Carbohydrate Polymers in Amorphous States: An Integrated

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Biomacromolecules 2005, 6, 864-879

Carbohydrate Polymers in Amorphous States: An Integrated Thermodynamic and Nanostructural Investigation Duncan Kilburn,† Johanna Claude,‡ Thomas Schweizer,§ Ashraf Alam,† and Job Ubbink*,‡ H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom, Nestle´ Research Center, Vers-chez-les-Blanc, CH-1000 Lausanne 26, Switzerland, and Department of Materials, ETH Zu¨rich, CH-8093 Zu¨rich, Switzerland Received October 13, 2004; Revised Manuscript Received November 29, 2004

The effect of water on the structure and physical properties of amorphous polysaccharide matrices is investigated by combining a thermodynamic approach including pressure- and temperature-dependent dilatometry with a nanoscale analysis of the size of intermolecular voids using positron annihilation lifetime spectroscopy. Amorphous polysaccharides are of interest because of a number of unusual properties which are likely to be related to the extensive hydrogen bonding between the carbohydrate chains. Uptake of water by the carbohydrate matrices leads to a strong increase in the size of the holes between the polymer chains in both the glassy and rubbery states while at the same time leading to an increase in matrix free volume. Thermodynamic clustering theory indicates that, in low-moisture carbohydrate matrices, water molecules are closely associated with the carbohydrate chains. Based on these observations, we propose a novel model of plasticization of carbohydrate polymers by water in which the water dynamically disrupts chains the hydrogen bonding between the carbohydrates, leading to an expansion of the matrix originating at the nanolevel and increasing the number of degrees of freedom of the carbohydrate chains. Consequently, even in the glassy state, the uptake of water leads to increased rates of matrix relaxation and mobility of small permeants. In contrast, low-molecular weight sugars plasticize the carbohydrate matrix without appreciably changing the structure and density of the rubbery state, and their role as plasticizer is most likely related to a reduction of the number of molecular entanglements. The improved molecular packing in glassy matrices containing low molecular weight sugars leads to a higher matrix density, explaining, despite the lower glass transition temperature, the reduced mobility of small permeants in such matrices. Introduction Carbohydrate polymers are widely used in various industrial applications in foods, pharmaceuticals, textiles, paper, and environmental technology.1 Whereas high-molecular weight water-soluble carbohydrates are principally employed as viscosity enhancers and structure builders in solutions and gels,2,3 water-soluble carbohydrates of low- and intermediate molecular weight are routinely used in dehydrated states as matrices for the encapsulation, stabilization, and release of active ingredients, like flavors,4 drugs,5,6 and nutrients.7 The properties of carbohydrate polymers in dilute solutions and gels have been extensively researched, leading to a detailed molecular understanding of the structure-property relations of these so-called hydrocolloids.2,3 Much less is known about the molecular properties of carbohydrate polymers in dense matrices of low water content. Carbohydrates in dense matrices may occur in crystalline states of varying degree of order, from perfectly crystalline mono- and disaccharides to partially organized high-molecular weight carbohydrates such as starch and cellulose. For * To whom correspondence should be addressed. Tel.: +41-21-785 9378. Fax: +41-21-785 8554. E-mail: [email protected]. † University of Bristol. ‡ Nestle ´ Research Center. § ETH Zu ¨ rich.

most applications, however, carbohydrates in dense states are used in amorphous form.6,8 The principal advantages of using amorphous carbohydrates are that they combine interesting mechanical properties with the ability of forming films, particles, and matrices of adjustable morphology. In addition, under controlled conditions in the glassy state, they combine high physical and chemical stability with very high barrier properties for gases such as oxygen and nitrogen9 and organic molecules.10 Because of this combination of properties, amorphous carbohydrates are particularly useful as materials for the encapsulation of sensitive active ingredients in foods and pharmaceutics. The properties of amorphous carbohydrates are strongly dependent on a number of factors including the quantity of water present in the matrix. Water is a strong plasticizer of amorphous carbohydrates, and the glass transition temperature (Tg) of carbohydrates is a strongly decreasing function of the water content.11 Notwithstanding the extensive research on the properties of water in amorphous carbohydrates and the effect of carbohydrate plasticization on various related properties such as the stability of pharmaceutical and food products, relatively little is known about the molecular mechanism of water sorption by amorphous carbohydrates and the subsequent effects of sorbed water on the structure and dynamics of the carbohydrate matrix.

10.1021/bm049355r CCC: $30.25 © 2005 American Chemical Society Published on Web 01/12/2005

Carbohydrate Polymers in Amorphous States

Carbohydrate polymers differ substantially from synthetic polymers in a number of important respects. In the dry state, carbohydrate polymers have a glass transition temperature which is much higher than for almost all synthetic polymers of similar molecular weight. For instance, the Tg of highmolecular weight polystyrene and polyethylene are 372 K and 140 K,12 respectively, whereas the Tg of dry starch is 520 K.13 This hints at the important role of intermolecular interactions in the formation and stabilization of carbohydrate matrices, in effect forming clusters of higher molecular weight than the individual constituent molecules. These interactions are most likely hydrogen-bonding interactions between the hydroxyl and ether groups of the sugar rings.14 This immediately explains the dramatic effect of water on carbohydrate properties. As it is difficult to directly probe hydrogen bonding in carbohydrates, in particular for those in amorphous states, most information confirming strong interactions between carbohydrates in aqueous environments is indirectly derived, for instance from rheology15 and neutron scattering.16 Several aspects of water in amorphous carbohydrates have been addressed using a wide range of techniques including differential scanning calorimetry (DSC),17,18 dynamic mechanical thermal analysis (DMTA),19 dilatometry,20,21 infrared spectroscopy,22 NMR spectroscopy,23,24 and neutron scattering.16,25 Important insights into the thermodynamic properties of carbohydrate-water systems have been obtained from dilatometry and moisture sorption studies. In particular, from the pressure-volume-temperature (PVT) behavior of thermoplastic starch20 and ethylcellulose,26 it was inferred that carbohydrate systems closely fulfill a principle of corresponding states. Consequently, to a good approximation, the thermodynamic properties of the carbohydrate-water system can be expressed in terms of a reduced pressure, temperature, and volume. Lacking detailed structural insights, however, it is difficult to arrive at a quantitative model of water in amorphous carbohydrate matrices. Recently, we have explored the applicability of positron annihilation lifetime spectroscopy (PALS) to probe the structure of amorphous carbohydratewater systems.27 PALS is a powerful technique by which the size of voids in dense materials can be determined, and the technique is currently finding increased application in the analysis of the void structure of polymer matrices.28 From the PALS analysis of a glassy carbohydrate matrix we have observed, surprisingly, that the average hole volume of the carbohydrate matrix increases strongly with increasing water content. Combined with thermodynamic analysis showing that the carbohydrate glass both densifies and expands upon the sorption of water, it was concluded that the interaction of water with the carbohydrate polymer occurs on very small length scales, in line with an interpretation involving both the hydrogen bond formation and disruption and rearrangements of the matrix free volume.27 In the present paper, we combine PALS analysis with temperature and pressure dependent dilatomety to quantitatively study the relation between molecular and macroscopic properties of amorphous carbohydrate matrices in lowmoisture states. As a model, maltodextrins of varying

Biomacromolecules, Vol. 6, No. 2, 2005 865

molecular weight distributions are used. Maltodextrins are the products of a controlled hydrolysis of starch and are mixtures of R-(1f4) linked glucose oligo- and polysaccharides with occasional R-(1f6) branches.29 The industrial properties of maltodextrins depend strongly on the degree of hydrolysis. In particular for applications in encapsulation it is found that, in addition to the high-molecular weight carbohydrate polymers, a sufficient content of low molecular weight sugars is critical to achieve the desired barrier properties.4 This is inspite of the fact that low molecular weight sugars lower the glass transition temperature of the matrix. Our focus is on low-moisture systems, with particular emphasis on the glassy state of the carbohydrate-water system, the glass transition, and the early stages of the rubbery state. We vary in a systematic way the water activity of the samples, and, for two water activities, the molecular weight distributions. PALS and dilatometry are complemented by a thermodynamic characterization of the system, including analysis of the glass transition by calorimetry, the moisture sorption by the carbohydrate matrices, and the analysis of the distribution of water in the matrices by a thermodynamic clustering approach. Theoretical Considerations One of the important structural aspects of amorphous systems including polymer matrices is the spatial and size distribution of interstitial holes or voids between the constituent molecules. The size of these holes can be probed by determining the average lifetime or the lifetime distribution of o-positronium captured in the matrix. In a formulation explicitly incorporating the holes or voids as structural elements, the volume of the amorphous carbohydrate-water system may then be considered as consisting of occupied volume and unoccupied or void volume. When expressed per unit mass of the system, we may write Vsp ) Vsp,occ + Vsp,unocc

(1)

where the subscript sp indicates that we are dealing with specific volumes. The unoccupied volume is distributed over distinct individual holes Vsp,unocc )

∫Nh(r)‚Vh(r) dr

(2)

where Nh is the number density of holes of size r and volume Vh. For the purpose of the present paper, we will assume the hole size distribution to be monodisperse, i.e., Vsp,unocc ) NhVh. Whereas the average hole volume or the hole size distribution may be determined from PALS, the specific volume of the overall system may be determined by dilatometry as a function of pressure and temperature. From eqs 1 and 2, it is clear that the partitioning of the specific volume between the occupied and nonoccupied volume is not fixed because the number density of holes is not known. The unoccupied volume in a system arises because of the molecular packing, density fluctuations, and kinetic and

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Kilburn et al.

topological constraints. For a system which is able to reach thermodynamic equilibrium, molecular packing and density fluctuations are in turn completely determined by the composition of the system, temperature, and pressure. In physicochemical terms, the volume of the carbohydratewater system may conveniently be stated in terms of partial molar quantities30,31 V ) npVjp + nwVjw

(3)

where ni is the mole number and Vji the partial molar volume of component i. The subscripts p and w refer to the polymer repeating unit and to water, respectively. The partial molar volumes are defined by30,31 Vji )

( ) ∂V ∂ni

(4)

T, p,nj*i

where index j refers to all components except component i. In contrast to eq 1, the partial molar volume of a component includes the unoccupied space introduced by the component into the system. This unoccupied volume arrives from the molecular packing, the entropy of the system, and the intermolecular interactions. In principle, the structure of a system is completely determined at one given instant of time when the coordinates and orientation of the individual molecules are known. The average structural and physical properties of the system and their fluctuations may then be deduced from the time evolution of the system. A general way of obtaining the average properties of liquidlike systems is by determining the molecular pair distribution function of the constituent molecules in the system,32,33 for instance by neutron scattering. An experimentally simpler approach providing information on the effect of intermolecular interactions on the overall structure of the system is by using the clustering theory of Zimm and Lundberg.34 The cluster integral Gww ) 1/V∫∫(F2(i,j) - 1) di dj, which is the positional average of the pair distribution function F2 of, for instance, two water molecules signified by the sets of coordinates i and j is related to the activity coefficient of water in the polymer matrix via the following relation:

[

∂(aw/φw) Gww ) -φp Vjw ∂aw

]

-1

(5)

T, p

which is generally valid as long as the system compressibility may be neglected. In eq 5, φw and φp signify the volume fractions of water and polymer, respectively. The average number of water molecules clustering around any individual water molecule in excess of the mean concentration of water molecules is φwGww/Vjw and the function Gww/Vjw is accordingly known as clustering function. Positive values of the clustering function indicate that the water in the matrix forms small cluster pockets between the polymer chains. Conversely, strongly negative values of the clustering function signify a highly disperse state of water in the matrix. Use of eq 5 is highly convenient as for a volatile compound like water the clustering function may be determined from the

sorption isotherm and dilatometry, to some extent circumventing the need for advanced scattering techniques. The sorption of water by biopolymers and carbohydrates is a complicated process and several regimes may be identified. At very high water content, the biopolymer dissolves or forms an aqueous gel. At somewhat lower concentrations of water, we obtain a biopolymer melt in the rubbery state. For these two regimes, it is found that the water sorption isotherm is well described by liquid-state models, like for instance the Flory-Huggins theory.35 When the concentration of water is further lowered, the biopolymer matrix will pass into the glassy state and a liquidlike approach will fail. Instead, it is observed that the moisture sorption of glassy biopolymers strongly resembles the sorption on a rigid adsorbate with a heterodisperse distribution of adsorption sites.27,35 The simplest isotherm model applying to such a rigid, heterogeneous system is the Freundlich equation36 Q′ ) Ka1/c w

(6)

with K and c (c g 1) constants representative for the system. Q′ ) mw/mp is the weight ratio of water to polymer. mw and mp are the weights of water and polymer, respectively, and are related to the mole numbers by mw ) Mwater nw and mp ) Mp np, where Mwater is the molecular weight of water and Mp the molecular weight of the monomer (anhydroglucose; Mw ) 162 Da). The stoichiometric ratio of water to anhydroglucose is defined by ηw ) nw/np. Significant effort has been devoted to the evaluation of an isotherm model suitable to describe the overall moisture sorption by an amorphous biopolymer matrix. Of the various models, the so-called Guggenheim-Anderson-de Boer (GAB) isotherm has turned out to be most useful11 Q′ )

KCWmaw (1 - Kaw)(1 - Kaw + KCaw)

(7)

where K, C and Wm are constants characterizing the system. Although having some theoretical foundation as an extension of the Brunauer-Emmett-Teller (BET) isotherm,37 the GAB isotherm should be considered as a phenomenological model for a complex system like water in a biopolymer matrix. The polymer matrix may expand or shrink by the sorption of water or by changes in pressure and temperature. The degree of volumetric swelling induced by the uptake of water is defined by27 θ)

V F0 1 ) ‚ V0 F Qp

(8)

where F is the density and the subscript 0 refers to the dry state of the system. Qp ) mp/(mp + mw) is the weight fraction of polymer, and Qw ) 1 - Qp is the weight fraction of water. The volume fraction of water in the polymer matrix is then given by27 φw )

Vw VjwQw F ) V Mw

(9)



where Vw is the volume of water in the system. The volume fraction of polymer is φp ) 1 - φw. At constant composition, the volume of the system is not fixed but dependent on the pressure and temperature. The isothermal compressibility κT, the bulk modulus K, and the coefficient of thermal expansion R are defined by31 κT )

1 1 ∂V ) K V ∂p T,ni

( )

(10a)

1 ∂V V ∂T p,ni

(10b)

R)

( )

∂Vsp /∂T ∂Vh /∂T

(12)

In the Discussion section, we will employ eq 12 in an analysis of the temperature and composition dependent changes in free and unoccupied volume, along with the equation-of-state approach discussed in the Appendix. Materials and Methods

Perturbations of a system lead to changes in its molecular packing and consequently to changes in the unoccupied volume of the system. Such perturbations include temperature and pressure changes but also changes in composition, for instance caused by the sorption of water. Estimates of the unoccupied volume can be given from specific volume data using the van der Waals radius of atoms and molecules. In free volume theories, a distinction is usually made between the unoccupied volume and the free volume of a system. The free volume, which is much smaller than the unoccupied volume, is considered as the fraction of the unoccupied volume enabling molecular reorganizations and is therefore implied in phenomena like viscoelastic flow, diffusion, and the transition between the glassy and rubbery states. Although free volume theories such as those based on lattice-fluid equations of state have a long standing in the polymer field, the physical significance of the free volume for biopolymerwater systems still needs to be established. Dilatometry combined with PALS may be used to relate macroscopic changes in sample volume as a function of pressure, temperature, and composition to changes in the molecular hole structure. In principle, if the free volume of a system is known, for instance from an equation of state, the hole size as derived from PALS may be used to calculate the number density of holes as in eqs 1 and 2. One of the most successful equations of state used in the analysis of polymer properties is the Simha-Somcynsky equation of state,38 which is introduced in the Appendix and the applicability of which we will explore for the polysaccharide-water systems. In an alternative approach focusing on the unoccupied volume, we may depart from eq 2 and generally write for any changes in unoccupied volume dVh dNh dVsp dVsp,unocc ≈ ) Nh + Vh dT dT dT dT

Nh )

(11)

where we neglect any changes in matrix expansion due to temperature-dependent changes in molecular size and bond distances. Our PALS and dilatometric experiments show that both Vsp and Vh are linear functions of T to a high degree of accuracy. As a consequence, within the current approximation, Nh is required to remain constant over our experimental temperature interval. In fact, in the PALS analysis of polymer structure, this is an often-used and fairly well-founded assumption.39 We may thus obtain an estimate of the number density of holes from

Preparation of Matrices. All maltodextrin materials were obtained from Roquette Fre`res (Lestrem, France). The following dextrose equivalents (DE) were used: DE 6 (Glucidex IT-6, lot. no. E4489); DE 12 (Glucidex IT-12, lot. no. E8950); DE 21 (Glucidex IT-21, lot. no. 729083); and DE 33 (Glucidex IT-33, lot. no. 729084). The molecular weight characterization of the samples is summarized in Table 1. The degree of hydrolysis of maltodextrins is indicated by the DE value,29 which denotes the percentage fraction of reducing sugars in the sample (DE 1 is equivalent to non-hydrolyzed starch, DE 100 is equivalent to glucose) and is thus proportional to the number average molecular weight. All materials were used without further purification as the carbohydrate content of all lots was higher than 98% on dry weight. Matrices were prepared by solvent casting and controlled evaporation as previously described.27 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 200 and 300 µm were used for water-activity equilibration and all further experiments. Samples for PALS and PVT experiments were prepared by compaction of about 0.12 and 0.75 g of water-activity equilibrated powder into disks (diameter 1 cm, thickness ∼1.1 mm and ∼7 mm respectively) using a laboratory press. Water Activity Equilibration. Samples were equilibrated at 25 °C at various water activities in desiccators containing saturated salt solutions of known relative humidity [aw ) 0.11 (LiCl), 0.22 (CH3COOK), 0.33 (MgCl2), 0.43 (K2CO3), 0.54 (Mg(NO3)2), and 0.75 (NaCl)].40 The sorption of water was followed gravimetrically until equilibrium was achieved (generally within 35 days). Determination of Water Content. The water content was determined using a home-built extraction unit as described previously.27 The extraction of water was followed as a function of time by monitoring the decrease of the water peak at λ ) 1940 nm in near infrared reflectance spectroscopy (Infra-analyzer 500, Bran + Lu¨bbe, Germany). The variation between duplicates was T ), 0.09; T , 2; g g g Vsp at Tg, 7 × 10-4. All in units as in the table. All correlation coefficients 2 b c are R g 0.99. Calculated using Vsp at Tg as reference value. Defined as the temperature of intersection of the linear regression of the PVT data in the rubbery and glassy states.

Figure 4. Hole volume (a) and specific volume (b) of annealed DE 12-matrices as a function of the temperature for various water activities equilibrated at 25 °C. Open circles: aw ) 0.11; filled circles: aw ) 0.22; open triangles: aw ) 0.33; filled triangles: aw ) 0.43; open diamonds: aw ) 0.54; filled diamonds: aw ) 0.75. The slightly larger symbols at 25 °C in part b represent the specific volume of the nonannealed moisture-equilibrated state.

Tg. As our interest is principally in the thermally annealed state of the carbohydrate polymers, we report here only the PVT results for the experiments with decreasing temperatures. However, we note that qualitatively no differences were observed between the PVT experiments with increasing and decreasing temperatures, apart from some changes in density in the glassy state because of the variation in sample history. The reproducibility of the experiments is very good. For example, if two curves of DE 12 measured both with decreasing temperature in the range from 30 to 140 °C were brought to overlap, the deviation of the data was never larger than 5 × 10-4 cm3/g. In addition, the Tg determined from PVT data does not depend on the sign of the temperature change (data not shown). In Figure 4b, the specific volume of the DE 12 sample is shown as a function of the temperature for the range of water activities between 0.11 and 0.75. The specific volume clearly shows two linear branches as a function of temperature, with the thermal expansivity being lower for the low-temperature branch. The quality of the linear regression of the experimental data is very good (Table 7). We identify the point of intersection of the low- and high-temperature branches as the glass transition temperature of the matrix. A comparison of the Tg data in Tables 5 and 7 shows a very good agreement between the results obtained by DSC and dilatometry, with the variation between the two techniques being less than 5-10 °C over the whole range of water activities. Apart from confirming that DSC and dilatometry essentially probe the

same molecular phenomena, it demonstrates that the water content of the samples is not changing during PVT experiments. To assess the effect of thermal annealing on the solventcast samples, we have included the specific volume of the initial moisture-equilibrated samples in Figure 4b (the larger symbols at 25 °C). For the highest water activity, aw ) 0.75, the initial and final specific volumes are identical, confirming that in the rubbery state the matrix is already fully annealed. For water activities between 0.11 and 0.43, some matrix relaxation is observed upon heating the samples to above the Tg and cooling again. For all four samples, the specific volume is found to increase somewhat during the annealing. The sample at aw ) 0.54 is peculiar because no relaxation of the specific volume is observed although the sample should still be in the glassy state at 25 °C. It could be that specifically for this water activity, the dense, solvent cast matrix is structurally already in an annealed state. Apart from thermal treatment, solvent casting is an alternative way of obtaining matrices in a representative glassy state. Alternatively, it could well be that the absorbed water is allowing certain matrix reorganizations in a small temperature window below the glass transition temperature, for instance by a mechanism of “cold” relaxation. In the annealed glassy state, the density of the DE 12 matrix increases with increasing water activity (Table 6; Figure 4b). A similar trend has been observed before for amorphous starch and it has been linked to an increase in the free volume of the matrix.20 In contrast, the density of so-called minimally aged glasses of the disaccharide maltose was found to decrease continuously with increasing water content,21 most likely reflecting the behavior of small sugars versus carbohydrate polymers. The increase in density with increasing water persists, albeit in a less pronounced form, in the rubbery state. It is likely that the fairly substantial dependence of the sample density as a function of the water activity is related to both the intrinsic packing of water and carbohydrate polymer and the glass transition of the carbohydrate-water system. As the glass transition temperature is higher for the matrices containing less water, we expect that intermolecular entanglements become important at higher temperatures for matrices containing less water and thereby limit formation of a well-ordered and dense molecular packing.

872


Figure 5. Hole volume (a) and specific volume (b) of annealed maltodextrin matrices equilibrated at aw ) 0.22 (25 °C) as a function of the temperature for various molecular weight distributions. Open circles: DE 6; filled circles: DE 12; open triangles: DE 21; filled triangles: DE 33. The slightly larger symbols at 25 °C in part b represent the nonannealed moisture-equilibrated state.

In Figures 5b and 6b, the specific volume is shown for annealed matrices with varying molecular weight distributions equilibrated at aw ) 0.22 and aw ) 0.54, respectively. Again, to a very good approximation, the specific volume is linearly dependent on the temperature both below and above the glass transition temperature (Tables 8 and 9). The glass transition temperatures as determined from the PVT measurements agree reasonably well with the DSC results; the Tg on average being about 10 °C higher in our PVT analysis. For two samples, larger deviations between the PVT and DSC experiments are observed (DE 21 and DE 33 equilibrated at aw ) 0.54). However, these samples are already visibly in the rubbery state at room temperature, and the distinction between a low- and high-temperature branch in the PVT data is therefore difficult to make. Interestingly, very little matrix relaxation is observed, not only for the samples equilibrated at aw ) 0.54 but also for the samples equilibrated at aw ) 0.22. For the samples equilibrated at aw ) 0.54, we are close to the glass transition temperature for the DE 21 and DE 33 matrices, and some degree of “cold” relaxation or careful solvent casting could explain the well-defined glassy state we observe in the PVT experiments. The PVT behavior of the carbohydrate polymers is strongly dependent on the state of the matrix. In the rubbery state, effectively universal behavior is observed with the specific volume of the matrix being virtually independent of the molecular weight of the carbohydrates. The differences in matrix density of the carbohydrates in the rubbery state

Kilburn et al.

Figure 6. Hole volume (a) and specific volume (b) of annealed maltodextrin matrices equilibrated at aw ) 0.54 (25 °C) as a function of the temperature for various molecular weight distributions. Open circles: DE 6; filled circles: DE 12; open triangles: DE 21; filled triangles: DE 33. The slightly larger symbols at 25 °C in part b represent the nonannealed moisture-equilibrated state. Table 8. Thermal Expansion and Glass Transition Temperature of Annealed Maltodextrin Equilibrated at aw ) 0.22 (25 °C) as a Function of the Molecular Weighta DE

R [K-1] ×104 (T < Tg)b

Tg [°C]c

Vsp at Tg [cm3 g-1]

R [K-1] ×104 (T > Tg)b

6 12 21 33

2.08 1.50 2.16 2.41

106 81 68 55

0.6649 0.6590 0.6557 0.6522

4.27 3.95 3.97 4.03

a In the calculation of the coefficient of thermal expansion, the specific volume at the glass transition temperature is taken as reference value. Typical standard errors are: R(T < Tg), 0.08; R(T > Tg), 0.09; Tg, 1; Vsp at Tg, 7 × 10-4. All in units as in the table. All correlation coefficients are R2 g 0.98. b Calculated using Vsp at Tg as reference value. c Defined as the temperature of intersection of the linear regression of the PVT data in the rubbery and glassy states.

are in effect solely determined by the water activity or the water content of the matrices. In the glassy state, the density of the matrix increases with decreasing molecular weight (i.e., with increasing dextrose equivalent). Upon cooling the polymer-water melt, the temperature at which the molecules will start to feel the effect of molecular entanglements increases with the molecular weight. As the glassy state of the matrices will reflect the density at which the glass transition takes place, the higher molecular weight matrices will have a density which is lower than of the lower molecular weight matrices. In Figure 7, the bulk modulus of the carbohydrate-water matrices is shown as a function of the temperature. In Figure 7a, the bulk modulus is plotted for the DE 12 sample with varying water activity; in Figure 7b, the bulk modulus is


Carbohydrate Polymers in Amorphous States Table 9. Thermal Expansion and Glass Transition Temperature of Annealed Maltodextrin Equilibrated at aw ) 0.54 (25 °C) as a Function of the Molecular Weighta DE

R [K-1] ×104 (T < Tg)b

Tg [°C]c

Vsp at Tg [cm3 g-1]

R [K-1] ×104 (T > Tg)b

6 12 21 33

2.2 2.8 2.5 n.d.

73 57 51 20d

0.6532 0.6513 0.6475 0.6386e

4.00 3.91 3.88 4.16

a Typical standard errors are: R(T < T ), 0.1; R(T > T ), 0.06; T , 2; g g g Vsp at Tg, 7 × 10-4. All in units as in the table. All correlation coefficients 2 b c are R g 0.99. Calculated using Vsp at Tg as reference value. Defined as the temperature of intersection of the linear regression of the PVT data in the rubbery and glassy states. d Estimated. e At 20 °C.

Table 10. Linear Regression of PALS Data for Annealed Maltodextrin DE 12 as a Function of the Water Activitya

aw at 25 °C

gradient T < Tg [Å3 K-1]b

Tg [°C]c

Vh(Tg) [Å3]

gradient T > Tg [Å3 K-1]b

0.11 0.22 0.33 0.43 0.54 0.75

0.14 0.14 0.18 0.19 0.23 n.d.

97 88 80 70 61 n.d.

47 47 49 50 52 n.d.

0.35 0.34 0.40 0.44 0.49 0.42

a Typical standard errors are: gradient (T < T ), 0.01; gradient (T > g Tg), 0.02; Tg, 2; Vh at Tg, 4. All in units as in the table. All correlation 2 b coefficients are R g 0.97. Gradient of the linear regression of the hole volume versus temperature. c Defined as the temperature of intersection of the linear regression of the PALS data in the rubbery and glassy states.

Table 11. Linear Regression of PALS Data for Annealed Maltodextrin Equilibrated at aw ) 0.22 (25 °C) as a Function of the Molecular Weighta DE


Tg [°C]c

Vh(Tg) [Å3]


6 12 33

0.32 0.14 0.15

116 88 49

70 47 37

0.43 0.34 0.47

a Typical standard errors are: gradient (T < T ), 0.01; gradient (T > g Tg), 0.01; Tg, 2; Vh at Tg, 4. All in units as in the table. All correlation coefficients are R2 g 0.97. b Gradient of the linear regression of the hole volume versus temperature. c Defined as the temperature of intersection of the linear regression of the PALS data in the rubbery and glassy states.

Figure 7. Bulk modulus of maltodextrin matrices as a function of the temperature. (a) Dependence on the water activity (25 °C). Open circles: aw ) 0.11; filled circles: aw ) 0.22; open triangles: aw ) 0.33; filled triangles: aw ) 0.43; open diamonds: aw ) 0.54; filled diamonds: aw ) 0.75. (b) Dependence on the molecular weight distribution for samples equilibrated at aw ) 0.22 and 25 °C. Open circles: DE 6; filled circles: DE 12; open triangles: DE 21; filled triangles: DE 33.

shown for the varying molecular weight distributions equilibrated at aw ) 0.22. As a function of both water activity and molecular weight, the bulk modulus shows a sigmoidal decrease with temperature. At room temperature, the bulk modulus is between 8 and 10 GPa for all samples except the two highest water activities of the DE 12 matrix, which are already in or close to the rubbery state. The bulk modulus decreases by a factor of about 1.5 to about 5-6 GPa when the samples pass into the rubbery state. Interestingly, this decrease starts already 20-30 °C below the glass transition temperature as determined by DSC and PALS. Clearly, in the rubbery state and in the glassy state close to Tg, the matrices become more ductile because of the increased number of degrees of freedom. The value of the bulk modulus is well in line with values previously reported for

amorphous starch20 and is higher than for most synthetic polymers.12 This probably reflects the strong intermolecular interactions between the carbohydrate chains. Hole Structure and Properties. PALS experiments have been performed starting both in the glassy and rubbery states and with increasing and decreasing temperatures, respectively. As our focus is on the properties of thermally annealed systems, we only report the PALS experiments with decreasing temperature. Some of the PALS measurements starting from the glassy state have been reported elsewhere.27 In Figure 4a, we have plotted the average hole volume as determined from PALS as a function of the temperature for the DE 12 matrices equilibrated at the full water activity range. From Figure 4a, it is immediately apparent that the hole volume is strongly dependent on both temperature and water activity, in both the rubbery and glassy states. For a given water activity sample, the hole volume is a linear function of temperature both below and above the Tg (Table 10). The variation in hole size is quite significant: for the aw ) 0.75 sample, it increases from about 50 Å3 at 30 °C to about 75 Å3 at 80 °C, i.e., an increase of a factor 1.5 in a temperature interval of 50 °C. For the other water activities, similar increases in hole volume are observed. The hole size is also a strongly increasing function of the water activity in both the rubbery and glassy states. The hole size increases by about 15 Å3 in the glassy state and by about 30-40 Å3 in the glassy state. The molecular weight dependence of the hole volume is investigated at two water activities: aw ) 0.22 (Figure 5a; Table 11) and aw ) 0.54 (Figure 6a; Table 12). The rubbery state data indicate the strong structural similarities between

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Kilburn et al.

Table 12. Linear Regression of PALS Data for Annealed Maltodextrin Equilibrated at aw ) 0.54 (25 °C) as a Function of the Molecular Weighta DE


Tg [°C]c

Vh(Tg) [Å3]


6 12 21 33

0.22 0.23 0.21 0.20

68 61 50 37

57 52 49 40

0.33 0.49 0.47 0.44

a Typical standard errors are: gradient (T < T ), 0.02; gradient (T > g Tg), 0.02; Tg, 2; Vh at Tg, 5. All in units as in the table. All correlation 2 b coefficients are R g 0.96. Gradient of the linear regression of the hole volume versus temperature. c Defined as the temperature of intersection of the linear regression of the PALS data in the rubbery and glassy states.

the various molecular weight samples as the hole volume in the rubbery state is virtually indistinguishable for the various molecular weight distributions at constant water activity. This observation at the nanoscale is in striking agreement with the macroscopic PVT results on the same materials and clearly reflects the effects of molecular structure and properties on macroscopic behavior. We will discuss these issues in more detail below. Besides DSC and dilatometry, PALS constitutes the third technique by which the glass transition temperature of the carbohydrate polymers can be determined. We have collected the glass transition temperatures as determined from the PALS results in Tables 10 (DE 12 samples), 11 (aw ) 0.22 samples), and 12 (aw ) 0.54 samples). A comparison with both the DSC results (Table 5) and the PVT results (Tables 7-9) demonstrates the excellent overall agreement between the techniques. In general, the Tg values as determined from DSC are 5 °C to occasionally 10 °C lower than the values determined by both PALS and dilatometry. This could be due to the fact that we are reporting the Tg(onset) values, which indicate the start of the glass transition (which is generally 20-30 °C wide for biopolymers17). A generalization of eq 1 appropriate for individual holes as measured by PALS and their contribution to the total specific free volume is given by Vsp ) Vsp,occ + Vsp,unocc,0 + NhVh

(16)

where Vsp,unocc,0 is a term to account for any under- or overestimation of hole size due to, for example, the holes not being spherical in shape or a preference for larger holes due to energy considerations. The last two terms on the right of this equation therefore constitute the free volume fraction. Furthermore, we assume that Vsp,unocc,0 is constant with temperature and so has no effect on the determination of the number of holes via eqs 11 and 12. Justification for this assumption has been published by some of us59 where, for the synthetic polymer poly(styrene-co-acrylonitrile), Vsp,unocc,0 was found to be zero. Our analysis is thus far based on the average hole size and the way it changes with molecular weight, water content, and temperature. In principle, we should consider the distribution of hole sizes around their mean value, in particular as changes in the hole size distribution may provide information on the mechanism of hole formation. The hole size distribution may be determined if we allow a distribution

Figure 8. Degree of matrix swelling θ and density increase F/F0 as a function of the water content Qw (25 °C). Open symbols: θ; filled symbols: F/F0. Circles: DE 6; triangles down: DE 12; diamonds: DE 21; triangles up: DE 33. Table 13. Dry Density, Rate of Volumetric Swelling, and Partial Molar Volume of Water for the Various Matrices after Annealing above Tg DE

F0 [g cm-3]

dθ/dQ′ [-]

R2

vjw [cm3 mol-1]

6 12 21 33

1.5094 1.5059 1.5093 1.5093

0.7364 0.7178 0.6933 0.6124

0.99 1.00 0.99 0.98

8.8 8.6 8.3 7.3

of o-Ps lifetimes in data analysis. Performing such an analysis on room-temperature spectra with a high number of counts per spectrum (∼5 × 106), we find that there is no apparent variation in the width of the distribution with water activity, as for all samples the FWHM ) 15 ( 2 Å3 (data not shown). It is noted, however, that due to the relatively low o-Ps lifetimes in these substances (in the range 1.3-1.9 ns) there is some difficulty in separating the o-Ps lifetime from lower lifetimes. Analysis on all temperature run spectra has been performed fitting with discrete lifetimes, which also delivers greater stability of components for spectra with ∼ 1 × 106 counts. Discussion In low-moisture carbohydrate matrices, water is strongly associated with hydrophilic moieties located on the carbohydrate chains, as indicated for instance by the clustering function (Figure 3) and the increase of the matrix density upon the sorption of water (Table 6). The sorption of water leads to both an increase in density and an expansion of the various carbohydrate matrices, as is shown in Figure 8. The volumetric swelling varies from about 6% for the DE 33 matrix to about 10% for the DE 6 matrix if the water activity is increased from 0 to 0.54. In the same water activity interval, the density of the matrices increases by 2.8% (DE 6) to 3.5% (DE 33). Both the volumetric expansion and the increase in density are approximately linear functions of the water content of the matrix in the water activity range between 0 and 0.75 (Figure 8; Table 13). If the water activity of the matrices is further increased, both the density and the degree of swelling will start to decrease as the properties of water need to be attained in the limit of a vanishing polymer concentration. The densities of the dry maltodextrins as reported in Table 13 agree well with the literature values


for the densities of amorphous maltose (1.5195 g/cm3)21 and thermoplastic starch (1.498 g/cm3)20 at zero water content. The swelling of the carbohydrate matrices is remarkable as it takes place largely in the glassy state: all of the DE 6 samples equilibrated between aw ) 0.11 and 0.75 are in the glassy state, and even for the sample with the lowest average molecular weight (DE 33), all systems equilibrated at aw ) 0.43 or below are in the glassy state. The transition in sorption properties between the glassy and the rubbery states is a gradual one for the polysaccharide matrices, as no sudden change in slope of the degree of swelling and the increase in density is apparent between the samples in glassy and rubbery states (Figure 8). The partial molar volume of water in the carbohydrate matrices is much lower than the molar volume of pure water (Table 13) and decreases systematically with polymer molecular weight from about 8.8 cm3/mol for the DE 6 matrix to about 7.3 cm3/mol for the DE 33 matrix. In effect, water in carbohydrate matrices is packed with twice the density of liquid water and the partial molar volume of water is close to the van der Waals volume of the water molecule, 7.1 cm3/mol.50 The variation of the partial molar volume with molecular weight is most likely due to the molecular packing of water and carbohydrate. An important issue with glassy matrices which could impact the distribution of plasticizer molecules is the thermal history of the sample. In principle, glassy materials never attain their true equilibrium state because of kinetic constraints. The hypothetical state of true equilibrium can be approached, however, by suitable procedures such as solvent casting and thermal annealing.12 Whereas in the present paper results are reported for thermally annealed systems, in a previous communication,27 we have investigated the properties of moisture-equilibrated DE 12 matrices prepared by solvent casting. The partial molar volume of water in these systems with different history turns out to be virtually the same, namely 8.7 cm3/mol for the matrix prepared by solvent casting and 8.6 cm3/mol for the thermally annealed matrix. From literature data for amorphous maltose21 and thermoplastic starch,20 the partial molar volume of water in these two related systems may be calculated. Interestingly, whereas for starch, a partial molar volume is obtained which varies from 7.6 cm3/mol for the water content range between 0 and 2.5% to 11.9 cm3/mol for the range of water content between 0 and 12%, the partial molar volume we calculate for the disaccharide maltose is 16.5 cm3/mol for a water content varying between 0 and 30%. This latter value is much closer to the value for the molar volume of water, and the significant difference between the maltose data on one hand and the maltodextrin and starch data on the other may be due to the polymeric nature of the latter two classes of compounds. The dramatic effect of water on the nanoscale structure and macroscopic properties of the carbohydrate polymer matrices is shown in Figure 9, where the specific volume is plotted as a function of the hole volume. It turns out that for a specific water activity the specific volume and hole volume are linearly related, as shown for the DE 12 system in Figure 9a. It may again be observed that, at constant specific volume, the hole volume increases strongly with increasing


Figure 9. Specific volume versus hole volume of annealed maltodextrin matrices as a function of the temperature. (a) DE 12 matrix; dependence on the water activity (25 °C). Open circles: aw ) 0.11 (R2 ) 0.99); filled circles: aw ) 0.22 (R2 ) 0.99); open triangles: aw ) 0.33 (R2 ) 0.99); filled triangles: aw ) 0.43 (R2 ) 0.99); open diamonds: aw ) 0.54 (R2 ) 1.00); filled diamonds: aw ) 0.75 (R2 ) 0.99). (b) Dependence on the molecular weight distribution for two water activities (25 °C). Open symbols: aw ) 0.22; filled symbols: aw ) 0.54. Circles: DE 6; triangles down: DE 12; diamonds: DE 21; triangles up: DE 33. Correlation coefficients of the linear fits: R2 ) 0.98 (aw ) 0.22); R2 ) 0.97 (aw ) 0.54).

water activity. Interestingly, in Figure 9b, it is demonstrated that at constant water activity the various molecular weight distributions fall essentially on the same Vsp(Vh) line. Consequently, whereas water strongly modifies the nanostructure of the carbohydrate matrix, low molecular weight sugars do not have such an effect. The disparate effect of water and low molecular weight sugars as plasticizers for carbohydrate polymers strongly suggests that water acts as a plasticizer mainly by interacting with the carbohydrate polymers and interfering with their hydrogen bonding. Low-molecular weight sugars, conversely, do not modify the interactions between the carbohydrate polymers so much, but owing to their small size, they reduce the average number of entanglements experienced by a polymer chain and thus enable molecular reorganizations under conditions where the polymer chains themselves would already be frozen into a glassy state. The differences in glassy state properties observed for the various molecular weight distributions in the temperature dependence of both hole volume and specific volume are thus essentially determined by the value of the glass transition temperature for the specific combination of molecular weight distribution and water activity. This has important technological implications as the barrier properties of carbohydrates in the glassy state increase with decreasing molecular weight although the glass transition temperature decreases.4

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From the hole size and the specific volume of the system, the number density of holes may be calculated provided that there is a relation between the specific volume and the unoccupied volume or the free volume. Given the complexity of the system under study, it is not immediately clear that any of the theoretical approaches developed for synthetic polymers will apply to our strongly interacting and structurally complex biopolymer system. As outlined above, we nevertheless attempt to calculate the number density of holes as a function of the molecular weight and water activity using the well-established equation of state developed by Simha and Somcynsky.38 As this theory, which we outline in the Appendix, does not a priori apply to our system, we complement it by the simple model introduced above. Before discussing the results of the Simha-Somcynsky analysis, it is instructive to comment on what precisely is meant by terms such as the occupied- and free-volume fraction: y and h () 1 - y), respectively. It should be borne in mind that y and h do not refer simply to the geometrical space occupied and unoccupied by the constituent molecules’ van der Waals volume, that is, the volume which is impenetrable to other molecules with thermal energies at normal temperatures.48 Rather, the definition is modelspecific in a way that is rather akin to that of “excess free volume” in models relating molecular relaxation to the free volume of an amorphous melt, for example due to Doolittle.49 The occupied fraction, then, contains some “free space” and is defined in this theory according to a minimization of the Helmholtz free energy (see Appendix). In Figure 10a, the specific free volume Vf ) hVsp ) NhVh as calculated using the Simha-Somcynsky equation of state is plotted as a function of temperature for the maltodextrin DE 12 sample equilibrated at various water activities. The reduced parameters V* and T* are collected in Table 14. As expected, the specific free volume is an increasing function of the temperature for all water activities. In the rubbery state, the specific free volume is seen to increase with increasing water activity, implying that the interaction of water with the carbohydrates is increasing the degrees of freedom of the polymer chains. In the glassy state, we do not observe a systematic increase of the specific free volume with water activity. It should be noted, however, that the SimhaSomcynsky equation of state is principally only valid in the rubbery state. The increase in specific free volume with increasing water activity reflects a corresponding decrease in occupied volume fraction, y (see Appendix for derivation). This linear decrease with respect to weight fraction of water from 0.960 at aw ) 0.11 (Qw ) 0.0526) to 0.937 at aw ) 0.75 (Qw ) 0.1319), at 130 °C and DE 12, is close to that observed previously20 for thermoplastic starch in a similar water content range: y ) 0.961 and 0.939 for Qw ) 0.0585 and 0.1357, respectively (also at 130 °C, values estimated from Figure 10 in ref 20). In Figure 10b, the specific free volume according to the equation-of-state approach is plotted as a function of the hole volume for the various molecular weight distributions equilibrated at aw ) 0.22 and 0.54. As was found for the specific volume versus the hole volume (Figure 9b), the various molecular weight systems equilibrated at the same

Kilburn et al.

Figure 10. Specific free volume versus hole volume of annealed maltodextrin matrices as a function of the temperature. (a) DE 12 matrix; dependence on the water activity (25 °C). Open circles: aw ) 0.11 (R2 ) 0.99); filled circles: aw ) 0.22 (R2 ) 0.99); open triangles: aw ) 0.33 (R2 ) 0.99); filled triangles: aw ) 0.43 (R2 ) 0.99); open diamonds: aw ) 0.54 (R2 ) 1.00); filled diamonds: aw ) 0.75 (R2 ) 0.99). (b) Dependence on the molecular weight distribution for two water activities (at 25 °C). Open symbols: aw ) 0.22; filled symbols: aw ) 0.54. Circles: DE 6; triangles down: DE 12; diamonds: DE 21; triangles up: DE 33. Correlation coefficients of the linear fits: R2 ) 0.96 (aw ) 0.22); R2 ) 0.99 (aw ) 0.54). Table 14. Reduced Parameters of the Simha-Somcynsky Equation of State as Applied to Maltodextrin DE 12 Equilibrated at Various Water Activitiesa

a

aw at 25 °C

T*

V*

0.11 0.22 0.33 0.43 0.54 0.75

1.57 × 104 1.49 × 104 1.48 × 104 1.47 × 104 1.41 × 104 1.41 × 104

0.677 0.670 0.669 0.668 0.663 0.658

The standard deviation is about 200 for T* and about 0.002 for V*.

water activity essentially fall on the same line. The free volume strongly increases with increasing water activity, but interestingly, there seems to be no significant effect of the carbohydrate molecular weight on the free volume. In Table 15, the number density of holes calculated following eq 12 and the equation of state is given as a function of the water activity for the DE 12 matrix. Both below and above the glass transition, the number density of holes is a weakly decreasing function of the water activity. The value of the hole density, on the order of 1020 holes per gram of sample, converts into about one hole per 7 sugar residues. Even though the number density of holes decreases with increasing water activity, the unoccupied volume in the system increases because the hole size increases more rapidly


Carbohydrate Polymers in Amorphous States Table 15. Hole Density of Annealed Maltodextrin DE 12 as a Function of the Water Activity, Calculated Using the Assumption of a Constant Hole Density above and below Tga

aw at 25 °C

Nh

× (T < Tg)

Nh [g-1] × 1020 (T > Tg) Vsp vs vh (1)

Nh [g-1] × 1020 (T > Tg) hVsp vs vh (2)

8.5 7.0 7.4 6.9 8.0 n.d.

7.1 7.8 6.8 6.4 5.9 5.7

4.6 4.8 4.2 3.7 3.8 3.7

[g-1]

0.11 0.22 0.33 0.43 0.54 0.75

1020

a (1) and (2) refer to methods of calculating N as detailed in the text. h In method (1), the hole density is calculated from relation between the specific volume and the hole volume. Method (2) involves comparing total free volume as determined via the Simha-Somcynsky equation of state and the individual hole sizes from PALS. Typical standard errors are: 0.4; 0.3; 0.3; 0.04 for values in columns from left to right. All in units as in the table. All correlation coefficients are R2 g 0.96.

Table 16. Hole Density of Annealed Maltodextrin as a Function of the Molecular Weight Distribution, Calculated Using the Assumption of a Constant Number Density of Holes above and below Tga

aw ) 0.22 (25 °C) [g-1]

[g-1]

aw ) 0.54 (25 °C)

DE

Nh × 1020 (T < Tg)

Nh × 1020 (T > Tg)

Nh [g-1] × 1020 (T < Tg)

Nh [g-1] × 1020 (T > Tg)

6 12 21 33

4.3 7.0 n.d. 10.8

6.7 7.7 n.d. 5.6

6.7 6.4 7.7 n.d.

7.8 ((1.5) 4.8 5.4 5.9

a Typical standard errors are: 0.4 for values for all values. All in units as in table.

as a function of the water activity. We infer that the effect of water on the nanostructure of the carbohydrate matrix is twofold. In the first place, water molecules will preferentially fill up small inclusions in the close vicinity of the carbohydrate chains. In the second place, the interference of the absorbed water with the hydrogen bonding between the carbohydrates will lead to a gradual coming apart of the carbohydrate chains. We calculate the number density of holes from the plot of the specific volume as a function of the mean hole volume,60 as measured by PALS, over a range of temperatures, shown in Figure 10. If one fits eq 16 to such a plot, assuming negligible occupied volume expansion, the gradient is equal to the number of holes per gram. Alternatively, the occupied volume can be ignored altogether by equating the free volume terms in eq 16 to the specific free volume as calculated using the Simha-Somcynsky equation of state: Vsp,unocc ) hVsp ) Vsp,unocc,0 + NhVh. The gradient of a plot of hV vs Vh, therefore, also gives Nh, and this is shown in Figure 10b. Values calculated using these two methods, labeled as methods (1) and (2) are shown in Table 16. The number density of holes turns out to be essentially independent of the molecular weight of the carbohydrate polymers (Table 16), both above and below Tg and for the two water activities 0.22 and 0.54. This observation is of major importance as we have seen that the hole volume is also independent of the molecular weight distribution of the carbohydrate matrix. Consequently, the free volume of the

Figure 11. Schematic depiction of the mechanism of sorption of water by amorphous carbohydrates. At low water concentrations, all water molecules form hydrogen bonds with the hydroxyl residues on the carbohydrate chains and they are well-dispersed in the matrix. 1. The water sorption takes place without extensive swelling of the matrix. This will lead to a densification of the matrix and a reduction of its free volume. 2. The water sorption is accompanied by significant swelling of the matrix, even in the glassy state. This will lead to an increase in average hole size. For amorphous carbohydrate polymers, the actual mechanism is between the two limiting cases 1 and 2.

carbohydrate matrix is essentially independent of the molecular weight, as was indeed concluded from the equationof-state analysis. The synthesis of all experimental and theoretical data strongly hints at the important role of interactions, in particular hydrogen bonding, on the properties of amorphous carbohydrate matrices. It is therefore unfortunate that the precise mode of water binding is difficult to determine, as no techniques are available by which hydrogen bonding in carbohydrates can be determined at sufficiently high resolution,14,51,52 in particular in amorphous systems. In our opinion, one of the most useful routes to analyze the details of hydrogen bonding in amorphous carbohydrate polymers is by computer simulation.53-56 Although confirming a number of our principal conclusions, most of the existing simulations are carried out at water contents which are substantially higher than in our experiments.54-56 In addition, we feel that the novelty and complexity of the physical phenomena observed for these important biomaterials warrant the development of a quantitative statistical mechanical theory of polymer melts which includes hydrogen bonding interactions. Water acts as a plasticizer for amorphous carbohydrate polymers principally by interfering with the hydrogen bonding between the carbohydrate chains. In doing so, it increases the number of degrees of freedom of the carbohydrate chains, which leads to a swelling of the carbohydrate matrix at both molecular and macroscopic scales. In Figure 11, we have schematically depicted this phenomenon for two principal mechanisms of hydrogen bonding between water and the carbohydrate chains. It should be borne in mind, however, that a static picture like the one in Figure 11 is of limited value as the dynamics of the hydrogen-bonded network need to be taken into account. Concluding Remarks Water is a highly efficient plasticizer of amorphous carbohydrates because of its ability to interfere with the hydrogen bonding between the carbohydrate chains. Thermodynamic clustering theory demonstrates that in lowmoisture carbohydrate matrices water is closely associated with the carbohydrate chains. The increased degrees of freedom of the carbohydrate chains which are introduced

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by water enable matrix relaxations in both the glassy and rubbery states. This leads to a macroscopic expansion of the matrix which originates at the nanolevel. In contrast, low molecular weight carbohydrates, which also act as plasticizers for polysaccharides, do not appreciably change the structure and density of the rubbery state. Consequently, the plasticizing effects of small sugars are related to the strong reduction in molecular entanglements upon a shift of the molecular weight distribution to lower molecular weights. Water strongly increases the mobility of small permeants including gases and low-molecular weight organic compounds because it facilitates reorientations and relaxations of the carbohydrate chains even in the glassy state. In contrast, low molecular weight carbohydrates might in fact reduce the mobility of such permeants because they lead to an improved molecular packing as demonstrated by the increase in matrix density and decrease in hole size in the glassy state. This is in spite of the fact that low molecular weight carbohydrates depress the glass transition temperature. In conclusion, carbohydrate polymers form a class of materials with interesting properties which are in particular related to their interaction with water. We expect that the improved molecular understanding of these properties will have a technological impact, in particular for their use as matrices for encapsulation and in the optimization of their barrier properties for gases and organic compounds. Acknowledgment. We are grateful to Phillipe Looten and Jean-Michel Roturier (Roquette Fre`res) for the determination of the molecular weight distributions. We thank Ju¨rg Hostettler, Maria-Isabelle Alonso and Jean-Pierre Marquet for analytical support and Gunter Dlubek for discussions on positron annihilation in polymers. Jessica Kru¨ger and HansJo¨rg Limbach are thanked for a critical reading of the manuscript. Appendix: Application of the Simha-Somcynsky Equation of State The Simha-Somcynsky equation of state describes a macromolecular liquid as a collection of cells of equal volume, each one of which is either occupied or unoccupied.38 Each cell in the occupied fraction contains the van der Waals volume of an s-mer as well as an inherent free volume. An s-mer is defined by envisioning each of the total of N molecules, each consisting of n chemical repeating units, n-mers, with molecular weight Mrep, as being divided into s (s is material dependent) equivalent segments (the s-mers), sM0 ) nMrep, where M0 is the molecular mass of an s-mer. The occupied fraction, y, consisting of sN cells, is given by SS y ) sN/(sN + N SS h ), where N h is the number of unoccupied cells. These unoccupied cells contain, as the name implies, only unoccupied space and they constitute the excess free volume in the liquid where the free, or hole fraction is defined as h ) 1 - y. The Simha-Somcynsky equation of state is based on the principle of corresponding states,57 whereby a single equation of state in terms of reduced variables is valid for all macromolecular liquids. These reduced variables are P ˜ )

Kilburn et al.

P/P*, V ˜ ) V/V*, and T˜ ) T/T*. P*, V*, and T* are characteristic, material-dependent scaling parameters and are related by the equation (P*V*/T*)M0 ) (c/s)R

(A.1)

R is the gas constant and 3c is the number of external degrees of freedom per macromolecular chain. c and s are further linked by the condition that 3c/s ) 1, meaning that each s-mer, or chain segment, has one external degree of freedom, and for general macromolecular systems it is assumed that s f ∞. The Simha-Somcynsky equation of state then follows from the pressure equation P ) -(∂F/∂V)T, where F ) F(V, T, y) is the configurational (Helmholtz) free energy F of the liquid P ˜V ˜ ˜ )-1/3]-1 + ) [1 - y(21/2yV T˜ y ˜ )-2] (A.2) [2.002(yV ˜ )-4 - 2.409(yV T˜ For comparison with PALS data, we assume P ) 0, and therefore, the left-hand side of eq A.2 also equals zero. The occupied volume fraction y is coupled with T˜ and V ˜ in a second equation derived from the minimization condition (∂F/∂y)V,T ) 0. It can be shown that both equations may be replaced in the temperature and pressure ranges T˜ ) 0.0160.071 and P ˜ ) 0-0.35 by the interpolation expression58 lnV ˜ ) a0 + a1T˜ 3/2 + P ˜ [a2 + (a3 + a4P ˜ + a5P ˜ 2)T˜ 2] (A.3) The values of the constants a0 to a5 are given in ref 58. A similar expression is written for h in terms of T˜ and V ˜ but there is presently no generally valid relationship for the h-function in the glassy state. Equation A.3 is useful as it gives an analytical expression, which can be fitted to experimental data in order to determine the scaling parameters for use in eq A.2. The Simha-Somcynsky equation of state, eq A.2, is derived under the general assumption of equilibrium. However the specific assumption that the free energy is a minimum has not been made. Therefore, it is usual to calculate the h values from the specific volume below Tg(P) (the pressure-dependent glass transition) via eq A.2 assuming constant scaling parameters P*, V*, and T*. These values are considered to be sufficiently good approximations for conditions not too far from equilibrium.59 We aim to calculate, for a given polymer-water mixture, the occupied and unoccupied fractions as a function of temperature and pressure. Within the framework of the equation of state, the unoccupied volume Vunocc equals the free volume Vf. To this aim, we carried out the following steps: 1. A nonlinear least-squares fit of eq A.3 to zero pressure volume data (P ) 0) was carried out to determine T* and V*. Since eq A.3 is valid for the rubbery phase, only the temperature above Tg was fitted. 2. Solving eq A.2 numerically using experimental PVT data and V* and T* determined from the previous step enables the calculation of y and h at all measured temper-


atures. The specific occupied and free volume, Vocc and Vf, respectively, are subsequently calculated by simply multiplying the relevant fraction by the total specific volume. References and Notes (1) Wilkes, E. S. Industrial Polymers handbook. Volumes 3 and 4: Biopolymers and their DeriVatiVes; Wiley-VCH: Weinheim, Germany, 2001. (2) Dickinson, E. Food Polymers, Gels and Colloids. Spec. Publ. R. Soc. Chem. 1991, 82. (3) Hill, S. E.; Ledward, D. A.; Mitchell, J. R. Functional Properties of Food Macromolecules, 2nd ed.; Aspen: Gaithersburg, MD, 1998. (4) Ubbink, J.; Schoonman, A. Flavor Delivery Systems. Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, 2003. (5) Langer, M.; Ho¨ltje;Urbanetz, N. A.; Brandt, B.; Ho¨ltje, H.-D.; Lippold, B. C. Int. J. Pharm. 2003, 252, 167. (6) Levine, H. Amorphous Food and Pharmaceutical Systems. Spec. Publ. R. Soc. Chem. 2002, 281. (7) Risch, S. J.; Reineccius, G. A. Encapsulation and Controlled Release of Food Ingredients. ACS Symp. Ser. 1995, 590. (8) Blanshard, J. M. V.; Lillford, P. J. The Glassy State in Foods; Nottingham University Press: Nottingham, U.K., 1993. (9) Schoonman, A.; Ubbink, J.; Bisperink, Ch.; Le Meste, M.; Karel, M. Biotechnol. Prog. 2002, 18, 139. (10) Gunning, Y. M.; Parker, R.; Ring, S. G. Carbohydr. Res. 2000, 329, 377. (11) Roos, Y. H. Phase Transitions in Foods. Academic Press: San Diego, CA, 1995. (12) Van Krevelen, D. W. Properties of polymers, 3rd ed.; Elsevier: Amsterdam, 1990. (13) Van den Berg, C. Vapour sorption equilibria and other water-starch interactions: a physico-chemical approach. Ph.D. Thesis, Wageningen Agricultural University: Wageningen, 1981. (14) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures; Springer: Berlin, 1991; Chapter 13. (15) Angell, C. A.; Stell, R. C.; Sichina, W. J. Phys. Chem. 1982, 86, 1540. (16) Di Bari, M.; Deriu, A.; Albanese, G.; Cavatorta, F. Chem. Phys. 2003, 292, 333. (17) Noel, T. R.; Ring, S. G.; Whittam, M. A. Trends Food Sci. Technol. 1990, 1, 62. (18) Karel, M.; Anglea, S.; Buera, P.; Karmas, R.; Levi, G.; Roos, Y. Thermochim. Acta 1994, 246, 249. (19) Le Meste, M.; Roudaut, G.; Davidou, S. J. Therm. Anal. 1996, 47, 1361. (20) Bencze´di, D.; Tomka, I.; Escher, F. Macromolecules 1998, 31, 3055. (21) Lourdin, D.; Colonna, P.; Ring, S. G. Carbohydr. Res. 2003, 338, 2883. (22) Wolkers, W. F.; Oliver, A.; Tablin, F.; Crowe, J. H. Carbohydr. Res. 2004, 339, 1077. (23) Hopkinson, I.; Jones, R. A. L.; Black, S.; Lane, D. M.; McDonald, P. J. Carbohydr. Polym. 1997, 34, 39. (24) Do¨ss, A.; Paluch, M.; Sillescu, H.; Hinze, G. Phys. ReV. Lett. 2002, 88, 095701-1.

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Carbohydrate Polymers in Amorphous States: An Integrated

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