Deliquescence lowering in mixtures of NaCl and sucrose powders elucidated by modeling the water activity of corresponding solutions Marina Dupas-Langlet ⇑ , Mohammed Benali, Isabelle Pezron, Khashayar Saleh, Léa Metlas-Komunjer UTC/ESCOM, Équipe d’Accueil ‘‘Transformations Intégrées de la Matière Renouvelable’’ (EA 4297), Rond-Point Guy Deniélou, 60200 Compiègne, France article info Article history: Received 7 August 2012 Received in revised form 18 October 2012 Accepted 26 October 2012 Available online 5 November 2012 Keywords: Mixture of deliquescent substances Eutonic composition Regular solutions model Norrish’s equation abstract A significant number of models allowing the calculation of water activity (a w ) in aqueous solutions of electrolytes or of organic substances was proposed and verified experimentally in the last few decades. In case of a mixture of organic and inorganic solutes the lowering of water activity with respect to cor- responding single solutes was often observed but, to the best of our knowledge, did not find sound phys- ical explanation yet. Present work proposes a thermodynamic model covering wide range of solution concentrations and applicable to multiple solutes, in particular to the mixtures of high total solid con- tents, situation relevant to powder caking. Deliquescence lowering is evidenced by means of qualitative visual observation and quantitative measurements of water uptake. Excellent agreement between the measured values of a w for different compositions of NaCl–sucrose–water mixtures and the model calcu- lation of the water activity at any composition is obtained. A diagram relating water activity to the com- position of a ternary system is proposed. It facilitates foreseeing the conditions of ambient relative humidity where partial or total dissolution of mixtures of NaCl and sucrose will take place. In addition, it furnishes a better understanding of deliquescence lowering reported in the earlier works. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Water molecules may interact with food powders in many dif- ferent ways depending on their physical state (Kwok et al., 2010; Rahman, 2006; Hartmann and Palzer, 2011). In particular case of highly soluble hygroscopic substances, the phenomenon known as deliquescence can lead to the significant deterioration of a prod- uct containing such substances. The so-called capillary condensa- tion taking place at contact points between particles and/or inside the pores is at the origin of this phenomenon. Partial disso- lution of a solid gives rise to the formation of a homogeneous aque- ous solution, which is a first step in powder caking, the second step being the re-crystallization of the solid due to subsequent water evaporation. In order to induce deliquescence, the partial vapor pressure of water in atmosphere must be higher than the vapor pressure of the saturated solution of the substance, characterized by a critical water activity ða w Þ or deliquescence relative humidity (DRH) de- fined at a given temperature (Martin, 2000; Mauer and Taylor, 2010; Langlet et al., 2012). If there is more than one deliquescent substance present in a mixture of solids, the DRH of the mixture is lower than the lowest DRH of the individual substances. The phenomenon is called deli- quescence lowering and the corresponding DRH is termed the mu- tual deliquescence relative humidity (MDRH). Deliquescence lowering was observed in mixtures of inorganic salts such as fertil- izers (Mauer and Taylor, 2010), sugars mixed with organic sub- stances (Kwok et al., 2010), mixtures of deliquescent pharmaceuticals (Salameh and Taylor, 2005), of food ingredients such as sucrose, glucose, fructose, citric acid (Salameh and Taylor, 2006; Hiatt et al., 2008). According to Mauer and Taylor (2010), the MDRH of mixture of deliquescent substances is expected to vary with temperature in a fashion similar to the variation of solubility of solids present in the mixture. In the present paper, we propose to study the ternary system NaCl–sucrose–water and to apply the regular solutions model in order to calculate the water activity of the mixture. A detailed description of the regular solutions model will be given. It will be checked whether the model can be applied to NaCl–water and sucrose–water binary systems before generalizing the law to the ternary system. Other models will be also presented and compared to the proposed model. It will be shown that the regular solutions model is appropriate for the water activity prediction of ternary systems. The comparison between different models will highlight the supremacy of the regular solutions model when dealing with mixtures of organic substances, salts and water. 2. Theoretical background The term ‘‘regular solutions’’ was first proposed in 1929 by Hildebrand then developed by Bragg and Williams in 1946. The 0260-8774/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2012.10.042 ⇑ Corresponding author. Tel.: +33 344 234 744. E-mail address: [email protected](M. Dupas-Langlet). Journal of Food Engineering 115 (2013) 391–397 Contents lists available at SciVerse ScienceDirect Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Transcript
Journal of Food Engineering 115 (2013) 391–397
Contents lists available at SciVerse ScienceDirect
A significant number of models allowing the calculation of water activity (aw) in aqueous solutions ofelectrolytes or of organic substances was proposed and verified experimentally in the last few decades.In case of a mixture of organic and inorganic solutes the lowering of water activity with respect to cor-responding single solutes was often observed but, to the best of our knowledge, did not find sound phys-ical explanation yet. Present work proposes a thermodynamic model covering wide range of solutionconcentrations and applicable to multiple solutes, in particular to the mixtures of high total solid con-tents, situation relevant to powder caking. Deliquescence lowering is evidenced by means of qualitativevisual observation and quantitative measurements of water uptake. Excellent agreement between themeasured values of aw for different compositions of NaCl–sucrose–water mixtures and the model calcu-lation of the water activity at any composition is obtained. A diagram relating water activity to the com-position of a ternary system is proposed. It facilitates foreseeing the conditions of ambient relativehumidity where partial or total dissolution of mixtures of NaCl and sucrose will take place. In addition,it furnishes a better understanding of deliquescence lowering reported in the earlier works.
Water molecules may interact with food powders in many dif-ferent ways depending on their physical state (Kwok et al., 2010;Rahman, 2006; Hartmann and Palzer, 2011). In particular case ofhighly soluble hygroscopic substances, the phenomenon knownas deliquescence can lead to the significant deterioration of a prod-uct containing such substances. The so-called capillary condensa-tion taking place at contact points between particles and/orinside the pores is at the origin of this phenomenon. Partial disso-lution of a solid gives rise to the formation of a homogeneous aque-ous solution, which is a first step in powder caking, the second stepbeing the re-crystallization of the solid due to subsequent waterevaporation.
In order to induce deliquescence, the partial vapor pressure ofwater in atmosphere must be higher than the vapor pressure ofthe saturated solution of the substance, characterized by a criticalwater activity ða�wÞ or deliquescence relative humidity (DRH) de-fined at a given temperature (Martin, 2000; Mauer and Taylor,2010; Langlet et al., 2012).
If there is more than one deliquescent substance present in amixture of solids, the DRH of the mixture is lower than the lowestDRH of the individual substances. The phenomenon is called deli-quescence lowering and the corresponding DRH is termed the mu-
ll rights reserved.
anglet).
lowering was observed in mixtures of inorganic salts such as fertil-izers (Mauer and Taylor, 2010), sugars mixed with organic sub-stances (Kwok et al., 2010), mixtures of deliquescentpharmaceuticals (Salameh and Taylor, 2005), of food ingredientssuch as sucrose, glucose, fructose, citric acid (Salameh and Taylor,2006; Hiatt et al., 2008). According to Mauer and Taylor (2010), theMDRH of mixture of deliquescent substances is expected to varywith temperature in a fashion similar to the variation of solubilityof solids present in the mixture.
In the present paper, we propose to study the ternary systemNaCl–sucrose–water and to apply the regular solutions model inorder to calculate the water activity of the mixture. A detaileddescription of the regular solutions model will be given. It willbe checked whether the model can be applied to NaCl–water andsucrose–water binary systems before generalizing the law to theternary system. Other models will be also presented and comparedto the proposed model. It will be shown that the regular solutionsmodel is appropriate for the water activity prediction of ternarysystems. The comparison between different models will highlightthe supremacy of the regular solutions model when dealing withmixtures of organic substances, salts and water.
2. Theoretical background
The term ‘‘regular solutions’’ was first proposed in 1929 byHildebrand then developed by Bragg and Williams in 1946. The
Fig. 2. Water activity at 25 �C as a function of molar fraction of water in NaCl–waterbinary system; data points from Scatchard et al. (1938).
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model deals with solutions which deviate slightly from idealitywithout any specific strong interactions. The mixing entropy of aregular solution is the same as the one of an ideal system of thesame composition in a random mixture. But, contrary to the idealcase, the mixing enthalpy is not null since the regular solutionsmodel takes into account the nature of molecules by distinguishingthe different types of interaction energies (Murrel and Jenkins,1994). An extended development of this theory is given in sectionSupplementary material A.
The model of regular solutions predicts water activity in binarysystems, aw, following the equation, often named Norrish’s equa-tion (Norrish, 1966):
aw ¼ xw expðax2s Þ ð1Þ
where xw and xs are the molar fractions of water and solute respec-tively, a is a constant called the interaction parameter which char-acterizes the tendency to mix, i.e. the affinity between water andsolute molecules. If a value is negative, mixing is energeticallyfavorable whereas if it is positive, solute and water do not mix.
Eq. (1) represents the most widely used means for the predic-tion of water activity in binary non-electrolyte solutions of foodinterest in the domain of under-saturated solutions. Baeza et al.(2010) and Galmarini et al. (2008) showed that Norrish’s equationcan be applied to the binary system sucrose-water: interactionparameter a equal to �6.47 indicating an important differencewith respect to ideality (i.e. a = 0), translates a strong affinity be-tween water and sucrose, i.e. an important tendency to mix. Thephenomenon is illustrated by Fig. 1 where the evolution of wateractivity, aw, at 25 �C of aqueous solutions of sucrose as a functionof the molar fraction of water, xw is shown. The experimentalpoints are taken from Scatchard et al. (1938)’s work. The line rep-resents the fitted Norrish’s equation by adjusting the characteristicparameter a by minimizing the differences between the experi-mental points and the model. The best fit corresponds to the inter-action parameter a equal to �6.40, close to �6.47 cited by Baezaet al. (2010). The water activity of an ideal solution representingRaoult’s law is also shown as a light gray dotted line. The wateractivity of a saturated sucrose solution at 25 �C, a�w;sucrose, equal to0.848 with a molar fraction of water equal to 0.90 is also indicatedon Fig. 1. One can notice that for highly diluted solutions(xw > 0.97) both experimental points and calculated values basedon the regular solutions theory are very close to the ideal behaviorwhile significant difference appears as sucrose concentration in-creases. The excellent agreement between the experimental dataand the calculated values of aw confirms that the regular solutions
0.8
0.82
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0.86
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0.92
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0.98
1
0.8 0.85 0.9 0.95 1
Wat
er a
ctiv
ity,
aw
[-]
Molar water fraction, xw [-]
aw*
xw*
Fig. 1. Water activity at 25 �C as a function of molar fraction of water in sucrose–water binary system; data points from Scatchard et al. (1938).
theory is applicable in a large domain of under-saturated solutionsof sucrose in water.
An analogous graph for binary system NaCl–water is presentedin Fig. 2. As already pointed out by Chuang and Toledo (1976), thea-parameter of Norrish’s equation varies with NaCl concentration.Here we propose a linear relationship between a and NaCl molal-ity, b. By fitting Norrish’s equation with the experimental data ofScatchard et al. (1938) an excellent agreement is obtained fora ¼ 0:59� 0:54b. Fig. 2 shows negative deviation from idealityfor salt solutions of concentration higher than xs = 0.10(xw = 0.90), illustrating the affinity between NaCl ions and water,similarly to the effect observed for sucrose and water. The wateractivity of a saturated NaCl solution at 25 �C, a�w;Nacl, equal to0.750 with a molar fraction of water equal to 0.82 is also indicatedon Fig. 2.
In this study, we propose to check whether the model of regularsolutions can be used for the prediction of water activity in the ter-nary system NaCl–sucrose–water. Because of its relevance tohygroscopic powder caking we are particularly interested in situa-tions where small quantity of water is involved i.e., when aqueoussolutions are concentrated with respect to one or both solutes.However, as the composition of a multi-component mixture ofpowders varies, the complete dissolution of one or several constit-uents can occur.
From Eq. (1) by generalizing the law, the expression of wateractivity can be written as:
aw ¼ xw expða1x21 þ a2x2
2 þ a12x1x2Þ ð2Þ
where the subscripts 1 and 2 correspond to the two solutes and a12
is a parameter of mutual interaction in the presence of water. Wewill take here the subscript 1 for NaCl and 2 for sucrose. In orderto calculate the solution concentrations in the appropriate manner,it is important to take into account the amount of solute which canbe dissolved in a given quantity of water present in the ternary sys-tem. When certain amount of a mixture NaCl/sucrose is introducedin limited quantity of water, some solute will remain as excess solidphase while the solution composition remains constant. Detailsabout the calculations of the molar fractions x1, x2 and xw in sucha case are given in the section Supplementary material C. Takinginto account the large domain of solution concentrations studiedhere, the observed slight variations of solubility were neglectedi.e. the invariability of solubility of substances in presence of co-solute is assumed.Various models allowing the determination ofthermodynamic properties of solutions are proposed in the litera-ture (Sereno et al., 2001; Comesana et al., 2001; Cohen et al.,1987). For example, well-known model for electrolytes developed
M. Dupas-Langlet et al. / Journal of Food Engineering 115 (2013) 391–397 393
by Pitzer is applied to mixed organic/inorganic aerosols by (Clegget al., 2001). Solution osmotic coefficient, /, is defined as:
/� 1 ¼ ð/0 � 1Þ b1
b1 þ b2þ ð/00 � 1Þ b2
b1 þ b2þ /000 � 1 ð3Þ
where b1 and b2 are the NaCl and sucrose molalities, respectively, /0
is the osmotic coefficient contribution from the ionic components, /0 0 is the contribution from the organic solute and /0 0 0 is the contribu-tion from ion-organic solute interactions. Water activity is then de-fined as:
aw ¼ �ðmb1 þ b2ÞM
1000expð/Þ ð4Þ
where t is the number of ions after dissociation and M the molarmass of water. In order to test the use of Clegg’s model to the ter-nary system NaCl–sucrose–water, for /’ we will take the values gi-ven by Tang et al. (1986) and for /0 0 and /0 0 0 the values given byClegg et al. (2001).
The model proposed by Ross is based on the assumption thatthere is little interaction between solutes, and that their contribu-tions to the chemical potential are therefore additive. Henceforth,according to Gibbs Duhem equation, one can multiply the individ-ual contributions of the solutes and obtain the water activity ofsolution as a product of corresponding single component wateractivities (Kwok et al., 2010; Ross, 1975):
aw ¼Y
i
awðiÞ ð5Þ
where aw(i) is the water activity of solution containing only the sol-ute i at its molality.
3. Experimental
3.1. Materials
Sodium chloride and sucrose crystals (Sigma Aldrich) of micro-metric size of purity superior to 99.5% were used as provided. Itwas beforehand checked that NaCl and sucrose are not chemicallylabile when they are mixed in water at 25 �C: no hydrate can beformed at 25 �C (Shalaev and Franks, 1995) and the solutions arenot acid enough to allow sucrose hydrolysis (Salameh and Taylor,2006).
3.2. Environmental scanning electron microscopy
The environmental scanning electron microscopy (ESEM)instrument was used to characterize the deliquescence and cakingof NaCl and sucrose visually. Images are acquired under controlledconditions of water vapor pressure, and temperature. After theintroduction of the sample, air is evacuated from the observationchamber. Desired RH is then established by increasing the watervapor pressure in step by step fashion with steps of 0.1 Torr. Longenough period of time was allowed for steady image to be ob-tained. By maintaining the temperature at 5 �C and varying thewater vapor pressure between about 3.4 and 5 Torr (450 and666 Pa), significant variations of RH between 51% RH and 74% RHcan be achieved.
3.3. Moisture sorption isotherms
10–15 mg samples of pure substances or mixtures of NaCl andsucrose with crystal size superior to 300 lm were submitted tothe continuous gas flow of 200 cm3/min combining dry and watersaturated nitrogen flows in proportions corresponding to desiredrelative humidity. Mass variations due to the uptake of water fromthe gas phase were measured by an accurate microbalance system
[Dynamic Vapor Sorption (DVS), Surface Measurement Systems]with a precision of 0.1 lg. The obtained points correspond to thewater uptake of powders exposed to a constant RH during 6 h, theywere acquired every 2% RH between 0% and 90% RH. Temperature,here fixed to 25 �C, and humidity are controlled at 0.1 �C and 0.5%RH, respectively.
3.4. Water activity measurements
For each water activity measurement, the mixture NaCl–sucrose–water was prepared by dissolving a known amount ofthe solid (weighted in a Mettler AE 240 analytical balance to0.1 mg) into a known amount of deionized water (18 M Ohm).Samples contain 5 g of various proportions of NaCl and sucrosewhile the amount of water added was between 1.5 g and 8 g. Thesamples were equilibrated during 48 h at 25 �C. The water activityof solutions was determined using a dew point hygrometer, Aqua-lab Series 3B (Decagon Devices, Pullman, Washington). The aw-meter was previously calibrated using saturated salt solutions at25 �C. According to the instrument specifications, the water activ-ity accuracy is ±0.003. Each water activity measurement was theaverage of three determinations of three replicates, which providesan uncertainty of 0.01.
Measurements of water activity at 25 �C at various composi-tions of the ternary system NaCl–sucrose–water were carried outfor 57 samples forming six series of constant total solid content(TS). For a given TS, we define the mass solid fraction, fNaCl/Sucrose,such as:
fNaCl=Sucrose ¼mNaCl
mNaCl þmSucroseð6Þ
where mNaCl and mSucrose are the masses of NaCl and sucroserespectively.
4. Results and discussion
Fig. 3 shows details of ESEM images of two pairs of NaCl and su-crose crystals observed simultaneously. The cube at the top ofimages is the sucrose crystal while the polydron at the bottom isthe NaCl crystal. Two different configurations are chosen: onFig. 3a NaCl and sucrose crystals are close to each other but notin contact while on Fig. 3b, the two crystals are in contact. The va-por pressure of 3.4 Torr at 5 �C imposed in the observation cham-ber corresponds approximately to 51% RH. It can be checked onthe images 3a. and 3b. that at this RH, the two pairs of crystalsdo not present any noticeable difference. In Fig. 3c the vapor pres-sure is elevated to 5 Torr, i.e. 74% RH, just below the deliquescencepoint of NaCl (75% RH); one can observe that both crystals keeptheir initial shape as in Fig. 3a and do not seem to dissolve. Onthe contrary in the same conditions, in Fig. 3d, the formation of aliquid bridge of condensed water is observed. The comparison ofFig. 3c and d proves that an intimate contact between crystals ofNaCl and sucrose induces the phenomenon of dissolution at RHinferior to the DRH of both solids.
Measurements by Dynamic Vapor Sorption apparatus were car-ried out in order to determine precisely the deliquescence point ofmixtures NaCl/sucrose. Fig 4 compares the water uptake of mixtureof NaCl/sucrose with the water uptake of single substances. Eachpoint corresponds to the amount of water taken by the sample dur-ing the period of 6 h of exposure.
Water uptake remains negligible (<0.5%) up to approximately76% RH for pure NaCl (⁄) and 85% RH for pure sucrose (�) whileat higher RH an increase of water uptake up to 300% for NaCland 50% for sucrose approximately can be observed. The valuesof 76% RH and 85% RH match well the deliquescence points of pureNaCl (Tang et al., 1986; Mauer and Taylor, 2010) and sucrose
Fig. 3. ESEM images of sucrose crystal (cube at the top) and NaCl crystal (polyhedron at the bottom) at 51% RH for images (a) and (b) and at 74% RH for images (c) and (d).
0
50
100
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250
300
50 60 70 80 90
Wat
er u
ptak
e [m
ass
perc
ent]
Relative humidity, RH [%]
Fig. 4. Water uptake after 6 h at given RH by pure sucrose (e), pure NaCl (⁄) and bythe mixture of NaCl–sucrose 50/50 (N) at varying relative humidity.
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er a
ctiv
ity,
aw
[-]
Mass solid fraction of NaCl, fNaCl/Sucrose [-]
TS=77%TS=71%TS=56%TS=45%TS=38%TS=33%
Fig. 5. Water activity at 25 �C of ternary solutions as a function of mass solidfraction of NaCl for different mass total solid contents (TS) in various shapes of grey.Points correspond to experimental data while dotted lines represent the aw ofcorresponding solutions calculated according to the regular solutions model.
394 M. Dupas-Langlet et al. / Journal of Food Engineering 115 (2013) 391–397
(Salameh and Taylor, 2006; Mauer and Taylor, 2010). The mixtureof NaCl and sucrose takes up a significant quantity of water atabout 66% RH, i.e. far below the deliquescence point of both puresubstances. Two other proportions of sucrose and NaCl tested,namely 25/75 and 75/25 gave the same results suggesting thatthe observed mutual deliquescence point is independent of thecomposition of the powder mixture.
The ESEM images on Fig. 3 showed that in order to observe dis-solution characterizing deliquescence lowering the contact be-tween NaCl and sucrose individual crystals was necessary whilethe results shown in Fig. 4 confirm and quantify the phenomenonon a sample of several crystals in contact. In what follows we willcompare the experimental measurements of water activity of solu-
tions of NaCl and sucrose in water with the calculated wateractivity.
In Fig. 5, measured values of aw data are shown as a function ofcomposition of a system expressed via the parameter fNaCl/Sucrose.They are to be compared to the calculated values of aw based onthe regular solutions model via Eq. (2). The parameters a1, a2 anda12 were adjusted by minimizing the differences between theexperimental values and the model. The results are representedby the curves in dotted lines.
The points on the left-hand side y-axis of ordinates correspondto aqueous sucrose solutions with no NaCl present; the measured
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1
ater
act
ivit
y, aw
[-]
M. Dupas-Langlet et al. / Journal of Food Engineering 115 (2013) 391–397 395
water activities indicate that they correspond to under-saturatedsolutions whose water activity increases when sucrose content de-creases. The two points corresponding to TS = 71% and TS = 77%represent sucrose solutions close to saturation of 6.05 mol/kg ofwater. Data on the right-hand side y-axis correspond tofNaCl/Sucrose = 1 when no sucrose is present, i.e. there is only NaClin solution. Water activity remains constant since for all total solidcontents studied, the quantity of NaCl in a mixture is higher thansaturated solution composition, i.e. saturated NaCl solution is inequilibrium with the excess of solid NaCl. The corresponding val-ues of aw are equal to the critical water activity of NaCl, 0.755.
For all different mixtures of NaCl and sucrose with water forfNaCl/Sucrose between 0.1 and 0.8, there is a minimum in water activitywhich decreases when fNaCl/Sucrose decreases and when TS increases,i.e. there is more sucrose than NaCl in concentrated solution.The minimum aw is equal to 0.749 when TS = 38% forfNaCl/Sucrose = 0.8; it is equal to 0.720 when TS = 56% forfNaCl/Sucrose = 0.4 and to 0.634 when TS = 77% for fNaCl/Sucrose = 0.15to fNaCl/Sucrose = 0.30 for example. It means that deliquescence lower-ing intensifies in concentrated solutions when sucrose mass contentis high with respect to NaCl content. An absolute minimum reachedexperimentally is at aw = 0.634 approximately for the compositionof fNaCl/Sucrose = 0.15 to fNaCl/Sucrose = 0.30 when TS = 71% and TS = 77%.
The model of regular solutions was applied to the 57 experi-mental water activities by adjusting the characteristic parametersa1, a2 and a12. An absolute minimum is reached when TS is above71%. At TS = 77%, a plateau of 0.641 in water activity appears be-tween fNaCl/Sucrose = 0.12 and fNaCl/Sucrose = 0.36. It characterizes satu-ration with respect to both, NaCl and sucrose. To the left of thisabsolute minimum, solution is saturated with respect to sucrosewhile to the right of this point; the solution is saturated with re-spect to NaCl. On the plateau, water activity is then constant andequal to 0.641.This value is in perfect agreement with the RH valueof 64% reported for a 50:50 w/w mixture of NaCl and sucrose byMauer and Taylor (2010). With the technique used here the mea-sured minimum of water activity was found equal to 0.634, closeto the product of the deliquescence relative humidities of each sol-ute as predicted by Ross (1975), i.e. 0.750⁄0.848 = 0.636.
The minimum in water activity characterizes the eutonic point,which is defined by the amounts of solutes with respect to theirrespective saturation. Thus, the eutonic point corresponds to themolar composition of xwater = 0.75, xNaCl = 0.17 and xsucrose = 0.08 inagreement with literature data (Mauer and Taylor, 2010; Kwoket al., 2010). By fitting the experimental data with the model ofregular solutions, the interaction parameters for water/NaCl,water/sucrose and NaCl/sucrose in the presence of water are ob-tained. The corresponding values are given in the Table 1.
The data shown in Figs. 1 and 2 representing the binary mix-tures sucrose–water and NaCl–water respectively indicate that inconcentrated solutions the interaction between water and a soluteis stronger compared to interactions between water molecules orsolute–solute interactions.
By comparison with the interaction parameters obtained in theternary system, interaction water–ion and sucrose–water seem tobe similar. As regards a12, it is negative and corresponds to theinteraction between sucrose and NaCl ions, defined as:
Table 1Interaction parameters deduced from the regular solutions model in the system NaCl–sucrose–water and the corresponding values for binary systems.
Obtained values for the ternary systemNaCl–sucrose–water
Corresponding values forbinary mixtures
a1 2.93–0.86b1 0.59–0.54b1
a2 �5.11 �4.88a12 �4.42
a12 ¼ kðu1w þ u2w � u12 � uWWÞ ð7Þ
where k is a positive constant parameter depending on the modeland u12, uww, u1w and u2w are the interaction energies between aNaCl ion and sucrose, two water molecules, a NaCl ion and water,and sucrose molecule and water, respectively (see section Supple-mentary material B). Knowing that attractive interaction energiesare always negative, we have:
u12 þ uWW > u1w þ u2w ð8Þ
Likewise, as a1 and a2 are both negative in concentrated solu-tions, we can add that:
u1w >u11 þ uWW
2ð9Þ
u2w >u22 þ uWW
2ð10Þ
Finally, by replacing those two inequalities in Eq. (8), we obtain:
u12 >u11 þ u22
2ð11Þ
This last equation indicates that in the presence of water theinteraction between the two solutes is stronger compared to theinteraction ion–ion and sucrose–sucrose. Those favorable interac-tions between solutes which only exist in solution retain watermolecules thus leading to a diminution of vapor pressure and del-iquescence lowering.
It can be interesting to compare the performance of other mod-els for the ternary system studied here. Clegg’s model takes into ac-count long range and ionic forces and other contributionsapplicable to electrolytes in the presence of organic impuritieswhile Ross’ model predicts water activity lowering based on thethermodynamic theory of solutions. Fig. 6a and Fig. 6b show wateractivity calculated by Clegg’s and Ross’ models for solutions under-saturated with respect to sucrose and under-saturated to saturatedwith respect to NaCl. The experimental data of Fig. 5 as well aswater activities calculated by the regular solutions model are alsopresented.
Fig. 6a shows that the three models follow the same tendency:water activity decreases dramatically between fNaCl/Sucrose = 0 andfNaCl/Sucrose = 0.56, all three models are very close and in very goodagreement with the experimental points, Clegg’s model being theclosest one. At fNaCl/Sucrose > 0.56, an increase of aw is predicted byall models while Clegg’s model presents a slight gap with respect
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W
Mass solid fraction of NaCl, fNaCl/Sucrose [-]
Fig. 6a. Water activity at 25 �C of ternary solutions as a function of mass solidfraction of NaCl when TS = 38% – experimental points are represented by (j), wateractivity calculated according to the regular solutions model (+), the ones calculatedby Clegg’s model (�) and the ones from Ross’ model (�).
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er a
ctiv
ity,
aw
[-]
Mass solid fraction of NaCl, fNaCl/Sucrose [-]
Fig. 6b. Water activity at 25 �C of ternary solutions as a function of mass solidfraction of NaCl when TS = 56% – experimental points are represented by (j), wateractivity calculated according to the regular solutions model (+), the ones calculatedby Clegg’s model (�) and the ones from Ross’ model (�).
396 M. Dupas-Langlet et al. / Journal of Food Engineering 115 (2013) 391–397
to experimental data. In this range of composition, the regularsolutions model shows the best fit with experiments.
In Fig. 6b, the data corresponding to higher solid content of 56%are given. Water activity decreases with increasing fNaCl/Sucrose
until fNaCl/Sucrose = 0.25 where a break in tendency appears. AtfNaCl/Sucrose > 0.25 Clegg’s model predicts an increase followed by adecrease of water activity but does not fit the experimental points.At the total solid content of 56%, the solution is saturated with re-spect to NaCl for fNaCl/Sucrose = 0.25. Water activity should tend tothe critical water activity of NaCl, 0.75, when fNaCl/Sucrose is closeto 1. But Clegg’s model becomes divergent when solution is satu-rated with respect to NaCl due to the /’’’ term which is dependenton the powers of NaCl molality. Ross’ model and the model of reg-ular solutions are similar and follow the experimental points. Nev-ertheless, Ross’ model slightly deviates from the experimentalwater activities, like on Fig. 6a.
Regular solution model allows establishing a ‘‘phase diagram’’of the ternary system NaCl–sucrose–water, as shown in Fig. 7. Byconsidering the mass solid fraction of NaCl, the amount of waternecessary for dissolution of both NaCl and sucrose can be calcu-lated while corresponding water activity can be deduced fromEq. (2). This limit can be called the ‘‘solubility limit’’ and is repre-sented in black lines crossing at point M. Therefore, when all NaCland sucrose are completely dissolved in solution, water activity is
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Wat
er a
ctiv
ity,
aw
[-]
Mass solid fraction of NaCl, fNaCl/Sucrose [-]
M
I
II III
Fig. 7. Phase diagram at 25 �C of the ternary system NaCl–sucrose–water – Zone Icorresponds to the domain of homogeneous aqueous solution; zone II correspondsto the domain of solution saturated with respect to sucrose and zone III correspondsto the domain of saturated with respect to NaCl. M corresponds to the eutonic point.
situated above this limit. It corresponds to the zone I. Below the‘‘solubility limit’’, one of the two solutes is in excess. The excess re-mains in solid state and solution is saturated by this component.The ‘‘solubility limit’’ is made of two branches corresponding tothe saturation of each solute. The intersection of the branches cor-responds to the limit of saturation with respect to both solutes, i.e.to the eutonic point, represented by the point M. For a low fractionof NaCl in zone II, solution is saturated with respect to sucrosewhile NaCl is completely dissolved. Zone III is the domain wheresolution is saturated with respect to NaCl while sucrose is com-pletely dissolved. Finally, when the solution is saturated with re-spect to both NaCl and sucrose, water activity remains constantand equal to 0.641. In Fig. 7, it is represented by the dotted line,passing by M.
As can be seen by inspecting the curve delimiting zone II of thediagram shown in Fig.7, even small amount of NaCl added to thesucrose lowers significantly the water activity of the mixtures. Inother words, the presence of small quantity of salt will diminishthe value of RH at which the mixture will completely dissolve.On the contrary, adding sugar to the salt will only moderatelyinfluence the critical RH of such mixtures, as can be seen fromthe slow variation of the path of curve delimiting zone III. How-ever, at a particular composition noted as point M correspondingto the eutonic composition containing 16% of NaCl and 84% of su-crose, the mixture shall deliquesce if the product is exposed toRH > 64.1% at 25 �C. For all other proportions of salt and sugar, onlypartial dissolution is to be observed for relative humidities be-tween 64.1% and the values given by the curves materialized byblack lines in Fig. 7.
5. Conclusion
In this study, the deliquescence lowering phenomenon in NaCl/sucrose mixture is considered on microscopic level of molecularinteractions and on macroscopic level via ternary phase diagram.The existence of interactions between Na+ and Cl� ions with su-crose comparable to the interaction between water and Na+ orCl� is brought to light via the determination of correspondinginteraction parameters. The model based on the regular solutionstheory shows a very good agreement between experimental dataand the calculated values of aw in a large domain of concentrations.From a simple measurement of water activity, a value of critical aw
equal to 0.634 is obtained. It is comparable to the experimentalvalues of water uptake determined by gravimetry and by ESEMobservations of individual crystals in the presence of water vapor.A ternary ‘‘state-diagram’’ shows that the solid compositionstrongly influences the water activity of the solution saturatedwith respect to the solute in excess. It suggests that the tendencyto cake will be influenced by the solid content in the mixture.Other systems containing an electrolyte and an organic compoundin water such as KCl–glucose–water and malic acid–fructose–water are under study in order to further validate the model of reg-ular solutions in such complex mixtures.
Acknowledgements
The help of F. Nadaud with ESEM experiments is greatly appre-ciated. Constructive reviewers’ comments contributed significantlyto the quality of the paper.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jfoodeng.2012.10.042.
M. Dupas-Langlet et al. / Journal of Food Engineering 115 (2013) 391–397 397
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