Among thermo-physical criteria, the apparent cooking activation energy (E a ) is an important parameter used for process modelling. In order to take into account the pulp heterogeneity, E a estimates will be investigated using differential scanning calorimetry (DSC) 1,2,3,4 and dynamic thermomechanical analysis (DMTA).
DMTA procedure in 4 steps Fig 3a Correction of tan δ(T) lags with β i Fig 3b Numeric determination of [T o T f ] Fig 3c Computation of α by tan δ
normalisation Fig 3d Kissinger equation plot
DSC 7 ® nonisothermal conditions 9 Stainless steel reference and sample sealed pans 9 Empty reference pan 9 14 to 20mg dry matter micro-samples 9 6 heating rates β i from 25 to 120°C 9 Pure indium calibration at different β i
Measured parameters 9 Heat flux φ (mW) versus T (°C) and t (s)
Estimation of the activation energy by DMTA:
an original approach for considering biological heterogeneity
Cooking bananas and plantains represent a major starchy resource in central African and Latin American countries. One of the most common banana traditional cooking process involves boiling into water. The cooking stage (irreversible gelatinisation reaction) induces some massive water and heat transfers from the solution into the pulp and some simultaneous counter-current transfers of soluble solutes that leach from the pulp into the cooking solution.
Material and methods Material and methods
¾ Computation
Conclusion and perspectives Conclusion and perspectives Background and objectives Background and objectives
References References
1
Vyazovkin S. A unified approach to kinetic processing of nonisothermal data. International J. Chem. Kinet. 28 p95-101 (1996).
2
Ojeda CA, Tolaba MP and Suarez C. Modeling starch gelatinization kinetics of milled rice flour. Cereal Chem. 77(2) p145-147 (2000).
3
Calzetta Resio A. and Suarez C. Gelatinization kinetics of amaranth starch. Int. J. Food Sci. Technol. 16 p441-448 (2001).
4
Spigno G. and De Faveri DM. Gelatinization kinetics of rice starch studied by non-isothermal calorimetric technique: influence of extraction method, water concentration and heating rate. J Food Eng. 62 p337-344 (2004).
5
Vyazovkin S. and Sbirrazzuoli N. Confidence intervals for the activation energy estimated by few experiments. Anal. Chim. Acta 355 p175-180 (1997).
6
Ozawa T. A new method of analyzing thermogravimetric data. Bull. Chem. Soc. Jpn. 38 p1881-1886 (1965).
7
Vyazovkin S. Model-free kinetics - Staying free of multiplying entities without necessity. J. Therm. Anal. Calorim. 83 p 45-51 (2006).
8
Kissinger HE. Reaction kinetics in differential thermal analysis. Anal. Chem. 29, 1702-1706 (1957).
Results Results
DMTA 7e ® nonisothermal conditions 9 20mm diameter parallel plates
9 17mm diameter grease weatherproofed cylinders 9 linear viscoelastic range
9 500mN static & 450mN dynamic forces 9 N= 1Hz, strain amplitude > 500μm 9 6 heating rates β i from 25 to 120°C 9 Pure indium calibration at different β i Measured parameters
9 Tan δ versus T (°C) and t (s)
Fig 1. DMTA and DSC sampling areas
Estimated DSC E α seemed to depend on the sampling area (Fig 4), probably due to the raw material heterogeneity (water gradient). A continuous decrease in E α was observed while α rise using both DSC and DMTA methods (Fig 4 & 5), suggesting a multi-steps process of different E α 1,7 . Nevertheless, ‘the kinetic scheme of the process’ did not correspond to one of the most characteristic E α ( α ) dependency shapes reviewed 1 . E α Relative Variation percentage (IV) between DSC and DMTA was relatively low in the 0.1 - 0.8 range (below 15%).
Higher differences in Ea estimates at α > 0.8 were probably due to some shrinkage of grease weatherproofed samples and to the systematic error induced by Arrhenius computation with ‘DMTA estimated sample temperature’ (thermocouple acquired temperature is distant from the sample).
An estimation of E α during the irreversible gelatinization process could then be obtained using a thermo-mechanical nonisothermal isoconversional approach.
E α estimated differences between DSC and DMTA were relatively low in the 0.1 - 0.8 α range (< 25 KJ.mol -1 );
Such estimation could be sufficient for later process modelling with decouple transfers;
A better estimation of E α may be later obtained using some recent numerical algorithms 5,7 . It may help to determine the contribution of the individual steps to the overall reaction rate and getting a better comprehension of the complex gelatinization process.
¾ Kinetic considerations
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝ + ⎛ −
⎥ =
⎦
⎢ ⎤
⎣
⎡
i i i
RT k E
T 2 , ,
ln
α α α β
The kinetic analysis of solid state decompositions is commonly based on a single-step kinetic equation (I) which could be rearranged considering the explicit temperature dependence of the rate constant k(T) into the Arrhenius equation 5 . It gives the traditional kinetic description based on A, E α and f(α) which has been widely used 1,5,6,7,.. for kinetic predictions (II):
Recent ‘model-free kinetic’ as an isoconversional method produces a dependence of E α on α, without requiring knowledge of the reaction model or the preexponential factor 1,7 . Among potential solutions in non-isothermal conditions, the equation (III) describes below the linear relationship between ln (β/T 2 ) and 1/T in which the apparent activation energy can be directly estimated via the slope of the straight line 5 :
The equation (III) is known as “the Kissinger equation” 4,8 here with an isoconversional form (T α,i and E α depending on the extent or degree of conversion α). The straight line Y-axis origin k may be used to estimate preexponential factor 2 .
) ( )
( α
α k T f
dt
d = (I) α exp ( α )
RT f A E dt
d a ⎟
⎠
⎜ ⎞
⎝
= ⎛ − (II)
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝ + ⎛ −
⎥ =
⎦
⎢ ⎤
⎣
⎡
i i
i
RT k E
T 2 , ,
ln
α α α
β (III)
Fig 4. DSC E α dependency on the extent of conversion α
Green plantains (Musa paradisiaca) at green stage of ripeness were processed using DSC and DMTA devices :
¾ DSC and DMTA operating conditions
m o C p
= × β φ
dT C
H
to T
T p
t
= ∫
Δ
H H
tΔ
= Δ
α 3,4
) ( tan ) ( tan
) ( tan ) ( tan
o f
o
T T
T T
δ
δ δ δ
α = − −
Area II (peripheral area) Area I (central area)
DSC procedure in 4 steps Fig 2a Correction of φ (T) lags with β i and
determination in [T o T f ] range Fig 2b Computation of heat capacity (Cp)
with real β values and computation of Δ H in [T o T f ] range
Fig 2c Computation of α Fig 2d Kissinger equation plot
α
α
345 350 355 360 365 370 375 380 385
T (K) 11.6
11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5
Cp (J.K-1.g−1)
ΔH ΔHt
t
Fig. 2b
2.60 2.62 2.64 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.84 2.86
1000/T (K-1) 0.0
0.2
0.4
0.6
0.8
1.0
α
Fig. 2c
-9.8 -9.6 -9.4 -9.2 -9 -8.8 -8.6
2.67 2.731000/T (K-1)2.79 2.85
ln (β/Τ2)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Fig. 2d
-10.3 -10.1 -9.9 -9.7 -9.5 -9.3 -9.1 -8.9
2.74 2.79 2.84 2.89
1000/T (K-1) ln (β/T2)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Fig. 3d To
Tf
Time (min)
Heat Flow Endo up (mW)
Fig. 2a
Fig. 3c
2.74 2.76 2.78 2.80 2.82 2.84 2.86
1000/T (K-1) 0.0
0.2
0.4
0.6
0.8
1.0
α
Fig. 3b
60 70 80 90 100 110
Temperatur e (°C) 0.23
0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32
tan δ
-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020
dtan δ/dT
tan δ dtan δ/dT)
To Tf
Fig. 3a
60 70 80 90 100 110
Temperature (°C) 0.23
0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32
tan δ
