Towards an improved understanding of glass transition and relaxations in foods: molecular mobility in the glass transition range

Trends in Food Science & Technology 11 (2000) 41±55

Review

Towards an improved understanding of glass transition and relaxations in foods: molecular mobility in the glass transition range Dominique Champion, Martine Le Meste and Denise Simatos Laboratoire d'IngeÂnierie MoleÂculaire et Sensorielle de l'Aliment, ENSBANA 1, Esplanade Erasme, 21 000 Dijon, France Recent research has contributed to a better understanding of the glass±liquid transition (GLT) and its relationship with relaxation processes in the material. This paper reviews models and theories that are currently used to describe and explain the physical changes in the GLT temperature range (Tg); ageing below Tg, changes in mechanical properties above Tg, and the concept of fragility are described. Measurements of the GLT temperature are now practised routinely in many food laboratories, but lack of information on the experimental conditions may lead to discrepancies between results. Several examples from the food domain are reported, illustrating that the GLT has been mainly used to interpret, with more or less success, changes in low

moisture foods and biomaterials. Taking the temperature of GLT into consideration alone cannot suciently explain changes as a function of temperature or water content, particularly when chemical/biochemical reactions are concerned. The relationship between molecular mobility and the GLT is discussed. More measurements of the various types of molecular motions are necessary, specially in close vicinity to the GLT and in the glassy state. # 2000 Elsevier Science Ltd. All rights reserved.

The ®rst mention of the glass transition in food and biological systems appeared in the literature in the 1960s [1±3]. The huge variety of possible applications in food science and technology, however, was highlighted in the 1980s by Levine and Slade [4,5]. As the stability of foods is mainly dependent on the water content and because the glass transition temperature (Tg) is also highly sensitive to this parameter, the glass transition concept appeared to be a powerful tool for understanding the mechanisms of processes in food products and for controlling their shelf-life. Indeed, the glass transition temperature was considered as a reference temperature: below Tg, the food was expected to be stable; above this temperature, the di€erence (TÿTg) between Tg and the storage temperature T was assumed to control the rate of physical, chemical and biological changes. The glass transition was also shown to allow the identi®cation of the water content (and temperature) domains where a product could exhibit either a hard, crispy texture or a soft, rubbery or viscous one. Moreover, the variations of mechanical and transport properties in the glass transition range could contribute to a better control of some food processing operations such as drying and freeze-drying, extrusion and ¯aking. Investigations to establish up to what point these working hypotheses could be veri®ed have been carried out [6±10]. More recent publications have aimed at a deeper understanding of the basic physical aspects of glass transition in order to determine its real impact in food technology [11±13]. Even though the true nature of the glass transition is still under investigation, improved knowledge of the relaxation phenomena within the glass is beginning to contribute in explaining some changes in food products below Tg. In parallel to the fundamental aspects, several questions have been raised concerning

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the use of glass transition principles in applied domains. Do we know, now, the relevant parameter(s) (if they exist) to characterize food materials and to predict their stability? Does the scienti®c knowledge make available to the food technologist, tools to enable glass transition phenomena to be taken into account in the formulation and process control of food products? This paper will be presenting some examples showing how the glass transition concept can be used to understand the physical behaviour of food materials during processing and storage, and also indicate where further research e€orts are necessary.

The glass transition concept

The present knowledge about glass transition is essentially phenomenological; very little is known about theoretical aspects. So far this knowledge mainly concerns non-food materials (mineral glasses, natural and synthetic polymers). From what is known so far about food products and ingredients, it appears, however, that essential features are similar. What makes the food materials seem di€erent is on one hand the frequent heterogeneity in chemical composition and on the other the predominant role of the water as a plasticizer. Glass transition or glass±liquid transition (GLT) is the name given to phenomena observed when a glass is heated until it behaves like a supercooled melt. . A material in the glassy state behaves as a brittle solidÐwith a rigidity or storage modulus typically about 109PaÐits microstructure is non-crystalline (=amorphous), exhibiting a short-range order only, as in a liquid. . The supercooled melt is the non-crystalline state observed between the GLT and the melting point. The mechanical behaviour can be that of a viscoelastic `rubber' in the case of a polymeric material, or mainly viscous as a liquid, for low molecular weight materials.

As the temperature of a glassy material is raised through the temperature range of the GLT, rather abrupt changes in many physical properties are observed: increase in entropy and heat capacity and decrease in rigidity and viscosity. The glass transition corresponds to the temperature zone where the viscosity reaches the value of 1010±1012 Pa.s (Box 1).

a and b relaxations

The GLT is a kinetic and relaxation process associated to the primary relaxation of the material. The supercooled melt is in a metastable state, the liquid-like structure of which is `frozen' in the glass; the latter is an out-of-equilibrium state. The relaxation time (characteristic time of mobility) is the time that is necessary for the recovery of equilibrium

conditions after perturbation of one property of the material. The relaxation time can be calculated from the phenomenological equations describing the rheological properties of highly viscous liquids developed by Maxwell± Kelvin±Voigt: tmol ˆ Z=G1

…1†

where Z=viscosity. G*1, the factor of proportionality, has the dimension of a modulus of elasticity and corresponds to the value of the modulus at an in®nite frequency; it changes only slightly (from 2 to 4109 Pa) from one substance to another [14,15]. The GLT region is the temperature range where this relaxation time of the material is similar to the experimental time scale [11,16]. As a relaxation phenomenon, GLT can be studied with techniques such as mechanical or impedance spectroscopies that allow tests at di€erent frequencies, changing the time scale of observation. The observed relaxations, a relaxation linked to the glass transition and the sub-Tg relaxations, are shifted to higher temperature when the measurement frequency is increased. The sensitivity of the relaxation processes to temperature depends on the motion concerned and can be characterized with an apparent activation energy (Ea). When the temperature is well above Tg, the molecules or the structural units (such as the repetitive element of a polymer) can move independently from each other because there is enough free volume between entities. The activation energy corresponds to the minimum interaction energy between units and is independent of the temperature (Arrhenius behaviour of the dynamic properties). In the supercooled melt, the free volume between units is not so important and there is an increase in interaction energy, inducing co-operative motions of molecules. The apparent activation energy is then under the in¯uence of both the changes with temperature of the intermolecular interactions and the variation of free volume. It increases as the temperature decreases, attaining high values close to Tg: values from 200 to 400 kJ/mol are common. Higher values are generally found for biopolymers than for materials composed of small molecules. The molecular organization in the material is strongly dependent on temperature above Tg but it is relatively stable below Tg: molecules stay in an isocon®gurational state, the co-operativity e€ect being restricted. Within the glassy state, the change in dynamic properties obeys the Arrhenius law again, with an apparent activation energy that is lower than at T>Tg but still high [11,17]. However, molecular relaxation processes also take place in the temperature range below the GLT. Molecular motions still persist in the glassy state with a lower amplitude and co-operativity than for the glass transition. Indeed, relaxation processes can be observed in the

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55 Box 1. Changes in physical properties at the glass±liquid transition

(a) Thermodynamic properties Ðrate of variation of enthalpy (H) Ðrate of variation of volume (V)

(b) Rheological properties Ðrate of variation of viscosity (Z)  for T between Tg and Tg +100 WLF relation: log (ZT/ZTg)=C1g (T-Tg)/C2g+(T-Tg)) VTF relation: ZT=Z0 exp(BT0/(T-T0))

 for T
Ðabrupt change in heat capacity (Cp) Ðabrupt change in expansion coecient (a)

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D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

glassy state with mechanical or impedance spectroscopies; they also give rise to endothermic features on di€erential scanning calorimetry (DSC) curves. Sub-Tg relaxations are named according to their relative position to the main relaxation a. Even if several relaxations can be observed for biopolymers, only the secondary b relaxation has been extensively studied, its origin still being investigated. As described by Johary [18] it corresponds to more localized molecular motions that persist in the glassy state [19]. In sugar molecules, the b process was ®rstly linked to the presence and the motions of -OH groups. More recently, it has been demonstrated that this relaxation is sensitive to the molecular structure of the carbohydrate and could be due to the rotation of the whole molecule in heterogeneities of the matrix. The Ea value range for a b relaxation in sugars (maltose or glucose) is between 40 and 70 kJ/mol. b relaxations have also been reported for starch components [20±24]. When a glassy material is stored between GLT and b relaxation, a microstructural change may take place, which corresponds to the system approaching the metastable equilibrium, with some extra loss in enthalpy and volume (Box 1a). This ``physical ageing'' can be regarded as a continuation of the a relaxation. The more compact molecular organization and the strengthening of interactions result in changes in mechanical and also in transport properties. The relevance of this process to some food technology applications is being increasingly recognized as shown, for instance, with cereal products [23±25]. Physical ageing is responsible for the appearance of various features on DSC curves: endothermic overshoot that expresses rapid enthalpy recovery after ageing below Tg (Box 1a), but also an exothermic event when a rapid cooling is followed by a much slower rewarming [26]. The endothermic overshoot may be deliberately used to help in detecting the glass transition, with materials for which the heat capacity jump is particularly small and smeared out over a broad temperature range. Yet it may be carefully considered for a correct interpretation of calorimetric studies as was shown for starch by Seow [27].

Descriptive models

Most important to the food technologist are models describing the changes in physical properties in the GLT range. Although originally based on observation, the current models are more or less successfully supported by the various theoretical approaches, which aim at giving a physical (microstructural/molecular) meaning, to the parameters. Above Tg, the temperature dependence of viscosity of supercooled liquids cannot be described by an Arrheniuslike relationship. Several expressions, the most popular being the Vogel±Tammann±Fulcher (VTF) and the Williams±Landel±Ferry (WLF) expressions, describe the

temperature dependence of the dynamic properties above the glass transition: ZT ˆ Z0 exp…BT0 =…T ÿ T0 ††

…2†

log…ZT =ZTg † ˆ C1 …T ÿ Tg †=…C2 ‡ …T ÿ Tg ††

…3†

where ZT and ZTg are viscosities at T and Tg, respectively; Z0, B, T0, C1 and C2 are phenomenological coef®cients. Both expressions can be inter-converted according to the relations between coecients (with B0 =B/ln(10)): C1 ˆ B0 T0 =…Tg ÿ T0 †

…4†

C2 ˆ Tg ÿ T0 :

…5†

It should be noted that expressions similar to equations (2)±(3) can be written with the tmol obtained with, for example, mechanical spectroscopy. C1 and C2 can ¯uctuate slightly [28] around the `universal' values given by Williams et al. [29] (ÿ17.4 and 51.6, respectively) as a function of the considered material. The variations of C2 and of B correspond to the classi®cation proposed by Angell [12,30] of strong/fragile materials according to the variation of their properties through the glass transition. The fragility parameter, m, was introduced to di€erentiate fragile systems (100
…6†

This parameter m can be calculated with the VTF and WLF coecients: m ˆ C21 =B0 ‡ C1

…7†

or it may be deduced from DSC or mechanical spectroscopy data. A discussion of the application of various methods to estimate m for food materials can be found in Refs. [13] and [26]. From the few experimental data so far available, sugars (glucose, fructose, sucrose) can be classi®ed as rather fragile materials. But increasing the water content seems to result in a decrease of fragility in the case of sucrose [12]. Pure water, indeed, appears to have a complex behaviour. Angell [31] presented arguments suggesting that amorphous solid water (obtained for instance by hyper-quenching of tiny droplets) behaves as a very strong liquid in a small temperature range above Tg. Within a limited range of water content,

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

however, no signi®cant di€erence in fragility could be found with maltose (10±25.3% w/w water) [32] or with sucrose (6±18% w/w water) [33]. For proteins, the scarce experimental data seem to indicate a strong behaviour. Angell [12] found for poly-l-asparagine (15± 25% w/w water) a fragility parameter m40.5, which appears as strong, or stronger than the strongest chain polymer: polyisobutylene. Very similar values could be calculated from mechanical spectroscopy data reported for elastin and gluten [13]. Polysaccharides (amylopectin, phytoglycogen, pullulan, dextran, with 10±16% w/w water) were found to behave as fragile materials, with the fragility decreasing with increasing water content [24]. These latter results would need con®rmation, however, as the method used (determination of the limit temperature by DSC) is known to overestimate the apparent activation energy when compared with methods based on the usual Tg measurement [26]. The practical signi®cance of the strong/fragile classi®cation with respect to food technology should be emphasized. Indeed, a small variation in the m value for two products may result in a large di€erence in stability as the sensitivities to temperature around Tg are di€erent. Moreover, food technology applications, such as extrusion, pung or ¯aking, could bene®t from a better knowledge of the strong/fragile behaviour of the materials being processed. Besides the glass transition temperature and the fragility, at least two other characteristics are necessary to describe dynamic behaviour in the GLT domain: . Non-linearity, which means that the characteristic is changing with time, as it depends on the structure of the glass. . Non-exponentiality, which means that the process of a relaxation cannot be described by a single relaxation function, due to microstructural heterogeneities. Non-exponentiality is most commonly interpreted as a distribution of relaxation times and mathematically represented by a so-called stretched exponential function: …t† ˆ exp‰ÿ…t=t †b Š

…8†

The exponent b is close to 1 for strong liquids (nearly exponential relaxation). For fragile liquids, it changes from near 1 at high temperature to a value close to 0.3± 0.5 near Tg. Not much consideration has yet been given to these properties in the food science area, although a wide distribution of relaxation times is often claimed in food materials.

The GLT associated theories

A large number of theories have been developed in order to explain the molecular basis of the GLT. Some

45

of them are listed in Table 1; for more details, extended reviews can be found in the literature. From a practical point of view, the interest of these theories is to allow a better prediction of the in¯uence of product composition and/or of the plasticizing e€ect of small molecules. Most of the models treat supercooled liquids as being composed of heterogeneous domains, which are named di€erently depending on the theory: free volume, entropy ¯uctuations, density ¯uctuations, nano-defects. Of the more recently developed models, the extended version of the MCT [39] has stimulated intense interest because the model ®ts the change that is observed in the mobility mechanism above Tg in numerous supercooled liquids at a temperature Tc. However, the MCT does not include any information about the molecular properties of the material. The hierarchical correlated molecular motion theory proposed by Perez [11] is developed here because it better takes into account the molecular basis of the GLT and makes it possible to obtain a large-scale quantitative temperature dependence of dynamic variables (viscosity or relaxation time), especially in the vicinity of Tg. A hierarchy of degrees of freedom, from fast (corresponding to the secondary b relaxation) to slow (the main a relaxation) has been considered. The slowest motions are possible only when the fastest ones have occurred with such amplitude that they leave enough free space. According to this model, the primary and secondary relaxations are linked; changes in the latter have an e€ect on the former. A better knowledge of the parameters that control the sub-Tg relaxations may be helpful for understanding both the possible changes below Tg and the e€ect of temperature above Tg (i.e. the strong or fragile characteristic of a material). From the hierarchical correlated molecular motion theory proposed by Perez [11], the following expression is derived: tmol ˆ t0 …t =t0 †1=b;

…9†

where t0 is a scaling parameter and tb is the characteristic time for the secondary b relaxation. The parameter b expresses the e€ectiveness of correlation e€ects (0 for most highly bounded particles, 1 for non-interacting Table 1. Some theories developed for understanding the glass± liquid transition Theories

Authors

Refs.

 Free volume theory  Entropy-controlled co-operative motions  Mode coupling theory (MCT)  Frustration-limited domains  Hierarchical correlated molecular motions

Cohen & Turnbull Adams & Gibbs

[34] [35]

SjoÈgren Kivelson Perez

[36,37] [38] [11,17]

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D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

ones), and is therefore related to the microstructure of the material. This parameter is a function of the concentration of defects: . it is assumed to be constant in the glass, hence the Arrhenius behaviour of the dynamic properties. . b is temperature-dependent at T>Tg, resulting in the non-Arrhenius behaviour for tmol. Strong/fragile behaviours respectively correspond to materials with a few defects (small number of possible con®gurations in the supercooled liquid) with a high individual energy level, and to those with a high number of possible con®gurations and/or a low energy level.

The plasticizing e€ect of water

Water is the major food component acting as a strong plasticizer. The Tg value of a given hydrophilic substance is decreased with an increase of the water content following a non-linear function as described by the Gordon±Taylor equation: Tg ˆ

cs Tgs ‡ kcw Tgw ; cs ‡ kcw

…10†

where cs and cw are the mass fractions of the substance and of water, Tgs and Tgw their Tg values, respectively, and k a constant. The state diagram (Fig. 1) is a valuable tool in order to know in which manner a glassy material behaves upon addition of water or raising temperature. Small molecules such as sugars have also been found to act as plasticizers in biopolymer systems, increasing the free volume (or the defect concentration) between the molecules (providing there is no phase separation).

Glass transition measurements

Several techniques are available for the determination of the glass transition temperature and they are com-

Fig. 1. Sucrose state diagram, the dotted line is the ice melting curve (Tm) and the continuous line is the GLT curve (Tg) corresponding to the midpoint of the Cp jump in DSC (10 K.minÿ1) (Blond et al. [40], with permission).

plementary depending on the nature of the studied material (Box 2). The most popular one is di€erential scanning calorimetry (DSC). The GLT occurs over a wide range of temperatures. There is, nevertheles, no consensus for the de®nition of the Tg point on a DSC curve among the various points that may be chosen (onset, midpoint, end). It has become increasingly recognized that a GLT should be characterized by at least two parameters indicating its onset or midpoint and the width of the transition. Moreover, due to the kinetic character of GLT, the temperature Tg is under the dependence of the cooling and heating rates and of the eventual ageing. The experimental conditions used should always be reported with Tg values. For products containing starch or ¯our, DSC does not seem to be sensitive enough to detect the glass transition [41,42], but the sharp evolution of the rheological properties through the glass transition can be used to detect the primary relaxation associated with the GLT by mechanical spectroscopy (or dynamic mechanical thermal analysis=DMTA). Here again it is necessary to specify how the transition temperature is de®ned from the experimental curves. The temperature or frequency of the a relaxation is commonly taken from the maximum of the loss factor (tan d) which is more easily determined. The maximum of the loss modulus (E00 or G00 ;) is, however, much better for Ta determination from the point of view of its physical meaning. When a sinusoidal perturbation is applied on a system, the maximal absorption of energy, i.e. the loss modulus peak, is observed when the frequency of measurement and the most probable relaxation time are related by: t=1/2pf. Moreover, no tan d peak is expected with small molecular weight systems. It must be emphasized that the temperatures Tg and Ta should not be considered as fully equivalent. In DSC and DMTA the sample is submitted to stresses of different physical nature (change of temperature in DSC, shearing or compression in DMTA). The experimental time may also be di€erent (depending on cooling±heating rates in DSC, on measurement frequency in DMTA). A di€erent coupling of the imposed perturbations with the structural units (with particular relaxation times) may be responsible for discrepancies in the data obtained with di€erent techniques. Although it is often observed that similar temperature values are obtained in DSC with cooling±heating rates of about 10 K/min and in DMTA with a frequency of about 1 Hz, this may not apply for any material. The characteristic times that can be associated with enthalpy and mechanical relaxation are di€erent. A `decoupling' between di€erent relaxation modes [30] may be observed. Following the expanding custom in materials science, we should restrict the use of Tg to the DSC values (10 K.minÿ1) and name Ta the temperature determined by DMTA (with identi®cation of the measurement frequency).

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55 Box 2. Determination of transitions

(a) Di€erential scanning calorimetry: Tg determination Ðfor a low water product Determination of Tg as the midpoint of the transition

Ðfor a frozen product The Tg for the maximally freeze concentrated phase (Tg0 ) is located between Tg1 and Tg2

Ðafter ageing The aging at 10 K below Tg (curve 2) induces a change of the Tg value and an energy overshoot for the transition

(b) Dynamic mechanical thermal analysis:  and transitions 9 at di€erent Ðdecrease of the storage modulus E0 (G0 ) > > > > = temperatures Ðpeak of the loss modulus E00 (G00 ) as a function Ðtan d: > > > of frequency for polymer: maximum > ; for small molecule: no maximum

(c) Dielectric spectroscopy:  and transitions Ðpeak of e00 Ðmaximum of tan d

9 = ;

at di€erent temperatures as a function of frequency

47

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D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

Impedance spectroscopy (or dielectric thermal analysis=DETA) studies the variations of the dielectric constant as a function of temperature or/and frequency. This technique was demonstrated as particularly e€ective for the study of secondary relaxations in products with low water contents. It provides a good alternative to mechanical spectroscopy for very brittle products [43]. Calorimetric or spectroscopic techniques have some limitations in terms of sample size and shape, and water content control. Some other methods that allow the determination of molecular mobility in heterogeneous systems have been proposed to characterize the GLT. NMR (nuclear magnetic resonance) and EPR (electronic paramagnetic resonance), which measure the mobility of nuclei (mainly 1H and 13C) or spin probes (or labels), respectively, have been recognized as potential tools for the study of GLT. However, more research is de®nitely necessary to bring these techniques to practical applications [44] and to demonstrate their sensitivity to the glass transition. Mobility maps representing the relaxation times versus temperature can be constructed (usually with Arrhenius representation) (Fig. 2). The use of various techniques allows the determination of the characteristic times of the main or sub-Tg relaxations on a wide range of temperatures and times. Due to the decoupling between di€erent relaxation modes monitored by the di€erent techniques, shifts between sets of data may be observed. Such maps however may be useful to food technologists, particularly when the in¯uence of water content on the various relaxations is known. The glass transition temperature is dicult to determine in real food systems due to their complexity and/or heterogeneity. However, the study of the di€erent

Fig. 2. Mobility map of sorbitol as a function of the temperature. The relaxation times were obtained with di€erent techniques (~ mechanical spectroscopy, * viscosity, & dielectric spectroscopy, & neutron spin echo spectroscopy) (from Faivre [45], with permission).

ingredients separately in model systems allows the determination of the temperature/water content area where the physical properties of the system may evolve sharply with temperature.

Tg as a reference temperature for stability?

The concept of glassy/rubbery states was mainly used to interpret the stability of low moisture foods and biomaterials. Physical and chemical reactions that are dependent on the di€usion of reactant molecules would be quite slow in the supercooled liquid or rubber, in the vicinity of the Tg, and kinetically controlled by mobility or viscosity. Well above the Tg, in liquid systems, the translational (Dtrans) or rotational (Drot) di€usion of molecules that are possible reactants in an alteration reaction, can be predicted according to the Stokes±Einstein or Debye± Stokes relations (SE): Dtrans ˆ kB T=6pZr

…11†

Drot ˆ kB T=8pZr3

…12†

where kB is the Boltzmann constant, T the temperature (K), r the hydrodynamic radius of the di€using molecule and Z the viscosity (Pa.s). Considering that on the one hand, di€usion and viscosity are linked according to the 355 SE relation and on the other hand, viscosity evolves with temperature following a WLF kinetic, the use of Tg as a reference temperature for the prediction of the rate of a di€usioncontrolled reaction appears to be relevant.

Physical changes

The crystallization of lactose in products such as ice cream and milk powder has been studied since 1930 [46]. Indeed, the crystallization induces a decrease in ¯owability of powders and brings about an unpleasant granular texture in ice-cream. The plasticizing e€ect of water, inducing depression of the GLT down to a temperature lower than room temperature, is the main cause of sugar crystallization in amorphous products [8]. The e€ects of temperature and water content on crystallization kinetics have been predicted using the WLF relation for lactose [8], sucrose [47] and for lactose in milk powder [48]. Starch retrogradation and the loss of water during storage contribute to the ageing and staling of bread. The crystallization rate of the gelatinized starch could be predicted using the WLF relation just above Tg [4]. The caking and agglomeration of food powders during the drying process or storage are deleterious phenomena that limit the use of sugar-rich powders. On the other hand, the controlled agglomeration of powders improves their wetability, which allows instantaneous dissolution. The main cause of caking and agglomera-

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

tion is water sorption inducing the plasticization of the particle surface. The formation of interparticle liquid bridges between adjacent particles and aggregation take place when the surface viscosity reaches the critical value 106±108 Pa.s (for a particle diameter of 1±10 mm with 1±10 s contact time) [49,50]. The parallel evolution of agglomeration temperature and Tg as a function of the water content was observed in sucrose±fructose mixes [49,51]. Moreover, Aguilera et al. [52] have shown that the caking kinetics of ®sh protein hydrolysate powders can be described by using a WLF-type relationship. The collapse of freeze-dried products induces the loss of structure, the reduction of pore size and volume of the food material, which results in the loss of desirable appearance, texture and volatile substances. During the freeze-drying operation, if the temperature of the porous layer or its water content is increased (the product being then above its Tg), the viscosity is not high enough to support the structure of the solid material and collapse occurs [47,53±55]. The same mechanism as for agglomeration is involved: the viscosity reduction allows material ¯ow and the subsequent densi®cation under capillary force [53]. The collapse temperature is often observed to correspond to Tg+12 C and this temperature changes as a function of water content and average molecular weight of the product as Tg does. Indeed, the characteristic time for the collapse of freezedried maltodextrin or sucrose±fructose mixes evolves following a WLF kinetic [47]. The collapse temperature (as the caking temperature) can be raised by the addition of high molecular weight materials [56]. It has been shown, however, that addition of small amounts of high molecular weight macromolecules may prevent the collapse (reduction of the tendency to ¯ow) without signi®cantly changing Tg [57]. Physical changes such as crystallization, agglomeration and structure collapse were therefore successfully explained and predicted using the GLT concept on the basis of Tg as a reference temperature. Such physical transformations have indeed been observed to occur only above Tg and to be kinetically controlled by the ¯ow rate i.e. the viscosity (collapse, caking ...) or by long-distance di€usion of molecules (crystallization). Figure 3 describes the viscosity ranges that can be predicted for physical changes [58] on the basis of the observed temperature and the WLF evolution of viscosity for sucrose. Some of these values (collapse) could be satisfactorily correlated with experimental data [53]. It is important to note, however, that these predicted viscosity values are dependent on the characteristic times of the methods used to monitor the changes. For instance, Lloyd et al. [59], using longer experimental times than previous authors, determined a caking temperature for amorphous lactose close to the Tg onset.

49

Fig. 3. Schematic representation of physical changes kinetically depending on the di€erence T±Tg in the experimental time (adapted from Sun [58], with permission).

Chemical/biochemical reactions

The possible changes in frozen or low-water food products are also the result of chemical or biochemical reactions such as non-enzymatic browning, oxidation or enzymatic reactions [60,61]. The relevance of Tg as a reference temperature for predicting the rate of chemical or enzymatic reactions has often been discussed but no clear relationship has been established yet. Karmas et al. [62] studied the temperature e€ect on the reaction rate constant of non-enzymatic browning in model food systems. They showed that the rate of the reaction is low at temperatures below Tg and increases as the temperature di€erence (T±Tg) increases above Tg. These authors [62], however, underlined that the reaction is also controlled by several other factors such as structural changes or water content independently of its plasticizing e€ect. Roos and Himberg [63] have also studied this reaction and showed that it is not stopped by the GLT of the maltodextrin, lysine and xylose matrix, and is possible in the glassy state. Oxidation phenomena occur too in low-water systems (fat oxidation [64,65] or ascorbic acid oxidation [64,66]). Shimada et al. [64] demonstrated that the rate of oxidation of methyl linoleate in a freeze-dried lactose matrix increased with T±Tg. However, the authors noticed that the reaction was induced by the collapse of the matrix, itself controlled by the GLT. So there is still no evidence of direct control of the oxidation reaction by the GLT. The kinetics of aspartame degradation were evaluated in poly (vinyl) pyrrolidone model system [67,68]. Reaction rates at constant water activity but di€erent Tg values were not signi®cantly di€erent. Moreover, rates at the same distance from Tg (T±Tg) but di€erent aw were signi®cantly di€erent. It was also found that sucrose acid hydrolysis occurs to a signi®cant extent in the glassy state in both native and gelatinized starch [69]. Moisture content a€ected the reaction rate but its

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D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

e€ect was not attributable to the plasticizing e€ect of water. Temperature was the critical factor controlling sucrose inversion. The stability of enzymes in low water systems was analysed according to the GLT concept. The stability of lactase during heating at 70 C was studied in di€erent amorphous glassy matrices: trehalose, maltodextrin or poly (vinyl) pyrrolidone [70]. The protective e€ect of the maltodextrin and poly (vinyl) pyrrolidone matrices on the enzyme was attributed to their glass transition temperature, but the trehalose matrix is much more ecient for enzyme stability independent of its Tg value. Similar results were reported for invertase [71,72]. Several enzymatic reactions can occur at low water contents [73,74] or in the frozen state [75±79] such as those catalysed by alkaline phosphatase [80,81], lipoxygenase [82], lipase or invertase [74]. Enzyme reactions were often considered as di€usion-controlled in dry foods because mobility is limiting for substrates, enzyme and also for enzyme segments, this latter contributing to the enzyme activity. The e€ect of temperature on the reaction rate depends on the relative value of the di€usion of reactants and the activity of the enzyme in such concentrated media. Karel and Saguy [60] have proposed a model showing the e€ect of di€usion on reaction rate: Kap ˆ k=‰1 ‡ k=…aD†Š

…13†

with Kap, the apparent reaction constant of a di€usioncontrolled reaction, k the rate constant in dilute systems with no limitation for di€usion (e.g. in a stirred reactor), a a constant and D the translational di€usion coecient. The observed reaction rate Kap is limited by the mobility of reactants, which is under the in¯uence of viscosity and is supposed to evolve according to the WLF relation. The reaction rate constant k is expected to follow Arrhenius behaviour as a function of temperature with constant activation energy if no conformational changes of the enzyme are caused by the low-water content in the media. As will be reported later, when the reaction medium is strongly concentrated and if the enzyme does not undergo any modi®cation, the reaction constant Kap can be predicted starting from di€usion. Lipoxygenase [82] and alkaline phosphatase [80] were shown to catalyse di€usion-limited reactions in highly concentrated sucrose solutions. Indeed, the structural changes of soybean lipoxygenase are responsible for changes in enzyme activity and speci®city [81]. With the decrease in water content, the solvation of the enzyme by forming hydrogen bonds with water is reduced and the enzyme adopts a more rigid conformation. Modi®cation of the reaction medium induces also some e€ects on the enzyme activity, which can be either ampli®ed or decreased. The activity of alkaline phospha-

tase is lower in glycerol solutions than in sucrose solutions although the solutions have the same viscosity [80]. In conclusion, the inter- and intra-molecular mobility controls the enzyme/substrate association but the enzyme activity can be a€ected di€erently as a function of the considered enzyme or medium [75,79], it appears hazardous to propose a uni®ed theoretical model to predict the rate of reactions in such concentrated materials. Frozen products represent a particular situation because two di€erent glass transition temperatures have to be considered depending on the storage temperature (Ts): either the temperature Tg corresponding to a product where no ice is present (Tg curve in Fig. 1) or Tg0 the glass transition temperature of the maximally freezeconcentrated phase (intersection point of the curves Tg and Tm in Fig. 1). If the product is stored at a temperature Ts
D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

broadly considered as glassy (only one Tg determined by DSC), in some micro-regions supposed to be nonglassy. Further studies are needed to investigate e€ects of non-homogenous water distribution and/or phase separation on reaction rates. Finally, the relevance of the GLT concept as a predictive model for the stability of food rests upon the validity of the SE relations. The relationship between relaxations of the material and di€usion of molecules especially water and other small molecules, however, is not yet well de®ned in systems close to Tg. In the following, the discussion will be focused on the relationship between viscosity and di€usion.

Relationship between glass transition and di€usion Water di€usion

Considering the SE relation, the di€usion time of a water molecule over 1 AÊ distance should be more than 106 years at room temperature in a glassy matrix (ZTg=1012 Pa.s, T=293 K). As we know, the time scale for the loss of stability in food at low water content is not so large. The mobility of water molecules has been reported to be relatively high in the vicinity of the GLT and in glassy material and to have only low sensitivity to the physical state of the surrounding media [84,85]. Ablett et al. [84] have measured translational di€usion coecients of water using the pulsed-®eld gradient NMR technique (PFG NMR) in 80.9% pullulan preparations (Fig. 4). They showed that the Dtrans of water in this polysaccharide is around 410ÿ11 m2 sÿ1 at Tg and that the water has a much higher degree of mobility than the polymer. No important change in the evolution of the water di€usion was observed at Tg.

51

Solute di€usion

When the molecular size of the di€using molecule is very small compared with the molecules of the matrix, the SE relation is inadequate to predict the reactant di€usion. In this situation, indeed, the macroscopic viscosity (commonly measured) does not re¯ect the local neighbourhood of the di€using species and is not the determining factor that controls di€usion [86,87]. For instance, this is the case when a small solute is dispersed in a hydrophilic polymer network. We measured the translational di€usion of ¯uorescein (r=5 AÊ) using the FRAP method (¯uorescence recovery after photobleaching) or the concentration pro®le method and the rotational di€usion of Tempol (r=2.5 AÊ) using ESR (electron spin resonance) in concentrated sucrose solutions: 67.5% sucrose solution and 57.5% sucrose +10% dextran (di€erent molecular weights up to 2106 Da). The great increase in viscosity resulting from the replacement of sucrose by dextran did not signi®cantly reduce the translational di€usion of the small probe. The same was observed for the rotational di€usion coecient [88]. At values greater than, but near to, Tg several authors have shown a decoupling e€ect between viscosity of the di€usion medium and di€usion of a small molecule. This decoupling, ®rstly observed in non-polar substances [89±92], was then studied in aqueous systems for the di€usion of water in highly concentrated maltose solutions [85] and for di€usion of ¯uorescein in sucrose solutions [33]. According to the Stokes±Einstein relation (11), the expression [T/(Dtrans.Z)] should give a constant value that is a function of the hydrodynamic radius of the di€using species. The ¯uorescein Dtrans was mea-

Fig. 4. Temperature dependence of the translational di€usion of water in 80.9% pullulan followed by PFG NMR (from Ablett et al. [84], with permission).

52

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

sured in concentrated sucrose solutions (30±96%) in a temperature range from ÿ15 to 20 C, using the FRAP method. The evolution of the ¯uorescein Dtrans. with temperature is in agreement with the SE relation when the temperature is higher than 1.2 Tg (Tg/T=0.86). In the vicinity of Tg, the di€usion of this small molecule is higher than predicted by viscosity using the SE relation (Fig. 5) and the discrepancy increases as T gets close to Tg [33]. The observed temperature for the decoupling (1.2 Tg) coincides with the Tg proposed by the mode coupling theory and was argued to correspond to the b±a relaxations crossover [89,90]. In the close vicinity of the

main relaxation, the evolution of di€usion as a function of temperature instead of following a WLF kinetic, was better described using an Arrhenius plot (as the secondary relaxation does) (Fig. 6). Indeed, the motion of small probes in such viscous materials may be facilitated by the presence of nanodefects and/or by local motions in the material (secondary relaxations). As described with these latter examples, a better knowledge of the sub-Tg relaxation appears to be desirable to understand and predict the loss of stability in food products at low water content and to predict the evolution with temperature of the main relaxation according to the model proposed by Perez [11].

Fig. 5. Translational di€usion coecients of ¯uorescein in concentrated sucrose solutions. The solid line corresponds to the evolution as a function of the SE relation, the dotted line is just a guide for the eye showing the decoupling between translational di€usion and viscosity (from Champion et al. [33], with permission).

Fig. 7. In¯uence of water content on the descriptor `crispy' of extruded bread (from Roudaut et al. [95], with permission).

Fig. 6. Translational di€usion coecients of ¯uorescein in sucrose± water solutions at di€erent concentrations as a function of T±Tg. The line corresponds to the di€usion rates calculated with the SE relation using the WLF predicted viscosity (from Champion et al. [33], with permission).

Fig. 8. In¯uence of water content on the loss factor values measured at 25 C 5 Hz with DMTA, for white bread (*) and for extruded bread (+), the line is a guide for the eye (from Roudaut et al. [95], with permission).

D. Champion et al. / Trends in Food Science & Technology 11 (2000) 41±55

Relationship between relaxation and texture

The loss of stability due to water sorption was observed for complex food products below Tg. If the moisture content of crispy products such as chips crackers, corn ¯akes and other extrudate products increases due to water sorption or if the temperature is increased during storage, the crispy texture is lost. Crispness is one of the main sensory properties required by the consumer for these products [93,94]. Roudaut et al. [95] have shown that the loss of the crispy texture of dried white bread corresponds to a critical water content (9±10% w/w) (Fig. 7) for which samples are in the glassy state (Fig. 8). Indeed, the main increase in loss factor (tan d) at water content above 15% corresponds to the GLT, but the minor tan d increase around 9% which coincides with the loss of crispy texture, could result from sub-Tg relaxations, or could be associated with motions just preceding the onset of the a relaxation.

Conclusions

Several physical evolutions in food products at low water content or in the frozen state can be predicted by the GLT concept that makes clearer the e€ect of water content and temperature on the stability. However, various physical and chemical reactions can still occur in the glassy state, suggesting that Tg cannot be considered as an absolute threshold temperature for stability. Sub-Tg relaxations and physical ageing are phenomena showing that the molecular mobility below Tg cannot be neglected. Loss of crispness observed in cereal products with sensory evaluation, for instance, does not appear to be a consequence of GLT but should be initiated by molecular motions due to reorganization in the glass as revealed by dielectric spectroscopy. The occurrence of chemical reactions below Tg is an incentive for more work on the possibility of molecular mobility in glasses. Above the GLT temperature, a simple WLF model based on viscosity is not sucient to account for the e€ect of temperature and water content on kinetics of transformations or on mechanical properties. Measurements as closely related as possible to the property of interest have to be considered: translational/rotational di€usion for chemical reactions, viscosity for ¯ow, mechanical spectroscopy for texture. Thanks to the use of various measurement techniques, mobility maps o€er the possibility of estimating mobility in a broad temperature range and to present a comprehensive view of the di€erent kinds of motions occurring in a material. Moreover, it is increasingly recognized that Tg is only one parameter among others, such as: fragility, ab crossover temperature, and distribution of relaxation times. The strong and fragile classi®cation proposed by Angell [12] and the hierarchical correlated molecular

53

motion model of Perez [11] are examples of theoretical approaches which can be used by food technologists to better understand the impact of molecular structure on the behaviour of food materials as a function of temperature. Important experimental work, however, is necessary for the determination of the parameters speci®c to food products, and their variation with water content. This will allow the GLT concept to be even more ecient in rationalizing formulation and process control for foods.

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