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J. Phys. Chem. B 2010, 114, 1568–1578
Specific Volume-Hole Volume Correlations in Amorphous Carbohydrates: Effect of Temperature, Molecular Weight, and Water Content Sam Townrow,† Mina Roussenova,† Maria-Isabelle Giardiello,‡ Ashraf Alam,† and Job Ubbink*,‡ H.H. Wills Physics Laboratory, UniVersity of Bristol, Tyndall AVenue, Bristol BS8 1TL, United Kingdom, and Nestle´ Research Center, Vers-chez-les-Blanc, CH-1000 Lausanne 26, Switzerland ReceiVed: September 2, 2009; ReVised Manuscript ReceiVed: NoVember 5, 2009
The specific volume and the nanostructure of the free volume of amorphous blends of maltose with a narrow molecular weight distribution maltopolymer were systematically studied as a function of temperature, water content, pressure, and blend composition. Correlations between the hole free volume and the specific volume were investigated in the glassy and rubbery phases and in solution using positron annihilation lifetime spectroscopy (PALS) and pressure-volume-temperature (PVT) measurements, with the aim to provide a consolidated mechanistic understanding of the relation between changes in molecular packing and at the molecular level and the behavior of the specific volume at the macrolevel. Both specific volume and hole volume show a linear dependence on the temperature, but with a slope which is higher in the rubbery state than in the glassy state. As a function of temperature, the hole volume and the specific volume are linearly related, with no discontinuity at the glass transition temperature (Tg). In the glassy state, both the specific volume and the hole volume decrease nonlinearly with the addition of maltose to the maltopolymer matrix, due to a more efficient molecular packing. For variations in carbohydrate composition, a linear dependence between the hole volume and the specific volume was again observed. The role of water was found to be significantly more complex, with increasing water content causing an increase in density in both the glassy and rubbery phases indicating that water exists in a highly dispersed state with a significantly lower specific molar volume than in bulk water. At very low water contents, the hole volume and the specific volume both decrease with increasing water content, which suggests that water acts as both a hole filler and a plasticizer. In the glassy state at slightly higher water contents, the specific volume continues to slowly decrease, but the hole size passes through a minimum before it starts to increase. This gives rise to a negative correlation between the hole volume and the specific volume which has not previously been observed and which can be interpreted in terms of water molecules which are dispersed within the glassy carbohydrate matrix and which thereby influence the hydrogen bonding between the carbohydrate molecules. Introduction Over the last twenty years, significant progress has been made in the understanding of the physical properties of carbohydratewater systems in terms of their temperature- and waterdependent phase transitions. This has resulted in the widespread use of phase and state diagrams to predict the stability of systems based on carbohydrate-based foods1,2 and pharmaceutics.3 Of particular importance in this context is the glass transition temperature (Tg) of amorphous carbohydrates, its depression by water, and the relation to the rheology of the carbohydrate system.4 Amorphous carbohydrates in the glassy state are widely used as matrices for the encapsulation and stabilization of nutrients, pharmaceutics,5,6,12 and other bioactive compounds.7,8 In these applications, the glass transition temperature of the amorphous matrix has been used as the central physical parameter for the optimization of processing conditions and storage stability. In several recent studies aimed at the analysis of the molecular structure of amorphous carbohydrate matrices in the glassy state,9,10 we have emphasized that, apart from Tg, the molecular weight dependence of the molecular packing of the carbohydrate * To whom correspondence should be addressed. E-mail: johan.ubbink@ rdls.nestle.com. † University of Bristol. ‡ Nestle´ Research Center.
molecules in the glassy state is of fundamental importance in understanding the encapsulation and barrier properties of such matrices. Specifically, we have observed that, when the molecular weight of a glassy carbohydrate matrix is decreased, the density of the matrix increases and, at the same time, the molecular hole size, as probed by positron annihilation lifetime spectroscopy (PALS), decreases. The increase in density and decrease in hole size have been related to improvements in barrier properties of these materials.11 For practical applications, these improvements can most easily be achieved by adding defined amounts of a low molecular weight carbohydrate to a matrix largely consisting of carbohydrate polymers. Apart from the effect of carbohydrate molecular weight, there are strong indications that water is influencing the molecular structure of the carbohydrate matrices in complex ways. Experiments using PALS have shown that, depending on the water content, the molecular hole size in glassy carbohydrates may decrease via a hole-filling mechanism or may increase with increasing water content via a plasticization-dominated mechanism.10 In addition, anomalous properties of water in glassy carbohydrates have been witnessed using infrared spectroscopy,14 pressure-volume-temperature (PVT) analysis,13 nuclear magnetic resonance spectroscopy,14,15 electron spin resonance spectroscopy,16 and neutron scattering.17
10.1021/jp908462k 2010 American Chemical Society Published on Web 01/08/2010
Specific Volume-Hole Volume in Carbohydrates In this study, we explore the relation between the specific volume and the hole volume of amorphous carbohydrate matrices as a function of the thermodynamic variables temperature, water content, and carbohydrate composition. In addition, we investigate the effect of pressure on the specific volume of the matrices. For this purpose, we have prepared a series of solvent-cast carbohydrate matrices consisting of a bidisperse blend of a fractionated maltopolymer and the disaccharide maltose, with a systematic variation in blend composition. These matrices are investigated using PALS and PVT analysis combined with calorimetry and water sorption experiments. Our principal objective is to provide a consolidated mechanistic understanding of the relation between changes in molecular packing at the molecular level and the behavior of the specific volume at the macrolevel for the various physical regimes (glassy and rubbery states, solutions). We anticipate that, in comparison with conventional materials interacting primarily via van der Waals forces, the strong hydrogen bonding between the carbohydrate and water molecules will influence the behavior of the free volume and/or the specific volume in potentially interesting ways. Materials and Methods Preparation of Matrices and Solutions. Matrices were prepared by solvent casting of mixtures of a fractionated maltopolymer and maltose, with weight fractions of maltopolymer and maltose of 100% and 0% (weight fraction of maltose on total carbohydrate φm ) 0), 95%-5% (φm ) 0.05), 90%-10% (φm ) 0.1), 80%-20% (φm ) 0.2), 60%-40% (φm ) 0.4), 30%-70% (φm ) 0.7), and 0%-100% (φm ) 1). The maltopolymer LAB 2490 (lot no. 337301E, Roquette Fre`res, Lestrem, France) is a chromatographically fractionated starch hydrolysate of intermediate molecular weight (Mw ) 1.2 × 104 Da) and with a polydispersity which is rather narrow for such materials (Mw/Mn ) 2.2). LAB2490 is further characterized by a limited degree (6.8%) of R-(1f6) branching. The disaccharide maltose (4-O-R-D-glucopyranosyl-D-glucose; Mw ) 342 Da) was obtained in the form of analytical grade maltose monohydrate from Fluka (Buchs, Switzerland). Both samples were used without further purification. After casting, the cast samples were ground and further dried until a final water activity of about 0.1 was reached. The ground samples were sieved into size fractions; the size fractions between 100 and 300 µm were used for water-activity equilibration and all further experiments. Highwater-content samples were prepared by dissolution of a known quantity of carbohydrate in water, taking into account the initial water content of the carbohydrate powders. In setting up the sample preparation procedure, we have used X-ray scattering to ascertain that long-range order is absent in samples prepared following our solvent-casting method. In addition, polarized light microscopy was routinely used to verify that all samples are in the amorphous state after solvent casting and after water-activity equilibration. Determination of Water Content. The water content of the samples after preparation was determined using a home-built extraction unit as described previously.9 Water Activity Equilibration. Samples were equilibrated at 25 ( 1 °C at various water activities in desiccators containing saturated salt solutions of known relative humidity (aw ) 0.11 (LiCl); aw ) 0.22 (CH3COOK); aw ) 0.33 (MgCl2); aw ) 0.43 (K2CO3); aw ) 0.54 (Mg(NO3)2); aw ) 0.75 (NaCl)).18 The sorption of water was followed gravimetrically until equilibrium was achieved.19
J. Phys. Chem. B, Vol. 114, No. 4, 2010 1569 Determination of Specific Volume. The specific volume of the samples was determined using an Accupyc 1330 pycnometer (100 mL cell with 10 mL insert) (Micromeritics, USA). Helium was used as the displacement gas at an equilibration rate of 0.1 kPa · min-1. Ten sample runs were found sufficient for values of the specific volume significant up to the third decimal place.9 The PVT experiments where carried out using a GNOMIX volume dilatometer following procedures described elsewhere.9 Positron Annihilation Lifetime Spectroscopy. PALS measurements were taken using a fast-fast system with a resolution comprising two Gaussian functions 198 ps (98%) and 760 ps (2%). Spectra were collected over a period of 5 h to generate ∼5 × 106 events. Sodium-22 was used as a positron source and was prepared from aqueous 22NaCl deposited between two sheets of 8 µm thick Kapton foil. The sample discs were placed at either side of the positron source, and the source-sample sandwich sealed in an airtight copper sample chamber. Full details of the system are available elsewhere.9 For experiments on carbohydrate solutions and pure water, a second source was produced, consisting of a source similar to that used for solid phase measurements encapsulated between two additional sheets of 8 µm Kapton foil and sealed with epoxy resin. This source had a higher background component compared with the unmodified one (13.9% vs 6.9%), but it was more resistant against water ingress. The solution source was held in a cradle inside the sample chamber to ensure better comparability between measurements. The size of the free volume holes can be related to the mean ortho-positronium (o-Ps) lifetime, τo-Ps, using a simple quantum mechanical model where the o-Ps is localized in a spherical potential well of infinite depth and of radius r ) rh + δr:20,21
[ ][ -1
1
τo-Ps )
∑ i)0
fiλi
1-
(
rh 2πrh 1 + sin rh + δr 2π rh + δr
)]
-1
(1)
where rh is the radius of the hole and the positronium has an overlap with molecules within a layer of δr of the potential wall. fi is the fraction of positronium with spin i (1/4 for parapositronium, p-Ps, spin 0, 3/4 for o-Ps, spin 1), and λi is the corresponding annihilation rate in vacuum (0.125-1 and 142-1 ns-1, respectively). Spectra were analyzed using the routine LT9.022,23 assuming a three-component fit with the ratio Ip-Ps/ Io-Ps ) 1/3 and with a continuous o-Ps lifetime distribution. Results Specific Volume. The dependence of the specific volume on the water content was determined at T ) 25 °C using both maltopolymer-maltose blends equilibrated at a range of water activities between aw ) 0 and aw ) 0.75 (low and intermediate water contents) and aqueous solutions of the carbohydrate blends (dilute and moderately concentrated solutions). The water content, denoted by Qw, is the weight fraction of water in the system and is given by Qw ) mw/(mw + mc), where the subscripts “w” and “c” refer to the components water and carbohydrate, respectively. The carbohydrate blend is defined by the weight fraction of maltose φm ) mm/mc, with mc ) mm + mp, mc the total weight of carbohydrate, mm the weight of maltose, and mp the weight of carbohydrate polymer. In solution and in the rubbery state (Figure 1a), the specific volume of the carbohydrate blends is linearly dependent on the water content, attaining the density of pure water in the limit of no carbohydrate and a hypothetical “ideal” amorphous
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Townrow et al. TABLE 1: Rate of Change of Specific Volume with Increase in Water Content, Specific Volume in the Anhydrous State, and Partial Molar Volume Wm,w of Water for Maltopolymer-Maltose Matrices with Varying Maltose Content on Total Carbohydrate Om φm
δVsp/δQw [cm3 · g-1]a
Vsp,0 [cm3 · g-1]
Vm,w [cm3 · mol-1]
0 0.05 0.1 0.2 0.4 0.7 1
-0.132 -0.131 -0.140 -0.131 -0.142 -0.094 -0.067
0.670 0.669 0.668 0.664 0.662 0.657 0.654
9.7 9.5 9.7 10.6 11.9 12.7 12.7
a
Figure 1. Specific volume of the maltopolymer-maltose blends as a function of the water content at T ) 25 °C. Panel (b) is an enlargement of (a) containing only the glassy state data. The blends are characterized by the weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]). The solid line in (a) is the linear regression of the solution data; correlation coefficient R2 ) 1.00. The correlation coefficients R2 of the linear fits to the glassy state data (solid lines in (b)) are between 0.98 and 1.00.
carbohydrate specific volume of 0.60 cm3 · g-1 (density ) 1.67 g · cm-3) for the anhydrous blends. Small deviations from linearity occur in solution and the rubbery state. These have been attributed to the nonideality of mixing of carbohydrates and water, and have been quantified using the concept of the excess specific volume VspE ) Vsp,exp - Vsp,ideal and the excess molar volume VmE ) Vm,exp - Vm,ideal, where the subscripts “exp” and “ideal” denote the experimental and ideal quantities, respectively.24,13 A similar behavior was recently observed in molecular dynamics simulations.25 The agreement between the simulations and the experiments is virtually quantitative: in the simulations, a value of 0.62 cm3 · g-1 was obtained for the hypothetical “ideal” amorphous carbohydrate specific volume. Even though understanding the effects of mixing at the molecular level in liquid mixtures is helpful, the excess functions are thermodynamically defined and are strictly valid only under ergodic conditions.26 As, however, the carbohydrate-water systems pass through a glass transition upon lowering the water content to below a critical value dependent on the chemical nature of the carbohydrate, the molecular weight, and the temperature, the systems become nonergodic and the mixing behavior of carbohydrate-water systems should not be analyzed using the excess functions, as these will be influenced by the specific-volume anomalies related to the glass transition. The realization that at low water contents the matrices pass through a glass transition also provides insight into the dependence of the specific volume on the water content. In solutions at very high water contents, and in rubbery states at
In the glassy state. Typical standard errors are 0.004 cm3 · g-1.
intermediate water contents, carbohydrate molecules and water molecules form thermodynamic mixtures of which the mixing behavior is not too divergent from ideal behavior. Small deviations from ideal mixing behavior occur, but these are difficult to quantitatively analyze as a proper thermodynamic reference state for the pure carbohydrate systems is lacking. In the glassy state, large-scale molecular rearrangements vanish altogether. The carbohydrate matrices will not be able to fully accommodate further reductions in water content by changing their local packing and therefore the specific volume will start to deviate from the ideal behavior observed in the rubbery state and in solution. At constant temperature, the glassy state is reached for a water content which increases with increasing carbohydrate molecular weight; deviations from ideal mixing behavior are progressively occurring at higher water contents for matrices with increasing maltopolymer content (Figure 1b). The dependence of the specific volume of the glassy matrices on the water content is rather complex in nature, as it is determined by a number of factors, in particular molecular structure and size, and intermolecular interactions. Interestingly, for the specific case of water in glassy carbohydrates, we observe that the specific volume in the glassy state increases with decreasing water content.9,10 A similar behavior was observed for potato starch27 and for thermoplastic starch.13 For the latter, a gradual decrease in specific volume with increasing water content until a minimum was reached at a water content of Qw ∼ 0.04, with Vsp slowly increasing again above this value while still in the glassy state.13 Conversely, Vsp was observed to continuously increase with increasing water content for amorphous maltose in the glassy state,24 which could reflect differences in thermal history of the matrices. In Table 1, the specific volume of the anhydrous matrices Vsp,0 and the change in specific volume with water content δVsp/ δQw in the glassy state are collected for the different blend compositions. At a given water content in the glassy state, the specific volume decreases with increasing φm. For the five samples with φm < 0.4, the slope of δVsp/δQw is broadly constant at ∼ -0.135 ( 0.005 g · cm-3. For higher maltose contents, this value drops to -0.094 g · cm-3 for the 30% maltopolymer-70% maltose sample and to -0.067 g · cm-3 for the pure maltose sample. The effect of the addition of maltose to the maltopolymer matrix on Vsp is shown in Figure 2 for two water contents Qw ) 0 and 0.05. The data for Qw ) 0.05 is an interpolation of specific volume measurements taken over a series of water activities and using sorption isotherms19 to generate values at the selected water content. The specific volume of the maltopolymer is greater than that of maltose at both water contents,
Specific Volume-Hole Volume in Carbohydrates
J. Phys. Chem. B, Vol. 114, No. 4, 2010 1571
Figure 2. Specific volume as a function of the maltose content for the various maltopolymer-maltose blends at Qw ) 0 (O) and Qw ) 0.05 (b) (T ) 25°). The solid line is the best fit to the specific volume data using eq 2 (Vsp,p ) 0.670 g · cm-3, Vsp,m ) 0.654 g · cm-3, k ) 1.83 (Qw ) 0); Vsp,p ) 0.664 g · cm-3, Vsp,m ) 0.651 g · cm-3, k ) 3.62 (Qw ) 0.05)); the dashed lines are mapped from the best fit of the hole volume data from ref 10 using eq 2 and the linear regression of the Vsp-Vh data (Figure 9) (Vsp,p ) 0.675 g · cm-3, Vsp,m ) 0.656 g · cm-3, k ) 6.09 (Qw ) 0); Vsp,p ) 0.666 g · cm-3, Vsp,m ) 0.651 g · cm-3, k ) 4.37 (Qw ) 0.05)).
by 0.016 cm3 · g-1 (Qw ) 0) and 0.013 cm3 · g-1 (Qw ) 0.05). The addition of small amounts of maltose to the pure maltopolymer has a much greater effect on the specific volume of the system than would be expected from ideal mixing behavior based on the weight fractions of the two components. For the blends with φm < 0.1, the effect on the specific volume of the matrix is close to double of what would be expected from an ideal mixture for the anhydrous system, and triple of the ideal behavior for the system at Qw ) 0.05. The mechanism by which maltose enhances the molecular packing of the matrix can only feasibly be investigated using computer simulations3,28 due to the complex intermolecular interactions and structure of the constituent molecules, but a semiempirical relation was derived in ref 10 to quantitatively evaluate the molecular packing of maltose based on its effective, rather than actual, weight fraction:
Ω ) φp′Ωp + φm′Ωm )
φp kφm Ωp + Ω φp + kφm φp + kφm m
(2)
where Ω signifies either Vsp or Vh. φp, φp′ and φm, φm′ are the actual and effective weight fractions of, respectively, maltopolymer and maltose and k is the overlap factor introduced in ref 10. The specific volume as a function of temperature is presented in Figure 3a for a series of carbohydrate blends equilibrated at aw ) 0.33 (at T ) 25 °C). The data were collected on descending temperature runs, after an initial heating run, erasing the previous thermal history of the samples. In the PVT experiments, an effective cooling rate of ∼ 0.1 °C · min-1 was used in all cases, giving all the samples identical thermal histories during the cooling runs. The data show two linear branches, with lower values of the thermal expansion coefficient for the lowtemperature branch. The temperature at which the two branches intersect has been identified as the glass transition temperature,29 and values are summarized in Table 2. Comparison of the Tg values determined from the PVT experiments with those determined using differential scanning calorimetry (DSC) (Table 3) shows a good agreement between the two techniques, with
Figure 3. (a) Specific volume as a function of temperature for the various maltopolymer-maltose blends equilibrated at aw ) 0.33 (T ) 25 °C). Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]). The data for φm ) 0.7 and φm ) 1 have been shifted down by 0.003 and 0.005 cm3 · g-1. (b) Specific volume at 25 °C after solvent casting (O) and after thermal annealing (b).
TABLE 2: Glass Transition Temperaturea and Coefficient of Thermal Expansion as a Function of the Maltose Content on Total Carbohydrate Omb φm [-] Tg [°C]c R [×104 °C-1] (T < Tg)d R [×104 °C-1] (T > Tg)e 0 0.05 0.1 0.2 0.4 0.7 1
100.8 85.0 76.5 65.6 48.1 28.7 n.d.
1.31 1.37 1.40 1.15 1.70 n.d. n.d.
2.88 2.90 2.86 2.96 2.66 2.55 2.58
a Determined from the intersection of linear correlations of the specific volume with temperature above and below Tg. b The matrices have been equilibrated at aw ) 0.33 (T ) 25 °C). c Typical standard deviation ) 2.7 °C. d Typical standard deviation ) 1.9 × 10-5 °C-1. e Typical standard deviation ) 1.8 × 10-5 °C-1.
differences in Tg as determined following the two techniques being in the same range as those of maltodextrins.9 The coefficient of thermal expansion is defined by
R)
1 ∂V V ∂T
( )
p,nw,np,nm
(3)
where V is the volume of the sample and nw, np, and nm denote the mole fractions of water, carbohydrate polymer, and maltose, respectively. In the glassy state, the coefficient of thermal expansion is lower than that in the rubbery phase and is independent of sample composition at 1.4 ( 0.2 × 10-4 °C-1
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Townrow et al.
TABLE 3: Water Content and Glass Transition by DSC of the Maltopolymer-Maltose Matrices Equilibrated at aw ) 0.33 (T ) 25 °C) φm
Qw [-]a
Tg [°C]b
0 0.05 0.1 0.2 0.4 0.7 1
0.091 0.087 0.083 0.073 0.063 0.055 0.065
98.0 88.3 77.1 59.5 37.9 35.4 29.7
a From water sorption isotherms.10 b Determined from the onset of the change in heat flow observed at the second heating ramp, measured by DSC.19
Figure 4. Pressure dependence of the specific volume for the maltopolymer-maltose blends equilibrated at aw ) 0.33 (T ) 25 °C). Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]).
(Table 2). The samples with higher values of φm have a smaller specific volume than the matrices with a higher average molecular weight, which is consistent with the data presented in Figure 2. In the rubbery state, the specific volume increases more rapidly with temperature to 2.7 ( 0.2 × 10-4 °C-1, again independent of matrix composition, but now the blends superpose onto a single master curve with no vertical offset between them, apart from small deviations observed for the two samples highest in maltose content. During the PVT experiments, some annealing may occur, as is witnessed in Figure 3b, where the specific volume at 25 °C is plotted before and after heating to above the glass transition temperature. The degree of thermal annealing is limited for most samples, which is expected as the samples are effectively annealed by the slow evaporation of water during the solvent casting process. The exception is the 100% maltose sample (φm ) 1), which at 25 °C is already in the rubbery state and should thus be annealed already before the experiment but nevertheless shows a significant change in specific volume. This however could be an experimental artifact. The pressure dependence of the specific volume is presented in Figure 4. The specific volume was measured for increasing pressure and shows a linear dependence on the pressure for all matrix compositions in the range 0-200 MPa with correlation coefficients R2 above 0.99. The isothermal compressibility is defined by
κT )
1 1 ∂V ) K V ∂p
( )
T,nw,nc,nw
(4)
Figure 5. Hole size (a) and ortho-positronium intensity component Io-Ps (b) as a function of the water content for the various maltopolymermaltose blends measured at T ) 25 °C. The blends are characterized by the weight fraction of maltose φm in the matrix: φm ) 0 (O), φm ) 0.2 (1), φm ) 1 (3). The crosses at Qw ) 1 indicate the hole size and Io-Ps in pure water. The inset in (a) is an enlargement of the graph of the hole size at low water contents.
where K is the bulk modulus. The isothermal compressibility is independent of blend composition within the margin of experimental error. Values for κT are in the range of 8 ( 1 × 10-5 MPa-1 for the glassy samples and 13 ( 1 × 10-5 MPa-1 in the rubbery state at about 90 °C. These values are slightly lower than those determined for maltodextrin matrices in ref 9. The dependence of the specific volume on the independent thermodynamic variables is summarized in Table 5 for the various physical states. It is again obvious that whereas the specific volume scales as expected for most parameters, the effect of water on the specific volume in the glassy state is more intricate. Hole Structure and Properties. The hole free volume Vh and ortho-positronium intensity Io-Ps in carbohydrate matrices were determined for three different blend compositions (φm ) 0, 0.2, 1) for the full range of water content between Qw ) 0 and Qw ) 1 (Figure 5). Over this range, the samples pass from the glassy state through the rubbery state into solutions which are increasingly dilute. In the glassy state, the hole volume initially decreases upon the addition of small amounts of water to the anhydrous state. The hole size has a minimum at a characteristic water content which depends on the composition of the carbohydrate blend, and varies from 4.5% for the pure maltose sample (φm ) 1) to 5.3% for the sample containing 20% maltose on total carbohydrate (φm ) 0.2) and to 6% for the pure maltopolymer sample (φm ) 0). The minimum in Vh becomes shallower with increasing maltose content: the minimum hole size in the pure maltopolymer sample is 12% below the hole size in the anhydrous state,
Specific Volume-Hole Volume in Carbohydrates
J. Phys. Chem. B, Vol. 114, No. 4, 2010 1573 TABLE 4: Glass Transition Temperaturea and Rate of Hole Volume Expansion as a Function of the Maltose Content on Total Carbohydrate Omb φm Tg [°C]c δVh/δT [Å3 · °C-1] (T < Tg)c δVh/δT [Å3 · °C-1] (T > Tg)e 0 0.05 0.1 0.2 0.4 0.7 1
89.7 78.0 68.6 49.4 40.9 31.3 26.5
0.318 0.272 0.245 0.152 0.120 0.099 0.120
0.679 0.775 0.634 0.528 0.52 0.41 0.53
a
Figure 6. Temperature dependence of the hole size in the maltopolymermaltose blends equilibrated at aw ) 0.33 (T ) 25 °C). Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]).
decreasing to 8% for the sample with φm ) 0.2 and to only 3% for the pure maltose sample. At higher water contents, the hole volume increases, even in the glassy state, but more rapidly once the sample has passed through the glass transition. The hole volume is largest in the pure maltopolymer sample and decreases with the addition of maltose. In solution, the hole volume determined from the o-Ps lifetime is greater than that in the rubbery phase, and increases slowly with increasing water content to a maximum around Qw ) 0.9, independent of blend composition, above which it drops to the value for pure water.30 For these high water contents, ortho-positronium lifetime ceases to be an indicator of the molecular structure of the matrix, in contrast to the glassy state and the rubbery states. This is because in solution the structural relaxation times become shorter than the average o-Ps lifetime. Consequently, in dilute and moderately concentrated solutions, positronium will create its own self-trapping cage. In this socalled “bubble regime”,30-32 the volume of the hole (bubble) created by the positronium is determined by the balance between zero point energy of the localized positronium and the surface tension of the liquid (carbohydrate-water solution) at the inner surface of the bubble. This “void” is unrelated to the size of the free volume holes which arise due to the disorder in the molecular structure of the matrix. If the chemical parameters governing the positronium formation remain unchanged, the ortho-positronium intensity is a rough measure of the number density of free volume holes present in the sample38 (see also the Discussion section). Io-Ps decreases in a linear fashion through the glass transition and rubbery phase from 35 ( 2% in the anhydrous state to 29% at Qw ) 0.14. In solution, Io-Ps is independent of both water content and blend composition and is slightly lower at 26%. The temperature dependence of the hole volume is presented in Figure 6 for a series of matrix blends at constant water activity aw ) 0.33 (T ) 25 °C). The samples were heated to a temperature between Tg + 40 °C and Tg + 60 °C for several hours to erase their previous thermal history, and the hole volumes were determined from the positronium lifetimes for the descending temperature runs (effective cooling rate ∼0.1 °C · min-1). As for the PVT experiments, the data show two linear branches separated by the glass transition (Figure 6, Table 4). As for the PVT experiments, a good agreement with the Tg values as determined using DSC is obtained (Tables 3 and 4), with the differences between the two methods falling in about
Determined from the intersection of linear correlations of the hole volume above and below Tg. b The matrices have been equilibrated at aw ) 0.33 (T ) 25 °C). c Typical standard error ) 1.0 °C. d Typical standard error ) 0.004 Å3 · °C-1. e Typical standard error ) 0.010 Å3 · °C-1.
the same range as previously observed for maltodextrins.9,29 In the glassy state the hole volume increases more slowly with increasing temperature, with thermal expansion coefficients in the range between 0.09 and 0.32 Å3 · °C-1. In the rubbery state, the hole volume increases much more rapidly with temperature as the molecules vibrate more freely and with greater frequency, with thermal expansion coefficients in the range of 0.41-0.77 Å3 · °C-1. In both the glassy and rubbery states the thermal expansion of the hole size decreases with increasing maltose content.33 It should be noted that, at a defined water activity (here aw ) 0.33), the water content of the blends will vary (Table 3). The behavior of the hole volume as a function of the water content, blend composition, and temperature is summarized in Table 6. Discussion In Figure 7, the matrix expansion θ(Qw) ) V(Qw)/V0 and normalized increase of matrix density F(Qw)/F0 ) Vsp,0/Vsp(Qw) are plotted as a function of the water content for samples close to and below Tg. Here, the subscript “0” refers to the anhydrous samples. The data for the various carbohydrate blends superpose, creating a single master curve with a gradient of ∼0.9 (R2 ) 0.99), indicating that the matrix swelling is independent of carbohydrate composition. The density of these matrices also increases on the addition of water, but with a gradient of ∼0.2 (R2 ) 0.95). The matrix expansion and increase of matrix density upon the sorption of water indicate that the properties of water in these systems are significantly different from those in bulk. Assuming that the absorbed water occupies only the volume generated through the swelling, and does not interact with the carbohydrate, the effective density of the water would be approximately 1.9 g · cm-3, nearly double that of bulk and close to the volume it would occupy based on the van der Waals volume of the water molecule.34 The partial molar volume of water in the glassy carbohydrate matrices is consequently much lower than in pure water. The partial molar volume in the glassy state increases slightly with increasing maltose content from about 9.6 cm3 · mol-1 for the pure maltopolymer matrix to about 12.7 cm3 · mol-1 for the pure maltose matrix (Table 1). This argumentation is however naive, as it is based on the assumption that the nanostructure remains constant throughout the sorption process, which the hole volume analysis shows is not the case. Water does not exist as an independent state in the matrices, but it will interact with the carbohydrates and strongly influence the local molecular organization. The initial reduction in hole volume from the fully anhydrous state by the addition of small amounts of water shows that water can act as
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TABLE 5: Dependence of the Specific Volume on the Thermodynamic Parameters in the Glassy and Rubbery States and in Solution glassy state water content
carbohydrate molecular weight distribution temperature
pressure
rubbery state
solution
decreases with increasing water content; water highly dispersed (Figures 1b, 7b)
increases linearly with increasing water content toward the properties of pure water (Figure 1a)
increases with increasing molecular weight; “molecular packing” (Figure 2)
independent of molecular weight (Figure 1a)
increases with increasing temperature; R ≈ 1.4 ×10-4 °C-1 (Figure 3a)
increases with increasing temperature; R ≈ 2.7 × 10-4 °C-1 (Figure 3a)
increases with increasing temperature
decreases with increasing pressure; κT ≈ 8 × 10-5 MPa-1 (Figure 4)
decreases with increasing pressure; κT ≈ 1.3 × 10-4 MPa-1
not investigated
TABLE 6: Dependence of the Hole Volume on the Thermodynamic Parameters in the Glassy and Rubbery States and in Solution glassy state water content
carbohydrate molecular weight distribution temperature
very low water content: decreases with increasing water content; “antiplasticization” (Figure 5a)
in approach to Tg: increases with increasing water content; “plasticization” (Figure 5a)
increases with increasing molecular weight; “molecular packing” (Figure 5a) increases with increasing temperature; hole size expansion coefficient ) 0.10-0.32 Å3 · °C-1 (Figure 6)
an antiplasticizer (Figure 5a). This has previously been explained as being due to hole filling10 (see also Figure 3a of ref 10). The water molecules entering the system preferentially bind to the carbohydrate chains rather than to each other. We infer that the water molecules are molecularly dispersed in the matrix and most likely occupy positions on the edges of the holes, thereby reducing the average hole size. The minimum hole volume occurs at water contents between Qw ≈ 0.04 and Qw ≈ 0.06, which corresponds to between ∼2 × 1021 and ∼3 × 1021 molecules per cubic centimeter (Figure 5a; Figure 3a of ref 10). Using the framework set out in Kilburn et al.,9 we determined the hole density in a similar maltopolymer blend to be ∼1.5 × 1021 holes per cubic centimeter, equivalent to a minimum hole volume when there are, on average, 1-2 water molecules per hole. The largest reduction in hole volume is observed for the pure maltopolymer, with a decrease of 5.0 Å3 as the water content was increased to 0.059. The van der Waals volume of a water molecule is 11.7 Å3,35 and at a water content of 0.059 there would be 2 water molecules per hole with a total volume of 23.4 Å3. This is a factor of 5 greater than the observed reduction in hole volume. It is therefore clear that most of the water molecules are not located in the holes but are instead bound to the carbohydrates, and consequently, the term “hole filling” must be treated with care to avoid potential confusion. Upon further increasing the water content, the hole size starts to increase, implying the role of water as a plasticizer has overtaken that of a hole filler (Figure 5a). Interestingly, as observed before,9 this hole size expansion occurs already in the
rubbery state
solution
increases with increasing water content; hole size expansion coefficient ) 200 Å3 per unit Qw (Figure 5a)
becomes almost independent of the water content; “bubble state” (Figure 5a)
independent of molecular weight (Figure 5a) increases with increasing temperature; hole size expansion coefficient ) 0.41-0.77 Å3 · °C-1 (Figure 6)
not investigated; “bubble state”
glassy state. Long-range coordinated rearrangements of the polymer chains are frozen out in the glassy state, but significant local mobility turns out to be still possible. This creates a somewhat more open structure which allows diffusion of small, polar molecules. The changes associated with the sorption of water will be slow, and whereas water will equilibrate slowly taking into account the heterogeneous chemical and structural environment in the glassy state, the carbohydrate molecules themselves will still not be able to attain equilibrium even after prolonged storage.36 The continued sorption of water causes the matrices to pass from the glassy into the rubbery state, where the structural rearrangements occur on a time scale of seconds or less (Figure 5a). As noted before, in the rubbery state, the carbohydrate molecular weight has almost no effect on the hole size.10 The water molecules have to a significant degree disrupted the hydrogen bonding between the carbohydrate molecules, and the interchain distances increase due to the greater amplitude of molecular vibrations. In Figure 5b, we observe a decrease in Io-Ps as Qw increases and the carbohydrate matrices pass through the glass transition. Even though Io-Ps is related to the number density of holes, it cannot be universally scaled to this parameter as the positronium formation probability may in addition depend on chemical parameters.37,38 However, given the similar chemical environments of all samples, the decrease in Io-Ps suggests that while the hole size is, on average, constant or increasing, the total number of observed holes decreases (Figure 5b). A previous study on water in crystalline trehalose39 did confirm such a
Specific Volume-Hole Volume in Carbohydrates
Figure 7. (a) Matrix expansion θ as a function of the water content for the various maltopolymer-maltose blends at T ) 25 °C. Solid line: linear regression of the experimental data with a defined intercept 1; R2 ) 0.99. Dashed line: linear regression of the experimental data; R2 ) 1.00. (b) Normalized density increase F/F0 as a function of the water content for the various maltopolymer-maltose blends at T ) 25 °C. Solid line: linear regression of the experimental data with fixed intercept 1; R2 ) 0.94. Dashed line: linear regression of the experimental data; R2 ) 0.95. Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (4), φm ) 1 (]).
general trend. The decrease in Io-Ps is probably caused by the redistribution of the free volume (where the smallest holes disappear), caused by the interaction between water and the carbohydrate network. In the solution range (Qw > 0.5), Io-Ps reflects the formation probability of the self-localizing positronium bubbles in the carbohydrate-water solution mentioned earlier. Even though the number density of holes decreases with increasing water content in the glassy and rubbery states, the total free volume is expected to increase with water content in the rubbery state as the product of the hole volume and Io-Ps increases with increasing water content. Unfortunately, it is not possible to prepare carbohydrate-water systems with a water content between ∼0.16 and ∼0.4. When equilibrating samples at high water activities, the equilibration times are very long and crystallization of, in particular, maltose will occur. Samples at these intermediate water contents can therefore not be prepared by directly mixing carbohydrate and water, because of the very high viscosities. Nevertheless, it is interesting to hypothesize how the transition from a rubber with a meaningful hole volume to a solution with a “bubble” volume independent of the matrix composition could take place. A continuous, smooth transition suggests that, in the transition regime between the rubbery state and solution, sufficiently large water clusters develop in the carbohydrate matrix to enable the
J. Phys. Chem. B, Vol. 114, No. 4, 2010 1575 formation of positronium bubbles by the positronium captured in these clusters. The average hole size as determined using PALS would then be a weighted mean of the size of the structural holes and the positronium bubbles. If, alternatively, in the rubbery state, there would be a discontinuous change as a function of the water content, it should be possible to obtain meaningful hole volume data up to the intersection point at Qw ≈ 0.25. Insight into the relation between nanoscale and macroscopic properties is obtained by combining hole size and specific volume measurements. We will explore the relation between the hole volume and the specific volume for variations in three of the four important thermodynamic variables describing the state of these ternary systems: (1) water content, (2) carbohydrate composition, and (3) temperature (Table 7). One important thermodynamic parameter, namely, the pressure, we unfortunately cannot access in this way, as our PALS equipment does not allow us to perform measurements at elevated pressures. The relation between the specific volume and the hole volume is relatively complex, and reflects the role of water as both a hole filler and a plasticizer (Figure 8). In the glassy state, at low water contents, for samples with φm > 0.4, significant changes in the specific volume occur for only small changes in hole volume as the water content varies. These small changes in hole volume reflect the shallow minimum in hole volume observed in Figure 5a for the pure maltose matrix and the 80% maltopolymer-20% maltose sample. As the maltopolymer content increases, however, a positive correlation between the hole volume and specific volume for variations in water content is observed. At these low water contents, water is to some extent filling the molecular holes between the carbohydrate molecules and is thereby acting as an antiplasticizer. As argued above, the role of water is not solely as a hole filler but it is also modulating the hydrogen bonds between the carbohydrate molecules, and the water molecules are most likely situated at the interface between the molecular holes and the carbohydrate molecules. As the water content further increases, while still in the glassy state, a strong negative correlation between hole volume and specific volume is observed for all blend compositions. In this regime, the matrices are increasing in density while the hole size is increasing, implying that changes in the occupied volume are behind this phenomenon. Water is plasticizing the matrix and locally increases the molecular mobility as the water molecules occupy positions very close to the carbohydrate molecules. In this way, we can explain the highly unusual negative correlation between specific volume and hole volume. The samples with higher maltose content do not appear to show this behavior to the same extent, most likely because the maltose molecules reduce the glass transition temperature of the matrix and in this sense allow the structure to relax and approach equilibrium already at very low water contents. The negative correlation between specific volume and hole volume does not extend to water contents much beyond the data presented in Figure 8, as the specific volume increases rapidly at water contents greater than ∼0.2 while the hole volume continues to increase and eventually reaches the plateau associated with bubble formation. Thus, in the rubbery state, we again expect a positive correlation between the specific volume and the hole volume, at least as long as the bubble regime is not reached. It is also apparent from Figure 8 that the matrices containing higher fractions of the maltopolymer are characterized by higher values of both the specific volume and the hole volume. As
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TABLE 7: Correlations between Specific Volume and Hole Volume in Different Physical Regimes glassy state water content
low water contents: positive correlation; decrease of both hole volume and specific volume; “antiplasticization” (Figure 8)
in approach to Tg: negative correlation; increase of hole volume and decrease of specific volume; “plasticization” (Figure 8)
carbohydrate molecular weight distribution
positive linear correlation (Figure 9)
temperature
positive linear correlation (Figure 10)
we have established in a previous paper,10 this is caused by the inability of the carbohydrate polymers to pack with the same efficiency as their base units. When maltose is added to a pure maltopolymer matrix, both the hole volume and specific volume decrease in a nonlinear fashion (Figure 2; Figure 3a of ref 10). The correlation between hole volume and specific volume at 25 °C is presented in Figure 9 for Qw ) 0 and 0.05.10 At both water contents, all blend compositions will be in the glassy state, although for the samples with φm > 0.7 the water content required for the Tg to be 25 °C is below 0.06, so it is possible that these samples are behaving in a slightly different manner. There is a positive correlation between the hole volume and specific volume for both data series, with linear regression coefficients R2 ) 0.93 (Qw ) 0) and R2 ) 0.96 (Qw ) 0.05). The two linear correlations almost superpose, with the anhydrous blends having slightly larger specific and hole volumes than the matrices at Qw ) 0.05. The slope of the two regressions is also different, with the hydrated blends having a steeper gradient of δVsp/δVh ) 1.1 × 10-3 cm3 · g-1 · Å-3 compared with 8 × 10-4 cm3 · g-1 · Å-3 for the anhydrous matrices. Using the relation between the specific volume and the hole volume, we can also convert the hole sizes in Figure 3a of ref 10 into specific volumes (dashed lines in Figure 2). For the sample at Qw ) 0.05, we observe a very good agreement between the fit of the specific volume data and the fit derived from the hole volume data. For the samples at Qw ) 0, the agreement is less quantitative, although the main features are still captured. This
Figure 8. Correlation between the hole volume and the specific volume as a function of the water content in the glassy state for the various maltopolymer-maltose blends measured at T ) 25 °C. Data above the dashed line are in the glassy state, and data below are in the rubbery state. Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]).
rubbery state
solution
positive correlation; increase of both hole volume and specific volume (Figure 8)
decoupling of Vsp and Vh; “bubble state” for positronium (Figure 8)
Vsp and Vh independent of molecular weight (Figures 1a, 5a) positive linear correlation (Figure 10)
not investigated; “bubble state” for positronium
is probably because the hole volume data show more scatter at at Qw ) 0 than at Qw ) 0.05. In the glassy state, maltose is primarily acting as a packing enhancer, affecting the free volume and the molecular packing which in turn affects the macroscopic properties. The mechanisms by which maltose causes these effects have been discussed previously,9,10 but they will be summarized briefly here. In a pure maltopolymer matrix, the carbohydrate polymers are strongly entangled, and in addition the carbohydrate molecules are extensively hydrogen bonded. It is primarily the strong intermolecular hydrogen binding between the carbohydrates which causes the glass transition of carbohydrate polymers at low water contents to be much higher than that of synthetic polymers of equivalent molecular weight.40,41 As maltose is introduced into the system, some of the polymer-polymer bonds will be replaced by polymer-monomer ones, reducing the number of entanglements and allowing greater segmental freedom. This results in a lowering of the glass transition temperature and in a more dense packing of the carbohydrate molecules in the glassy state, and consequently to smaller hole volumes and a reduced specific volume. There is little effect of blend composition on the temperature dependence of the specific volume in the rubbery state (Figure 3 and Table 2), and in the glassy state the isothermal expansion coefficients are essentially independent of the blend composition. In contrast, the coefficients for the slopes of δVh/δT (Table 4) increase with increasing maltopolymer content. In previous investigations on polydisperse malto-
Figure 9. Correlation between the hole volume and the specific volume as a function of the maltose content at Qw ) 0 (O) and Qw ) 0.05 (b) (T ) 25 °C). The solid lines are the linear regressions of the experimental data; R2 ) 0.93 (Qw ) 0) and R2 ) 0.95 (Qw ) 0.05). The specific volume data for the anhydrous matrices are shifted upward by 0.005 cm3 · g-1.
Specific Volume-Hole Volume in Carbohydrates
J. Phys. Chem. B, Vol. 114, No. 4, 2010 1577 Concluding Remarks
Figure 10. Correlation between the hole volume and the specific volume as a function of temperature for the various maltopolymer-maltose blends equilibrated at aw ) 0.33 (T ) 25 °C). Solid line: linear regression of the experimental data; R2 ) 0.92. Weight fraction of maltose φm in the carbohydrate matrix: φm ) 0 (O), φm ) 0.05 (b), φm ) 0.1 (3), φm ) 0.2 (1), φm ) 0.4 (4), φm ) 0.7 (2), φm ) 1 (]).
dextrins, the slopes of δVh/δT were found to be independent of the degree of hydrolysis of the maltodextrins.9 This discrepancy is likely due to a combination of two factors: (1) The molecular weight range of the carbohydrate blends used in this work is much larger than that of the maltodextrins investigated in ref 9. (2) The experiments are performed with samples which are equilibrated at constant water activity (aw ) 0.33 at T ) 25 °C), which results in a systematic variation of the water content with blend composition (Table 3).19 Care needs to be taken to distinguish the influence of each of these factors. Data from ref 9 allows us to assess the impact of the water content on the slopes of Vsp versus Vh. It turns out that, in the glassy state, the slope of δVh/δT of the DE-12 matrix increases somewhat with increasing water activity and, consequently, with increasing water content. As the water content of the maltopolymer-maltose blends decreases at aw ) 0.33 (at T ) 25 °C) with increasing maltose content,19 this most likely explains the variation in the slope of δVh/δT with variations in blend composition. It should be noted that the variation with the carbohydrate composition of the water content in the glassy state is considerable: at aw ) 0.33, the equilibrium water content is 0.091 for the pure maltopolymer sample, decreasing monotonously with increasing maltose content to 0.055 for the blend at φm ) 0.7 (T ) 25 °C). The exception in this series is formed by the pure maltose sample, which is already in the rubbery phase at aw ) 0.33 (at T ) 25 °C) and therefore has a higher water content than the φm ) 0.7 blend. A positive linear correlation between the hole volume and the specific volume is observed for variations in temperature for all the maltopolymer-maltose blends (Figure 10). In addition, as noticed before for maltodextrin matrices,9 there is no discontinuity at Tg. This implies that the hole volume and the specific volume in the glassy and rubbery state are directly related. The slope of Vsp and Vh increases as the weight fraction of the maltose increases, with a maximum of δVsp/δVh ) 6.71 × 10-4 cm3 · g-1 · Å-3 for the blend at φm ) 0.4. The sample at φm ) 0.8 is slightly lower at 6.45 × 10-4 cm3 · g-1 · Å-3, but the pure maltose sample is significantly lower at 4.98 × 10-4 cm3 · g-1 · Å-3. It is possible that these variations are related to differences in water content of the samples (all equilibrated at aw ) 0.33 (T ) 25 °C)).
We have systematically explored the effects of water, matrix composition, and temperature on the hole volume of amorphous carbohydrate-water systems, in relation to changes in the specific volume. In addition, we have obtained information on the pressure dependence of the specific volume. Our principal aim is to provide a consolidated mechanistic understanding of the relation between changes in packing at the molecular level and the behavior of the specific volume at the macrolevel for the various physical regimes (glassy and rubbery states, solutions). Our motivation was in part that we anticipated that, in comparison with conventional materials interacting primarily via van der Waals forces, the strong hydrogen bonding between the carbohydrate and water molecules would influence the behavior of the free volume and/or the specific volume in potentially interesting ways. Indeed, it has turned out that the physics of the carbohydrate-water systems is strongly dependent on principally the amount of water in the system and the physical state of the matrix. Whereas the effect of temperature on the hole size and the specific volume and the effect of pressure on the specific volume may be understood in physically simple terms, carbohydrate composition and, in particular, water content affect the hole volume and specific volume in rather interesting ways. In the glassy state, increasing the concentration of a low molecular weight carbohydrate in a carbohydrate matrix consisting of a carbohydrate polymer decreases both the hole volume and the specific volume following a process we have previously designated as enhanced molecular packing. The role of water in amorphous carbohydrate matrices is an even more complex one. At low water contents close to the fully anhydrous matrix, the hole volume and the specific volume both decrease with increasing water content, which suggests that water acts as both a hole filler and an antiplasticizer. In contrast, at water contents which are slightly higher but still low enough to guarantee that the matrix is still in the glassy state, the specific volume continues to slowly decrease, but the hole size passes through a minimum before starting to increase. This gives rise to a negative correlation between the hole volume and the specific volume which has not previously been observed for these systems and which can be understood in terms of water molecules which are dispersed within the glassy carbohydrate matrix and which thereby influence the local hydrogen bonding between the carbohydrate molecules. This in turn allows a certain degree of freedom to the carbohydrate molecules and a moderate expansion in hole size. Acknowledgment. We thank Jean-Pierre Marquet for technical assistance and Thomas Schweizer (ETH Zu¨rich) for the PVT measurements. Ph. Looten (Analytical Division, Roquette Fre`res, France) is gratefully acknowledged for the gift of maltopolymer LAB2490. References and Notes (1) Roos, Y. H. Phase Transitions in Foods; Academic Press: San Diego, 1995. (2) Adamson, A. W. Physical Chemistry of Surfaces, 2nd ed.; Interscience: New York, 1967. (3) Roberts, C. J.; Debenedetti, P. G. J. Chem. Phys. B 1999, 103, 7308. (4) Slade, L.; Levine, H. AdV. Food Nutr. Res. 1995, 38, 103. (5) Langer, M.; Ho¨ltje, M.; Urbanetz, N. A.; Brandt, B.; Ho¨ltje, H.D.; Lippold, B. C. Int. J. Pharm. 2003, 252, 167. (6) Levine, H., Ed. Amorphous Food and Pharmaceutical Systems; Royal Society of Chemistry: London, 2002.
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(7) Risch, S. J.; Reineccius, G. A. Encapsulation and Controlled Release of Food Ingredients; ACS Symposium Series; American Chemical Society: Washington, DC, 1995; Vol. 590. (8) Ubbink, J.; Schoonman, A. Flavor Delivery Systems. Kirk-Othmer Encyclopedia of Chemical Technology; John Wiley & Sons: Hoboken, NJ, 2003. (9) Kilburn, D.; Claude, J.; Schweizer, T.; Alam, A.; Ubbink, J. Biomacromolecules 2005, 6, 864. (10) Townrow, S.; Kilburn, D.; Alam, A.; Ubbink, J. J. Phys. Chem. B 2007, 111, 12643. (11) Ubbink, J. Structural Advances in the Understanding of Carbohydrate Glasses. In Modern Biopolymer Science: Bridging the DiVide between Fundamental Treatise and Industrial Application; Kasapis, S., Norton, I. T., Ubbink, J., Eds.; Academic Press: New York, 2009; pp277-293. (12) Crowe, J. H.; Oliver, A. E.; Hoekstra, F. A.; Crowe, L. M. Cryobiology 1997, 35, 20. (13) Bencze´di, D.; Tomka, I.; Escher, F. Macromolecules 1998, 31, 3062. (14) Derbyshire, W.; Van den Bosch, M.; Van Dusschoten, D.; MacNaughtan, W.; Farhat, I. A.; Hemminga, M. A.; Mitchell, J. R. J. Magn. Reson. 2004, 168, 278. (15) Roudaut, G.; Farhat, I.; Poirier-Brulez, F. D. Carbohydr. Polym. 2009, 77, 489. (16) van den Dries, I. J.; van Dusschoten, D.; Hemminga, M. A.; van der Linden, E. J. Phys. Chem. B 2000, 104, 10126. (17) Cicerone, M. T.; Soles, C. L. Biophys. J. 2004, 86, 3836. (18) Greenspan, L. J. Res. Natl. Bur. Stand. (U.S.) 1977, 81A, 89. (19) Ubbink, J.; Giardiello, M.-I.; Limbach, H.-J. Biomacromolecules 2007, 8, 2862. (20) Tao, T. J. J. Chem. Phys. 1972, 56, 5499. (21) Eldrup, M.; Lightbody, D.; Sherwood, J. N. Chem. Phys. 1981, 63, 51. (22) Kansy, J. LT for Windows, Version 9.0, March 2002, PL-40-007 Katowice; Institute of Physical Chemistry of Metals, Silesian University: Bankowa 12, Poland; private communication. (23) Kansy, J. Nucl. Instrum. Methods Phys. Res., Sect A 1996, 374, 235. (24) Lourdin, D.; Colonna, P.; Ring, S. G. Carbohydr. Res. 2003, 338, 2883.
Townrow et al. (25) Limbach, H. J.; Ubbink, J. Soft Matter 2008, 4, 1887. (26) Callen, H. B. Thermodynamics and an introduction to thermostatistics, 2nd ed.; John Wiley: New York, 1986. (27) Haine, V.; Bizot, H.; Buleon, A. Carbohydr. Polym. 1985, 5, 91. (28) Molinero, V.; Goddard, W. A. Phys. ReV. Lett. 2005, 95, 045701. (29) Kilburn, D.; Claude, J.; Mezzenga, R.; Dlubek, G.; Alam, A.; Ubbink, J. J. Phys. Chem. B 2004, 108, 12436. (30) Schrader, D. M.; Jean, Y. C. Positron and Positronium Chemistry; Elsevier: Amsterdam, 1988. (31) Jean, Y. C.; Mallon, P. E.; Schrader, D. M., Eds. Principles and applications of positron and positronium chemistry; World Scientific: Riveredge, NJ, 2003. (32) Mukherjee, T.; Gangopadhyay, D.; Das, S. K.; Ganguly, B. N.; Dutta-Roy, B. J. Chem. Phys. 1999, 110, 6844. (33) The entries in Tables 11 and 12 of ref 9 should read (DE: gradient (T < Tg [Å3 · K-1], Tg [°C], Vh(Tg) [Å3]), gradient (T > Tg [Å3 · K-1]): Table 11: 6: 0.195, 101, 57, 0.511; 12; 0.208; 93; 53; 0.598; 33; 0.224; 76; 43; 0.582 Table 12: 6: 0.213, 64, 56, 0.378; 12: 0.187, 51, 50, 0.381; 21: 0.199, 48, 48, 0.467; 33: 0.258, 43, 42, 0.455). (34) Franks, F. Water Second Edition: a matrix of life; Royal Society of Chemistry; Cambridge, UK, 2000. (35) Gunning, Y. M.; Parker, R.; Ring, S. G. Carbohydr. Res. 2000, 329, 377. (36) Noel, T. R.; Parker, R.; Brownsey, G. J.; Farhat, I. A.; MacNaughtan, W.; Ring, S. G. J. Agric. Food Chem. 2005, 53, 8580. (37) Mogensen, O. E. J. Chem. Phys. 1974, 60, 998. (38) Procha´zka, I.; Cˇ´ızˇek, J.; Motycˇka, V. Radiat. Phys. Chem. 2007, 76, 180. (39) Kilburn, D.; Townrow, S.; Meunier, V.; Richardson, R.; Alam, A.; Ubbink, J. Nat. Mater. 2006, 5, 632. (40) Van der Berg, C. Vapour sorption equilibria and other water-starch interactions: a physico-chemical approach. Ph.D. Thesis, Wageningen Agricultural University, Wageningen, The Netherlands, 1981. (41) Van Krevelen, D. W. Properties of polymers, 3rd ed.; Elsevier: Amsterdam, The Netherlands, 1990.
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