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Shelf Life Testing:
O-zsNv1PX*j*E0Procedures and Prediction Methods for Frozen食品伙伴个性空间,J[.wf0C
Foods食品伙伴个性空间 M"R3_s(Dp v
Bin Fu
'`Ay-nM3u.gj0Kellogg's Battle Creek MI
.K;\ K }JB Ne`h(lRg0Theodore P. Labuza
c7ad/B+RRZL0Dept. of Food Science & Nutrition, University of Minnesota
8c5} tk0|SS;L01334 Eckles Ave., St. Paul, MN 55108食品伙伴个性空间 {)e]|%q
2
hj!s^Yv(_019.1 Introduction
L5Tq7o+U4fb/R u0The shelf life of a food can be defined as the time period within which the food is safe食品伙伴个性空间r.|f%?2Su$y
to consume and/or has an acceptable quality to consumers. Just like any other food,
*o x~(W7@0frozen foods deteriorate during storage by different modes or mechanisms, as食品伙伴个性空间/F#o(W m^0Bn d
summarized in Table 1. Microbes usually are not a problem since they cannot grow at食品伙伴个性空间1re mg"K?2vGZ
freezing temperatures unless subjected to extensive temperature abuse above the
Iwj2~kJ|7Y'`0freezing point. Enzymes are a big concern for frozen foods, which can cause flavor食品伙伴个性空间G5t5mz2s+| Eh { V
change (lipoxygenase) in non-blanched fruits and vegetables and accelerated
rP@D/n`J0deterioration reactions in meat and poultry (enzymes released from disrupted食品伙伴个性空间}.qS3b#J
membranes during precooking). Cell damage or protein and starch interactions during
*VRHSwf(B3H0freezing cause drip and mushiness upon thawing. Discoloration could occur by nonenzymatic食品伙伴个性空间UNR!{ZfAR]
browning, bleaching, and freezer burn. Vitamin C loss is often a major
^'VcwXh3n;I0concern for frozen vegetables. Physical changes, such as package ice formation,食品伙伴个性空间(Mvn.lu
moisture loss, emulsion destabilization, recrystallization of sugars and ice of frozen食品伙伴个性空间Y[dA#KU#UGi
desserts are often accelerated by fluctuating temperatures.
b$DaEjhxf(E\0For any specific frozen product, which mode determines its shelf life, depends
'Z5hf(bb0on the product characteristics (raw materials, ingredients, formulation), pre-freezing食品伙伴个性空间8D,|6u(M0N3\2z;Q
treatment, freezing process, packaging film and processes, and of course storage食品伙伴个性空间}J6l\lx;e
conditions. All of the quality deterioration and potential hazards are usually
j4_ H V-k| t7G0exaggerated or complicated by a fluctuating time-temperature environment (e.g.食品伙伴个性空间t7~7IFw_v6y%`
freeze/thaw cycle) during storage. On the other hand, the shelf life of a frozen food
1Zw`+qbZ5^0can be extended through ingredient selection, process modification and change of食品伙伴个性空间'F$R"K~]SU
package or storage conditions, as discussed in Section 3 of this book.
wL~+e7c3w/m R5[0This chapter will focus on shelf life testing of frozen foods for product食品伙伴个性空间HZ+YU}
development and market practices. Shelf life testing consists basically of selecting the食品伙伴个性空间~ AV'Mu
quality characteristics which deteriorate most rapidly in time and the mathematical食品伙伴个性空间6y6Ue;pCJ
modeling of the change. Table 19.1 can be used as a reference for the selection of
)a"W3r4mUm0quality characteristics, which depends on the specific product and usually requires
reKon-Q9}0professional judgment. Mathematical modeling of quality deterioration will be食品伙伴个性空间8X,hJ_;\/L,Nx4m wi
discussed next.
N%fAi-K^&e03食品伙伴个性空间OtN6LVlG_\
Table 19.1 Deterioration modes of frozen foods
.V? ~4[YMV-M0Frozen Foods Deterioration Modes
'b8b8JM%K.TH0Frozen meats, poultry and seafood Rancidity
3lBKm4f wU(U0Toughening (protein denaturation)食品伙伴个性空间$ws7A:g'E;A
Discoloration食品伙伴个性空间$\*|l7~c
Desiccation (freezer burn)
e;| H)YTQ%h0Frozen fruits and vegetables Loss of nutrients (vitamins)食品伙伴个性空间V5CM3{b
Loss of texture (temperature abuse)
K7qk@1bBC#`Q%P\0Loss of flavor (lipoxygenase, peroxidase)食品伙伴个性空间8]`o `rdG
Loss of tissue moisture (forming package ice)食品伙伴个性空间o+~6ZSPm3te'T~C
Discoloration
3\5J\La0N} JYG0Frozen concentrated juices Loss of nutrients (vitamins)
%S#PWw)_'o3N$n iF0Loss of flavor食品伙伴个性空间0tZ+_(h~"YZ[
Loss of cloudiness食品伙伴个性空间5R(iDH&d;H1a3P.DM
Discoloration食品伙伴个性空间8f%R&xh&|4OjIY;S
Yeast growth (upon temperature abuse)食品伙伴个性空间"?]H9r xmP
Frozen dairy products食品伙伴个性空间1|B Z$p3[
(ice cream, yogurt, etc.)
Sc X#[z#Lg#v.W0Iciness (recrystallization of ice crystals)
/EP9x-L*x` f0Vkq1H0Sandiness (lactose crystallization)食品伙伴个性空间([(q#Yn k fNj
Loss of flavor食品伙伴个性空间)pnG-YD ?{
Disruption of emulsion system
kk3v[q)y0Frozen convenience foods Rancidity in meat portions食品伙伴个性空间5^nEEI3OQ5xp7DJ+Y
Weeping and curdling of sauces
.n:W!{h4D#E2q3H)h@A}0Loss of flavor食品伙伴个性空间2Q ]2a:m(R+mx
Discoloration
O~ can usually be represented by the following kinetic equation:
p3s+M r"`'r,K0- dA/dt = k An (19.1)食品伙伴个性空间'H xU4gK,zP6D
where k is called a rate constant depending on temperature, product and packaging
/N[X6h*OJ0characteristics; n is a power factor called reaction order which defines whether the rate
0\2}]J.adp04
'O/oU [o+|Cj2P0of change is dependent on the amount of A present. If environmental factors are held
-VuvZ5x~Bk&p0constant, n also determines the shape of deterioration curve.
F.Q*LqV0Ao食品伙伴个性空间9Fk})Mir-{r
A a食品伙伴个性空间EB ]4CwHCPo
b食品伙伴个性空间G5g:bw#h\7PcS6Q
c
6v0X W!re-y S^0t
5s!J/feQ!?:w2N{0d食品伙伴个性空间ac)}4rd ts
e食品伙伴个性空间_d|.nRe \
Figure 19.1 Quality deterioration curves: a) linear; b) exponential;
y4rNiS+R%OBy0c) hyperbolic; d) quadratic; e) complex.食品伙伴个性空间0Kn(j!k&iCB0FJ ]
19.2.2 Zero and first order kinetics食品伙伴个性空间8]mXtJ6YW Ug
Equation 19.1 can also be written as:食品伙伴个性空间!s4g Emm!MQ5j
f(A) = k t (19.2)
:D]7Y*@R o sA3L0where f(A) is the quality function, k and t are the same as above. The form of f(A)食品伙伴个性空间W/`;d1n/J2t-J&J
depends on the value of n. When n is equal to zero it is called zero order reaction食品伙伴个性空间 ^ol&}JG`Xdl Q'bo
kinetics, which implies that the rate of loss of quality is constant under constant
w(n-P)C y6b0environmental conditions (curve (a) in Fig. 19.1). If n is equal to one it is called first食品伙伴个性空间/xRVUt/_Z.NgI
order reaction kinetics, which results in an exponential decrease in rate of loss as
~B*f2Q K f-\%r0quality decreases (curve (b) in Fig. 19.1, which becomes a straight line if plotted on a
-L E#u;i#N6E9em0semi-log plot). These quality functions can be expressed as follows:食品伙伴个性空间1I([Q7L3rX0R&~s"|
f(A) = Ao - A = kzt zero order (19.3a)
-oE9vn+O6@0f(A) = ln Ao - ln A = kft first order (19.3b)食品伙伴个性空间(s l5UbA8}
5食品伙伴个性空间z%a$_6e;qG
where Ao is the initial quality value. If Ae corresponds to the quality value at the end of
lGar-i@!b"]0shelf life, the shelf life (q) of the food is inversely proportional to the rate
[ F-yqK_.[0constant:
T']JmeG0q = (Ao - Ae) / kz zero order (19.4a)
'g P&g3{W YpF0q = ln (Ao/Ae) / kf first order (19.4b)
Rk S"^;]0It should be noted that most chemical reactions leading to quality loss in frozen食品伙伴个性空间~{h0c*~sc\
food systems are much more complex. However, the reaction kinetics can be食品伙伴个性空间&}.I+~/J7t1c+g y[
simplified into either pseudo-zero order or pseudo-first order kinetics. In the case of
,lK&Fp8YCv6u0complex reaction kinetics with respect to reactants, an intermediate or a final product食品伙伴个性空间a?H%t dr({9k/I
(e.g. peroxides or hexanal in lipid oxidation ) could be used as a quality index. There
2\"q"?1VD7VJ.x0are few cases where neither zero nor first order kinetics apply. Curve (c) in Fig. 19.1
&W4`^}7G:\T0shows the degradation curve for a 2nd order reaction (with single reactant), which also食品伙伴个性空间9S}8qTl!D%Y jN
shows a straight on a semi-log paper. A fractional order should be used to describe
C7E:N:SvIk9d0the curve (d) in Fig. 19.1.食品伙伴个性空间)QhXh.{5gkI
Sometimes, there is an induction period or lag time before the quality食品伙伴个性空间)Y6]6N1PG'yF:L}4i7{$I
deterioration begins (e.g. browning pigment formation in the Maillard reaction or a食品伙伴个性空间vi)Lj&Sos
microbial growth lag phase, as shown in curve (e) in Fig. 19.1. The length of the lag食品伙伴个性空间L6E4w0k^
depends on many factors, but temperature is a predominant factor. Given this,食品伙伴个性空间O6u A$yq*r
modeling of both the induction or lag period and deterioration phase are necessary for食品伙伴个性空间!?!`\'\LH7P
accurate prediction of quality loss or shelf life remaining. An example of such work has
.@Pl#kvZj0been demonstrated by Fu et al. (1991) for the growth of bacteria in milk.
4z M0J9hH0o0In certain circumstances (e.g. A represents a sensory hedonic score), a nonkinetic食品伙伴个性空间Tmq H:V8_Fmd
approach, e.g. a statistical data fitting technique can also be used to describe
Kf(qT2Kn0the deterioration curves. Varsanyi and Somogyi (1983) found that the change in食品伙伴个性空间.N-M X:wK'H#V5KY'j
quality characteristics as a function of time could be approximately described with食品伙伴个性空间%~.v!U-do
linear, quadratic and hyperbolic functions and that storage temperature and packing
,h4W.W*Q:I"xa0conditions affected the shape of the deterioration curves. However, the parameters
fyx'FCvfU)Hg0determined by data fitting are difficult to use for prediction under variable storage
^8W4X3f8Z z8\\yp0conditions except for the linear curve.
?%c:Nk\019.2.3 Temperature dependence of deterioration rate
2X C.D0D5}Z019.2.3.1 Arrhenius kinetics
,IS'v7t0p)Q6i0Once a frozen product is made and packaged and starts its journey from the食品伙伴个性空间!]@3B!La+P [
manufacturer's plant to warehouse, distribution center, retail store and finally
(]pP@6?tf?,j.dC N06食品伙伴个性空间3W9hW f"V
consumer's freezer, the rate of quality loss is primarily temperature dependent食品伙伴个性空间5P5Oj*d8L&bL}
(Zaritzky, 1982). The Arrhenius relationship is often used to describe the temperature食品伙伴个性空间1By&?c$zEPu'r"PR
dependence of deterioration rate where for either zero or first order:食品伙伴个性空间 k X(D"c0ti K
k = ko exp (-Ea/RT) (19.5a)
i+fHL/E+ZST-E%W0or ln k = ln ko - Ea/(RT) (19.5b)
NK*j x X9Tc-Wd0where ko is a pre-exponential factor; Ea is an activation energy in cal/mol; R is the gas食品伙伴个性空间1q yLej'j9}
constant in cal/mol K and equal to 1.986; T is an absolute temperature in K (273 + °C).
2ci Y6}J3|$r0Thus, a plot of the rate constant on semi-log paper as a function of reciprocal absolute
Ks1d7v8TJ7C x0temperature (1/T) gives a straight line as shown as Fig. 19.2. The activation energy is食品伙伴个性空间h R+@2GI2`XH_i
determined from the slope of the line (divided by the gas constant R). A steeper slope食品伙伴个性空间` lu8CPo
means the reaction is more temperature sensitive, i.e., a small change in T produces
,lMN%W/l \'i_0are large change in rate.食品伙伴个性空间]&|~,~g&R [
Figure 19.2 Arrhenius plot食品伙伴个性空间7vI1H*Td M"V
ln k食品伙伴个性空间 `,j&bv(Sm(j
1/T食品伙伴个性空间!B1sr%@Y M
slope = -Ea/R
!~B f|:G.` @'q0Thus, by studying a deterioration process and measuring the rate of loss at two食品伙伴个性空间$mrDv-eq
or three temperatures (higher than storage temperature), one could then extrapolate食品伙伴个性空间.M,S7uXT&};w-Df
on an Arrhenius plot with a straight line to predict the deterioration rate at the desired
/`S ~1lH:X qy0storage temperature. This is the basis for accelerated shelf life testing (ASLT), which食品伙伴个性空间d r4bQ&mt5?0P-DC
will be discussed later. One should note however that in some cases a straight line
hnQ2f#B:^0will not ensue for a variety of reasons, especially if a phase change occurs (Labuza食品伙伴个性空间2rS5p:^N#j&^;x Z
7食品伙伴个性空间QI5i \G
and Riboh, 1982). Thus for frozen foods, extrapolation from temperatures above 0¥C食品伙伴个性空间:Y(P&mccIS
are meaningless for shelf life prediction.
!M6O1v z)SnQ7? k019.2.3.2 WLF kinetics食品伙伴个性空间RgD1J/Q&o{:L
Besides the Arrhenius equation, another popular equation at least in the more recent食品伙伴个性空间KR-W[A&qN
food literature, is the Williams Landau Ferry (WLF) model (Williams et al., 1955). Its
sf] Y@oP0original form was based on the variation of the viscosity in the temperature range
O4S+\#j:`"fE t4q0above Tg as addressed in Chapter 3. When the rate constant at Tg' is substituted for Tg
!H?w7Y7P*U @ S0(Tg' is the Tg of a maximally freeze-concentrated system), the WLF model can be
zi\e:bF0written as follows:食品伙伴个性空间!G I]E'R5M9QS
log (kT/kg) = C1(T-Tg')/[(C2+(T-Tg')] (19.6a)
Zn"d DTL0or [log (kT/kg)]-1 = (C2/C1)/(T-Tg') + 1/C1 (19.6b)
\-N2o7n'?h}U0where C1 and C2 are constants. Thus a plot of [log (kT/kg)]-1 vs. (T-Tg)-1 will be a食品伙伴个性空间{qr![,mVm5_S2~]
straight line with the slope equal to C2/C1 and the intercept equal to 1/C1. As can be食品伙伴个性空间K@Q.j"m
seen this is a two parameter temperature dependent model as is the Arrhenius
w*g^%j:EIA5ai0equation.
!De5~-Fc|,l6a#l2i6_0Frozen foods stored below Tg' are stable to ice recrystallization and other食品伙伴个性空间8z@!x3aG8C7`q
physical changes. Levine and Slade (1988) postulated that stability is related to the食品伙伴个性空间#i:^~&{)ZLv
temperature difference between storage temperature and Tg'. This cryostabilization of
:aX)E+hw%~p*@'F$l5F%d0foods assumes stability below Tg' and rapid decrease of stability above Tg' according
Mfw2R*u`R"go0to the WLF relationship, exhibiting an increase in reaction rate, much higher than食品伙伴个性空间 y O;R/I*F1u*~
expected from the Arrhenius kinetics. However, this may not be true since the rate of食品伙伴个性空间W,kvM3Tu2F
chemical reactions can be expected to be influenced by temperature increase in a
?E2mq4t0complex way: (i) an increase of the rate constant, resulting from both the viscosity食品伙伴个性空间I-Yl0y@:g^
decrease and the increased molecular mobility (Fennema 1996); (ii) a decrease of the
#qI j:U/Qh0reaction rate as a consequence of the increasing dilution of the reactants Roos et al.
}bB.N5R%Y0(1996). For these reasons, it seems that the WLF model over predicts the temperature食品伙伴个性空间n9qkFl%c7L-Dt_b
effect of rate constant (Simatos et al., 1989). As noted by Nelson and Labuza (1994),
M#NE@P [0because of the small temperature range over which foods are stored, e.g., about D30°C
H5{Be%OoQ4PSP0for dry foods and D20°C for frozen foods, both the Arrhenius and the WLF model give食品伙伴个性空间y*Z8LD:N!L Fv G
good correlations as long as one does not use the universal coefficients suggested by食品伙伴个性空间6A;R*qRsQ8?
Slade and Levine (1991). In fact as shown by Nelson and Labuza (1994), their use of食品伙伴个性空间 _Q`_}|
the Lim and Reid (1991) data for enzymatic activity in the frozen state as shown in 19.3食品伙伴个性空间u6Y [S PLd@
is not proof that the Arrhenius relationship does not apply, WLF was assumed because食品伙伴个性空间l ?0MU1`+k
the rate was negligible below -10°C which was the measured Tg. But as seen in
8ImlZ"g5[08食品伙伴个性空间r Bc [T,d
Figure 19.3b if the data is plotted as Arrhenius plot an r2 of 0.999 ensues. The食品伙伴个性空间^v+N L!J!i
challenge in applying the WLF model for stability or shelf life prediction is that (1) Tg is食品伙伴个性空间n/g*sD"GKH,Z
not known; (2) Tg is difficult to determine; and (3) the universal coefficients of Levine食品伙伴个性空间'e.@t'jmo mki
and Slade (1986) are not applicable.
8tW8k)m!~ vy00 50 100 150 200 250食品伙伴个性空间 W5p x)k-y
0
F i&d
O-zsNv1PX*j*E0Procedures and Prediction Methods for Frozen食品伙伴个性空间,J[.wf0C
Foods食品伙伴个性空间 M"R3_s(Dp v
Bin Fu
'`Ay-nM3u.gj0Kellogg's Battle Creek MI
.K;\ K }JB Ne`h(lRg0Theodore P. Labuza
c7ad/B+RRZL0Dept. of Food Science & Nutrition, University of Minnesota
8c5} tk0|SS;L01334 Eckles Ave., St. Paul, MN 55108食品伙伴个性空间 {)e]|%q
2
hj!s^Yv(_019.1 Introduction
L5Tq7o+U4fb/R u0The shelf life of a food can be defined as the time period within which the food is safe食品伙伴个性空间r.|f%?2Su$y
to consume and/or has an acceptable quality to consumers. Just like any other food,
*o x~(W7@0frozen foods deteriorate during storage by different modes or mechanisms, as食品伙伴个性空间/F#o(W m^0Bn d
summarized in Table 1. Microbes usually are not a problem since they cannot grow at食品伙伴个性空间1re mg"K?2vGZ
freezing temperatures unless subjected to extensive temperature abuse above the
Iwj2~kJ|7Y'`0freezing point. Enzymes are a big concern for frozen foods, which can cause flavor食品伙伴个性空间G5t5mz2s+| Eh { V
change (lipoxygenase) in non-blanched fruits and vegetables and accelerated
rP@D/n`J0deterioration reactions in meat and poultry (enzymes released from disrupted食品伙伴个性空间}.qS3b#J
membranes during precooking). Cell damage or protein and starch interactions during
*VRHSwf(B3H0freezing cause drip and mushiness upon thawing. Discoloration could occur by nonenzymatic食品伙伴个性空间UNR!{ZfAR]
browning, bleaching, and freezer burn. Vitamin C loss is often a major
^'VcwXh3n;I0concern for frozen vegetables. Physical changes, such as package ice formation,食品伙伴个性空间(Mvn.lu
moisture loss, emulsion destabilization, recrystallization of sugars and ice of frozen食品伙伴个性空间Y[dA#KU#UGi
desserts are often accelerated by fluctuating temperatures.
b$DaEjhxf(E\0For any specific frozen product, which mode determines its shelf life, depends
'Z5hf(bb0on the product characteristics (raw materials, ingredients, formulation), pre-freezing食品伙伴个性空间8D,|6u(M0N3\2z;Q
treatment, freezing process, packaging film and processes, and of course storage食品伙伴个性空间}J6l\lx;e
conditions. All of the quality deterioration and potential hazards are usually
j4_ H V-k| t7G0exaggerated or complicated by a fluctuating time-temperature environment (e.g.食品伙伴个性空间t7~7IFw_v6y%`
freeze/thaw cycle) during storage. On the other hand, the shelf life of a frozen food
1Zw`+qbZ5^0can be extended through ingredient selection, process modification and change of食品伙伴个性空间'F$R"K~]SU
package or storage conditions, as discussed in Section 3 of this book.
wL~+e7c3w/m R5[0This chapter will focus on shelf life testing of frozen foods for product食品伙伴个性空间HZ+YU}
development and market practices. Shelf life testing consists basically of selecting the食品伙伴个性空间~ AV'Mu
quality characteristics which deteriorate most rapidly in time and the mathematical食品伙伴个性空间6y6Ue;pCJ
modeling of the change. Table 19.1 can be used as a reference for the selection of
)a"W3r4mUm0quality characteristics, which depends on the specific product and usually requires
reKon-Q9}0professional judgment. Mathematical modeling of quality deterioration will be食品伙伴个性空间8X,hJ_;\/L,Nx4m wi
discussed next.
N%fAi-K^&e03食品伙伴个性空间OtN6LVlG_\
Table 19.1 Deterioration modes of frozen foods
.V? ~4[YMV-M0Frozen Foods Deterioration Modes
'b8b8JM%K.TH0Frozen meats, poultry and seafood Rancidity
3lBKm4f wU(U0Toughening (protein denaturation)食品伙伴个性空间$ws7A:g'E;A
Discoloration食品伙伴个性空间$\*|l7~c
Desiccation (freezer burn)
e;| H)YTQ%h0Frozen fruits and vegetables Loss of nutrients (vitamins)食品伙伴个性空间V5CM3{b
Loss of texture (temperature abuse)
K7qk@1bBC#`Q%P\0Loss of flavor (lipoxygenase, peroxidase)食品伙伴个性空间8]`o `rdG
Loss of tissue moisture (forming package ice)食品伙伴个性空间o+~6ZSPm3te'T~C
Discoloration
3\5J\La0N} JYG0Frozen concentrated juices Loss of nutrients (vitamins)
%S#PWw)_'o3N$n iF0Loss of flavor食品伙伴个性空间0tZ+_(h~"YZ[
Loss of cloudiness食品伙伴个性空间5R(iDH&d;H1a3P.DM
Discoloration食品伙伴个性空间8f%R&xh&|4OjIY;S
Yeast growth (upon temperature abuse)食品伙伴个性空间"?]H9r xmP
Frozen dairy products食品伙伴个性空间1|B Z$p3[
(ice cream, yogurt, etc.)
Sc X#[z#Lg#v.W0Iciness (recrystallization of ice crystals)
/EP9x-L*x` f0Vkq1H0Sandiness (lactose crystallization)食品伙伴个性空间([(q#Yn k fNj
Loss of flavor食品伙伴个性空间)pnG-YD ?{
Disruption of emulsion system
kk3v[q)y0Frozen convenience foods Rancidity in meat portions食品伙伴个性空间5^nEEI3OQ5xp7DJ+Y
Weeping and curdling of sauces
.n:W!{h4D#E2q3H)h@A}0Loss of flavor食品伙伴个性空间2Q ]2a:m(R+mx
Discoloration
O~ can usually be represented by the following kinetic equation:
p3s+M r"`'r,K0- dA/dt = k An (19.1)食品伙伴个性空间'H xU4gK,zP6D
where k is called a rate constant depending on temperature, product and packaging
/N[X6h*OJ0characteristics; n is a power factor called reaction order which defines whether the rate
0\2}]J.adp04
'O/oU [o+|Cj2P0of change is dependent on the amount of A present. If environmental factors are held
-VuvZ5x~Bk&p0constant, n also determines the shape of deterioration curve.
F.Q*LqV0Ao食品伙伴个性空间9Fk})Mir-{r
A a食品伙伴个性空间EB ]4CwHCPo
b食品伙伴个性空间G5g:bw#h\7PcS6Q
c
6v0X W!re-y S^0t
5s!J/feQ!?:w2N{0d食品伙伴个性空间ac)}4rd ts
e食品伙伴个性空间_d|.nRe \
Figure 19.1 Quality deterioration curves: a) linear; b) exponential;
y4rNiS+R%OBy0c) hyperbolic; d) quadratic; e) complex.食品伙伴个性空间0Kn(j!k&iCB0FJ ]
19.2.2 Zero and first order kinetics食品伙伴个性空间8]mXtJ6YW Ug
Equation 19.1 can also be written as:食品伙伴个性空间!s4g Emm!MQ5j
f(A) = k t (19.2)
:D]7Y*@R o sA3L0where f(A) is the quality function, k and t are the same as above. The form of f(A)食品伙伴个性空间W/`;d1n/J2t-J&J
depends on the value of n. When n is equal to zero it is called zero order reaction食品伙伴个性空间 ^ol&}JG`Xdl Q'bo
kinetics, which implies that the rate of loss of quality is constant under constant
w(n-P)C y6b0environmental conditions (curve (a) in Fig. 19.1). If n is equal to one it is called first食品伙伴个性空间/xRVUt/_Z.NgI
order reaction kinetics, which results in an exponential decrease in rate of loss as
~B*f2Q K f-\%r0quality decreases (curve (b) in Fig. 19.1, which becomes a straight line if plotted on a
-L E#u;i#N6E9em0semi-log plot). These quality functions can be expressed as follows:食品伙伴个性空间1I([Q7L3rX0R&~s"|
f(A) = Ao - A = kzt zero order (19.3a)
-oE9vn+O6@0f(A) = ln Ao - ln A = kft first order (19.3b)食品伙伴个性空间(s l5UbA8}
5食品伙伴个性空间z%a$_6e;qG
where Ao is the initial quality value. If Ae corresponds to the quality value at the end of
lGar-i@!b"]0shelf life, the shelf life (q) of the food is inversely proportional to the rate
[ F-yqK_.[0constant:
T']JmeG0q = (Ao - Ae) / kz zero order (19.4a)
'g P&g3{W YpF0q = ln (Ao/Ae) / kf first order (19.4b)
Rk S"^;]0It should be noted that most chemical reactions leading to quality loss in frozen食品伙伴个性空间~{h0c*~sc\
food systems are much more complex. However, the reaction kinetics can be食品伙伴个性空间&}.I+~/J7t1c+g y[
simplified into either pseudo-zero order or pseudo-first order kinetics. In the case of
,lK&Fp8YCv6u0complex reaction kinetics with respect to reactants, an intermediate or a final product食品伙伴个性空间a?H%t dr({9k/I
(e.g. peroxides or hexanal in lipid oxidation ) could be used as a quality index. There
2\"q"?1VD7VJ.x0are few cases where neither zero nor first order kinetics apply. Curve (c) in Fig. 19.1
&W4`^}7G:\T0shows the degradation curve for a 2nd order reaction (with single reactant), which also食品伙伴个性空间9S}8qTl!D%Y jN
shows a straight on a semi-log paper. A fractional order should be used to describe
C7E:N:SvIk9d0the curve (d) in Fig. 19.1.食品伙伴个性空间)QhXh.{5gkI
Sometimes, there is an induction period or lag time before the quality食品伙伴个性空间)Y6]6N1PG'yF:L}4i7{$I
deterioration begins (e.g. browning pigment formation in the Maillard reaction or a食品伙伴个性空间vi)Lj&Sos
microbial growth lag phase, as shown in curve (e) in Fig. 19.1. The length of the lag食品伙伴个性空间L6E4w0k^
depends on many factors, but temperature is a predominant factor. Given this,食品伙伴个性空间O6u A$yq*r
modeling of both the induction or lag period and deterioration phase are necessary for食品伙伴个性空间!?!`\'\LH7P
accurate prediction of quality loss or shelf life remaining. An example of such work has
.@Pl#kvZj0been demonstrated by Fu et al. (1991) for the growth of bacteria in milk.
4z M0J9hH0o0In certain circumstances (e.g. A represents a sensory hedonic score), a nonkinetic食品伙伴个性空间Tmq H:V8_Fmd
approach, e.g. a statistical data fitting technique can also be used to describe
Kf(qT2Kn0the deterioration curves. Varsanyi and Somogyi (1983) found that the change in食品伙伴个性空间.N-M X:wK'H#V5KY'j
quality characteristics as a function of time could be approximately described with食品伙伴个性空间%~.v!U-do
linear, quadratic and hyperbolic functions and that storage temperature and packing
,h4W.W*Q:I"xa0conditions affected the shape of the deterioration curves. However, the parameters
fyx'FCvfU)Hg0determined by data fitting are difficult to use for prediction under variable storage
^8W4X3f8Z z8\\yp0conditions except for the linear curve.
?%c:Nk\019.2.3 Temperature dependence of deterioration rate
2X C.D0D5}Z019.2.3.1 Arrhenius kinetics
,IS'v7t0p)Q6i0Once a frozen product is made and packaged and starts its journey from the食品伙伴个性空间!]@3B!La+P [
manufacturer's plant to warehouse, distribution center, retail store and finally
(]pP@6?tf?,j.dC N06食品伙伴个性空间3W9hW f"V
consumer's freezer, the rate of quality loss is primarily temperature dependent食品伙伴个性空间5P5Oj*d8L&bL}
(Zaritzky, 1982). The Arrhenius relationship is often used to describe the temperature食品伙伴个性空间1By&?c$zEPu'r"PR
dependence of deterioration rate where for either zero or first order:食品伙伴个性空间 k X(D"c0ti K
k = ko exp (-Ea/RT) (19.5a)
i+fHL/E+ZST-E%W0or ln k = ln ko - Ea/(RT) (19.5b)
NK*j x X9Tc-Wd0where ko is a pre-exponential factor; Ea is an activation energy in cal/mol; R is the gas食品伙伴个性空间1q yLej'j9}
constant in cal/mol K and equal to 1.986; T is an absolute temperature in K (273 + °C).
2ci Y6}J3|$r0Thus, a plot of the rate constant on semi-log paper as a function of reciprocal absolute
Ks1d7v8TJ7C x0temperature (1/T) gives a straight line as shown as Fig. 19.2. The activation energy is食品伙伴个性空间h R+@2GI2`XH_i
determined from the slope of the line (divided by the gas constant R). A steeper slope食品伙伴个性空间` lu8CPo
means the reaction is more temperature sensitive, i.e., a small change in T produces
,lMN%W/l \'i_0are large change in rate.食品伙伴个性空间]&|~,~g&R [
Figure 19.2 Arrhenius plot食品伙伴个性空间7vI1H*Td M"V
ln k食品伙伴个性空间 `,j&bv(Sm(j
1/T食品伙伴个性空间!B1sr%@Y M
slope = -Ea/R
!~B f|:G.` @'q0Thus, by studying a deterioration process and measuring the rate of loss at two食品伙伴个性空间$mrDv-eq
or three temperatures (higher than storage temperature), one could then extrapolate食品伙伴个性空间.M,S7uXT&};w-Df
on an Arrhenius plot with a straight line to predict the deterioration rate at the desired
/`S ~1lH:X qy0storage temperature. This is the basis for accelerated shelf life testing (ASLT), which食品伙伴个性空间d r4bQ&mt5?0P-DC
will be discussed later. One should note however that in some cases a straight line
hnQ2f#B:^0will not ensue for a variety of reasons, especially if a phase change occurs (Labuza食品伙伴个性空间2rS5p:^N#j&^;x Z
7食品伙伴个性空间QI5i \G
and Riboh, 1982). Thus for frozen foods, extrapolation from temperatures above 0¥C食品伙伴个性空间:Y(P&mccIS
are meaningless for shelf life prediction.
!M6O1v z)SnQ7? k019.2.3.2 WLF kinetics食品伙伴个性空间RgD1J/Q&o{:L
Besides the Arrhenius equation, another popular equation at least in the more recent食品伙伴个性空间KR-W[A&qN
food literature, is the Williams Landau Ferry (WLF) model (Williams et al., 1955). Its
sf] Y@oP0original form was based on the variation of the viscosity in the temperature range
O4S+\#j:`"fE t4q0above Tg as addressed in Chapter 3. When the rate constant at Tg' is substituted for Tg
!H?w7Y7P*U @ S0(Tg' is the Tg of a maximally freeze-concentrated system), the WLF model can be
zi\e:bF0written as follows:食品伙伴个性空间!G I]E'R5M9QS
log (kT/kg) = C1(T-Tg')/[(C2+(T-Tg')] (19.6a)
Zn"d DTL0or [log (kT/kg)]-1 = (C2/C1)/(T-Tg') + 1/C1 (19.6b)
\-N2o7n'?h}U0where C1 and C2 are constants. Thus a plot of [log (kT/kg)]-1 vs. (T-Tg)-1 will be a食品伙伴个性空间{qr![,mVm5_S2~]
straight line with the slope equal to C2/C1 and the intercept equal to 1/C1. As can be食品伙伴个性空间K@Q.j"m
seen this is a two parameter temperature dependent model as is the Arrhenius
w*g^%j:EIA5ai0equation.
!De5~-Fc|,l6a#l2i6_0Frozen foods stored below Tg' are stable to ice recrystallization and other食品伙伴个性空间8z@!x3aG8C7`q
physical changes. Levine and Slade (1988) postulated that stability is related to the食品伙伴个性空间#i:^~&{)ZLv
temperature difference between storage temperature and Tg'. This cryostabilization of
:aX)E+hw%~p*@'F$l5F%d0foods assumes stability below Tg' and rapid decrease of stability above Tg' according
Mfw2R*u`R"go0to the WLF relationship, exhibiting an increase in reaction rate, much higher than食品伙伴个性空间 y O;R/I*F1u*~
expected from the Arrhenius kinetics. However, this may not be true since the rate of食品伙伴个性空间W,kvM3Tu2F
chemical reactions can be expected to be influenced by temperature increase in a
?E2mq4t0complex way: (i) an increase of the rate constant, resulting from both the viscosity食品伙伴个性空间I-Yl0y@:g^
decrease and the increased molecular mobility (Fennema 1996); (ii) a decrease of the
#qI j:U/Qh0reaction rate as a consequence of the increasing dilution of the reactants Roos et al.
}bB.N5R%Y0(1996). For these reasons, it seems that the WLF model over predicts the temperature食品伙伴个性空间n9qkFl%c7L-Dt_b
effect of rate constant (Simatos et al., 1989). As noted by Nelson and Labuza (1994),
M#NE@P [0because of the small temperature range over which foods are stored, e.g., about D30°C
H5{Be%OoQ4PSP0for dry foods and D20°C for frozen foods, both the Arrhenius and the WLF model give食品伙伴个性空间y*Z8LD:N!L Fv G
good correlations as long as one does not use the universal coefficients suggested by食品伙伴个性空间6A;R*qRsQ8?
Slade and Levine (1991). In fact as shown by Nelson and Labuza (1994), their use of食品伙伴个性空间 _Q`_}|
the Lim and Reid (1991) data for enzymatic activity in the frozen state as shown in 19.3食品伙伴个性空间u6Y [S PLd@
is not proof that the Arrhenius relationship does not apply, WLF was assumed because食品伙伴个性空间l ?0MU1`+k
the rate was negligible below -10°C which was the measured Tg. But as seen in
8ImlZ"g5[08食品伙伴个性空间r Bc [T,d
Figure 19.3b if the data is plotted as Arrhenius plot an r2 of 0.999 ensues. The食品伙伴个性空间^v+N L!J!i
challenge in applying the WLF model for stability or shelf life prediction is that (1) Tg is食品伙伴个性空间n/g*sD"GKH,Z
not known; (2) Tg is difficult to determine; and (3) the universal coefficients of Levine食品伙伴个性空间'e.@t'jmo mki
and Slade (1986) are not applicable.
8tW8k)m!~ vy00 50 100 150 200 250食品伙伴个性空间 W5p x)k-y
0
F i&d