Physical and moisture sorption thermodynamic properties of Sukkari date (Phoenix dactylifera L.) powder

ABSTRACT

Physical properties of Sukkari date powder (SDP) at different particle sizes, namely, moisture content, water activity, tapped and bulk densities, compressibility index, Hausner ratio, water absorption, and solubility indices, swelling capacity, and color parameters were experimentally determined. The SDP moisture sorption experiments were conducted using a dynamic vapor sorption instrument in the relative humidity range 10%–90% at 20, 40, and 60^°C. Among the ten tested sorption models, the GAB and modified GAB models best fitted SDP sorption data. The monolayer moisture content decreased with increasing temperature. The differential enthalpy and entropy, and net integral enthalpy and entropy decreased consistently with increasing moisture content. The linear relationship between differential enthalpy and entropy confirmed the applicability of the compensation theory. The estimated values of the isokinetic and harmonic temperatures and the Gibbs free energy change revealed that the sorption process is non-spontaneous and enthalpy driven.

RESUMEN

En el presente estudio se analizaron experimentalmente las propiedades físicas del polvo del dátil Sukkari (SDP) en diferentes tamaños de partículas; las propiedades analizadas incluyen: contenido de humedad, actividad acuosa, densidad aparente y densidad compactada, índice de compresibilidad, ratio de Hausner, absorción de agua e índices de solubilidad, capacidad de hinchamiento y parámetros de color. Los experimentos de sorción de humedad SDP se llevaron a cabo utilizando un instrumento de sorción de vapor dinámico en el rango de 10% a 90% de humedad relativa y a temperaturas de 20, 40 y 60°C. Entre los 10 modelos de sorción probados, se constató que el modelo GAB y los modelos GAB modificados se adaptaron mejor a los datos de sorción SDP. El contenido de humedad de la monocapa disminuyó a medida que se elevó la temperatura. La entalpía y la entropía diferenciales, así como la entalpía y la entropía integrales netas, disminuyeron consistentemente al aumentar el contenido de humedad. La relación lineal entre la entalpía y la entropía diferenciales confirmó la aplicabilidad de la teoría de la compensación. Los valores estimados para las temperaturas isocinéticas y armónicas y el cambio de energía libre de Gibbs dieron cuenta de que el proceso de sorción no es espontáneo y es impulsado por la entalpía.

KEYWORDS:

• Date powder
• particle size
• physical properties
• temperature
• sorption models
• sorption properties

PALABRAS CLAVE:

• polvo de dátil
• tamaño de partícula
• propiedades físicas
• temperatura
• modelos de sorción
• propiedades de sorción

1. Introduction

Dates, the fruit of the date palm tree (Phoenix dactylifera L.), is a commercially valuable crop in several regions of the world. The fruit is a portion of nourishing natural food. The Sukkari date cultivar is the second widely produced and the most popular date cultivar in the Kingdom of Saudi Arabia. The relatively high sucrose content in Sukkari dates facilitates the drying and consequently conversion into date powder (Zhang et al., 2015).

Production of free-flow powder from dates is highly desirable as a stable and convenient nutritious ingredient for use in several food manufacturing applications such as extruded food products, dairy products, and several bakery formulations. Several drying methods were used to produce date powder including, freeze-drying, spray drying, drum drying, vacuum drying, and conventional oven drying (Farahnaky et al., 2016; Manickavasagan et al., 2015; Sablani et al., 2008; Sahari et al., 2008; Seerangurayar et al., 2017). Measurement of powder’s physical properties is essential in characterizing their flow properties and, consequently, their behavior during storage, handling, and processing (Barbosa-Cánovas et al., 2005). Notable physical features of powders include bulk and tapped density, moisture content and water activity, water absorption, water solubility indices, swelling capacity and flowability, and cohesiveness properties. Several types of research reported on the physical properties of food and date powders (Borchani et al., 2012; Farahnaky et al., 2016; Koc et al., 2011, 2014; Sablani et al., 2008; Seerangurayar et al., 2017).

Subjecting a food material to different temperatures and humidity allows determination of the moisture sorption thermodynamic properties from moisture sorption isotherms. The major moisture sorption thermodynamic properties are the differential enthalpy (q_st) and entropy (S_d), total heat of sorption (Q_st), and net integral enthalpy (Q_in) and entropy (S_in) (Al-Mahasneh et al., 2010; Kaya & Kahyaoglu, 2005).

Adsorption of moisture by the solid phase releases energy known as the heat of adsorption. The net isosteric heat of sorption quantifies the binding strength of water to solid particles. It is also a measure of material stability during storage (Fasina et al., 1997). Binding or repulsive forces and the number of available sorption sites in the sorption system relate to the differential entropy (Togrul & Arsalan, 2006). Pascual-Pineda et al. (2014) reported that the linear relationship between differential enthalpy and entropy could explain the physicochemical interaction between water and food.

During moisture adsorption, spreading pressure lower the liquid surface tension as a result of the difference in the energy of the liquid and solid phases. The net integral enthalpy (Q_in) is a measure of the binding strength of water molecules to food particles, and the water molecules movement randomness and disorder is measured by the net integral entropy (S_in) (Alpizar-Reyes et al., 2017; Moreira et al., 2008).

Physical and moisture sorption properties are essential for the characterization of packaging requirements, suitable storage conditions and stability, and shelf life of date powder, in addition to the design of handling and processing unit operations. Hence, this work objectives were to experimentally determine physical properties of the Sukkari date powder (SDP) at different particle sizes, construct the moisture sorption isotherms at three temperatures 20, 40, and 60ºC in the equilibrium relative humidity range 10%–90% and determine monolayer moisture content, fit temperature-dependent moisture sorption models to experimental data, and evaluate the thermodynamic properties.

2. Materials and methods

2.1. Powder preparation

A local date factory provided the Sukkari date cultivar at Tamr stage of maturity (fully ripe, reduced moisture, edible) and an average moisture content of 25 ± 1.3 (kg water/kg date flesh). It was sorted, washed, and dried at room temperature (23ºC). The fruits were sliced to remove the seeds, then minced with a mechanical mincer (Motore Asincrono, Italy). Produced date paste was cut into thin slices and dried in a vacuum drying oven (Vacutherm model VT 6025, Heraeus Instrument, D- 63450, Hanauer, Germany) at 60 ± 1ºC until attaining constant weight. The dried date paste slices were then ground in a grinding machine (Gold mill, GM-203, Korea) to produce Sukkari date powder (SDP). The dried powder was immediately transferred into tightly closed glass jars and stored in a refrigerator at 5 ± 0.5ºC for further analysis.

2.2. Particle size distribution

The weighted mean diameter of SDP particles as well as size distributions were determined using a vibratory sieve shaker (Analysette 3 Spartan model, Fritsch GmbH, Germany) with a series of nine sieves. The sieve sizes were 2000, 1000, 500, 355, 250, 180, 125, 90, 63 μm mesh, and a pan. A known amount of date powder was fed on top sieve and operated for 5 min, followed by recording the weight of samples retained on each sieve. Experiments were carried out in triplicate. The categories of particle size distributions were; coarse >355 μm, moderately fine (355–180 μm), fine (<180–125 mm), and very fine (<125 μm). Most of the Sukkari date powder (81.5%) was moderately fine particle size (355–180 μm). Figure 1 illustrates a digital image of the whole date fruit, dried date paste slices, and the Sukkari date powder (SDP) at various particle sizes categories

Figure 1. A digital image of: (a) whole Sukkari date fruit (b) dried date paste slices (c) coarse Sukkari date powder (SDP) (d) moderately fine SDP (e) fine SDP (f) very fine SDP.

Figura 1. Imagen digital de (a) fruta entera del dátil Sukkari (b) rebanadas de pasta de dátil seca (c) polvo de dátil Sukkari grueso (SDP) (d) SDP moderadamente fino (e) SDP fino (f) SDP muy fino

2.3. Moisture content and water activity

The SDP moisture content was determined using a vacuum oven (Vacutherm model VT 6025, Heraeus Instrument, D- 63450, Hanauer, Germany) at 60ºC. An Aqualab instrument (Model CX-2T, readability 1 mg, Decagon Devices Inc., Washington, USA) was used to measure water activity at 23ºC.

2.4. Bulk and tapped density

A tapped density instrument (Labhut AT 2000 Tap Density Tester (atlas), Labhut, UK) was used to measure the SDP bulk and tapped densities. The unsettled volume of a 100 ± 0.1 g of date powder in a graduated cylinder determined the bulk density (BD). The tapped volume of the same sample at 250 ± 15 taps per minute with a 3 ± 0.2 mm drop height until no significant difference in the volume (typically 2%), was determined. Tapped density (TD) is the sample mass per tapped volume.

2.5. Carr index and Hausner ratio

The compressibility index (CI %) -also known as Carr index (Carr, 1965)-, and Hausner ratio (HR) were evaluated from the bulk and tapped densities (BD and TD) of the SDP as: CI = ((TD-BD)/TD) X100% and HR = TD/BD, respectively.

2.6. Water absorption and solubility indices

The procedure of De Mesa et al. (2009) with slight modification was used to determine the water absorption (WAI) and solubility (WSI) indices. One gram of SDP was added to 10 ml of distilled water in a 50 ml centrifuge tube and stirred with vortex, then left for 30 min at 20ºC, and centrifuged at 72576 RFC (g force) for 15 min. The supernatant was then carefully separated and dried overnight at 105 °C. WAI is the weight of the remaining gel as grams of gel per gram of original dry powder. WSI is the percentage of the mass of solids recovered from dried supernatant divided by the mass of the original dry powder.

2.7. Swelling capacity

The procedure of Robertson et al. (2000), with some modification, was followed to determine the SDP swelling capacity (SC). Mass of 0.2 g of date powder was mixed with 10 ml distilled water and left for 18 h at 25ºC to hydrate. The final sample volume was a measure of the SC (ml/g).

2.8. Color evaluation

Date powder color parameters L*, a*, and b* of the CIE system were measured using Color Flex (Hunter Lab-Color Flex, Hunter Associates Laboratory, Inc-Reston, US). A white tile standard was the reference color. Other color parameters were chroma (C*), hue angle (H^o), and browning index (BI) following Pathare et al. (2013).

2.9. Moisture sorption isotherms and models

The moderately fine powder (particle size 355–180 µm) was selected for the moisture sorption experiments because it represented 81.5% of the produced date powder mass. The adsorption of moisture at a different relative humidity (10–90%) applied in steps of 10%, and temperatures (20, 40 and 60ºC) was measured using a dynamic vapor sorption instrument (Aquadyne DVS, Quantachrome Instruments, Boynton Beach, FL, USA). Its two ultrasensitive microbalances can detect changes in mass during the adsorption process. The instrument was calibrated using dry microcrystalline cellulose (CRM #302) powder. In the experiment, the two ultrasensitive microbalances were used to place the pre-dried Sukkari date powder (SDP) samples (54 ± 1 mg each), and bone dried through purging. Data were, collected for mass, temperature, and humidity at 30s time intervals. Change in the mass of less than 0.001 mg/min, implied the achievement of equilibrium.

Ten popular moisture sorption models as shown in Equations 1(1) $\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\left(\mathrm{C}/\mathrm{T}\right)\mathrm{B}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\left(\mathrm{C}/\mathrm{T}\right)\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)}$(1) –10(10) $\mathrm{C}\mathrm{a}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{X}=\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{A}+\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)$(10) , were used to fit the experimental moisture adsorption data and evaluate their adequacy (Muzaffar & Kumar, 2016; Udomkun et al., 2015). The non-linear regression procedure (IBM SPSS Statistics, version 20, USA) was applied to fit moisture sorption equations to experimental data. The coefficient of determination (R²), the root means square error (RMSE), and the mean absolute percentage error (PE) were used to evaluate the goodness of fit and confirm the best model describing the sorption behavior. Estimation of the monolayer moisture content and the solution of the spreading pressure equation were carried out using the original GAB sorption model (Equation 5(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5) ).

(1) $\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\left(\mathrm{C}/\mathrm{T}\right)\mathrm{B}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\left(\mathrm{C}/\mathrm{T}\right)\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)}$(1)

(2) $\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{O}\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{X}=\left(\mathrm{A}+\mathrm{B}\mathrm{T}\right){\left[\frac{{\mathrm{a}}_{\mathrm{w}}}{\left(1-{\mathrm{a}}_{\mathrm{w}}\right)}\right]}^{1/\mathrm{C}}$(2)

(3) $\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{y}\mathrm{X}={\left[-\frac{\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{A}+\mathrm{B}\mathrm{T}\right)}{\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{w}}}\right]}^{1/\mathrm{C}}$(3)

(4) $\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{B}\mathrm{E}\mathrm{T}\mathrm{X}=\frac{\left(\mathrm{A}+\mathrm{B}\mathrm{T}\right)\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-{\mathrm{a}}_{\mathrm{w}}\right)\left(1-{\mathrm{a}}_{\mathrm{w}}+\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(4)

(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5)

(6) $\mathrm{B}\mathrm{E}\mathrm{T}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}{\mathrm{a}}_{\mathrm{w}}}{\left(1-{\mathrm{a}}_{\mathrm{w}}\right)\left(1-{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)}$(6)

(7) $\mathrm{O}\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{X}=A{\left[\frac{{\mathrm{a}}_{\mathrm{w}}}{\left(1-{\mathrm{a}}_{\mathrm{w}}\right)}\right]}^{\mathrm{B}}$(7)

(8) $\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e}\mathrm{y}\mathrm{X}={\left[-\frac{\mathrm{A}}{\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{w}}}\right]}^{1/\mathrm{B}}$(8)

(9) $\mathrm{I}\mathrm{g}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{a}\mathrm{s}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{C}\mathrm{h}\mathrm{i}\mathrm{r}\mathrm{i}\mathrm{f}\mathrm{e}\mathrm{X}=A+B\left[\frac{{\mathrm{a}}_{\mathrm{w}}}{\left(1-{\mathrm{a}}_{\mathrm{w}}\right)}\right]$(9)

(10) $\mathrm{C}\mathrm{a}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{X}=\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{A}+\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)$(10)

where X is the dry basis moisture content, a_w is water activity, T is temperature, A, B and C are constants.

2.10. Differential enthalpy and entropy

The temperature dependence of the moisture sorption isotherms allows the derivation of the net isosteric heat of sorption or differential enthalpy (q_st) as a differential molar quantity. The summation of the water heat of vaporization or condensation (L_w) and the q_st define the total heat of sorption (Q_st) (McLaughlin & Magee, 1998). Based on thermodynamic principles, the Clausius-Clapeyron Equation (11)(11) ${\mathrm{Q}}_{\mathrm{s}\mathrm{t}}-{\mathrm{L}}_{\mathrm{w}}={\mathrm{q}}_{\mathrm{s}\mathrm{t}}=-\mathrm{R}{\left(\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(\frac{1}{{\mathrm{T}}_{\mathrm{a}}}\right)}\right)}_{\mathrm{X}}$(11) expresses the relationship between the effect of temperature (T_a) on water activity (a_w) at a constant dry basis moisture content (X) (Noshad et al., 2012):

(11) ${\mathrm{Q}}_{\mathrm{s}\mathrm{t}}-{\mathrm{L}}_{\mathrm{w}}={\mathrm{q}}_{\mathrm{s}\mathrm{t}}=-\mathrm{R}{\left(\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(\frac{1}{{\mathrm{T}}_{\mathrm{a}}}\right)}\right)}_{\mathrm{X}}$(11)

where R is the universal gas constant (8.314 J/mol K).

If (q_st) is assumed as independent of temperature, the integration of Equation (11)(11) ${\mathrm{Q}}_{\mathrm{s}\mathrm{t}}-{\mathrm{L}}_{\mathrm{w}}={\mathrm{q}}_{\mathrm{s}\mathrm{t}}=-\mathrm{R}{\left(\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(\frac{1}{{\mathrm{T}}_{\mathrm{a}}}\right)}\right)}_{\mathrm{X}}$(11) gives the following equation (Bahloul et al., 2008; Noshad et al., 2012):

(12) ${\left(\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{w}}\right)}_{\mathrm{X}}=-\frac{q_{st}}{\mathrm{R}{\mathrm{T}}_{\mathrm{a}}}+\frac{{\mathrm{S}}_{\mathrm{d}}}{\mathrm{R}}$(12)

where S_d is the differential entropy of sorption (J/mol K).

Equation (12)(12) ${\left(\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{w}}\right)}_{\mathrm{X}}=-\frac{q_{st}}{\mathrm{R}{\mathrm{T}}_{\mathrm{a}}}+\frac{{\mathrm{S}}_{\mathrm{d}}}{\mathrm{R}}$(12) readily allows determination of q_st and S_d from its slope and intercept, respectively.

2.11. Enthalpy-entropy compensation theory

Based on the compensation theory, a linear relationship exists between (q_st) and (S_d) for a specific reaction as shown in Equation 13(13) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}={\mathrm{T}}_{\beta }{\mathrm{S}}_{\mathrm{d}}+\mathrm{\Delta }{\mathrm{G}}_{\beta }$(13) (Simal et al., 2007):

(13) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}={\mathrm{T}}_{\beta }{\mathrm{S}}_{\mathrm{d}}+\mathrm{\Delta }{\mathrm{G}}_{\beta }$(13)

where T_β and ∆G_β are the isokinetic temperature, and the Gibbs free energy change, respectively. Water sorption is considered a spontaneous process if the Gibbs free energy change is negative (-∆G_β) and a non-spontaneous process if it is positive (+∆G_β) (Simal et al., 2007). Plotting q_st versus S_d and applying linear regression allows the calculation of T_β and ∆G_β.

A parameter called harmonic mean temperature T_hm (K) has been used to confirm the applicability of the compensation theory. Enthalpy–entropy compensation requires that T_β ≠ T_hm. If T_β > T_hm, the process is entropy-driven, otherwise it is not (McMinn et al., 2007). The following equation is used to estimate T_hm:

(14) ${\mathrm{T}}_{\mathrm{h}\mathrm{m}}=\left(\frac{\mathrm{n}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}(1/{\mathrm{T}}_{\mathrm{a}})}\right)$(14)

where n is the number of isotherms, and I the number of terms.

2.12. Net integral enthalpy and entropy

Determination of the net integral enthalpy (Q_in) is dependent on the determination of the spreading pressure (Φ) known as the surface potential representing the surface excess free energy that keeps the surface from spreading, and defined by the following equation (Moreira et al., 2008):

(15) $\mathrm{\Phi }=\frac{{\mathrm{K}}_{\mathrm{B}}\mathrm{T}}{{\mathrm{A}}_{\mathrm{m}}}\underset{0}{\overset{{\mathrm{a}}_{\mathrm{w}}}{\int }}\frac{\mathrm{X}}{{\mathrm{X}}_{\mathrm{m}}{\mathrm{a}}_{\mathrm{w}}}\mathrm{d}\left({\mathrm{a}}_{\mathrm{w}}\right)$(15)

where K_B is Boltzman constant, 1.38 × 10⁻²³ (J/K), A_m is the surface area of the water molecule, 1.06 × 10⁻¹⁹ (m²), and X_m is the monolayer moisture content (kg water/kg dm).

Substitution of the GAB sorption model (Equation 5(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5) ) into Equation (15)(15) $\mathrm{\Phi }=\frac{{\mathrm{K}}_{\mathrm{B}}\mathrm{T}}{{\mathrm{A}}_{\mathrm{m}}}\underset{0}{\overset{{\mathrm{a}}_{\mathrm{w}}}{\int }}\frac{\mathrm{X}}{{\mathrm{X}}_{\mathrm{m}}{\mathrm{a}}_{\mathrm{w}}}\mathrm{d}\left({\mathrm{a}}_{\mathrm{w}}\right)$(15) moreover, integrating results in the following expression for estimation of spreading pressure in the range a_w = 0.05–1.0 (Lago et al., 2013; Tao et al., 2018):

(16) $\mathrm{\Phi }=\frac{{\mathrm{K}}_{\mathrm{B}}\mathrm{T}}{{\mathrm{A}}_{\mathrm{m}}}\mathrm{l}\mathrm{n}\left[\frac{\left(1+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}-\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}{\left(1-\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}\right]$(16)

where B and C are parameters of the GAB sorption model (Equation 5(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5) ). The net integral enthalpy is defined by Equation 17(17) ${\mathrm{Q}}_{\mathrm{i}\mathrm{n}}=-\mathrm{R}{\left[\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(1/{\mathrm{T}}_{\mathrm{a}}\right)}\right]}_{\mathrm{\Phi }}$(17) at constant spreading pressure. Plotting ln(a_w) against 1/T_a at constant Φ allows determination of Q_in (Fasina et al., 1999).

(17) ${\mathrm{Q}}_{\mathrm{i}\mathrm{n}}=-\mathrm{R}{\left[\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(1/{\mathrm{T}}_{\mathrm{a}}\right)}\right]}_{\mathrm{\Phi }}$(17)

The integral entropy S_in could be related to entrapment of water in microcapillaries and matrix collapse of the SDP. Equation (18)(18) ${\mathrm{S}}_{\mathrm{i}\mathrm{n}}=-\frac{{\mathrm{Q}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{T}}_{\mathrm{a}}}-\mathrm{R}ln{\left({\mathrm{a}}_{\mathrm{w}}\right)}^{\ast }$(18) below was used to calculate the integral entropy S_in (Tao et al., 2018):

(18) ${\mathrm{S}}_{\mathrm{i}\mathrm{n}}=-\frac{{\mathrm{Q}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{T}}_{\mathrm{a}}}-\mathrm{R}ln{\left({\mathrm{a}}_{\mathrm{w}}\right)}^{\ast }$(18)

where ${\left(a_w\right)}^{\ast }$represents the geometric mean water activity. Obtained values of S_in were then plotted against moisture content.

2.13. Statistical analysis

Analysis of variance (ANOVA) and Duncan’s multiple range test (α = 0.05) was used to determine the difference between means of the date powder physical properties using the SPSS statistics for windows (IBM SPSS Statistics, version 20, USA).

3. Results and discussion

3.1. Physical properties

Figure 2 shows the size distribution of SDP as a cumulative mass percentage passing and mass percentage retained as a function of particle size. About 81.5% of the date powder produced was moderately fine particle sizes (355–180 μm) and, 8.6%, 7.3% and, 1.4% were coarse (>355 μm), fine (<180–125 μm) and very-fine (<125 μm) particle sizes, respectively.

Figure 2. Cumulative mass percentage passing through sieves and mass percentage retained versus particle size of SDP.

Figura 2. Porcentaje de masa acumulada que pasa a través de tamices y porcentaje de masa retenido versus tamaño de partícula de SDP

Table 1 shows the physical properties of SDP at different particle sizes. The bulk density (BD) and tapped density (TD) are both essential physical properties for characterization, handling, and processing of powder systems. Bulk density values were in the range 623.68–634.97 kg/m³, with no significant differences (P > .05) among all particle size categories of the SDP. The tapped density (TD) varied in the range 831.93–901.77 kg/m³ with the highest value (901.77 kg/m³) attained by the fine particles (<180–125 μm) and the lowest value (831.93 kg/m³) by the coarse particles (>355 μm). No significant differences (P > .05) were observed between coarse and moderately fine particles, and between fine and very fine particles. These results were within the ranges obtained for pitaya, pineapple, mango, and guava raw fruit powders (Saifullah et al., 2016).

Table 1. Physical properties of SDP at different particle sizes.

Tabla 1. Propiedades físicas de SDP a diferentes tamaños de partículas

		Particle size
Physical Property		Coarse (>355555μm)	Moderately fine(355-180555μm)	Fine (<180-125 555μm)	Very fine (<125 555μm)
BD (kg/m^3)		627.67^a ± 3.67	633.00 ^a ± 4.06	634.97 ^a ± 2.66	623.68 ^a ± 26.42
TD (kg/m^3)		831.93 ^b ± 13.08	854.93 ^b ± 16.40	901.77 ^a ± 9.12	892.57 ^a ± 4.71
CI (%)		24.55 ^b ± 0.79	25.95 ^b ± 1.14	29.58 ^a ± 1.00	30.12 ^a ± 3.29
HR		1.32 ^c ± 0.01	1.35 ^b,c ± 0.02	1.42 ^a,b ± 0.02	1.43 ^a ± 0.07
X (% db)		1.97 ^b ± 0.17	2.37 ^b ± 0.08	2.36 ^b ± 0.41	2.93 ^a ± 0.23
aw		0.16 ^b ±0.00	0.16 ^b ± 0.01	0.17 ^b ±0.00	0.22 ^a ±0.04
WAI(g/g)		3.06 ^c ± 0.04	3.31 ^b ± 0.02	3.39 ^a,b ± 0.02	3.74 ^a ± 0.07
WSI(%)		30.24 ^c ± 0.36	33.83 ^c ± 0.48	38.09 ^b ± 0.51	44.1 ^a ± 0.42
SC(ml/g)		2.08 ^c ± 0.46	2.60 ^b ± 1.20	2.88 ^b ± 0.39	3.14 ^a ± 0.87
Colour Parameters	L*	64.56 ^c ± 0.73	64.86 ^c ± 1.39	67.14 ^b ± 0.55	69.26 ^a ± 0.24
	a*	5.06 ^a,b ± 0.31	4.85 ^b,c ± 0.31	5.44 ^a ± 0.09	4.51 ^c ± 0.08
	b*	24.44 ^b ± 0.36	24.71 ^b ± 1.10	26.90 ^a ± 0.16	27.09 ^a ± 0.19
	C*	24.96 ^b ± 0.38	25.18 ^b ± 1.14	27.45 ^a ± 0.17	27.46 ^a ± 0.20
	H^o	78.30 ^b ± 0.65	78.91 ^b ± 0.20	78.58 ^b ± 0.12	80.55 ^a ± 0.10
	BI	52.29 ^b ± 1.50	52.35 ^b ± 1.58	55.95 ^a ± 1.05	53.19 ^b ± 0.75

For each property, values are expressed as means ± standard deviation. Values in the same row having the same letter are not significantly different (P > 0.05) by Duncan tests at a confidence level of 95%.

Para cada propiedad, los valores se expresan como medias ± desviación estándar. Los valores en la misma fila que tienen la misma letra no son significativamente diferentes (P > 0.05), según las pruebas de Duncan a un nivel de confianza del 95%.

The compressibility index (CI) and Hausner ratio (HR) both increased as the particle sizes were decreased and varied in the ranges of 24.15% to 30.12% for CI and 1.32–1.43 for HR. For CI, there was a significant difference (P < .05) as the particle size decreases from moderately fine to very fine. HR at different particle sizes showed no significant differences. The higher the compressibility of a bulk solid, the less flowable it is. CI and HR values for the date powder were comparable to data obtained for pitaya, pineapple, mango, and guava raw fruit powders (Saifullah et al., 2016). The flowability values for both CI and HR are in the ranges classified to be between passable and mediocre flowability powders (Jinapong et al., 2008). The sticky nature of the powder due to its high sugar content affects flowability values.

Among the essential physical properties which may affect flowability, stickiness, quality, and shelf life of powders are moisture content and water activity (Seerangurayar et al., 2017). The moisture content was in the range of 1.97 to 2.41 (% db), and it increased with decreasing particle size with no significant differences (P > .05) among the different particle sizes except for the very fine particle size. The water activity (a_w) was in the range of 0.16–0.22, with no significant differences (P > .05) among different particle sizes. These low values of the moisture content and water activity is an indication of favorable stability of the produced date powder from a biochemical and microbiological standpoint. Watermelon, acai, and Jamun fruit powders showed similar results (Quek et al., 2007; Santhalakshmy et al., 2015; Tonon et al., 2009).

The water absorption index (WAI) varied in the range of 3.06–3.74 g gel/g dry powder for different particle sizes. It increased with decreasing particle size with significant differences (P < .05). The water solubility index (WSI) was in the range of 30.24% to 44.10%, and it increased with decreasing particle size with significant differences between various particle sizes. Results were comparable to those reported for raspberry powders (Si et al., 2016). The property of swelling capacity (SC) indicates to what extent the powder samples swell as water is absorbed. SC spanned in the range 2.08–3.14 ml/g dm and increased with decreasing particle size with no significant differences between particle sizes.

Color is a critical quality factor related directly to the acceptability of food products and is an essential physical property to report for food powders. The lightness (L*) increased with decreasing particle size and was in the range 64.56–69.26. The color parameter a* (greenness–redness) varied in the range 4.51–5.44, with a significant difference between different particle size categories. The parameter b* (blueness–yellowness) showed no significant difference (P > .05) between the different particle sizes and varied in the range 24.44 − 27.09, with very fine particles attaining the highest value.

Aleid et al. (2014), reported comparable values of the color parameters L* and b* for the whole Sukkari date fruit surface; however, a* values were higher. Chroma (C*) values increased with decreasing particle size and was in the range 24.96–27.45 with significant differences between the paired categories coarse and moderate and fine and very fine. Chroma values are a measure of the degree of color saturation and are proportional to the strength of the color, and color intensity perceived by humans is higher at higher values of chroma (Pathare et al., 2013).

The hue angle (H°) refers to the qualitative attribute of color. Accordingly, colors are traditionally defined, as reddish, greenish, and so on. The hue angle (H^o) spanned in the range 78.30–80.55, with the highest value for very fine particle size powder. It defines the difference of a specific color concerning grey color with the same lightness (Pathare et al., 2013). The hue angle range of the date powder represents a yellow hue. The browning index (BI) evaluated the extent of browning (Quintas et al., 2007). In this work, BI values varied in the range 52.29–55.95, with no significant differences (P > .05) among all particle sizes except the fine particle size.

3.2. Moisture sorption isotherms and models

Figure 3 shows the moisture sorption isotherms of SDP at temperatures 20, 40, and 60°C (±0.2). The curves are of type III with a J shape, which, in general, for high sugar food. At constant temperature, moisture adsorption increased with increasing water activity up to a_w = 0.81, then almost coincided after that. The variation of the equilibrium moisture content (EMC) with temperature in the water activity range a_w = 0.8–0.88 was minimal. The date powder absorbed less moisture (0.00 to about 0.17 kg water/kg dm) in the water activity range a_w = 0.1–0.6 and absorbed much higher moisture (0.17 to about 0.88 kg water/kg dm) in the water activity range a_w = 0.6–0.88. Several researchers reported similar results and referred the behavior to the characteristics of high sugar foods, particularly their composition and solubility of sugars (Noshad et al., 2012; Rodriguez-Bernal et al., 2015). Borojo and orange juice powders showed similar results (Rodriguez-Bernal et al., 2015; Sormoli & Langrish, 2015).

Figure 3. Experimental moisture adsorption isotherms of SDP at different temperatures and prediction lines of MGAB model.

Figura 3. Isotermas experimentales de adsorción de humedad de SDP a diferentes temperaturas y líneas de predicción del modelo MGAB

Table 2 lists the constants of the ten tested moisture sorption models and the corresponding statistical parameters. Based on the goodness of fit criteria (the highest R², lowest RMSE, and PE ≤10), the modified GAB (MGAB) model in the temperature range 20–60ºC and the original GAB model at the three temperatures 20, 40, and 60ºC were the best models for fitting the experimental moisture sorption data of SDP throughout the entire range of water activity (0.1–0.9). As depicted in Figure 3, the MGAB model adequately predicted the moisture sorption experimental data for the tested temperatures 20, 40, and 60ºC.

Table 2. Constants and statistical parameters of the moisture sorption isotherm models used to fit Sukkari date powder experimental data.

Tabla 2. Constantes y parámetros estadísticos de los modelos de isotermas de sorción de humedad utilizados para ajustar los datos experimentales de polvo de dátil Sukkari

		Model Constants			Statistical Parameters
		A	B	C	R^2	RMSE	PE%
Modified GAB		0.07	1.05	59.82	0.998	0.010	07.28
Modified Oswin		0.09	-3.42X10^−5	0.86	0.993	0.020	17.02
Modified Halsey		-2.11	-5.24X10^−4	0.74	0.994	0.018	23.34
Modified BET		0.14	3.63X10^−5	0.441	0.992	0.021	17.04
T (°C)
GAB	20	0.092	1.726	1.021	1.000	0.001	0.951
	40	0.084	1.041	1.040	1.000	0.001	0.187
	60	0.079	0.725	1.049	1.000	0.002	0.724
BET	20	0.111	1.132	-	0.999	0.003	2.664
	40	0.140	0.424	-	0.999	0.005	4.499
	60	0.178	0.216	-	0.999	0.005	5.574
Halsey	20	0.112	0.859	-	0.999	0.003	3.324
	40	0.119	0.736	-	1.000	0.002	4.265
	60	0.121	0.665	-	1.000	0.002	4.009
Oswin	20	0.117	0.983	-	0.999	0.004	2.970
	40	0.086	1.174	-	0.999	0.004	4.273
	60	0.066	1.321	-	0.999	0.005	6.060
Iglesias and Chirife	20	0.007	0.112	-	1.000	0.003	1.205
	40	-0.022	0.119	-	0.993	0.012	12.064
	60	-0.042	0.124	-	0.983	0.020	30.183
Caurie	20	-5.018	5.379	-	0.986	0.014	7.751
	40	-6.302	6.961	-	0.987	0.016	12.066
	60	-7.463	8.353	-	0.989	0.016	15.153

The SDP monolayer moisture content (X_m) values determined using the original GAB model (Equation 5(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5) ) were, 0.092, 0.084, and 0.079 (kg water/kg dm) at 20, 40 and 60ºC, respectively. Values were comparable to X_m of unroasted carob and blueberry fruit powders (Cervenkaa et al., 2019; Tao et al., 2018). X_m linearly decreased with T as represented by Equation 19(19) ${\mathrm{X}}_{\mathrm{m}}=-0.0003\mathrm{T}+0.098\left({\mathrm{R}}^2=0.983\right)$(19) .

(19) ${\mathrm{X}}_{\mathrm{m}}=-0.0003\mathrm{T}+0.098\left({\mathrm{R}}^2=0.983\right)$(19)

3.3. Differential enthalpy and entropy

The differential enthalpy (q_st) was calculated from Equation (12)(12) ${\left(\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{w}}\right)}_{\mathrm{X}}=-\frac{q_{st}}{\mathrm{R}{\mathrm{T}}_{\mathrm{a}}}+\frac{{\mathrm{S}}_{\mathrm{d}}}{\mathrm{R}}$(12) and plotted in Figure 4a as a function of moisture content in the range 0.05–0.50 (kg water/kg dm). As moisture content increased, q_st decreased consistently. At the lowest moisture content (0.05 kg water/kg dm) SDP had the largest q_st (9.366 kJ/mol), and the lowest q_st (0.262 kJ/mol) at the highest moisture content (0.5 kg water/kg dm). These values are comparable to values reported for spray-dried pure orange juice powder (Sormoli & Langrish, 2015), spray-dried mango mix powders (Cano-Higuita et al., 2015), and pineapple pulp powder (Gabas et al., 2007). As shown in Figure 4a, the isosteric (total) heat of sorption (Q_st) also consistently decreased with increasing moisture content and approached the heat of vaporization of pure water (L_w = 43.35 kJ/kg at 40ºC) at the highest moisture content. The following equation adequately represented the dependence of the SDP differential enthalpy (q_st) on moisture content (X):

(20) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}=0.0994{\left(\mathrm{X}\right)}^{-1.581}\left({\mathrm{R}}^2=0.990\right)$(20)

As shown in Figure 4b the differential entropy (S_d) consistently decreased with increasing moisture content from 20.412 (J/mol K) at 0.05 (kg water/kg dm) to −0.758 (J/mol K) at 0.5 (kg water/kg dm). Similar reported observations were spray dried tomato pulp (Goula et al., 2007), and corn stover fractions (Igathinathane et al., 2007).

Figure 4. Net isosteric (q_st) and isosteric (total, Q_st) heats of sorption (a) and differential entropy (S_d) of SDP (b) as a function of dry basis moisture content (X).

Figura 4. Calores de sorción (a) isostérico (q_st) e isostérico (total, Q_st) netos y entropía diferencial (S_d) de SDP (b) en función del contenido de humedad en base seca (X)

3.4. Enthalpy‐entropy compensation theory

The SDP differential enthalpy (q_st) varied linearly with differential entropy (S_d), as shown in Equation (21)(21) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}=425.93{\mathrm{S}}_{\mathrm{d}}+0.772\left({\mathrm{R}}^2=0.998\right)$(21) , indicating the validity of the compensation theory within the studied range of moisture contents.

(21) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}=425.93{\mathrm{S}}_{\mathrm{d}}+0.772\left({\mathrm{R}}^2=0.998\right)$(21)

From Equation (21)(21) ${\mathrm{q}}_{\mathrm{s}\mathrm{t}}=425.93{\mathrm{S}}_{\mathrm{d}}+0.772\left({\mathrm{R}}^2=0.998\right)$(21) , the isokinetic temperature (T_β) equals 425.93 K, and Gibbs free energy change ∆G_β is equal to 0.772 (kJ/mol). The harmonic mean temperature (T_hm) calculated from Equation 14(14) ${\mathrm{T}}_{\mathrm{h}\mathrm{m}}=\left(\frac{\mathrm{n}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}(1/{\mathrm{T}}_{\mathrm{a}})}\right)$(14) is 312.23 K. Since T_β > T_hm the moisture sorption process is enthalpy driven. The positive ∆G_β value of the SDP indicates that the adsorption process is non-spontaneous. Similar reported behavior of enthalpy-driven and non-spontaneous sorption process for unroasted carob powder (Cervenkaa et al., 2019) and oatmeal biscuit and flakes (McMinn et al., 2007).

3.5. Net integral enthalpy and entropy

According to Equation (16)(16) $\mathrm{\Phi }=\frac{{\mathrm{K}}_{\mathrm{B}}\mathrm{T}}{{\mathrm{A}}_{\mathrm{m}}}\mathrm{l}\mathrm{n}\left[\frac{\left(1+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}-\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}{\left(1-\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}\right]$(16) , calculation of the spreading pressure (Φ) of the SDP was carried out, and Figure 5 depicted its dependence on water activity at different temperatures. At a constant temperature, Φ increased with increasing a_w, and at constant a_w it increased with decreasing temperature. Similar behavior for oat-meal biscuit, oat flakes, quince, and pestil was reported (Kaya & Kahyaoglu, 2005; McMinn et al., 2007; Noshad et al., 2012). At high spreading pressures, water molecules tend to confer a high level of adaptability to an active site, and consequently, an increased product hygroscopicity.

Figure 5. Variation of spreading pressure with water activity and temperature of SDP.

Figura 5. Variación de la presión de propagación con la actividad del agua y la temperatura de SDP

Equation 17(17) ${\mathrm{Q}}_{\mathrm{i}\mathrm{n}}=-\mathrm{R}{\left[\frac{\mathrm{\partial }ln{\mathrm{a}}_{\mathrm{w}}}{\mathrm{\partial }\left(1/{\mathrm{T}}_{\mathrm{a}}\right)}\right]}_{\mathrm{\Phi }}$(17) was used to calculate the SDP net integral enthalpy (Q_in) by plotting ln(a_w) against 1/T_a at constant Φ. In Figure 6 the integral enthalpy decreased with increasing moisture content from a value of 11.51 (kJ/mol) at a moisture content of 0.027 (kg water/kg dm) to 0.40 (kJ/mol) at 0.749 (kg water/kg dm). The following exponential equation fitted the data very well:

(22) ${\mathrm{Q}}_{\mathrm{i}\mathrm{n}}=10.434{\mathrm{e}}^{-4.565\mathrm{X}}\left({\mathrm{R}}^2=0.983\right)$(22)

Figure 6. Net integral enthalpy (Q_in) and net integral entropy (S_in) as a function of dry basis moisture content (X) of SDP.

Figura 6. Entalpía integral neta (Q_in) y entropía integral neta (S_in) en función del contenido de humedad en base seca (X) del SDP

The highest value of the integral enthalpy at the lowest moisture content may be explained by the swelling of the date powder caused by moisture adsorption on powder surface accessible sites. Consequently, opening new high energy locations and more water binding. At higher moisture content above 0.15 (kg water/kg dm), much fewer locations were accessible leading to much lower values of Q_in. Investigations on food powders reported a similar explanation (Cervenkaa et al., 2019; Farahnaky et al., 2016).

Figure 6 shows the relationship between the net integral entropy (S_in) estimated from Equation (18)(18) ${\mathrm{S}}_{\mathrm{i}\mathrm{n}}=-\frac{{\mathrm{Q}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{T}}_{\mathrm{a}}}-\mathrm{R}ln{\left({\mathrm{a}}_{\mathrm{w}}\right)}^{\ast }$(18) , with moisture content (X). The S_in of SDP decreased with increasing moisture content from a maximum value of 13.81 (J/mol K) at moisture content 0.027 (kg water/kg dm) to a minimum value of 1.21 (J/mol K) at moisture content 0.749 (kg water/kg dm). The following power type equation adequately fitted variation of S_in with moisture content:

(23) ${\mathrm{S}}_{\mathrm{i}\mathrm{n}}=0.9859{\mathrm{X}}^{-0.746}\left({\mathrm{R}}^2=0.998\right)$(23)

The integral entropy of winged-been seed and gari (Fasina et al., 1999), and defatted sesame meal (Al-Mahasneh et al., 2007) followed similar behavior.

4. Conclusions

The Sukkari date powder was predominantly (81.5%) moderately fine particle size (355–180 μm). Most of the measured physical properties of the date powder were comparable to published data of several food powders.

Moisture adsorption isotherms of the moderately fine particle size SDP was determined at three temperatures 20, 40, and 60^°C and equilibrium relative humidity in the range 10%–90% (i.e a_w in the range 0.1–0.9). The original and temperature-dependant GAB equations best fitted the experimental moisture adsorption data. The monolayer moisture content (X_m) estimated from the original GAB model decreased linearly with increasing temperature from 0.092 (kg water/kg dm) at 20°C to 0.079 (kg water/kg dm) at 60°C. As moisture content increased both the differential enthalpy and entropy decreased consistently. The linear relationship between the differential enthalpy and entropy confirmed the validity of the compensation theory. The moisture sorption process was enthalpy driven and non-spontaneous. Both the integral enthalpy and entropy decreased with increasing moisture content, and the behaviour may be related to the swelling that may occur during the moisture adsorption process. Further work is needed to characterize packaging requirements, suitable storage conditions, and shelf life of date powder.

Nomenclature

(aw)*	=	Geometric mean water activity
a*, b*, L*	=	CIE System color parameters
A, B, C	=	Parameters of temperature incorporated modified sorption models
Am	=	Surface area of the water molecule, 1.06 × 10−19 (m2)
aw	=	Water activity
BD	=	Bulk density (kg/m3)
BI	=	Browning index
CI	=	Compressibility index (%)
D, K	=	Parameters of GAB sorption model
db	=	Dry basis
dm	=	Dry matter
HR	=	Hausner ratio
i	=	Number of terms
KB	=	Boltzman constant, 1.38 × 10−23 (J/K)
Lw	=	Heat of vaporization or condensation of water (J/mol)
N	=	Number of observations
n	=	Number of isotherms
Qin	=	Integral enthalpy (kJ/mol)
Qst	=	Isosteric (total) heat of sorption (kJ/mol)
qst	=	Net isosteric heat of sorption (kJ/mol)
R	=	Universal gas constant (8.314 J/mol K)
R2	=	Coefficient of determination
SC	=	Swelling capacity (ml/g)
Sd	=	Differential entropy of sorption (J/mol K)
Sin	=	Net integral entropy (J/mol K)
T	=	Temperature (°C)
Ta	=	Absolute temperature (K)
TD	=	Tapped density (kg/m3)
Thm	=	Harmonic mean temperature (K)
Tβ	=	Isokinetic temperature (K)
WAI	=	Water absorption index (g gel/g dry powder)
WSI	=	Water solubility index (%)
X	=	Moisture content (kg water/kg dm)
Xexp	=	Experimental moisture content (kg water/kg dm)
Xm	=	Monolayer moisture content (kg water/kg dm), Xm=A in Equation 5(5) $\mathrm{G}\mathrm{A}\mathrm{B}\mathrm{X}=\frac{\mathrm{A}\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}}{\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}\right)\left(1-\mathrm{B}{\mathrm{a}}_{\mathrm{w}}+\mathrm{B}\mathrm{C}{\mathrm{a}}_{\mathrm{w}}\right)}$(5)
Xpred	=	Predicted moisture content (kg water/kg dm)
Yexp,i	=	Experimental value for instant i
Ypred,i	=	Predicted value for instant i for the same instant N
ΔGβ	=	Gibbs free energy change (kJ/mol)
Φ	=	Spreading pressure (J/m2)

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was funded by the National Plan for Science, Technology, and Innovation (MAARIFAH), King Abdul-Aziz City for Science and Technology (KACST), Kingdom of Saudi Arabia, Grant number 10-AGR1194-02.