Permeation of Volatile Compounds through Starch Films

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Biomacromolecules 2004, 5, 650-656

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Permeation of Volatile Compounds through Starch Films Gu¨lden Yılmaz,*,† Remy O. J. Jongboom,§ Herman Feil,‡ Cees van Dijk,† and Wim E. Hennink| Agrotechnology & Food Innovations, Bornsesteeg 59 P.O. Box 17, NL-6700 AA Wageningen, The Netherlands, Rodenburg Biopolymers, Denariusstraat 19, 4903 Rc Oosterhout, The Netherlands, Tournois Dynamic Innovations bv., Agro bussiness park 40 nl-6708-pw, Wageningen, The Netherlands, and Department of Pharmaceutics, Utrecht Institute for Pharmaceutical Sciences (UIPS), Utrecht University, P.O. Box 80.082 3508 TB Utrecht, The Netherlands Received November 26, 2003

The aim of this study was to gain insight into the factors that affect the permeation of volatiles through starch films. These films were obtained by casting gelatinized starch/water/glycerol mixtures. The films were dried and conditioned under different conditions (temperature and relative humidity) resulting in films that vary in the degree of starch crystallinity and glycerol and water content. The permeation of two model volatiles (carvone and diacetyl) at 20 °C and at 30, 60, or 90% relative humidity (RH) was analyzed gravimetrically. Further, the solubility of the two model compounds (under conditions where the permeation experiments were carried out) was determined. From the obtained permeation and solubility data, the diffusion coefficients of these compounds in the different starch films were calculated. The crystallinity in the starch films increased with increasing water content of the films during preparation. The water content of the resulting films in turn increased with increasing glycerol and when the films were exposed to a higher RH during drying or conditioning. For films with the same composition, the flux for diacetyl was greater than for carvone. The solubilities of diacetyl and carvone were slightly dependent on the properties of the films. It was found that with increasing starch crystallinity the diffusion coefficient for both compounds decreases, which is probably due to the impermeability of starch crystallites. Interestingly, in films with about the same extent of crystallinity, the diffusion can be described with the free volume model, with water and glycerol determining the amount of free volume. Introduction Controlled release is defined as a method, by which one or more active agents are made available at a desired site, time, and at a specific rate.1 Considerable interest exists to release volatile compounds such as flavors, perfumes, essential oils, herbicides, pesticides and pheromones in a controlled manner for different types of application.2-5 Starch is frequently used as a matrix material for the encapsulation and controlled release of volatile compounds.6-12 This biopolymer has several advantages such as oxygen barrier properties,11 mild processing, biodegradability, and easily modifiable physical characteristics.6-8 Many processing techniques have been described to encapsulate volatiles in starch based matrixes.6-12 It is known that the physical properties of starch matrixes such as molecular weight of the starch and plasticizer (e.g., water or glycerol) content, or other constituents that are present, significantly affect the release behavior of an encapsulated volatile compound.13-18 For example, it has been observed that the release of a volatile compound decreases with * To whom correspondence should be addressed. E-mail: gulden. [email protected]. † Agrotechnology & Food Innovations. § Rodenburg Biopolymers. ‡ Tournois Dynamic Innovations. | Utrecht University.

increasing molecular weight of starch.13 Additionally, it has been observed that the release of volatile compounds decreases with decreasing water and plasticizer content of the starch matrix.13-16 Finally, the volatile release depends also on the presence of nonvolatile constituents such as oils and fats in the matrix. It was observed that the presence of such compounds resulted in a decreased release rate.14,18 Additionally, the studies investigating the permeability of films prepared using biopolymers such as starch show that the permeability is very much influenced by the presence of water and other plasticizers.19-21 However, in the studies mentioned above, the factors that affect the permeation and diffusion of volatile compounds were not investigated individually. Therefore, a more quantitative description of the relation between the matrix properties on one hand and the permeation/diffusion of volatile compounds through/in these matrixes on the other hand is not available. The aim of this study is to investigate the factors that affect the permeation of volatiles through starch films differing in crystallinity and water/glycerol content. With this approach, insight into the underlying mechanism of diffusion of volatile compounds through starch films is obtained. Materials and Methods Materials. Native potato starch (17.5% moisture content) was purchased from Avebe, The Netherlands. Glycerol was

10.1021/bm034493m CCC: $27.50 © 2004 American Chemical Society Published on Web 01/28/2004

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Permeation through Starch Films Table 1. Compositions and the Conditions Used to Dry and Equilibrate the Different Starch Filmsa film no.

aimed film thickness (mm)

% glycerol (w/w, based on dry starch)

drying conditions (temp-RH)

RH during equilibrationb

1 2a 2b 3 4 5 6 7 8a 8b 9 10 11 12 13 14

0.350 0.165 0.350 0.350 0.350 0.350 0.350 0.350 0.165 0.350 0.350 0.350 0.350 0.350 0.350 0.350

30% 40% 40% 40% 40% 60% 40% 40% 40% 40% 30% 40% 40% 60% 40% 40%

20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-90% 70 °C-lowc 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-30% 20 °C-90% 70 °C-lowc

30% 30% 30% 60% 90% 30% 30% 30% 30% 30% 30% 60% 90% 30% 30% 30%

a Films 1-7 were used for permeation experiments with diacetyl; films 8a-14 were used for the permeation experiments with carvone. b The temperature was 20 °C; the same conditions (temperature and RH) were used during the permeation experiments (RH ) relative humidity). c Film dried under vacuum.

purchased from Chemproha Chemicals Distributors B.V, The Netherlands. Diacetyl (2,3-butanedione; purity > 98%) was obtained from Merck. Carvone (p-menthe-6, 8-dien-2-one, M ) 150.22, oil of caraway, 95%) was purchased from Erven Th. Koomen B.V., The Netherlands. All other reagents used in the experiments were of analytical grade. Preparation of the Films. The films were prepared by weighing 5 g of native potato starch (4.1 g dry basis) in a glass beaker, followed by the addition of 100 mL of demineralized water. Glycerol was added to these waterstarch mixtures (final concentration of 30%, 40%, and 60% (w/w) on dry starch basis). Gelatinization of the starch suspensions was performed by heating the mixtures on a hot plate (heating rate 2 °C/ min, final temperature 110 °C) under continuous mixing with a mechanical propeller stirrer (IKA, Ru¨hrwerke RW 20) at a constant speed of 650 rpm. During the gelatinization procedure, the beaker was covered with aluminum foil in order to avoid excessive evaporation of water.22 Films were obtained by casting the gelatinized starch solutions into 12 cm × 12 cm polystyrene trays. These solutions were subsequently dried at 30, 60, or 90% relative humidity (RH) at 20 °C for 5-14 days, or at 70 °C in a vacuum oven for 1 day. These different conditions ensure the formation of films with varying degrees of starch crystallinity.23 Next, the films were equilibrated during 3-9 days prior to the permeation experiments under the conditions where the experiments were performed (Table 1). To obtain films with a thickness of around 0.165 or 0.350 mm, about 35 or 70 g of starch solution was transferred into the polystyrene trays. The thicknesses of the films are reported as the average value of 5 measurements of each film, which were prepared in triplicate. Determination of the Moisture Content of the Films. To determine the moisture content of the films, water was

Figure 1. Schematic representation of the diffusion chamber.

completely removed from the samples using a hot air oven at 80 °C for 48 h. The moisture content (%) was calculated from the measured weight loss and is expressed in % (w/w). The water content of the amorphous phase of the films was calculated as follows: Wtotal ) Xeq.Wcryst. + (1 - Xeq.)Wamorphous

(1)

where Wtotal is the total water content (w/w), Xeq. is the % crystallinity (B-type), Wcryst is the water content in the crystalline phase (25% w/w23,24), and Wamorphous is the water content of the amorphous phase. Determination of Starch Crystallinity. The films were cryogenically ground using a Polymix A-10 grinder (Kinematica, Switzerland). Diffractograms of the powdered samples were recorded on a Philips PC-APD diffractometer, consisting of a PW1830 generator operating at 50 mA and 40 kV, a PW3710 generator and a PW3020 goniometer. Diffractograms were recorded in reflection geometry using a Nickelfiltered Cu KR emitter. The samples were scanned from 4 to 40° (2θ) with a scan speed of 1.5° per minute. The diffractograms were baseline corrected. The crystallinity of the films was calculated by dividing the area of the diffraction peak at 17° (2θ) between the diffraction angles 15.5-18.0° (2θ) by the total area under this peak.23 The measurements were performed in duplicate using two independently prepared films. The crystallinity of the films was measured after drying (Xdry), after equilibration (Xeq.), and after the permeation experiments (Xperm.). Determination of the Flux of the Volatiles through the Films. After equilibration of the films for 3-9 days, measurements were performed to determine the permeation of the volatiles through the different starch films. Permeation measurements were performed using aluminum diffusion chambers (diameter ) 10 cm, height ) 1.2 cm) equipped with a sample container and a cover, in which the films were fitted. The chamber was filled with around 10 g of diacetyl or carvone. All connection parts were Teflon coated to avoid evaporation through the joints. A schematic representation of the equipment is shown in Figure 1. The weight of the chamber was determined at different times. From the soobtained steady-state flux (J) expressed in (mg/cm2 h), the diffusion coefficient (D) expressed in (cm2/h) of the volatile in the starch matrix was calculated using Fick’s first law: J ) D ∆C/h

(2)

where h is the thickness of the film in cm, ∆C (mg/cm3) is the concentration difference between the two sides of the film (∆C is equal to the concentration of the volatile at the lower end (receiving side) of the film, since the concentration the upper end (exciting side) is assumed to be zero, and ∆C therefore equals the experimentally determined solubility of the volatile in the different films). Permeation measurements were performed in triplicate using independently prepared films.

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Table 2. Characteristics of the Different Starch Filmsa moisture content (% w/w) film no.

film thickness (mm)

after processing

after equilibration

1 2a 2b 3 4 5 6 7 8a 8b 9 10 11 12 13 14

0.351 ( 0.002 0.164 ( 0.002 0.348 ( 0.002 0.353 ( 0.002 0.356 ( 0.004 0.352 ( 0.005 0.354 ( 0.003 0.347 ( 0.007 0.165 ( 0.002 0.351 ( 0.002 0.351 ( 0.003 0.352 ( 0.002 0.352 ( 0.005 0.348 ( 0.003 0.350 ( 0.004 0.351 ( 0.007

10.3 ( 0.7 18.3 ( 1.6 18.1 ( 1.4 18.1 ( 2.2 17.8 ( 0.9 25.6 ( 2.2 34.2 ( 2.0 11.8 ( 1.2 18.2 ( 1.3 17.9 ( 1.1 10.1 ( 3.7 18.3 ( 1.2 18.4 ( 1.6 25.0 ( 1.9 35.1 ( 1.5 12.3 ( 1.1

9.8 ( 0.9 18.2 ( 2.2 17.9 ( 1.4 24.3 ( 2.6 32.7 ( 2.8 25.5 ( 1.9 24.3 ( 2.3 18.3 ( 2.0 18.2 ( 3.1 17.9 ( 1.4 10.0 ( 2.4 24.1 ( 2.1 32.2 ( 1.7 24.9 ( 1.3 25.2 ( 1.4 17.9 ( 1.4

crystallinity (%)

amorphous

phaseb

6.7 ( 1.1 16.3 ( 1.9 15.9 ( 2.1 24.1 ( 2.7 37.8 ( 3.9 25.7 ( 2.8 23.9 ( 2.5 18.3 ( 2,2 16.7 ( 1.8 16.1 ( 2.1 6.9 ( 0.9 24.4 ( 1.7 34.7 ( 2.8 25.3 ( 2.1 24.9 ( 1.5 18.4 ( 2.1

after processing

after equilibration

19 ( 1 20 ( 2 22 ( 1 17 ( 1 21 ( 1 24 ( 1 31 ( 3 none 19 ( 2 21 ( 1 19 ( 2 18 ( 1 22 ( 2 24 ( 1 31 ( 2 none

17 ( 2 22 ( 1 22 ( 1 19 ( 2 22 ( 2 24 ( 2 29 ( 1 11 ( 2 18 ( 1 21 ( 1 18 ( 1 18 ( 2 23 ( 2 25 ( 1 31 ( 1 12 ( 2

a Films 1-7 were used for permeation experiments with diacetyl; films 8a-14 were used for the permeation experiments with carvone. b Moisture content in the amorphous phase (after equilibration) of the films is calculated according to eq 1 and is expressed in weight % in the amorphous phase.

Figure 2. X-ray diffraction spectra of some starch films after drying. Top to bottom: films 6, 5, 2b, 1, and 7.

Determination of the Solubility of Diacetyl and Carvone in the Starch Films. The solubility of either carvone or diacetyl in the different starch films was performed using an exsiccator (5 l) with a controlled RH (30, 60, or 90% RH) containing 200 mL of the volatile at 20 °C. At different time intervals (24-48 h), a piece (1 × 1 cm) of the film, which was exposed to the vapor only, was removed. The amount of dissolved volatile (mg/cm3) was determined using a GC-headspace analysis method as described previously.25,26 Equilibrium was observed after around 100 h for diacetyl and around 240 h for carvone. Triplicate measurements were performed using independently prepared films. Data Analysis. Least ordinary squares regression to establish linear relationships and the confidence intervals between the reciprocal values of the hydration and the logarithm of the diffusion coefficients were performed according to Draper et al.27,28 Results and Discussion Film Properties B-type crystallinity was detected in all starch films dried at 20 °C.29-31 X-ray diffraction spectra of some films are shown in Figure 2; their crystallinity data are given in Table 2.

For the films dried at 20 °C, the extent of crystallinity detected after processing depended both on the amount of glycerol in the formulation and the relative humidity during drying of the samples. A slight increase in crystallinity was observed with increasing amounts of glycerol. The crystallinity of the films dried at 30% RH was between 19 and 22% for films with 30, 40, or 60% glycerol (films 1/9, 2a/ 2b/3/4/8a/8b/10/11 and 5/12, Table 2) prior to equilibration. Table 2 shows that, with increasing glycerol content, the water content increased. Likely, a higher glycerol content in the matrix gives a higher water absorbing capacity. A higher water content in turn lowers the glass transition temperature of starch, which is probably the cause for the slightly higher crystallinity (∼24%; films 5 and 12) observed in the films with higher glycerol.23,29-31 The films with 40% glycerol dried at 90% RH instead of 30% had a higher water content (Table 2, compare films 6 and 13 with film 2a/2b/ 3/4/8a/8b). Likewise, a higher water content in these films resulted in a higher degree of crystallinity. In contrast, the films that were dried under vacuum at 70 °C did not show any detectable crystallinity (Table 2, film 7 and 14) prior to equilibration. Before the permeation experiments were performed, the films were equilibrated at 20 °C and at different relative humidity. The films that were dried at 20 °C did not show significant changes in the degree of crystallinity (Table 2). As expected, the films, which were dried at 30% RH and thereafter equilibrated at the same RH, did not show changes in their water content (film 1, 2a/2b, 8a/8b, 5, 9, 12; Table 2). The films dried at 30% RH and subsequently conditioned at 60 or 90% RH absorbed water (films 3, 4, 10, and 11). The degree of crystallinity was also determined after the equilibration and permeation experiments. No significant changes in crystallinity were observed in films dried at 20 °C and 30% RH, and subsequently equilibrated at different RHs. The films dried at 90% RH and thereafter exposed at 30% RH showed loss of water (film 6 and 13), but no change in crystallinity, even after the permeation experiments were observed.

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Permeation through Starch Films

Figure 3. Permeation of diacetyl and carvone through starch films (films 2a and 2b, 8a and 8b; Table 2) at 30% RH and 20 °C. Bars show the standard deviations. Table 3. Solubility, Steady State Flux, and Diffusion Coefficients of Diacetyl and Carvonea film no.

solubility (mg cm-3)

J (mg cm-2 h-1 × 103)

diffusion coefficient (cm2 h-1 × 104)

1 2a 2b 3 4 5 6 7 8a 8b 9 10 11 12 13 14

2.11 ( 0.04 2.41 ( 0.03 2.42 ( 0.02 2.41 ( 0.02 3.30 ( 0.03 3.14 ( 0.03 2.14 ( 0.02 2.18 ( 0.02 0.60 ( 0.03 0.61 ( 0.03 0.43 ( 0.14 0.62 ( 0.02 0.63 ( 0.05 0.76 ( 0.02 0.57 ( 0.04 0.67 ( 0.01

13.1 ( 1.1 47.4 ( 0.3 22.3 ( 0.1 36.1 ( 2.3 52.3 ( 1.5 36.2 ( 0.9 11.2 ( 0.6 53.3 ( 4.9 7.4 ( 2.0 2.8 ( 2.8 2.1 ( 0.1 3.0 ( 0.1 3.9 ( 0.2 5.5 ( 1.1 1.8 ( 0.1 6.9 ( 0.4

1.4 ( 0.3 3.2 ( 0.4 3.2( 0.7 4.6 ( 0.3 5.4 ( 0.2 4.1 ( 1.0 1.6 ( 0.2 8.5 ( 0.5 2.0 ( 0.2 1.8 ( 0.2 1.5 ( 0.4 1.7 ( 0.2 2.2 ( 0.1 2.6 ( 0.3 1.2 ( 0.1 3.6 ( 0.3

a Films 1-7 were used for permeation experiments with diacetyl; films 8a-14 were used for the permeation experiments with carvone.

When the initially amorphous films (film 7 and 14; dried at 70 °C under vacuum) were conditioned at 20 °C and 30% RH, both absorption of water and development of crystallinity was observed. Obviously, absorption of water by the matrix lowers the glass transition temperature, which in turn facilitates the formation of a crystalline phase.23,31,32 These films even showed a further increase in crystallinity from 11% to 14% (data not shown) during the permeation experiments while the other films were structurally stable. This is not surprising since the crystallization after the initial stage generally takes place at a decreased rate.23,31,32 Permeation of Diacetyl and Carvone through Starch Films. The starch films with different degrees of crystallinity, water, and glycerol content were used to quantify the solubility, steady-state flux, and diffusion coefficients of diacetyl and carvone. The permeation data are shown in Figures 3-6, and Table 3 summarizes the results. Figure 3 shows the permeation of the two model volatile compounds through starch films with the same composition and having different thickness at 20 °C and 30% RH. It is shown that after a certain lag time the amount of volatile permeated through the films is proportional to time (steady state flux). Importantly, the diffusion coefficients, calculated from Fick’s first law using the experimentally determined

solubility and steady-state flux are independent of the film thickness for both compounds (Table 3, films 2a/2b and 8a/ 8b for diacetyl and carvone, respectively). This suggests that the films are nonporous and demonstrates that with these experiments the permeation through homogeneous films is evaluated. Figure 3 also shows that the steady state flux of diacetyl is substantially higher than the flux of carvone. This great difference can be ascribed to the higher diffusion coefficient and to a substantially higher solubility of diacetyl as compared with carvone. Since the partial vapor pressures of these compounds at 20 °C are about the same, the higher flux of diacetyl (compared to carvone) is not surprising given the more hydrophilic character of this compound.33 Figure 4 shows the steady-state flux of diacetyl and carvone through starch films at 20 °C and 30% RH. The flux for both of these compounds increases with increasing amounts of glycerol in the films. This increase in flux (Table 3) can be partially ascribed to an increase in solubility of diacetyl and carvone in the films. This increase in solubility, however, cannot fully explain the observed increase in flux. It is therefore concluded (using Fick’s first law) that the higher flux is also due to an increasing diffusivity of diacetyl and carvone in starch films with increasing glycerol contents. Table 2 shows that with increasing glycerol the degree of crystallinity also slightly increases. This in turn would result in a decrease in diffusivity (see discussion of Figure 6). However, the opposite is observed (Table 3) indicating that the increase in diffusivity is caused by the increase in water and glycerol in these films (see discussion of “mechanism of diffusion”). Figure 5 shows that the steady state flux of diacetyl and carvone through films with the same amount of glycerol increases with relative humidity. It can be seen that the flux of diacetyl is more strongly affected by the RH. In Table 2, it is shown that when films with the same composition are exposed to different RHs they absorbed water, whereas no significant changes in degree of crystallinity were found. This increase in water results in an increase in the solubility of especially diacetyl in the film (Table 3). This higher solubility results, as observed, in a higher flux. In case of carvone, its solubility is hardly affected by water content of the films, likely because of its more hydrophobic character. Consequently, the flux of this compound through starch films is only slightly affected by the water content of the films. Films 2b, 6, and 7 as well as films 8b, 13, and 14 have the same glycerol content but differ substantially in degree of starch crystallinity (Table 2). Although the water contents in films 2b, 7, 8b, and 14 are comparable, films 6 and 13 have higher water contents prior to the diffusion experiments (Table 2). Generally, this increase in the water content would result in an increase in the flux. However, these films also have a higher starch crystallinity. It can be seen that the increase in crystallinity resulted in a significant decrease in steady state flux although these high crystalline films have more water (Figure 6). Apparently, the effect of crystallinity dominates over the effect of water resulting in a decrease in the flux of the permeating compounds. Since the solubility of diacetyl and carvone in the films only differed slightly,

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Figure 4. Permeation of carvone (A) and diacetyl (B) through films (films 8b, 9, and 10 for carvone and 1, 2b, and 5 for diacetyl) as a function of the glycerol content in the films (30, 40, and 60% glycerol based on dry starch). Bars show standard deviation.

Figure 5. Permeation of carvone (A) and diacetyl (B) through starch films (films 8b, 10, and 11 for carvone and 2b, 3, and 4 for diacetyl) at 20 °C as a function of relative humidity of the environment. Bars show standard deviations.

Figure 6. Permeation of carvone (A) (films 8b, 13, and 14) and diacetyl (B) through films (films 2b, 6, and 7) with different crystallinity (Table 2). The steady flux for the low crystalline film was calculated from the amount diacetyl permeated from 100 to 400 h. Bars show standard deviations.

the decreased flux is due to a decreased diffusivity of these compounds as a function of the crystallinity. This is in line with expectations, since it is well-known that crystalline domains, due to their compact and ordered structure, can act as barriers for diffusion. Figure 6 also shows that for the for the films with very low crystallinity (Table 3) the flux decreases with time. This can be explained by the fact that in these films crystallinity increases during the permeation experiment (films 7 and 14, data not shown).

Mechanism of Volatile Diffusion through Starch Films. The diffusion of solutes through polymeric matrixes have been, in a quantitative sense, described with the obstruction model and the free volume model.33-44 The obstruction model has been used to describe the diffusion of solutes in, for example, hydrogels and assumes that the polymer segments and solvent molecules have the same size and that the crosslink density is low. This model predicts a decreased solute diffusion in swollen polymeric networks compared to dif-

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in starch films with about the same degree of crystallinity correlates with the free volume present in the films determined by the total amount of plasticizer. Conclusions This study demonstrates that the diffusion of a volatile in a starch matrix is mainly determined by the percentage crystallinity and the total amount of plasticizer present. The diffusivity strongly decreases with increasing starch crystallinity and decreasing amount of plasticizer. Interestingly, the diffusion appears to correlate with the free volume present determined by the total amount of plasticizer. References and Notes

Figure 7. Logarithm of the diffusion coefficient of diacetyl and the reciprocal of the hydration (water in the amorphous phase + glycerol content; Table 2). The independently determined diffusion coefficients (films 1-5 and 8-12, for each formulation three different films were used); R 2 values are 0.89 and 0.74 for diacetyl and carvone, respectively.

fusion in solvents, which is caused by an increased diffusion path due to the presence of impermeable polymer chains. The free-volume model focuses on the concept that for diffusion through a medium a penetrant has to jump from one void to another, and the rate of diffusion is then determined by the amount of free volume. For hydrogels, the effective free volume available for diffusion is essentially present in the water phase. For various systems, a linear relation was shown between the logarithm of the diffusion coefficient (D) and the reciprocal value of hydration (1/H; hydration is the volume fraction of water in the material).35-37 Figure 6 shows that the flux of the permeating volatile decreases significantly with an increase in crystallinity, indicating an obstruction effect. Interestingly, in this study, we have also available permeation data of diacetyl and carvone through films, which only slightly differ in crystallinity (Figures 3-5). This allows an analysis of the effects of the matrix properties other than the crystallinity on the diffusivity and permeation of volatiles through starch films. In other studies it has been demonstrated that the free volume of starch/glycerol/water systems is determined by the glycerol and, predominantly, by the water content.45,46 For this reason, the total plasticizer content (water in the amorphous phase, as the permeation mainly occurs via the amorphous phase, and glycerol) was used to calculate the hydration (H). Figure 7 shows that a linear relation exists between log D and 1/H for the matrixes with the same degree of crystallinity (films 1-5 and 8-12; crystallinity around 20%). This means that the diffusivity of diacetyl and carvone

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