Hygroscopic properties and glass transition of dehydrated mango, apple and banana

Abstract

An undesirable crispiness loss occurs when some dry fruits reach a critical moisture content (X _c) and their glass transition temperature (T _g) matches the storage temperature. Models for sorption isotherms and onset T _g values for dry mango, apple, and banana were used to estimate X _c values at 25 and 32 °C. All models yielded R ² > 0.97 but information theory criteria strongly supported GAB in all but one case (40 °C, mango). The Gordon–Taylor T _g model (GT) yielded high R ² values for apple and banana but resulted in R ² = 0.834 for mango. As moisture approached zero, mango T _g estimates displayed a downward concavity contrasting with a rapidly increasing trend for apple and banana. The Khalloufi–Maslouhi–Ratti (KMR) model for T _g as a function of a _w showed a linear behavior. Although the KMR model fitted data with R ² > 0.996, it requires more parameters and when a _w approached 0, estimated T _g values increased at a slower rate than for the GT model. In the case of banana and mango, both models predicted approximately the same X _c at 25 °C but not at 32 °C. Finally, all X _c values estimated based on T _g were lower than the monolayer values obtained with the GAB (apple and banana) and BET (mango) models. These results indicate that the glass transition induced by moisture uptake dominates the quality degradation of these dry fruits.

Introduction

The growing consumer interest in healthier snack products has increased the demand for dehydrated fruits and vegetables (da Silva et al. 2014). Although the appropriate selection of the drying method and the operating parameters yields products with desirable texture, they remain sensitive to moisture gain during storage (Konopacka et al. 2002; Phomkong et al. 2006). Upon moisture gain, dried fruits and vegetables can lose crispness, a consumer desired quality (Lewicki 2004; Welti-Chanes et al. 1999). Early work showed that crispness loss is due to water plasticization changing a dried product from a glassy into an undesirable rubbery state. This occurs when moisture uptake lowers the glass transition temperature (T _g), defined as the temperature at which a material transitions from the amorphous glassy to a rubbery state (Roos 1995; Roos and Karel 1991). Glass transition is a second order thermodynamic phase transition altering the intrinsic properties of foods including heat capacity, free volume, and viscosity. In differential scanning calorimetry (DSC) measurements, the change in heat capacity due to a glass transition alters the heat flow over a temperature range (Goula et al. 2008). Therefore, several authors prefer to report the temperature at which the glass transition begins (T _g), stating that changes in water mobility causing a quality loss in dried products begin at this temperature (Moraga et al. 2011). The critical moisture content for this change (X _c), and its corresponding water activity (a _wc), increases with the molecular weight of the components in the glassy structure (Djendoubi Mrad et al. 2012b). Mathematical models expressing T _g as a function of X or a _w are used to determine the X _c or a _wc value at which T _g equals the temperature of the dehydrated fruit surroundings (Khalloufi et al. 2000).

The moisture barrier properties of films used to pack dried fruits to increase shelf-life must consider not only the prevailing temperature and relative humidity storage conditions but also fruit composition effects on T _g values. The relationship describing dry basis food moisture content (X, g water/100 g dry solids) as a function of the relative humidity or water activity (a _w) of its surroundings at constant temperature and pressure is known as the moisture sorption isotherm (Djendoubi Mrad et al. 2012b; Jain et al. 2010; Kawai et al. 2005). Since isotherms reflect the interactions between food components and water, the shape of X versus a _w plots will also depend on the chemical composition of foods (Phomkong et al. 2006). Numerous mathematical models have been proposed to describe food moisture sorption isotherms. Widely used models include the Guggenheim, Anderson and de Boer (GAB) equation to describe products with a high sugar (Eq. 1, Talla et al. 2005; Varghese et al. 2014) and starch content (Sharma et al. 2009) below ~ 0.8 a _w; the Brunauer, Emmett and Teller (BET) model describing well the isotherm behavior below ~ 0.5 a _w (Eq. 2, McMinn and Magee 1997); the equation proposed by Iglesias and Chirife (Eq. 3, Ayranci et al. 1990) used for products with high sugar content; and the Henderson equation for products with high sugar and starch content (Eq. 4, Basu et al. 2013; Johnson and Brennan 2000). Food composition affects the moisture content-a _w–T _g relationship (Djendoubi Mrad et al. 2012b; Kawai et al. 2005). Thus, mathematical models adequately relating a _w, T _g, and moisture content are critical for the design of the drying process, food packaging, and selection of storage condition.

$$X=\frac{X_{m}CK{a}_w}{\left(1-K{a}_w\right)\left(1+(C-1)K{a}_w\right)};X_m:\text{monolayer}\text{value};C,K:\text{constants}$$ 1

$$X=\frac{X_{m}C{a}_w}{\left(1-a_w\right)\left(1+(C-1)a_w\right)};X_m:\text{monolayer}\text{value};C:\text{constant}$$ 2

$$X=A+B\left(\frac{a_w}{1-a_w}\right);A,B:\text{constants}$$ 3

$$X={\left[-\frac{1}{A}ln\left(1-a_w\right)\right]}^{1/C};A,C:\text{constants}$$ 4

In this study, model selection was performed using commonly used measures of goodness of fit (error sum of squares, SSE; coefficient of determination, R ²; variance estimate, ${\widehat{\mathit{\sigma }}}^2$) and information theory criteria (maximum log-likelihood estimate, ℓ; Akaike Information Criteria, AIC) to determine mathematical expressions best describing the moisture sorption isotherms of dried apple, banana and mango at 25, 32, and 40 °C. Goodness of fit indicates how well a model describes the available experimental observations. Model fit can be improved by increasing the model complexity although the resulting model may describe random error or noise instead of the true underlying relationship. AIC provides a balance between the goodness of fit of the model and its complexity (Serment-Moreno et al. 2015). Furthermore, fruit samples conditioned at 25 and 32 °C to reach a _w in the 0.10–0.70 range were also used to determine their T _g value by DSC. Finally, mathematical models describing T _g as a function of sample moisture content or water activity were similarly evaluated and used to determine the critical moisture content (X _c) for dried fruits stored at ambient (25 °C) or higher (32 °C) temperature.

Materials and methods

Fruit samples

Dry apple (Malus domestica var. Golden delicious), banana (Musa paradisiaca, var. Cavendish), and mango (Mangifera indica, var. Kent) samples (500 g) were obtained from a commercial processor (Frescos y Procesados Orgánicos Cultivare S.P.R. de R.L., Puebla, México) and characterized as summarized in Table 1 (AOAC 1996; Miller 1959; NMX-F-090-S 1978).

Table 1.

Apple, banana and mango samples dry basis composition (g/100 g dry solids)

Sample	Moisture contenta	Total sugarsb	Reducing sugarsb	Starchc	Crude fiberd	Ashd
Apple	3.4 ± 0.1	76.4 ± 3.2	57.8 ± 2.5	0.4 ± 0.1	7.2 ± 0.2	2.1 ± 0.1
Banana	3.0 ± 0.1	62.3 ± 3.7	51.8 ± 3.1	13.1 ± 0.6	0.8 ± 0.0	2.9 ± 0.0
Mango	4.4 ± 0.3	70.5 ± 4.9	24.6 ± 1.5	7.4 ± 0.2	3.3 ± 0.1	2.1 ± 0.1

^aAOAC Official Method 934.06 (1996)

^bMiller (1959)

^cEnzymatic kit K-SUCGLK (Megazyme International Ireland Ltd., Wicklow, Ireland)

^dNMX-F-090-S (1978)

Moisture sorption isotherms

Moisture sorption isotherms were determined by the gravimetric method (Kaymak-Ertekin and Sultanoglu 2001). Hermetically sealed glass containers containing saturated salt solutions ranging from a _w 0.111 to 0.904 (López-Malo et al. 1994) were kept in temperature-controlled incubators at 25, 32, and 40 °C. Samples (~ 2 g) were weighed every 4 days until the change between two consecutive weight measurements was < 0.001 g (Wolf and Spiess 1985). The moisture content for each a _w was measured by adding the recorded weight change to the initial moisture content. For moisture determination at a _w > 0.75, a vial containing sodium azide was placed next to the fruit samples to minimize microbial activity (Baucour and Daudin 2000). Moisture measurements at each specific a _w were performed in triplicates.

Mathematical modeling of sorption moisture isotherms

The BET, GAB, Henderson, and Iglesias–Chirife equations (Eqs. 1–4) were fitted to triplicate moisture sorption data at 25, 32, and 40 °C. The error sum of squares (SSE; Eq. 5) of each isotherm replicate were simultaneously minimized using Microsoft Excel Solver to yield three sets of parameter estimates for every model, and the average of parameter estimates was then reported.

$$SSE=\sum _{i=!}^n{\left(y_i-{\widehat{y}}_i\right)}^2$$ 5

Glass transition temperature

The determination of onset T _g values as affected by a _w (0.115, 0.226, 0.323, 0.436, 0.525, 0.578, 0.708) was performed by DSC (Model Diamond, Perkin Elmer, Waltham, MA) operating with a 20 ml/min nitrogen gas flow. Hermetically-sealed aluminum pans with dried fruit samples (12 mg) equilibrated at each desired a _w level in temperature-controlled incubators at 25 and 32 °C were cooled at 10 °C/min until the sample temperature was at least 30 °C below its expected T _g value and held constant for 5 min prior to heating at 10 °C/min for apple and mango (Venir et al. 2007) and 15 °C/min for banana. An empty aluminum pan was simultaneously heated to serve as reference. T _g values were determined in triplicates.

The Gordon–Taylor (GT; Eq. 6) and Khalloufi–Maslouhi–Ratti (KMR; Eq. 7) models were used to describe T _g as a function of X and a _w, respectively (Khalloufi et al. 2000). The critical moisture content value was defined as the moisture level at which T _g is equal to the storage temperature (T _storage) set as 25 or 32 °C for this study.

$$Tg=\frac{T{g}_s{W}_s+kT{g}_w{W}_w}{W_s+k{W}_w}$$ 6

$$Tg=\frac{a{a}_w^2+b{a}_w+c}{\mathit{\alpha }{a}_w^2+\mathit{\beta }{a}_w+1}$$ 7

Statistical evaluation of model performance

The goodness of fit for each model was evaluated based on the SSE (Eq. 5), coefficient of determination (R ²; Eq. 6), and information theory criteria (Serment-Moreno et al. 2015). The maximum log-likelihood estimate (ℓ; Eq. 9) was determined assuming model errors followed a normal distribution, and the variance estimate (${\widehat{\mathit{\sigma }}}^2$) was calculated as in Eq. (10). The Akaike Information Criteria (AIC; Eq. 11) provides a balance between goodness of fit via ℓ (first term, Eq. 11), and the indiscriminate use of model coefficients (p, second term, Eq. 11). The model displaying the lowest AIC is considered as the most adequate to describe the current dataset. Since AIC values vary among distinct datasets, differences (ΔAIC_i) between the AIC of the tested models are reported by considering the lowest AIC (AIC_min) as a reference (Eq. 12). As a rule of thumb, ΔAIC_i indicates substantial (ΔAIC_i ≤ 2), moderate (2 < ΔAIC_i ≤ 4), or slight (ΔAIC_i > 4) evidence supporting the model fit to the observed data set (Burnham and Anderson 2002).

$$R^2=1-\frac{\sum {\left(y_i-{\widehat{y}}_i\right)}^2}{\sum {\left(y_i-{\overline{y}}_i\right)}^2}$$ 8

$$\ell =-\frac{n}{2}ln{\widehat{\mathit{\sigma }}}^2$$ 9

$${\widehat{\mathit{\sigma }}}^2=\frac{\sum {\left(y_i-{\widehat{y}}_i\right)}^2}{n}$$ 10

$$AIC=-2\ell +2p$$ 11

$$\mathrm{\Delta }AI{C}_i=AI{C}_i-AI{C}_{\text{min}}$$ 12

Results and discussion

Sorption moisture isotherms

The moisture sorption isotherms at 25, 32 and 40 °C (Fig. 1) displayed the distinctive Type II sigmoidal shape for high sugar content foods (Al-Muhtaseb et al. 2002). Only minor moisture changes were observed for a _w < 0.5, where it is hypothesized that simple sugars interact with fiber, starch and each other, leaving few binding sites for water molecules. Conversely, water uptake greatly increases for a _w > 0.5 when dissolution of simples sugars begins (Moraga et al. 2011). At 25 °C, the moisture content of apple was higher (3–16 g of water/100 g dry solids) than for mango samples, which showed the lowest moisture sorption capacity among the dried fruits tested (Fig. 1). Despite having similar amounts of total sugar content (70–76 g/100 g dry solids), the reducing sugar content in apple samples was approximately two times higher when compared to mango (Table 1) resulting in notable differences in moisture sorption capacity. Non-reducing sugars have a lower moisture sorption capacity (Harnkarnsujarit and Charoenrein 2011; Venir et al. 2007), which is consistent with the composition (Table 1) and moisture sorption isotherms of apple and mango observed in this study (Fig. 1).

Fig. 1.

Moisture sorption isotherms of fruits (symbols) and GAB model fit (lines). a Mango. b Banana. c Apple

Temperature had no clear effect on the equilibrium moisture content of banana and mango samples, whereas apple sorption isotherms displayed lower moisture content values as temperature increased from 25 to 40 °C (Fig. 1). At a _w = 0.84, the same water content (~ 49 g/100 g solids) was observed at 32 and 40 °C. For a _w ~ 0.9, a higher water content was observed at 40 °C (83 g/100 g solids) than at 32 °C (79 g/100 g solids). The superposition of apple isotherms at 32 and 40 °C for a _w > 0.85 has been previously reported for foods with high sugar content, and it can be attributed to the increase with temperature of the solubility of simple sugars (Kansci et al. 2008). The sorption moisture isotherms for apple and mango at 25 °C were similar to those previously reported (Djendoubi Mrad et al. 2012a; Moreira et al. 2009), and showed a similar behavior as other fruits (guava, pineapple) with high sugar content (Goula et al. 2008; Kansci et al. 2008).

Mathematical modeling of sorption moisture isotherms

All tested models (Eqs. 1–4) adequately fitted moisture sorption data, as noted by R ² which ranged from 0.974 to 1.0 for all datasets (Table 2). Information theory criteria showed that the GAB equation outperformed all other models despite having one more parameter. The GAB model registered ΔAIC = 0 for all apple and banana isotherms, whereas moderate supporting evidence (ΔAIC > 2) was recorded only for the 40 °C mango isotherm (ΔAIC = 2.5; Table 2). The Henderson equation followed the GAB model as the best model alternative by achieving ΔAIC ~ 2 for all mango isotherms, and at 40 °C for apple and banana. Even though the BET and Iglesias–Chirife models had R ² > 0.97, information theory criteria only occasionally indicated moderate evidence of support for these two models (Table 2).

Table 2.

Statistical summary of model fit to moisture sorption isotherms of fruits and parameter estimates of the GAB and BET models^a,b

T (°C)	Statistical criteria	Apple				Banana				Mango
		GAB	BET	Henderson	Iglesias–Chirife	GAB	BET	Henderson	Iglesias–Chirife	GAB	BET	Henderson	Iglesias–Chirife
25	R 2	0.998	0.995	0.988	0.992	0.999	0.996	0.995	0.993	0.993	0.980	0.992	0.979
	SSE	15.4	37.1	110.2	61.1	6.6	25.1	46.3	43.8	45.0	117.9	48.8	126.2
	ℓ	− 2.1	− 6.6	− 12.0	− 9.1	2.1	− 4.6	− 7.7	− 7.4	− 7.5	− 12.3	− 7.9	− 12.7
	AIC	12.3	19.1	30.0	24.1	3.8	15.2	21.3	20.8	23.0	30.7	21.9	31.4
	ΔAIC i	0.0*	6.8	17.7	11.8	0.0*	11.4	17.5	17.0	1.2*	8.8	0.0*	9.5
	X m	11.8 ± 2.7	10.0 ± 0.0			10.8 ± 0.5	9.9 ± 0.2			24.8 ± 4.8	4.1 ± 0.4
	C	1.572 ± 0.667	4.989 ± 0.182			4.433 ± 0.692	1.913 ± 0.278			0.321 ± 0.077	9.246 ± 3.776
	K	0.972 ± 0.021				0.983 ± 0.005				0.907 ± 0.013
32	R 2	0.999	0.987	0.996	0.980	1.000	0.989	0.995	0.983	0.994	0.991	0.993	0.990
	SSE	2.7	64.5	25.9	93.4	0.0	53.4	29.5	78.8	45.7	63.2	56.7	69.9
	ℓ	6.6	− 9.3	− 4.8	− 11.2	57.4	− 8.4	− 5.4	− 10.3	− 7.6	− 9.2	− 8.7	− 9.7
	AIC	− 5.2	24.6	15.5	28.3	− 106.9	22.8	16.8	26.6	23.2	24.4	23.3	25.4
	ΔAIC i	0.0*	29.8	20.7	33.5	0.0*	129.6	123.7	133.5	0.0*	1.2*	0.2*	2.2+
	X m	10.0 ± 0.8	10.3 ± 0.6c			12.1 ± 0.8	9.1 ± 0.5b			19.1 ± 1.6	4.5 ± 0.1b
	C	2.36 ± 0.617	2.465 ± 0.507c			1.950 ± 0.144	2.585 ± 0.630b			0.306 ± 0.036	6.671 ± 3.316b
	K	0.959 ± 0.008				0.947 ± 0.014				0.953 ± 0.007
40	R 2	0.993	0.991	0.991	0.989	0.997	0.981	0.996	0.974	0.992	0.987	0.993	0.987
	SSE	38.8	52.2	63.6	66.6	13.0	93.9	20.2	129.7	40.8	65.7	38.7	66.5
	ℓ	− 6.8	− 8.3	− 9.3	− 9.5	− 1.3	− 11.2	− 3.5	− 12.8	− 7.0	− 9.4	− 6.8	− 9.5
	AIC	21.6	22.5	24.5	25.0	10.6	28.4	13.0	31.6	22.1	24.8	19.5	24.9
	ΔAIC i	0.0*	1.0*	2.9+	3.4+	0.0*	17.8	2.4+	21.0	2.5+	5.3	0.0*	5.4
	X m	16.6 ± 1.9	7.9 ± 0.4c			11.3 ± 1.4	10.7 ± 0.3b			15.0 ± 2.8	3.2 ± 0.2b
	C	0.969 ± 0.188	2.552 ± 0.239c			1.332 ± 0.390	1.704 ± 0.246b			0.409 ± 0.081	15.273 ± 5.669b
	K	0.915 ± 0.015				0.975 ± 0.014				0.955 ± 0.015

^aSubstantial evidence supporting model fit (ΔAIC ≤ 2), ⁺Moderate evidence supporting model fit (2 < ΔAIC ≤ 4)

^b X _m = monolayer moisture content (g water/100 g dry solids); C = constant related to the heat of sorption of the monolayer region; K = constant related to the heat of sorption of the multilayer region

^cDetermined by fitting moisture sorption isotherm data in the 0.11 − 0.52 a _w range

Parameter estimates of the GAB model showed similarities between apple and banana samples (Table 2). No clear temperature effect was observed except for the parameter C of banana and X _m for mango (Table 2), which can be attributed to the isotherm overlaying observed in Fig. 1. The mango X _m value decreased from 24.8 ± 4.8 to 15.0 ± 2.8 (g water/100 g dry solids) as temperature increased from 25 to 40 °C. The experimental mango moisture content at a _w = 0.11 for every temperature level (X ~ 1.8–2.5 g water/100 g dry solid; Fig. 1) was significantly lower than X _m values shown in Table 2, suggesting that the X _m values can be related to the GAB model fit but have no physical interpretation. This statement is further supported by analyzing the K and C parameters of mango samples, which consistently had lower numerical values when compared to parameter estimates obtained for the other fruits (Table 2), and despite the similar shape exhibited by the moisture sorption isotherms of all fruits (Fig. 1). A similar conclusion may be drawn for the set of GAB parameters of apple at 40 °C, where X _m = 16.6 ± 1.9 (g water/100 g dry solids) was observed.

The parameter X _m is crucial in drying process design as it indicates the moisture content at which further application of heat will result in a minor moisture removal since water in the monolayer region is strongly bound to the food matrix. The GAB model can be considered as an extension of the BET model in which the constant K is included to describe the heat of sorption in the multilayer water region, but both models have a similar theoretical basis to describe X _m and the heat of sorption of water (C) in the monolayer region. The BET model is better suited to describe moisture sorption isotherms in the 0.11–0.52 a _w range, and parameter estimates for all fruits in this water activity range are shown in Table 2. Similarities between the BET and GAB X _m values were observed for banana at all temperatures and apple at 25 and 32 °C with BET X _m values ranging from 9.1 to 10.7 (g water/100 g dry solids). Significantly lower BET X _m values were obtained for mango (3.2–4.5 g water/100 g dry solids), which can be attributed to its lower reducing sugar content (24.6%) when compared to apple (57.8%) and banana (51.8%; Table 1). Reducing sugars have lower water sorption capacity and a higher amount of energy is required to keep water molecules bound as reflected in large BET C estimates in mango (C = 6.7–15.2) contrasting those for apple (C = 2.4–4.9) and banana (C = 1.7–2.5; Table 2).

Glass transition temperature (T_g) and critical moisture content (X_c)

In the 0.11 to 0.71 a _w range, banana showed the highest T _g values (Fig. 2a, b). As previously stated, food composition affects glass transition and long chain polymers like starch may increase T _g. Thus, values observed in this study are consistent with the composition of banana (Table 1), which presented the highest starch content (13.1 ± 0.6%) among the fruits evaluated in this study. Mango presented a slightly lower starch content (7.4 ± 0.2%) but non-reducing sugars with low T _g value (Syamaladevi et al. 2009) represented 53.2% of its total weight.

Fig. 2.

Glass transition temperature (T _g) at different a _w. a Gordon–Taylor, b Khalloufi–Maslouhi–Ratti model fit, and c estimation example of the glass transition temperature (T _g) limited critical moisture content for dried banana showing (T _g) values (open circle) and the moisture sorption isotherm at 25 °C (triangle)

The GT model adequately fitted T _g as a function of X for apple and banana (R ² = 0.997; Table 3). However, the GT model yielded R ² = 0.834 in the case of mango, a large deviation in the T _g fit was observed around a _w = 0.2–0.5, and the prediction line displayed a downward concavity shape (Fig. 2a, b). This behavior contrasts with the trend that the GT model predicted for apple and banana, where T _g seems to rapidly increase as a _w approximates zero (Fig. 2a, b). Nevertheless, the mango T _g was just 10 K lower than for apple (Table 3). Experimental T _g values and GT model T _gs parameter estimates of apple and banana were in accordance with those reported by other authors (Bai et al. 2001; Moraga et al. 2011), whereas no references were found for mango. The KMR predictions yielded fairly straight lines between T _g and a _w (R ² > 0.996), but it requires a large number of parameters (p = 5). Furthermore, the extrapolation towards a _w = 0 of the KMR model would indicate that T _g increases at a much slower rate than the prediction by the GT model (Fig. 2c). In fact, no X _c values could be calculated for apple with the KMR model since T _g = T _storage only when a _w < 0. In the case of banana and mango, both models predicted approximately the same X _c for T _storage = 25 °C (Table 3). At T _storage = 32 °C, the mango X _c = 1.536 (g water/100 g dry solids) predicted by the GT model was higher than the value obtained at 25 °C (X _c = 0.834 g water/100 g dry solids), although this may reflect the poor fit for the mango data (R ² = 0.834). Finally, T _g-limited X _c values for the three dried fruits in this study (3.0–9.3 g water/100 g dry solids, Table 3) were lower than the X _m values obtained with the GAB (apple and banana) and BET (mango) equations (Table 2), suggesting that the plasticizing effect of moisture dominates the quality degradation of the fruits included in this study is dominated by the plasticizing effect of moisture. In mango, glass transition may have already started at 25 °C, since both X _m (3.2–4.5 g/100 g dry solids) and X _c (~ 0.8 g/100 g dry solids) values were lower than the initial moisture content (4.4 g/100 g dry solids). The GT model indicated that mango should be stored under refrigeration (T < 2.7 °C) to preserve its crunchiness.

Table 3.

Gordon–Taylor and Khalloufi–Maslouhi–Ratti parameter estimates, and critical moisture content (X _c) of fruits at 25 and 32 °C

Model	Parameter	Apple	Banana	Mango
Gordon–Taylor	T gs (K)	315.7 ± 0.3	326.8 ± 2.6	305.3 ± 1.5
	k	4.423 ± 0.048	5.032 ± 0.144	5.386 ± 0.188
	R 2	0.997 ± 0.000	0.997 ± 0.001	0.834 ± 0.010
	X c, 25 °C	2.481 ± 0.027	3.553 ± 0.250	0.824 ± 0.147
	X c, 32 °C	ND	2.707 ± 0.228	1.536 ± 0.075
Khalloufi–Maslouhi–Ratti	C	10.542 ± 0.033	10.210 ± 0.344	10.602 ± 0.028
	D	10.913 ± 0.002	10.812 ± 0.157	10.942 ± 0.005
	E	295.1 ± 1.9	317.0 ± 5.8	309.8 ± 1.5
	c	0.419 ± 0.054	0.628 ± 0.094	0.340 ± 0.042
	d	0.326 ± 0.048	0.270 ± 0.094	0.387 ± 0.030
	R 2	0.997 ± 0.001	0.996 ± 0.001	0.997 ± 0.001
	X c, 25 °C	ND	3.354 ± 0.301	0.800 ± 0.061
	X c, 32 °C	ND	2.260 ± 0.564	0.219 ± 0.046

ND not determined

Conclusion

The sorption moisture isotherms were determined by the static gravimetric method for mango, apple and banana at 25, 32 and 40 °C. Although all isotherm models evaluated yielded R ² > 0.97, the GAB model was the best alternative as supported by information theory criteria showing substantial evidence supporting model fit (ΔAIC = 0–2) in all but one isotherm case (40 °C, mango). The moisture content level and the starch and reducing sugar content affected the T _g values of the dehydrated fruits in this study, yielding higher values for banana followed by mango and apple. For the fruits and temperature levels included in this study, X _c values were always lower than the GAB/BET X _m values, indicating that the moisture plasticizing effect will determine the shelf life of dried apple, banana and mango. This information can be used to establish the desired dehydration process and storage conditions maximizing the stability of these products.

List of symbols

AIC

Akaike Information Criteria

a

Constant in Khalloufi–Maslouhi–Ratti equation

a_w

Water activity

b

Constant in Khalloufi–Maslouhi–Ratti equation

BET

Brunauer–Emmett–Teller sorption isotherm model

c

Constant in Khalloufi–Maslouhi–Ratti equation

C

Constant related to the heat of sorption of the monolayer region, BET and GAB models

DSC

Differential scanning calorimetry

GAB

Guggenheim–Anderson–de Boer sorption isotherm model

GT

Gordon–Taylor glass transition temperature model

K

Constant related to the heat of sorption of the multilayer region, GAB model

KMR

Khalloufi–Maslouhi–Ratti glass transition temperature model

k

Constant relating the ratio between the change of heat capacity of water and dry solids, Gordon–Taylor model

ℓ

Maximum log-likelihood estimate

n

Number of experimental data

p

Number of model parameters

R²

Coefficient of determination

T_g

Glass transition temperature [=] °C, K

T_g,onset

Onset glass transition temperature [=] °C, K

T_gs

Glass transition temperature of solids, Gordon–Taylor model [=] °C, K

T_storage

Storage temperature [=] °C, K

T_gw

Glass transition temperature of water, Gordon–Taylor model [=] °C, K

W_s

Solids weight fraction, Gordon–Taylor model

W_w

Water weight fraction, Gordon–Taylor model

X

Moisture content [=] g water/100 g dry solids

X_c

Critical moisture content [=] g water/100 g dry solids

X_m

Monolayer moisture content, BET and GAB models [=] g water/100 g dry solids

y_i

Experimental value

${\widehat{y}}_i$

Estimated value

Greek letters

α

Constant in Khalloufi–Maslouhi–Ratti equation

β

Constant in Khalloufi–Maslouhi–Ratti equation

ΔAIC

AIC differences indicating strong (0 < ΔAIC ≤ 2), moderate (2 < ΔAIC ≤ 4) or slight (ΔAIC > 4) support of model fit

${\widehat{\mathit{\sigma }}}^2$

Variance estimate