol-free beer ).

Density gradient centrifugation

In the density gradient centrifugation of living cells or their components, substances such as sucrose as the carrier of the density gradient can often be replaced by high molecular weight substances with only low osmotic activity (low osmotic value) in order not to expose the cells to osmotic stress during centrifugation.

Reverse osmosis

→ Main article : reverse osmosis

In reverse osmosis (also called reverse osmosis or antiosmosis ), a substance is concentrated against a concentration gradient by applying pressure. This process is used in particular for the treatment ( e.g. desalination ) of drinking water .

Osmotic power plant

→ Main article : osmotic power plant

In the osmotic power plant concept, osmotic work is used to generate energy. The power plant uses the differences in the chemical potential between salty seawater and freshwater to operate turbines to generate electricity. Pre-purified fresh water flows through a membrane into a pipe with salt water and thus increases the osmotic pressure in this pipe. Turbines are driven with part of the brackish water produced in this way, while the greater part (2/3) increases the pressure of the freshly flowing salt water via a pressure exchanger. Osmosis power plants are not yet in commercial use; Prototypes with an output of up to three megawatts have already been developed for a number of years, and a first small power plant was put into operation by Statkraft on the Norwegian Oslo fjord in November 2009 . At the end of 2013 Statkraft withdrew from its commitment to osmotic power plants and justified this with the fact that the technology would not be cost-efficient enough to compete on the energy market in the foreseeable future.

Osmosis in the gaseous state of aggregation

A light gas (helium; yellow spheres) under the beaker spreads through the porous wall into the clay cylinder filled with air (green molecules). The resulting increase in pressure is propagated in the Erlenmeyer flask and causes the water fountain.

An osmosis test can also be carried out with helium or hydrogen and air. Helium / hydrogen is allowed to flow under a beaker that is placed over a porous clay cylinder. The air in it is initially under atmospheric pressure. The wall of the clay cylinder does not create an obstacle for the light gas, it also spreads into the cylinder and thus approaches the most probable macrostate , an even distribution in the volume of the beaker. The heavier molecules in the air diffuse much more slowly, so the penetrating atoms / molecules quickly increase the pressure. This osmotic pressure can be made visible by letting it act on water in an Erlenmeyer flask via a pipe, which then sprays out of a nozzle as a fountain. The cause is the spontaneous increase in entropy (entropy of mixing) in the beaker / clay cylinder system. If the beaker is then removed, a negative pressure is created in the clay cylinder, so that the air flowing in through the nozzle bubbles up into the liquid.

Osmosis in everyday life

• In the preservation of foods by Einzuckern or curing the water present is removed by osmosis, since the concentration of sugar or salt is outside very much higher than in the interior of the food. Existing microorganisms can no longer multiply and therefore no longer have a decomposing effect. Food preserved in this way often changes drastically as a result of the dehydration.
• When cooking vegetables, salt is added to the water to prevent the influx of water into the (slightly salty) vegetables and the associated loss of taste.
• A leaf salad made with salad sauce loses its firmness ( turgor ) after a relatively short time . It normally gets this from the water present in the cells, which is released into the salad dressing through osmosis.
• The bursting of ripe fruits after rain is caused by the osmotic influx of rainwater and the resulting osmotic pressure inside the fruit.

Salted eggplants

• Eggplants are often sprinkled with salt before cooking. The water is withdrawn from them by means of osmosis, which makes them softer when seared.

See also

• Colloid Osmotic Pressure
• Compatible solutes
• Membrane technology

literature

• Peter W. Atkins, Julio de Paula: Physical chemistry . Wiley-VCH, 2005, ISBN 3-527-31546-2 .
• Luis Felipe del Castillo: El Fenómeno Mágico De La Ósmosis . Fondo De Cultura Economica USA, 2001, ISBN 968-16-5241-X . Comprehensive monograph on osmosis (Spanish). Online edition at Bibliotheca Digital del ILCE
• Walter J. Moore, Dieter O. Hummel: Physical chemistry . Walter de Gruyter, Berlin 1986, ISBN 3-11-010979-4 .
• RH Wagner, HD Moore: Determination of Osmotic Pressure. In: A. Weissengerber (Ed.): Physical Methods of Organic Chemistry. Part 1, 3rd edition. Interscience, New York 1959.
• Gerd Wedler: Textbook of physical chemistry . Verlag Chemie, 1982, ISBN 3-527-25880-9 .

Web links

• Wilhelm Pfeffer: Osmotic investigations - studies on cell mechanics , Verlag Wilhelm Engelmann, Leipzig, 1921, digitized at archive.orghttp: //vorlage_digitalisat.test/1%3D~GB%3D~IA%3Dosmoticunters00pfef~MDZ%3D%0A~SZ%3D~doppelseiten%3D~LT%3DDigitalisat%20bei%20archive.org~PUR%3D .
• Uri Lachish: Osmosis, Reverse Osmosis and Osmotic Pressure - what they are. (html; English). 
• R.Keller: Photos of an osmotic garden. (html, Java-Script) Physics lecture collection - Ulm University. Retrieved November 2, 2019 . 
• Video: Osmosis and osmotic pressure according to VAN'T HOFF - Solvent molecules migrate voluntarily into the more concentrated solution? . Jakob Günter Lauth (SciFox) 2013, made available by the Technical Information Library (TIB), doi : 10.5446 / 15678 .
• Johannes Kottonau: NetLogo simulation model for teaching. (Java applet) Retrieved November 2, 2019 . 

Commons : Osmosis  - album with pictures, videos and audio files

Wiktionary: Osmosis  - explanations of meanings, word origins, synonyms, translations

Individual evidence

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3. ^ ^{A b} Frank G. Borg: What is Osmosis. arXiv.org, e-Print 2003.
4. ↑ David C. Guell, Howard Brenner: Physical Mechanism of Membrane Osmotic Phenomena . 1996 doi: 10.1021 / ie950787f
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8. ^ Henri Dutrochet: L'Agent Immédiat du Movement Vital Dévoilé dans sa Nature et dans son Mode d'Action chez les Végétaux et chez les Animaux (Paris: Dentu, 1826), p. 115 and 126.
9. ↑ Henri Dutrochet: Nouvelles Recherches sur l'Endosmose et l'Exosmose, suivies de l'application expérimentales de ces actions physiques à la solution duprobleme de l'irritabilité végétale . Paris, 1828 ( limited preview in Google Book search).
10. ↑ ^{a b c} Wilhelm Pfeffer: Osmotic investigations - studies on cell mechanics . Engelmann, Leipzig 1877.http: //vorlage_digitalisat.test/1%3D~GB%3D~IA%3Dosmoticunters00pfef~MDZ%3D%0A~SZ%3D~doppelseiten%3D~LT%3DWilhelm%20Pfeffer%3A%20%27%27Osmotic%20Untersuchungen% 20% E2% 80% 93% 20Studies% 20 to% 20 Cell mechanics% 27% 27.% 20 Engelmann% 2C% 20 Leipzig% 201877. ~ PUR% 3D at archive.org
11. ^ Harmon Northrop Morse: The Osmotic Pressure of Aqueous Solutions: Report on Investigations Made in the Chemical Laboratory of the Johns Hopkins University During the Years 1899-1913 . Carnegie institution of Washington, 1914, pp. 222 ( archive.org ).
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13. ^ JH van 't Hoff: The role of osmotic pressure in the analogy between solutions and gases. In: Journal of physical chemistry. 1, 1887, pp. 481-508. (on the Uri Lachish website (English, PDF; 187 kB))
14. ^ JH van 't Hoff: Osmotical pressure and chemical equilibrium. 1901 Nobel Lecture (PDF; 40 kB)
15. ↑ ^{a b} Albert Einstein: About the motion of particles suspended in liquids at rest, required by the molecular kinetic theory of heat. In: Annals of Physics. 17, 1905 University of Vienna (PDF; 717 kB)
16. ^ CE Reid, B. Breton: Water and Ion Flow Across Cellulosic Membranes . In: Journal. Applied Polymer Sci. 1, 1959, pp. 133-143.
17. ↑ S. Loeb S. Sourirajan: Sea Water Demineralizationby Means of an Osmotic Membrane . In: Adv. Chem. Ser. 38, 1962, p. 117.
18. ↑ Julius Glater: The early history of reverse osmosis membrane development . In: Desalination . tape 117 , no. 1 , September 20, 1998, pp. 297-309 , doi : 10.1016 / S0011-9164 (98) 00122-2 .
19. ↑ water potential. In: P. Sitte, EW Weiler, JW Kadereit, A. Bresinsky, C. Körner: Strasburger - textbook of botany. Spectrum Gustav Fischer, 2002, ISBN 3-8274-1010-X , p. 254.
20. ↑ Peter W. Atkins, Julio de Paula: Physical chemistry. Wiley-VCH, 2005, ISBN 3-527-31546-2 , p. 166.
21. ↑ Kortüm, Lachmann: Introduction to chemical thermodynamics . Vandenhoeck & Ruprecht, 1981, p. 245, footnote 3.
22. ^ ^{A b} Sun-Tak Hwang, Karl Kammermeyer: Membranes in separation. (Techniques of chemistry, v. VII) . John Wiley & Sons, Rochester, NY 1975, ISBN 0-471-93268-X , p. 24.
23. ↑ ^{a b c} J.H. van 't Hoff: The role of osmotic pressure in the analogy between solution and gases. In: Journal of Physical Chemistry. 1 (1887), pp. 481-508. Website Uri Lachish (English, PDF; 187 kB)
24. ↑ AJStaverman: The theory of measurement of osmotic pressure . In: Rec. Trav. Chim. 70, 1951, p. 344.
25. ↑ David Charles Guell: The Physical Mechanism of Osmosis and Osmotic Pressure . A Hydrodynamical Theory for Calculating the Osmotic Reflection Coefficient. Massachusetts Institute of Technology, Cambridge 1991, OCLC 24393943 (English, hdl.handle.net [accessed November 27, 2015] Doctoral thesis, Dept. of Chemical Engineering.).
26. ^ AE Hill: Osmosis in Leakey Pores: The Role of Pressure . In: Proc R. Soc. Lond. B 237, 1989, pp. 363-367.
27. ^ ^{A b} Francis P. Chinard, Theodore Enns: Osmotic pressure . In: Science. 124, 1956, pp. 472-474.
28. ↑ ^{a b c d} Moore, Hummel: Physical chemistry . Verlag de Gruyter, 1986, ISBN 3-11-010979-4 .
29. ↑ Peter W. Atkins, Julio de Paula: Physical chemistry. Wiley-VCH, 2005, ISBN 3-527-31546-2 , p. 169.
30. ^ R. Ash, RM Barrer, A. Vernon, J. Edge, T. Foley: Thermo-osmosis of sorbable gases in porous media. Part IV . In: J. Membr. Sc. 125 1997, pp. 41-59.
31. ^ Adolf Fick: On liquid diffusion. Philos. Mag., 10:30, 1855.
32. ↑ A. Mauro: Nature of solvent transfer in osmosis . In: Science. 126, 1957, p. 252.
33. ↑ Christoph Steinert. Thermo-osmosis in liquids . Dissertation at the Technical University of Aachen, 1958.
34. ^ W. Grosse, HB books, H. Tiebel: Pressurized ventilation in wetland plants . In: Acquatic Botany. 39, 1991, pp. 89-98.
35. ↑ G. Czihak, H. Langer, H. Ziegler: Biologie, Ein Lehrbuch . 2nd Edition. Springer-Verlag, Berlin 1978, ISBN 3-540-08273-5 .
36. ↑ ^{a b} Stefanie Brookmann: Osmolytes and Osmolyte Strategies of Human and Murine Hemotopoietic Stem and Progenitor Cells . Inaugural dissertation 2007, DNB 987347217 .
37. ↑ Welf A. Kreiner: Entropy - what is it? doi: 10.18725 / OPARU-2609 - An overview
38. ↑ F. Kiil: Kinetic model of osmosis through semipermeable and solute-permeable membranes. 2002. doi: 10.1046 / j.1365-201X.2003.01062.x
39. ↑ Hans Keune: "chimica, Ein Wissensspeicher", Volume II, VEB Deutscher Verlag für Grundstoffindindustrie Leipzig, 1972, Osmotic Coefficient, p. 146, equation 8.49.
40. ↑ Hans Keune: "chimica, a knowledge store", Volume II, VEB Deutscher Verlag für Grundstoffindindustrie Leipzig, 1972, Osmotic Coefficient, p. 146, Gl.8.50.
41. ↑ Hans Keune: "chimica, a knowledge store", Volume II, VEB German publishing house for basic industry Leipzig, 1972, Osmotic coefficient, p. 147, equation 8.55.
42. ↑ Hans Keune: "chimica, a knowledge store", Volume II, VEB Deutscher Verlag für Grundstoffindindustrie Leipzig, 1972, ionic strength and osmotic coefficient, p. 146, equation 8.46.
43. ↑ Video: Traubeschezelle , Institute for Scientific Film (Ed.), 1982, doi : 10.3203 / IWF / C-1454
44. ↑ H. Sehon: Physical Chemistry. Herder publishing house, Freiburg. i. Brsg. 1976, ISBN 3-451-16411-6 .
45. ↑ water potential. In: P. Sitte, EW Weiler, JW Kadereit, A. Bresinsky, C. Körner: Strasburger - textbook of botany. Spectrum Gustav Fischer, 2002, ISBN 3-8274-1010-X .
46. ↑ https://www.spektrum.de/lexikon/biologie-kompakt/kohaesionstheorie-der-wasserleitung/6497 Spektrum-Verlag : Compact Lexicon of Biology: Cohesion Theory of Water Piping , accessed on 27 Sep. 2019
47. ↑ https://www.jstor.org/stable/55646?read-now=1&seq=1#page_scan_tab_contents U. Zimmermann, A. Haase, D. Langbein, F. Meinzer: Mechanisms of Long-Distance Water Transport in Plants: A Re-Examination of Some Paradigms in the Light of New Evidence , in Philosophical Transactions: Biological Sciences vol. 341, no. 1295, The Transpiration Stream (Jul 29, 1993), pp. 19-31, accessed Sep 27. 2019
48. ↑ H. Plattner, J. Hentschel: Cell Biology . 3. Edition. Georg Thieme Verlag, Stuttgart 2007, ISBN 978-3-13-106513-1 , p. 361 .
49. ^ Lehninger, Nelson, Cox: Lehninger Biochemie. 3. Edition. Springer textbook, Berlin 2001, ISBN 3-540-41813-X .
50. ↑ Osmotic Power. Statkraft, Norway, archived from the original on November 10, 2013 ; accessed on November 27, 2015 (English). 
51. ↑ Salt in our tank: fresh water plus salt water equals electricity. ( Memento from January 24, 2008 in the Internet Archive ) In: Financial Times Deutschland. Jan. 23, 2008.
52. ^ Crown Princess of Norway to open the world's first osmotic power plant. In: press release. Statkraft, Norway, October 7, 2009, accessed November 27, 2015 . 
53. ↑ Statkraft halts osmotic power investments. Statkraft, Norway, December 20, 2013, accessed November 27, 2015 . 

This version was added to the list of articles worth reading on February 28, 2008 .