Water Potential and Water Content

4.1 Water Potential and Water Content

Two types of variables are required to describe the state of matter or energy. One describes the amount, while the other describes the quality or intensity. For example, the thermal state of a substance is described in terms of its heat content and its temperature. While the two variables are related (the higher the temperature of a substance, the higher the heat content), they are not equivalent. The heat content depends on the mass,

heat, and temperature of the substance, and gives no indication of which direction heat will flow

object is placed in contact with another object. The temperature of an object specifies the intensity or quality of the heat, and temperature differences relate directly to direction and rate of heat flow.

Variables like temperature, which describe intensity of quality are called intensive variables, while variables describing amount are called extensive variables. Temperature is intensive while heat is extensive. To refer to thermal time as

units" is a confusion of intensive and extensive variables. Describing the state of water in a system also requires the use of inten- sive and extensive variables. The extensive variable is familiar to most, and is called the water content. The intensive variable, called the water potential, is less familiar. Like temperature, it determines the direction and rate of water flow. As with temperature, there is often a relationship between the water content and the water potential of a substance, though it is always much more complicated than is the case for temperature. The important thing to realize is that water in soil, or in the tissues of living

Liquid Water in Organisms and their Environment

is not like the water in a glass. It is bound by the tissue or soil matrix, diluted by solutes, and sometimes is under pressure or tension. Its energy state is therefore quite different from that of water in a glass.

The water content is simply the ratio of the volume of water in a material to its total volume, or the ratio of mass of water to dry or wet mass of the material. Different bases are used as the standard in different disciplines, and all are called water content, so it is easy to make mistakes if one is not careful. In this book water content is defined as:

where V is the volume, m is the mass, and subscripts w , t, and d refer to water, total, and dry volume or mass. We call volumetric water content and w the mass water content. These are related by

where the bulk density

Water potential is defined as the potential energy per mole, per unit mass, per unit volume, or per unit weight, of water, with reference to pure water at zero potential. In thermodynamic terms, the energy per mole is

the molar Gibbs free energy of the water in the system. A gradient of the water potential is the driving force for liquid water movement in a

system. As indicated, several sets of units are in use to describe water potential. For consistency with the rest of this book, we should use energy per mole, but this has not been used elsewhere, and may be completely unfamiliar to readers. Our preference is for energy per unit mass

The units clearly show energy and mass, and, unlike volume, the mass does not vary with the density of the water. Energy per unit volume

is dimensionally equivalent to pressure

These units are frequently used for water potential, but fail to indicate a relationship to specific energy and have a less sound basis for the computation (the specific volume of water varies with density and is therefore dependent on temperature and binding energy). While these are minor objections to the use of pressure for water potential, it should be pointed out that there certainly are no advantages to the use of pressure units, and the mass-based units have historical priority. Energy per unit weight

or

is dimensionally equivalent to the height of

a water column (m) in a gravitational field. It is used mainly in soil water flow problems where height of a physical water column is a convenient reference for other potentials. If the density of water is assumed to be 1

and the gravitational constant is

9.8 m

then

Water Potential and Water Content

In this book we use but the reader can consider those equivalent to if pressure units are more familiar. The water potential is made up of several components. The total potential is usually written as the sum of the components:

where the subscripts, g, m, p, and o are for gravitational, matric, pressure, and osmotic components. While each of these components (and others that could be defined) can contribute to the total potential, there are many situations where only one or two of the component potentials are active.

The gravitational potential is the potential energy of water as a result of its position in a gravitational field. A reference height must be specified in order to compute a gravitational potential. The gravitational potential is then:

where is the gravitational constant (9.8 m and h is the vertical dis- tance fromthe reference height to the location where potential is specified. Above the reference h is positive and below the reference it is negative.

The matric potential arises from the attraction between water and soil particles, proteins, cellulose, etc. Adhesive and cohesive forces bind the water and reduce its potential energy compared to that of free water.

For any substance that imbibes water there exists a relationship between water content and matric potential. This relationship is called the moisture characteristic. Figure 4.1 shows moisture characteristics for soils with three different textures. Most of the water in the clay is held very tightly (at low potential) because the large surface area of the clay is able to bind the water. Most of the water in the sand is held loosely (at high potential) because the sand matrix is ineffective in binding water. Similar curves

could be made for cellulose, protein, etc., and they would have similar shapes. Tracy (1976) obtained a moisture characteristic for a whole frog.

Note that the matric potential is always negative or zero. An empirical equation that closely approximates most moisture characteristics over a

wide range of matric potentials is:

where w is the water content and a and b are constants from data. The pressure potential arises as a result of an applied hydrostatic or pneumatic pressure. Examples of this potential are the blood pressure in an animal, the water pressure under a water table in the soil, the turgor pressure inside plant cells, or the air pressure inside a pressure vessel

which measures water potential in leaves or matric potential in soil. In many cases the pressure potential is hard to distinguish from the matric

potential. For example, in soil a positive hydrostatic pressure is called a pressure potential and a negative pressure a matric potential. In the xylem

of plants the pressures are generally negative, but the potential is referred

56 Liquid Water in Organisms and their Environment

0.4 I

Matric Potential

F IGURE 4.1. Soil moisture characteristics for three soil textures.

to as a pressure potential. Confusion arises because the components of the water potential differ in different systems, and because the components are defined primarily by method of measurement rather than on some rig- orous thermodynamic basis. For our definitions, we attempt to distinguish between pressure and matric potential in terms of the nature of the forces acting on the water. Matric potential is defined as the reduction in water potential from short-range forces near interfaces (capillary forces or van der Waals forces). It is always negative. Pressure potential is considered a more macroscopic effect acting throughout a larger region of the system.

The pressure potential is computed from:

where P is the pressure (Pa) and is the density of water. The pressure potential can be either positive or negative, but usually is just positive. The osmotic component arises fromthe dilution effect when solutes are dissolved in water. It does not really act as a potential or driving force for water movement unless the solutes are constrained by a semipermeable membrane. This occurs mainly in plant and animal cells and at air-water interfaces. When the solute is constrained by a perfect membrane, the osmotic potential can be computed from:

Water Potential and Water Content

where is the concentration of solute the osmotic coef- ficient, v is the number of ions per molecule

2 for for and 1 for sucrose), R is the gas constant

and T is the kelvin temperature. The osmotic coefficient has a value of one for an ideal solute, and is generally within ten percent of that value for

solutions encountered in organisms and their environment. More accu- rate values are available in Robinson and Stokes (1965).

Two examples from nature illustrate the balance of potentials and the way they sum. In plant cells, concentrations of solutes are quite high. The cell membrane is permeable to water but not to the solutes, so water

tends to move into the cell. The cell wall prevents volume expansion, so the pressure inside the cell increases. When the sum of the pressure and osmotic potential is equal to the water potential in the xylem, water ceases to move into the cell. If the cell walls of plants were not rigid and able to withstand high pressures, water would continue to move into the cell, diluting its contents until life processes would cease.

The other example has to do with blood in the circulatory system of animals. Solutes are

to diffuse through the walls of the capillary system, but proteins are too large and are kept in the blood stream. The negative matric potential of the blood proteins just balances the positive blood pressure potential. The blood matric potential (referred to as colloid osmotic pressure in the medical literature), provides just enough "suction" to keep the blood in the circulation system.

Example 4.1. If the reference for gravitational potential is the water table at 2 m depth, what is the gravitational potential at the soil surface?

19.6 m 2 From the example in Ch. 1, we know that this is equivalent to 19.6

Solution. Using Eq.

= 2m x

9.8 m

Example 4.2. If the osmotic potential of plant sap is equivalent to 0.3 molal

and the total water potential of the tissue is -700 what is the turgor pressure?

Solution. Using Eq. (4.6) to get the osmotic potential, with

1, and v = 2 gives:

mol

-0.3- 1 2 8.31 mol

Now use Eq. (4.2) to obtain the turgor pressure. Assume that all compo- nents except the osmotic and pressure components are negligible:

= 761 P

- = -700

- (-1461

761 x kg/m 3 1 Wa. One atmosphere is 101 so the pressure inside the cell is 7.5 atmospheres.

plant were turgid

Liquid Water in Organisms and their Environment

(water potential of the leaf equal to zero), the pressure would be almost twice this value. These are typical values for plant leaves and illustrate the amazingly high pressures that routinely exist in living systems.