Ind. Eng. Chem. Res. 1994,33, 981-992
981
Kinetics of the Hydroxyethylation of Starch in Alkaline Salt-Containing Aqueous Slurries Anne van Warners, Eize J. Stamhuis,' and Antonie A. C. M. Beenackers Department of Chemical Engineering, The University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
A two-phase kinetic model is presented for the base-catalyzed hydroxyethylation of potato starch using ethylene oxide a t temperatures between 293 and 318 K in aqueous starch slurries containing sodium sulfate. The rate of the hydroxyethylation of starch as a function of starch anion concentration (cRo,~), ethylene oxide concentration in the aqueous phase (CEO), and temperature is described by: R H E =~ 0.958 X lo9 exp(-74680/RT)c~oc~o,~ kmol m-3 of starch s-l. The observed kinetics of an important side reaction, the hydrolysis of ethylene oxide to ethylene glycol, is in accordance with literature data. In the starch phase the hydrolysis rate is considerably smaller than that in the ~ ko o of~ the hydrolysis continuous water phase. In aqueous salt solutions the rate constants k ~ and of ethylene oxide are enhanced by 46 96 and reduced by 7 96 per kmol/m3of ionic strength, respectively. The hydroxyethylation of glycol follows the rate equation (in the absence of starch and salt): RDEG = 50.2 exp(-34500/RT)cEo0'62CEC0'45CoH0'9s kmol m-3 s-l. The hydroxyethylation of sulfate proceeds according to: R"s = 8.48 X lo8 exp(-86000/RT)c~ocso,.
Introduction Low-substituted hydroxyethyl starch is an industrially important compound. Chemically, it differs from native starch in the conversion of some of the hydroxyl groups into -0CH2CH20H groups. The degree of conversion is conveniently expressed as molar substitution (MS), i.e., the number of moles of ethylene oxide (C2H40)substituted per mole of anhydroglucose units (AGU, C6H1005)of the polymer (MAGU= 162). Low-substituted hydroxyethyl starch with an MS lower than 0.1 is usually produced in a reaction of a starch slurry in water with ethylene oxide, catalyzed by hydroxide ions, at temperatures below 50 "C. Usually a swelling-inhibitingsalt is added to prevent gelatinization of the granules (Kesler and Hjermstad, 1950a; Moser, 1986). However, under these conditions, ethylene oxide not only reacts with starch but also is consumed in several side reactions. Particularly, the main reaction with water toward ethylene glycol is of importance. Both uncatalyzed hydrolysis as well as hydrolysis catalyzed by OH ions takes place. Also side reactions with various salts may occur (Kesler and Hjermstad, 1950b; Parker and Isaacs, 1959). Finally the consecutive reaction of ethylene oxide with ethylene glycol is possible, resulting in diethylene glycol (Parker and Isaacs, 1959). To develop optimal process conditions, the kinetics of both the main and the side reactions should be known as a function of the composition of the reaction medium in both reacting phases, starch and water. Since a difference in the rate of hydrolysis of ethylene oxide in the granules from that in the water phase may not a priori be excluded, experiments with several starch concentrations were necessary. Furthermore, it is known that dissolved salts influence the distribution of alkali between starch and water phases (Leach et al., 1961),but it is unknown whether the reaction rate constants are a function of the salt concentration. Finally, in a reactor system that recycles slurry liquid, the reaction of ethylene oxide with the hydrolysis product ethylene glycol will become increasingly important at higher recycle ratios. Therefore, we investigated the kinetics of the reactions of ethylene oxide in aqueous slurries of potato starch granules as a function of ethylene glycol and sodium hydroxide concentrations and at several
* To whom correspondence should be addressed. 0888-5885/94/2633-0981$04.5010
concentrations of sodium sulfate and sodium chloride, respectively. In addition, the influence of the temperature on the kinetics of these reactions was determined.
Reaction Model Granules of potato starch in water have a water content of about 50 5% by weight on a dry basis (Brownand French, 1977; Evans and Haisman, 1982). Like in earlier publications (Jetten et al., 1980; Homan Free et al., 1985) the swollen starch granules are considered as a homogeneous dispersed phase in the surrounding liquid which forms the continuous phase. Most of the NaOH added to a starch-water slurry is absorbed by the starch phase (Leach et al., 1961). In the granules, the hydroxide ions react in part with the phosphate groups bound to the potato starch according to (Jetten et al., 1980) R-OPO,H-
+ OH-
K.,PlKw
e R-OPOt-
+ H2O
(1)
Here, R denotes the starch chain. If R = glucose, as in the case of glucose-l-phosphate, the pKat 303 K is 6.51 (Ashby et al., 1955). The number of phosphate groups in potato starch is approximately 0.004 mol/mol of anhydroglucose units (AGU) (Schoch, 1942). Especially a t pH values higher than 10,some of the slightly acidic hydroxyl groups of starch also react according to K.,JKw
R-OH+OH-
s R-O-+H20
The pK of the anhydroglucose unit in amylose, the unbranched polymer of glucose, is approximately 12.7 in aqueous solution at 298 K and depends on the amylose concentration (Doppert and Staverman, 1966). Ethylene oxide is completely soluble in the aqueous phase of the slurries in the 0-0.2 M concentration range used in the experiments. The dissolved ethylene oxide penetrates, like other small organic solutes (BeMiller and Pratt, 1981),into thegranules, untilequilibrium is obtained between the starch and the aqueous phase. Reactions with starch can occur in the granules only, whereas reactions with water are possible in both phases. 0 1994 American Chemical Society
982 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
This leads to the following reaction scheme: R-OH
-
C,H,O
R-OCH,CH,OH
kRo
+ C2H40+ H,O
R-0-
-
kRoH
+ C,H,O
R-OCH,CH,OH
-
C2H,0 + H 2 0
kH,O
+ OH- + H,O
koH
-
(3)
+ OH-
HOCH,CH,OH HOCH,CH,OH
(4) (5)
+ OH-
(6)
Reactions 3 and 4 yield hydroxyethyl groups; reactions 5 and 6 produce ethylene glycol. Ethylene glycol itself can react with ethylene oxide to form diethylene glycol (DEG): C,H,O
+ OH- + EG
-
kW0H
HOCH,CH,OCH,CH,OH (DEG)
+ OH-
(7)
kci
+ C1- + H 2 0 s
C1-CH2CH20H + OH- (8)
kECH
To the best of our knowledge, the reaction of ethylene oxide with sulfate ions has not been reported before. However, analogous to the reaction of chloride ions with ethylene oxide a reaction with sulfate anions can be proposed, producing the anion of hydroxyethyl hydrogen sulfate: C,H,O
+ SO:- + H 2 0
-
k80‘
-OSO,CH,CH,OH
with RDEG being the production rate of diethylene glycol from a consecutivereaction of ethylene glycolwith ethylene oxide. The consecutive reaction with ethylene glycol is catalyzed by hydroxide (Gee et al., 1959). Based on eq 7 we tested the following rate equation:
RDEG= ~EGOHCEGCOHCEO
+ OH-
= kCICEOCCl - lZECHCECHCOH
(13)
Here, ECH stands for ethylene chlorohydrin. The equilibrium constant of reaction 8, KCI,defined as k d k ~ c ~ , is known (Porret, 1944) and decreases from 3.25 X 10-4 at 293 K to 1.64 X lo4 at 323 K. At 293 K reaction 8 virtually reaches equilibrium within 1 h, which is fast relative to the other reactions involving ethylene oxide. Once at equilibrium, all concentrations in eq 13 remain constant during an experiment (the concentration of ethylene oxide is continuously kept constant by addition of fresh ethylene oxide). So, then RECH= 0 and the production of alkali catalyst stops. Production of hydroxide ions also occurs if sulfate is added as a swelling inhibitor instead of chloride. A kinetic equation analogous to eq 13 is proposed:
RHHS= ~SO,CEOCSO, - ~HHSCHHSCOH
(9)
Due to reactions 8 and 9 the pH of the slurry increases and the concentration of the reactive RO- groups also increases. The reaction of ethylene oxide with RO- does not lead to an increase of hydroxide ions because of the acid-base equilibrium between ROH and RO-: the OH-, formed by reaction 4, will immediately create a new RO- group via reaction 2. It is likely that at relatively low MS values most hydroxyl anions will originate from ROH groups and not from ROCH&H20H, because ROH is present in excess and the hydroxyl group of ROCH2CHzOH is not expected to be much more acidic than ROH. This is confirmed by the fact that most hydroxyethyl groups do not react further with ethylene oxide as long as the MS is low (Merkus et al., 1977). It does not seem useful to consider the possibility of a reaction between ethylene oxide and phosphate monoand dianions, because the maximum MS to be obtained by this reaction will be 0.004 for the case in which all phosphate groups react once with ethylene oxide. Reaction Rate Equations. A review on the kinetics of the reactions of epoxides (Parker and Isaacs, 1959) shows that any reported reaction with a nucleophilic species under neutral or alkaline conditions is of first order in both epoxide and nucleophile. To our knowledge,the kinetic equations of the reactions 3, 4, 7, and 9 have not been reported before. For the hydroxyethylation of potato starch we will test the following equation:
(12)
The kinetic equation for equilibrium reaction 8 has been shown to be (Porret, 1944) RECH
I t is well-knownthat ethylene oxide reacts with the anions of several salts (Parker and Isaacs, 1959). With chloride ions, the reaction products are ethylene chlorohydrin and hydroxide ions: C,H,O
which assumes a reaction of ethylene oxide with both undissociated starch hydroxyl groups and starch anions. Based on the work of Lichtenstein and Twigg (19481, the reaction rate equation for the formation of ethylene glycol in neutral and alkaline aqueous solutions is
(14)
with HHS standing for hydroxyethyl sulfate. From the literature (Kesler and Hjermstad, 1950a; Lichtenstein and Twigg, 1948) it can be concluded that rates of the reactions of ethylene oxide with both water and starch are low. It can be calculated (see Appendix) that during reaction concentration gradients inside the starch granules are negligible. Because reactions 1 and 2 are muchfaster than reactions 3-7, they can be assumed to be at equilibrium, and as a consequence the kinetics of reactions 1 and 2 will not occur in the overall rate equation. Based on the aforementioned facts and assumptions, a kinetic model can now be proposed. The overall rate equation for ethylene oxide follows from the summation of the rates of the six parallel ethylene oxide consuming reactions in the two phases, leading to four different products. At most one of the salts, NaCl or Na2S04, is present. The starch-phase concentrations are not directly measurable. They can be expressed in terms of the waterphase concentrations by means of distribution coefficients defined as
The subscripts s and w refer to the starch and water phase, respectively. The distribution coefficient of OH- cannot be measured, therefore it is initially assumed that C O H , ~= C0H.w.
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 983
If sodiumsulfate is present the overallproposed reaction rate of ethylene oxide is
-Rm = [ ~ E O @ R O C R O , ~+ ~EO@ROHCEOH, 1-c,)(kH20 + koHCoH) + (mEomE&
+ ( ~ E O E+ ~
1-@ZE~Hc&oH
(mEOmSO,'~ + l-fa)kSO,%O,lcEO
(mHHS's
-
+ 1-~~)kHHScHHScOH(16)
In this rate equation all concentrations refer to the water phase, unless otherwise stated. Further, e. is the volume fraction of starch. The relevant rate constants in the starch phase are initially assumed to be equal to those in the water phase. Experimental Section Materials. Potato starch out of 50-kgbags from Avebe was used without purification. Ethylene oxide from HoekLoos was purified by evaporation from a container before use. Sodium hydroxide (Titrisol, Merck), sodium chloride, and sodium sulfate (Merck) were of analytical grade. The purity of ethylene glycol (Janssen) was higher than 99 % . Kinetic Measurements
A. Batch. The kinetics of the hydroxyethylation of potato starch was studied batchwise a t 303 K in stirred aqueous slurries of starch granules. In all runs the water/ dry starch ratio was 3.851 by weight. Gelatinization of the starch was prevented by addition of sodium sulfate. OnceaconstantpH was obtained after additionofadesired amount of 1.00 M sodium hydroxide, the reaction was started by addition of a 2.5 kmol m3 aqueous solution of ethylene oxide. The reaction of ethylene oxide with sulfate anions produces hydroxide ions, thus increasing the pH of the slurry. To maintain a constant pH, diluted sulfuric acid was added by a pH-controlled motor-driven burette and recorded versus time. In this way, the rate of formation of hydroxide ions could be determined. Samples were taken and centrifuged for 60 8 in a preheated closed tube in order to separate the phases at the reactor temperature and to prevent loss of ethylene oxide by evaporation. Gas chromatographic analysis of the liquid phase was carried out with a Packard Becker 428 (GLC) equipped with a glass column (length 0.25 n, internal diameter 3 mm), packed with Porapak PS. Isopropyl alcohol was added to the liquid phase as an internal standard. The OH concentration of the water phase was determined by titrationwithO.lMHC1. Thevolumeofthestarchfraction was measured by adding Blue Dextran polymer to the slurry and measuring its concentration, according to the method of Dengate et al. (1978). The distribution coefficient of ethylene oxide was obtained via eq 15. The amount of ethylene glycol formed was measured at the end of a run, by filtering 0.020 kg of slurry on a glass filter and washing the cake three times for a t least 300 8 with 10 cm3of fresh water. Then the collected filtrate underwent the gas chromatographic analysis described above. The molar substitution of the starch at the end of an experiment was determined by Lortz's modification of Morgan's method with hydroiodic acid (Lortz, 1956). B. Semibatch. The experimental setup is schematically shown in Figure 1. A thermostated glass vessel was used as a reactor; it consists of a lower part (0.5 dm3) with a diameter of 0.1 m that contained the slurry and an upper part (4.5 dm3) that has a diameter of 0.19 m. The reactor was closed by a thermostated stainless steel hollow cover,
-
....................................................................... Figure 1. Experimental setup.
f
:
sealed by vacuum grease. Both the gas phase and the liquid phase were stirred with Rushton impellers on a common shaft; the stirrer shaft had two bearings, one just above and one just below the cover, and was sealed by mercury. The pH was measured with a Xerolyt pressureresistant glass electrode. The temperature and the presence were recorded via a Pel00 resistance thermometer and a Siemens 80&1100 mbar external pressure transducer, respectively. The reactor was connected to a thermostated gas cylinder via a magnetic valve. The gas cylinder was placed on an electronic balance. Control and data acquisition were carried out with a personal computer. The gas pressure could be raised by the addition of ethylene oxide, and the pH could be lowered by the addition of acid from a motor-driven burette. The reaction kinetics were studied fed hatch in stirred aqueousslurriesof potato starchgranules. Sodiumsulfate or chloride was added to prevent gelatinization of the starch. The reaction was started as soon as a constant pH was obtained after the addition of the desired amount of 1.00 M sodium hydroxide. Ethylene oxide was added continuously and automatically so as to maintain a constant pressure of ethylene oxide above the liquid. The amount of ethylene oxide added was followed by continuously recording the weight of the gas cylinder. After arapid initialabsorption of ethylene oxide in both the liquid and the granules, a pseudo-steady-state was reached during which the ethylene oxide consumption was used for reaction only. The composition of the slurry was analyzed by the procedure described above.
Results and Discussion To check the proposed reaction rate equations a t one temperature, a series of batch experiments was carried out at 303.0 K at identical concentrations of Na2S04 and at several NaOH concentrations. The experimental conditions are summarized in Table 1. The final conversion of ethylene oxide was at least 90%. As an example, the decrease of the concentration of ethylene oxide in the water phase is shown in Figure 2 on a semilogarithmic scale for the case when NN~OH is 0.040 mol/mol of AGU. An overall mass balance for ethylene oxide for a twophase liquid-solid batch process is d dt(CEO,CsV+ cEO,w(l-%)Q = REOV with V being the volume of the reaction mixture.
(17)
984 Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
-
of the right-hand side of eq 20 into selectivities will be obvious. hob = S H E + S SEG~, ~ ~ ~+ S H H S ~ (21) ~ Sj is defined as (moles of EO in product j)/(total moles of EO reacted) with j being one of the products, hydroxyethyl starch (HES), ethylene glycol (EG), or hydroxyethyl hydrogen sulfate (HHS), respectively. Combining eqs 20 and 21 gives
5;--
‘
50
1
I
100
150
I 200
I 250
t [ksl
Figure 2. Decrease of the ethylene oxide concentration in the water phase, withNN.OH = 0.040kmol/kmol AGU. Conditions: See Table 1. Table 1. Experimental Conditions temperature 303.0K 0.324kg (=2mol of AGU) weight of dry starch 1.250 kg total amount of water 0.120 kg (=0.845mol) amount of NazSOl *0.010 kg (=0.227mol) amount of ethylene oxide (initial) 1150 kg m-9 slurry density 1080 kg m-3 liquid phase density volume of the slurry 1.47 X 10-9 m3 1.36 kmol m-9 of slurry starch concentration CAGU
The result, after integration, is
CEO,~,Ois the initial ethylene oxide concentration in the water phase, and k’so4is a volume-averaged pseudo-firstorder rate constant for the reaction of ethylene oxide with sulfate:
~so4cso,.w
(19)
If the parameters of the right-hand side of eq 18 are not dependent on the degree of substitution, the decrease of the ethylene oxide concentration in the water phase during a batch run at a constant pH can be described with a pseudo-first-order overall rate contant: cEO,w In = -kobst (!EO,w,O
with
[
mE0t8 E
EO
+ l-eB(kROHCROH + kROCRO) +
8
The observed rate constant kob is a summation of the contributions of five different reactions, leading to three different products. Since the kinetics of the reactions were actually studied by determining the concentration of these three products together with that of the reactant ethylene oxide as a function of time, a transformation of the terms
‘EG’obs
= kOHCOH + kH,O
(23) (24)
The values of the parameters hob, SHES, SEG, SHHS, mEo, and c, have been determined for each batch experiment. Figure 2 confirms that the reactions that occur are first order in ethylene oxide, because In decreases linearly with time, as predicted with eq 20. The slope of the logarithmic plot is -hobs. The values of hob of all experiments are shown in Table 2, together with the other measured parameters. Effect of NaOH. Thereactant concentrations CRO and COH both increase with increasing NaOH concentration. With mEO and E, nearly constant (Table 21, k o b should increase according to eq 20. This is actually the case. Despite the large number of starch hydroxyl groups the contribution of these groups in undissociated form to the production of hydroxyethyl starch is very low. This can in combination with a low be concluded from the low SHES kobs in exp 1(column 1, Table 21, where no alkali has been added and thus CRO = 0 in eq 22. The low selectivity to the desired product hydroxyethyl starch in the absence of alkali shows why an alkaline catalyst is necessary. An explanation in terms of a low reactivity of ROH seems obvious. However, the fact that starch hardly reacts with ethylene oxide without alkali addition could also have been caused by a low ethylene oxide concentration in the granules under those conditions. However, Table 2 shows that the value of mEO is similar to that for the experiments with higher concentrations of NaOH. The conclusion remains, therefore, that the reactivity of ROH is much lower than that of RO-. If no alkali is added, kobs is not zero. This is mainly caused by the side reactions of ethylene oxide with H20 and SO2-. So a t “low” pH values low starch reactivity is observed and this is accompanied by a low selectivity. The effect of the amount of NaOH added per AGU on the selectivities is shown in Figure 3. Figure 3 also shows that a substantial amount of ethylene oxide can disappear by reaction with the swelling inhibitor (SHHS). Swelling of the Starch Granules. In aqueous slurries the starch granules swell by uptake of water. This is confirmed by our measurements of E,: the total volume of the swollen starch granules, t,V, is higher than that calculated from the dry starch with a density of approximately 1500 kg m3 (Haine et al., 1985). The swelling is stimulated by OH- ions. However, up to a OH- concentration of the water phase of 0.005 kmol m-3, the swelling is hardly a function of this concentration, as is shown in Table 2 (experiments 1-6, column 1). However, the values of e, in Table 2 indicate a sharp increase in the swelling of the starch granules from an amount of approximately 0.050 mol NaOH/mol of AGU. Additional measurements of ee confirm this, as is shown
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 986 Table 2. Kinetic Data, Selectivities, and Distribution Coefficients of the Hydroxyethylationof Starch in Aqueous Slurry Phase Experiments at 303 K NN~OH, kmol/kmol 0.00 0.0075 0.015 0.025 0.0325 0.040 0.060 0.075
exP 1 2 3 4 5 6 7 8 a
10bk&,
s-1
0.32 0.35 0.57 0.74 0.86 1.17 1.54 1.94
SHES
SED
0.07 0.22 0.42 0.51 0.54 0.53 0.68 0.62
0.59 0.60 0.30 0.31 0.29 0.20 0.14 0.17
SHHs 0.28 0.21 0.114 0.078 0.048 nma 0.030 nma
COHt
CROP
mol m-S 0.0 0.9 1.9 2.8 3.5 3.6 4.6 13.0
kmol m-S 0.0 0.0169 0.0567 0.105 0.155 0.191 0.244 0.286
mm 0.22 0.23 0.23 0.25 0.23 0.24 0.29 0.29
0.53 0.50 0.25 0.39
0.44 0.49 0.53 0.55
nm = not measured. Lo 0.8
r
1
S
LHS of Eq.1251
[-I
s-l~
I
,*
0 &-. 0.00
L - . - l - . - U - l l E05
0.10
0.15
020
0.25
0.30
cRO I k ~ n o l . m - ~ ]
NNaOH [kmol/krnol AGUI
Figure 5. Graphical determination of ~ = 303 K.
Figure 3. Effect of alkali on the selectivities.
0.32 Oa4
028
1 i
The left-hand side of eq 25 is plotted versus CRO as shown in Figure 5 with a value of mEO = 0.46. The fact that the experimental points are located on a straight line confirms the first-order kinetics of the hydroxyethylation reaction with respect to RO-. The fact that the apparent order does not shift toward one-half-order kinetics in RO- at high RO- concentrations is additional proof of the absence of diffusion limitation of ethylene oxide in the starch granules at the experimental conditions used. The uncatalyzed reaction (eq 3) is almost negligible. With CROH = 17.7 kmol m3 a value of k ~ =o(1.1~f 0.08) X lo-' m3 kmol-l s-l was calculated. From the slope of the line in Figure 5 a value for k ~ =o (2.54 f 0.18) X lo-' m3 kmol-l s-1 was derived. In further results at other temperatures we will neglect the uncatalyzed starch hydroxyethylation. The kinetics of the side reactions are discussed below. The experiments at conditions other than 303 K and 0.7 M NazSOr were carried out in a semibatch reactor, at a stationary concentration of ethylene oxide. The experimentally observed reaction rate (-REO) at constant ethylene oxide concentration is a summation of the contributions of several reactions, all consuming
+
o'oo 0
0.02
0.04
0.06
0.08
"=OH
010
0.12
0.14
T
slurry is absorbed by the starch phase. A deviation of 1% in C E O , ~ , Oresults therefore in a deviation of 10% in mm. As is shown below, an averaged value of m m of 0.46 fO.09 m3 of water phase/m3 of starch phase, independent of the concentration of NaOH, fits the kinetic model to the experiments very well. Kinetics of the Starch Hydroxyethylation. In order to calculate k ~ and o ~~ R Ofrom eq 22, this equation is rewritten as
/
1
R and O ~ R O from H eq 25.
036
[krnol/kmol AGUI
Figure 4. Effect of alkali on the volume fraction of the starch granules. Conditions as in Table 1.
in Figure 4. The low es corresponds with a water uptake of 0.48 kg/kg of starch, and the high value of e, with 0.77 kg/kg of starch. The low values agree well with earlier measurements under slightly different conditions (Brown and French, 1977; BeMiller and Pratt, 1981; Evans and Haisman, 1982). The increased swelling can be a reason to keep the NaOH concentration below 0.050 mol/mol of AGU in industrial practice, in order to avoid gelatinization. Distribution of Ethylene Oxide. The variation of mEO with N N ~ Osee H , Table 2, is caused by a low accuracy of the distribution measurements. Only approximately 10% of the total amount of ethylene oxide added to the
986
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994
Table 3. Rate Constants of Starch Hydroxyethylationand Experimental Conditions CClt
cso.
kmol m 3
CEG, kmol m 3
CEO,
CRO,
kmol m 3
kmol m 3
mEO
MS
l@mEOhlO, m3 kmol-1 s-1
T = 293 K 0.26 0.26
0.062 0.046 0.018
0.428 0.605 0.600
0.053 0.093 0.045 0.053 3.353 6.660 0.208 0.060 0.021
0.285 0.286 0.320 0.356 0.250 0.118 1.200 0.419 0.314 ref 6
0.095 7.00 0.060 0.094
0.178 0.088 0.146 0.201
0.059 0.139 0.184
0.69 0.54 0.58
0.054 0.109 0.080
0.485 0.429 0.433
0.0672 0.0672 0.0828 0.116 0.188 0.181 0.235 0.138 0.219
0.52 0.57 0.48 0.50 0.30 0.25 0.66 0.45 0.41 0.45
0.050 0.091 0.063 0.075 0.070 0.038 0.128 0.225 0.116
1.53 1.59 1.43 1.22 1.18 1.21 1.08 1.55 1.36 1.17
0.0432 0.125 0.211 0.156
0.64
