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log( k ref k ) = C 1(T-T ref ) C 2 +(T-T ref ) (36) where k ref the rate constant at the reference temperature T ref (T ref >T g ) and C 1 , C 2 are system-dependent coefficients. Williams et al (1955), for T ref =T g , using experimental data for different polymers, estimated average values of the coefficients: C 1 =-17.44 and C 2 =51.6. In various studies these are used as universal values to establish the applicability of WLF equation for different systems. This approach can be misleading (Ferry,1980; Peleg, 1990; Buera and Karel,1993) and effort should be made to obtain and use system specific values. Alternative approaches for accessing the applicability of the WLF model and calculating the values of C 1 and C 2 have been evaluated (Nelson, 1993; Buera and Karel, 1993). Eq. (36) can be rearranged into an equation of a straight line. Thus the plot of [log k ref 1 k ]-1 vs. T-T ref is a straight line with a slope equal to C 2 /C 1 and an intercept of 1/C 1 . If the glass transition temperature, Tg, is known, the WLF constants at Tg can be calculated (Peleg,1992): C 1 g = C 1 C 2 C 2 +T g -T ref and C 2 g =C 2+T g - T ref (37) These values can be compared to the aforementioned average WLF coefficients. When Tg and reaction rate data at many higher temperatures are available, k g , C 1 and C 2 can be estimated from eq.(36) using non linear regression methodology. Ferry (1980) proposed an additional approach for verifying the WLF equation and determining the coefficients. A temperature T ∞ , at which the rate of the reaction is practically zero, is used. T ∞ can be approximated by the difference between the reference temperature and C 2 i.e. T ∞ =T ref -C 2 . Rearranging eq. (36) log( k ref k ) = C 1(T-T ref ) T-T ∞ (38) 30
i.e. if T ∞ is chosen correctly, a plot of log(k/k ref ) vs. (T-T ref )/(T-T ∞ ) is linear through the origin with slope equal to C 1 . T g -50° C was proposed as a good initial estimate of T. Buera and Karel (1993) used this approach to test the applicability of WLF equation in modeling the effect of temperature on the rate of nonenzymatic browning, within several dehydrated foods and carbohydrate model systems. Table 4 gives the calculated values of the coefficients of the WLF equation for the different systems at the used reference temperature as well as at T g , for different moisture contents. 31
Page 1 and 2: THE HANDBOOK OF FOOD ENGINEERING PR
Page 3 and 4: It is a working definition for the
Page 5 and 6: 10.2 KINETICS OF FOOD DETERIORATION
Page 7 and 8: very small, allowing us to treat it
Page 9 and 10: Data can be fitted to these equatio
Page 11 and 12: criterion. The value of the R 2 , f
Page 13 and 14: of reaction systems involved in foo
Page 15 and 16: Lund, 1985). The standarized residu
Page 17 and 18: When a Michaelis-Menten rate equati
Page 19 and 20: ∂ ln K eq ∂ (1/T) = - ∆Eo R (
Page 21 and 22: are available, the confidence range
Page 23 and 24: kinetic data is compared. Its main
Page 25 and 26: plot will give a relatively straigh
Page 27 and 28: temperatures (Fennema et al., 1973)
Page 29: Glass transition phenomena are also
Page 33 and 34: A number of recent publications deb
Page 35 and 36: The study of the temperature depend
Page 37 and 38: and bakery goods, upon losing moist
Page 39 and 40: ambient temperatures (e.g loss of c
Page 41 and 42: temperature and is an area of curre
Page 43 and 44: and variable temperature conditions
Page 45 and 46: Figure 8. Characteristic fluctuatin
Page 47 and 48: 10.3 APPLICATION OF FOOD KINETICS I
Page 49 and 50: time at each selected temperature.
Page 51 and 52: TTI can be used to monitor the temp
Page 53 and 54: 10.4 EXAMPLES OF APPLICATION OF KIN
Page 55 and 56: Figure 10. Thiamin retention of a m
Page 57 and 58: S = SS {1+ N p n-Np F[N p, n-N p ,
Page 59 and 60: 10.4.2. Examples of shelf life mode
Page 61 and 62: In Fig. 12a aspartame concentration
Page 63 and 64: the approach to follow to increase
Page 65 and 66: REFERENCES Arabshashi, A. (1982). E
Page 67 and 68: Fennema, O., Powrie, W. D., Marth,
Page 69 and 70: Labuza, T. P. (1975) Oxidative chan
Page 71 and 72: Mohr, P. W., Krawiec, S. (1980) Tem
Page 73 and 74: Sapru, V., and T.P. Labuza (1992) G
Page 75: Yoshioka, S., Aso, Y., Uchiyama, M.

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