Mechanisms of folate losses during processing: Diffusion vs. heat degradation

Abstract

Though folates are sensitive to heat treatments, leaching appears to be a major mechanism involved in folate losses in vegetables during processing. The aim of our study was to study folate diffusivity and degradation from spinach and green beans, in order to determine the proportion of each mechanism involved in folate losses.
Folate diffusivity constant, calculated according to Fick’s second law (Crank, 1975), was 7.4 × 10−12 m2/s for spinach and 5.8 × 10−10 m2/s for green beans, which is the same order of magnitude as for sugars and acids for each vegetable considered. Folate thermal degradation kinetics was not monotonous in spinach and green beans especially at 45 °C and did not follow a first order reaction. The proportion of vitamers changed markedly after thermal treatment, with a better retention of formyl derivatives. For spinach, folate losses were mainly due to diffusion while for green beans thermal degradation seemed to be preponderant.

Full text

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Mechanisms of folate losses during processing: diffusion vs. heat degradation. 5
6
Nicolas Delchiera,b; Christiane Ringlingc; Jean-François Maingonnata,b; Michael Rychlikc,d; 7
Catherine M.G.C. Renarda,b,*. 8
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a INRA, UMR408 Sécurité et Qualité des Produits d'Origine Végétale, Domaine Saint Paul, 10
Site Agroparc, F-84000 Avignon, France. 11
b Université d'Avignon et des Pays du Vaucluse, UMR408 Sécurité et Qualité des Produits 12
d'Origine Végétale, F-84000 Avignon, France. 13
c Bioanalytik Weihenstephan, Research Center of Nutrition and Food Sciences, Technische 14
Universität München, Alte Akademie 10, D-85354, Freising, Germany. 15
d Chair of Analytical Food Chemistry, Technical University of Munich, Alte Akademie 10, D-16
85354, Freising, Germany. 17
18
* Corresponding author: nicolas.delchier@gmail.com 19
INRA – UMR 408 SQPOV 20
Domaine St Paul, Site Agroparc 21
F-84000 Avignon, FRANCE 22
Phone: +33 (0)4.32.72.25.28 Fax: +33 (0)4.32.72.24.92 23
24 © 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license 25
http://creativecommons.org/licenses/by-nc-nd/4.0/ 26
27
Published in:
Food Chemistry, 157 (2014) 439-447
The final publication is available at Elsevier via https://doi.org/10.1016/j.foodchem.2014.02.054

Highlights: 28
1. pH and temperature have no effect on folate diffusivity constant 29
2. Vegetable matrices have effect on diffusivity constant 30
3. Folate stability during thermal treatment depend on their nature 31
32
Abstract: 33
Though folates are sensitive to heat treatments, leaching appears to be a major mechanism 34
involved in folate losses in vegetables during processing. 35
The aim of our study was to study conjointly folate diffusivity and degradation from spinach 36
and green beans, in order to determine the proportion of each mechanism involved in folate 37
losses. 38
Folate diffusivity constant, calculated according to Fick’s second law (Crank, 1975), was 39
7.4×10-12 m
2/s for spinach and 5.8×10-10 m
2/s for green beans, which is the same order of 40
magnitude as for sugars and acids for each vegetable considered. Folate thermal degradation 41
kinetics was not monotonous in spinach and green beans especially at 45 °C and did not follow 42
a first order reaction. The proportion of vitamers changed markedly after thermal treatment, 43
with a better retention of formyl derivatives. For spinach, folate losses were mainly due to 44
diffusion while for green beans thermal degradation seemed to be preponderant. 45
46
47
48
Keywords: 49
Vitamins; folate; vegetables; process; leaching; heat degradation; kinetics; Fick’s second law 50
51

Introduction 52
Folate is the generic term used for different water-soluble vitamers which differ by the nature 53
of carbon groups linked to nitrogen 5 or 10, the oxidative state and the length of the glutamate 54
tail. They are involved in the “one carbon metabolism” especially being donor of methyl group 55
during DNA synthesis. It is well established that folates can protect against neural tube defects 56
(Czeizel & Dudás, 1992) and neurodegenerative diseases (Snowdon, Tully, Smith, Riley & 57
Markesbery, 2000). Folates are also involved in the methylation of homocysteine, which is one 58
risk factor for heart diseases (Robinson, 2000). 59
One of the main contributors for folate intake are vegetables and particularly green vegetables, 60
which represent circa 40 % of the folate intake in the French diet (Lafay, 2009). In France, 61
authorities recommend an intake of folate from 300 µg per day for women to 330 µg per day 62
for men, with an increase to 1 mg per day during pregnancy (ANSES). However, there is a gap 63
between the real and the recommended intake from around 20 % for women to 15 % for men 64
(Lafay, 2009). 65
Evolution of lifestyles means that most of fruits and vegetables are consumed after processing, 66
whether domestic processing (cooking, heating, microwaves) or industrial processing such as 67
canning or freezing, hence there is a need to better understand the impact of processing on 68
folate content. 69
Folate losses from spinach during boiling or blanching represent 20 to 80 % of initial folates 70
and from 0 to 20 % in green beans (Klein, Lee, Reynolds & Wangles, 1979; Desouza & 71
Eitenmiller, 1986; McKillop et al., 2002; Melse Boonstra et al., 2002; Delchier, Reich & 72
Renard, 2012). However steaming and microwave cooking did not cause folate losses (Klein et 73
al., 1979; McKillop et al., 2002; Delchier et al., 2012). Few studies measured folates in cooking 74
liquids but Delchier et al. (2012) showed that leached folates represent half of folate losses 75
from fresh spinach and the whole of folates losses from frozen spinach and green beans, after 76

boiling in water. Data concerning the impact of industrial processing on folate losses is really 77
scarce. Our previous study showed that blanching had no effect on folate losses both during 78
spinach freezing process and green beans canning process. Losses occur during the washing 79
step for spinach and after sterilization for green beans, with folate found in the covering liquid 80
(Delchier et al., 2013). 81
These study on folate loss during industrial processing led us to suspect that diffusion may play 82
a major role in folate loss, especially when heating steps are limited. 83
Therefore this study aims to determine the relative importance of diffusion and thermal 84
degradation during spinach and green beans heat treatments. For this, two parallel experiments 85
were set up: one in which vegetables were only subjected to heat, and one in which they were 86
subjected to heat and diffusion. 87
88

2. Material and methods 89
2.1. Plant material 90
2.1.1. Diffusion 91
Fresh spinach and green beans were bought at a local supermarket on the day of the 92
experiments or stored at 4 °C for maximum of 48 h after purchase. Spinach and green beans 93
were first blanched in phosphate buffer pH 7 (0.01 mol/L) or in citrate phosphate buffer pH 5 94
(0.01 mol/L) for 10 min at 100 °C with solid-liquid ratio of 50 g/L and 100 g/L respectively, in 95
order to inactivate enzymes and destroy cell compartmentalization. After blanching, spinach 96
and green beans were drained, weighted and immediately put into a large receptacle (with the 97
same solid-liquid ratio of 50 g/L), to start the diffusion. 98
99
2.1.2. Thermal degradation 100
Purees were prepared from spinach and green beans stored in cans bought at local supermarket 101
in two batches for each temperature condition. Cans were opened and vegetables were drained. 102
200 g of vegetables were put into 400 mL of water and ground with an UltraTurax (S25 18G, 103
IKA, Staufen, Germany) at 13,000 rpm for 1 min. Spinach purees were diluted, for facilitating 104
stirring during time course. For this purpose, 50 ml of water was added to 50 mL of spinach 105
puree. 106
107
2.2. Time course experiments 108
2.2.1. Diffusion 109
Diffusions experiments were carried out in phosphate buffer pH 7 (0.01 mol/L) or citrate 110
phosphate buffer pH 5 (0.01 mol/L), under stirring. Temperature and pH were monitored and 111
controlled all along the time course, which were performed for three temperatures (25, 45 and 112

65 °C) and at pH 5 and pH 7 during 4 h. At pH 7, three batches of spinach and green beans 113
were independently studied and two batches at pH 5. 114
For each kinetic point, an aliquot of 35 g of spinach or green beans was collected and directly 115
stabilized by freezing in liquid nitrogen, and stored at - 80 °C until analysis. The folate content 116
was determined in the vegetables at each point along the time course. 117
118
2.2.2. Thermal degradation 119
Heat degradation was carried out in a beaker immersed in a water bath. Purees were stirred all 120
along the experiments by a propeller stirrer of 55 mm diameter turning at 600 rpm (VOS 16, 121
VWR, Fontenay sous bois, France). Time courses were performed in two independent batches 122
for three temperatures: 45, 65 and 85 °C. Purees were heated and kinetics started when they 123
were at the desired temperature. 10 mL of puree were sampled at different points during 4 h 124
and directly put at -80 °C. 125
126
2.3. Modelling 127
2.3.1. Diffusion 128
Diffusivity constant (D) was calculated for folates, sugars and acids according to Fick’s second 129
law (Equation 1): 130
2
2
r
C
D
t
C




 (1) 131
Where C represents the concentration, t the time and r a characteristic distance. 132
Spinach leaves were considered as a plane sheet where Fick’s second law solution, given by 133
Crank (1975), is (Equation 2): 134





















2
2
2
02
2
04
12
exp
12
8
1
)(
l
tnD
n
CC
CtC
n


(2)
135
Where C(t) is the concentration at time t, C0 is the initial concentration and C∞ the 136
concentration at infinite time, D the diffusivity constant and l the half thickness of the plane. 137
In case of green beans, diffusivity constant was determined according to the cylinder solution 138
given by Crank (1975) (Equation 3): 139

tD
aCC
CtC
n
nn
2
1
22
0
exp
4
1
)(









(3)
140
Where C(t) is the folates concentration at t time, C0 is the initial concentration and C∞ the 141
concentration at infinite time, D the diffusivity constant and a the radius. In this equation αn is 142
the root of Bessel function of order 0 (Equation 4). 143

0
0
n
aJ

(4) 144
The model was adjusted by maximizing the correlation coefficient r2 calculated as follow 145
(Equation 5): 146












 

2
2
21
Th
mExp
ThExp
r (5) 147
Where Exp is the experimental concentration; Th is the theoretical data obtained by modelling, 148
and mTh is the mean of theoretical data obtained by modelling. 149
150
2.3.2. Thermal degradation 151
Linearization of folate thermal degradation was carried out according to the mean of the two 152
batches for each temperature studied, using a first order with partial conversion model, as 153
described below (Equation 6): 154

kt
C
C








0
ln (6) 155
Where C is the folate concentration, C0 is the initial folate concentration, k is the degradation 156
rate constant and t the time. 157
158
2.3. Analytical procedures 159
2.3.1. Folate measurement 160
2.3.1.1. Total folates content 161
Total folate content was determined by HPLC with fluorimetric detection. After extraction all 162
folate vitamers were deconjugated into mono and diglutamate, reduced and methylated into 5-163
CH3-H4folates. The latter were purified from the extract by affinity chromatography using 164
Folate Binding Protein, and quantified by RP-HPLC with fluorimetric detection (RF-1AXL, 165
Shimadzu inc., Kyoto, Japan). For experimental details, see Delchier et al. (2013). 166
167
2.3.1.2. Stable isotope dilution assay 168
Before extraction, labelled standards of folate vitamers were added and all folates were 169
deconjugated into their monoglutamate forms. Vitamers were purified on SPE SAX cartridges 170
after adding acetonitrile (10 mL) and centrifugation. Folate analysis was carried out on an 171
HPLC (Shimadzu inc., Kyoto, Japan) coupled with a triple quadrupole mass spectrometer (API 172
4000 Q-Trap, AB-Sciex, Foster City, CA, USA). A Pro-C18 HPLC-column (150 x 3, 3 µm, 173
130 Å, YMC, Japan) with water plus 0.1 % (v/v) formic acid (A) and acetonitrile plus 0.1 % 174
(v/v) formic acid (B) as mobile phases was used. The gradient started at 5 % B. After a linear 175
increase to 10 % B in 5 min and holding this condition for 5 min, another linear increase to 176

15 % B during 10 min and to 50 % B in 2 min, which was maintained for 2 min. Within 2 min 177
B was decreased linearly to 5 % and the column was equilibrated for 9 min. 178
Concentration of the single vitamers in the food samples was calculated using the response 179
factors reported recently (Ringling & Rychlik, 2013). For more experimental details see 180
Ringling & Rychlik (2013). 181
182
2.3.2. Acid and sugar measurement 183
Acid and sugar concentrations were determined by spectrophotometry (Xenius, Safas, Monaco) 184
by determining concentrations of NADPH and NADH respectively, at 340 nm using enzymatic 185
kits. Enzymatic kits for citric acid (reference: 10.139.076), for malic acid (reference: 186
10.139.068), for glucose (reference: 10.716.251), for fructose (reference: 10.139.106) and for 187
sucrose (reference: 10.716.251) were obtained from R-Biopharm (Darmstadt, Germany). 188
Sugars and acids were extracted from 200 mg of spinach or green beans powder, to which 189
1 mL of deionised water was added. The mix was stirred for 1 min and then centrifuged 190
(Bioblock Scientific 1K15, Illkirch, France) for 10 min at 7400 g at 4 °C. 5 µL of supernatant 191
were pipetted into the microplate. 250 µL of enzymatic reagents were added. 192
The concentrations were determined against external calibration from 0 to 1 g/L for citric and 193
malic acids, from 0 to 2 g/L for fructose and glucose and from 0 to 4 g/L for sucrose. 194
195
196

3. Results 197
3.1. Thermal degradation 198
In spinach, for each temperature the folate concentration decreased over time, with appearance 199
of a plateau at 120 min at 45 °C, 60 min at 65 °C and 30 min at 85 °C (Fig. 1). However, this 200
decrease was not monotonous, concentration increased particularly between 10 and 20 min at 201
45 °C. For each temperature, the difference in concentrations between the two batches was 202
relatively low. For all temperatures, degradation of the folates under study was not complete, a 203
plateau was reached with C∞/C0 ratio of 40 % at 45 °C, 42 % at 65 °C and 48 % at 85 °C. 204
In green beans, evolution of folate concentrations at 45 °C showed an increase in the first 20 205
min, which was more marked for batch 2, followed by a decrease until reaching a plateau at 206
120 min (Fig. 1). At higher temperatures the concentration decrease was monotonous, except at 207
60 min, and 65 °C, for the two independent kinetics. This decrease reached a plateau at 90 min 208
for the two batches at 65 °C and at 20 min for the two batches at 85 °C. Variability between 209
batches for each temperature was low. Overall, temperature accelerated folate degradation, the 210
plateau being reached more rapidly at 85 °C than at 65 °C or 45 °C. However, folates 211
degradation was not complete; the level of the C∞/C0 ratio was 20 % both at 45 °C and 65 °C. 212
Folate thermal degradation kinetics were modeled using first order with partial conversion. 213
However, this model was not satisfying at 45 °C, where the folate concentration increased in 214
the first minutes of the kinetics. 215
216
3.2. Folate losses during diffusion 217
3.2.1. Total folate 218
Total folate concentration was determined in vegetables by HPLC with fluorimetric detection 219
after precolumn derivatization, and expressed as 5-CH3-H4folate in mg/kg of fresh weight. 220

For spinach, the folate concentration at the beginning of the experiments, for both pH and the 221
three temperatures studied, varied slightly between different batches. In all conditions, the 222
folate concentration first decreased rapidly over time. This decrease was exponential until 223
reaching a plateau after 60 min (data not shown). For green beans, the folate concentration at 224
the beginning of the diffusion time course was the same (about 0.2 mg/kg expressed in fresh 225
material) for both pH and temperatures studied. The decrease in folate concentration was much 226
more dependent on temperature. Thus, at pH 5 and 25 °C the folate content was almost stable. 227
However, it decreased at 45 °C and more markedly at 65 °C. Folate decrease appeared to be 228
exponential until reaching a plateau at 120 min, at least at 65 °C (data not shown). 229
The decrease in folate was faster for spinach than for green beans at the beginning of the time 230
course. The plateau was also reached faster for spinach than for green beans with a higher level 231
for green beans than for spinach. Indeed, the residual ratio in spinach (Table 1), expressed by 232
the ratio C∞/C0 at the plateau, was on average 26 % of the initial concentration at pH 7 and in 233
the same order of magnitude at pH 5. At pH 7, temperature had no effect on residual ratio while 234
at pH 5 temperature had an effect especially at 65 °C. For green beans, the residual ratios 235
(C∞/C0) were on average 62 % of the initial concentration at pH 7 and 72 % of the initial 236
concentration at pH 5 (Table 1). Temperature seemed to have an effect on the residual ratio 237
both at pH 7 (from 0.7 at 25 °C to 0.41 at 65 °C) and at pH 5 (from 1.17 at 25 °C to 0.43 at 65 238
°C). 239
Finally, the folate residual ratios (C∞/C0) were lower than those observed during the thermal 240
degradation studies (40 % at 45 °C and 42 % at 65 °C), for spinach at pH 5. For green beans, 241
these residual ratios were higher than those observed in thermal degradation at pH 5 (20 % at 242
45 °C and 65 °C), the pH corresponding to that of spinach and green beans purees used during 243
thermal degradation kinetics. 244
245

3.2.2. Folate derivatives 246
Concentrations of folate derivatives in mg/kg as fresh weight, in the initial sample and in the 247
final sample of the diffusion kinetic studies were determined by stable isotope dilution assays. 248
Results are presented in Table 2 for spinach and Table 3 for green beans. 249
Both in spinach and green beans, the main compound was 5-CH3-H4folate which represented 250
about 70 % of folates at the beginning of diffusion and also revealed the highest loss of all 251
derivatives during diffusion. At pH 7, 5-CH3-H4folate residual ratios (C∞/C0) in spinach 252
decreased with increasing temperature. The same trend was observed with higher residual ratio 253
(C∞/C0) at pH 5. For green beans, 5-CH3-H4folate residual ratio (C∞/C0) decreased with 254
temperature increase at pH 7 and pH 5. 255
The second main class of folates derivatives was formyl derivatives. 10-HCO-PteGlu and 5-256
HCO-H4folate represented 6 to 16 % in spinach and 7 to 12 % in green beans respectively. 5-257
HCO-H4folate residual ratios (C∞/C0) increased with the temperature increase both in spinach 258
and green beans between pH 7 and pH 5. 10-HCO-PteGlu residual ratios (C∞/C0) were quite 259
stable at 25 °C both at pH 7 and 5 while it increased with rising temperature both at pH 7 and 5. 260
Residual ratios (C∞/C0) of minor derivatives (PteGlu, H4folate, 5,10-CH+-H4folate and 261
10-HCO-H2folate) were very low and appeared quite variable during kinetics, both for spinach 262
and green beans. 263
Finally, C∞/C0 obtained by determining concentrations by HPLC with fluorimetric detection 264
were globally higher than those obtained by the sum of concentrations of derivatives (as folic 265
acid) by stable dilution assay, especially at 65 °C and pH 7. Analytical imprecision could be 266
involved in this variation, especially by an over expression of concentrations resulting from the 267
sample preparation for HPLC with fluorimetric detection. 268
269

3.3. Diffusion modelling 270
Modelling of experimental data was carried out according to Fick’s second law for two 271
reasons: 272
- Fick’s second law is usually applied for describing of diffusion phenomena of water soluble 273
compounds. 274
- The evolution of concentrations in the vegetables along the time course, with an exponential 275
initial decrease followed by a plateau corresponding to Fick’s second law model both for plate 276
(with an average thickness of spinach leaves of 2.74 ± 0.8 x 10-4 m) and cylinder (with an 277
average green beans diameter of 6.66 ± 1.36 x 10-3 m). 278
The modeling was performed in the same way for all conditions of pH and temperature studied, 279
both for folate, sugar and acid diffusion from spinach and green beans. An example is 280
presented in Fig. 2, diffusion of folates for spinach at pH 7 and 45 °C (A) and for green beans 281
at pH 7 and 65 °C (B), where lozenges represent experimental data and the line represents the 282
diffusion model. 283
Model fitting was satisfactory both for spinach and green beans where the exponential shape 284
curve was in accordance with experimental data (Fig. 2). In order to validate the model, 285
correlation coefficients were maximized, both for spinach and green beans. The correlation 286
coefficients considering folate diffusion were between 0.87 and 0.99 for spinach and between 287
0.77 and 0.99 for green beans. For sugars and acids, the correlation coefficients varied from 288
0.82 to 0.99 for spinach and from 0.93 to 0.99 for green beans. 289
The high level of the correlation coefficients and the correlation between experimental data and 290
model show an adequacy between the model calculated and the phenomena observed both for 291
folates, sugars and acids in spinach and green beans. 292
293

3.3.1. Sugars and acids 294
Acids and sugars are water-soluble molecules and stable at pH 5 and 7 and temperatures, from 295
25 °C to 65 °C, which were the conditions used in our study. 296
For spinach, only glucose and malic acid presented a sufficient initial concentration for relevant 297
model fitting. Therefore, the diffusivity constant was calculated in spinach only for these two 298
substances. The concentration of glucose and malic acid in spinach decreased until a plateau at 299
about 60 min. Both for glucose and malic acid, temperature and pH did not have an effect on 300
residual ratios. 301
For both pH and temperature the concentration in sugars and green beans decreased in green 302
beans until reaching a plateau at about 120 min. Plateau levels (C∞/C0) decreased with 303
temperature at pH 7, and between 25 and 45 °C at pH 5, for glucose (Table 1). The residual 304
ratio (C∞/C0) for fructose decreased with temperature both at pH 7 and 5 while sucrose residual 305
ratio appeared stable. There was an effect of temperature on the reduction of the residual ratio 306
(C∞/C0) of malic acid. In addition, it appeared that residual ratios (C∞/C0) of malic acid were 307
higher at pH 5 than at pH 7 and at 45 and at 65 °C. 308
Both for spinach and green beans, diffusion of sugars and acids was determined as the mean of 309
three batches for pH 7 and two batches for pH 5 for the three temperatures studied. 310
For spinach, the diffusivity constant determined was on average 5.5×10-12 m2/s both for sugars 311
and acids (Table 1). Glucose, fructose and sucrose from green beans showed a similar 312
diffusivity constant, therefore only glucose, the most abundant compound, is presented. The 313
temperature and pH did not seem to have any influence on the rate of diffusion of sugars in 314
green bean, which was on average 6.1×10-10 m2/s 315
Diffusion of acids (citric and malic acids) from green beans showed diffusivity constants of the 316
same order for both acids at all temperatures and pH, on average about 4.6×10-10 m2/s (Table 317

1). However, plateau levels were very different. Citric acid was almost completely extracted 318
while malic acid was still present in green beans. The temperature and pH did not seem to have 319
any effect on the rate of diffusion for the two acids studied. However, the diffusivity constant 320
of citric acid was higher than that of malic acid and the diffusion was faster for citric acid than 321
for malic acid. 322
323
3.3.2. Folates 324
Folate diffusion took place in the first 60 min for spinach and 120 min for green beans, until 325
reaching a plateau after 60 min for spinach and 120 min for green beans. Correlation 326
coefficients exceeded 0.9 both for spinach and green beans. Results are presented in Table 1. 327
Folate diffusivity constants averaged at 7.45×10-12 m
2/s for spinach and 5.86×10-10 m
2/s for 328
green beans. For green beans, the folate diffusivity constant was hundred times higher than for 329
spinach meaning that the diffusion of folates is faster for green beans than for spinach. For 330
spinach, neither temperature nor pH had an effect on the folate diffusivity constant. For green 331
beans, the folate diffusivity constant appeared variable between batches for the same 332
conditions. Indeed, the low slope of folate concentration decrease did not allow distinguishing 333
a significant effect of pH or temperature on folate diffusivity constant. 334
The diffusivity constants calculated for folates both from spinach and green beans were in the 335
same order of magnitude than those calculated for acids and sugars from the same matrix. 336
4. Discussion 337
Our study was carried out at three temperatures (25, 45 and 65 °C), two of which were 338
sufficient to allow thermal degradation of folates over the time scale used (45 and 65 °C). For 339
diffusion kinetics, incubation at 85 °C proved to be impossible as the vegetables disintegrated 340
over the time-course. 341

342
4.1. Diffusion of water soluble compounds 343
We could not follow folate, sugar and acid diffusion at 85°C because of the matrix instability at 344
this temperature. Indeed, at 85 °C for 4 hours, spinach and green beans would have been 345
completely disintegrated. 346
Overall, little data are currently available concerning water soluble molecule diffusion from 347
plant tissues. The few studies available concern acid and sugar diffusion. 348
Vukov & Monszpart Senyi (1977) have determined diffusivity constants of sugars and acids 349
from apple slice to water at 75 °C as 11.8×10-10 m2/s for sugars and 14.2×10-10 m2/s for acids. 350
Some experiments quantified diffusivity constants of glucose and sucrose from alginate gels to 351
water, which are 2.55×10-10 at 5 °C for glucose and from 2.85×10-10 m2/s to 4.13×10-10 m2/s at 352
5 °C to 20 °C, for sucrose. From agar gels to water diffusivity constants are in the same range 353
of magnitude at 2.47×10-10 m2/s at 5 °C (Friedman & Kraemer, 1930). Moreover, Schwartzberg 354
& Chao (1982), determined diffusivity constants of glucose, fructose and sucrose to water at 25 355
°C from 0.69×10-9 to 0.54×10-9 m2/s. 356
Diffusivity constants calculated for acids and sugars in our study were in the range of 10-11 m2/s 357
from spinach and 10-10 m2/s from green beans. From green beans, the constant we found is in 358
agreement with those found in the literature for green beans (Friedman & Kraemer, 1930; 359
Vukov & Monszpart Senyi, 1977; Schwartzberg & Chao, 1982). In contrast, diffusivity 360
constants from spinach calculated in our study are lower than those found in the literature. 361
However, the diffusivity constants of sugars and acids were calculated from alginate, agar gels 362
or apple slices. These matrixes are different from those we studied, particularly the 363
physiological barriers such as the cuticles which could explain the difference observed for 364
spinach. For folates, currently no data are available in literature. The diffusivity constant 365

calculated for folates are in the same order of magnitude as those calculated for sugars and 366
acids, with the same difference between the two matrices. 367
The system we have developed to study the diffusion of water-soluble molecules such as 368
sugars, acids and folates from spinach and green beans appear to be efficient. 369
370
4.2. Impact of pH and temperature 371
Diffusivity constants calculated for folates from spinach and green beans, both at pH 7 and pH 372
5, were close to 10-12 m2/s and 10-10 m2/s respectively, and similar were the constants calculated 373
for sugars and acids for both vegetables and at both pH. The pH had no effect on folate, sugar 374
and acid diffusion. At pH 5 and pH 7, the global negative electric charge of malic or citric 375
acids, has the same polarity as that of cell walls. We can assume the existence of electrostatic 376
repulsion between the cell walls and sugars and acids resulting in a limitation of diffusion. For 377
green beans, a difference between the diffusivity constant of citric acid and malic acid of about 378
a factor of ten was observed, although they are of similar size and charge in the conditions 379
used. This difference could be due to the nature of the salts which neutralize citric acid which 380
has a greater ability to complex divalent cations. At pH 5 and pH 7, the overall electrical 381
charge of folates is also negative (Zhao, Matherly & Goldman, 2009). Thus, it seems that the 382
assumptions described for sugars and acids are transposable to folates, including the effects of 383
electrostatic repulsion with cell walls. Moreover, folate interactions with macromolecules such 384
as proteins could limit their diffusion under these pH conditions. Interaction between folates 385
and proteins did not seem to be involved in our study because similar diffusivity constant were 386
obtained for folates and sugars. The pH does not seem to be an important physico-chemical 387
parameter for the diffusion of sugars, acids and folates. 388

Temperature did not have a significant effect on diffusion of water soluble compounds 389
whatever matrix was considered but had a significant effect on the residual ratio (C∞/C0) 390
particularly for folates. 391
Residual levels of folates are lower for spinach (20 % at pH 7 and 10 to 30 % at pH 5) than for 392
green beans (40 to 70 % at pH 7 and 40 to 60 % at pH 5). This indicates that folates are more 393
extracted from spinach than from green beans. Spinach and green beans represent two different 394
tissues, consisting of leaf and pod respectively. Spinach leaves are composed of two layers, 395
each with only a few cell layers. In contrast, green beans are composed of pods and seeds 396
parenchyma, which are two different histological structures. The existence of these different 397
compartments and the possibility that folates are retained in these compartments by bondage to 398
macromolecules would result in a lower residual ratio and a slower rate of diffusion. In beans, 399
the existence of a compartmentalization of folates in the parenchyma and in the seeds is clearly 400
established. This was verified here: folate concentration in the parenchyma was 0.252 mg/kg 401
while it was three times higher in the seeds with a concentration of 0.709 mg/kg. 402
403
4.3. Folate thermal degradation 404
Generally for each temperature, folate degradation kinetics were comparable in spinach and 405
green beans. For all temperatures, a plateau was reached for both vegetables. The kinetics 406
neither followed a first order nor a second order reaction, and a first order reaction with a 407
partial conversion was still not satisfying, for the three temperatures and the two matrixes 408
studied. This is in contradiction other studies where authors observed total folate degradation 409
following a first order reaction (Paine-Wilson & Chen, 1979; Mnkeni & Beveridge, 1983; Oey, 410
Verlinde, Hendrickx & Van Loey, 2006). 411
Two effects could explain this phenomenon: the predominant loss was due to oxidation during 412
thermal degradation and the second one was due to evolution of each individual derivative and 413

their degradation products during the kinetics. Moreover, folate concentrations in samples from 414
thermal degradation were determined by HPLC with fluorimetric detection after derivatization. 415
This could lead to an artifact as it involved conversion of all derivatives to 5-CH3-H4folate. It 416
could also convert degradation products formed during the kinetics into 5-CH3-H4folate, which 417
would lead to an overestimation of the folate residual ratio. 418
419
4.4. Thermal degradation and industrial processing 420
Folate degradation observed in industrial processes (Delchier et al., 2013) appear low 421
compared to the model systems which could be explained by the difference between the time 422
considered during the experiments (4 hours) and during processing (few minutes). Moreover, 423
during sterilization of green beans, the can is a relatively small closed system, with less oxygen 424
included than in our experiments. During this stage of the process, we observed a slight 425
degradation of folates by about 10 %. Moreover, the treatment time is 6-15 min, and therefore 426
relatively short. During blanching, the system behaves similarly to the kinetics of thermal 427
degradation that we have performed here. During this stage, no losses of folates for both 428
spinach and green beans were observed (Delchier et al., 2013). The blanching time applied in 429
industrial processing is relatively short compared to those applied to the kinetics of thermal 430
degradation (blanching of spinach: 70 s to 120 s; green beans: 4-8 min) (Delchier et al., 2013). 431
Moreover, the high temperatures used correspond to very low solubilized oxygen content 432
(Winkler, 1888). 433
Finally, the matrices entering blanching step are not disrupted yet. Thus, the results observed 434
during industrial blanching are relatively consistent with the conclusions of the kinetics of 435
thermal degradation. 436
437
4.5. Integrative model: impact of thermal degradation during diffusion kinetics 438

The thermal degradation kinetics conducted under the same oxygen conditions as the diffusion 439
kinetics show residual folate amounts slightly higher at the end of the thermal degradation 440
kinetics for spinach (diffusion: 35 %, thermal degradation: 40 %) (Fig. 3). In contrast to this, in 441
green beans, the residual ratio (C∞/C0) measured at the end of the diffusion kinetics are higher 442
than those measured at the end of the thermal degradation kinetics (diffusion: 59 % at 45 °C 443
and 43 % at 65 °C; thermal degradation: 20 % for both temperatures). In addition, residual 444
ratios are obtained with very different compositions. So it seems that the relative shares of 445
losses by diffusion and thermal degradation vary according to the vitamers considered. 446
Moreover, the thermal degradation kinetics were performed on purees obtained from ground 447
vegetables in cans, where grinding could play a role, either by facilitating the access of oxygen 448
into puree or by modifying the local environment. 449
450
Conclusion 451
Our study enabled us to determine folate diffusivity constants, using a novel and efficient 452
experimental device where neither pH nor temperature had a significant effect on the 453
diffusivity constant, in contrast to the significant effect of the two vegetables matrices. 454
Evolution of vitamers during diffusion was dependent on their nature. 5-CH3-H4folate and folic 455
acid (PteGlu) were the two main derivatives lost during diffusion. These derivatives are more 456
stable at pH 5 than at pH 7, so we can not exclude that these derivatives have been degraded 457
over time, thus reducing the final concentration and inducing an increase in the total amount 458
extracted. Evolution of derivatives during thermal degradation seems to be a key point for 459
folate degradation by oxidation, which is why a next step of this study would be to determine 460
the evolution of vitamers during oxidation in presence of different oxygen conditions. 461
By contrast, thermal degradation of folates in spinach and green beans was not monotonous 462
especially at 45 °C and kinetics modelling by a first order with partial conversion was not 463

satisfying yet. Comparison between diffusion and thermal degradation showed that folates were 464
more sensitive to thermal degradation for green beans, while for spinach diffusion mechanism 465
appears to be predominant over thermal degradation. 466
467
Acknowledgements 468
This work benefited from financial support of ANR-09-ALIA-014 RIBENUT project: New 469
approaches for microbial risk – nutritional benefits assessment in the case of heat processed 470
vegetables. It was conducted as part of the UMT "Micronutriments des produits végétaux 471
transformés" of ACTIA and with the financial support of the Ministère de l'Agriculture, de 472
l'Alimentation, de la Pêche, de la Ruralité et de l'Aménagement du Territoire. 473
The authors thank Caroline Garcia and Laura Badard for their excellent technical help. 474
475

References 476
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http://www.anses.fr/Documents/ANC-Ft-TableauVitB9.pdf, uploaded January 2012. 478
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by Periconceptional Vitamin Supplementation. New England Journal of Medicine, 327(26), 480
1832-1835. 481
Crank, J. (1975). The mathematics of diffusion (2nd ed.). Oxford, London: Claredon Press. 482
Delchier, N., Ringling, C., Le Grandois, J., Aoudé-Werner, D., Galland, R., Georgé, S., 483
Rychlik, M., Renard, C.M.G.C. (2013). Effects of industrial processing on folate content in 484
green vegetables. Food Chemistry, 139, 815-824. 485
Delchier, N., Reich, M., & Renard C.M.G.C. (2012). Impact of cooking methods on folates, 486
ascorbic acid and lutein in green beans (Phaseolus vulgaris) and spinach (Spinacea oleracea). 487
LWT - Food Science and Technology, 49, 197-201. 488
DeSouza, S.C., & Eitenmiller, R.R. (1986). Effects of Processing and Storage on the Folate 489
Content of Spinach and Broccoli. Journal of Food Science, 51(3), 626-628. 490
Friedman, L., & Kraemer, E. O. (1930). Diffusion of non electrolytes in gelatin gels. Journal of 491
the American Chemical Society, 52, 1305. 492
Klein, B. P., Lee, H. C., Reynolds, P. A., & Wangles, N. C. (1979). Folacin content of 493
microwave and conventionally cooked frozen vegetables. Journal of Food Science, 44(1), 286-494
288. 495
Lafay, L. (2009). Etude Individuelle Nationale des Consommations Alimentaires 2(INCA-2). 496
http://www.anses.fr/Documents/PASER-Ra-INCA2.pdf. (in french), uploaded January 2012. 497
McKillop, D.J., Pentieva, K., Daly, D., McPartlin, J.M., Hughes, J., Strain, J.J., Scott, J.M., & 498
McNulty, H. (2002). The effect of different cooking methods on folate retention in various 499
foods that are amongst the major contributors to folate intake in the UK diet. British Journal of 500
Nutrition, 88(06), 681-688. 501
Melse-Boonstra, A., Verhoef, P., Konings, E.J.M., van Dusseldorp, M., Matser, A., Hollman, 502
P.C.H., Meyboom, S., Kok, F.J., & West, C.E. (2002). Influence of Processing on Total, 503
Monoglutamate and Polyglutamate Folate Contents of Leeks, Cauliflower, and Green Beans.
504
Journal of Agricultural and Food Chemistry, 50(12), 3473-3478. 505
Mnkeni, A. P., & Beveridge, T. (1983). Thermal destruction of 5-methyltetrahydrofolic acid in 506
buffer and model food systems. Journal of Food Science, 48(2), 595-599. 507
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Food Research and Technology, 223(1), 71-77. 510
Paine-Wilson, B., & Chen, T.S. (1979). Thermal destruction of folacin: effect of pH and buffer 511
ions. Journal of Food Science, 44(3), 717-722. 512

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Deutschen Chemischen Gesellschaft, 21, 2843–2855. 525
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529

Figure Captions 530
Fig. 1. Folates’ thermal degradation in spinach and green beans purees 531
The left part of the graphic represents the thermal degradation of total folates expressed as folic 532
acid in mg/kg of fresh weight at 45 °C (A), 65 °C (B) and 85 °C (C) in spinach under 533
atmospheric oxygen conditions. The right part of the graphic represent the thermal degradation 534
of total folates (mg/kg of fresh weight) at 45 °C (D), 65 °C (E) and 85 °C (F) under 535
atmospheric oxygen conditions in green beans. Empty lozenges correspond to data from batch 536
1 and empty squares represent data from batch 2. 537
538
Fig. 2. Folate diffusion from spinach and green beans 539
On the left graphic (A) experimental and modelling data for folate diffusion from spinach at pH 540
7 and 45 °C are presented and on the right graphic (B) the respective data for folate diffusion 541
from green beans at pH 7 and 65 °C. Experimental concentrations of folates during diffusion 542
are expressed in mg/kg of fresh weight in equivalent 5-CH3-H4folate monoglutamate and 543
represented by full lozenges. Concentrations determined by second Fick’s law model are 544
represented by the dotted line. Right graph (A) 545
546
Fig.3. Model of folate losses from spinach and green beans: diffusion vs thermal 547 degradation 548
Folate C/C0 evolution over time both for diffusion + thermal degradation and for thermal 549
degradation are represented by full triangle and empty squares respectively. On the top data for 550
spinach at 45 °C (A) and 65 °C (B) are presented and on the bottom the respective data for 551
green beans at 45 °C (C) and 65 °C (D). 552
553

Fig.1. Delchier et al. 554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
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576
577
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579
580
581
582
583
584
585
586
587
588
Time (min)
A : 45 °C
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
C : 85 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
B : 65 °C
mg.kg-1 as Folic acid
Time (min)
D : 45 °C
mg.kg-1 as Folic acid
0.04
0.08
0.12
0.16
0.20
030 60 90 120 150 180 210 240
Time (min)
030 60 90 120 150 180 210 240
0.04
0.08
0.12
0.16
0.20
E : 65 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
F : 85 °C
mg.kg-1 as Folic acid
Time (min)
A : 45 °C
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
mg.kg-1 as Folic acid
Time (min)
A : 45 °C
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
C : 85 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
C : 85 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
B : 65 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
B : 65 °C
mg.kg-1 as Folic acid
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
B : 65 °C
mg.kg-1 as Folic acid
Time (min)
D : 45 °C
mg.kg-1 as Folic acid
0.04
0.08
0.12
0.16
0.20
030 60 90 120 150 180 210 240
Time (min)
D : 45 °C
mg.kg-1 as Folic acid
0.04
0.08
0.12
0.16
0.20
030 60 90 120 150 180 210 240
Time (min)
030 60 90 120 150 180 210 240
0.04
0.08
0.12
0.16
0.20
E : 65 °C
mg.kg-1 as Folic acid
Time (min)
030 60 90 120 150 180 210 240
0.04
0.08
0.12
0.16
0.20
E : 65 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
F : 85 °C
mg.kg-1 as Folic acid
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
Time (min)
0.04
0.08
0.12
0.16
030 60 90 120 150 180 210 240
F : 85 °C
mg.kg-1 as Folic acid

Fig.2. Delchier et al. 589
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0
0.04
0.08
0.12
0 30 60 90 120 150 180 210
B
mg.kg
-1
(FW)
as 5-CH
3
-H
4
folate
Time (min)
0
0.05
0.10
0.15
0.20
0.25
0 30 60 90 120 150 180 210 240
Time (min)
A
mg.kg
-1
(FW)
as 5-CH
3
-H
4
folate
0
0.04
0.08
0.12
0 30 60 90 120 150 180 210
B
mg.kg
-1
(FW)
as 5-CH
3
-H
4
folate
Time (min)
0
0.05
0.10
0.15
0.20
0.25
0 30 60 90 120 150 180 210 240
Time (min)
A
mg.kg
-1
(FW)
as 5-CH
3
-H
4
folate

Fig.3. Delchier et al. 613
614
0.4
0.8
1.2
050 100 150 200 250
0.4
0.8
1.2
050 100 150 200 250 Time (min)
Time (min)
C/C0C/C0
AB
0.4
0.8
1.2
050 100 150 200 250
Time ( min)
C/C0
C
0.4
0.8
1.2
050 100 150 200 250
Time (min)
C/C0
D
0.4
0.8
1.2
050 100 150 200 250
0.4
0.8
1.2
050 100 150 200 250 Time (min)
Time (min)
C/C0C/C0
AB
0.4
0.8
1.2
050 100 150 200 250
Time ( min)
C/C0
C
0.4
0.8
1.2
050 100 150 200 250
Time (min)
C/C0
D

Table 1: Diffusivity and C/C0 of folates, sugars and acids in spinach and green beans
D corresponds to the diffusivity constant calculate for folates, Glucose, fructose, Sucrose, Malic acid and Citric acid in m2.s-1. For folates diffusivity constant,
results are expressed as mean ± standard deviation.
C/C0 corresponds to the residual concentration calculate for folates, Glucose, fructose, Sucrose, Malic acid and Citric acid. For folates, C/C0 is expressed as mean ±
standard deviation.
Diffusivity constant for folates was calculated from concentrations expressed as 5-CH3-H4folate monoglutamate (after conversion of all derivatives)
T corresponds to the temperature in degree Celsius.
Folates Glucose Fructose Sucrose Malic acid Citric acid
pH T D C/C0 D C/C0 D C/C0 D C/C0 D C/C0 D C/C0
Spinach 7 25 7 ± 2.1 .10-12 0,28 ± 0.07 3.0.10-12 0.50 - - - - 3,5.10-12 0,49 - -
45 7 ± 1.7.10-12 0,23 ± 0.03 1.0.10-11 0.30 - - - - 6,0.10-12 0,19 - -
65 6 ± 1.1.10-12 0,28 ± 0.12 - 0.86 - - - - 2,5.10-11 0,52 - -
5 25 6 ± 2.1.10-12 0,33 ± 0.01 6,0.10-12 0,54 - - - - 3,5.10-12 0,57 - -
45 9 0,38 ± 0.14 8,0.10-12 0,02 - - - - 5,5.10-12 0,55 - -
65 8 ± 1.4.10-12 0,12 ± 0.04 9,5.10-12 0,27 - - - - 2,5.10-11 0,27 - -
Green 7 25 7 ± 1.1.10-10 0,73 ± 0.03 3,0.10-10 0,61 1,5.10-10 0,57 1,0.10-09 0,51 1,0.10-09 0,87 9,0.10-09 0,05
beans 45 8 ± 1.7.10-10 0,70 ± 0.06 3,0.10-10 0,52 1,5.10-10 0,55 2,5.10-10 0,51 5,0.10-10 0,44 9,0.10-09 0,06
65 6 ± 2.0.10-10 0,41 ± 0.04 2,5.10-10 0,39 6,0.10-10 0,39 5,0.10-09 0,63 2,5.10-10 0,36 5,0.10-09 0,03
5 25 - 1,17 ± 0.21 1,7.10-10 0,71 3,0.10-10 0,75 1,0.10-07 0,61 5,0.10-10 0,75 4,0.10-09 0,07
45 5 ± 1.4.10-10 0,59 ± 0.08 1,5.10-10 0,48 2,1.10-10 0,43 5,0.10-10 0,44 3,5.10-10 0,51 5,0.10-09 0,06
65 3 0,43 1,5.10-10 0,47 2,0.10-10 0,38 5,0.10-10 0,55 2,0.10-10 0,48 5,0.10-09 0,06

29
Table 2: Residual concentration of folate derivatives in spinach during diffusion kinetics 615
Results are expressed in mg kg-1 of fresh weight, in blanched spinach (t0) and blanched 616
spinach after diffusion (t180 or t240). 617
C/C0 is the ratio between the initial concentration and the final concentration. 618
°C corresponds to the temperature in degree Celsius. 619
620
621
622
pH °C Time 5-CH3-
H4folate
5-HCO-
H4folate
10-
HCO-
PteGlu
H4folate PteGlu
5,10-
CH+-
H4folate
10-
HCO-
H2folate
Total
folates
(as folic
acid)
7 25 t0 0,302 0,057 0,022 0,015 0,003 0,003 0,010 0,395
t180 0,069 0,007 0,005 0,001 0,001 0,000 0,003 0,083
C/C0 0,22 0,12 0,24 0,07 0,35 0,07 0,26 0,21
45 t0 0,189 0,010 0,027 0,004 0,001 0,000 0,010 0,230
t240 0,017 0,002 0,003 0,001 0,001 0,000 0,001 0,024
C/C0 0,09 0,18 0,12 0,41 0,58 0,42 0,07 0,11
65 t0 0,137 0,027 0,020 0,005 0,002 0,001 0,010 0,193
t240 0,002 0,001 0,001 0,000 0,001 0,000 0,000 0,005
C/C0 0,01 0,05 0,06 ø 0,31 ø ø 0,03
5 25 t0 0,280 0,064 0,013 0,012 0,002 0,002 0,003 0,361
t240 0,102 0,056 0,011 0,004 0,002 0,002 0,003 0,171
C/C0 0,36 0,86 0,86 0,33 0,76 0,85 0,86 0,48
45 t0 0,344 0,109 0,008 0,039 0,002 0,003 0,002 0,484
t240 0,051 0,045 0,008 0,002 0,002 0,000 0,002 0,105
C/C0 0,14 0,41 1,08 0,05 0,81 0,02 1,24 0,22
65 t0 0,350 0,126 0,009 0,035 0,003 0,003 0,003 0,506
t240 0,002 0,036 0,013 0,002 0,001 0,000 0,001 0,052
C/C0 0,007 0,28 1,41 0,05 0,48 0,01 0,41 0,10

30
Table 3: Residual concentration of folate derivatives in green beans during diffusion kinetics 623
624
625
626
Results are expressed in mg kg-1 of fresh weight, in blanched green beans (t0) and blanched 627
green beans after diffusion (t180 or t240). 628
C/C0 is the ratio between the initial concentration and the final concentration. 629
°C corresponds to the temperature in degree Celsius. 630
631
632
633
pH °C Time 5-CH3-
H4folate
5-HCO-
H4folate
10-
HCO-
PteGlu
H4folate PteGlu
5,10-
CH+-
H4folate
10-
HCO-
H2folate
Total
folates
(as folic
acid)
7 25 t0 0,543 0,13 0,042 0,028 0,66 0,008 0,020 1,404
t210 0,353 0,07 0,038 0,005 0,001 0,002 0,014 0,465
C/C0 0,65 0,54 0,91 0,18 0,21 0,28 0,69 0,33
45 t0 0,517 0,06 0,058 0,016 0,002 0,003 0,026 0,651
t240 0,216 0,04 0,043 0,009 0,002 0,003 0,015 0,315
0,43 0,41 0,73 0,73 0,55 0,81 1,02 0,56 0,48
65 t0 0,330 0,06 0,060 0,009 0,001 0,002 0,020 0,463
t240 0,027 0,04 0,039 0,007 0,002 0,006 0,012 0,128
C/C0 0,08 0,67 0,65 0,80 2,35 2,36 0,59 0,28
5 25 t0 0,342 0,07 0,032 0,014 0,001 0,002 0,009 0,449
t180 0,362 0,07 0,036 0,005 0,001 0,002 0,013 0,464
C/C0 1,05 0,97 1,13 0,35 0,74 1,10 1,37 1,03
45 t0 0,541 0,07 0,039 0,012 0,001 0,003 0,021 0,661
t240 0,112 0,05 0,037 0,008 0,002 0,000 0,007 0,210
C/C0 0,20 0,74 0,92 0,63 1,38 0,10 0,35 0,32
65 t0 0,448 0,09 0,040 0,014 0,001 0,003 0,013 0,582
t240 0,008 0,05 0,048 0,003 0,001 0,000 0,004 0,104
C/C0 0,01 0,52 1,20 0,22 0,92 0,04 0,27 0,18