PLANT BIOPHYSICS - Y. I. Posudin - 2004

II. TRANSPORT PROCESSES IN THE SOIL-PLANT-ATMOSPHERE SYSTEM

6. MASS TRANSPORT

6.4. COMPONENTS OF WATER POTENTIAL

Water potential is characterized by specific components that drive water fluxes: Ψ_в = Ψ_g + Ψ_s + Ψ_р + Ψ_м, where Ψ_g, Ψ_s, Ψ_р, and Ψ_м are the potentials representing the effects of gravity, solutes, pressure, and matrix, respectively, on the Free energy of water.

The gravitational potential Ψ_g is determined by the potential energy of water at a height h relative to a reference level (e.g., the soil surface):

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where ρ_в is the density of water, g is the acceleration due to gravity, and h is the elevation of the water. The value of p_вg equals 9.8·10^-3 MPa·m^-1. Thus, if water rises to a height of 1 m, The change in gravitational potential will be ΔΨ_g = 0.01 MPa; for a height of 10 m (an average tree), ΔΨ_g = 0.1 MPa; and for a height of 100 m (a redwood), ΔΨ_g = 1 MPa.

Example. Determine the gravitational potential of 2 kg of pure water at a height of 1 m above the soil surface.

Solution. The potential energy of water is E_п=mgh = 2 kg·9.806 kg·m·s^-2·1 m = 19.61 J.

The potential energy per unit mass is E_п/m = gh = 9.8 J.

The potential energy per mole is (Е_п/m)·0.018 = 0.18 J·mol^-1.

The volume occupied by 2 kg of water is determined by the expression V = m/ρ = 2 kg/10³kg·m^-3 = 2·10^-3 m³.

Thus, the potential energy per unit volume of water is Е_п/V = 19.61 J/2·10^-3 m³ = 9.806·10^-3 Pa.

The gravitational potential is positive above the reference level and negative below it. Under typical conditions where agricultural crops grow, the gravitational potential can be neglected.

The osmotic potential Ψ_s depends on the concentration of solutes dissolved in the Cells (cations, salts, organic acids, sugars, Amino Acids). An increase in solute concentration leads to an increase in osmotic pressure. The magnitude of osmotic pressure can be estimated using the following practical formula:

where C is the solute concentration (mol·l^-1), ф is the osmotic coefficient (ф = 1 for an ideally dissolved substance and ф = 0.1 for real solutions in a living Organism), v is the number of ions per molecule (e.g., v = 2 for NaCl, v = 3 for CaCl₂, etc.), R is the universal gas constant (8.314 J·mol^-1·K^-1), and T is the absolute Temperature.

The values of RT and osmotic potential as a function of temperature T are given in Table 6.1.

Table 6.1. Values of RT and osmotic potential as a function of temperature

The osmotic potential is always negative, ranging from -2.5 to -1.5 MPa.

Example. Determine the concentration of a sugar solution at a temperature of 30 °C if the osmotic potential is -0.252 MPa.

Solution. Using equation (6.9), we find the concentration of the solution:

Where:

Another unit of measurement for water potential is also used in literature, namely J·kg^-1. This unit is derived from the expression:

where Ψ is The water potential, p is the pressure, and ρ_s is the density of water.

Substituting the Units of Measurement into the last equation, we obtain:

For water, whose density is ρ_в = 10³ kg·m^-3, 1 J·kg^-1 corresponds to 10^-3 MPa.

Example. Determine the turgor potential of plant sap if the total water potential is - 700 J·kg^-1, and the osmotic potential is equivalent to a concentration of 0.3 mol·kg^-1 KCl.

Solution. Substituting the numerical values into equation (6.9):

From this, the turgor potential is determined as follows:

This value corresponds to 0.761 MPa.

Pressure potential ψ is expressed either as the hydrostatic pressure in the xylem vessels (the vascular tissue responsible for the primary transport of water and mineral nutrients in plants) or as the cellular turgor potential. Turgor potential in a Cell arises from the pressure exerted by The Cell wall in response to osmotic pressure. The range of turgor potential variation is 0–1.2 MPa. The turgor potential reaches its maximum value when the total water fluxes driven by turgor and osmosis become equal in magnitude but opposite in direction.

Matrix potential ψ_м characterizes the decrease in the free energy of water when it exists as a thin surface layer one to two molecules thick, formed On the surface of dry soil particles, cell walls, or Cellulose. It is so named because it accounts for the water imbibition process by which water is retained within a matrix. Matrix potential arises from the forces binding water molecules to structural elements or colloids (Structure/103.html">Van der Waals and hydrogen bonding), which reduce the ability of these molecules to participate in Chemical Reactions in the bulk solution and to evaporate into the external gas phase. The matrix potential is always negative or equal to zero. In living plant cells, the matrix potential is negligible due to the absence of large air spaces.

The ranges of variation for water potential and its main components depending on water content are presented in Table 6.2.

Table 6.2. Typical values of water potential components in the soil-plant-atmosphere continuum [Nobel, 1970]