Abstract The temperature dependence of rheologicalparameters as firmness indicators for potato tissue wasdetermined within the temperature range 50–100 °C using four different objective methods. The rate of ther-mal softening of potato tissue by water treatment at50 °C, 90 °C, and 100 °C was consistent with one pseu-do first-order kinetic mechanism, while at 70 °C and80 °C the rate of softening was consistent with two si-multaneous pseudo first-order kinetic mechanisms. Ki-netic theory was suitable to detect an increase of firm-ness through heating at 60 °C, mainly between 20 minand 40 min, presumably by pectinesterase activation.This study shows that two substrates Sa and Sb may beinvolved in providing firmness to potato tissue at 70 °Cand 80 °C. For these temperatures, mechanism 1 is moreprobably due to gelatinization and light cooking, where-as mechanism 2 is more likely to represent the changesof the pectic substances in the cell wall and interlamellarregion. At 90 °C and 100 °C the gelatinization processwas fast and therefore the simple mechanism fitted pre-sumably reflects the degree of solubilization of the pec-tic substances. At 50 °C and 60 °C there was practicallyno gelatinization, so that the simple mechanism fittedpresumably represented incipient solubilization of pecticmaterial. In water heating, gelatinization contributes lessthan the cell wall structure to potato tissue firmness onthe basis of either kinetic parameters or microscopic ob-servations. Maximum breaking compression force andmodulus of rigidity were the most suitable rheologicalparameters for studying the softening of potato tissue inwater heating.

Keywords Potato · Kinetic parameters · Rheologicalproperties · Pectinesterase activity · Water heating

Introduction

Optimal thermal process design relies on relevant andaccurate kinetic data for quality evolution [1]. Nutritio-nal value, texture, color, and flavor are usually damagedto a greater or lesser extent during the thermal process.Texture is one of the major components of quality inmost foods and excessive softening during thermal pro-cessing renders some foods unsaleable. Also, the differ-ent thermal processes involved in the production of fro-zen potatoes affect overall textural quality in differentways. Tissue softening occurs at different rates and isgoverned by different physicochemical mechanisms, andit is therefore necessary to establish softening kineticsand derive kinetic parameters relating to the softeningthat takes place in the tissue in each of the stages com-prising the full production process [2, 3, 4].

As a result of technological advances, the various op-erations entailed in the process of vegetable freezingnowadays take place in different media and/or under dif-ferent processing conditions. Tissue softening inducedby thermal treatments in different media depends on thetemperature reached at the thermal center of the productin the heating medium, and on the heating rate attained.These two parameters determine the shape of the tissuesoftening curves and hence the associated kinetic param-eters.

It was found that applying the theories of chemical ki-netics to the rate of thermal softening of vegetable tissuecould provide useful insights into the softening mecha-nisms, and could point the way to developing technolo-gies that produce firmer-textured processed products,even though the progress of the reaction is measured bya physical test (firmness) instead of a chemical test [5, 6,7]. In most studies quantifying loss of firmness, the ther-mal softening of vegetable tissues has been described byone or two first-order kinetic rate processes [5, 6, 8, 9,

M.D. Alvarez (✉ ) · W. CanetDepartment of Plant Foods Science and Technology, Instituto del Frío-CSIC, Ciudad Universitaria s/n, E-28040 Madrid, Spaine-mail: ifrat44@if.csic.es

M.E. TortosaDepartment of Plant Physiology and Biology, Escuela Técnica Superior de Ingenieros Agrónomos, Ciudad Universitaria s/n, E-28040 Madrid, Spain

Eur Food Res Technol (2001) 212:588–596DOI 10.1007/s002170100295

O R I G I N A L PA P E R

María Dolores Alvarez · Wenceslao Canet María Estrella Tortosa

Kinetics of thermal softening of potato tissue (cv. Monalisa) by water heating

Received: 21 August 2000 / Revised version: 21 November 2000 / Published online: 31 March 2001© Springer-Verlag 2001

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10, 11]. Different authors have used different mechanicalprocedures and generally only one rheological parameteras an indicator of product texture. Kozempel [8], Huangand Bourne [5], and Bourne [6] used a back-extrusiontest cell, taking maximum force readings as a texturemeasurement. Harada et al. [10, 11] and Harada andPaulus [12] used the maximum shear force to character-ize the behavior of potatoes and three other low-starchtubers during cooking. Verlinden et al. [13] used a uni-axial compression test in which the rupture force wastaken as a measure of texture. Paulus and Saguy [14] es-tablished the kinetics of softening of cooked carrots us-ing compressive maximum stress as a measure of thetexture degradation. By estimating kinetic parametersfrom different rheological parameters, it is possible toestablish what rheological parameters are best suited topredict tissue softening and the relationships between theapparent rate constants of the rheological parameters ifdifferent treatment methods are used [4].

Only a few kinetic studies are accompanied by histo-logical analyses and chemical and biochemical studieswith which to ascertain the true role of the main structu-ral components in thermal softening. Changes in texturethat occur during processing result from changes in thechemistry of cell wall and middle lamella hydrophilicpolymer material that affect the physical properties [7,15, 16]. However, in potato tissue, where starch is themajor component of the dry matter, it can be assumedthat the phenomena associated with gelatinization are in-volved in the texture changes during cooking [13, 17].

The aim of this study was to determine kinetic param-eters to characterize the softening of potato tissue by water heating using compression, shear, tension, andstress-relaxation rheological parameters to represent tis-sue firmness, and to determine what structural compo-nents and changes in such components could be contrib-uting to potato tissue firmness during water heating. Ki-netics of thermal softening of potato tissue have alsobeen studied in relation to different heating and cookingmethods. These studies will be published in due course,thus providing a complete characterization of potato tis-sue softening with the various different methods usedand ultimately enabling a comparison of the estimatedkinetic parameters in terms of factors related to tissuesoftening in each one.

Materials and Methods

Test material. The potato samples (Solanum tuberosum, L., cv.Monalisa) came from Segovia (Spain) and consisted of potatoeshaving weights (in grams) within the confidence interval(153.83≤µ≤186.56) and specific weights (g/cm3) within the inter-val (1.0635≤µ≤1.0796); P≤0.01. The material was kept in a coldstore (4 °C and 85% relative humidity) during the experiment. Cy-lindrical samples were prepared by boring, using a cork bore (di-ameter 25.4 mm), and calibrating to a height of 10 mm.

Thermal treatment procedure. Sample treatments under the dif-ferent temperature-time combinations were carried out in a He-tofrig CB60VS waterbath (–30 °C to +110 °C) with a constant

product weight:water volume ratio of 1:20. After treatment witheach temperature-time combination, the product was cooleddown for 3 min to 20 °C throughout the tissue using iced waterwith a constant product weight/iced water volume ratio of 1:5.Water and product temperatures were monitored by K-type ther-mocouples (NiCr/NiAl; –200 °C to +1000 °C) using a hardwareand software system developed with the LabWindows/CVI pack-age (C for Virtual Instrumentation) for automation of the ther-mal process control [18]. The software permitted real-time data-gathering, storage and calculation of either heating and coolingrates.

Mechanical tests. Compression, shear and tension tests were performed using an Instron Food Testing Instrument Model 4501[2, 19]. Ten replicates were performed for each of the mechanicaltests. Stress-relaxation tests were carried out using a TA-HD Texture Analyzer (Stable Micro Systems LTD, Godalming, UK).Five replicates were performed for stress-relaxation tests. Cylin-drical specimens (diameter 25.40 mm, height 10 mm) were com-pressed between parallel plates at a deformation rate of 200 mmmin–1. This test allowed for measurement of the maximum compression force [Fc (N)], the apparent modulus of elasticity [Ec (MPa)] and the energy required for breaking per unit of volume [Uc (µJ mm–3)]. Shear tests were performed on cylindricalspecimens (diameter 25.40 mm, height 10 mm) using a shear cell [16] at a deformation rate of 400 mm min–1 to give the maximum shear force [Fs (N)], the modulus of rigidity [Gs (kPa)],and the shear energy required for breaking per unit of volume [Us (µJ mm–3)]. The tension test was performed on 5-mm-thickbone shaped specimens (dimensions: 75 mm long, 20 mm wide atthe retaining ends, and 8 mm wide at the neck) at a deformationrate of 100 mm min–1, using a cell consisting of two compressed-air clamps (0.15 MPa) fitted to the specimen ends by filter paperto prevent slippage and failure, to give the maximum tension force[Ft (N)], the apparent modulus of elasticity [Et (MPa)], the energyrequired for breaking per unit of volume [Ut (µJ mm–3)], and themaximum deformation [Dt (mm)].

In the stress-relaxation test, cylindrical specimens (diameter25.40 mm, height 10 mm) were compressed to a distance of 2 mm(20% strain based on original size) between parallel plates, at adeformation rate of 400 mm min–1. The deformation was then heldconstant and the specimens were allowed to relax for 1 min fol-lowing deformation. Following previous studies [20, 21], the re-laxed force [Fr (%)] was calculated as

F(1 min)=(F0-Fi)/F0

where F0 is the maximum compression force for deformation of2 mm and Fi is the force recorded after 1 min of relaxation. Therelaxation gradient [Sr (N s–1)] is the slope of the straight line join-ing the maximum compression force and relaxed force points after1 min. The residual relaxation area [Ar (N s)] is the area below thecurve force-time. Since the relaxed force increased with treatmenttemperature and time, the kinetic parameters of this rheologicalproperty were calculated from unrelaxed force [Funr (%)], whichwas obtained as the difference between the total force needed toachieve 20% deformation of the specimen and the relaxed forceafter one minute.

Statistical analysis. In order to compare the mean values obtainedfor rheological parameters in the various samples of potato corre-sponding to different thermal treatments, Statgraphics softwareversion 5.0 was used to perform analyses of variance and LSDtests at a 99% confidence level. The software was also used to cal-culate a regression.

Estimation of kinetic parameters. Time and temperature depen-dencies of the softening of potato tissue during water heating aredescribed using kinetic laws and Arrhenius equations assumingthat each rheological parameter can be considered as a measure-ment of the tissue firmness [4]. In this way, by analogy withHuang and Bourne [5], the conventional chemical kinetics theory

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can be adapted to the experimental data as follows. Let there betwo components contributing to firmness, “a’’ and “b’’. Then:

fast process: ln A=ln A0–Ka×t

and

slow process: ln B=ln B0–Kb×t

where A is the amount of the rapidly degraded firmness due tosubstrate a, and B is the amount of the slowly degraded firmnessdue to substrate b at time t, and A0 and B0 are the quantificationsof the two kinds of firmness due to substrates a and b respectivelyin the untreated potato. Ka and Kb are the apparent first-order soft-ening rate constants.

The temperature dependence of a reaction rate constant can beexpressed by the Arrhenius equation:

K=K0 e-Ea/RT

where K is the reaction rate constant, K0 is the frequency factor,that is the reaction rate constant at T=∞, Ea is the activation ener-gy, R is the universal gas constant, and T is the absolute tempera-ture. By plotting ln K vs 1/T, the slope of the resulting line is Ea/R,which can be used to obtain a value for the activation energy [5, 6,7, 8, 9].

Structural examination. Tissue structure was examined by SEMusing a Hitachi model S-2500 microscope [22]. Tissue sampleswere fixed in 50% or 70% ethyl alcohol (90 ml), glacial acetic ac-id (5 ml), and formol (5 ml) for 2 h and dehydrated in a series ofvolumes of ethanol of increasing concentration, i.e., 70–100%.The samples were immersed for 15 min in each ethanol concentra-tion (70%, 80%, and 90%) and twice for 1 h in 100% ethanol. Fi-nally, the specimens were preserved in acetone until processed in acritical-point drier, then mounted and sputter-coated with platinum(400-Å) in a P-S1 diode sputtering system metallizer. Photomicro-graphs were taken with a Mamiya camera using Ilford 6×9-cm FF-4 film. Films were processed following the standard method;the magnification was ×78 (1 cm=260 µm)

Results and discussion

Figure 1 shows the softening curves obtained for a rheo-logical parameter derived from each of the mechanicaltests performed, by plotting log Fc, log Gs, log Ft, andlog Sr vs process time in the range of temperature studied. Although not shown, similar curves were ob-tained for most of rheological parameters and processconditions. A comparison of the plots indicates that at50 °C, although little had changed, as well as at 90 °Cand 100 °C, the softening curves are mostly representedby a rectilinear plot, and therefore simple first-order ki-netics can be applied to express the tissue softening atthese temperatures. At 60 °C, many rheological parame-ters detected a firmness effect, which was especially no-ticeable between 20 min and 40 min (Fig. 1). However,at 70 °C and 80 °C most of the parameters showed quali-tatively similar softening curves, characterized by an ini-tial steep negative slope that was almost linear but whichcurved off into a second straight line with a shallow neg-ative slope at longer process times. The shape of theseexperimental curves was similar to that obtained for thesum of two independent simultaneous first-order pro-cesses occurring at different rates [7]. Some rheologicalparameters produced exceptions. The shape of log Etat 50 °C, log Uc, log Funr, and log Ar at 60 °C, and theshape of log Sr at 90 °C, were also consistent with twofirst-order processes.

Tables 1 and 2 show the kinetic parameters obtainedfor compression and shear, and tension and stress-relax-ation rheological parameters respectively. These parame-ters are: the apparent first-order rate constant Ka for

Fig. 1 Softening curves forrheological parameters in waterheating

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mechanism 1 and the apparent first-order constant Kb formechanism 2 (calculated from the lines of best fit); thefrequency factor K0 and the apparent activation energyEa calculated from mechanism 1; the total firmness [rep-resented by the value of the rheological parameter at zero process time from mechanism 1 (F01)], and theamount of firmness that is resistant to degradation [inter-cept on the y axis (F02)], as well as their ratios (F02/F01)for the temperatures and rheological parameters in whichthe rate of softening was consistent with two simulta-neous first-order kinetic mechanisms. Correlation coeffi-cients (r) for the lines of best fit are also included.

The apparent rate constants (Ka) for mechanisms 1 in-creased linearly with temperature and in all cases weregreater than the apparent rate constants (Kb) for mecha-nisms 2 at 70 °C and 80 °C. Also, the latter were greaterat 80 °C than at 70 °C. However, at 60 °C, apparent rateconstants for mechanisms 1 calculated from compres-sion, shear, and tension rheological parameters werelower, or in some cases only slightly higher, than the

constants estimated at 50 °C. In water heating of potatotissue this could be the response to activation of the pec-tinesterase enzyme at 60 °C; the activity was especiallysignificant in the time range 20–40 min. Plots indicatethat modulus of rigidity and relaxation gradient at 60 °Cbetween 20 min and 40 min were higher than those ob-tained for lower treatment times (Fig. 1). Indeed, for thisreason it was not possible to obtain apparent rate con-stant at 60 °C for the maximum deformation in tension(Table 2). These results are consistent with the findingsof other researchers. Optimum conditions for stepwiseblanching of frozen/thawed potato tissues were in tem-perature and time ranges of 60–65 °C and 25–35 min us-ing different rheological parameters to detect the firmingeffect of pectinesterase enzyme [23]. Also, stationarypoints for the first step of stepwise blanching showingmaximum PE activity exhibited critical temperature andtime values at 64.39 °C and 28.02 min after freezing andsteaming of potato tissue [3]. PE activity retention was50% of fresh tissue activity in water heating at 60 °C for

Table 1 Kinetic parameters for compression and shear rheological parameters in water heating

Rheological T (°C) Mechanism 1 Mechanism 2 ra rb K0 (min–1) r Total Residual Firmnessparameter Ka (min–1) Kb (min–1) Ea (kJ/mole) firmness firmness ratio

(F01) (F02) (F02/F01)

(Fc) 50 1.021E–3 – –0.978 – 704.389 – –60 6.185E–4 – –0.959 – 4.1×1013 675.149 – –70 4.899E–3 1.610E–3 –0.985 –0.990 104.404 –0.957 704.693 561.040 0.79680 0.021 3.840E–3 –0.968 –0.969 713.181 352.209 0.49490 0.050 – –0.989 – 698.876 – –

100 0.074 – –0.992 – 648.485 – –(Ec) 50 1.167E–3 – –0.970 – 4.559 – –

60 8.325E–4 – –0.826 – 1.5×1011 4.224 – –70 6.888E–3 8.828E–4 –0.968 –0.993 88.203 –0.945 4.601 3.074 0.66880 0.025 4.300E–4 –0.980 –0.999 4.543 2.277 0.50190 0.029 – –0.941 – 3.985 – –

100 0.046 – –0.985 – 4.142 – –(Uc) 50 1.010E–3 – –0.860 – 389.404 – –

60 7.235E–3 7.345E–4 –0.921 -0.804 1.5×1010 394.639 336.434 0.85270 0.017 6.186E–4 –0.950 –0.878 79.602 –0.947 395.822 237.793 0.60180 0.040 2.366E–3 –0.936 –0.967 348.739 210.911 0.60590 0.042 – –0.982 – 391.291 – –

100 0.066 – –0.994 – 376.877 – –(Fs) 50 2.867E–4 – –0.988 – 92.760 – –

60 3.324E–4 – –0.864 – 2.2×1015 92.982 – –70 5.115E–3 2.064E–4 –0.978 –0.996 117.367 –0.966 94.428 71.482 0.75780 0.017 2.878E–3 –0.885 –0.971 89.929 72.728 0.80990 0.022 – –0.975 – 85.566 – –

100 0.058 – –0.992 – 99.747 – –(Gs) 50 3.652E–4 – –0.899 – 16.640 – –

60 8.016E–4 – –0.860 – 7.0×1012 17.723 – –70 5.460E–3 6.708E–4 –0.983 –0.999 100.491 –0.980 16.846 14.676 0.87180 0.015 1.610E–3 –0.912 –0.936 16.580 13.029 0.78690 0.021 – –0.991 16.364 – –

100 0.041 – –0.979 16.147 – –(Us) 50 5.574E–4 – –0.956 – 249.345 – –

60 4.525E–4 – –0.672 – 1.8×1015 244.568 – –70 3.765E–3 – –0.998 – 116.127 –0.972 248.085 – –80 0.012 – –0.990 – 235.830 – –90 0.051 – –0.990 – 260.315 – –

100 0.079 – –0.994 – 269.463 – –

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60 min [24]. Also, Moledina et al. [25] reported 83% re-tained PE activity for water blanching at 60 °C for30 min and none at 75 °C for 10 min. Many theories toaccount for the effect of the blanching under certain tem-perature-time conditions on the firmness of vegetable tis-sues attribute this to pectinesterase activity. Under cer-tain conditions, heating causes a loss of membrane selec-tive permeability, giving rise to diffusion of cations tothe cell wall. This activates the enzyme, leading to thede-esterification of pectins, and facilitates the formationof divalent bridges between residues of galacturonic acidbelonging to adjacent pectic chains. The divalent ionpectin complex thus formed acts as an intercellular ce-ment to give firmness to tissues [3, 16, 24, 25, 26]. Inspite of the firmness effect detected by the rheological

properties at 60 °C, it was possible to estimate kineticparameters for most of the parameters used as firmnessindicators although, as the tables show, the fits of therheological parameters at 60 °C had the lowest correla-tion coefficients, because the experimental values did notpresent a clear tendency to decrease with increased treat-ment time. Figure 2 shows typical Arrhenius plots for Fc,Gs, Ft, and Sr. These parameters offered the best fits fromeach mechanical test. The rate constants of the firstmechanisms at 60 °C (3×10–3 K–1) were the least linear;this effect is mainly apparent in plots for maximum com-pression and tension forces (in plots, rate constants at60 °C are circled). This could be another consequenceand evidence of the fact that in the experimental potatovariety the optimum temperature for activation of the PE

Table 2 Kinetic parameters for tension and stress-relaxation rheological parameters in water heating

Rheological T (°C) Mechanism 1 Mechanism 2 ra rb K0 (min–1) r Total Residual Firmness parameter Ka (min–1) Kb (min–1) Ea (kJ/mole) firmness firmness ratio

(F01) (F02) (F02/F01)

(Ft) 50 1.219E–3 – –0.992 – 26.260 – –60 6.553E–4 – –0.932 – 4.3×1012 25.119 – –70 7.820E–3 1.647E–3 –0.993 –0.977 97.516 –0.929 25.698 22.620 0.88080 0.033 4.696E–3 –0.970 –0.998 25.165 19.120 0.76090 0.047 – –0.992 – 23.714 – –

100 0.057 – –0.982 – 22.403 – –(Et) 50 4.207E–4 1.078E–3 –0.980 –0.976 K01=6.0×1021 3.478 1.777 0.511

60 0.011 1.084E–3 –0.999 –0.996 Ea1=153.826 –0.949 3.357 1.939 0.57870 0.026 1.587E–3 –0.964 –0.903 K02=6.4×109 3.188 1.972 0.61880 0.068 2.906E–3 –0.970 –0.952 Ea2=80.906 –0.911 3.156 1.622 0.51490 0.029 – –0.832 – 2.181 – –

100 0.038 – –0.892 – 2.193 – –(Ut) 50 1.165E–3 – –0.980 – 164.059 – –

60 9.992E–4 – –0.804 – 2.5×1014 166.112 – –70 2.466E–3 – –0.912 – 109.194 –0.952 165.577 – –80 0.021 7.900E–3 –0.999 –0.978 161.102 94.406 0.58690 0.087 – –0.981 – 152.265 – –

100 0.101 – –0.990 – 150.235 – –(Dt) 50 4.627E–4 – –0.628 – 10.924 – –

60 – – – – 1.1×1012 – – –70 –1.108E–3 – –0.929 – 96.317 –0.955 10.782 – –80 4.230E–3 – –0.983 – 10.437 – –90 0.028 – –0.977 – 11.285 – –

100 0.035 – –0.964 – 11.092 – –(Funr) 50 3.469E–3 – –0.989 – 43.762 – –

60 0.013 1.131E–3 –0.995 –0.953 1384.092 41.248 28.536 0.69270 0.019 1.724E–3 –0.910 –0.981 33.313 –0.845 39.655 27.498 0.69380 0.012 – –0.843 – 30.620 – –90 0.022 – –0.896 – 32.923 – –

100 0.026 – –0.890 – 31.769 – –(Sr) 50 1.482E–4 – –0.939 – –2.534 – –

60 3.225E–4 – –0.486 – 8.1×1014 –2.627 – –70 3.160E–3 4.814E–4 –0.979 –0.987 115.682 –0.971 –2.520 –2.206 0.87580 0.013 4.500E–4 –0.945 –0.837 –2.446 –1.839 0.75290 0.016 5.240E–3 –0.934 –0.958 –2.505 –2.123 0.847

100 0.029 – –0.894 – –1.842 – –(Ar) 50 3.213E–3 – –0.986 – 8476.177 – –

60 0.017 1.329E–3 –0.958 –0.939 1.1×105 7493.764 3901.216 0.52070 0.036 1.713E–3 –0.936 –0.990 44.959 –0.801 7309.708 2901.376 0.53480 0.013 – –0.797 – 5279.588 – –90 0.026 – –0.859 – 5704.269 – –

100 0.066 – –0.977 – 6821.816 – –

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enzyme is close to 60 °C. Huang and Bourne [5] pro-posed that two substrates Sa and Sb could be involved inproviding firmness in several canned vegetables duringthe retort process, with mechanism 1 acting on substrate“a’’ and mechanism 2 acting on substrate “b’’. This hy-pothesis has also been more widely used to explain thesoftening of vegetable tissues by cooking [9, 13]. Mech-anism 1 was attributed to pectic changes in the interla-mellar layer. Low temperature blanching activated thepectinesterase system in carrots and green beans, but thefirmer texture was attributed primarily to an increase inthe amount of the slow softening substrate and not tochanges in the apparent first-order rate constants [6, 7].Rheological parameters from stress-relaxation test weresuitable for detecting pectinesterase activity at 60 °C(Fig. 1), but the apparent rate constants obtained fromthese parameters at that temperature were higher than at50 °C according to these researchers. However, rate con-stants at 60 °C were lower than rate constants for com-pression and tension forces, modulus of elasticity incompression and shear and tension energies, the best fitbeing found for the maximum compression force (highercorrelation coefficient at 60 °C). These results indicatethat the kinetic theory can validly be applied to thermalsoftening of tissue in water to account for the activity ofthe PE enzyme, the kinetic parameters showing that thetissue was firmer at 60 °C than at 50 °C.

However, it has also been shown that gelatinization isinvolved in potato texture degradation in cooking at dif-ferent temperatures [13]. These authors developed acompartmental texture model where two quantities wereconsidered which contribute to the overall texture. The

first is due to the ungelatinized starch and the second isdue to the cell wall structure. The overall texture was as-sumed to be due to the additive effect of both, althoughthe gelatinization process was simulated using the gela-tinization kinetics found by Pravisani et al. [17]. It wasconcluded that in a first range of cooking time and tem-perature combinations, texture changes and gelatiniza-tion occurred together, whereas in the second cookingtime range, the gelatinization process was fully complet-ed and starch gelatinization did not affect the texturechange. The authors concluded that the ungelatinizedstarch fraction contributed only 11% of the initial overalltexture.

Scanning electron micrograph A in Fig. 3 shows asection of potato tissue treated for 20 min at 50 °C.There was no detectable gelatinization and the structureof starch granules appeared intact and well-defined.Starch granules are mostly small and oval or spherical.They are located in the interior of the cytoplasm veryclose to the cell walls, which are thin and slightly plas-molyzed. Ungelatinized starch could account for the sim-ple first-order mechanism fitted for rheological parame-ters at 50 °C, which would be the response to incipientsolubilization of the pectic substances. Verlinden et al.[13] found that at 60 °C the gelatinization process in po-tatoes was very slow, and after 20 min only 1–5% of thestarch had been gelatinized. Photomicrograph B shows atissue treated under these last conditions; it can be seenhow there are only some partially gelatinized granules,which appear hydrated and slightly deformed. The hy-dration of the starch was accompanied by swelling ofsome granules. Similarly, the low rate and extent of gela-

Fig. 2 Arrhenius plots of ln apparent rate constants vs re-ciprocal absolute temperaturefor potato tissue treated in water

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tinization at 60 °C could account for the simple first-order mechanism fitted for this temperature. Note howthe cell walls are folded without any apparent cracking,which may be the response to the biochemical processesassociated with PE activation at 60 °C. In the tissuetreated at 70 °C for 20 min (Fig. 3C), starch granule gel-atinization was also partial if appreciable and was ac-companied by expansion of the granule volume. Many ofthe granules still retain their original shape. Gelatiniza-tion involved loss of crystallinity of the granules as com-pared to the tissue treated at 50 °C. In the tissue treatedat 80 °C for 5 min (Fig. 3D), there is greater swellingand gelatinization of the granules and more plasmolysis,although again gelatinization is not complete. Waterheating at 82 °C and 75 °C required 4 min and 5 min re-spectively to produce complete gelatinization of thegranules; however after cooking at 90 °C for 3 min andat 100 °C for 2 min, potato starch is completely gelati-nized [13]. In our own tissues treated at 90 °C for 5 min(Fig. 3E) and at 100 °C for 10 min (Fig. 3F), completegelatinization was achieved, with total deformation andfusion of the granules, which filled the cell. The fit of

two pseudo first-order mechanisms to characterize thesoftening at 70 °C and 80 °C may be the response to thefact that over very short times at these temperatures, po-tatoes undergo starch gelatinization and they cook slow-ly. Mechanisms 1 would reflect gelatinization and only aslight degree of cooking (gelatinization process pluscooking) [8], whereas mechanisms 2 fitted for longertimes may reflect the solubilization of the pectic sub-stances in the cell wall and middle lamella (cooking) [7].On the other hand, at 90 °C and 100 °C, a rate of soften-ing consistent with a simple mechanism is justified bythe fact that the gelatinization process reached equilibri-um or was completed rapidly over very short treatmenttimes; these simple mechanisms would reflect the solubi-lization of the pectic material in the cell wall and middlelamella by cooking. Figure 2 shows that the rate con-stants at 80 °C (2.83×10–3 K–1) are also nonlinear, main-ly as derived from an Arrehnius plot for relaxation gradi-ent; this could be due to biochemical processes associat-ed with the advance of gelatinization at 80 °C.

In the temperature range studied, apparent activationenergies are mostly within the range 40–125 kJ/mole,

Fig. 3 A Potato tissue treatedfor 20 min at 50 °C in water.B Potato tissue treated for20 min at 60 °C in water.C Potato tissue treated for20 min at 70 °C in water.D Potato tissue treated for5 min at 80 °C in water.E Potato tissue treated for5 min at 90 °C in water.F Potato tissue treated for10 min at 100 °C in water.1 cm=260 µm

which is suggested as being typical for the loss of tex-ture, color and flavor [27]. Estimation of the activa-tion energy from Gs had the best correlation coefficient(Table 1), which was very close to the value reported byother researchers [7, 8, 13]. The lowest activation ener-gies were given by the unrelaxed force and the residualrelaxation area, indicating that these parameters under-went less drastic changes with the temperature. Thehighest value was obtained from maximum shear force.It is worth noting the two pseudo first-order mechanismswhich were fitted for the apparent modulus of elasticityin traction at 50 °C, 60 °C, 70 °C, and 80 °C. From thiswe were able to derive an Arrhenius model for eachmechanism separately, and hence the apparent activationenergy for each one (Table 2). From the Arrhenius equation for mechanism 1 a frequency factor was derived K0=6×1021 min–1 and Ea/R=18502.10 K. Fromthe Arrhenius equation for mechanism 2 a value ofK0=6.4×109 min–1 and Ea/R=9731.28 K was derived. Ac-tivation energy for mechanism 2 is lower than activationenergy for mechanism 1, as was pointed out by Huangand Bourne [5] for other vegetables. These authors pro-posed the term “thermal firmness” to designate theamount of substrate Sb present in the tissue at zero treat-ment time (designated here as F02) and considered thisvalue to be a good indicator of how firm the product willbe after processing. By analogy, the term “radiation firm-ness” was proposed to describe the amount of firmnessthat is resistant to degradation by irradiation in carrots[28], and also the term “frozen storage firmness” to de-scribe the amount of firmness that is resistant to degrada-tion by freezing with temperature fluctuations duringfrozen storage and final thawing of potato tissue [2].However, Harada et al. [11] showed that the total firm-ness (F01) and the residual firmness (F02) varied depend-ing on the variety and lot of potatoes. Kozempel [8] pro-posed that the ratio of texture to the original texture(F02/F01) be used as a measure of the amount or degreeof cooking. By choosing firmness ratios of the rheologi-cal parameters with the best fits from each mechanicaltest (Fc, Gs, Ft, and Sr), we find that substrate “b’’ con-tributed between 80% and 88% at 70 °C and between49% and 79% at 80 °C to the total firmness of the freshpotato tissue. The high percentages of the total firmnessretained in the tissue after mechanisms 1 at 70 °C and80 °C reflect the low degree of cooking produced by wa-ter heating at these temperatures. Thus, although at thesetemperatures the first of the mechanisms found could in-deed be attributed mostly to gelatinization, the resultstend to confirm that gelatinization determines the tissuepotato softening caused by water heating only to a limit-ed extent. However, under other heating methods, the ef-fect of gelatinization on tissue softening could be moreimportant.

In order to ascertain whether the rate constant formechanism 1 was independent of the mechanical test, weused the same four rheological parameters Fc, Gs, Ft, andSr. Since the four groups of rate constants correlated sowell, (correlation coefficients varied between 0.95 and

0.99), and since the Arrhenius plots of these propertieswere very similar (Fig. 2), it was concluded that the rateconstant is independent of the mechanical test used, pro-vided that the kinetic parameters are calculated fromthese mechanical properties.

The rate of thermal softening of potato tissue in watertreatment at 50 °C, 90 °C, and 100 °C is consistent withone pseudo first-order kinetic mechanism, while at 70 °Cand 80 °C the rate of softening is consistent with two si-multaneous pseudo first-order kinetic mechanisms. Al-though the first mechanism found for these last two tem-peratures may reflect the gelatinization process, theircontribution to thermal softening is very limited and isdetermined mainly by the degree of solubilization of thepectic substances, once the starch is gelatinized. Kinetictheory was found to be suitable for detecting higherfirmness in water heating at 60 °C, mainly between20 min and 40 min, presumably the result of pectinester-ase activation. Maximum compression force and modu-lus of rigidity were the best rheological parameters forestablishing the kinetics of thermal softening of potatotissue by water heating.

Acknowledgements We are indebted to the CICyT for financialsupport (project ALI98–1055) and to the Comunidad de Madridfor the postdoctoral scholarship granted to author MD Alvarez.The authors wish to thank M.C. Rodríguez for technical assistancewith the SEM.

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