Liquid–Liquid Equilibrium Data, Viscosities, Densities, Conductivities

Article pubs.acs.org/jced

Liquid−Liquid Equilibrium Data, Viscosities, Densities, Conductivities, and Refractive Indexes of Aqueous Mixtures of Poly(ethylene glycol) with Trisodium Citrate at Different pH Mohsen Pirdashti,*,† Kamyar Movagharnejad,† Abbas Ali Rostami,‡ Pegah Akbarpour,§ and Mahnam Ketabi§ †

Faculty of Chemical Engineering, Babol University of Technology, P.O. Box, 484, Babol 46161-19987, Iran Faculty of Chemistry, University of Mazandaran, P.O. Box 453, Babolsar 46161-19987, Iran § Faculty of Chemical Engineering, Shomal University, P.O. Box 731, Amol 46161-19987, Iran ‡

ABSTRACT: The phase diagrams and compositions of coexisting phases have been determined and correlated for poly(ethylene glycol) (PEG) 3000 + trisodium citrate aqueous two-phase systems (ATPS’s) at 25 °C and different pH values (6.1, 7.5, and 9.0). It was found that an increase in pH caused the binodal curve to be displaced downward and also the expansion of the two-phase region. The experimental binodal data of the mentioned system has been successfully correlated with Bleasdale equations (high R2 and low AARD). Furthermore, the viscosities, densities, electrical conductivity, and refractive index of binary (PEG 3000 + water; trisodium citrate + water) and ternary (PEG 3000 + trisodium citrate + water) systems at the above pH value have been measured and correlated. The density data show a linear variation with mass fraction of the polymer and also the salt. The viscosity data of PEG 3000 solutions were correlated as a function of mass fraction, using a nonlinear equation. The effect of tie line lengths on density and viscosity of the aqueous two-phase systems has also been represented.

1. INTRODUCTION

2. EXPERIMENTAL SECTION 2.1. Materials. Polyethylene glycol, with a mass average 3000 g mol−1, trisodium citrate (anhydrous GR for analysis, > 99 %), sodium hydroxide (NaOH; mass purity > 0.99) and sulfuric acid ((95 to 97) % H2SO4, GR for analysis, > 95.0 %) were obtained from Merck (Darmstadt, Germany) and used without further purification. Distilled, deionized water was used for the preparation of solutions. All other materials were analytical grade. 2.2. Apparatus and Procedure. The binary (PEG 3000 + water; trisodium sulfate + water) and ternary (PEG 3000 + trisodium sulfate + water) systems were prepared by adding the suitable mass of individual solution to 10 g by the addition of double-distilled−deionized water in 15 mL graduated tubes utilizing an analytical balance (A&D., Japan, model GF300) with a precision of ± 10−4 g. To achieve the constant temperature (25 °C) with an uncertainty of 0.05 °C, the tubes were placed in a thermostatic bath (Memert., Germany, model INE400) and then the densities, viscosities, electrical conductivities, and refractive indexes of the solutions were measured. The densities of pure liquids and their mixtures were measured using an Anton Paar oscillation U-tube densitometer (model: DMA 500) with the

Aqueous two-phase system (ATPS), a liquid−liquid extraction (LLE) strategy, is now recognized as a potential technique because of its multiple advantages including biologic compatibility,1 ease of continuous process,2−7 low interfacial tension,8 short processing time,9 low material cost,10,11 low energy consumption,12,13 good resolution,14 a high yield,15a relatively high load capacity,16 scaling up feasibility,17−19 selective extraction,20 separation of metal ions,21−24 and efficient procedure for separation of various biological materials such as recombinant proteins and enzymes.25−31 Phase diagram data and data on the composition and the physical properties of the phase forming are necessary for the design, optimization, and scale up of such processes and also necessary for the development of models that predict phase partitioning.32−34 This work is devoted to obtaining phase equilibrium data and the correlation of binodal data for ATPSs containing PEG 3000 + trisodium citrate at pH 6.1, 7.5, and 9.0. Also, an attempt is made to measure and correlate the viscosity, density, and electrical conductivity, and refractive index of binary (PEG 6000 + water; trisodium citrate + water) and ternary (PEG 6000 + trisodium citrate + water) systems and also the top and bottom phases of the two-phase system. © 2015 American Chemical Society

Received: August 19, 2015 Accepted: October 20, 2015 Published: October 28, 2015 3423

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accuracy of ± 10−4 g·cm−3 calibrated with double- distilled water and air. An Anton Paar viscometer Lovis 2000 M with different capillary sizes (1.59 mm and 1.8 mm) for measuring a range of (0.5 to 300) mPa·s with an accuracy of up to 0.5 % was used to measure the viscosities of the solutions at 25 °C. The uncertainties of the measurement of viscosity were ± 0.002 mPa·s. Electrical conductivity was measured at 298.15 K using a JENWAY 4510 model, having a precision 0.01 μS to 1 mS. The refractive index was measured by a (CETI Belgium model) refractometer with a precision of 0.0001 nD. A titration method was applied to determine the binodal curves. A salt solution of known concentration was titrated with the polymer solution or vice versa, until the solution turned turbid. The composition of the mixture was determined by mass. According to phase composition data obtained from the above experiments, feed samples (10 g) were prepared by mixing appropriate amounts of polymer, salt, and water in 15 mL graduated tubes at 25 °C, and the pH values of the salt solutions were adjusted by mixing the appropriate ratio of trisodium citrate, sodium hydroxide, and sulfuric acid, respectively. The pH values of the solutions were measured precisely with a Metrohm 827 pH Lab meter (Swiss made). The contents of the test tube were rigorously vortexed for 5 min, before being placed in the 25 °C thermostatic bath for 2 h. To separate the resulting phases, the tubes were centrifuged (Hermle Z206A, Germany) at 6000 rpm for 5 min. The resulted phases showed no turbidity and the top and bottom samples were easily separated. Then the densities, viscosities, electrical conductivity refractive indexes and of both the top and bottom phases were measured at 25 °C. All data measurements were conducted in duplicate, and the average values are reported. The concentration of PEG 3000 was measured by the refractive index method, while the concentration of the trisodium citrate was determined by the conductivity method.35−37 The calibration method was applied to measure both the refractive index and conductivity of the phases at 25 °C. First, the calibration plots of refractive index and conductivity were prepared for the known phase composition. Then, the measured values are interpolated. The average relative deviation of salt and polymer concentration by this method is about 0.1 (wt %).

Table 1. Density, ρ, Viscosity, Refractive Index, nD, and Electrical Conductivity, k, for the PEG 3000 (p) + Water System at 298.15 K at Various Mass Fractions of PEG, wP ρ wp 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

kg.m

η −3

0.9970 1.0061 1.0115 1.021 1.0305 1.0395 1.0487 1.0569 1.0662 1.0751 1.0857

k

mPa·s

nD

mS·cm−1

0.894 1.575 2.204 3.950 5.962 9.714 14.090 21.620 27.180 35.900 58.330

1.3327 1.3401 1.3450 1.3517 1.3600 1.3661 1.3747 1.3815 1.3881 1.3964 1.4030

0.00 0.13 0.24 0.32 0.44 0.54 0.64 0.73 0.83 0.93 1.02

Table 2. Density, ρ, Viscosity, Refractive Index, nD, and Electrical Conductivity, k, for the Trisodium Citrate + Water System at 298.15 K at Various Mass Fractions of Salt, ws

3. RESULTS AND DISCUSSION The viscosities, densities, electrical conductivities, and refractive indexes of aqueous solutions of PEG 3000 + water and trisodium citrate + water at 25 °C are given in Tables 1 and 2. As shown in Figures 1 to 4, the density and viscosity data show a linear and nonlinear increase, respectively, with increasing mass fraction of the PEG 3000. These effects also were observed in the trisodium citrate + water system. An increase in the refractive index with increasing concentration was found in the salt solution and also in the polymer solution. Obviously both these changes were linear. The electrical conductivity of the polymer solution is very different compared to that of the salt solution. In both solutions, the electrical conductivity will increase by increasing the concentration, but the electrical conductivity of the polymer solution is very low. A change of PEG3000 concentration in the range of 0 % to 50 % (w/w) results in a 1.02 mS·cm−1 conductivity of the solution which is negligible comparated to 66.45 mS·cm −1 changes that occur in the citrate salt concentration. This finding agrees with most of the data reported in the literature for similar systems.32,35,38−41

ρ

η

ws

kg.m−3

mPa·s

nD

mS·cm−1

0.00 0.02 0.04 0.06 0.08 0.10 0.20 0.30 0.40 0.50

0.9970 1.0080 1.0193 1.0300 1.0403 1.0540 1.1219 1.1881 1.2433 1.2952

0.894 0.940 1.033 1.065 1.126 1.210 1.805 3.067 5.952 9.700

1.3327 1.3357 1.3388 1.3416 1.3450 1.3480 1.3638 1.3800 1.3932 1.4069

0.00 11.01 21.30 28.50 35.20 40.60 49.41 57.60 62.56 66.45

k

Figure 1. Density, ρ, and viscosity, η, of binary system PEG 3000 + H2O at 298.15 K as a function of the PEG mass fraction (wP). The solid curves represent the empirical model.

The viscosities, densities, electrical conductivities, and refractive indexes of the PEG 3000 + trisodium citrate + water systems are given in Table 3. For the correlation of physical properties of the mentioned binary and ternary systems some empirical expressions were proposed (Tables 4 and 5). These correlations also have been shown in Figures 1 to 4. All attempts were made to decrease the complexity of model and increase the accuracy. Additionally, some well-known equations applied to correlate the viscosity of the PEG 3000 + trisodium citrate + water systems 3424

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Table 3. Density, ρ, Viscosity, Refractive Index, nD, and Electrical Conductivity, k, for the Aqueous Single-Phase System (PEG 3000 (p) + Trisodium Citrate (s) + Water System) at 298.15 K ρ

Figure 2. Refractive index, nD, and electrical conductivity, k, of binary system PEG 3000 + H2O at 298.15 K as a function of the PEG mass fraction (wP). The solid curves represent the empirical model.

Figure 3. Density, ρ, and viscosity, η, of binary system trisodium citrate + H2O at 298.15 K as a function of the salt mass fraction (ws). The solid curves represent empirical model.

wp

ws

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.06 0.08 0.08 0.08 0.08 0.08 0.10 0.10 0.10

kg·m

η −3

1.0172 1.0254 1.0341 1.0442 1.0521 1.0624 1.0696 1.0798 1.0297 1.0384 1.0477 1.0571 1.0648 1.0746 1.0835 1.0394 1.0503 1.0597 1.0695 1.0788 1.0504 1.0607 1.0709 1.0808 1.0914 1.0639 1.0780 1.0883

k

mPa·s

nD

mS·cm−1

1.656 2.317 4.152 6.267 10.21 14.81 22.73 28.57 1.820 2.547 4.565 7.110 11.23 16.56 25.41 1.876 2.678 4.799 7.393 11.80 1.983 2.897 5.147 7.876 12.84 2.131 2.985 5.350

1.3435 1.3491 1.3558 1.3639 1.3705 1.3790 1.3857 1.3924 1.0297 1.0384 1.0477 1.0571 1.0648 1.0746 1.0835 1.0394 1.0503 1.0597 1.0695 1.0788 1.0504 1.0607 1.0709 1.0808 1.0914 1.0639 1.0780 1.0883

10.19 8.01 6.66 5.48 4.37 3.20 2.83 1.85 16.53 14.00 11.39 8.59 8.12 5.65 2.88 22.10 17.95 14.90 10.99 8.71 29.70 25.00 17.65 10.65 4.54 33.90 28.10 22.30

Table 4. Some Proposed Semiempirical Relations To Predict the Physical Properties of Binary Systems coefficients of equation binary system

PEG3000 + water

as shown in Table 6. According to the Table 6, the Grunberg-like equation agrees well with the experimental data. Furthermore, binodal data obtained from turbidimetric titrations of the mixtures of polyethylene glycol 3000 + trisodium citrate + water at different pH values (6.1, 7.5, and 9.0) at 25 °C are presented in Table 7. For the correlation of binodal data, the Bleasdale equation42 can be suitably used to reproduce the binodal curves of the investigated system. wp = (a + bws)−1/ c

AARDa (%)

0.9956

0.1770

0.0316

1 a + bwp

1.0033

−0.1638

0.0224

η = aebwp

1.4799

7.2946

7.9212

1 nD = a + bwp

0.7506

−0.0759

0.0151

nD = a + bwp

1.3317

0.1419

0.0184

k = a(1 − e−bwp)

4.5444

0.5064

1.3423

k = a + bwp

0.0250

2.0164

0.7452

ρ = a + bws

0.9954

0.6138

3.5887

0.7104

5.2296

3.5882

1.3330

0.1505

0.0179

9.5676

1.3988

η = ae trisodium citrate + water

b

ρ = a + bwp

ρ=

Figure 4. Refractive index, nD, and electrical conductivity (k) of binary system trisodium citrate + H2O at 298.15 K as a function of the salt mass fraction (ws). The solid curves represent empirical model.

a

equation

bws

nD = a + bws k = a(1 − e

k = a + bws

−bws

)

63.4891 17.5093

116.198

9.2678

a

Average absolute relative deviation AARD = (1/N)∑IN= 1(((100(ρexp − ρcal))/ρexp)2)0.5.

(1) 3425

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Table 5. Some Proposed Semi-empirical Relations to Predict the Physical Properties of Ternary Systems coefficients of equation a

b

c

AARD (%)

0.9941

0.1846

0.6293

0.0253

0.2485

0.1501

0.5986

0.0350

350.5760

2.0637

0.1391

6.4899

191.9533

−40.2025

−71.3201

58.4015

8.8679

10.8497

−5.5232

79.4118

27.7914

12.1930

nD = a(wp + ws )

0.3580

0.02162

−0.2567

1.20273

nD = a + b ln wp + c ln ws

0.5608

0.0116

−0.1960

1.2969

nD = a + bwp + cws

1.2928

0.1669

−3.3445

1.6202

k = a + bwp + cws

12.0086

−48.0956

180.8864

12.2259

23.0723

−8.0875

8.2525

14.6120

0.3782

0.2598

−0.5660

23.0081

equation

ρ = a + bwp + cws

ρ = a + be b

η = awp ws

wp

+ ce

ws

c

2

η = awp − bws η = a + be

wp

+ ce

ws

η = a + bwp + cws b

c

k = a + b ln wp + c ln ws

k = 1/(a + be

wp

ws

+ ce )

8.8161

Table 6. Comparison of Some Semi-empirical Models with the Proposed Model in This Work To Predict the Physical Properties of Ternary Systems model

equation

constant

Grunberg-like

⎛ w ⎞ ⎛ wp ⎞ s ⎟⎟ln ws + wpwa ⎟⎟ln η + ⎜⎜ ln η = ⎜⎜ s ps p ⎝ wp + ws ⎠ ⎝ wp + ws ⎠

Grunberg−Nissan

ln η = wp ln ηp + ws ln ws + wpwD s ps

Arrhenius

log η = wp log ηp + ws log ws

pH = 7.5

100 ws

100 wp

100 ws

100 wp

100 ws

19.50 16.70 13.72 10.83 9.54 8.84 8.19 4.68 4.13 4.08 2.16 1.27 1.11 1.03 1.00 0.95 0.50 0.22

9.12 10.00 12.28 14.26 15.40 15.97 16.55 18.98 20.09 19.88 22.50 24.15 24.46 24.52 25.67 25.93 26.34 28.83

21.20 18.16 17.27 16.63 16.24 10.28 10.08 9.98 9.97 8.11 7.99 7.92 7.86 5.35 4.36 3.50 3.02 2.10 1.24 0.75 0.36 0.23 0.15

7.10 8.12 8.39 8.59 8.68 10.99 11.13 11.05 11.19 12.56 12.51 12.51 12.46 14.10 14.76 15.74 16.22 17.40 19.00 21.30 23.90 5.12 26.10

22.43 17.50 15.22 14.36 13.58 12.97 10.28 7.01 6.91 6.51 4.82 4.28 2.41 1.29 0.91 0.86 0.64 0.43 0.28 0.24

4.63 6.02 6.63 6.91 7.01 7.12 8.15 9.51 9.32 9.53 10.75 11.17 12.80 14.37 15.74 16.40 18.70 21.70 24.40 25.90

2.4668 7.8279 13.5825

where a, b, and c represent the fitting parameters, and wp and ws represent the mass fraction of polymer and salt, respectively. The binodal data of the above expression were correlated by leastsquares regression (Table 8). Experimental and correlated binodal curves of studied systems are shown in Figure 5.

pH = 9.0

100 wp

1.777 118.4

Table 7. Binodal Curve Data of the PEG3000 + Sodium Citrate + Water System at 298.15 K at Different pH Values pH = 6.1

AARD (%)

Table 8. Values of Parameters of eq 1 for PEG3000 + Trisodium Citrate + Water at Different pH Values pH

a

b

c

AARD (%)

R2

6.1 7.5 9.0

6.636439 2.812207 1.000135

−0.226462 −0.091112 −0.0000008

−0.515813 −0.252284 −0.000031

5.94669 5.155643 5.751086

0.998545 0.999439 0.996289

Figure 5 shows the influence of the pH on the binodal curve of PEG 3000 + trisodium citrate aqueous two-phase system. From this figure it can be observed that the binodal was displaced downward as the pH of the moderate increased, demonstrating that the smaller concentration of the phase polymers is required to form ATPSs. A comparable conduct was also described.43−45 As the charge of the solute and ratio of the charged species are functions of pH, the binodal location is also a function of pH. It is known that the hydrogen-bond interactions of PEG are weakened as the pH rises, and this fact may lead to the saltingout phenomenon. The salt’s ability to promote the water structure may be responsible for this salting-out. The stronger affinity of citrate salt ions toward water in comparison to PEG may result in a decrease in hydration and the solubility of PEG. The ultimate result of this process may be the exclusion of PEG from the rest of solution.44 3426

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Figure 6. Effect of pH on the equilibrium phase compositions and on the slope and length of tie lines for the PEG3000 + trisodium citrate + H2O system: ▲, total composition; ■, bottom phase composition; ●, top phase composition.

Figure 5. Experimental and correlated binodal curves of ATPSs of PEG3000 + trisodium citrate + water at different pH values. The solid curves represent correlated binodals.

The equilibrium phase compositions, tie line data, and physical properties of the top and bottom phases are shown in Table 9. Experiments were carried out with three feed solutions containing PEG 3000 + trisodium citrate + water at three pH values. The experimental results for the feed solutions and additionally for the resulting coexisting phases are also given in Table 9. Likewise it can be recognized from the data of Table 9 that an increment in salt composition at constant pH increases the concentration of PEG in the top phase. This may be clarified by the hydration impact of salt. The tie-line length (TLL) is an empirical measure of the compositions of the two phases, which can be calculated by the following equation: TLL =

(Cp top − Cp bottom)2 + (Cs bottom − Cs top)2

PEG3000 + trisodium citrate + H2O system. The TLL and STL for the above system increased with an increase in pH. A comparable conduct was likewise depicted.39,44This phenomenon may be due to the hydrodynamic volume decrease of the solution. Waziri et al. (2003) and Shahbazinasab and Rahimpour (2012) reported that decreasing the pH leads to reduction in intrinsic viscosity of the polymer solution.44,46 As we know that the hydrodynamic volume of polymers in solution is proportional to their intrinsic viscosity, it can be found that the pH decrease leads to more compact structure of polymer chains. It is reported that as the pH of the aqueous PEG−salt two-phase system increases, the concentration in the PEG-rich phase increases and the concentration in the salt-rich phase decreases. The effect of tie line lengths on density, dynamic viscosity, and kinematic viscosity of the aqueous two-phase systems has also been considered. The density difference between the phases (Δρ) and the viscosities difference between the phases (Δη), increase with an increase in the TLL and decrease with an increase in pH. From Figures 7, 8, and 9, it is observed that the density and viscosities differences between the phases show a linear relationship with the TLL. A comparable conduct was likewise depicted.43,44

(2)

The slope of the tie line (STL) is given by the ratio of the difference between the concentration of the polymer (CP) and of the salt (CS) in the top and bottom phases, as presented in eq 3: STL =

Cp top − Cp bottom Cs bottom − Cs top

(3)

Figure 6 show the effect of pH on the equilibrium phase compositions and on the slope and length of tie lines for the

Table 9. Phase Composition, Tie Line Data and Physical Properties of PEG3000 + Sodium Citrate + Water Aqueous Two Phase System at Various pH top phase (% mass) ρ

total system (% mass)

bottom phase (% mass) η

−3

ρ

η −3

pH

100 wp

100 ws

100 wp

100 ws

kg·m

mPa·s

100 wp

100 ws

kg·m

6.1

10.0 7.0 7.0 10.0 10.0 5.0 6.0 5.0 5.0

18.0 20.0 18.5 16.0 14.5 17.0 21.0 17.0 13.5

17.35 15.64 13.05 18.06 15.30 13.25 24.60 21.65 18.54

9.88 11.02 12.89 8.01 9.18 9.68 4.19 4.98 5.82

1.0891 1.0944 1.1018 1.0791 1.0858 1.0834 1.0603 1.0602 1.0602

7.321 6.101 4.327 7.292 5.610 4.373 10.89 8.324 7.019

0.42 0.79 1.95 0.31 0.45 1.11 0.32 0.81 1.03

29.01 26.35 22.90 26.20 23.80 20.13 25.90 20.20 15.80

1.1798 1.1645 1.1447 1.1617 1.1464 1.1212 1.1599 1.1239 1.0988

7.50

9.00

3427

TLL

STL

mPa·s

%

%

3.345 3.161 2.980 2.765 2.125 2.051 2.681 1.970 1.863

25.55 21.34 14.95 25.42 20.84 16.02 32.57 25.81 20.15

0.88 0.97 1.11 0.98 1.02 1.16 1.12 1.37 1.75

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the Bleasdale equation. Moreover, the densities, viscosities, electrical conductivities, and refractive index of the binary and ternary mixtures of PEG 3000 + trisodium citrate + water-based aqueous two-phase systems were measured and correlated at 25 °C. Some empirical models were developed to describe the physical properties of binary and ternary systems. The models can be able to reproduce the experimental data precisely.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 7. Relationship between density difference (Δρ) and tie line length (TLL) for the PEG 3000 + trisodium citrate + water at different pH values.

REFERENCES

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Figure 8. Relationship between viscosity difference (Δη) and tie line length (TLL) for the PEG 3000 + trisodium citrate + water at different pH values.

Figure 9. Relationship between kinematics viscosity difference (Δν) and tie line length (TLL) for the PEG 3000 + trisodium citrate + water at different pH values.

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CONCLUSIONS New experimental results are presented for liquid−liquid equilibrium data for the PEG3000 + trisodium citrate + water system at various pH values of 6.1, 7.5, and 9.0 at 25 °C. It was found that the two-phase area is expanded with increasing pH. It was also observed that with increasing pH the slope and length of equilibrium tie-lines for the mention biphasic system increased. The experimental binodal data were satisfactorily correlated with 3428

DOI: 10.1021/acs.jced.5b00705 J. Chem. Eng. Data 2015, 60, 3423−3429

Journal of Chemical & Engineering Data

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DOI: 10.1021/acs.jced.5b00705 J. Chem. Eng. Data 2015, 60, 3423−3429