Biotechnol. Prog. 1991, 7,178-184
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Water Diffusivity in Starches at High Temperatures and Pressures Vaios T. Karathanos,*George K. Vagenas,t and George D. Saravacost Department of Food Science and Center for Advanced Food Technology, Rutgers University, New Brunswick, New Jersey 08903 ~~
~~
The method of distance-concentration curves was applied to the estimation of water diffusivities in starches a t high temperatures (25-140 "C) and pressures (up to 40 atm). Temperature had a positive (Arrhenius) effect on the water diffusivity. Pressure decreased the water diffusivity and caused an increase of the energy of activation for diffusion of water in starch, especially a t pressures of 1-10 bar. Water diffusivities to 30 X 10-lom2/s, and they were higher in hydrated starches varied from 0.3 X than in gels, evidently due to the higher porosity. The water diffusivity in hydrated granular starch decreased with increasing moisture content, due to their lower porosity.
Introduction Water diffusivity is an important physical property describing the transport of water, which is useful in calculations and predictions of numerous processes. It is particularly important to many processes applied to foods, like drying, rehydration, packaging, and storage stability. High pressure and/or temperature diffusivity data are of importance in food processes, such as manufacture of extruded pasta, puff drying, high temperature cooking of starch, and extrusion cooking. In extrusion cooking,water is mixed with a starch-based food powder, which is heated under pressure, gelatinized, and expanded to an extruded product of desirable physicochemical properties. During the extrusion process, penetration of water into the starch might control the gelatinization reaction (Atwell et al., 1988;Biliaderis et al., 1986),shift it to lower temperatures, and affect the rheological properties of starch (Herh and Kokini, 1990). Modeling of extruders and incorporation of diffusion, as well as other processes such as mixing and reaction kinetics, was reported by Chella and Ottino (1982) and Gopalakrishna et al. (1989). Diffusivity data are also required to predict the rate of bubble nucleation in the postextrusion process (Han and Han, 1990). Limited data on water diffusivity in foods are found in the literature, especially at conditions of high pressures and temperatures. The theoretical prediction of transport properties (Rotstein, 1987; Vrentas and Duda, 1979) is difficult, because of the variable physical and chemical structure and water content of each food. Therefore, it is necessary to obtain these data from experimental procedures. Starch is the most abundant constituent of a variety of foods that are involved in water transport processes. Therefore, the study of moisture diffusivity in starch model systems can provide the needed data for more complex food systems. Water concentration was found to affect significantly the diffusion coefficient (water diffusivity). An exponential increase of water diffusivity in starch gels with increasing moisture content was reported by Fish (1957).
* Author to whom correspondence should be addressed. Current address: Department of Chemical Engineering, National Technical University, Athens, 15773, Greece. t
8756-793.99 1/3007-0178$02.50/0
In hydrated granular starches the water diffusivity increases with decreasing moisture content in a drying experiment and passes through a maximum at low moisture contents, approximately 0.1 kg of water/kg of dry starch (Marousis et al., 1989). This diffusivity increase was attributed to the contribution of vapor diffusion, caused by the increased porosity at the end of the drying experiment. In starch gels,however, a continuous decrease of diffusivity with decreasing moisture content was found, due only to a small increase of porosity at the last stages of drying (Saravacos et al., 1989). Temperature also affects diffusivity. In most cases an Arrhenius relationship has been proposed. The energies of activation for diffusion vary from 16to 80 kJ/mol (Chirife, 1983). Frisch and Stern (1983) observed a break of the Arrhenius relationship at the region of glass transition temperature (T,) of polymers. Higher energies of activation were found above the Tgthan below it. Ehlich and Sillescu (1990) proposed the WLF equation to describe the temperature dependence of the diffusion coefficient for the temperature range 0-100 "C above Tg. The pressure effect on diffusivity has been studied mainly for gases. Gaseous diffusivity is inversely proportional to the pressure (Reid et al., 1987). The pressure dependence of diffusion coefficients has also been examined for the atomic transport mechanism (e.g., C in ferrous lattice); high pressure resulted in a diffusivity drop, as discussed by Bolsaitis and Spain (1977). Diffusion in dense fluids can be related to viscosity through the Stokes-Einstein equation, which gives the coefficient of self-diffusion for molecules of diameter r, in a medium of viscosity n. It follows that the diffusivity varies inversely to the viscosity. The latter is increased with applied pressure. Some reported data for tetramethylsilane indicate that the diffusion coefficient drops with increasing pressure (Streett, 1982). Feist and Schneider (1982)reported that the diffusion coefficients of some substances such as caffeine and benzene in supercritical C02 decrease by about 50% as pressure increases from 80 to 160 bar. The pressure effect on the effective diffusivity of water in solid food materials has not been studied extensively. Only at subatmosphericpressures are there some published data. Saravacos and Stinchfield (1965) found that in porous food materials at pressures lower than atmospheric, a pressure decrease resulted in an increase of diffusivity.
0 1991 American Chemical Society and American Institute of Chemical Engineers
Biotechnol. Prog., 1991, Vol. 7, No. 2
No data have been reported for the effect of high mechanical pressures on diffusivity in food materials. Recently, however, the effect of high pressures on gas diffusivities (Al-Rqobah et al., 1988) in inorganic solids and water diffusivities in granular food systems (Marousis, 1989) was reported. Mechanical pressure affects diffusivity indirectly, through a decrease of the bulk porosity (Marousis et al., 1990). The bulk porosity (e) of a material is expressed as (1) where V, and v b are the solid and bulk specific volumes and ,Ob and ps are the bulk and solid densities of the starch. The bulk volume, vb, is determined from the outside geometric characteristics of a sample, and the solid volume, V,, is measured by helium stereopycnometry. Helium molecules can penetrate the open pores, which are larger than 3.5 A. Two types of physical structures were used in our investigation: hydrated mixtures of starch and starch gels. These two forms were selected in order to investigate the role of starch gelatinization on the water diffusivity. Several methods have been proposed for diffusivity measurements in polymer systems (Crank and Park, 1968; Frisch and Stern, 1983): permeation methods, nuclear magnetic resonance studies, chromatography methods, sorption techniques, drying methods, and analysis of the distance-concentration curves. The concentration profile in the last method is found from changes in refractive index, determined by light interference (in the case of plastic material), by radiation absorption methods, gravimetrically, or chemically (Crank and Park, 1968). This technique can be used in diffusivity measurements in both liquid and solid phases. This method has been used for measurement of diffusion of solutes such as NaC1, sugars, or dyes in food materials (Naesens et al., 1981; Hendrickx et al., 1986; Gros and Ruegg, 1987). In their data analysis, they calculated only one diffusion coefficient from the whole curve. In our study, two diffusion coefficients were assumed, one for each of the two cylindrical parts. The measured water diffusivity is an overall transport property and it is usually called effective diffusivity. It combines the different water transport mechanisms, including liquid diffusion, vapor diffusion, capillary flow, and surface diffusion. In low porosity systems liquid diffusion predominates, while in higher porosity systems vapor diffusion becomes significant. e
= 1- v,/vb = 1-pb/p,
Materials and Methods Materials. A native granular starch powder (Amioca, by National Starch and Chemical Corp.), containing 98% amylopectin, was used. This starch contained 11% water, dry basis. The starch material (Amioca) was prepared in two forms: hydrated granular starch and gelatinized starch. The hydrated starches were prepared by thorough mixing of the granular starches with distilled water at room temperature to a desired moisture content, varying from 0.3 to 0.5 kg of water/kg of dry solids. The hydrated starch was left to equilibrate overnight in a saturated (1007% relative humidity) chamber. Gelatinized Amioca was prepared by heating a hydrated sample, containing 7 5 % water (dry basis), for 10 min at 100 OC in a water bath. The completeness of the gelatinization process was checked by differential scanning calorimetry (Karathanos, 1990) or X-ray diffractometry (Marousis et al., 1989). Moisture Distribution Method. In the distanceconcentration method, two cylinders, composed of starch
179
materials and initially having two different but constant moisture contents, are brought together by joining their ends. Water diffuses from the high water concentration cylinder to the low concentration one. The experimental materials were contained in a plastic cylinder 1.3 cm in diameter and 10 cm long, open from both ends. About half of it was filled with high-moisture material [hydrated (30-50% water, dry basis) or gel (75% water)] and the other half with a low-moisture sample (granular starch, containing 11% water, dry basis). When experiments at high pressures were made, the cylinder was closed at one end; otherwise, both ends were closed. The two starch materials were put into the plastic cylinder and pressed to obtain low porosity. The bulk porosity of each sample was kept constant in each experiment ( E = 0.28 for the 50% granular Amioca, t 0.36 for the 11% granular Amioca, and e = 0.05 for the gel). The porosity depends on the bulk and solid density of starch (eq l ) , and it increases when the moisture content decreases (Marousis, 1989). However, due to small moisture changes in the two cylinders during the experiment, the porosity was not altered significantly. The interface of the two cylinders was prepared flat and perpendicular to the axis of the plastic cylinder. For the experiments at high pressure, the two joined cylinders were put in a pressure reactor (Parr Instruments Co.), which maintained the desired pressure by introducing pressurized air through a pressure regulator (Figure 1). For experiments at high temperature, the pressure reactor was placed in an oil bath (constant temperature circulator Model MGW Lauda C20, by Fisher Scientific). Air pressures from 1 to 40 bar and temperatures from 25 to 140 "C were used. The temperature of the sample reached the temperature of the oil bath in a short time; therefore, isothermal conditions can be assumed. The air (80% nitrogen, 20 76 oxygen), which is used as pressure medium, does not dissolve significantly into the starch; therefore, plasticization due to the air does not occur. The air pressure is therefore equivalent to mechanically applied pressure (Assink, 1977). The cylinder, containing the starch material, remained at the appropriate pressure and temperature for 2-48 h, depending on the experimental conditions. The two cylindrical parts were sliced with an electric knife into slices of about 1-3 mm thick, in the case of gels. The starch powder slices were cut 2-5 mm thick. The weight of each slice was measured immediately. The weight of the dry solids was measured after drying of slices under vacuum at 70 "C for 24 h. The measured moisture content was assumed to be constant at each slice, and it corresponded to the center plane of the slice. For each slice (experimental point) the moisture content and its distance from the interface were measured. The distance of the experimental points from the interface (location) was estimated before slicing and was corrected after measuring the thickness of the slice with a micrometer. Estimation of Water Diffusivity. The effective water diffusivity was estimated by assuming that the overall transport of water in the two cylinders is described by Fick's law of diffusion. A simulation method was used in conjunction with a nonlinear regression technique. The theoretical analysis is described by Carlsaw and Jaeger (1959) and Crank (1975). The problem is stated as follows: Diffusion takes place into a semiinfinite medium and the surface z = m (far from the interface) is maintained at a constant concentration, CI(Z) = C I ( ~ =) C1. The moisture concentration at the interface (21= 0) is measured experimentally; therefore, Cl(0) is a known quantity.
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Similarly, the quantities C2(--ob) at 2 2 = and C2(0) at = 0 (interface) are known quantities. Diffusion coefficients are considered constant: D = D2 at < 22 < 0 at any time and 22, and similarly, D = D1 at 0 < z1 < for any time and 21. The diffusivities were considered to be independent of moisture content, since their dependence is not a very strong function of moisture, as can be seen from the results obtained. A t time t, cl(z1) is the theoretical (predicted) concentration at 0 < 21 and ~ ( 2 2 at 22 < 0. Left and right of the interface the second law of Fick applies: --ob
Exhaust
22
8p E
--ob
Safe Ring
-ob
dcl/dt = D,d2cl/dz12 cl(zl) = C1(-ob)
= Cl(-ob)
cl(-ob)
for 0 < z1< -ob
(2)
for z1> 0, t = 0
(3)
>0
(4)
for z1= -ob, t
and c1 = Cl(0)
at z1= 0
)
Low-moisture
Compressed Air Tank
(5)
Similarly
< z2 < o
d c 2 / d t = ~ , a ~ c , / a ~ , 2 for --ob c2(z2)= C2(--ob) c2(--ob)
= C2(--ob)
c2 = C2(0)
for z2 < 0, t = 0 for z2 =
-OD,
(6) (7)
t >0
at z2 = 0
(8)
(9)
The solution of the Fick diffusion equation (eq 2) under the above considerations (eqs 3-5) is
Similarly, the solution of eqs 6-9 is
The error function is given by the integral erf(x) =
s,'e-t2 dt
(12)
and erfc(x) = 1 - erf(x) (13) The error function can be also approximated by the series (Carlsaw and Jaeger, 1959, p 482)
C
2 erf(x) = -
TOe5n=O
(-l)nx2n+1 (2n + l)n!
when x
< 1.4
when x
> 1.4 (15)
The first six terms of each series were considered, since the accuracy of the approximation is very good (error less than 0.01% of the actual value). A numerical simulation method was used to estimate the two diffusivities iteratively. The initial concentrations C1 and C2 were known. The moisture contents Cli and C2i were measured gravimetrically at time t at various
Figure 1. Apparatus for water diffusivity experiments under high pressure.
distances zi. Cl(O), Cl(-ob), C2(0), and Cz(--ob), which are the experimental moisture contents at the interface (z = 0) or at z = were also measured. The above values are the experimental observations. Then, two diffusivities D1 and 0 2 were assumed and through eqs 10 or 11 the predicted values of cli and cpi were calculated. The optimum D1 and 0 2 values were the values that minimize the merit function &-ob
F = minimize x j x i ( C j i , p r e d - c ~ ~ ,(16) ~ where cji is the moisture content (dry basis) in the ith experimental point (1< i < N, N = number of experimental points in one cylinder) and j is referred to the cylinder 0' = 1, low moisture content cylinder; j = 2, high moisture content cylinder). Cji,pred are the theoretical (predicted) values, which correspond to moisture diffusivities D1 and D2,and Cji,exp are the experimental moisture contents. A nonlinear regression analysis was used to estimate the two diffusion coefficients over the two cylindrical parts of the system. The computer optimization method is the steepest descent technique (Shoup and Mistree, 1987)and it tries to minimize the merit function (eq 16).
Results and Discussion The Moisture Concentration-Distance Curve. A moisture concentration-distance profile for a two-cylinder system is shown in Figure 2. The high moisture content cylinder is Amioca gel, containing 75 % moisture, and the low moisture content cylinder is Amioca powder, containing 11%moisture (dry basis). The sample was kept at 25 "C and 1 atm for 167 h. The continuous line represents the concentration curve as predicted, using water diffusivity values D1 = 0.8 X 10-lom2/s for Amioca gel and D2 = 4.0 X 10-lom2/s for the low moisture content granular Amioca powder. The agreement between experimental and predicted values in both cylinders, left and right of the interface, is quite good. A t the left side of the interface, which is the powder (low moisture content), the slope of the adjacent curve to the interface is smaller than in the right cylinder (high moisture content
~ ~ )
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Biofechnol. Prog., 1991, Vol. 7, No. 2 80
Im ."...-.*"..."
EXPERIMENTAL PREDICTED
TIME
=
167 hr
GRANULAR AMIOCA 11% (d.b.)
AMIOCA GEL 75% moisture (d.b.)
0
zy" INTERFACE
-10
-5
0 DISTANCE,
5
10
cm
0
Figure 2. Distance-concentration profiles in two experiments of Amioca gel 75% water (dry basis)/Amioca granular starch 11%water (dry basis). Pressure 1 atm, temperature 25 "C, contact time 167 h.
Amioca gel), indicating that the diffusivity is larger in the powder than in the gel. The standard deviation of the water diffusivity, determined by the moisture distribution method, varied from 5 to 15% of the mean value for granular starches. More accurate results were obtained in gelatinized than in granular starches, due to more homogeneous samples. Water Diffusivity in Granular Starch. The results from the application of the optimization technique to a number of experiments are shown in Figures 3,4, and 5. Each graph gives the water diffusivities of granular Amioca starch at one moisture level. From these graphs it is evident that (1) water diffusivities increased with temperature significantly,(2) water diffusivities decreasedwith pressure considerably, and (3) water diffusivities of granular material decreased when the moisture content was increased. The data of Figures 3-5 were analyzed statistically by linear regression using the SAS program (SAS, 1985). Several empirical equations were considered. The equation that fitted the data best was In D = 10.882 - 2851(1/T) - 0.3122(1n P) - 1.5111X
25
60
100
120
140
0
TEMPERATURE ( C)
Figure 3. Effective water diffusivity in granular Amioca starch (115% moisture, dry basis) by the distance-concentration method.
25
60
100
120
140
TEMPERATURE ("C)
(17)
In the above equation D is the water diffusivity (XlO-lO m2/s), 7' is the absolute temperature in Kelvins, P is the pressure in atmospheres, and X is the moisture content, dry basis. The F-value was 210.85 and R2 = 0.893; all parameters were significant (at the 5% level). Equation 17 can be also written as
where R = gas constant, 1.987 kcal/(mol K). Comparison of eqs 17 and 18 gives Ea = 5.66 kcal/mol, k l = 0.3122, k2 = 1.5111 (kg of water/kg of dry starch)-l, and DO(XIO-lo m2/s) = exp(10.882). The energy of activation for diffusion, Ea, is in the same range with the energies of activation found for water diffusivity in drying experiments (Karathanos, 1988; Marousis et al., 1989) or sorption experiments (Fish, 1957). According to Figures 3-5 or the regression equation (17), pressure was responsible for a reduction of water diffu-
Figure 4. Effective water diffusivity in granular Amioca starch (40 C;; moisture, dry basis) by the distance-concentration method.
sivity, when an experiment was performed a t a constant temperture or moisture content. It should be noted that although the pressure was variable, the porosity was set at e = 0.36-0.28 [for low (11%)and high (50%) moisture content, dry basis], applying light hand pressure. These porosity values are considered relatively low. Therefore, the decrease of diffusivity was not caused by the decrease of porosity, due to pressure, but rather by the difficulty of water molecules moving under pressure. This is also the prediction of the statistical theory of gases (Reid et al., 1987). Pressure, therefore, might decrease the mobility of water in the vapor phase (vapor diffusion), which is a significant water transport mechanism in porous media, resulting, in turn, in lowering the effective (overall) diffusivity. Moisture content also affects water diffusivity. One would expect an increase of the diffusivity value with the moisture, due to plasticization of the starch granular
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Biotechnol. Prog., 1991, Vol. 7, No. 2 40
--
20
cn .
A
m
E
30
el
E
0, 0
0
r
7
X
X
W
*
L in
W
* c L
20
U 3
U 3
k
k
n U w
t 3
10
in
0
U
10
W
t3
0
0.
25
60
100
120
140
TEMPERATURE ("C)
25
60
100
120
140
TEMPERATURE ("C)
Figure 5. Effective water diffusivity in granular Amioca starch (50 "0 moisture,dry basis) by the distance-concentration method.
Figure 6. Effective water diffusivity in gelatinized Amioca starch
material. In the starch granular state, however, the water is responsible for the cohesiveness of the starch granules and for a porosity decrease through the incorporation of the water molecules within the starch granules and particles. The porosity has been found to be a significant factor in affecting the water mobility (Marousis, 1989). Therefore, increasing the moisture content may decrease the porosity, reducing the effective water diffusivity. The porosity was higher in the low moisture content (11% ,dry basis) starch ( E = 0.36) and lower in the 50% moisture starch (dry basis) ( e = 0.28). Water Diffusivity in Gelatinized Starch. The water diffusivities of completelygelatinized Amioca starch (water content 75% dry basis) appear in Figure 6. From this figure, the positive effect of temperature and the negative influence of pressure on water diffusivity of gels are evident. The best empirical regression equation found by the SAS program that could relate these data was of the type
temperature increase of 60 "C); this is close to the kind of temperature dependence of water diffusivity in starches. The effect of pressure on the water diffusivity in starch gels can be partially explained in terms of pressure diminishing vapor diffusivity, because the overall porosity was kept low in the two-cylinder method experiments for the case of gels (t = 0.05); thus, there was limited vapor diffusion. High pressure, however, might cause a reduction in the free volume of the system. This could result in a decrease of the water diffusivity in a starch gel with increasing pressure. Some limited data for self-diffusion coefficients of tetramethylsilane [Si(CH&] at high pressures show a similar behavior (reduction of diffusivity as pressure decreases; Streett, 1977). Assink (1977) published data on the effect of external applied pressure (in his case by helium gas) on the diffusivity of CC12F2 in poly(dimethylsi1oxane). The external applied pressure tended to reduce the diffusion coefficient of the penetrant gas into the polymer. He found that a pressure dependence similar to eq 19 could be applied, and he explained it in terms of a reduction of the free volume, which caused a subsequent decrease of the diffusion coefficient. The free volume of a polymer is a thermodynamic parameter that is calculated from thermal expansion data. A t the region close to the glass transition temperature (T,)the fractional free volume, fg, is about 2.5% of the polymer's total volume as calculated by the Williams, Landel, and Ferry (WLF) equation (Ferry, 1980). The free volume reduction upon application of pressure was mentioned by Ferry (1980) and Frisch and Stern (1983). According to Ferry, by increasing pressure the total volume of a polymer system decreases; this is due to both free volume collapse and diminution of the occupied volume of the molecules. In contrast to the temperature effect on free volume, which is a linear function of the temperature difference (T- Tg)[f = fg - a(T - Tg), where CY is the difference between the expansion coefficient for melt and glass], the free volume decrease due to applied pressure is markedly nonlinear and it is more significant at low pressures (the compressibility factor is a function of pressure and decreases with increasing pressure). This might explain the relative leveling off of water diffusivity
D = Do exp(-EJRT - k,P) (19) with F-value = 210.77 and R2 = 0.961, where D~(xlo-~O m2/s) = exp(10.848),E, = 6.66 kcal/mol, and kl = 0.02717 atm-l. The effect of temperature on the water diffusivity is similar to the effect of drying temperature on diffusivity (Karathanos, 1988) or the effect of temperature during a sorption experiment (Fish, 1957). The energyof activation for diffusion of water is about 6.66 kcal/mol, which agrees with most researchers (Chirife, 1983;Fish, 1957;Marousis et al., 1989). The effect of temperature on diffusivity in polymer systems might be stronger than in the water/starch system and can change the diffusion coefficient by 5 orders of magnitude in a temperature range of 100 "C above the glass transition temperature, as referred by Ehlich and Sillescu (1990). They, however, used very concentrated systems (low solvent concentration). Vrentas and Duda (1979) worked in a wider range of solvent concentrations. Their results from the free-volume model for diffusivity prediction indicate that at very low solvent concentration the effect of temperature is very strong. However, at higher solvent concentrations (50% per weight) the effect of temperature was less severe (1 order of magnitude for a
(75 96 moisture,dry basis) by the distance-concentration method.
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Table I. Energies of Activation for Diffusion of Water (kcal/mol) for Granular Amioca Starch at Various Moisture Contents and Pressures.
P, atm 1
X
= 0.11
SEb
X = 0.30 SE
X = 0.40 SE
X = 0.50 SE mean
4.41 0.34 (0.982) 4.10 0.23 (0.990) 4.58 0.20 (0.994) 4.01 0.31 (0.982) 4.276
20
40
mean
5.87 0.66 (0.963) 5.84 1.71 (0.784) 6.33 0.65 (0.969) 6.53 1.26 (0.901) 6.142
6.10 0.51 (0.979) 6.57 1.05 (0.930) 6.46 1.02 (0.931) 6.96 1.18 (0.921) 6.522
5.55
10 5.81 0.61 (0.968) 5.79 0.82 (0.943) 6.00 0.31 (0.992) 5.78 1.23 (0.880) 5.846
5.57 5.84 5.82
W
a Moisture content, X,is expressed in kg of water/kg of dry solids. Pressure, P, is expressed in atm. Energies of activation are given in kcal/mol. R2 for each regression is shown in parentheses. *SE, standard error.
with increasing pressure in gelatinized systems (for the same temperatures): the water diffusivity at pressures above 10 atm did not decrease considerably with applied pressure. Effect of Pressure on the Energy of Activation for Diffusion. Another treatment of the data can be made by plotting diffusivity data found at various temperatures (25, 60, 100, 120, and 140 "C) but at the same pressure (e.g., P = 20 atm) and moisture content (e.g., X = 0.3).Out of these data an energy of activation for diffusion can be as shown in Table I. The found (by plotting log D vs values varied from 4.01 to 6.96 kcal/mol. The R2 values of the regression were higher than 0.9 and the standard errors of the energy of activation estimates were (with two exceptions) less than 20% of the average value. There is a characteristic trend of the energy of activation increasing as the pressure was increased, for a given moisture content. Considering all the data for each pressure level (combining diffusivity data at all moisture contents and temperatures, but for constant pressure, and applying the SAS program), we obtained regression equations of the type
l/n
In D = In Do- E J R T - k,X
(20)
The energies of activation for various pressures (eq 20), along with their confidence intervals (for 95 70 confidence) are shown in Figure 7). They are close to the mean values of the energies of activation given in the last row of Table I, which were found by averaging the energies of activation for all moisture contents examined. The effect of pressure was significant from 1 to 10 atm at the 5% significance level. The higher energy of activation at high pressures suggests that there are stronger starch-water interactions at high pressures, resulting from possible alteration of the starch structure, due to the applied pressure. A possible explanation is an increase of the diffusion path for water molecules due to a decrease of free volume. Similar results on the effect of molding pressure on the diffusion of small molecules into polyethylene were reported in the literature by Dale and Rogers (1971), who found that the energy of activation increased from 4 to 7 kcal/mol as the draw ratio (during the molding process) was increased. By a similar statistical analysis, the energies of activation for diffusion, related to various moisture content levels,
0
20
10
30
40
50
Pressure, atm
Figure 7. Pressure dependence of the energy of activation for diffusion (E.) ingranular Amiocastarch. Bars are 95%confidence intervals. Table 11. Energies of Activation for Diffusion of Water ( E ) in Gelatinized Amioca Starch (75% moisture, dry basis) at Various Pressures pressure, atm
E, kcal/mol
SE," (kcal/mol)
R2
6.03 6.44 6.48 7.75
0.27 0.19 1.78 1.86
0.999 0.999 0.946 0.957
1
10 20 40 a
SE. standard error.
were estimated (Table I). The moisture dependence was not significant at the 5 % significance level. A similar trend of the effect of pressure on the activation energy for diffusion was found in gelatinized Amioca (Table 11). The energy of activation for diffusion (E,) in starch gels was higher than in granular starches. This is in agreement with results found by Marousis et al. (1989) in drying of granular and gelatinized starches. The dual effect of pressure on the water diffusivity and on the activation energy for diffusion in starches indicates that some physicochemical changes occurred upon pressure application. These might involve a stronger cohesion of starch chains by creation of new sites of hydrogen bonding, which might result in a free volume reduction.
Conclusions The moisture distribution (two-cylinder) method has been applied successfully to water diffusivity measurements in starch materials at high temperatures and pressures. Two diffusivities, one for each of the high- and low-moisture cylinders, were assumed to count for the dependence of diffusivity on moisture content. The method showed good repeatability. The water diffusivities in gelatinized starches are significantly lower than in granular material, evidently due to their lower porosity. Temperature had a positive effect on the moisture diffusivity. An Arrhenius relationship fitted well the experimental data over the temperature range 25-140 O C . Pressure had a negative effect on the water diffusivity in granular, gelatinized, and extruded materials, possibly due to reduced vapor diffusivity and a decrease of the free volume the system. The energies of activation for diffusion of water varied with the pressure from 4 to 7.7 kcal/mol and they were higher in gels than in granular systems,
Biotechnol. Prog., 1991, Vol. 7, No. 2
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indicating stronger interactions. With increasing pressure, the energy of activation increased, possibly due to a better cohesion of starch chains and stronger starch-water interactions. The increase of the energy of activation was more pronounced at pressures of 1-10 atm and tended to level off at higher pressures.
Acknowledgment This is New Jersey Agricultural Experiment Station Publication No. D-10544-15-90, supported by State funds and the Center for Advanced Food Technology, Rutgers University. The Center for Advanced Food Technology is a New Jersey Commission on Science and Technology Center.
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