and n-Dodecane - American Chemical Society

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Density, Viscosity, and Interfacial Tension of Binary Mixture of Tri-iso-amyl Phosphate (TiAP) and n‑Dodecane: Effect of Compositions and Gamma Absorbed Doses Mani Lal Singh,†,‡ Subhash C. Tripathi,§,* Manisha Lokhande,§ Pritam M. Gandhi,§ and Vilas G. Gaikar‡ †

Nuclear Recycle Board, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Department of Chemical Engineering, Institute of Chemical Technology, Matunga, Mumbai 400 019, India § Fuel Reprocessing Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India ‡

S Supporting Information *

ABSTRACT: The changes in interfacial tension against water, density, and coefficient of viscosity of a binary mixture of tri-iso-amyl phosphate (TiAP) and n-dodecane have been measured before and after gamma radiolysis. Density, viscosity, and interfacial tension of binary mixtures are additive functions of mole fractions of TiAP and gamma absorbed dose, which respectively form a plane in three-dimensional plots of linear−linear−linear, loge− loge−linear, and loge−loge−linear scales. Logarithmic interfacial tension also forms a threedimensional plane with density and viscosity in loge−linear−linear plot. Redlich−Kister type equations (RK-eq) have been introduced to model excess properties of binary mixtures, where a second independent variable is the absorbed dose. The parametric coefficients of RK-eqs pertaining to excess molar volume, viscosity deviations, and interfacial tension deviations of the mixtures are linear functions of the absorbed dose. Molecular interactions between solute−solute and solute−solvent have also been quantified in terms of apparent molar volume at infinite dilution, among others.

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(283.15 to 363.15) K, which differ significantly.17 Compositional effect on density and viscosity of TiAP + n-dodecane has not been reported. The studies dealing with the effect of gamma radiolysis on density and viscosity of TiAP + n-dodecane as well as interfacial tension of TiAP + n-dodecane against water have also not been traceable in the literature. This has motivated us to generate fresh experimental data for deriving the volumetric and excess properties of the binary system and subsequently provide a discussion of the intra−molecular and inter− molecular interactions of species. In order to establish the advantage of substitution of TiAP for TBP as an extractant mixed with n-dodecane as diluent for the recovery of actinides, TiAP + n-dodecane should have physicochemical properties superior or at least comparable to that of the TBP + n-dodecane system. Accurate measurements of density, viscosity and interfacial tension (IFT) are required to determine the specific area of contact, mass transfer, and hydrodynamic behaviors of mono as well as biphasic mixtures, for a given type of contactor. In order to perform calculations for process design18 of contactors and simulation of process flow sheets,19,20 reliable correlations based on precise data on the physicochemical properties are required to develop and validate. Hence, it is important to develop sound correlations for the physicochemical properties of TiAP + n-dodecane based on

INTRODUCTION Reprocessing of spent nuclear fuel is based on the PUREX process employing 0.26 mol fraction of tri-n-butyl phosphate (TBP)1,2 in n-paraffin, for selective separation of uranium and plutonium from fission products. Choice of this extraction system is based on its inherent advantages, viz. radiation viability, optimal density, interfacial tension, and distribution coefficient for target actinide ions. In spite of the above proven advantages, the viability of TBP for the reprocessing of fast reactor fuels with high plutonium content has certain drawbacks like formation of a third phase2 beyond a threshold limit of metal loading, significant aqueous solubility,3 and adverse effects of solvent radiolysis.4−7 Problems associated with aqueous solubility of the extractant are far fewer in the case of tri-iso-amyl phosphate (TiAP) (∼ 0.019 kg·m−3) as compared to that with TBP8 (∼ 0.4 kg·m−3). The phenomenon of third phase formation during the reprocessing of Pu−rich fuel is also considerably lesser in case of TiAP than that with TBP owing to its longer alkyl chain. Thus, TiAP appears to be a promising alternative to TBP for the reprocessing of FBR fuel9−13 as demonstrated by Russian scientists.14 Reports on comparative investigation of physicochemical properties of TiAP with other organophosphorous extractants have been scant in the literature.1,12,13,15 Density at temperatures from (298 to 338) K and viscosity at temperatures from (301 to 338) K have been reported for pure TiAP.16 Density of pure TiAP has also been reported at temperatures from © 2014 American Chemical Society

Received: May 22, 2013 Accepted: February 11, 2014 Published: February 27, 2014 1130

dx.doi.org/10.1021/je400493x | J. Chem. Eng. Data 2014, 59, 1130−1139

Journal of Chemical & Engineering Data

Article

Table 1. Purity Grade, Density ρ/kg·m−3, Viscosity η/mPa·s, and Interfacial Tension γ/mN·m−1 (against Water) of Components at 298.15 K and 0.1 MPa ρ/kg m−3 chemical name TiAP n-dodecane

source HWP, Tuticorin

s.d. Fine Chemicals water (only Millipore for IFT) Simlicity System

initial mole fraction purity 0.987

purification method

final mole fraction purity analysis method

alkaline wash, distillation

0.991

0.995

0.995

0.999

0.999

expt

accurately measured values of density,17,21−28 viscosity,21,21−28 and IFT29−32 of binary mixtures before and after gamma irradiation. In this work, theory and model of additive physical properties (density, viscosity, and IFT) of binary liquid mixtures have been proposed and validated with measured experimental data. The scope of Redlich−Kister type equation (RK-eq) has been involved for the first time to address the dose-dependent changes in physical properties of binary liquid mixtures. Apparent molar volumes of solute in solution have been calculated and discussed in terms of their intermolecular and intramolecular interactions.

lit

expt

lit

expt

lit

95716

gas−liquid chromatography

specific conductivity

γ/mN·m−1

η/mPa s

745.29

745.7921

1.35

1.33621

52.5

52.5532

997.022

997.126

0.89

0.89426

72.1

72.0926 71.9927

optimized conditions using thermal conductivity detection. The uncertainty of the mole fraction calculation was less than ± 1·10−4. The experimental uncertainty in density is about ± 5·10−3 kg·m−3, while the average uncertainty in excess molar volume is estimated to be ± 3·10−9 m3·mol−1. Kinematic viscosities of pure liquids and binary mixtures were measured with a digital Stabinger viscometer SVM 3000/ G2 from Anton Paar. One of the two cells housed in the instrument is used for measuring the density of the sample. The U tube is filled with the sample liquid and excited to oscillate using magnetic coils. Measurement of density is based on the relation between oscillation period and sample density. The other cell containing a straight tube filled with sample is used for dynamic viscosity. The tube rotates at a constant speed. A measuring rotor made of low density material, with a built-in magnet floats inside this tube, which is centered by the centrifugal force. A rotating magnet of SVM 3000 induces an eddy current field, whose speed depends on break torque. After the start of the experiment, rotor promptly attains a constant speed determined by equilibrium between the brake torque and the viscosity−dependent driving torque. Viscosity−dependent driving torque is proportional to the difference in speed between the tube and the rotor. The stated reproducibility in the measurement of dynamic viscosity is 0.0035 η and that of density is 0.2 kg m−3 in the temperature interval (288.15 to 323.15) K. The temperature in the cell was regulated to ± 0.01 K with a built in solid−state thermostat. Dynamic viscosity were obtained by multiplying the kinematic viscosity data generated from SVM 3000 with the corresponding data of density acquired by DMA 5000. The uncertainty in dynamic viscosity measurements was estimated to be within ± 2·10−3 mPa s in viscosity. Interfacial Tension. For the measurement of Interfacial tension the drop−volume method was used.29−32 The diameter of the capillary tip used was of 1 mm. The micrometric syringe made by ST BURET TIPS, Micrometric Inst. Co., Cleveland, Ohio was used with a micrometer capable of delivering volumes as low as 0.001 mL. The capillary end of the micro pipet was immersed in the organic phase to a constant depth for all measurements, and the aqueous phase was dropped slowly by turning the micrometer head. The volume of the drop was calculated from the weight difference between the weight of the glass vial before and after the aqueous phase addition and the density of the aqueous phase. From the measured drop weight and the radius of the capillary, the interfacial tension value was arrived at by using the equation

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EXPERIMENTAL SECTION Materials. TiAP supplied by Heavy Water Plant, Tuticorin, India, was purified33 and dried over 4 Å molecular sieves before measurements, and the same was degassed by ultrasound prior to use. Normal dodecane was obtained as an analytical reagent from s.d. Fine Chemicals, Mumbai, India. ASTM grade double distilled deionized and degassed water having a specific conductivity of 1·10−2 Ω−1·m−1 was used exclusively as a second face for interfacial tension measurements. The percentage compositions of organic reagents were determined by standardized gas chromatographic method using a Shimadzu model gas chromatograph (2010) equipped with a FID detector. The purities of organic chemicals were greater than 0.991 mol fraction and are reported in Table 1, which were further checked by measuring and comparing the densities,1,11,12,17−28 viscosities,17,21−28 and interfacial tensions26,27,32 with their literature values. All molar quantities were based on the IUPAC relative atomic mass table. Density and Viscosity. Densities, ρ, of pure liquids as well as binary mixtures were measured as per ASTM-D4052, using an Anton Paar (Austria) DMA 5000 digital vibrating U-tube densitometer (with automatic viscosity correction) having a stated accuracy of ± 5·10−3 kg·m−3. The temperature in the cell was controlled to ±0.01 K with a built in solid−state thermostat. Temperature in the cell was measured by means of two integrated Pt 100 platinum thermometers. Temperature stability was better than ± 0.002 K. ASTM grade I water with resistivity of 18.2 MΩ·cm and < 15·10−9 TOC from Millipore Simlicity system as per ASTM−D1193 was used for density and viscosity standard. Apparatus was calibrated daily using ambient air34 (ρ = 1.1839 kg·m−3 and η = 0.0186 mPa·s) and Millipore quality water35 (ρ = 997.043 kg·m−3 and η = 0.89 mPa·s) at 298.15 K. All mixtures were prepared by mass, using an electronic balance (PRESICA XB 220A) with a uncertainty of ± 1·10−7 kg, to minimize the errors in composition, using the cell and the procedure described elsewhere.24 The compositions of TiAP were estimated by gas chromatography under

γ /mN·m−1 = V /m 3·(ρaq − ρor )/kg·m−3·g /m·s−2 ·(2πr /m·fs )−1 (1) 1131



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where fs is shape correction factor. The ambient condition was monitored with Cole−Parmer relative humidity indicator (± 0.1%) with thermometer (± 0.1 K) and pressure sensor (± 0.1 kPa). Density, viscosity and interfacial tension of the samples before and after radiolysis were estimated quantitatively, using standard analytical protocol with an accuracy of ± 5·10−3 kg·m−3, ± 0.02 mPa·s, and ±0.2 mN·m−1, respectively. Experiments were repeated a minimum of four times and the results were averaged. Measurement of volume and mass has been found to have an error of ± 2·10−9 m3 and ± 1·10−6 kg, respectively. Gamma Irradiation Studies. Gamma irradiation of binary liquid mixtures (0, 0.1001, 0.2002, and so on up to 1 mol fraction of TiAP in n-dodecane) used in the present studies was carried out using a 60Co gamma source of 21 MGy·h−1 dose

rate. The dose rate of the irradiator was each time calibrated using Fricke dosimetry (model GC5000, BRIT, Mumbai, India). The uncertainty in measurement of gamma absorbed dose was estimated to be within ± 0.03 D Gy.

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RESULTS AND DISCUSSION Measured interfacial tensions, viscosities, and densities have been given in Table 2, along with their mol fraction dependencies shown in Figure 1(a to c). Interfacial−tension deviations, viscosity deviations, and excess molar volumes of the binary mixture have been plotted in Figure 2(a to c), followed by the plots of binary interaction parameters of respective deviations in Figure 3(a to c) for understanding inter− molecular and intra−molecular interactions. Figure 3(a to c) shows the dependence of binary interaction parameters of (a)

Table 2. Experimental Values of Density (kg·m−3), Viscosity (mPa·s), and Interfacial Tension (mN·m−1) (against Water) of Binary Mixtures of Tri-iso-Amyl Phosphate (2) + n-Dodecane (1), as a Function of Mole Fraction x2 of TiAP and Gamma Absorbed Dose, at 298.15 K and 0.1 MPaa ρ/kg·m−3 x2

0.0 Gy

25 000 Gy

50 000Gy

75 000Gy

100 000Gy

125 000Gy

150 000Gy

0 0.0999 0.1998 0.3001 0.4002 0.5001 0.5999 0.7002 0.7998 0.9001 1

745.29 765.49 785.78 805.91 826.05 846.25 866.75 888.26 909.12 929.41 946.95

746.91 767.36 787.82 808.22 828.59 849.04 869.64 889.89 910.42 930.84 951.28

748.50 769.05 789.49 809.86 830.21 850.66 871.26 891.50 912.02 932.45 952.91

750.18 770.65 791.12 811.51 831.85 852.28 872.87 893.12 913.64 934.05 954.55

751.81 772.26 792.74 813.12 833.46 853.88 874.47 894.73 915.28 935.70 956.13

753.44 773.87 794.36 814.76 835.09 855.52 876.13 896.41 916.97 937.39 957.76

755.02 775.42 795.64 816.06 836.62 857.22 877.81 897.94 918.41 938.92 959.34

η/mPa·s x2 0 0.0999 0.1998 0.3001 0.4002 0.5001 0.5999 0.7002 0.7998 0.9001 1 x2 0 0.0999 0.1998 0.3001 0.4002 0.5001 0.5999 0.7002 0.7998 0.9001 1

0.0 Gy 1.347 1.488 1.678 1.896 2.119 2.391 2.674 3.015 3.375 3.804 4.267 0.0 Gy 52.6 35.3 25.5 20.5 18.0 17.5 16.4 16.2 15.2 15.1 14.4

25 000 Gy 1.347 1.485 1.693 1.941 2.217 2.518 2.842 3.18 3.538 3.91 4.295 25 000 Gy 52.5 34.7 25.0 19.9 17.4 16.9 15.8 15.5 14.6 14.4 13.7

50 000Gy 1.347 1.486 1.697 1.947 2.225 2.529 2.856 3.197 3.559 3.935 4.324 50 000Gy 52.5 34.2 24.5 19.4 16.8 16.3 15.2 14.9 13.9 13.8 13.1

75 000Gy 1.347 1.487 1.7 1.952 2.234 2.541 2.871 3.216 3.581 3.96 4.353 γ/mN·m−1 75 000Gy 52.5 33.7 23.9 18.8 16.2 15.7 14.5 14.2 13.2 13.1 12.4

100 000Gy 1.348 1.489 1.704 1.958 2.243 2.552 2.886 3.234 3.603 3.986 4.383

125 000Gy 1.348 1.49 1.707 1.964 2.251 2.564 2.901 3.253 3.625 4.012 4.413

100 000Gy 52.5 33.2 23.4 18.2 15.6 15.1 13.8 13.5 12.5 12.4 11.6

125 000Gy 52.5 32.7 22.8 17.6 15.0 14.4 13.2 12.8 11.8 11.6 10.9

150 000Gy 1.348 1.492 1.711 1.971 2.26 2.576 2.917 3.272 3.648 4.038 4.443 150 000Gy 52.5 32.2 22.2 17.0 14.3 13.7 12.5 12.1 11.1 10.9 10.1

a x2 is before equilibration with water. Standard uncertainties u are u(T) = 0.01 K, u(x2) = 1·10−4, u(D) = 10 Gy, u(ρ) = 5·10−3 kg·m−3, u(η) = 2·10−3 mPa·s and u(γ) = 0.2 mN·m−1. Combined expanded uncertainties Uc are Uc(ρ) = 0.3 kg·m−3 for SVM 3000; Uc(η) = 0.004 mPa·s, and Uc(γ) = 0.4 mN·m−1 unless or otherwise indicated (level of confidence = 0.95, k ≈ 2).

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Figure 1. Dependence of (a) interfacial tension (γ) (against water), (b) viscosity (η), and (c) density (ρ) of binary TiAP + n-dodecane mixture, as a function of mol fraction of TiAP, at different gamma absorbed doses: □, 0.0 Gy; ○, 25 000 Gy; Δ, 50 000 Gy; ∇, 75 000 Gy; solid left pointing triangle, 100 000 Gy; +, 125 000 Gy; *, 150 000 Gy; solid curves, calculated using eqs 19 to 21 of this work; symbols, experimental values.

Figure 3. Dependence of binary interaction parameters of (a) interfacial tension deviations (gγm), (b) viscosity deviations (gηm), and (c) excess molar volume (gVm) of binary mixture of TiAP + ndodecane, as a function of mol fraction of TiAP, at different gamma absorbed doses: □, 0.0 Gy; ○, 2 5000 Gy; Δ, 50 000 Gy; ∇, 75 000 Gy; solid left pointing triangle, 100 000 Gy; +, 125 000 Gy; *, 150 000 Gy; solid curves, calculated using Redlich−Kister type eq 16; symbols, experimental values.

fraction, xi, and molality (or molonity), mi of solute i at various absorbed doses, at ambient temperature and pressure. The apparent molar volumes, VΦ,i of a solute i is defined as the difference between the volume of the solution m and the volume of the pure solvent j per mole of solute i and is given by37 VΦ, i/cm 3·mol−1 = (Vm/m 3·mol−1 − (nj /mol)·V j0/m 3·mol−1)·(ni /mol)−1

(2)

where Vm denotes the volume of the solution, ni and nj are number of moles of solute and solvent, respectively, and V0j is the molar volume of pure solvent. The values of apparent molar volumes, VΦ,1 of solute i in the solvent j were calculated from the density data using the following equation: VΦ, i /m 3·mol−1 = [Mi /kg·mol−1) ·(ρm /kg·m−3)−1 − 1000 ·{(ρm /kg·m−3)−1 − (ρj /kg·m−3)−1} ·(mi /mol ·kg −1)−1] (3)

Figure 2. Dependence of (a) interfacial tension deviations (Δγ), (b) viscosity deviations (Δη), and (c) excess molar volume (VE) of binary mixture of TiAP + n-dodecane, as a function of mol fraction of TiAP, at different gamma absorbed doses: □, 0.0 Gy; ○, 25 000 Gy; Δ, 50 000 Gy; ∇, 75 000 Gy; solid left pointing triangle, 100 000 Gy; +, 125 000 Gy; *, 150 000 Gy; solid curves, calculated using Redlich− Kister type equation 16; symbols, experimental values.

where Mi and mi are the molar mass and molality of the solute i, respectively. ρm and ρj are densities of mixture and component j, respectively. The calculated apparent molar volumes VΦ,2 as well as VΦ,2 of respective solutes in solutions (TiAP (2) + n-dodecane (1)) are given in Table 3. Figure 4(a to b) shows the dependence of VΦ,1 values of (a) solute−TiAP VΦ,2, and (b) solute−n-dodecane VΦ,1, in TiAP + n-dodecane binary mixture, on mole fraction of TiAP, at all gamma absorbed doses under study. With increase in solute concentration, apparent molar volume of solute increases, as per expectation and the binary mixture tends to acquire a regular pattern of association between TiAP and n-dodecane. Increase in gamma absorbed dose leads to greater molecular

interfacial tension deviations gγm, (b) viscosity deviations gηm, and (c) excess molar volume gVm of binary mixture of TiAP + n-dodecane, as a function of mol fraction of TiAP, at different gamma absorbed doses. The densities, ρm, of a dry binary mixture comprising of components i and j, were measured as a function of mole 1133



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Table 3. Derived Values of Apparent Molar Volumes, VΦ,i/m3 mol−1, of (a) Solute TiAP (2) in n-Dodecane and (b) Solute n-Dodecane (1) in TiAP As a Function of TiAP Molality/mol kg−1, at Different Gamma Absorbed Doses D (= 0.0 to 1 500 000) Gy m1 y 0 0.0999 0.1998 0.3001 0.4002 x2 0.5001 0.5999 0.7002 0.7998 0.9001 1

mol·kg

10−6 VΦ,1/m3·mol−1 of solute n-dodecane

m2 −1

mol·kg

0.00000 0.65159 1.46586 2.51725 3.91712 m1

−1

29.23800 12.99647 7.56820 4.86353

D/Gy = 0.0

D = 25 000

D = 50 000

228.55 231.11 233.49 235.79 237.90

228.05 230.62 233.05 235.35 237.50

227.57 230.10 232.52 234.83 236.98 10−6

m2

5.8638 8.8209 13.679 23.4978 52.8959

3.24376 2.16427 1.38941 0.81228 0.36016 0.00000

336.85 334.22 331.14 328.68 326.54 325.42

335.49 332.93 330.57 328.25 326.06 323.94

D = 75 000

D = 100 000

227.06 226.57 229.61 229.11 232.01 231.51 234.31 233.80 236.46 235.94 VΦ,2/m3 mol−1 of solute TiAP

334.90 332.36 330.00 327.69 325.50 323.39

334.34 331.80 329.44 327.14 324.96 322.83

D = 125 000

D = 150 000

226.08 228.62 231.01 233.29 235.43

225.60 228.15 230.64 232.92 234.96

333.78 331.25 328.89 326.58 324.40 322.30

333.20 330.66 328.30 325.99 323.82 321.75

332.56 330.05 327.78 325.51 323.30 321.22

comparison to TiAP due to the increase in gamma absorbed dose. An increase in absorbed dose leads to enhancement of molecular aggregation, resulting in compaction in volume, which increases viscosity and conversely decreases interfacial tension of the binary mixture, as shown in Figure 1. The dependence of apparent molar volumes on the gamma absorbed dose is positive for solute TiAP in solvent n-dodecane. The apparent molar volume values were found to be adequately represented by a linear equation, as molality of solute mi tends to zero. VΦ, i /m 3·mol−1 = V Φ∞,i + Sv, i·mi /mol ·kg −1

(4)

∞ where VΦ,i is the partial molar volume at infinite dilution, which equals the standard partial molar volume. Similar to eq 4, the apparent molar volume of solute n-dodecane (2) in solvent TiAP could be represented by a linear equation, as m2 tends to zero. The values of V∞ Φ,2 and slope Sv have been calculated by least-squares regression analysis listed in Table 4, along with their standard errors. The sign of Sv shows the nature of the solute−solute interactions, while V∞ Φ reflect the presence of solute−solvent interactions.37 The standard partial molar volumes, V∞ Φ are much greater than those of Sv values for TiAP + n-dodecane, which suggest that the solute−solvent interactions dominate over solute−solute interactions in the mixture in the domain 0.0 ≤ D ≤ 150 000 Gy. The positive values of V∞ φ for solute TiAP in n-dodecane studied indicate stronger solute−solvent interactions in comparison to intra− molecular interactions; also stronger than solute−solvent interactions between solute n-dodecane in TiAP; which

Figure 4. Apparent molar volumes, (a) VΦ,2/m3 mol−1 of TiAP (solute) and (b) VΦ,1 of n-dodecane (solute) in binary TiAP + ndodecane mixtures, a function mol fraction of TiAP, at various gamma absorbed doses: □, 0.0 Gy; ○, 25 000 Gy; Δ, 50 000 Gy; ∇, 75 000 Gy; solid left pointing triangle, 100 000 Gy; +, 125 000Gy; *, 150 000 Gy; solid lines, straight lines between derived values.

compaction shown in Figure 4(b) by lowering in molar volume. It is also evident that dodecane is almost unaffected in

3 −1 3 −2 Table 4. Values of the Standard Partial Molar Volumes of Solute (TiAP or Dodecane), V∞ Φ /m ·mol , Slope, Sv/m ·mol ·kg with Standard Deviations ±σ(VΦ)/ m3·mol−1, for TiAP + n-dodecane, at Different Gamma Absorbed Doses D (=0.0 to 1 500 000) Gy

TiAP (solute) + dodecane D/Gy

V∞ Φ,1

Sv,1

0 25 000 50 000 75 000 100 000 125 000 150 000

2.2936·10−4 2.2886·10−4 2.2836·10−4 2.2786·10−4 2.2737·10−4 2.2688·10−4 2.2643·10−4

2.3431·10−6 2.3684·10−6 2.3616·10−6 2.3562·10−6 2.3490·10−6 2.3430·10−6 2.3506·10−6

dodecane (solute) + TiAP ± σ(VΦ,1)

V∞ Φ,2

Sv,2

± σ(VΦ,2)

8.9272·10−5 3.7972·10−1 7.8012·10−7 7.8235·10−7 7.8210·10−7 7.8008·10−7 8.3585·10−7

3.2562·10−4 3.2488·10−4 3.2432·10−4 3.2377·10−4 3.2323·10−4 3.2266·10−4 3.2216·10−4

3.6559· × 10−6 3.5107·10−6 3.4999·10−6 3.4965·10−6 3.4923·10−6 3.4864·10−6 3.4438·10−6

5.6300·10−7 8.1060·10−7 8.1097·10−7 8.1210·10−7 8.0735·10−7 7.9321·10−7 8.1876·10−7

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3 −1 3 −2 −1 Table 5. Parametric Coefficients of Quadratic Equations Standard Partial Molar Volume,V∞ Φ,1/m ·mol and Slope, Sv/m ·mol ·kg , of Solute (Tri-iso-amyl Phosphate or n-Dodecane) in Mixtures of {Tri-iso-amyl Phosphate (1) + n-Dodecane) (2)}, at Different Gamma Absorbed Doses D (=0.0 to 1 500 000) Gy.

solute + solvent

v0

v1

v2

± σ(V∞ Φ,1)

s0

s1

s2

± σ(Sv,1)

TiAP (solute) + dodecane dodecane(solute) + TiAP

2.2937·10−4 3.2558·10−4

−2.0607·10−11 −2.6021·10−11

6.5330·10−18 2.1962·10−17

1.1209·10−8 4.3870·10−8

2.3523·10−6 3.5864·10−6

1.9346·10−13 −2.5208·10−12

−1.6770·10−18 1.0209·10−17

9.81121·10−9 4.39647·10−8

where γm is the interfacial tension of the mixtures and γ1 and γ2 are the interfacial tension values of components 1 and 2 against water, respectively. In practice, it was observed28,36,39 that eqs 8 to 10 predicted either higher or lower values than the experimental values for various liquid mixtures owing to exclusion of molecular interactions. To deal with nonideality of the such binary mixtures arising from molecular interactions in a binary system, we introduce another eq 10 to express interfacial tension of the mixture analogous to eqs 8 and 9 that define the excess molar volume and viscosity deviations in the form of a binary interaction parameter as follows:

decreases with increasing gamma absorbed dose. This also implies that there is a proportional relationship between gamma absorbed dose and temperature of the binary mixture. Absorbed dose D in irradiated system is analogues to heat capacity in thermal system. Partial molar volume at infinite dilution, V∞ Φ , as well as slope Sv have been observed to be quadratic functions of gamma absorbed dose, which could be expressed as i=0

Sv /kg·m 3·mol−2 =

∑ Si·(D/Gy)i

(5)

2

and

V E /m 3·mol−1 = x1·x 2·gV

(11)

Δη /mPa·s = x1·x 2·g η

(12)

m

i=0

V Φ∞/m 3·mol−1 =

∑ vi·(D/Gy)i

m

(6)

2

Δγ /mN·m−1 = x1·x 2·g γ

Parameters of eqs 5 and 6 have been provided in Table 5. 3 −1 −1 and isobaric dose Partial molar expandivity E∞ Φ /m ·mol ·Gy expand constant αp/Gy−1 have been introduced and deliberated in the Supporting Information (SI), in terms of properties of structure maker or structure breaker of solute in the binary mixture.38 Proposed Theory and Model of Additive Physical Properties of a Binary Liquid Mixture. Changes in density, viscosity, and interfacial tension (against water) of a binary liquid mixture are additive function of their compositions and gamma absorbed dose, which can be plotted as equations of a plane in linear−linear−linear, log−log−linear, and log−log− linear scale, respectively. It is proposed that the change in physical properties (z) or loge(z) are equations of planes, comprised of mol fraction(x) or loge(x) (in the order) and gamma absorbed dose (y) at 298.15 K and 0.1 MPa. z = a·x + b·y + c

where gvm, gηm, and gγm are binary interaction parameter for excess molar volume, viscosity deviations, and interfacial tension deviations of the mixtures. Equations 11 to 13 can be combined as follows: Δq = x1·x 2·g q

where, q represents physical properties, like, molar volume (V), viscosity (η), and interfacial tension (γ). For a multicomponent mixture, eqs 11 to 14 can be represented as i=1

qm =

ij

(15)

n i

i=0

(8)

(16)

where x2 is the mole fraction of TiAP (2) and Aqi are adjustable parametric coefficients of property q, which have been found to depend on gamma absorbed dose for the first time, as follows:

where ρm is the density of the mixtures and ρ1 and ρ2 are the densities of components 1 and 2, respectively. M1 and M2 are molecular masses of components 1 and 2, respectively. The viscosity deviations have been calculated from the following correlations:39

n

Aq = i

∑ Bq ·(D/Gy)i ij

j=0

(9)

(17)

where Bqij is coefficient of polynomial of eq 17. In each case, the optimum numbers of coefficients (Aqi and Bqij) were determined from an examination of the variation of the standard derivation/uncertainty:

where ηm is the viscosity of the mixtures and η1 and η2 are the viscosities of components 1 and 2 of the binary liquid mixtures, respectively. Analogous to eq 9, we hereby introduce interfacial tension deviations which may be calculated from the following correlations: Δγ /mN·m−1 = γm − x1·γ1 − x 2·γ2

xi·xj·gq

n

Y = x1·x 2·∑ A q ·(2x1 − 1)i

− {(x1·M1/kg·mol−1·(ρ1 /kg·m−3)−1

Δη /mPa·s = ηm − x1·η1 − x 2·η2

n

where xi and xj are mole fractions of constituents of the mixture. Polynomial Equation of Redlich−Kister. The values of excess molar volume, viscosity deviations and interfacial tension deviations for each mixture have been fitted one by one into following RK-eq:40

V E/m 3·mol−1 = [{(x1·M1/kg·mol−1 + x 2·M 2 /kg·mol−1)}·(ρi /kg·m−3)−1 + x 2·M 2 /kg·mol ·(ρ2 /kg·m ) }]

i = 1 j = 1, i ≠ j

∑ xi·qi + ∑ ∑ n

where a, b, and c are coefficients of eq 7. Common Working Equations. For excess molar volumes (or molar volume−deviation) arising from mixing of two liquid components of a binary mixture is given by eq 11, as follows:21

−3 −1

(14)

m

(7)

−1

(13)

m

σ(Y ) = [∑ (Ypred − Yexp)2 ·(n − p)−1]0.5

(10) 1135

(18)



Article

Table 6. Parametric Coefficients of Redlich−Kister Equation (16) and Standard Deviation for Excess Molar Volumes, Viscosity Deviations and Interfacial Tension Deviations (against Water) of the Binary Mixture of TiAP + n-Dodecane, at Different Gamma Absorbed Doses D (=0.0 to 1 500 000) Gy, at 298.15 K and 0.1 MPaa D/Gy

AV0

AV1 −6

AV2 −6

0 25 000 50 000 75 000 100 000 125 000 150 000 D/Gy

5.7430·10 4.7984·10−6 4.2621·10−6 3.7267·10−6 3.2010·10−6 2.6630·10−6 2.1163·10−6 Aη0

−1.3884·10 −1.2062·10−6 −1.2191·10−6 −1.2301·10−6 −1.2532·10−6 −1.3000·10−6 −1.4412·10−6 Aη1

0 25000 50000 75000 100000 125000 150000 D/Gy

−0.42083 −0.3027 −0.30638 −0.30894 −0.31298 −0.31625 −0.31904 Aγ0

−0.08032 0.08928 0.08837 0.0911 0.09161 0.09319 0.09432 Aγ1

0 25000 50000 75000 100000 125000 150000

−16.25966 −16.4829 −16.77242 −17.04804 −17.28648 −17.57579 −17.87457

15.91424 16.1094 16.24471 16.4732 16.69185 17.00935 17.34067

AV3 −6

± σ(VE)

AV4

−7.6850·10 −5.8043·10−6 −5.8012·10−6 −5.8130·10−6 −5.8357·10−6 −5.8516·10−6 −5.2355·10−6 Aη2

9.0070·10 7.4415·10−7 7.4772·10−7 7.2051·10−7 6.9955·10−7 7.0261·10−7 8.9107·10−7 Aη3

2.0048·10 4.9769·10−8 4.4225·10−8 1.0331·10−7 1.3532·10−7 1.7650·10−7 −6.6021·10−7 Aη4

5.6590·10−8 3.6749·10−8 3.7902·10−8 3.6096·10−8 3.6073·10−8 3.5831·10−8 4.0837·10−8 ± σ(Δη)

0.3928 0.25917 0.26474 0.26564 0.2701 0.27273 0.27786 Aγ2

0.10423 −0.07464 −0.07255 −0.07604 −0.07605 −0.07764 −0.07933 Aγ3

0.01883 0.03245 0.02913 0.03036 0.02959 0.02972 0.02604 Aγ4

0.00652 0.00143 0.00154 0.00129 0.00151 0.0013 0.00162 ± σ(Δγ)

−14.75776 −14.69466 −14.5576 −14.54725 −14.46316 −14.69433 −14.77823

13.09336 12.6572 12.71167 13.13007 13.16639 13.16771 13.09528

0.23599 0.21803 0.23332 0.2456 0.26358 0.21797 0.22327

4.03492 4.28642 4.30475 4.07827 4.12195 4.10201 4.29828

−7

−6

Standard uncertainties u are u(x2) = 1·10−4, u(D) = 10 Gy, u(ρ) = 0.074 kg·m−3, u(η) = 0.022 mPa·s, and u(γ) = 0.2 mN·m−1. Combined expanded uncertainties Uc are Uc(D) = 20 Gy, Uc(ρ) = 0.015 kg·m−3, Uc(η) = 0.044 mPa·s and Uc(γ) = 0.4 mN·m−1 (level of confidence = 0.95, k = 2).

a

where ρ0 = 745.29 kg·m−3 at 298.15 K and 0.1 MPa. When mole fraction and gamma absorbed dose become zero, eq 19 yields a value 745.29 kg m−3, that corresponds to the density of n-dodecanereported elsewhere.17,24,25 When gamma absorbed dose is zero, eq 19 yields a value 946.86 kg·m−3, when mole fraction of TiAP is one.11,12 Equation 19 of a plane of density along with experimental data has been shown in linear−linear− linear three-dimensional plot in Figure S1 in the Supporting Information. Excess molar volume of the binary liquid mixture has been fitted to the fourth order RK-eq 16, and its parametric coefficients have been related linearly to the gamma absorbed doses. Parametric coefficients of RK-eq 16 for excess molar volume, viscosity deviation, and interfacial tension deviation are given in Table 6 and corresponding coefficients of linear eq 17 of RK-eq parameters are provided in Table 7. Because of the difference in shape, size, and free volume41,42 of TiAP and n-dodecane molecules, molecules of TiAP and n-dodecane cannot come closer easily thereby giving rise to increase in the total volume of TiAP + n-dodecane. Also, breaking down of solvation and hydrogen bonds gives rises to positive excess molar volumes. Hence, are the positive values of excess molar volumes shown in Figure 2(c). Interaction parameter (gVm) of the mixtures is also smooth polynomial of compositions, as shown in Figure 3(c). Increase in the chain length of n-paraffinic diluent results in the increase of viscosity of TiAP + n-dodecane, which is a nonlinear function of mole fraction and gamma absorbed dose. Equation 10 has been solved by applying multiple linear leastsquare-based regression analysis as a numerical method, using

where n is the total number of experimental values and p is the number of parameters in equation of Ypred. Validation of Theory and Model of Additive Physical Properties of a Binary Liquid Mixture. Figure 1(a to c) shows the changes in IFT, viscosity and density of binary mixture at different gamma absorbed dose as a function of mole fraction of TiAP. The IFT value of the system decreases sharply and assumes asymptotic behavior at higher TiAP mole fractions toward a Pure TiAP solution. Of the two components, TiAP, due to presence of phosphate moiety (surface active species) give rise to lowering of IFT converging to the value pure TiAP species. The effect of the gamma absorbed dose is found most dominant (decrease) on IFT of the system followed by viscosity (increase) and density (increase) respectively, as indicated by the coefficients of absorbed dose of eqs 19 to 21. Gamma radiolysis of alkanes generally leads to elongation of carbon−carbon chain length, which results in the increase in the viscosity and density of the solute and/or solvent. While radiolytic effect is likely to cause simultaneous dealkylation of TiAP molecules leading to formation of ROH and alkyl phosphoric acid, each of which are surface active and hence causes lowering of the IFT of the system (against water) with absorbed dose. Subsequent changes in the IFT of the system with increasing dose may be the result of secondary degradation products whose qualitative and quantitative information are rare to find in literature. Application of multiple linear least-square-based regression analysis method to eq 10, after substitution of observed density values from Table 2, yields the following equation of density plane: (ρm − ρ0 )/kg· m−3 = 204.18699·x 2 + 6.56438·10−5·D/Gy (19) 1136


Standard uncertainties u are u(x1) = 1·10 , u(D) = 10 Gy, u(ρ) = 0.559 kg·m , u(η) = 0.195 mPa·s and u(γ) = 0.2 mN·m . Combined expanded uncertainties Uc are Uc(D) = 20 Gy, Uc(ρ) = 1.117 kg·m−3, Uc(η) = 0.391 mPa·s and Uc(γ) = 0.4 mN·m−1 (level of confidence = 0.95, k = 2).

ln((ηm − η0)/mPa ·s) = 1.33134 ln(x 2) + 3.91078 ·10−7 ·D/Gy + 1.0715 (20)

−1

where η0 =1.3467 mPa s at 298.15 K and 0.1 MPa. When mole fraction of TiAP and absorbed dose are zero, the eq 20 gives a value 1.347 mPa·s, that corresponds to the viscosity of n-dodecane reported elsewhere.17 When gamma absorbed dose is zero, eq 20 yields a value 4.267 mPa·s, when mole fraction of TiAP is one. Equation 20 of plane of viscosity along with experimental data has been shown in three-dimensional loge− loge−linear Figure S2 provided in the Supporting Information. The viscosity deviations as shown in Figure 2(b) are symmetrically negative and is the lowest at about x1 ≈ 0.4. Viscosity−deviations increases with gamma absorbed doses, because of de−clustering of molecules of mixtures. Interaction parameter (gηm) of the mixtures are also smooth polynomial of compositions, as shown in Figure 3(b). Viscosity deviations of the binary liquid mixture has been fitted to the fourth order RK-eq 16 and it is parametric coefficients have been related linearly to the gamma absorbed doses. Transport of hydrophilic constituents of degradation species across the interface lowers the interfacial tension of TiAP + n-dodecane (against water) drastically, up to x2 ≈ 0.40 as shown in Figure 1(a), which tapers down subsequently. Interfacial tension deviations shown in Figure 2(a) clearly indicate the drastic fall in interfacial tension values. Interaction parameters (gVm) of the mixtures are also smooth polynomials of composition, as shown in Figure 3(a). Using the experimental values of interfacial tension, in the Supporting Information, eq 10 has been solved, employing numerical methods based multiple linear least-square-regression, to get the following equation:

−3

1.56078

experimental values of coefficient of viscosity, given in Table 2. The resulting equation is as follows:

ln((γ0 − γm)/mN·m−1) = 0.26574· ln(x 2) + 1.29075 ·10−6 ·D/Gy + 3.6296 (21) −1

where γ0 =52.5 mN·m at 298.15 K and 0.1 MPa. When mole fraction of TiAP and absorbed dose are zero, eq 21 yields a value of 52.5 mN·m−1.32 When gamma absorbed dose is zero, eq 21 yields a value 14.8 mN·m−1, when mole fraction of TiAP is unity. Equation 21 of a plane of interfacial tension along with experimental data has also been shown in three-dimensional loge−loge−linear plot in Figure S3 given in the Supporting Information. Interfacial tension deviations of the binary liquid mixture have been fitted to the fourth order RK-eq 16 and its’ parametric coefficients have been related linearly to the gamma absorbed doses. Modeling of data of interfacial tension−deviation by RK-eq 16 has been found to be poor, with standard deviation of 0.2 mN·m−1. Predictions by three parametric eqs 19 to 21 of this work have been compared in the Table 8, with predictions made by the corresponding five parametric RK-eq 16 for density, viscosity and IFT, to establish their superiority. Correlation also exists among interfacial tension, viscosity, and density of the binary mixture under study. Logarithm of

−4

0.89723

0.0047 0.02624 Aη4 6.22644·10−7 −1.09292·10−11 1.08451·10−6 Aν4

Article

a

−1.39936·10−4 12.79248

0.88844

2.37571·10−8

Aγ 4

1.29965·10−4 16.99244 −2.28771·10−13 7.89488·10−7 Aν3

9.3707·10−8

0.00973

0.0578

0.46368

Aη3

−8.00257·10−7

Aγ 3

−9.37533·10−6

1.88265·10 60.84628

−51.30106 Aγ 2

Aγ 1

0.31961

3.85714·10 6.10714

Aη2 1.03134·10−11 −6.77726·10−6

5.87192·10−7

1.85714·10 2.60714

Aν2

−5

Aν1

2.09591

Aη1

0.0447

0.6268

0.07261

−5

−4.462·10−7

−5

± σ(Aγi) Bγ1

−4.4294·10−5 −64.82994

Bγ0 para.

Aγ 0 0.0397

± σ(Aηi) Bη1

Aη0

3.881·10−7

Bη0

−0.35584

para. ± σ(AVi)

Aν0

1.33779·10−7

BV1

−2.316·10−11

BV0

5.52421·10−6

parameter

Table 7. Absorbed Dose dependent Parametric Coefficients of RK-eqs 19 20 and Standard Deviation for Excess Molar Volumes Viscosity−Deviations and Interfacial Tension Deviation (against Water) of Binary Mixture of TiAP (2) + n-Dodecane (1), at 298.15 K and 0.1M Pa, 0.0 ≤ D ≤ 150 000 Gya


1137


Journal of Chemical & Engineering Data Table 8. Comparison of Three and Five Parametric Equations of Density, Viscosity, and Interfacial Tension for Binary Mixture of TiAP + n-Dodecane As a Function of Composition of TiAP and Gamma Absorbed Dose, at 298.15 K and 0.1M Pa, 0.0 ≤ D ≤ 150 000 Gy three parametric equation (this work)

±σ

eq 19

0.395 kg·m−3

eq 20

0.036 mPa·s

eq 21

0.18 mN·m−1

five parametric RK-eq eq 16 for density eq 16 for viscosity eq 16 for IFT

±σ 0.559 kg·m−3 0.195 mPa·s 0.20 mN·m−1

(22)

Standard deviation of ln(γm) of eq 22 is ± 0.11296 mN·m−1. Logarithm of interfacial tension (against water) forms a plane with density and viscosity in three-dimensional Cartesian co− ordinate plot in Figure S4, given in the Supporting Information.

■

CONCLUSIONS Density and viscosity of binary mixture of tri-iso-amyl phosphate (TiAP) + n-dodecane at 298.15 K and 0.1 MPa increases, while interfacial tension of the liquid mixture against water decreases with both mole fraction (x2) of TiAP and gamma absorbed dose (D). Based on the proposed theory of additive physical properties, density, viscosity and interfacial tension of the liquid mixtures are multilinear function of x2 and D, representable in three-dimensional plots of linear− linear−linear, loge−loge−linear, and loge−loge−linear scales, respectively, applicable in range of gamma absorbed dose from zero to 150 000 Gy or J kg−1. Interfacial tension is also a multilinear function of density and viscosity in loge−linear−linear scale. Predictions based on equation of additive physical properties yield accurate values better than that predicted by fourth order RK-eq. Parametric constants of RK-eq have also been related to gamma absorbed doses for the first time, as a linear equation. Binary interaction parameters (gqm) pertaining to excess molar volume, viscosity deviations, and interfacial tension deviations are also a function of TiAP + dodecane compositions and absorbed doses. Poor TiAP-dodecane interaction and poor correlation of molecular orientation are the reasons of negative excess molar volumes. Breakings of self-association and weak TiAP-dodecane interaction are the reasons of negative viscosity deviations. ASSOCIATED CONTENT

■

AUTHOR INFORMATION

■

REFERENCES

(1) Singh, M. L.; Tripathi, S. C.; Venkata, P. P. K.; Gaikar, V. G. Correlations among composition, temperature, and density, viscosity, or derived thermodynamic properties of binary mixtures of tri−n-butyl phosphate with n-hexane or n-dodecane. Ind. Eng. Chem. Res. 2014 DOI: 10.1021/ie4036912. (2) Suresh, A.; Srinivasan, T. G.; Vasudeva Rao, P. R. Extraction of U(VI), Pu(IV) and Th(IV) by some trialkyl phosphates. Solvent Extr. Ion Exch. 1994, 22, 727−744. (3) Higgins, C. E.; Baldwin, W. H.; Soldano, B. A. Effects of electrolytes and temperature on the solubility of TBP in water. J. Phys. Chem. 1959, 63, 113−118. (4) Tripathi, S. C.; Sumathi, S.; Ramanujam, A. Effects of solvent recycling on Radiolytic degradation of 30% TBP−n-dodecane−HNO3. Sep. Sci. Technol. 1999, 34, 2887−2903. (5) Tripathi, S. C.; Bindu, P.; Ramanujam, A. Studies on the identification of harmful radiolytic products of 30% TBP−ndodecane−HNO3 by gas−liquid chromatography Part I: Formation of diluent degradation products and their role in Pu retention behaviour. Sep. Sci. Technol. 2001, 36, 1463−1478. (6) Tripathi, S. C.; Gupta, K. K.; Ramanujam, A. Studies on the identification of harmful radiolytic products of 30%TBP−n-dodecane− HNO3 by Gas liquid chromatography Part II Formation of high molecular weight organophosphates. Sep. Sci. Technol. 2001, 36, 2863− 2883. (7) Tripathi, S. C.; Ramanujam, A. Effect of radiation induced changes in the density and viscosity of 30% TBP−n-dodecane−HNO3. Sep. Sci. Technol. 2003, 38, 2307−2326. (8) Venkatesan, K. A.; Robertselvan, B.; Anthony, M. P.; Srinivasan, T. G.; Vasudeva Rao, P. R. The Effect of the Structure of Trialkyl Phosphate on their Physicochemical Properties and Extraction Behaviour. Solvent Extr. Ion Exch. 2006, 24, 747−763. (9) Siddall, T. H., III. Trialkyl phosphates and dialkyl alkyl phosphonates in Uranium and Thorium extraction. Ind. Eng Chem. 1959, 51, 41−44. (10) Siddall, T. H., III The effects of altering alkyl substituents in trialkyl phosphates on the extraction of actinides. J. Inorg. Nucl. Chem. 1960, 13, 151−155. (11) Hasan, S. H.; Shukla, J .P. Tri−iso−Amylphosphate (TAP): An alternative extractant to Tri− butyl phosphate (TBP) for reactor fuel reprocessing. J. Radioanal. Nucl. Chem. 2003, 283, 563−573. (12) Shukla, J. P.; Gautam, G. G.; Kedari, C. S.; Hasan, S. H.; Rupainwar, D. C. Extraction of Uranium(VI), Plutonium(IV) and some fission products by Tri−iso-amyl phosphates. J. Radioanal. Nucl. Chem. 1997, 219, 61−67. (13) Sahoo, T. K.; Srinivasan, T. G.; Vasudeva Rao, P. R. Note: Effect of temperature in the extraction of uranium and plutonium by Tri− iso−Amylphosphate. Solvent Extr. Ion Exch. 2011, 29, 260−269. (14) Nikiforov, A. S.; Zakharkin, B. S. ; Rozen, A. M.; Renard, Kh. V.; Smetanin, Eh. Ya. Actinide’89, Taskent, USSR, Sept 24−29, pp 20−21, 1989. (15) Suresh, A.; Srinivasan, T. G.; Vasudev Rao, P. R. The Effect of the Structure of Trialkyl Phosphates on their Physicochemical Properties and Extraction Behavior. Solvent Extr. Ion Exch. 2009, 27, 258−294. (16) Kannan, S.; Kishore, K. Absolute viscosity and Density of Trisubstituted Phosphoric Esters. J. Chem. Eng. Data 1999, 44, 649− 655.

ln(γm/mN·m−1) = 23.38385 − 2.86914· 10−2 ·ρm /kg· m−3

■

ACKNOWLEDGMENTS

Authors sincerely thank Mr. P. K. Wattal, Director, NRG, Mr. K. Agarwal, General Manager, NRG, and Mr. S. Basu, Chief Executive, NRB & Director, BARC, Mumbai for their keen interest and encouragement during the course of the present investigation. This article forms a part of the Doctoral Thesis of Mani Lal Singh.

interfacial tension is a multi−linear function of density and viscosity, as follows:

+ 1.4789·ηm /mPa· s

■

Article

S Supporting Information *

Introduced partial molar expandivity, E∞ Φ , and isobaric dose expand constant, αP, along with Table S3.3 and threedimensional plots (Figures S1−S3). This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Ph: +91 22 2559 1201. M: +91 9869 650 254. Fax:+91 22 2550 5340/2550 5185. Notes

Notes. The authors declare no competing financial interest. 1138



Article

(17) Kumar, S.; Das, B.; Mondal, P. Thermophysical properties of 36% and 100% TiAP solvents at 298.15 K. J. Radioanal. Nucl. Chem. 2011, 289, 267−273. (18) Kumar, A.; Hartland, S. Computational Strategies for Sizing Liquid−Liquid Extractors. Ind. Eng. Chem. Res. 1999, 38, 1040−1056. (19) Gonda, K.; Matsuda, T. Solvent Extraction Calculation Model for Purex Process in Pulsed Sieve Plate Column. J. Nucl. Sc. Tech. 1986, 23, 883−895. (20) Tsubata, T.; Asakura, T.; Morita, Y. Development of a Computer Code, PARC, for Simulation of Solvent Extraction Process in Reprocessing. Adv. Nucl. Engg. 2009, 8, 211−220. (21) Tian, Q.; Liu, H. Densities and viscosities of binary mixtures tributyl phosphate with hexane and dodecane from (298.15 to 328.15) K. J. Chem. Eng. Data 2007, 52, 892−897. (22) Trenzado, J. L.; Matos, J. S.; Segade, L.; Carballo, E. Densities, viscosities, and related properties of some (methyl ester + alkane) binary mixtures in the temperature range from o 313.15 K. J. Chem. Eng. Data 2001, 46, 974−983. (23) Nayak, J. N.; Aralaguppi, M. I.; Aminabhavi, T. M. Density, viscosity, refractive index and speed of sound for the binary mixtures of ethyl chloroacetate with n−alkanes (C6 to C12) at 298.15, 303.15 and 308.15 K. J. Chem. Eng. Data 2001, 46, 891−896. (24) Aminabhavi, T. M.; Patil, V. B. Density, refractive index, viscosity and speed of sound in binary mixtures of ethenyl benzene with hexane, heptane, octane, nonane, decane and dodecane. J. Chem. Eng. Data 1997, 42, 641−646. (25) Aralaguppi, M. I.; Jadar, C. V.; Aminabhavi, T. M. Density, refractive index, viscosity and speed of sound in binary mixtures of cyclohexanone with hexane, heptane, octane, nonane, decane, dodecaneand 2,2,4−trimethylpentane. J. Chem. Eng. Data 1999, 44, 435−440. (26) Rayer, A. V.; Sumon, K. Z.; Henni, A.; Tontiwachwuthikul, P. Physicochemical properties of {1−methyl piperazine (1) + water (2)} system at T = (298.15 to 343.15) K and atmospheric pressure. J. Chem. Thermodyn. 2001, 43, 1897−1905. (27) Vargaftik, N. B.; Volkov, B. N.; Voljak, L. D. International Tables of Surface Tension of Water. J. Phys. Chem. Ref. Data 1983, 12, 817−819. (28) Kumar, S.; Koganti, S. B. Prediction of liquid mixture viscosity for dry and water−saturated TBP/n-dodecane solutions. Nucl. Technol. 1998, 123, 335−340. (29) Vidyalakshmi, V.; Subramanian, M. S.; Rajeswari, S.; Srinivasan, T. G.; Vasudevrao, P. R. Interfacial Tension Studies of N,N−Dialkyl Amides. Solvent Extr. Ion Exch. 2003, 21, 399−412. (30) Harkins, W. D.; Brown, F. E. The determination of surface tension (free surface energy) and the weight of falling drops: the surface tension of water and benzene by the capillary weight method. J. Am. Chem. Soc. 1919, 41, 499−524. (31) Wawrzynczak, W. S.; Paleska, I.; Figaszewski, Z. Study of supporting electrolyte adsorption in the water−nitrobenzene partition mixture I. A new drop weight technique for IFT measurements. J. Electroanal. Chem. 1991, 319, 291−301. (32) Zeppieri, S.; Rodriguez, J.; Lόpez de Ramos, A. L. Interfacial Tension of Alkane + Water Systems. J. Chem. Eng. Data 2001, 46, 1086−1088. (33) Alcock, K.; Grimley, S. S.; Healy, T. V.; Kennedy, J.; McKay, H. A. C. The extraction of nitrates by Tri−n−butyl phosphate (TBP). Part 1.−The system TBP + Diluent + H2O + HNO3. Trans. Faraday Soc. 1956, 52, 39−47. (34) http://www.orau.org/ptp/PTP%20Library/library/cfr/ 40cfr050.pdf; National Primary and Secondary Ambient Air Quality Standards″, 40 CFR−Protection of the Environment, Chapter I, Part 50, Section 50.3, 1998 National Ambient Air Standards (visited on August 18, 2013). (35) http://www.millipore.com/lab_water/clw4/water_physico_ chemical (visited on August 18, 2013). (36) Klotz, I.; Rosenberg, R. M. Chemical Thermodynamics, basic theory and methods, 3rd ed.; W. A. Benjamin: Menlo Park, CA, 1972.

(37) Karkowiak, J.; Grzybkowski, W. Apparent Molar volume and Compressibility of Tetrabutylphosphonium Bromide in various Solvents. J. Chem. Eng. Data 2010, 55, 2624−2629. (38) Hepler, L. G. Thermal expansion and structure in water and aqueous solutions. Can. J. Chem. 1969, 47, 4613−4617. (39) Sandler, S. I. Chemical, Biochemical and Engineering Thermodynamics; Wiley: New York, 2006. (40) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (41) Yang, C.; Ma, P.; Jing, F.; Tang, D. Excess molar volumes, viscosities, and heat capacities for the mixtures of glycol + water from 273.15 to 353.15 K. J. Chem. Eng. Data 1997, 48, 836−840. (42) Prausnitz, J. M.; Litchtenthaler, R. N.; Gomes de Azevedo,E. Molecular Thermodynamics of Fluid−Phase Equilibria; Prentice Hall: Upper Saddle River, NJ, 1999.

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and n-Dodecane - American Chemical Society

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