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Food Chemistry
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A review, analysis and extension of water activity data of sugars and model honey solutions
Balaji Subbiah, Ursula K.M. Blank, Ken R. Morison
⁎Department of Chemical and Process Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
A R T I C L E I N F O
Keywords:
Honey Glucose Fructose Maltose Water activity Hydration number
A B S T R A C T
Water activity is a physical property measured in the food industry which helps predict shelf life and microbial activity. Honey normally has a water activity less than 0.6, but this can vary with the amount of crystallization in solution. The aim of this work was to obtain relationships, as fundamental as possible, that can be used to predict the water activity of solutions with compositions similar to honey. Water activity measurements of aqueous sucrose solutions have been well analysed in literature using hydration theory. The analysis based on hydration numbers was easily able to show the quality of data previously published, and hence relationships were proposed for the hydration numbers of glucose, fructose, maltose and glycerol. A model was proposed in this study, to predict the water activity of food systems containing high concentrations of sugars and some electrolytes. The model was analysed and validated using mostly literature data supplemented with new experimental data.
1. Introduction
Water activity is a very useful measurement for the prediction of shelf life of food products and it is very relevant to honey. In nature, bees reduce the water activity of honey by hydrolysis of sucrose and evaporation.Beuchat (1983)stated that some yeast can grow at a water activity of 0.62, but most moulds require a minimum water activity of at least 0.75. Honey normally has a water activity less than 0.60.
The main contributors to low water activity in honey are fructose, glucose and various disaccharides. Because of the complexity of honey it is easier to study model honey solutions, so, for example,Rüegg and Blanc (1981)used a dry-basis composition of 48% fructose, 40% glu- cose, 10% maltose and 2% sucrose with various amounts of water to model honey. Prediction of the water activities of such solutions re- quires reliable data and relationships for binary solutions.
Water activity in aqueous sugar solutions is affected by water-water, water-sugar and sugar-sugar interactions which are all concentration and temperature dependent (Starzak, Peacock, & Mathlouthi, 2000).
Water molecules are preferentially attracted to some solutes which are then referred to as being hydrated. Hydration of sugars is generally attributed to hydrogen bonding between water and hydroxyl groups on the sugars, but the orientation and availability of these groups, and hence hydration, depends on the type of sugar and its self-association (Suggett, 1975). The hydration number can be defined as the average number of water molecules that are bound to each solute molecule so
that they do not contribute to water activity (Scatchard, 1921).
Burakowski and Gliński (2012) proposed a more general definition:
“the average number of water molecules that are affected by interac- tions between the solute and solvent and cause an observable effect on a physical property of the solution”.
Various techniques have been used to determine the hydration of sugars in solution. Each technique measures a different physical prop- erty and hence there is no expectation of a unique hydration number.
All the techniques use a common conceptual model of a hydration shell that alters the size, compressibility or mobility of the water molecules within it, or of the hydrated solute. Branca et al. (2001) used the viscosity of sucrose, maltose and trehalose to determine the change volume fraction caused by hydration of the solute.Furuki (2002)re- lated the change in heat of fusion of disaccharide and oligosaccharide solutions to the proportion of unfrozen water and hence to hydration number. Burakowski and Gliński (2012) reviewed the calculation of hydration from measurements of the speed of sound which depends on the compressibility of the solution. Shiraga, Ogawa, Kondo, Irisawa, and Imamura (2013)used the change in refractive index in the ter- ahertz frequency range to obtain another estimate of number of hy- drated water molecules with slower dynamics than the bulk water. For this paper, water activity will be the physical property used.
Water activity is a representation of the colligative properties: va- pour pressure, freezing point depression, boiling point elevation, and osmotic pressure, all of which are unique and quantitative measures of
https://doi.org/10.1016/j.foodchem.2020.126981
Received 3 March 2019; Received in revised form 16 February 2020; Accepted 3 May 2020
⁎Corresponding author.
E-mail address:[email protected](K.R. Morison).
Available online 07 May 2020
0308-8146/ © 2020 Elsevier Ltd. All rights reserved.
T
the chemical potential of a solution at a given concentration, tem- perature and pressure (Berry, Rice, & Ross, 1980). In this paper values of hydration number determined only from the colligative properties will be used.
The aqueous sucrose system has been well studied and reviewed by Starzak et al. (2000). They gave a range of equations that have been applied to similar systems. Much of their analysis is based on the ap- proach ofScatchard (1921)who developed a theory based on hydration water in solution.
If and when honey crystallizes, glucose monohydrate crystals are formed, releasing the hydration water. In the case of the monohydrate, one molecule of water is taken with glucose into the crystal, but the net result is a net gain in the concentration of active water in the solution.
Therefore the water activity of honey rises over time after production as it crystallizes.Gleiter, Horn, and Isengard (2006)found that on average the water activity of crystallised honey was about 0.04 higher than the same honey when completely dissolved by heating and cooling.
The aim of this work was to obtain relationships, as fundamental as possible, that can be used to determine the water activity of solutions with compositions similar to liquid honey. To do this it was necessary to analyse previously published data to determine their accuracy. It is hypothesised that analysis using hydration number values determined from colligative properties will effectively show the consistency of data and it will enable prediction of water activity at high sugar con- centrations.
2. Theory
Water activity,aw, is defined as the ratio of the vapour pressure,p, of a solution to the vapour pressure of pure water, po, at the same temperature. It can be related to the mole fraction of water,xw, and its activity coefficient,γw.
≡ =
a p
p γ x
w w w
o (1)
In an ideal solution this ratio equals the mole fraction of water in the solution, but it is normally less than this so the water activity coefficient is introduced.
Accurate estimates of water activity can also be obtained from boiling point elevation, osmotic pressure or freezing point depression.
For example, Eq.(2)can be used for data of freezing point depression, T
Δ f (Berry, Rice, & Ross, 1980).
= −
a h T
ln ΔRTΔ
w
f f
f2
(2) HereΔhf is the heat of fusion of water (6010 J mol−1),Ris the universal gas constant, andTf is the normal freezing point of water (273.15 K).
Another variable that is commonly used is the osmotic coefficient, ϕ, which is defined by Eq.(3).
= −
a νmM ϕ
ln w w (3)
whereνis the number of species (normally ions) that form on dis- solution (ν= 1 for sugars),mis the molality of the sugar (mol kg−1 water), andMwis the molecular mass of water (kg mol−1).
Water activity has been related to the average hydration number (n−) of a species in solution (moles of water per mole of sugar) and in this paper the derivation fromScatchard (1921) is used. It assumes that some water molecules form a hydrate with the sugar molecules, hence are not active in solution, and are excluded from the concentration used to determine the active mole fraction of water. This approach essen- tially defines hydration number in terms of water activity. Here su- perscriptorefers to the nominal composition.
= = −
+ −
−
a x c nc−
c c nc
( )
w w active w s
w s s
,
o o
o o o
(4)
Dividing by total concentration, the concentrations can be con- verted into mole fractions,x.
= −
+ −
−
a x nx−
x x nx
( )
w w s
w s s
o o
o o o
(5) From this we get Scatchard’s equation
=
− + −
−
−
( )
( )
a
n n 1
w x x x x w s w s o o o
o (6)
which can be rearranged as:
= −
− n− x
x a
a 1
w s
w w o
o (7)
By using this definition, with water activity values determined from a colligative property, hydration number is a unique property of a de- fined solution at a given temperature and pressure. Thus there will be no variation due to modelling assumptions, but only to experimental errors. No claim is made that this analysis correctly represents mole- cular phenomena. However the calculation of hydration number using this approach will be shown to be very effective in discriminating be- tween different data sets.
Using this approach, the consistency of the hydration number is a very good indicator of experimental precision of water activity mea- surements, but at low solute concentrations the hydration number is very sensitive to small errors in water activity.
Given the water activity, the water activity coefficient,γw, can be calculated (aw/xw). A popular equation for the prediction of water ac- tivity coefficient has been that of Norrish (1966) which can be ex- pressed as Eq.(8), withKbeing a parameter for a particular compound.
=
γ K x
ln( )w (so 2) (8)
Maneffa et al. (2017)examined this equation and developed a sta- tistical thermodynamic basis for it, but found for sucrose thatKvaried from about−8 in dilute solutions to−4 at 80% w/w.
Starzak and Peacock (1997)analysed 56 data sets with 1255 data points of sucrose in water up to mass fractions of 95% and for tem- peratures from 0 to 148 °C. They selected and used Eq.(9), a form of the Margules equation (Gokcen, 1996), and determined the bestfit con- stants to beQ=–17638 J mol−1,b1=–1.0038 andb2=–0.24653.
(Thefirst squared term was incorrectly typed inStarzak et al., 2000).
Eqs.(1),(7) and (9)together enable calculation of hydration number and the effect of temperature.
= + +
γ Q
RT x b x b x
ln( )w ( so 2) [1 1 so 2( so 2) ]
(9) The effect of temperature is consistent with the Clausius-Clapeyron equation (as discussed by Sereno, Hubinger, Comesaña, & Correa, 2001) if the partial molar excess heat of mixing is constant with tem- perature. The effectiveness of this equation for sucrose, and its funda- mental properties (Gokcen, 1996), implies the likelihood that the same form of equation will be satisfactory for other sugars and perhaps for other non-electrolytes such as glycerol.
3. Materials and methods
While most of the data were obtained from published literature, some extra data points were measured. Glucose monohydrate (dextrose monohydrate) and fructose were provided by local food ingredients companies while sucrose was purchased from a supermarket. The moisture content of glucose was determined by drying at 105 °C for 24 h at 10 kPa abs. It was found to be 97% hydrated. The fructose was held at 25 °C in a freeze drier at 40 Pa abs with a condensing tem- perature of−47 °C for 3 days. The change in mass, and hence moisture content, was less than 0.1% and insignificant compared with
measurement uncertainties. The salt content of the sugars was de- termined from electrical conductivity and found to be equivalent to mass fraction of 3.1 × 10–5sodium chloride in dry sucrose and less for the other sugars. Each sugar component was analysed using high per- formance liquid chromatography and in each case only a single peak was obtained with a resolution of better than0.1%. Deionised Milli-Q water (18.2MΩat20°C) was used for all solution preparation.
Sugar solutions were prepared in 250 mL clear polystyrene con- tainers using a balance with a precision of 0.1 mg. For solutions con- taining glucose, the required amount of glucose monohydrate was calculated to get the reported mass fractions of anhydrous glucose in solution. The solutions were mixed in an IKA Incubator KS4000i at an orbital shaker speed of 165 rpm and a temperature of 60 °C for 4 h to ensure that all sugar crystals had been dissolved without forming air bubbles. Similarly for model honey systems, which had a higher visc- osity, the time was increased to8hours. The prepared sugar solutions were left to equilibrate to ambient temperature for at least one hour before any measurements.
Water activities of sugar solutions were measured using an AquaLab 4TE (Decagon, USA) water activity meter which works using the prin- ciple of dew point temperature. The water activity meter was calibrated frequently with standard solutions as purchased from the supplier with specified water activities. Apart from standard solutions, the water activity meter was also checked with deionized Milli-Q water giving a value of 1.0000 ± 0.0003. The primary focus was to develop a sound technique to measure water activity to an accuracy of better than ± 0.001. It was found that Decagon’s quoted accuracy of ± 0.003 could be obtained within minutes, but after 4 h of measurement the water activity reached a stable value with a repeatability of ± 0.0003.
4. Results and discussion
Data for sucrose was extensively reviewed byStarzak and Peacock (1997) and is effectively summarised by Eq. (9) with Q=–17638 J mol−1,b1=–1.0038 andb2=–0.24653.
As pointed out byStarzak et al. (2000)Eq.(7)is very sensitive the errors inaw. It can be shown, using theory fromFarrance and Frenkel (2002), that the error in hydration number (Δn−) is related to the error in mole fraction (Δxs) and water activity (Δaw)by
⎜ ⎟ ⎜ ⎟
= −⎛
⎝
⎞
⎠
− ⎛
⎝ −
⎞
⎠ n−
x x
a a
Δ 1
Δ 1
(1 ) Δ
s s
w w
2 2
2 2
2 2
2
(10) Fig. 1shows the effect of measurement error inawon the hydration number calculated
using Eqs.(1),(7) and (9)for sucrose together with the parameters determined byStarzak et al. (2000). In thisfigure the values of water activity were changed by ± 0.0001 and ± 0.001, and values of the solids mass fraction were changed by a relative ± 0.5%, and their effects were calculated at different concentrations. It can be seen that once the sucrose mass fraction exceeds about 0.4 (water fraction less than 0.6), the error in hydration number becomes relatively small but not insignificant. The relative error in the hydration number of glucose was found to be almost identical (not shown).Fig. 1is useful when considering the scatter of data points infigures below.
Useful data for glucose water activities is given by:Bhandari and Bareyre (2003)who used a water activity meter with a sensitivity of 0.001; Zamora, Chirife, and Roldán (2006), water activity meter;
Velezmoro, Oliveira, Cabral, and Meirelles (2000), water activity meter; Miyajima, Sawada, and Nakagaki (1983), isopiestic measure- ments;Bonner and Breazeale (1965), isopiestic measurements;Stokes and Robinson (1966), isopiestic measurements;Taylor and Rowlinson (1955), vapour pressure;Cooke, Jónsdóttir, and Westh (2002a), vapour pressure;Auleda, Raventós, Sánchez, and Hernández (2011), freezing point depression; andEbrahimi and Sadeghi (2016), vapour pressure osmometry. All these data were converted to hydration number and are shown inFig. 2.Mathlouthi and Genotelle (1998)claimed that sucrose will be fully hydrated at less than about one third of saturation con- centration, but beyond this intra- and inter-molecular hydrogen bonding reduces the number of available hydration sites. Therefore it seems very unlikely that the hydration number should decrease in more dilute systems, but as shown inFig. 1the value of hydration number is extremely sensitive to experimental error in dilute solutions, so any apparent reduction inn−is almost certainly due to small experimental uncertainties amplified by this sensitivity.
To carry out a statistical regression of the data, the resulting re- siduals (deviations from the fitted curve) should be normally dis- tributed and independent of concentration. A number of methods were tested for this attribute. Regression of water activity, water activity coefficient and hydration number gave residuals that were strongly concentration dependent, so these methods could not be used. Eq.(10)
Fig. 1.Sensitivity of sucrose hydration number to uncertainties in water activity of ± 0.001 and ± 0.0001, and relative uncertainties in sucrose mass fraction of ± 0.5% using parameters fromStarzak et al. (2000).
shows that if the error inaw is normally distributed and there are no other errors, then(1−aw)2 times the error inn−should be normally distributed. This did not prove to be the case when tested using a quantile to quantile (Q-Q) plot of residuals. A better distribution of errors was obtained by weighting the residuals with the semi-empirical factor 1−aw. Further weightings were applied based on the con- sistency of the data.
Hydration numbers were excluded from the data set if they were calculated to be negative or greater than twice the fitted value. The point for the mass fraction of 0.2789 from Velezmoro et al. was clearly a typographical error and was excluded. The increase in hydration number with temperature given byCooke et al. (2002a)is contrary to the expected decrease according to Eqs.(7) and (9). Therefore the data of Cooke et al. was given an additional weighting factor of 0.5. Some studies provided many more data points than others but with no reason to assume greater accuracy, so data sets with more than 10 points were weighted down to give them that same contribution as data sets with 10 points. After fitting, the data ofBhandari and Bareyre (2003) con- sistently had the highest residuals so an additional weighting factor of 0.2 was applied. Even then the weighted residuals for these points was about twice the average.
The method outlined byBox, Hunter, and Hunter (1978)was used for the estimation of parameter uncertainties for non-linear regression.
This method allows a parameter set to be accepted if sum of squared residuals is less than a critical value,SScr, as determined by Eq.(11)
⎜ ⎟
= ⎛
⎝
+ − − − ⎞
⎠
SS SS p
n pF p n p α
1 ( , , 1 )
cr min
(11) HereSSminis the minimum sum of squared residuals obtained from the curvefitting,pis the number of parameters in the equation,nis the number of data points, and1−αis the confidence level.
It was assumed that the three parameters of Eq.(9)were constant with temperature, and temperature effects were accounted for by the temperature term in this equation. The parameters for glucose and uncertainties (95% confidence region) were found to beQ =–7010 [-7900,−6400] J mol−1,b1=–1.3 [-2.1,−1.1] andb2= 0.28 [0.05, 2.0].
For clarity, hydration number is related to the mass fraction of water, but equally any other concentration units could be used. Further the fraction of water, rather than the fraction of sugar is used, because
as will be discussed later, in mixed systems the hydration is probably related to the amount of water, not the concentration of any individual solute. This graph provides a useful indication of the effect of tem- perature that will be used in later discussion. Of note is the very small effect of temperature compared with the wide variation in data.
It is acknowledged that a low water content is not physically fea- sible without significant supersaturation; however large super- saturation can occur in mixtures. The model curve is expected to pass through the origin as a positive y-axis intercept is impossible as this requires hydration without water, and a positive x-axis intercept seems unlikely as very small fractions of water are likely to be bound to the sugars.
The available data for fructose are given inFig. 3.Cooke, Jónsdóttir, and Westh (2002b)gave data for the vapour pressure of fructose so- lutions at 45 °C. It is apparent that the last two data points for fructose given by Cooke et al. have been typed incorrectly as they do not match theirfitted equation at all well. The same method of regression as for glucose was used. The data of Cooke et al. was given the same factor of 0.5 due to uncertainties revealed during analysis of their glucose data.
The parameters for fructose wereQ=–6570 with 95% confidence [-7200,−5750] J mol−1,b1=–1.14 [–1.8,–0.6] andb2= 0.05 [–0.5, 1.8]. These are not statistically different from the parameters for glu- cose. Comparisons can be made using studies that tested both glucose and fructose using the same methods. At about 60% sugar at 45 °C the hydration number of glucose was found by Cooke et al. (2000a, b) to be about 0.5 higher than for fructose.Zamora et al. (2006)obtained very similar water activities for glucose and fructose, with the hydration number of glucose being about 0.05 higher than fructose. Data was obtained from a figure given by Chirife, Favetto, and Ferro Fontán (1982)who concluded that the water activities of fructose could not be distinguished from glucose.Auleda et al. (2011)gave freezing point depression for glucose, fructose and sucrose. The calculated hydration numbers for fructose were about 0.4 lower than for glucose at about 40% sugar. Velezmoro et al. (2000) also showed lower values for fructose than glucose but data are too scattered to be reliable. On balance from the experimental data, it seems possible that the hydra- tion numbers of fructose are up to 20% lower than of glucose, but this has no statistical support. For greater certainty, experiments could be carried out with the specific aim of determining the difference between the two sugars.
Fig. 2.Hydration number of glucose. Curves were calculated using Eqs.(7) and (9)withQ=–6500 J mol−1,b1=–0.7 andb2= -0.3 at 0 °C, 25 °C and 45 °C.
Maltose data given byCooke et al. (2002a)from vapour pressure;
Uedaira and Uedaira (1969), isopiestic measurements; Ebrahimi and Sadeghi (2016), vapour pressure osmometry; and Weast (1978), freezing point depression (of unknown origin) are shown inFig. 4. The same regression method was used giving parametersQ=–13300 with 95% confidence [-14500,−10500] J mol−1,b1= 0.2 [-1.3, 2.2] and b2= -1.7 [-45, 3.4]. Thus the hydration numbers of maltose were found to be significantly lower than those of sucrose.Cooke et al. (2002a,b) provide data for maltose and sucrose with a hydration number about 0.5 higher for sucrose, and Ebrahimi and Sadeghi found that a positive difference of 1 to 1.5 for sucrose. Using different methods, Suggett (1976) found that the hydration number from dielectric measurements
was 5.0 for maltose and 6.6 for sucrose, butShiraga et al. (2013)using a refractive index technique to determine hydration number, found no difference between sucrose and maltose, andBranca et al. (2001)ob- tained values about 0.5 higher for maltose using viscosity data. More data is desirable for maltose in order to calculate hydration numbers.
The same approach worked well for glycerol using vapour pressure data from To et al. (1999), vapour pressure; Ninni, Camargo, and Meirelles (2000)dew point hygrometer;Marcolli and Peter (2005), dew point hygrometer, Scatchard, Hamer, and Wood (1938), isopiestic.
These data are shown in Fig. 1of supplementary data. The data of Weast (1978)was totally inconsistent with the other literature data and is not included. The parameters were found to be Q =–3070 [-3275, Fig. 3.Hydration number of fructose. Curves were calculated using Eqs.(7) and (9)withQ=–5650 J mol−1,b1=–1.14 andb2= 0.05.
Fig. 4.Hydration number of maltose. Curves were calculated using Eqs.(7) and (9)withQ=–14500 J mol−1,b1=–1.00 andb2= 3.00.
−2900] J mol−1, b1 =–0.92 [-1.2, 0.65] and b2 = 0.0 [-0.4, 0.4].
4.1. Mixtures containing more than one component
Sereno et al. (2001)detailed the different models that are available to calculate the water activity of aqueous solutions relevant to food systems. One approach is the Ross (1975)equation which gives the water activity of a mixture as the product of the component water ac- tivities calculated using the component water activities evaluated in binary solutions at the same molality of the component as in the mix- ture. Ross’s approach is based on the Gibbs-Duhem relationship so is exact as long as there are no new solute–solute interactions introduced in a multicomponent mixture.
∏
=
aw mix, aw i, (12)
or using activity coefficients
∏
= aw mix γ xw i
, , w i, (13)
It is proposed here that Scatchard’s approach can be extended to mixtures of sugars by using the same idea used by Scatchard that the water activity is the mole fraction of active water. In this equation the hydration numbers are calculated for binary solutions at the same mole fraction of water as the mixture. The use of mole fraction rather than mass fraction allows extension to systems with electrolytes that dis- sociate.
= − ∑
− ∑
−
a x −n x
(1 n x )
w
w i s i
i s i
o o,
,
o (14)
Herexs io, is the mole fraction of componenti(sugar or salt) andn−iis the hydration number of component evaluated for a binary solution evaluated at the water mole fraction,xwo.
Rüegg and Blanc (1981)obtained water activity measurements of model honey solutions using an electronic hygrometer. They used water fractions from 12.1% to 28% with a dry-basis composition of 48%
fructose, 40% glucose, 10% maltose and 2% sucrose. In addition four extra data points were obtained using the same dry-basis composition in the current work. Their results, new data points, and the predictions from Eq. (14)are given in Fig. 5. Calculations were also made with Ross’s equation using binary water activities calculated using the same equations as in this work but using the same molality. The agreement of
the data points of Rüegg and Blanc with Eq.(14)at moistures above 20% is very good, but the bottom two data points show positive de- viations from any smooth curve. Possibly the sugar was not fully dis- solved. In contrast the new experimental points from the current work fit well with most of the previous points.
Ross’s equation was much less effective at this moisture content.
Rüegg and Blanc obtained different values by using Eq.(12)but using the average osmotic coefficient from their data. Here it is noted that Eq.
(14) is ana prioricalculation whereas the calculation of Rüegg and Blanc was not.Ben Gaida, Dussap, and Gros (2006)also attempted tofit this data, but the deviations are much higher than those shown here.
The method was further extended to also include small amounts of salts to determine the possible effects of these in a honey like system.
The same approach could be used to determine the effect of any addi- tional component. It was not possible to estimate the hydration number of sodium chloride in solutions at the low moisture content of honey as this would require extrapolation well beyond the solubility limit of sodium chloride. Instead Eq.(14)was extended to explicitly include a term for sodium chloride.
= − ∑ −
− ∑ −
− −
− −
a x n x n x
n x n x
(1 )
w
w i s i NaCl NaCl
i s i NaCl NaCl
o o,
,
o (15)
Rearranging, Eq. (16)was obtained for the hydration number of NaCl.
= − − − ∑
−
−
−
n x a a n x
x a
(1 )
(1 )
NaCl w w w i s i
NaCl w
o
, o
(16) As before the hydration number of the sugars was determined for binary solutions at the mole fraction of water in the mixture. Complete dissociation of NaCl is assumed, so the molar concentration used to calculate mole fractions will be twice the concentration of NaCl.
However, in a system with low concentrations of water complete dis- sociation might not occur. Further, we consider, for the calculation, that the Na+and Cl–ions are equally hydrated, even though this will not be the case. Using Eq.(16) with measured water activity data, the hy- dration number of Na+and Cl-was calculated to be between 0.07 and 0.09 which is small but not insignificant. Using an average hydration number of 0.075 for Na+and Cl-the water activity was calculated as shown inFig. 6. The effect seen is mainly due to the effect of NaCl on the mole fractions and not due to hydration.
Fig. 5.Water activities of model honey fromRüegg and Blanc (1981)and current work with Eq.(14)and Ross’s equation.
5. Discussion and conclusions
The sensitive effect of water activity measurements on the hydration number calculation is illustrated inFig. 1. This suggests that there is little hope of getting accurate hydration numbers from water activity measurements at water mass fractions above about 0.7. However, at such concentrations, the water activity is close to 1.0 and of less in- terest. Further, crude estimates of hydration number will give accurate water activities. As also seen inFig. 1, at lower moisture contents, the accuracy of mass measurement becomes critical and hence an accurate moisture determination of the sugars using a method such as Karl Fi- scher titration would be desirable.
Figs. 2–4show that the use of hydration number is very effective when comparing water activity data from different sources. The ap- proach does not prove that Eq.(7)is correct, but Scatchard’s model is independent of the method used to obtain water activity and is hence a consistent basis for comparison. Hydration numbers could also be compared by using water activity equations from Norrish (1966), Maneffa et al. (2017), and others. The number of data is too small and scatter too great to be able to determine the best equations with high certainty. The figures show the concentrations at which more data would be useful. For example, thefitted equation for maltose relies too heavily on data fromCooke et al. (2002a,b)whose data for glucose and fructose were found to be inconsistent with other studies.
The proposed extension of Scatchard’s equation (Eq.(14)) for multi- component systems was found to be very effective. Both this method and that of Ross, use water activities, or their equivalent hydration numbers, from binary solutions of the components. A key difference is that Ross proposed, from theory, that the molal concentration be used, while here we propose that the mole fraction of water in the solution is used to determine the equivalent binary solution. As an example, for the model honey recipe of Rüegg and Blanc given above with 84% solids, Ross’s method evaluated the water activity of a binary glucose solution at a water mole fraction of 0.799, whereas the proposed method eval- uates it as 0.660. Neither method explicitly considers changes in so- lute–solute or solute-water interactions with concentrations. Effectively it is assumed in the current work, that the changes is interactions are incorporated by determining hydration numbers at the low mole frac- tion of water in the mixture. At high sugar concentrations in the mix- tures, the hydration numbers are obtained from regions on the graphs
where there are relatively few data points. However the imposed re- quirement that hydration is zero when the water content is zero, limits the uncertainty. More data for supersaturated binary sugars would decrease these uncertainties further.
In sugar solutions with glucose, fructose, sucrose, and NaCl, the hydration of dissociated NaCl was estimated. It was found that the hydration of NaCl was small and also noted that the main effect that NaCl had was by lowering the mole fraction of water in the system.
Hence when a food system with multiple sugars and these electrolytes are present, the data is best represented by mole fraction.
In none of the previous work seen, or in the experimental results here, was there any indication that small amounts of an extra substance would substantially alter the hydration and hence water activity.
Funding
This work was supported by a University of Canterbury, New Zealand, doctoral scholarship for Subbiah.
CRediT authorship contribution statement
Balaji Subbiah: Investigation, Validation, Funding acquisition, Writing - original draft, Data curation. Ursula K.M. Blank:
Conceptualization. Ken R. Morison: Software, Writing - review &
editing, Data curation, Formal analysis, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competingfinancial interests or personal relationships that could have appeared to influ- ence the work reported in this paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps://
doi.org/10.1016/j.foodchem.2020.126981.
Fig. 6.Effect of added sodium chloride on the water activity of solutions with equal concentrations of glucose and fructose at 20 °C. The total solids concentration was 83%.
References
Auleda, J. M., Raventós, M., Sánchez, J., & Hernández, E. (2011). Estimation of the freezing point of concentrated fruit juices for application in freeze concentration.
Journal of Food Engineering, 105, 289–294.
Ben Gaida, L., Dussap, C. G., & Gros, J. B. (2006). Variable hydration of small carbohy- drates for predicting equilibrium properties in diluted and concentrated solutions.
Food Chemistry, 96, 387–401.
Berry, R. S., Rice, S. A., & Ross, J. (1980).Physical Chemistry.NY: John Wiley and Sons.
Beuchat, L. R. (1983). Influence of water activity on growth, metabolic activities and survival of yeasts and molds.Journal of Food Protection, 46, 135–141.
Bhandari, B., & Bareyre, I. (2003). Estimation of crystalline phase present in the glucose crystal–solution mixture by water activity measurement.Lebensmittel-Wissenschaft &
Technologie, 36, 729–733.
Bonner, O. D., & Breazeale, W. H. (1965). Osmotic and activity coefficients of some nonelectrolytes.Journal of Chemical and Engineering Data, 10, 325–327.
Box, G. E. P., Hunter, W. G., & Hunter, S. J. (1978).Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building (p485).New York: John Wiley and Sons.
Branca, C., Magazù, S., Maisano, G., Migliardo, F., Migliardo, P., & Romeo, G. (2001).α, α-Trehalose/water solutions. 5 Hydration and viscosity in dilute and semidilute disaccharide solutions.Journal of Physical Chemistry B, 105, 10140–10145.
Burakowski, A., & Gliński, J. (2012). Hydration numbers of nonelectrolytes from acoustic methods.Chemical Reviews, 112, 2059–2081.
Chirife, J., Favetto, G., & Ferro Fontán, C. (1982). The water activity of fructose solutions in the intermediate moisture range.Lebensmittel-Wissenschaft & Technologie, 15, 159–160.
Cooke, S. A., Jónsdóttir, S. O., & Westh, P. (2002a). A thermodynamic study of glucose and related oligomers in aqueous solution: Vapour pressures and enthalpies of mixing.Journal of Chemical and Engineering Data, 47, 1185–1192.
Cooke, S. A., Jónsdóttir, S. O., & Westh, P. (2002b). The vapour pressure of water as a function of solute concentration above aqueous solutions of fructose, sucrose, raffi- nose, erythritol, xylitol and sorbitol.Journal of Chemical Thermodynamics, 34, 1545–1555.
Ebrahimi, N., & Sadeghi, R. (2016). Osmotic properties of carbohydrate solutions.Fluid Phase Equilibria, 417, 171–180.
Farrance, I., & Frenkel, R. (2002). Uncertainty of measurement: A review of the rules for calculating uncertainty components through functional relationships.Clinical Biochemist Reviews, 33, 49–75.
Furuki, T. (2002). Effect of molecular structure on thermodynamic properties of carbo- hydrates. A calorimetric study of aqueous di- and oligosaccharides at subzero tem- peratures.Carbohydrate Research, 337, 441–450.
Gleiter, R. A., Horn, H., & Isengard, H.-D. (2006). Influence of type and state of crystal- lisation on the water activity of honey.Food Chemistry, 96, 441–445.
Gokcen, N. A. (1996). Gibbs-Duhem-Margules Laws.Journal of Phase Equilibria, 17, 50–51.
Maneffa, A. J., Stenner, R., Matharu, A. V., Clark, J. H., Matubayasi, N., & Shimizu, S.
(2017). Water activity in liquid food systems: A molecular scale interpretation.Food Chemistry, 237, 1133–1138.
Marcolli, C., & Peter, Th. (2005). Water activity in polyol/water systems: New UNIFAC
parameterization.Atmospheric Chemistry and Physics, 5, 1545–1555.
Mathlouthi, M., & Genotelle, J. (1998). Role of water in sucrose crystallization.
Carbohydrate Polymers, 37, 335–342.
Miyajima, K., Sawada, M., & Nakagaki, M. (1983). Studies of aqueous solutions of sac- charides. I. Activity coefficients on monosaccharides in aqueous solutions at 25 °C.
Bulletin of the Chemical Society of Japan, 56, 1620–1623.
Ninni, L., Camargo, M. S., & Meirelles, A. J. A. (2000). Water Activity in Polyol Systems.
Journal of Chemical and Engineering Data, 45, 654–660.
Norrish, R. S. (1966). An equation for the activity coefficients and equilibrium relative humidities of water in confectionery syrups.Journal Food Technology, 1, 25–39.
Ross, K.D. (1975) Estimation of water activity in intermediate moisture foods, Food Technology, March, 26-34.
Rüegg, M., & Blanc, B. (1981). The water activity of honey and related sugar solutions.
Lebensmittel-Wissenschaft & Technologie, 14, 1–6.
Scatchard, G., Hamer, W. J., & Wood, S. E. (1938). Isotonic solutions. I. The chemical potential of water in aqueous solutions of sodium chloride, potassium chloride, sul- furic acid, sucrose, urea and glycerol at 25°C.Journal of Solution Chemistry, 60, 3061–3070.
Scatchard, G. (1921). The hydration of sucrose in water solutions as calculated from vapour-pressure measurements.Journal of the American Chemical Society, 43, 2406–2419.
Sereno, A. M., Hubinger, M. D., Comesaña, J. F., & Correa, A. (2001). Prediction of water activity of osmotic solutions.Journal of Food Engineering, 49, 103–114.
Shiraga, K., Ogawa, Y., Kondo, N., Irisawa, A., & Imamura, M. (2013). Evaluation of the hydration state of saccharides using terahertz time-domain attenuated total reflection spectroscopy.Food Chemistry, 140, 315–320.
Starzak, M., & Peacock, S. D. (1997). Water activity coefficient in aqueous solutions of sucrose - A comprehensive data analysis.Zuckerindustrie, 122, 380–387.
Starzak, M., Peacock, S. D., & Mathlouthi, M. (2000). Hydration number and water ac- tivity models for the sucrose-water system: A critical review.Critical Reviews in Food Science and Nutrition, 40, 327–367.
Stokes, R. H., & Robinson, R. A. (1966). Interactions in aqueous nonelectrolyte solutions.
I.Solute-solvent equilibria, The Journal of Physical Chemistry, 70, 2126–2131.
Suggett, A. (1975). Polysaccharides. In F. Franks (Vol. Ed.),Water: A Comprehensive Treatise: vol 4. New York: Plenum Press.
Taylor, J. B., & Rowlinson, J. S. (1955). The thermodynamic properties of aqueous so- lutions of glucose.Transactions of the Faraday Society, 51, 1183–1192.
To, E. C. H., Davies, J. V., Ticker, M., Westh, P., Trandum, C., Suh, K. S. H., & Koga, Y.
(1999). Excess chemical potentials, excess partial molar enthalpies, entropies, vo- lumes, and isobaric thermal expansivities of aqueous glycerol at 25°C.Journal of Solution Chemistry, 28, 1137–1157.
Uedaira, H., & Uedaira, H. (1969). Activity coefficients of aqueous xylose and maltose solutions.Bulletin of the Chemical Society of Japan, 42, 2137–2140.
Velezmoro, C. E., Oliveira, A. L., Cabral, F. A., & Meirelles, A. J. A. (2000). Prediction of water activity in sugar solutions using models of group contribution and equation of state.Journal of Chemical Engineering of Japan, 33, 645–653.
Weast, R. C. (1978).CRC Handbook of Physics and Chemistry((58th ed.).). Florida U.S:
CRC Press.
Zamora, M. C., Chirife, J., & Roldán, D. (2006). On the nature of the relationship between water activity and % moisture in honey.Food Control, 17, 642–647.