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AH{ AH0

where AH0 is the enthalpy change of the DSC endotherm without conversion, and AHl that with conversion. Thus X is equivalent to the degree of conversion and is defined as

There are two general approaches to analyzing kinetics data, namely, the differential and integral methods. In the differential method of test, the differential at each specific time is calculated, and after taking the logarithm, the data are plotted. The reaction order is the slope of a plot of log (d[l — X]/dt) versus log (1 — X), and the reaction-rate constant can be obtained from the intercept. In the integral method, a particular form of rate expression is assumed. After appropriate integration and mathematical manipulation, a certain concentration function versus time is plotted. If a reasonably good fit is obtained, then the rate equation is adopted to describe the reaction under study. There are advantages and disadvantages to each method. The advantages of the differential method are the ease of obtaining the appropriate reaction order and reaction rate, and the disadvantage is the magnification of experimental errors. The advantage of the integral method is that experimental data can be used directly, while the disadvantage is that a trial-and-error procedure must be followed. In general, it is suggested that the differential analysis be attempted first, then the integral analysis is performed to check if the obtained rate expression is appropriate or not. Most investigators apply the integral approach to the studies of starch gelatinization with an excess amount of water. The kinetics of starch gelatinization in the cooking of rice grains with 94% moisture content has been studied (19). The kinetics of the water diffusion and starch gelatinization at 91.4% moisture content has been reported (20). The kinetics of cooking of rice starch also in an excess amount of water has been studied (21). The gelation kinetics of barley starch in a diluted system (1% solid) has been investigated (22). A first-order kinetics equation has been employed by these investigators to describe the gelatinization of starch in an excess amount of water. The kinetics of starch conversion in a limited amount of water (40% or less) has not been as well studied, and that reaction order has been reported to be zero order (18,23).

In the presence of an excess amount of water (ie, >60% water for Amioca), different sources of starch gelatinize at different temperatures. The range of temperature is between 50 and 80°C. If a limited amount of water is used, the temperature at which gelatinization and melting (as detected in DSC thermogram) happen is elevated. Figure 1 shows the dependence of peak temperature Tp of the DSC thermogram on the water content of the Amioca samples. At water content higher than 60%, Tp stays constant, whereas at water content lower than 60%, there are two peaks in the thermogram. The second peak temperature, Tp, increases with decreasing water content according to

T—|—i—i—r-|—i—|—i—|—i—1—r T = 227.92- 2.674W

T—|—i—i—r-|—i—|—i—|—i—1—r T = 227.92- 2.674W

10 20 30 40 50 60 70 80 90 100 Moisture content (%)

Figure 1. Peak temperatures from DSC endotherms for amioca with various moisture contents.

10 20 30 40 50 60 70 80 90 100 Moisture content (%)

Figure 1. Peak temperatures from DSC endotherms for amioca with various moisture contents.

the linear equation Tp = 227.92 - 2.674 W, where W is the water content in wet wt %. To consider the combined effects of heat, moisture content, and the source of starch on the conversion of starch, a dimensionless temperature parameter T/Tp was developed (18). This parameter correlated well with the rates of conversion of starch. Figure 2 shows the plot of k, the zero-order rate of starch conversion versus T/Tp, T is the operating temperature and Tp, the second endotherm peak temperature, is a constant for a specific starch at a specified water content. In Figure 2, data from different studies are presented (18,19,24). Excluding data from Reference 19, which show obvious masstransfer resistance (diffusion controlling), the rest of the data can be represented by the following equation:

74.97x

where x = T/Tp and the limit for x is 0.63 < x < 1.06, for the equation to be meaningful.

Figure 2. A general correlation between starch conversion rate constant k, and T/Tp, a dimensionless temperature parameter. Tp is peak temperature of DSC thermogram. Source: O, Ref. 18; □, Ref. 24; A, Ref. 21; 0, Ref. 19.

Figure 2. A general correlation between starch conversion rate constant k, and T/Tp, a dimensionless temperature parameter. Tp is peak temperature of DSC thermogram. Source: O, Ref. 18; □, Ref. 24; A, Ref. 21; 0, Ref. 19.

This equation is useful for calculating reaction rates of various starch conversion at various water contents and various temperatures. The source of starch and water content determines the value of Tp, which is measured by using DSC endotherms.

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