The water sorption isotherm is the relation between the equilibrium moisture content of a material (expressed as mass of water per unit mass of dry matter) and water activity, at a given temperature. Such relationships are the key to understanding the water sorption properties of food, being of particular value when selecting suitable packaging materials and predicting stability and moisture changes during storage. Since Aw is temperature dependent, it follows that temperature has a significant effect on sorption isotherms. So, when a food is subjected to an upward temperature shift, at any constant moisture content, Aw increases with increasing temperature. This is explained on the basis of the fundamental thermodynamic equation:

    dG = dH - TdS

Since dG < 0 (sorption is spontaneous) and dS < 0 (adsorbed molecule is less free), then dH < 0.

The moisture sorption isotherm may be measured by addition of water to a dry sample (adsorption) or by removal of water from a wet sample (desorption). It has been established that in hygroscopic high pectin and sugar-containing materials the sorption-desorption isotherms are sigmoidal in shape and show marked hysteresis. Typically, this means that for values of aw below 0.40 the water content of the food will be greater during desorption than during adsorption. Several explanations have been proposed for the hysteresis phenomenon. One theory is based on the availability of active polar sites for the bonding of water molecules . Under this theory, in the original wet condition, the polar sites in the molecular structure of the material are almost entirely satisfied by adsorbed water. Upon drying and shrinkage, the molecules and their water-holding sites are drawn closely enough together to satisfy each other. This reduces the water holding capacity of the material upon subsequent adsorption. Another theory is related to the glass transition concept. Upon drying high sugar-containing materials the sugars may be converted to an amorphous form. At low water contents the glass transition may occur at about room temperature, being the transition between glassy and rubbery states one of the main reasons for hysteresis. In the rubbery state the diffusion of water to the product will be enhanced.

The sorption isotherm describes the interaction between water and the food product. Equations for fitting these data are of special interest in many aspects of food preservation by dehydration. Numerous mathematical equations have been reported in literature for describing water sorption isotherms of food materials. They vary a lot in terms of origin (empirical, semi-empirical or theoretical) and range of applicability (aw limit and type of food).

The high number of sorption equations developed suggests the difficulty of having a unique mathematical model for describing the sorption data in the whole range of water activity for different food products. This is due to a number of reasons:

  1. The depression of water activity in foods is due to a combination of factors each of them being predominant in a given range of water activity. In general, the insoluble macromolecules dominate the sorption behaviour at low aw and the soluble components exert their effects largely through their colligative properties over the high aw range.
  2. Moisture sorption isotherms of foods represent the integrated hygroscopic properties of numerous constituents whose sorption properties may change as a consequence of physical and/or chemical interactions induced by heating or other pre-treatments.
  3. As a food sorbs water, it usually undergoes changes of constitution, dimensions and other properties; water sorption also leads to phase transformations of the sugars contained in the food. When a sugar containing food, as a fruit, is freeze dried, the sugars can be converted to an amorphous form. When adsorption takes place, the sugars will slowly reconvert to the crystalline form.

The choice of a equation to fit the sorption data takes into account different factors:

    (i) the agreement between the sorption data and the model; (ii) the range of applicability; (iii) the theoretical basis of the parameters; (iv) the simplicity; (v) the desired objectives.
Some of the most commonly used isotherms for food sorption studies are presented bellow:

  1. Name : Chen

    Formula :
    Aw = exp (k + a exp(bW))

    Comments : Limited to situations where diffusion is the principal mode of mass transport

  2. Name : Halsey

    Formula :
    Aw = exp (- a/(RTW/Wm))

    Comments : Multilayer adsorption eq. developed to overcome limitations of BET. Range 0.10-0.80 Aw

  3. Name : Henderson

    Formula :
    -Aw = exp(-kWn)

    Comments : Empirical equation widely used

  4. Name : GAB Formula :
    W/Wm = CkAw/((1-kAw)*(1-kAW+CkAw))

    Comments : Has the greasted applicability and accuracy. Range 0-0.90 Aw

  5. Name : Oswin

    Formula :
    W = a ( Aw/(1-Aw))n

    Comments : Mathematical series expansion for sigmoidally shaped curves. Applicable up to 0.50 Aw

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