The parameters that have been discussed so far, orders, rate constants, activation parameters, etc., are actually all that is needed in (chemical) kinetics. However, it has become the habit to use several other kinetic parameters in food science. They originate from days gone by when it was necessary to derive parameters and models to describe (mainly microbial) changes in foods during processing and storage when no use was made of modern reaction kinetics. All these parameters can be related to the more fundamental parameters that we have discussed so far. We give a brief overview of these parameters so that the reader can see how they relate to the fundamental parameters discussed above.
The parameter Q10 describes the temperature dependence of a reaction as the factor by which the reaction rate is changed when the temperature is increased by 108C. If we link that to the reaction rate constant, it can be expressed as
Q10¼kTþ5
kT5 kTþ10
kT (5:33)
If the Arrhenius equation holds, it can be shown that Q10¼ exp 10Ea
RT2
(5:34)
The parameter is thus seen to be a rather poor measure of the activation energy, and a serious drawback is its quite strong temperature dependence especially at higher Ea(Figure 5.12).
Another drawback of the Q10 parameter when linked to the activation energy is that it does not incorporate the preexponential factor or the activation entropy. So, it makes only sense to use the Q10
parameter for reactions that do not differ too much in activation entropy=preexponential factor.
T⬘(⬚C) Q10
10 0 20 30 40 50 60 70 80
0 50 100 150
Ea=300 kJ mol–1
Ea=200 kJ mol–1
Ea=100 kJ mol–1
FIGURE 5.12 Temperature dependence of the parameter Q10as a function of the underlying activation energy.
Another parameter to describe temperature dependence is Z, which expresses the increase in tem-perature that would produce an increase in rate by a factor of 10. Z is defined as
Z¼2:303RT2 Ea
¼ 10
log Q10
(5:35)
Like the parameter Q10, Z is temperature-dependent which restricts its use (Figure 5.13). Z is frequently used in bacteriology to describe inactivation of microorganisms.
Also used is the parameter D, especially in thermobacteriology. It is the decimal reduction value, the time needed to reduce a concentration by a factor of 10. D is nothing else than an inverse rate constant.
For afirst-order reaction:
D¼2:303
k (5:36)
and for a second-order reaction:
D¼ 9
c0k (5:37)
A plot of log D versus T0(in8C) is usually taken to be a straight line (for a limited temperature range), see Figure 5.14. D relates to the Z value, like k is related to Ea:
log D¼ log DrefT0 Tref0
Z (5:38)
Dref is the reference value of D at the reference temperature Tref0 (often chosen as 2508F for historical reasons, which is equal to 121.18C). Equation 5.38 is referred to as the TDT curve (thermal death time curve) or the Bigelow model.
T⬘(⬚C)
Z (⬚C)
10 5 0 15 20 25 30 35 40
0 50 100 150 200
Ea=300 kJ mol–1 Ea=200 kJ mol–1 Ea=100 kJ mol–1
FIGURE 5.13 Temperature dependence of the parameter Z as a function of the underlying activation energy.
As shown, all these parameters can be linked to the more fundamental kinetic parameters. They still serve a purpose. On the one hand, they are usually estimated in real foods and as such reflect a time–
temperature dependence characteristic (not pretending it is something like an activation energy) that can be used for engineering purposes; less so, however, for understanding behavior at the molecular level. On the other hand, the parameters are used commonly by regulatory agents in food safety programs in relation to thermal treatments. We come back to them briefly in Chapter 13 when we discuss thermobacteriology.
Typical temperature effects for reactions in foods. When the effect of temperature on reactions in foods has been established, preferably in the form of the parameters discussed if it concerns elementary reactions, i.e., activation energy=enthalpy and activation entropy=preexponential factor, the value of the parameters needs some discussion. Occasionally, there seems to be some misunderstanding regarding interpretation of activation parameters. For instance, if a high activation energy is found, the conclusion is sometimes drawn that the reaction will proceed slowly or difficult. This is not necessarily true, because the reaction may proceed quite fast at very high temperature if the value of the preexponential factor A or, equivalently,DSz is high. Furthermore, if a high activation energy goes along with a high preexponential factor, the reaction may still proceed at a noticeable rate. The point is that a high activation energy indicates a strong temperature dependence, that is to say it will run very slowly at low temperature, but relatively fast at high temperature. Relevant for foods is that chemical reactions (e.g., the Maillard reaction) have a‘‘normal’’ activation energy of about 100 kJ mol1, whereas inactivation of microorganisms can be characterized by a high activation energy, say, 300 kJ mol1(even though, as already mentioned, it is incorrect to express it in this way; we will come back to this in Chapter 13). Figure 5.15 illustrates this. Such differences in activation energy are exploited in processes such as high-temperature short-time heating (HTST) and ultrahigh-temperature treatment (UHT).
These processes are designed by choosing such time–temperature combinations that desired changes are achieved (microbial inactivation) while undesired changes (chemical reactions leading to quality loss) are minimized as much as possible. Another important consequence for foods is that reactions with relatively low activation energy will continue at a measurable rate at low temperatures, for instance during storage, leading to a limited shelf life.
Quite different results are obtained with protein denaturation and microbial inactivation. (Microbial inactivation is according to some authors due to enzyme, i.e., protein, denaturation. It is questionable whether this is the sole cause of inactivation. We will come back to this in Chapter 13 on kinetics of microbial inactivation.) Protein denaturation is characterized by a high activation enthalpy=energy and
log D
2 1 0
−1
−2
Z
T⬘(⬚C)
FIGURE 5.14 Schematic example of a TDT curve and interpretation of the Z-value.
this is compensated for by a high activation entropy=preexponential factor. As a result, the temperature dependence of such reactions is very high, much higher than that of chemical reactions. A potential pitfall in the study of denaturation of proteins is the way in which protein denaturation is studied, as discussed in Chapter 10. Frequently, for instance, the protein aggregation that is measured results from protein denaturation. The resulting kinetic parameters are then a combination of unfolding and aggregation. It may happen that at the lower temperatures unfolding is the rate-limiting step, while at the higher temperatures aggregation becomes the rate limiting step. As a consequence, a change in temperature dependence will be seen. It may even happen that the rate of aggregation is the rate-limiting step throughout and then the kinetics of aggregation is established rather than kinetics of denaturation.
With biochemical reactions, i.e., enzyme-catalyzed reactions, moderate temperature dependence is found, as is to be expected for catalyzed reactions. However, with enzyme-catalyzed reactions, enzymes become inactivated above a certain temperature, and the catalyzed reaction comes effectively to an end.
Most enzymes relevant in food tend to become inactivated between 508C and 808C, though some notably heat-resistant enzymes are known. The same goes for microbial growth:first there is an increase with temperature but eventually microbes start to die. A highly schematic picture of the effect of temperature on microbial growth and enzyme action alike is in Figure 5.16; it should be noted that the actual response to temperature can be time-dependent. In the case of microorganisms, there is also a minimum temperature below which there is no growth.
Photochemical reactions and radical reactions are not or only weakly temperature-dependent because the changes at the molecular level do hardly depend on thermal energy. Both types of reactions are of importance in foods, as discussed to some extent in Chapter 4. Photochemical reactions cause for instance oxidation of vitamins, they may activate certain enzymes, and they may causeflavor defects.
Radical reactions are most notable for oxidation reactions (of unsaturated fats, of vitamins).