## Analysis of water sorption isotherms

The water sorption isotherm is the dependence of water content on water activity of the surrounding environment at a given temperature. There are two types of sorption isotherms: desorption isotherm and adsorption isotherm (Fig. 2.4a). Conventionally, a desorption isotherm is developed by drying fresh tissues over satu rated salt solutions in closed desiccators until constant weights are achieved, whereas an adsorption isotherm is developed by rehydrating dried tissues over saturated salt solutions. A desorption curve can also be developed during drying of tissues in any atmospheric condition by measuring, at various points in time, the water content of the tissue and the equilibrium RH of its surrounding air in a closed container. Similarly, the dry tissue can be rehydrate with a given quantity of water to raise the water content and equilibrium RH. Sophisticated instruments such as controlled atmosphere microbalance and dynamic vapour sorption systems (Surface Measurement Systems, London, UK) use the latter methods. Desorption and adsorption isotherms are used, respectively, to study the properties of dehydration and rehydration of plant tissues. Desorption and adsorption curves are rarely the same: the desorption curve usually gives a higher water content than the adsorption isotherm. The difference in the equilibrium water content between two curves is called hysteresis. Hysteresis is evidence of the irre-versibility of the sorption process, and therefore indicates the limited validity of the equilibrium thermodynamic approach to investigate the dehydration-rehydration properties of plant tissues. Hysteresis might be an important issue when considering critical water activities for desiccation stress during dehydration-rehydration cycles and when investigating storage stability after manipulation of moisture content of seeds and pollen.

### 2.4.2.1. Theoretical models

Plant tissues show a sigmoid sorption isotherm (Fig. 2.4a). The inflection point of the isotherm is believed to indicate either a change of water-binding capacity and/or the relative amount of 'bound' or 'free' water. Water sorption data are normally analysed using theoretical models, from which useful biophysical parameters of water relations are derived. Commonly used models include the Brunauer-Emmett-Teller (BET) model, the

Guggenheim-Anderson-de Boer (GAB) model and the D'Arcy-Watt model.

The BET model (Brunauer et al., 1938) is derived from statistical and thermodynamic considerations. The equation can be written as:

M mC

where aw is the water activity, Mw is equilibrium water content in the tissue, Mm is the BET monolayer (water content corre a w

Fig. 2.4. The analysis of water sorption isotherms. (a) The typical shape of desorption curves and adsorption curves of plant tissues. The difference between these two curves shows hysteresis, which indicates the irreversibility of water sorption in the tissues during dehydration and rehydration. The sigmoid shape of sorption curves is presumably due to the existence of three types of water-binding sites in tissues (strong (I), weak (II) and multilayer molecular sorption sites (III)). (b) Differential enthalpy (AH), free energy (AC) and entropy (AS) of hydration. Desorption curves can be used to calculate AH and AS of tissue hydration. See text for detailed discussion.

Fig. 2.4. The analysis of water sorption isotherms. (a) The typical shape of desorption curves and adsorption curves of plant tissues. The difference between these two curves shows hysteresis, which indicates the irreversibility of water sorption in the tissues during dehydration and rehydration. The sigmoid shape of sorption curves is presumably due to the existence of three types of water-binding sites in tissues (strong (I), weak (II) and multilayer molecular sorption sites (III)). (b) Differential enthalpy (AH), free energy (AC) and entropy (AS) of hydration. Desorption curves can be used to calculate AH and AS of tissue hydration. See text for detailed discussion.

sponding to the monolayer hydration) and C is temperature dependence for sorption excess enthalpy (Brunauer et al., 1938, 1940). BET equation parameters, Mm and C, can be calculated by plotting aw/[Mw (1 -aw)] against aw. The y-axis intercept of the straight line is equal to 1/(MmC) and the slope is equal to (C - 1)/Mm. The BET is valid only for aw < 0.5, thus data points within that range are used to estimate the monolayer value (Mm). The BET model is an effective method for estimating the amount of water bound specifically to polar sites (monolayer), but cannot be used to give a complete estimation of specific hydration parameters.

The GAB model is an extension of the BET model, taking into consideration the modified properties of the sorbing materials in the multilayer region and the bulk liquid properties through the introduction of a third constant, K. The GAB equation is written as:

where C and K are temperature-dependent coefficients. Constants, Mm, C and K are estimated via the curve fitting of sorption data. In the field of food sciences, the GAB model is the most widely accepted due to its accuracy and its validity over a wide range of water activities from 0.05 to 0.9 (Rahman and Labuza, 1999).

The D'Arcy-Watt model was developed for the analysis of sorption isotherms of non-homogeneous materials (D'Arcy and Watt, 1970). This model assumes that there is a fixed number of water-binding sites with different discrete binding energies. The D'Arcy-Watt equation can be written as:

K KOw

where K', K, c, k' and k are equation coefficients (adjustable parameters). The equation has three terms, which represent the amounts of water that are strongly bound, weakly bound and sorbed in multimolecular water clusters, respectively. For a tissue that is in equilibrium with a given aw, the amount of water in those three regions can be estimated. K is the number of strong water-binding sites, multiplied by the molecular weight of water and divided by Avogadro's number (6.02 3 X 1023); K is the strength of the attraction of the strong waterbinding sites for water; c is a measure (linear approximation) of the affinity and the number of weak water-binding sites; k' relates to the number of multimolecular water sorption sites; and k relates to the activity of water (D'Arcy and Watt, 1970). The number of water-binding sites in tissues can be calculated from the derived equation coefficients. The number of strong, weak and multimolecular water-binding sites are K'N/M, cM(Mpo), and k'N/M, respectively, where N is Avogadro's number, M is the molecular weight of water and po is the saturated vapour pressure of pure water.

The D'Arcy-Watt model has been used extensively for the analysis of desiccation-tolerant and desiccation-intolerant plant tissues (Vertucci and Leopold, 1986, 1987a, b; Sun et al, 1997). Both the GAB and the D'Arcy-Watt models are valid over a wider range of water activities for plant tissues. The GAB model has some advantages over the D'Arcy-Watt model, which assumes the three types of water-binding sites. The GAB model does not have such an assumption. For biological systems it is more reasonable to assume that the number of water-binding sites is changing continually along with the binding energies. Moreover, the GAB model can be more easily applied to other thermal analyses (e.g. water-clustering function).

### 2.4.2.2. Temperature dependency of water sorption

Desiccation involves the transfer of liquid water in plant tissues into the vapour phase. Temperature influences evaporation rate through the heat supply as well as through its effect on the partial water vapour pressure in air and the energy status of water in plant tissues. In isothermal conditions, air acts as an osmotic membrane and equilibrium is often slow and dependent on temperature. An increase in temperature generally results in a decrease in equilibrium water content of plant tissues at a given RH (i.e. water activity) or an increase in equilibrium water activity at constant tissue water content. The shift of water activity at the constant water content by temperature is mainly due to the change in water binding, dissociation of water, physical state of water or increase in solubility of solute in water. Tensile strength of water, the pressure holding molecules together, increases by 81.6 mbars on average for a reduction of 1°C. Temperature dependence of isotherm shift is described by the Clausius-Clapeyron equation:

where q is the excess heat of sorption; \w is the latent heat of vaporization for water (44.0 kJ kg"1 at 25°C); R is the gas constant; aw1 and aw2 are water activities for a given equilibrium water content at temperature T1 and T2, respectively. The plot of ln aw against 1/T at any given tissue water content is a straight line and its slope gives (q + \w)/R, from which the excess heat of sorption, q, can be derived (Fig. 2.5a).

In practice, some thermodynamic quantities of tissue hydration can be calculated according to isotherms at two different temperatures. The aw1 and aw2 for a given equilibrium water content at two temperatures can be taken from water sorption curves or calculated from fitted sorption equations (Fig. 2.5b and Fig. 2.7a). Differential enthalpy of hydration (AH, including q and \w), differential free energy of hydration (AG) and differential entropy of hydration (AS) are given by:

These thermodynamic quantities are the functions of water content in tissues. The relationships of AH/WC, AG/WC and AS/WC provide important information with regard to the hydration properties of tissues (Fig. 2.4b). Water sorption is an exothermic event. A high negative AH value at low water content suggests the strong affinity of adjacent water molecules toward ionic sites and/or other polar sites of the substrate. As water content increases, the AH becomes less negative (Fig. 2.4b). The primary hydration process (i.e. strong and weak binding sites) is considered to be completed when the differential enthalpy of hydration (AH) approaches zero (Luscher-Mattli and Ruegg, 1982; Rupley et al., 1983; Bruni and Leopold, 1991). The change of AS reflects the relative degree of order, and the AS peak is presumably associated with the saturation of all primary hydration sites. It should be clearly noted that the relationships of AH/WC, AG/WC and AS/WC describe ther-modynamic interactions between water and biomaterials, but not necessarily the functions of water and biological structures in physiological processes. A possible association between water sorption behaviours and desiccation tolerance of plant tissues was discussed in a number of studies (Vertucci and Leopold, 1987b; Farrant et al, 1988; Pritchard, 1991; Sakurai et al, 1995; Eira et al., 1999; Sun, 2000). No consistent difference in water sorption characteristics has been found between desiccation-sensitive (recalcitrant) and desiccation-tolerant (orthodox) seed tissues (Sun, 2000).

The van't Hoff relationship provides another convenient means to analyse temperature dependence of sorption isotherm. The van't Hoff equation and the Clausius-Clapeyron equation are essentially the same in theory, but different in their mathematical treatment of experimental data. The Clausius-Clapeyron equation handles two temperature points, whereas the van't Hoff equation can handle a series of temperature points at once. The van't Hoff equation expresses the relationship of the equilibrium water activity (aw) for a given water content against the temperature (1/T) (Fig. 2.5b), and is written in its differential mathematical form as:

where T is absolute temperature in kelvin, and R is the gas constant. The AH is the

differential enthalpy of water sorption. It is important to note that the relationship between ln(aw) and (1/T) is not necessarily a straight line. Within a relatively narrow range of temperature, linear approximation may be used to calculate AH accurately. However, there is considerable interest in studying water sorption properties of biological tissues at a much wider range of temperature. For example, long-term preservation of genetic resources may require the storage of desiccation-sensitive seeds and other tissues in a refrigerated condition or at liquid nitrogen temperature. When the extrapolation is used, the non-linear nature of the relationship between ln(aw) and (1/T) needs to be taken into consideration. The study on temperature dependence of water sorption using the van't Hoff equation (Fig. 2.5a and b) is used to establish the theoretic framework for the optimization of germplasm preser-

0.04

0.02

10 15

Temperature (°C)

Fig. 2.5. (a) Temperature dependence of water sorption for the same seed material at different water contents (i.e. the van't Hoff plot). Drawn with data from Eira et al. (1999). (b) Equilibrium water content at specific water activities as a function of temperature for whole seeds of Coffea arabica cv. Mundo Nova. This relationship is called 'isopleth'.

vation protocols (Vertucci et al., 1994, 1995; Eira et al, 1999).

2.4.2.3. Monolayer hydration and water-clustering function

The monolayer hydration values of plant tissues, the amount of water bound to specific polar sites, can be easily determined, using BET or GAB isotherm models. For most plant tissues and their major chemical components, the monolayer value at ambient temperature is estimated to be between 0.04 and 0.09 g g-1 dw using the BET or GAB model (Rahman and Labuza, 1999). The BET monolayer value of many orthodox seeds was also found to be in this range (Vertucci and Leopold, 1987a,b; Bruni and Leopold, 1991; Vertucci and Roos, 1993; Sun et al., 1997). The monolayer value of Typha pollen was much less than that of orthodox seeds (Buitink et al., 1998b). The monolayer hydration is generally complete at a water activity of 0.20-0.30 (i.e. -150 to -250 MPa). It is important to note that the monolayer value decreases rapidly as temperature increases, and increases as temperature declines. The monolayer water is of great importance for the survival of many dry organisms (e.g. spores, pollen grains and seeds) during storage. In food science, the water activity at the monolayer value is defined as the critical water activity. At a water activity above 0.20-0.30, the rate of chemical reactions begins to increase significantly because of the greater solubility and mobility of the reactants. At water contents below the monolayer value, the rate of lipid oxidation and associated free radical damage increases. The presence of mono-layer water inhibits the undesirable interactions between polar groups on adjacent carbohydrate or protein molecules, thereby preserving their rehydration ability and biological functions (Rahman and Labuza, 1999).

There is no defined monolayer parameter in the D'Arcy-Watt model. However, the first term of the D'Arcy-Watt equation may be used as an approximation, as it represents water that is bound strongly to polar hydration sites. A recent study using the D'Arcy-Watt model suggested that water redistribution among different types of hydration sites might be related to the rapid loss of seed viability during storage after osmotic priming and drying back (Sun et al., 1997).

Water clustering in binding sites is another important hydration event that is of significance to desiccation tolerance of plant tissues and the survival of tissue in the dried state. Clustering formation is related to a number of transport phenomena. For example, clustering reduces the effective mobility of water by increasing the size of the diffusing molecular group or by increasing the tortuosity of diffusion paths (Stannett et al., 1982). The range of water activity where the self-association of water takes place can be examined by the clustering function (Lugue et al., 1995; Dominguez and Heredia, 1999). The clustering function is written as:

where G11/V1 is the clustering function, V1 is the volume fraction of water, V2 is the volume fraction of biopolymers, and aw is water activity (Zimm and Lundberg, 1956). The subscript '11' in G11/V1 denotes the water-water interaction as a function of water content (component 1). The clustering function can be applied to an isotherm sorption model such as the GAB equation with some modifications. The GAB equation needs to be rewritten in terms of volume fraction instead of weight fraction. The GAB equation can be rewritten as:

MmCKp2V2

where p1 and p2 are the density of water and biopolymers. The density of sorbed water is assumed to be equal to 1.0 g cm"3. Substituting aw/V1 in Equation (20) with Equation (22), the clustering function can be expressed as:

11 1 MmCKP2

According to Equation (23), G11/V1 is proportionally related to aw and the reciprocal of polymer density (p2) function. G11/V1 can be solved easily by the substitution of Mm, C and K constants from the GAB equation. Figure 2.6 shows a plot of the water-clustering function of soybean axes. The clustering plot is basically a straight line against water activity. When G11/V1 is greater than -1, water is expected to cluster (Zimm and Lundberg, 1956). The autoassociation (clustering) of water in a few desiccation-tolerant seeds is observed to occur at water activity ranging from 0.55 to 0.60 (W.Q. Sun, unpublished data).

### 2.4.2.4. Occupancy of water-binding sites

The D'Arcy-Watt model can be used to examine the occupancy of water-binding sites as a function of water content according to Luscher-Mattli and Ruegg (1982). The occupancy represents the amount of water attached to certain hydration sites, expressed as the percentage of the corresponding maximum value in the fully hydrated tissues (Fig. 2.7b). Therefore, the occupancy relationship indicates the degree of hydration for different types of hydration sites during desiccation. Figure 2.7b shows that the occupancy for three types of hydration sites changes as the water content of Q. rubra seed tissues decreases during desiccation. Desiccation of seed tissues to 0.30 g g-1 dw (the critical water content) removed about 90% of multilayer molecular sorption water, but only about 10% of water molecules attached to the weak hydration sites in seed tissues. The removal of water from weak hydration sites appears to be related to desiccation damage in Q. rubra seeds (Sun, 1999). The critical water content of Q. robur axes also corresponds to the amount of matrix-bound water (Pritchard and Manger, 1998). However, the question of whether the water-binding or sorption behaviour in seed tissues is related to their desiccation tolerance remains unresolved. The loss of viability in many recalcitrant seeds occurs at a water content that is much higher than

Fig. 2.6. Water-clustering function showing the water-water association in soybean seed axes as a function of equilibrium water activity. Apparent water clusters first appear at a water activity of 0.58 (arrow). The water-clustering function Equation (23) was solved through the study on biopolymer volumetric change during hydration [i.e. P2= f(V1)] by applying water sorption analysis. See text for further explanation.

Fig. 2.6. Water-clustering function showing the water-water association in soybean seed axes as a function of equilibrium water activity. Apparent water clusters first appear at a water activity of 0.58 (arrow). The water-clustering function Equation (23) was solved through the study on biopolymer volumetric change during hydration [i.e. P2= f(V1)] by applying water sorption analysis. See text for further explanation.

that of 'bound' water (Pammenter et al., 1991; Berjak et al., 1992). Clearly, more comprehensive studies are needed.

Readers who wish to know more about water sorption analysis may refer to a recently released manual by Bell and Labuza (2000). This book generally discusses water activity in food materials, but the principles are also applicable to plant desiccation tolerance studies. Practical

Water activity

Fig. 2.7. (a) The interpretation of desorption isotherms of Quercus rubra cotyledonary tissues, using the D'Arcy-Watt model. Equation coefficients are derived though curve-fitting of experimental data (p/po = aw). See text for further explanation. (b) The occupancy for three types of hydration sites in Q. rubra cotyledonary tissues at different water contents. The occupancy is based on the percentage of the corresponding maximum values in the fully hydrated state (i.e. full turgor). The change of occupancy reveals how and when water is removed in different types of hydration sites during dehydration.

Water content (g g-1 dw)

Fig. 2.7. (a) The interpretation of desorption isotherms of Quercus rubra cotyledonary tissues, using the D'Arcy-Watt model. Equation coefficients are derived though curve-fitting of experimental data (p/po = aw). See text for further explanation. (b) The occupancy for three types of hydration sites in Q. rubra cotyledonary tissues at different water contents. The occupancy is based on the percentage of the corresponding maximum values in the fully hydrated state (i.e. full turgor). The change of occupancy reveals how and when water is removed in different types of hydration sites during dehydration.

examples are provided to elucidate how to solve many equations.

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