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Moisture sorption isotherms for crystalline, amorphous and predominantly crystalline lactose powders
ARTICLE IN PRESS
International Dairy Journal 14 (2004) 247–254
Moisture sorption isotherms for crystalline, amorphous and predominantly crystalline lactose powders John Bronlund*, Tony Paterson Institute of Technology and Engineering, PN 456, Massey University, Private Bag 11222, Palmerston North, New Zealand Received 3 February 2003; accepted 23 July 2003
Abstract Moisture sorption isotherms for amorphous lactose, crystalline a-lactose monohydrate and a predominantly crystalline lactose powder were measured. No temperature dependence was observed over the range investigated (12–40 C), except for amorphous lactose at 12 C, which absorbed less moisture than observed at higher temperatures. The amount of water absorbed by crystalline powders at high water activity was dependent on the packing density of the powder. This observation could be explained using the capillary condensation theory. The moisture isotherm of a partially amorphous lactose powder was successfully predicted by using a simple additive isotherm model to combine the isotherms of crystalline and amorphous lactose powders. Small quantities of amorphous lactose present on crystalline powders, causes significant changes to the moisture sorption isotherm. If the high water activity region of the isotherm of crystalline a-lactose monohydrate is of interest then the isotherm should be measured at the packing density of interest. r 2003 Elsevier Ltd. All rights reserved. Keywords: Moisture sorption isotherms; Lactose; Amorphous; Crystalline sugar
1. Introduction Lactose is a sugar that is derived from milk. The reduced sweetness, enhanced aroma binding abilities and low cost make it a commonly used replacement for more traditional sugars as a food ingredient. It is also one of the most commonly used excipients in tableting and granulation operations in the pharmaceutical industry (Harper, 1992). The most common form of lactose used in industry is crystalline a-lactose monohydrate (C12H22O11 H2O), which is prepared by crystallisation from aqueous solution below 93.5 C. Once separated from the mother liquor, refined, dried and milled, the product should be a free flowing fine white powder of similar consistency to icing sugar. Caking problems can occur after the product is packed and stored. Bronlund (1997) investigated the phenomena that cause caking in crystalline lactose powders. Liquid bridging between adjacent particles was found to occur in conditions of high humidity (>85%), causing *Corresponding author. Tel.: +64-6-3505542; fax: +64-6-3505604. E-mail address: [email protected] (J. Bronlund). 0958-6946/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0958-6946(03)00176-6
lumping. If these bridges were dried out, solid crystalline bridges formed and a caked product resulted. Bronlund (1997) also showed that the presence of amorphous lactose on the surface of the crystals was important. Thin layers of amorphous lactose are formed on the surface of the powder during flash drying and milling operations. If the glass transition temperature of the amorphous lactose is exceeded, then the particles can become sticky and the amorphous lactose crystallises, causing caking and lumping problems. To avoid caking and lumping complaints in predominantly crystalline lactose powders it is essential to understand how lactose interacts with the moisture in the air. Many other researchers have reported moisture sorption isotherms for crystalline a-lactose monohydrate (Loncin, Bimbenet, & Lenges, 1968; Audu, Loncin, & Weisser, 1978; Warburton & Pixton, 1978; Linko, Pollari, Harju, & Heikonen, 1982; Callahan et al., 1982) and amorphous lactose (Berlin, Anderson, & Pallansch, 1968; Warburton & Pixton, 1978; Linko et al., 1982; Roos & Karel, 1990; Jouppila & Roos, 1994). However, the effects of temperature and particle size have never been quantified. There have been no reports
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248
Nomenclature a aw c f h H H0
amorphous lactose content (kg kg1) water activity (dimensionless) BET constant (dimensionless) GAB constant (dimensionless) third stage sorption isotherm constant (dimensionless) third stage sorption isotherm intermediate (dimensionless) third stage sorption isotherm intermediate (dimensionless)
in the literature explicitly aimed at determining the moisture sorption isotherms for crystalline lactose powders with low levels of amorphous material present. In fact none of the reports on moisture sorption isotherms for crystalline lactose state that they ensured their samples were 100% crystalline. The aim of this work was to measure, and to characterise the effect of particle size and temperature on the moisture sorption isotherms for completely amorphous lactose, crystalline a-lactose monohydrate and a predominantly crystalline lactose powder.
2. Methods and materials 2.1. Lactose sources Commercially manufactured crystalline a-lactose monohydrate of differing particles sizes were obtained from Lactose New Zealand Ltd. The powders used were 100, 200 and 300 mesh and special dense (an unmilled powder with a wide particle size distribution) and greater than 99% purity. Pure amorphous lactose was produced by spray drying according to the method outlined by Lloyd, Chen, and Hargreaves (1996). A lactose product called Supertab, provided by The Lactose Company of New Zealand Ltd., was used as a partially amorphous lactose powder. This product contains approximately 10% amorphous lactose. 2.2. Moisture sorption isotherms The moisture sorption isotherms for each powder were measured using the static gravimetric method (Stitt, 1958). Air tight desiccators, containing saturated salt solutions (made from Analar grade salts and deionised water) placed inside temperature controlled rooms, were used to provide constant relative humidity and temperature environments. Approximately 10 g of
M M0 Pv Pw r R T V0 y s
moisture content (kg kg1 dry solid) BET mono-layer moisture content (kg kg1 dry solid) vapour pressure (Pa) saturated vapour pressure (Pa) capillary radius (m) universal gas constant (J mol1 K1) temperature (K) molar volume (m3 mol1) contact angle (rad) surface tension (N m1)
each powder were placed in the desiccators and allowed to equilibrate. Each sample was weighed periodically over a period of 3 weeks, using a Metler AE200 analytical balance, to ensure equilibrium was reached. The samples were covered air tight to avoid moisture adsorption or desorption during the weighing process. 2.3. Initial moisture content determination The initial moisture contents of the samples were determined by desiccation over phosphorus pentoxide for 3 weeks, when constant weight was observed. The isotherms were then determined from the weight change from the initial sample. By measuring the moisture sorption isotherm in this way, desorption occurred below the starting powder water activity, and adsorption occurred above this value. It should also be noted that the moisture content measurements are based on the moisture that can be removed by desiccation of the powder over phosphorus pentoxide, and therefore do not include any water of crystallisation that is present in powders containing a-lactose monohydrate, or water entrapped in the crystals. Heating to 120 C is required to remove all the water of crystallisation (Stecher, 1968). 2.4. Saturated salt solutions Table 1 summarises the range of conditions in which each powder was measured. For the measurement of the sorption isotherm of amorphous lactose, conditions below 60% RH were chosen as above this value, crystallisation occurs and therefore the isotherm data are not meaningful. For the crystalline and partially crystalline samples, isotherm data across the whole water activity range were measured, concentrating particularly on the high water activity region where capillary condensation was expected to occur.
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Table 1 Equilibrium relative humidity (%) conditions for moisture sorption isotherm measurements Saturated salt solutiona
Crystalline a-lactose monohydrate
LiCl KCH2COO MgCl2 K2CO3 Mg(NO3)2 NaCl (NH3)2SO4 KCl KNO3 K2SO4 a b
Amorphous lactose
Supertab
12 C
20 C
30 C
40 C
12 C
20 C
30 C
38 C
20 C
11 — 33 — 56 78 81 87 95 98
11 — 33 — 54 77 80 87 94 98
11 — 32 — 53 75 80 84 93 97
11 — 32 — 51 74 79 81 90 97
11 23 33 43 56 — — — — —
11 22 33 43 — — — — — —
11 21 32 — — — — — — —
11 21 31 — — — — — — —
11 — 31 — 54b 77b 80b 87b 94b 98b
Equilibrium relative humidity values were taken from Greenspan (1977). The amorphous lactose in these samples were expected to crystallise in these conditions.
3. Results and discussion 3.1. Amorphous lactose The moisture sorption isotherm for amorphous lactose is shown in Fig. 1. The absolute error in the measurements was found to be 70.04 g/100 g dry lactose by error analysis. Also included in Fig. 1 is the data reported by Jouppila and Roos (1994), Berlin et al. (1968), Roos and Karel (1990) and Warburton and Pixton (1978). Data were omitted at high water activity where the characteristic desorption associated with amorphous lactose crystallisation was evident. The literature data of Linko et al. (1982) and PritzwaldStegmann (1986) were also not included on the graph as they were markedly different from the other reported data. It can be seen that there is little difference between the literature data and those collected in this study, suggesting that the structure of freeze dried and spray dried powders are similar. The results also show negligible influence of temperature on the isotherm shape over the range investigated (20–40 C), except for the low temperature experiment (12 C) which deviates downward above 0.4 water activity. Because the driving force for crystallisation increases with temperature, the maximum water activity at which a measurement could be taken reduced with temperature. This meant that at a water activity of 0.54 only the sample held at 12 C, reached equilibrium and it is possible that partial crystallisation of this sample could have occurred. Jouppila and Roos (1994) fitted the Guggenheim, Anderson, de Boar (GAB) equation (Eq. 1) to their isotherm data for freeze dried amorphous lactose and they are also plotted in Fig. 1. GAB constants were fitted to the data collected in this study (see Fig. 1). The GAB parameters are shown in Table 2, along with those used by Jouppila and Roos (1994). Because the data of
Jouppila and Roos (1994) are consistently higher than the data collected in this work and to those reported by other researchers it is suggested that the GAB parameters obtained in this work should be used in the future. It should be noted that the fitted isotherm parameters are only valid in conditions that avoid amorphous lactose crystallisation (i.e. below the glass transition temperature): M¼
M0 cfaw : ð1 faw Þ½1 ð1 cÞfaw
ð1Þ
3.2. Crystalline lactose Fig. 2 shows the moisture sorption isotherm measured for unmilled a-lactose monohydrate (special dense) over the range of temperatures investigated (12–40 C). The uncertainty in the data was calculated by error analysis and found to be 70.029 g 100 g1 dry lactose. The literature data are not included in Fig. 2 because it is highly scattered. This is likely to be due to the various ways the moisture content of the samples has been determined. A drying technique that removes only a small fraction of the water of crystallisation can result in significant differences in free water content. It can be seen from Fig. 2 that there is no significant effect of temperature on the sorption isotherm over the range investigated (12–40 C). The powder adsorbs very little moisture over the low water activity range (0–0.85). It is only at water activities above 0.85 that significant amounts of moisture are adsorbed. The moisture content increases exponentially above this point and approaches an asymptote at a water activity of one. One reason for the exponential increase in moisture content at high water activities is capillary condensation, first proposed by Zsigmondy in 1911 (see Adamson, 1963). Capillary condensation is the process where direct condensation can occur, due to surface tension effects, in the capillaries formed at the contact points between
ARTICLE IN PRESS J. Bronlund, T. Paterson / International Dairy Journal 14 (2004) 247–254
250 16%
12°C 20°C
14%
30°C 38°C
M (g g-1 dry lactose)
12%
Jouplila and Roos (1994) (24°C) Roos and Karel (1990) (25°C)
10%
Warburton and Pixton (1978) (25°C) Berlin et.al. (1968) (24.5°C)
8%
GAB model (12°C) GAB model (20-38°C)
6%
GAB model (Joupilla and Roos 1994)
4%
2%
0% 0
0.1
0.2
0.3
0.4
0.5
0.6
Water activity
Fig. 1. Effect of temperature on the moisture sorption isotherm of amorphous lactose.
Table 2 GAB isotherm parameters for amorphous lactose (applicable in conditions where amorphous lactose crystallisation will not occur) GAB isotherm parameter
Isotherm data measured at 12 C
Isotherm data Isotherm data measured at measured by Jouppila 20–38 C and Roos (1994)
M0 (g g1 dry solids) f c
0.0693
0.0488
0.0491
0.77 3.39
1.16 3.23
1.18 4.33
adjacent particles. As a result the saturated vapour pressure in the capillary, above the liquid surface can be less than the vapour pressure of the bulk air. In this way direct condensation can occur in the capillaries even in conditions where the bulk air relative humidity is less than 100%. The water vapour pressure at which capillary condensation will occur is dependent on the radius of the capillary and is given by the Kelvin equation (Eq. (2)) (Adamson, 1963): Pv 2s cos yV0 aw ¼ ¼ exp : Pw rRT
ð2Þ
Using this equation it can be shown that capillary condensation can occur at relative humidities above about 80%. At relative humidities below 0.8 the capillary radii required to cause capillary condensation approach molecular dimensions where macroscopic properties such as surface tension and contact angle are not applicable (Adamson, 1963). As the capillary radius increases, the minimum water activity required for condensation to occur, increases.
This explanation of the sorption behaviour of water at high water activity has two important consequences. Firstly, the high water activity region of the measured isotherm shown in Fig. 2 will not apply for individual particles, as there will be no capillaries present for condensation to occur in. The isotherm is therefore only valid for packed beds of lactose powders. Secondly, the capillary size distribution of the powder may influence the shape of the isotherm curve at high water activity. In order to investigate the effect of capillary size distribution the moisture sorption isotherms were measured at 20 C for crystalline powders with differing particle sizes. Fig. 3 shows the results for lactose powders milled to 100 mesh, 200 mesh and 300 mesh particle size as well as the isotherm for unmilled lactose at 20 C. It can be clearly seen in Fig. 3 that there was less water adsorbed at equivalent conditions for the milled samples compared to the unmilled (special dense) powder in the high water activity range. This result is consistent with the nature of the powders. The finely milled samples have a relatively narrow particle size distribution where the unmilled powder has a wide distribution (Bronlund, 1997). For this reason there is a greater packing density for the unmilled powder (bulk density, 800 kg m3), and therefore a smaller voidage fraction, corresponding to a smaller average capillary radius between particles, than the milled samples (average bulk density, 625 kg m3). Fig. 4 was constructed by using the Kelvin equation (Eq. (2)) to calculate the effective capillary radius at each water activity that the powders were measured at. A contact angle of zero (a fully wetted surface) was assumed and the surface tension of a saturated lactose
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251
1.0% 12°C 20°C
0.9%
30°C 37°C
M (g g-1 lactose monohydrate)
0.8%
tss model
0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 2. Effect of temperature on the moisture sorption isotherm of crystalline a-lactose monohydrate.
1.0% Unmilled 100 mesh 200 mesh 300 mesh tss model (milled) tss model (unmilled)
0.9%
M (g g-1 lactose monohydrate)
0.8% 0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 3. Effect of particle size on moisture sorption isotherm for crystalline a-lactose monohydrate.
solution (0.068 N m1) measured by Bronlund (1997) was used to make these calculations. The moisture content measured at each water activity was then plotted against the calculated capillary radius. Any capillaries smaller than the calculated radius at any given water activity are full of water due to the process of capillary condensation. It can be seen from Fig. 4 that the unmilled powder adsorbed more moisture at a given capillary radius than the milled samples. This infers that the milled powders lower voidage fraction, forming small capillaries between particles compared with the unmilled powder. For
this reason, higher water activity conditions are required before significant amounts of moisture can be adsorbed by condensation into the larger capillaries that are present in the milled samples. Because of the difficulty in measuring the effective capillary size distribution of the bulk powder and also because the effective capillary radius increases as the moisture fills up the capillary, an alternative mathematical expression for the moisture sorption isotherm was investigated. The third stage sorption (TSS) isotherm was developed by Timmermann (1989) and Timmermann and
ARTICLE IN PRESS J. Bronlund, T. Paterson / International Dairy Journal 14 (2004) 247–254
252
1.0% Unmilled 100 mesh 200 mesh 300 mesh Linear fit (unmilled) Linear fit (milled)
0.9%
M [g g-1 dry lactose]
0.8% 0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
10
20
30
40
50
Capillary radius [nm] 0
0.85
0.90
0.95
0.96
0.97
0.98
Water activity
Fig. 4. Effect of capillary radius on moisture adsorption for crystalline a-lactose monohydrate.
Chiriffe (1991) to extend the GAB isotherm model to water activity ranges approaching unity. It is based on the premise that after a certain number of moisture layers exist, the moisture behaves as liquid water. The TSS isotherm has the advantage that it can be used to explain the whole of the isotherm where the capillary condensation approach is only valid in the high water activity region. The isotherm model is shown as equations (Eq. (3)–(5)): M¼
M0 cHfaw H 0 ; ð1 faw Þ½1 þ ðcH 1Þfaw
H ¼1þ
TSS isotherm parameter
M0 (g g f c h
1
dry solids)
Lactose powder sample Unmilled
Milled
2.29e-4 0.966 8.8 30
1.68e-4 0.878 8.8 30
ð3Þ
ð1 f Þ ðfaw Þh ; f ð1 aw Þ
ð4Þ
ðH 1Þð1 faw Þ ½h þ ð1 hÞaw : Hð1 aw Þ
ð5Þ
H0 ¼ 1 þ
Table 3 TSS isotherm parameters for crystalline a-lactose monohydrate
on simple powder measurements such as particle size distribution and porosity. 3.3. Partially amorphous lactose
At low to intermediate water activity values the parameters H and H 0 approach unity and the model becomes identical to the GAB isotherm equation. The TSS model was fitted to the isotherm data using the procedure outlined by Timmermann and Chiriffe (1991). The model parameters are given in Table 3 and the result is shown in Fig. 3. The result of these findings is that the moisture sorption isotherm for crystalline a-lactose monohydrate, and indeed any crystalline material, is a function of the packing of the powder. As such it is important to measure the isotherm for the packing conditions for which the isotherm is to be utilised. Future work utilising mercury poisiometry in conjunction with the isotherm measurement could help to establish ways of predicting the isotherm behaviour of such systems based
Because amorphous lactose absorbs approximately 100 times more water than crystalline lactose in the same conditions, it is necessary to be able to predict the isotherm for a crystalline powder with an amorphous surface. Amorphous surfaces on crystalline sugars can form during fast drying of the surface moisture on sugar crystals or during milling operations (Roth, 1976). If a small amount of amorphous lactose is present on a crystalline lactose powder, then a significant difference to the moisture sorption isotherm can result. To test this, the moisture isotherm of a predominantly crystalline lactose powder (Supertab) was measured. The amorphous lactose content of the sample used was quantified using the nuclear magnetic resonance (NMR) technique developed by Hargreaves (1995) and was found to contain 9.1% amorphous lactose on a weight basis.
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253
1.0% 0.9%
Supertab Dried Supertab Crystalline isotherm
0.8%
Additive isotherm (9%) Crystalline + water of hydration
M (g g-1 dry lactose)
0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 5. Moisture sorption isotherm of Supertab (partially amorphous lactose powder) at 20 C.
Fig. 5 shows the isotherm data collected for this powder at 20 C. At water activity values less than 0.4 it can be seen that significant moisture uptake occurred. However at water activities above 0.4, a drop in the amount of moisture adsorbed resulted. This is characteristic of amorphous lactose crystallisation which occurs at temperatures above the glass transition temperature (Roos & Karel, 1990). The isotherm of the crystallised product however was not the same as that measured above. It is thought that the reason for this was that the product of crystallisation included some water of crystallisation, which gave apparently high moisture contents. To confirm this, samples were dried over phosphorus pentoxide for 3 weeks to determine the true free (non-crystal water) moisture content. This is also shown in Fig. 5. It can be seen that for the samples above 0.7 water activity, the moisture content is identical to that predicted using the measured isotherm for crystalline lactose discussed above. At the intermediate water activity of 0.54, a product that contained free moisture was evident. This could be crystalline b-lactose anhydride or that the amorphous lactose crystallisation was not complete. Also shown in Fig. 5 is the crystalline lactose isotherm with the water of hydration added in, assuming all the amorphous lactose initially present had crystallised to alactose monohydrate. Because the measured data points are situated beneath this line it is evident that the crystallisation product is only partially a-lactose monohydrate and must contain some anhydrous a-lactose or b-lactose. In order to predict the isotherm for Supertab, an additive isotherm approach was taken. It was assumed that the crystalline surface, although covered, could still adsorb moisture as if it were completely crystalline. Because amorphous lactose absorbs moisture on a mass
basis, Eq. (6) could be used to determine the combined effects of the two components, where ‘a’ corresponds to the mass fraction of the powder that is amorphous: Mmixture ¼ ð1 aÞMcrystalline þ aMamorphous :
ð6Þ
The prediction (using Eq. (6)) for the Supertab powder measured in this work is shown in Fig. 5 which shows a very good fit with the data below 0.4 water activity. At higher water activity amorphous lactose will crystallise in a reasonable time frame (2–3 days) at 20 C and Eq. (6) is no longer valid. This indicates that the simple additive method for predicting isotherms for partially amorphous lactose powders works well. These results also show that the presence of relatively small amounts of amorphous lactose can dramatically change the shape of the isotherm for crystalline lactose samples. This can be seen more clearly in Fig. 6 which shows the predicted isotherm for crystalline lactose powders with different levels of amorphous lactose present. The additive isotherm approach allows for a simple gravimetric method of measuring the amorphous lactose content of lactose powders (Paterson, Bronlund, & O’Donnell, 1997).
4. Conclusions In the high water activity region (>0.85), the moisture sorption isotherm for crystalline lactose (and probably other crystalline powders) is dependent on the packing arrangement of the powder and due to capillary condensation between adjacent particles in the bulk powder. As a consequence of this, care should be taken to measure the moisture sorption isotherm of crystalline powders where the packing structure is consistent with the situation in which the isotherm is to be applied.
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0.6%
M [g g-1 dry solids]
0.5%
0.4%
0% amorphous 2% amorphous
0.3%
0.2%
1% 0.5%
0.1%
0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 6. The predicted effect of small amounts of amorphous lactose on the moisture sorption isotherm of crystalline a-lactose monohydrate.
The isotherm for crystalline powders was also found to be significantly effected by the presence of even very small quantities of amorphous lactose on the surface of the crystals. An additive isotherm approach was found to predict the moisture content of powders with a mixture of amorphous and crystalline lactose.
Acknowledgements The authors would like to acknowledge the support of The Lactose Company of New Zealand Ltd. for their financial support. References Adamson, A. W. (1963). Physical chemistry of surfaces. New York: Wiley. Audu, T. O. K., Loncin, M., & Weisser, H. (1978). Sorption isotherms of sugars. Lebensmittel-Wissenschaft Technologie, 11(1), 31–34. Berlin, E., Anderson, B. A., & Pallansch, M. J. (1968). Comparison of water vapour sorption by milk components. Journal of Dairy Science, 51(12), 1912–1915. Bronlund, J. (1997). The modelling of caking in bulk lactose. Ph.D. thesis, Massey University, Palmerston North. Callahan, J. C., Cleary, G. W., Elefant, M., Kaplan, G., Kensler, T., & Nash, R. A. (1982). Equilibrium moisture content of pharmaceutical excipients. Drug Development and Industrial Pharmacy, 8(3), 355–369. Greenspan, L. (1977). Humidity fixed points of binary saturated aqueous solutions. Journal of Research. National Bureau of Standards A. Physics and Chemistry, 81A(1), 89–96. Hargreaves, J. (1995). Characterisation of lactose in the liquid and solid state using nuclear magnetic resonance and other methods. Ph.D. thesis, Massey University, Palmerston North. Harper, W. J. (1992). Lactose and lactose derivatives. In J. G. Zadow (Ed.), Whey and lactose processing (pp. 317–360). Essex: Elsevier Science Publishers.
Jouppila, K., & Roos, Y. H. (1994). Water sorption properties and time-dependent phenomena of milk powders. Journal of Dairy Science, 77(7), 1798–1808. Linko, P., Pollari, T., Harju, M., & Heikonen, M. (1982). Water sorption properties and the effect of moisture on structure of dried milk products. Lebensmittel-Wissenschaft Technologie, 15(1), 26–30. Lloyd, R. J., Chen, X. D., & Hargreaves, J. B. (1996). Glass transition and caking of spray-dried lactose. International Journal of Food Science and Technology, 31(4), 305–311. Loncin, M., Bimbenet, J. J., & Lenges, J. (1968). Influence of the activity of water on the spoilage of foodstuffs. Journal of Food Technology, 3(2), 131–142. Paterson, A. H. J., Bronlund, J. E., & O’Donnell, A. (1997). The quantification of small amounts of amorphous lactose by moisture absorption. CHEMECA 97, Rotorua, New Zealand, 28 September–1 October, 1997. Pritzwald-Stegmann, B. F. (1986). Lactose and some of its derivatives. Journal of the Society of Dairy Technology, 39(3), 91–97. Roos, Y. H., & Karel, M. (1990). Differential scanning calorimetry study of phase transitions affecting the quality of dehydrated materials. Biotechnology Progress, 6(2), 159–163. Roth, D. (1976). Amorphous icing sugar produced during crushing and recrystallisation as the cause of agglomeration and procedures for its avoidance. Ph.D. thesis, University of Karlsruhe, Karlsruhem (in German). Stecher, P. G. (1968). The merck index. Rathway: Merck & Co. Stitt, F. (1958). Moisture equilibrium and the determination of water content in dehydrated foods. In Society of Chemical Industry. Fundamental aspects of the dehydration of foodstuffs (pp. 67–87). London: Metchim and Son. Timmermann, E. O. (1989). A BET like three sorption stage isotherm. Journal of Chemical Society, Faraday Transactions 1, 85(7), 1631–1645. Timmermann, E. O., & Chiriffe, J. (1991). The physical state of water sorbed at high activities in starch in terms of the GAB sorption equation. Journal of Food Engineering, 13(3), 171–179. Warburton, S., & Pixton, S. W. (1978). The moisture relations of spray dried skimmed milk. Journal of Stored Product Research, 14(2,3), 143–158.
International Dairy Journal 14 (2004) 247–254
Moisture sorption isotherms for crystalline, amorphous and predominantly crystalline lactose powders John Bronlund*, Tony Paterson Institute of Technology and Engineering, PN 456, Massey University, Private Bag 11222, Palmerston North, New Zealand Received 3 February 2003; accepted 23 July 2003
Abstract Moisture sorption isotherms for amorphous lactose, crystalline a-lactose monohydrate and a predominantly crystalline lactose powder were measured. No temperature dependence was observed over the range investigated (12–40 C), except for amorphous lactose at 12 C, which absorbed less moisture than observed at higher temperatures. The amount of water absorbed by crystalline powders at high water activity was dependent on the packing density of the powder. This observation could be explained using the capillary condensation theory. The moisture isotherm of a partially amorphous lactose powder was successfully predicted by using a simple additive isotherm model to combine the isotherms of crystalline and amorphous lactose powders. Small quantities of amorphous lactose present on crystalline powders, causes significant changes to the moisture sorption isotherm. If the high water activity region of the isotherm of crystalline a-lactose monohydrate is of interest then the isotherm should be measured at the packing density of interest. r 2003 Elsevier Ltd. All rights reserved. Keywords: Moisture sorption isotherms; Lactose; Amorphous; Crystalline sugar
1. Introduction Lactose is a sugar that is derived from milk. The reduced sweetness, enhanced aroma binding abilities and low cost make it a commonly used replacement for more traditional sugars as a food ingredient. It is also one of the most commonly used excipients in tableting and granulation operations in the pharmaceutical industry (Harper, 1992). The most common form of lactose used in industry is crystalline a-lactose monohydrate (C12H22O11 H2O), which is prepared by crystallisation from aqueous solution below 93.5 C. Once separated from the mother liquor, refined, dried and milled, the product should be a free flowing fine white powder of similar consistency to icing sugar. Caking problems can occur after the product is packed and stored. Bronlund (1997) investigated the phenomena that cause caking in crystalline lactose powders. Liquid bridging between adjacent particles was found to occur in conditions of high humidity (>85%), causing *Corresponding author. Tel.: +64-6-3505542; fax: +64-6-3505604. E-mail address: [email protected] (J. Bronlund). 0958-6946/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0958-6946(03)00176-6
lumping. If these bridges were dried out, solid crystalline bridges formed and a caked product resulted. Bronlund (1997) also showed that the presence of amorphous lactose on the surface of the crystals was important. Thin layers of amorphous lactose are formed on the surface of the powder during flash drying and milling operations. If the glass transition temperature of the amorphous lactose is exceeded, then the particles can become sticky and the amorphous lactose crystallises, causing caking and lumping problems. To avoid caking and lumping complaints in predominantly crystalline lactose powders it is essential to understand how lactose interacts with the moisture in the air. Many other researchers have reported moisture sorption isotherms for crystalline a-lactose monohydrate (Loncin, Bimbenet, & Lenges, 1968; Audu, Loncin, & Weisser, 1978; Warburton & Pixton, 1978; Linko, Pollari, Harju, & Heikonen, 1982; Callahan et al., 1982) and amorphous lactose (Berlin, Anderson, & Pallansch, 1968; Warburton & Pixton, 1978; Linko et al., 1982; Roos & Karel, 1990; Jouppila & Roos, 1994). However, the effects of temperature and particle size have never been quantified. There have been no reports
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Nomenclature a aw c f h H H0
amorphous lactose content (kg kg1) water activity (dimensionless) BET constant (dimensionless) GAB constant (dimensionless) third stage sorption isotherm constant (dimensionless) third stage sorption isotherm intermediate (dimensionless) third stage sorption isotherm intermediate (dimensionless)
in the literature explicitly aimed at determining the moisture sorption isotherms for crystalline lactose powders with low levels of amorphous material present. In fact none of the reports on moisture sorption isotherms for crystalline lactose state that they ensured their samples were 100% crystalline. The aim of this work was to measure, and to characterise the effect of particle size and temperature on the moisture sorption isotherms for completely amorphous lactose, crystalline a-lactose monohydrate and a predominantly crystalline lactose powder.
2. Methods and materials 2.1. Lactose sources Commercially manufactured crystalline a-lactose monohydrate of differing particles sizes were obtained from Lactose New Zealand Ltd. The powders used were 100, 200 and 300 mesh and special dense (an unmilled powder with a wide particle size distribution) and greater than 99% purity. Pure amorphous lactose was produced by spray drying according to the method outlined by Lloyd, Chen, and Hargreaves (1996). A lactose product called Supertab, provided by The Lactose Company of New Zealand Ltd., was used as a partially amorphous lactose powder. This product contains approximately 10% amorphous lactose. 2.2. Moisture sorption isotherms The moisture sorption isotherms for each powder were measured using the static gravimetric method (Stitt, 1958). Air tight desiccators, containing saturated salt solutions (made from Analar grade salts and deionised water) placed inside temperature controlled rooms, were used to provide constant relative humidity and temperature environments. Approximately 10 g of
M M0 Pv Pw r R T V0 y s
moisture content (kg kg1 dry solid) BET mono-layer moisture content (kg kg1 dry solid) vapour pressure (Pa) saturated vapour pressure (Pa) capillary radius (m) universal gas constant (J mol1 K1) temperature (K) molar volume (m3 mol1) contact angle (rad) surface tension (N m1)
each powder were placed in the desiccators and allowed to equilibrate. Each sample was weighed periodically over a period of 3 weeks, using a Metler AE200 analytical balance, to ensure equilibrium was reached. The samples were covered air tight to avoid moisture adsorption or desorption during the weighing process. 2.3. Initial moisture content determination The initial moisture contents of the samples were determined by desiccation over phosphorus pentoxide for 3 weeks, when constant weight was observed. The isotherms were then determined from the weight change from the initial sample. By measuring the moisture sorption isotherm in this way, desorption occurred below the starting powder water activity, and adsorption occurred above this value. It should also be noted that the moisture content measurements are based on the moisture that can be removed by desiccation of the powder over phosphorus pentoxide, and therefore do not include any water of crystallisation that is present in powders containing a-lactose monohydrate, or water entrapped in the crystals. Heating to 120 C is required to remove all the water of crystallisation (Stecher, 1968). 2.4. Saturated salt solutions Table 1 summarises the range of conditions in which each powder was measured. For the measurement of the sorption isotherm of amorphous lactose, conditions below 60% RH were chosen as above this value, crystallisation occurs and therefore the isotherm data are not meaningful. For the crystalline and partially crystalline samples, isotherm data across the whole water activity range were measured, concentrating particularly on the high water activity region where capillary condensation was expected to occur.
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Table 1 Equilibrium relative humidity (%) conditions for moisture sorption isotherm measurements Saturated salt solutiona
Crystalline a-lactose monohydrate
LiCl KCH2COO MgCl2 K2CO3 Mg(NO3)2 NaCl (NH3)2SO4 KCl KNO3 K2SO4 a b
Amorphous lactose
Supertab
12 C
20 C
30 C
40 C
12 C
20 C
30 C
38 C
20 C
11 — 33 — 56 78 81 87 95 98
11 — 33 — 54 77 80 87 94 98
11 — 32 — 53 75 80 84 93 97
11 — 32 — 51 74 79 81 90 97
11 23 33 43 56 — — — — —
11 22 33 43 — — — — — —
11 21 32 — — — — — — —
11 21 31 — — — — — — —
11 — 31 — 54b 77b 80b 87b 94b 98b
Equilibrium relative humidity values were taken from Greenspan (1977). The amorphous lactose in these samples were expected to crystallise in these conditions.
3. Results and discussion 3.1. Amorphous lactose The moisture sorption isotherm for amorphous lactose is shown in Fig. 1. The absolute error in the measurements was found to be 70.04 g/100 g dry lactose by error analysis. Also included in Fig. 1 is the data reported by Jouppila and Roos (1994), Berlin et al. (1968), Roos and Karel (1990) and Warburton and Pixton (1978). Data were omitted at high water activity where the characteristic desorption associated with amorphous lactose crystallisation was evident. The literature data of Linko et al. (1982) and PritzwaldStegmann (1986) were also not included on the graph as they were markedly different from the other reported data. It can be seen that there is little difference between the literature data and those collected in this study, suggesting that the structure of freeze dried and spray dried powders are similar. The results also show negligible influence of temperature on the isotherm shape over the range investigated (20–40 C), except for the low temperature experiment (12 C) which deviates downward above 0.4 water activity. Because the driving force for crystallisation increases with temperature, the maximum water activity at which a measurement could be taken reduced with temperature. This meant that at a water activity of 0.54 only the sample held at 12 C, reached equilibrium and it is possible that partial crystallisation of this sample could have occurred. Jouppila and Roos (1994) fitted the Guggenheim, Anderson, de Boar (GAB) equation (Eq. 1) to their isotherm data for freeze dried amorphous lactose and they are also plotted in Fig. 1. GAB constants were fitted to the data collected in this study (see Fig. 1). The GAB parameters are shown in Table 2, along with those used by Jouppila and Roos (1994). Because the data of
Jouppila and Roos (1994) are consistently higher than the data collected in this work and to those reported by other researchers it is suggested that the GAB parameters obtained in this work should be used in the future. It should be noted that the fitted isotherm parameters are only valid in conditions that avoid amorphous lactose crystallisation (i.e. below the glass transition temperature): M¼
M0 cfaw : ð1 faw Þ½1 ð1 cÞfaw
ð1Þ
3.2. Crystalline lactose Fig. 2 shows the moisture sorption isotherm measured for unmilled a-lactose monohydrate (special dense) over the range of temperatures investigated (12–40 C). The uncertainty in the data was calculated by error analysis and found to be 70.029 g 100 g1 dry lactose. The literature data are not included in Fig. 2 because it is highly scattered. This is likely to be due to the various ways the moisture content of the samples has been determined. A drying technique that removes only a small fraction of the water of crystallisation can result in significant differences in free water content. It can be seen from Fig. 2 that there is no significant effect of temperature on the sorption isotherm over the range investigated (12–40 C). The powder adsorbs very little moisture over the low water activity range (0–0.85). It is only at water activities above 0.85 that significant amounts of moisture are adsorbed. The moisture content increases exponentially above this point and approaches an asymptote at a water activity of one. One reason for the exponential increase in moisture content at high water activities is capillary condensation, first proposed by Zsigmondy in 1911 (see Adamson, 1963). Capillary condensation is the process where direct condensation can occur, due to surface tension effects, in the capillaries formed at the contact points between
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250 16%
12°C 20°C
14%
30°C 38°C
M (g g-1 dry lactose)
12%
Jouplila and Roos (1994) (24°C) Roos and Karel (1990) (25°C)
10%
Warburton and Pixton (1978) (25°C) Berlin et.al. (1968) (24.5°C)
8%
GAB model (12°C) GAB model (20-38°C)
6%
GAB model (Joupilla and Roos 1994)
4%
2%
0% 0
0.1
0.2
0.3
0.4
0.5
0.6
Water activity
Fig. 1. Effect of temperature on the moisture sorption isotherm of amorphous lactose.
Table 2 GAB isotherm parameters for amorphous lactose (applicable in conditions where amorphous lactose crystallisation will not occur) GAB isotherm parameter
Isotherm data measured at 12 C
Isotherm data Isotherm data measured at measured by Jouppila 20–38 C and Roos (1994)
M0 (g g1 dry solids) f c
0.0693
0.0488
0.0491
0.77 3.39
1.16 3.23
1.18 4.33
adjacent particles. As a result the saturated vapour pressure in the capillary, above the liquid surface can be less than the vapour pressure of the bulk air. In this way direct condensation can occur in the capillaries even in conditions where the bulk air relative humidity is less than 100%. The water vapour pressure at which capillary condensation will occur is dependent on the radius of the capillary and is given by the Kelvin equation (Eq. (2)) (Adamson, 1963): Pv 2s cos yV0 aw ¼ ¼ exp : Pw rRT
ð2Þ
Using this equation it can be shown that capillary condensation can occur at relative humidities above about 80%. At relative humidities below 0.8 the capillary radii required to cause capillary condensation approach molecular dimensions where macroscopic properties such as surface tension and contact angle are not applicable (Adamson, 1963). As the capillary radius increases, the minimum water activity required for condensation to occur, increases.
This explanation of the sorption behaviour of water at high water activity has two important consequences. Firstly, the high water activity region of the measured isotherm shown in Fig. 2 will not apply for individual particles, as there will be no capillaries present for condensation to occur in. The isotherm is therefore only valid for packed beds of lactose powders. Secondly, the capillary size distribution of the powder may influence the shape of the isotherm curve at high water activity. In order to investigate the effect of capillary size distribution the moisture sorption isotherms were measured at 20 C for crystalline powders with differing particle sizes. Fig. 3 shows the results for lactose powders milled to 100 mesh, 200 mesh and 300 mesh particle size as well as the isotherm for unmilled lactose at 20 C. It can be clearly seen in Fig. 3 that there was less water adsorbed at equivalent conditions for the milled samples compared to the unmilled (special dense) powder in the high water activity range. This result is consistent with the nature of the powders. The finely milled samples have a relatively narrow particle size distribution where the unmilled powder has a wide distribution (Bronlund, 1997). For this reason there is a greater packing density for the unmilled powder (bulk density, 800 kg m3), and therefore a smaller voidage fraction, corresponding to a smaller average capillary radius between particles, than the milled samples (average bulk density, 625 kg m3). Fig. 4 was constructed by using the Kelvin equation (Eq. (2)) to calculate the effective capillary radius at each water activity that the powders were measured at. A contact angle of zero (a fully wetted surface) was assumed and the surface tension of a saturated lactose
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1.0% 12°C 20°C
0.9%
30°C 37°C
M (g g-1 lactose monohydrate)
0.8%
tss model
0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 2. Effect of temperature on the moisture sorption isotherm of crystalline a-lactose monohydrate.
1.0% Unmilled 100 mesh 200 mesh 300 mesh tss model (milled) tss model (unmilled)
0.9%
M (g g-1 lactose monohydrate)
0.8% 0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 3. Effect of particle size on moisture sorption isotherm for crystalline a-lactose monohydrate.
solution (0.068 N m1) measured by Bronlund (1997) was used to make these calculations. The moisture content measured at each water activity was then plotted against the calculated capillary radius. Any capillaries smaller than the calculated radius at any given water activity are full of water due to the process of capillary condensation. It can be seen from Fig. 4 that the unmilled powder adsorbed more moisture at a given capillary radius than the milled samples. This infers that the milled powders lower voidage fraction, forming small capillaries between particles compared with the unmilled powder. For
this reason, higher water activity conditions are required before significant amounts of moisture can be adsorbed by condensation into the larger capillaries that are present in the milled samples. Because of the difficulty in measuring the effective capillary size distribution of the bulk powder and also because the effective capillary radius increases as the moisture fills up the capillary, an alternative mathematical expression for the moisture sorption isotherm was investigated. The third stage sorption (TSS) isotherm was developed by Timmermann (1989) and Timmermann and
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1.0% Unmilled 100 mesh 200 mesh 300 mesh Linear fit (unmilled) Linear fit (milled)
0.9%
M [g g-1 dry lactose]
0.8% 0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
10
20
30
40
50
Capillary radius [nm] 0
0.85
0.90
0.95
0.96
0.97
0.98
Water activity
Fig. 4. Effect of capillary radius on moisture adsorption for crystalline a-lactose monohydrate.
Chiriffe (1991) to extend the GAB isotherm model to water activity ranges approaching unity. It is based on the premise that after a certain number of moisture layers exist, the moisture behaves as liquid water. The TSS isotherm has the advantage that it can be used to explain the whole of the isotherm where the capillary condensation approach is only valid in the high water activity region. The isotherm model is shown as equations (Eq. (3)–(5)): M¼
M0 cHfaw H 0 ; ð1 faw Þ½1 þ ðcH 1Þfaw
H ¼1þ
TSS isotherm parameter
M0 (g g f c h
1
dry solids)
Lactose powder sample Unmilled
Milled
2.29e-4 0.966 8.8 30
1.68e-4 0.878 8.8 30
ð3Þ
ð1 f Þ ðfaw Þh ; f ð1 aw Þ
ð4Þ
ðH 1Þð1 faw Þ ½h þ ð1 hÞaw : Hð1 aw Þ
ð5Þ
H0 ¼ 1 þ
Table 3 TSS isotherm parameters for crystalline a-lactose monohydrate
on simple powder measurements such as particle size distribution and porosity. 3.3. Partially amorphous lactose
At low to intermediate water activity values the parameters H and H 0 approach unity and the model becomes identical to the GAB isotherm equation. The TSS model was fitted to the isotherm data using the procedure outlined by Timmermann and Chiriffe (1991). The model parameters are given in Table 3 and the result is shown in Fig. 3. The result of these findings is that the moisture sorption isotherm for crystalline a-lactose monohydrate, and indeed any crystalline material, is a function of the packing of the powder. As such it is important to measure the isotherm for the packing conditions for which the isotherm is to be utilised. Future work utilising mercury poisiometry in conjunction with the isotherm measurement could help to establish ways of predicting the isotherm behaviour of such systems based
Because amorphous lactose absorbs approximately 100 times more water than crystalline lactose in the same conditions, it is necessary to be able to predict the isotherm for a crystalline powder with an amorphous surface. Amorphous surfaces on crystalline sugars can form during fast drying of the surface moisture on sugar crystals or during milling operations (Roth, 1976). If a small amount of amorphous lactose is present on a crystalline lactose powder, then a significant difference to the moisture sorption isotherm can result. To test this, the moisture isotherm of a predominantly crystalline lactose powder (Supertab) was measured. The amorphous lactose content of the sample used was quantified using the nuclear magnetic resonance (NMR) technique developed by Hargreaves (1995) and was found to contain 9.1% amorphous lactose on a weight basis.
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1.0% 0.9%
Supertab Dried Supertab Crystalline isotherm
0.8%
Additive isotherm (9%) Crystalline + water of hydration
M (g g-1 dry lactose)
0.7% 0.6% 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 5. Moisture sorption isotherm of Supertab (partially amorphous lactose powder) at 20 C.
Fig. 5 shows the isotherm data collected for this powder at 20 C. At water activity values less than 0.4 it can be seen that significant moisture uptake occurred. However at water activities above 0.4, a drop in the amount of moisture adsorbed resulted. This is characteristic of amorphous lactose crystallisation which occurs at temperatures above the glass transition temperature (Roos & Karel, 1990). The isotherm of the crystallised product however was not the same as that measured above. It is thought that the reason for this was that the product of crystallisation included some water of crystallisation, which gave apparently high moisture contents. To confirm this, samples were dried over phosphorus pentoxide for 3 weeks to determine the true free (non-crystal water) moisture content. This is also shown in Fig. 5. It can be seen that for the samples above 0.7 water activity, the moisture content is identical to that predicted using the measured isotherm for crystalline lactose discussed above. At the intermediate water activity of 0.54, a product that contained free moisture was evident. This could be crystalline b-lactose anhydride or that the amorphous lactose crystallisation was not complete. Also shown in Fig. 5 is the crystalline lactose isotherm with the water of hydration added in, assuming all the amorphous lactose initially present had crystallised to alactose monohydrate. Because the measured data points are situated beneath this line it is evident that the crystallisation product is only partially a-lactose monohydrate and must contain some anhydrous a-lactose or b-lactose. In order to predict the isotherm for Supertab, an additive isotherm approach was taken. It was assumed that the crystalline surface, although covered, could still adsorb moisture as if it were completely crystalline. Because amorphous lactose absorbs moisture on a mass
basis, Eq. (6) could be used to determine the combined effects of the two components, where ‘a’ corresponds to the mass fraction of the powder that is amorphous: Mmixture ¼ ð1 aÞMcrystalline þ aMamorphous :
ð6Þ
The prediction (using Eq. (6)) for the Supertab powder measured in this work is shown in Fig. 5 which shows a very good fit with the data below 0.4 water activity. At higher water activity amorphous lactose will crystallise in a reasonable time frame (2–3 days) at 20 C and Eq. (6) is no longer valid. This indicates that the simple additive method for predicting isotherms for partially amorphous lactose powders works well. These results also show that the presence of relatively small amounts of amorphous lactose can dramatically change the shape of the isotherm for crystalline lactose samples. This can be seen more clearly in Fig. 6 which shows the predicted isotherm for crystalline lactose powders with different levels of amorphous lactose present. The additive isotherm approach allows for a simple gravimetric method of measuring the amorphous lactose content of lactose powders (Paterson, Bronlund, & O’Donnell, 1997).
4. Conclusions In the high water activity region (>0.85), the moisture sorption isotherm for crystalline lactose (and probably other crystalline powders) is dependent on the packing arrangement of the powder and due to capillary condensation between adjacent particles in the bulk powder. As a consequence of this, care should be taken to measure the moisture sorption isotherm of crystalline powders where the packing structure is consistent with the situation in which the isotherm is to be applied.
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0.6%
M [g g-1 dry solids]
0.5%
0.4%
0% amorphous 2% amorphous
0.3%
0.2%
1% 0.5%
0.1%
0.0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Water activity
Fig. 6. The predicted effect of small amounts of amorphous lactose on the moisture sorption isotherm of crystalline a-lactose monohydrate.
The isotherm for crystalline powders was also found to be significantly effected by the presence of even very small quantities of amorphous lactose on the surface of the crystals. An additive isotherm approach was found to predict the moisture content of powders with a mixture of amorphous and crystalline lactose.
Acknowledgements The authors would like to acknowledge the support of The Lactose Company of New Zealand Ltd. for their financial support. References Adamson, A. W. (1963). Physical chemistry of surfaces. New York: Wiley. Audu, T. O. K., Loncin, M., & Weisser, H. (1978). Sorption isotherms of sugars. Lebensmittel-Wissenschaft Technologie, 11(1), 31–34. Berlin, E., Anderson, B. A., & Pallansch, M. J. (1968). Comparison of water vapour sorption by milk components. Journal of Dairy Science, 51(12), 1912–1915. Bronlund, J. (1997). The modelling of caking in bulk lactose. Ph.D. thesis, Massey University, Palmerston North. Callahan, J. C., Cleary, G. W., Elefant, M., Kaplan, G., Kensler, T., & Nash, R. A. (1982). Equilibrium moisture content of pharmaceutical excipients. Drug Development and Industrial Pharmacy, 8(3), 355–369. Greenspan, L. (1977). Humidity fixed points of binary saturated aqueous solutions. Journal of Research. National Bureau of Standards A. Physics and Chemistry, 81A(1), 89–96. Hargreaves, J. (1995). Characterisation of lactose in the liquid and solid state using nuclear magnetic resonance and other methods. Ph.D. thesis, Massey University, Palmerston North. Harper, W. J. (1992). Lactose and lactose derivatives. In J. G. Zadow (Ed.), Whey and lactose processing (pp. 317–360). Essex: Elsevier Science Publishers.
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