As stated in the previous section, water activity shows some limitations as predictor for the stability of foods. Foods are complex systems where their main constituents, carbohydrates and proteins, are not in a thermodynamic equilibrium, being time, temperature and water content dependants. In addition numerous physical phenomena that affect foods such as crystallization, caking, stickiness, diffusivity, etc. cannot be explained entirely by water activity.
The glass transition temperature or Tg, which occurs over a temperature range, has been defined as a single temperature at which, on rapid cooling, an amorphous material becomes
Region I Region II Region III
Glassy State: A Way to Extend Shelf-Life of Food 153 extremely viscous (~10-12 Pa) [21]. Mechanically the material behaves as solid but maintains its amorphous structure as a liquid, therefore containing an excess in free energy. At temperatures below Tg, the molecular mobility is restricted to vibrations and short range rotational motions [22].
Thermodynamically, the glass transition temperature can be described as a second order transition, as it is characterised by a discontinuity in the heat capacity (Cp) or thermal expansion coefficient (αT), the first derivates of the thermodynamic quantities volume (V) and
enthalpy (H) as a function of temperature (Figure 2).
Modified from Roos [23].
Figure 2. Changes of thermodynamic functions volume (V), enthalpy (H) and entropy (S) as function of temperature. Glass transition is observed as a change in slope of the VHS curve and a change in heat capacity of the material (ΔCp). As the glass transition is a time dependant phenomenon, relaxation in thermal properties can occur (insert).
This is very important, as it is related to its non-equilibrium and time dependent physical state. Indeed, the phenomenological description of the glass transition in polymers considers the use of the concepts of free volume and the relaxation phenomenon. The free volume has been defined as the extra volume required for large scale and long range coordinated movement of the main chain of the polymer. Below the Tg, various configurations of free volumes exist depending on thermal history of the polymer, where the least free volume represent the most relaxed structure [24]. Figure 3 shows the various motions of a polymer chain following the crankshaft model [24], where free volume is required by a series of jointed segments for motions to occur. This model, although very simplistic, helps to describe the different relaxation scales as the polymer material is subjected to variations in
J. I. Enrione and P. Díaz-Calderón 154
temperature. The increase in movement, by side chains and small groups, results in greater compliance of the molecule, which has been describe as γ and β transitions [25]. If the temperature is increased, the Tg is reached where large scale coordinated motions of the polymer chain occur. This transition has also been defined as α transition or Tα [25]. The variations in free volume with respect to the Tg has been successfully described by the WLT empirical relation [26] (Eq. 3).
Figure 3. A schematic example of free volume and the crankshaft model showing motions scales of a polymer chains [24].
(3) where aT is the ratio of any mechanical and electrical relaxation times at temperature T to their values at the reference temperature Ts and C1 and C2 are constants (-17.4 and 51.6
respectively for biomaterials). Kasapis [27] applied the free volume concept to mathematically represent the change in viscosity with temperature of dehydrated foods. By using the time-temperature superimposition (TTS) principle, it was possible to assess the mechanical glass transition temperature of complex model systems such as gelatin and dried fruits. Shift factors
(a
T)
were calculated based on the superimposing of modulus tracesgenerated from frequency sweeps at different temperatures. The application of the WLF and Andrade equations [27] confirmed the description of the phase transition as the minimum value of the first derivate of the modulus with temperature. In a later study, Kasapis and Sablani [27] calculated the mechanical glass transition based of free volume and energy associated to molecular motions as deviation of the WFM predicted values to an Arrhenius like behaviour of the variations of the shift factors (log scale) with temperature on rapid cooling (Figure 4).
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Figure 4. Determination of Tg based on the reduction factor, aT , for a 80%gelatin suspensión plotted against temperature from the data of a master curve using the TTS principle [27].
Figure 5. Dependence of the Tg of maltodextrins with different DE on the water content. Filled squares: DE6; filled triangles: DE29; filled diamonds: DE32. The lines represent the best fit of the Couchman- Karasz model [28].
For the prediction of Tg for mixtures, several equations have been proposed based on free volume theory [29], which accounts for the true density of the polymer and plasticizer and their changes in thermal expansivity (∆α) at Tg [30]. Another approach follows thermodynamic considerations assuming Tg as a second order transition with a continuity in
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entropy and volume when this transition is reached [31]. The derived equation relates the heat capacity changes of pure polymer components at their Tg to the Tg of the mixture [32](Eq. 4).
(4) where Tg is the glass transition temperature of the mixture, ΔCpp is the change in specific
heat capacity of the polymer, ΔCpd a is the change in specific heat capacity of the diluent, Tgp
is the Tg of pure polymer and Tgd is the Tg of the pure diluent. wp and wd are the weight
fractions of the polymer and diluent, respectively. This equation has been successfully applied to represent the Tg of waxy maize starch-water-glycerol extrudates [32], starch, dextrans and pullulan [33], maltodextrins [28, 33, 34] (Figure 5) and bovine gelatine films [35].
As described previously, the reduction in Tg by the addition of plasticizers can be explained by the free volume theory, which indicates that low molecular weight compounds increase the free volume of a polymeric system increasing its overall molecular mobility and therefore improving its mechanical properties. However recent studies have showed that presence of low molecular weight can modify the matrix structure through densification (stated by a decrease in specific volume probed by gas pycnometry) at temperatures below Tg. This has been clearly observed when the mass fraction of low molecular weight compounds increase in polymeric matrices in the glassy state [36-38]. Such studies have been performed firstly in carbohydrate and recently in protein based systems (e.g. gelatin). When volumetric changes are evaluated at nanoscale, literature reports a lineal correlation between hole volume (a measurement of free volume between polymeric chains) and temperature (matrix thermal expansion) both below and above the glass transition temperature. Indeed a change in the slope of specific volume isoline is associated to the glass transition temperature with good agreement with DSC data [36, 39].
The hole volume decreases when the mass fraction of low molecular weight compounds increases, indicating a correlation between volumetric changes at macro (specific volume) and nano scale (free volume) (Figure 6). The role of water at nanoscale and its effect in volumetric changes in glassy materials has been related to plasticization and antiplasticization phenomenon. At very low water content a decrease in hole volume with increasing water content reflects the antiplasticization, while in approach to Tg an increase in hole volume with increasing water content correspond to plasticization phenomenon.
The effect of molecular weight distribution in changes in specific volume (macroscale) and hole volume (nanoscale) has been related with the novel concept of molecular packing, which represents the volumetric changes at macro and nanoscale with increasing molecular weight in the glassy state [38]. The increase in matrix density and decrease in hole size as a consequence of molecular packing appears to have a profound effect on numerous physical properties of polymeric matrices, such as diffusion of oxygen, the stabilization of sensitive biological materials by glassy state encapsulation and hydrogen bonding, and the sorption of water [36, 37].
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Figure 6. Correlation between the hole volume and the specific volume at two water content (Qw): open circles Qw=0 and filled circles Qw= 0.05 (T=25°C). The solids line are the regressions of the experimental data and were higher than 0.93 in both cases [38].
Figure 7. Average molecular hole volume as a function of increasing glycerol content for glassy gelatin matrices with well-defined water contents (Qw): Qw=0.02 (pink series), Qw=0.04 (purple series), Qw=0.06 (cyan series) and Qw=0.08 (white series) measured at 25°C [39].
Recently the effect of glycerol as an enhancer of molecular packing in gelatin films in the glassy state has been stated (Figure 7) [39], however the effect of water in hole volume size in this biopolymer has shown to be quiet complex. A pronounced increase in the average hole volume was observed, reaching a maximum value at water content near 10% (dry basis), after which a decrease in this parameter upon further sorption of water was detected (Figure 8) [39]. The initial increase in the average hole volume of the gelatin matrices upon sorption of water indicates that water acts as a plasticizer (confirmed by a decrease in Tg).The decrease in average hole volume above certain moisture content suggests a different structural conformation of the polymer which may be attributed to the formation of small
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pockets/clusters of water between the polypeptide chains [39, 40]. These recent findings provide new insights regarding the well-known antiplasticization phenomenon widely reported in the literature and possible mechanisms for its modulation with potential implications in food and pharmaceutical industries.
Figure 8. Average molecular hole size as a function of increasing water content for gelatin matrices with well-defined glycerol contents (Qg) measured at 25°C. Green series Qg=0.00; blue series Qg=0.02; yellow series Qg=0.06 and red series Qg=0.10. [39].
Figure 9. Diffusional exponent n as a function of glass transition temperature (Tg) T = 20oC calculated on experimental data obtained by DVS from 0 to 90 RH [32].
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