280Phase Transitionsin FoodsEquation (9.16) shows that a low value of D below Tg decreases the observed rate constant. At temperatures above Tg the reaction rate increases with increasing plasticization due to increasing diffusion and approaches the true constant, k, which applies when the system is well stirred. Figure 9.3 shows the ratio, k'/k, for a hypothetical reaction as a function of D based on the assumptions that equations (9.15) and (9.17) apply and that the ratio k/tr,D is significantly greater than zero. As was pointed out by Karel (1993) these assumptions are not likely to be valid in all cases. k'= k 1+~ tzD k (9.17)Equation (9.17), as was also shown in Figure 9.3, defines that a dramatic change in the observed reaction rate constant may occur over a fairly narrow range of diffusion coefficients, which, depending on the probability of theii ~mL . . . . . . . . ..0=-vv0.8-0 . 6-0.4-0.2-0IIiIIIii.i..,.-25-20log D (cm2/s)-15-10Figure 9.3 Effect of diffusion on the ratio of observed, k', and true reaction rate constants, k, assuming the validity of equations (9.15) and (9.17) for a hypothetical reaction. The diffusion coefficient increases with increasing temperature according to the Arrhenius-type temperature dependence below glass transition temperature, Tg. Exceeding Tg causes a dramatic increase in the observed rate constant as the increase of the diffusion coefficient with increasing temperature becomes more pronounced and follows the WLF relationship.
