Modeling of surface tension for ionic liquids using

Ionics DOI 10.1007/s11581-014-1347-1

ORIGINAL PAPER

Modeling of surface tension for ionic liquids using group method of data handling Saeid Atashrouz & Ershad Amini & Gholamreza Pazuki

Received: 13 May 2014 / Revised: 6 December 2014 / Accepted: 10 December 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract The group method of data handling (GMDH) was utilized to estimate the surface tension of 59 ionic liquids. In this regard, an extensive experimental data was selected from literature over the range 268.3 to 532.4 K. The GMDH model can predict the surface tension of ionic liquids by a grand polynomial correlation function of molar density, reduced boiling temperature, reduced temperature and pressure, acentric factor, and critical compressibility factor. The values of the GMDH model showed a very good regression with the experimental data. The average absolute relative deviation (AARD%) of the GMDH model for all ionic liquids was 4.59 % which indicated a good precision in comparison with those obtained from the generalized dimensionless equation, Mousazadeh–Faramarzi equation, and Parachor equation with AARDs% of 10.31, 13.02, and 11.89, respectively.

[C2C2im] [bti]

Keywords Surface tension . Ionic liquids . GMDH . Neural network . Modeling

[C5C5im] [bti]

Abbreviations IL [C2OHmim] [BF4]

[Bdmim] [bti]

[C10C10im] [bti] [C4C4im] [bti]

Ionic liquid 1-(2-Hydroxyethyl)-3methylimidazolium tetrafluoroborate 1,3-Decylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Dibutylimidazolium bis[(trifluoromethyl)sulfonyl]imide

S. Atashrouz : G. Pazuki (*) Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran e-mail: [email protected] E. Amini School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran

[C1C1im] [bti] [Dmim] [MSO4] [C3C3im] [bti] [C7C7im] [bti] [C6C6im] [bti] [C9C9im] [bti] [C8C8im] [bti]

[Bmpyr] [bti]

[Bdmim] [PF6] [Bmim] [bti] [Bmim] [Cl] [Bmim] [dca] [Bmim] [PF6] [Bmim] [I] [Bmim] [MSO4] [Bmim] [BF4]

1,3-Diethylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Dimethylimidazolium methylsulfate 1,3-Dipropylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Heptylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Hexylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Nonylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Octylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1,3-Pentylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide 1-Butyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Butyl-2,3-dimethylimidazolium hexafluorophosphate 1-Butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Butyl-3-methylimidazolium chloride 1-Butyl-3-methylimidazolium dicyanamide 1-Butyl-3-methylimidazolium hexafluorophosphate 1-Butyl-3-methylimidazolium iodide 1-Butyl-3-methylimidazolium methylsulfate 1-Butyl-3-methylimidazolium tetrafluoroborate

Ionics

[Bmim] [tca] [Bmim] [TfO] [Mbpy] [bti] [Mbpy] [BF4] [Emim] [bti] [Emim] [dca] [Emim] [ESO4] [Emim] [BF4] [Emim] [TfO] [N-epy] [bti] [Hpmim] [bti] [Hmim] [bti] [Hmim] [Cl] [Hmim] [PF6] [Hmim] [BF4] [Hpy] [bti] [Omim] [bti] [Omim] [PF6] [Omim] [BF4] [Pmim] [bti] [Prmim] [bti] [Prmim] [PF6] [Prmim] [BF4] [2-HDEA][HCO2] [Mbupy] [BF4] [Prmpy] [bti] [N1136] [bti]

1-Butyl-3-methylimidazolium thiocyanate 1-Butyl-3-methylimidazolium trifluoromethanesulfonate 1-Butyl-4-methylpyridinium bis[(trifluoromethyl)sulfonyl]imide 1-Butyl-4-methylpyridinium tetrafluoroborate 1-Ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Ethyl-3-methylimidazolium dicyanamide 1-Ethyl-3-methylimidazolium ethylsulfate 1-Ethyl-3-methylimidazolium tetrafluoroborate 1-Ethyl-3-methylimidazolium trifluoromethanesulfonate 1-Ethylpyridinium bis[(trifluoromethyl)sulfonyl]imide 1-Heptyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Hexyl-3-methylimidazolium chloride 1-Hexyl-3-methylimidazolium hexafluorophosphate 1-Hexyl-3-methylimidazolium tetrafluoroborate 1-Hexylpyridinium bis[(trifluoromethyl)sulfonyl]imide 1-Octyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Octyl-3-methylimidazolium hexafluorophosphate 1-Octyl-3-methylimidazolium tetrafluoroborate 1-Pentyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Propyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-Propyl-3-methylimidazolium hexafluorophosphate 1-Propyl-3-methylimidazolium tetrafluoroborate 2-Hydroxydiethylammonium formate 2-Methyl-N-butylpyridinium tetrafluoroborate 3-Methyl-1-propylpyridinium bis[(trifluoromethyl)sulfonyl]imide Dimethylhexyl(i-propyl)ammonium bis[(trifluoromethyl)sulfonyl]imide

[N1134] [bti] [Mbpyr] [dca] [P2444] [DEP] [N6222] [bti] [6,6,6,14-P] [bti] [6,6,6,14-P] [Cl] [N1114] [bti] [N111,10] [bti] [N1116] [bti] [N8111] [bti]

Dimethylpropylbutylammonium bis[(trifluoromethyl)sulfonyl]imide n-Methyl-n-butylpyrrolidinium dicyanamide Tributyl(ethyl)phosphonium diethylphosphate Triethylhexylammonium bis[(trifluoromethyl)sulfonyl]imide Trihexyltetradecylphosphonium bis[(trifluoromethyl)sulfonyl]imide Trihexyltetradecylphosphonium chloride Trimethylbutylammonium bis[(trifluoromethyl)sulfonyl]imide Trimethyldecylammonium bis[(trifluoromethyl)sulfonyl]imide Trimethylhexylammonium bis[(trifluoromethyl)sulfonyl]imide Trimethyloctylammonium bis[(trifluoromethyl)sulfonyl]imide

Nomenclature List of symbols a Polynomial coefficient in Eq. (1) and adjustable parameter in Eq. (7) b Adjustable parameter in Eq. (7) F(0) F(1) Functions in Eq. (6) k Boltzmann constant l Number of layers M Number of observations MW Molecular weight (g mol−1) n Number of data points N Intermediate layer P Pressure (bar) Pch Parachor ((mN m−1)1/4 cm3 mol−1) T Temperature (K) x Input parameters in Eq. (1) y0 Output Z Compressibility factor Greek letters γ Surface tension (mN m−1) σ Hard-sphere segment diameter (0A) ε/k Well depth parameter (K) ρ Density (g cm−3) ω Acentric factor Subscript b Boiling br Reduced boiling c Critical cal Calculated exp Experimental

Ionics

m r

Melting Reduced

Superscript exp Experimental GMDH Group method of data handling * Dimensionless

Introduction In recent years, ionic liquids have had far-reaching applications in chemical industry [1] due to their specific characteristics including excellent thermal stability, advantageous solvating properties for various compounds, nonionizing, highly viscous, low vapor pressure, and nonflammability [2, 3]. To design the industrial processes in which ionic liquids (ILs) are used, it is necessary to characterize their thermodynamics and thermophysical properties, such as density, viscosity, and surface tension. The surface tension is an imperative property in chemical processes [4] since it relates to phenomenon in which there is a vapor–liquid interface. Although the physical properties of ILs have been measured experimentally [5–7], these experimental data are very scarce. The experimental measurements are sometimes expensive, or they are limited to a specific range of temperature or pressure. Therefore, theoretical methods are needed to obtain more data in a broader range of temperature or pressure. One theoretical method, which has interested researchers, is artificial neural networks (ANNs). The ANN is practical and flexible model; hence, these characteristics have led them to be used in various fields to model complicated nonlinear connections [8, 9]. Some models have been proposed in the literature to predict physiochemical properties of ILs using quantitative structure–property relationship (QSPR) [10], ANNs [11, 12]. Gardas and Coutinho [10] implemented a QSPR correlation to predict the surface tension of 40 ILs using the molecular volume information. The experimental surface tension data were gathered from the literature. Their proposed model estimated surface tension with 4.5 % deviation. Heat capacity is another important characteristic of ILs. Using ANNs, a model was performed to correlate the binary heat capacity of ILs [11]. The experimental data were divided into two subsections: training and testing. The testing data were used to validate the proposed network. From the acquired data, the heat capacity of ILs was predicted with AARD% of

1.60. However, it should be noted that for heat capacity of ILs, there is the problem of lack of consistency of data between different authors. In this regard, selection of experimental data to develop a model is difficult. ANN’s structure is extremely complex and presents a massive complicated of equations throughout its nodes and layers. As well, the arrangement of network is selected manually or randomly which does not guarantee the best possible network. Whereas, the GMDH method provides a self-organizing neural network to state the genome of system as well as exploiting the most suitable configuration by means of minimization procedure. In the other word, the GMDH utilizes feedforward network whose coefficients are calculated using regression together with imitation of self-organizing activity [13, 14]. Estimation of vapor–liquid equilibrium of binary systems with the help of GMDH-type neural network was investigated by Ketabchi et al. [15]. A new model was proposed, which its results were in reasonable agreement with experimental data. In another study, Ghanadzadeh et al. [16] estimated liquid–liquid equilibrium (LLE) data for a ternary system (water + ethanol + trans-decalin) using GMDH-neural network (NN) and genetic algorithm. The results were compared with the experimental data as well the results of the UNIQUAC Functional Group Activity Coefficient (UNIFAC) model. The root-mean-square deviation (RMSD) between the observed and calculated mole fractions using GMDHNN and UNIFAC models were 0.53 and 8.14 %, respectively. To model partition coefficients of penicillin G acylase in polymer–salt aqueous two-phase systems, a hybrid GMDH-NN was developed by Pazuki and Seyfi [17]. The obtained results were more precise compared to the results of the UNIFAC-FV model. They showed that GMDH-NN is an appropriate method to model complex unstructured systems. Atashrouz et al. [14] proposed a hybrid GMDH-NN system for estimation of viscosity of nanofluids. The results showed that the hybrid GMDH-NN model could precisely predict the viscosity of nanofluids. Some studies have investigated the both effect of cation alkyl side chain length and symmetry on the surface tension in ILs [18–20]. Kolbeck et al. [18] and Carvalho et al. [20] revealed that surface tension for [CnC1im] [bti] decreases toward a constant value with increasing the alkyl chain length. Almeida et al. [19] have studied this subject for symmetric ILs [CnCnim] [bti]. The main objective of this study was to exploit a GMDH-NN for estimation of surface tension of ILs. To validate the proposed network, 801 surface tension data points in the wide range of temperature (268.3–532.4 K) were collected from previously published articles [2, 19–40].

Ionics

Group method of data handling With the help of GMDH-NN, a model can be developed as a series of neurons in which various pairs of them in each layer are related using a quadratic polynomial, and thus, new neurons are produced in the next layer. GMDH-NN algorithms are described by inductive process that carries out classifying the complex polynomial models to choose the best quadratic polynomial term. GMDH-NN algorithm initially was presented by Ivakhnenko in which the relation between input and output variables is estimated using Volterra–Kolmogorov– Gabor (VKG) series [41]: y 0 ¼ a0 þ

m m X X i¼1 j¼1

…

m X k¼1

ai j…k xni xnj …xnk n ¼ 0; 1; …; 2l ð1Þ

where xi, xj, and xk are the input parameters; y0 is the output; l is the number of layers; and a0 and aijk are the polynomial coefficients set by algorithm. The approach is to find a function which can approximate the output for a given input vector x=(x1, x2,… xn). This function is expected to be close to actual output. Therefore, the square of differences between the actual and predicted output should be minimized: M X i¼1

2

½ f i ðx1 ; x2 ; …xn Þ−yi  →min

ð2Þ

lack of accurate prediction of these properties especially in ILs, a semi-empirical semi-theoretical correlation was proposed to estimate the surface tension of ILs. Intensive properties including critical temperature (Tc) and pressure (Pc), acentric factor (ω), and critical compressibility factor ( Z c ) are required to predict the thermophysical properties; therefore, these intensive properties were considered in the proposed model. In order to achieve higher accuracy in the proposed GMDH-NN, in addition to the mentioned parameters, boiling temperature and molar density of ILs were considered. Thus, in the proposed GMDH-NN model, the surface tension of ILs was assumed to be a function of independent variables including molar density (b ρ), reduced boiling temperature (Tbr), reduced temperature (Tr), reduced pressure (Pr), acentric factor (ω), and critical compressibility factor (Zc). The values of density, boiling temperature, critical temperature and pressure, acentric factor, and critical compressibility factor of ILs were collected from literatures [42–50]. It should be emphasized that critical properties for all ILs were calculated based on the group contribution method of Valderrama et al. [43]. Furthermore, the surface tension of ILs was calculated using three different correlations containing Mousazadeh–Faramarzi, Parachor, and generalized dimensionless correlations. Mousazadeh and Faramarzi [51] proposed the following relation for the estimation of surface tension of ILs (γ): 

   γm γm γmT b γ ¼ 0:5 −0:819 T þ 0:819 Tb T b −T m T b −T m

where M is the number of observations.

Estimation of surface tension using group method of data handling neural network and thermodynamics models Thermophysical properties such as surface tension are generally calculated using equation of states. Due to the

ρˆ br

r 1

2

3

γ

r

ω

c

Fig. 1 A schematic of the proposed GMDH neural network

ð3Þ

where γm is the surface tension at the melting temperature. Tm and Tb are the melting temperature and boiling temperature, respectively. Melting temperature data were collected from [51–55]. However, it should be noted that it is difficult to obtain γm for wide range of ILs and this value can be very uncertain. Parachor-based model is a simple method to estimate the surface tension of ILs from their densities and vice versa of molecular weights [56]. The surface tensions were calculated using Parachor constants [9, 56]. Using Parachor constants, densities in gram per cubic centimeter unit, and molecular weight in gram per mole unit, the prediction of surface tension in millinewtons per meter units for imidazolium-based ILs can be calculated as follows:  γ¼

Pch ρ MW

4 ð4Þ

Ionics Table 1

Nodal expressions for GMDH neural network

Layer 1

N 1 ¼ 12:87 þ 106633bρ−136331bρT br −46880:2bρZ c þ 21627:7bρω þ 2632:17T br T r − 1946:14T r þ 918:441T r Z c −388:959T r ω Layer 2 N 2 ¼ 976:948 þ 79534:3bρ2 −3018:59T br −97:5025T br ω þ 6:3001T br N 1 þ 2350:26T 2br − 20:5528Pr N 1 −1:97291N 1 −0:00987252N 21 Layer 3

N 3 ¼ 433:238−606:545T br −366:54T br ω þ 1:84905T br N 2 þ 4267:07Pr Z c −599:306Z c þ 860:336Z 2c þ 359:9ω−0:00521937N 22 Genome expression

γ ¼ 16:0097 þ 3882:56bρ−11601:1bρZ c −318:638T r Z c þ 96:5168T 2r − 20:4012Z c N 2 þ 23:6514Z c N 3 −0:08944N 2 N 3 þ 0:090694N 22 ρ), reduced boiling temperature (Tbr), reduced temperature (Tr), reduced pressure (Pr), acentric factor (ω), critical compressibility factor Molar density (b (Zc), surface tension (γ)

Also, we proposed a generalized dimensionless equation for estimation of surface tension. The dimensionless experimental surface tension can be defined as follows: 3 2 " # 2 2 γ σ γ σ 1 7 6 exp exp γ *exp ¼ 4 ε : 5 ¼ ð5Þ k ε k

where σ and ε/k are the size and energy parameters of IL molecule, respectively. k is the Boltzmann constant and is equal to 1.3807×10−23 J K−1. The values of σ and ε/k for ILs were gathered from literature [57]. Meanwhile, the generalized dimensionless equation for estimation of surface tension has the following form: γ *cal ¼ F ð0Þ þ ωF ð1Þ

ð6Þ

where ω is the acentric factor [41] and F(0) and F(1) are defined as follows: F ð0Þ ¼ a0 þ a1 T r þ a2 T 2r þ a3 T 3r

to 70 % of the data set to train the model, and the rest was utilized for model validation. The percentages of average absolute relative deviation (AARD%) for training, testing, and overall data sets were 4.55, 4.68, and 4.59 %, respectively. The AARD% is calculated from the following equation:

   100 X n  γ GMDH −γ exp i  i AARD% ¼  i¼1  n γ exp i

ð9Þ

where n is the number of experimental data points. A schematic of proposed GMDH-NN model is shown in Fig. 1. The model has one input layer, three middle layers, and one output layer. The genome expression with its layer is presented in Table 1. Figure 2 depicts the comparison between experimental data and the estimated results. The GMDH-NN model falls closer to experimental data. Thus, a reasonable

ð7Þ 90 80

F ð1Þ ¼ b0 þ b1 T r þ b2 T 2r þ b3 T 3r

where ai and bi are the adjustable parameters. T r ¼

ð8Þ 

T



=T c is

the reduced temperature.

70

R=0.96

60 50 40 30 20 10

Results and discussion The GMDH network was applied to model the surface tension of ILs. The GMDH network was implemented

0

0

10

20

30

40

50

60

70

80

90

Fig. 2 Estimated surface tension versus experimental data (all ionic liquids)

Ionics Table 2

Comparison of GMDH-NN with various models.

Ionic liquid

Reference

Model (AARD%) GMDH-NN

[Dmim] [MSO4]

[40]

[Emim] [BF4] [Emim] [bti] [Emim] [ESO4] [Emim] [dca] [Emim] [TfO] [Prmim] [bti] [Prmpy] [bti] [Prmim] [BF4] [Prmim] [PF6] [Pmim] [BF4] [Bmim] [bti] [bmim] [Cl] [Bmim] [dca] [Bmim] [I] [Bmim] [MSO4] [Bmim] [PF6] [Bmim] [tca]

[28, 39] [20, 21, 25] [25, 28] [30] [28] [20, 21] [34] [36] [27] [36] [20, 21, 25] [27] [30] [27] [24] [24] [23]

4.81

[Bmim] [TfO]

[28]

[Bdmim] [bti] [Bmpyr] [bti] [Bdmim] [PF6] [Mbpy] [BF4] [Mbpy] [bti] [Mbpyr] [dca] [Mbupy] [BF4] [Pmim] [bti] [Hmim] [BF4] [Hmim] [bti] [Hpy] [bti] [Hmim] [Cl] [Hmim] [PF6] [Hpmim] [bti] [Omim] [BF4] [Omim] [bti] [Omim] [PF6] [6,6,6,14-P] [bti]

[33] [39] [2] [23] [34] [23] [34, 37] [20, 21] [28, 29] [20, 21] [35] [27] [24, 26, 29] [20] [27] [20] [27] [22, 31]

5.89 3.13 6.13 9.29 0.48 14.61 2.82 7.16 2.82 9.14 0.40 2.44 4.35 2.01 5.05 5.23 5.15 6.04

[6,6,6,14-P] [Cl] [P2444] [DEP] [N1114] [bti] [N8111] [bti] [N-epy] [bti] [N1134] [bti] [N1136] [bti]

[22, 31] [22] [22, 25] [22, 25] [34] [22] [22]

4.34 3.02 9.40 11.66 5.91 8.17 5.09

2.70 2.73 5.59 2.78 4.78 2.98 0.33 3.99 1.06 3.39 3.19 1.21 4.73 14.73 2.62 5.56 4.92 8.37

Generalized dimensionless equation – 12.42 5.77 – – – – – – – 9.67 7.28 – – – – 17.08 – – – – – – – – – – 7.39 13.26 – – 10.20 – 3.34 – 20.28

Eq.(3)

2.45

Parachor –

24.79 14.71 10.05 3.96 10.89 13.46 – 22.63 – 16.05 25.76 20.46 4.40 – 23.70 9.67

20.20 9.22 16.71 – 4.62 5.64 – 13.26 10.14 3.46 5.72 10.58 – 29.71 19.72 11.72

– 5.53

– 4.21

– 15.95 – – 13.77 – – – 12.43 – 12.06 – – – 10.41 – 8.73

– – – – – – – 6.59 22.07 4.53 – 7.75 10.24 7.61 17.31 6.67 16.82

–

–

–

– – – – – – –

– – – – 1.29 – –

– – – – – – –

Ionics Table 2 (continued) Ionic liquid

Reference

Model (AARD%) GMDH-NN

[N1116] [bti] [N111,10] [bti] [N6222] [bti] [2-HDEA] [HCO2] [C2OHmim] [BF4]

[22] [22] [22] [32] [38]

2.80 2.95 2.39 4.31 7.93

[C1C1im] [bti] [C2C2im] [bti] [C3C3im] [bti] [C4C4im] [bti] [C5C5im] [bti] [C6C6im] [bti] [C7C7im] [bti] [C8C8im] [bti] [C9C9im] [bti] [C10C10im] [bti] Overall

[19] [19] [19] [19] [19] [19] [19] [19] [19] [19] –

4.55 9.16 7.53 5.78 2.25 3.02 3.96 3.58 3.33 3.64 4.59

agreement between experimental data and the estimated result is observed. A comparison between AARD% of the proposed GMDH-NN model and of the other models for each IL is made in Table 2. It can be concluded that GMDH-NN is more accurate in predicting the surface tension of ILs. Figure 3 illustrates the comparison of experimental surface tension versus calculated for 1-ethyl-3methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

Generalized dimensionless equation

Eq.(3)

– – – – –

Parachor

– – – – –

– – – – – – – – – – 10.31

– – – – –

– 7.28 – – – – – – – – 13.02

– – – – – – – – – – 11.89

([emim][bti]). As shown, GMDH results are closer to experimental data. The dependency of surface tension on the alkyl chain length of the cation is shown in Fig. 4. The proposed GMDH could estimate the experimental surface tension data of Almeida et al. [19] for symmetric series of ILs [CnCnim][bti] (n=1−10) as a function of the total number of carbons. The surface tension initially decreases with increasing the number of carbons but reaches a plateau for alkyl chain lengths greater than n=6. 45

45 40 35 30

Experimental data

35

GMDH

30

25

Generalized equation

20

Parachor

15

Eq. (3)

10

Experimental

40

25 20 15

250

300

350

400

450

Fig. 3 Comparison of experimental surface tension versus calculated for [emim][bti]

GMDH

0

4

8

12

16

20

24

Fig. 4 Surface tension dependence, at 298 K, as a function of the total number of carbons in the aliphatic chains for [CnCnim] [bti] (n=1−10)

Ionics

Conclusion In the current study, a GMDH-NN model was developed using the experimental data for the surface tension of ILs over the temperature range of 268.3–532.4 K. The surface tension data were predicted by the GMDH-NN and the results compared with the experimental data as well as three different models. A reasonable agreement was obtained between the experimental and the calculated data. The AARD% and the regression coefficient (R) for all data points were 4.59 and 0.96, respectively. The GMDH-NN model assured a good accuracy compared to other models. Furthermore, the proposed GMDH could precisely estimate the experimental surface tension data for symmetric series of ILs [CnCnim][bti] (n=1−10) as a function of the total number of carbons. Thus, GMDH network is an appropriate method to model complex systems.

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