Density, Viscosity, Refractive Index, and Excess ... - ACS Publications

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Density, Viscosity, Refractive Index, and Excess Properties of Binary and Ternary Solutions of Poly(ethylene glycol), Water, and Dipotassium Tartrate at 298.15 K and Atmospheric Pressure Alireza Barani, Mohsen Pirdashti,* and Abbas Ali Rostami Chemical Engineering Department, Faculty of Engineering, Shomal University, PO Box 731, Amol, Mazandaran, Iran ABSTRACT: The refractive index (nD) and density (ρ) values of the poly(ethylene glycol) (PEG) 1500 + dipotassium tartrate + water ternary system and physical properties of PEG 1500 + water and dipotassium tartrate + water binary solutions have been measured at 298.15 K and atmospheric pressure. Moreover, the refractive index deviation (ΔnD), viscosity deviation (Δη), apparent specific volume (Vφ), excess molar volume (VE), and excess Gibbs energy of activation for viscous flow (ΔG‡E) were calculated from the experimental measurements to analyze the behavior of the binary solutions and the refractive index deviation (ΔnD) and excess molar volume (VE) of the ternary solution. These results were fitted to Redlich−Kister polynomial and Cibulka Equations to estimate the interaction parameters. Adjustments were made to the refractive index and density to obtain a third-order polynomial expansion model and a second-order equation, respectively. The intermolecular interactions between the mixing components were demonstrated by the obtained data from the calculated functions.

1. INTRODUCTION

thermodynamics properties of binary and ternary solutions of PEG 1500, water, and dipotassium tartrate. Many researchers have studied physical properties and excess thermodynamic properties consisting of PEG and different ionic liquids and alcohols. Romero et al.19 reported dynamic viscosity of binary and ternary solutions containing PEG 1500, potassium phosphate, and water at 303.15 K. Cruz et al.20 measured kinematic viscosities of different molecular weights of PEG (200, 400, 600, 1000, 1500, and 3350) at several temperatures ranging from 293.15 to 363.15 K. Graber et al.21 investigated density, refractive index, viscosity, and electrical conductivity in the Na2CO3 + PEG 2000 aqueous two phase system from 293.15 to 308.15 K and refractive index, density, and viscosity in the NaNO3 + H2O + PEG 4000 system at various temperatures.22 Li et al.23 investigated excess properties for the binary system of PEG 200 + 1, 2-ethanediamine at 303.15 to 323.15 K and the system’s spectroscopic studies. Moosavi et al.3 reported investigation on some thermophysical properties of PEG 200 binary solutions at different temperatures. Rostami et al.24 studied densities, viscosities, and excess Gibbs energy of activation for viscous flow, for binary solutions of dimethyl phthalate with 1-pentanol, 1-butanol, and 1propanol at two temperatures. Sharma et al.25 measured thermodynamic properties of ternary solutions containing ionic liquid and organic liquids: excess molar volume and excess isentropic compressibility. Moreover, an evaluation of the literature shows that many studies of physical properties of

Nowadays, physicochemical and thermodynamic properties of solutions are a vital division of the engineering calculations for designing industrial unit operations concerning the transport phenomena and for the interpretation of the liquid state.1 Therefore, the studies on liquid solution behavior of the industrially important chemicals have attracted the increasing attention of many researchers.2−4 Aqueous solutions containing poly(ethylene glycol) (PEG), inorganic salts (present in a wide range of molecular masses), and salt types (having an unusual combination of characteristics such as high water solubility, low operational cost, low toxicity, and low flammability have been targeted by many related studies focusing on a wide variety of applications in the biotechnology,5,6 pharmaceutical, and cosmetic products.7 Refractive index, density, and viscosity are very important physical properties and sufficient knowledge about them could result in a better understanding of the basic behavior of liquid systems concerning mass transport and fluid flow. PEG is a water-soluble hydrophilic and biocompatible polymer and has many uses in chemical partitioning,8,9 and most recently in extractive crystallization of inorganic salts.10 Also, tartrate salts are nontoxic,11 and some of them are valuable and can be recycled as well.12 They are commonly applied in medicine,13 electronics,14 and industry,15 and may be used as a suitable green alternative for traditional inorganic salts.16 Not only are they effective in partitioning biological materials, but the discharge of tartrate into the biological wastewater is safe for the environment and good for plants.17,18 According to our knowledge, there is no report on physical and © XXXX American Chemical Society

Received: August 9, 2017 Accepted: December 5, 2017

A

DOI: 10.1021/acs.jced.7b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Pure Components Used in This Work chemical name

CAS no

PEG 1500

25322−68−3

dipotassium tartrate hemihydrate (potassium L-tartrate hemihydrate)

6100−19−2

purity (in mass fraction %)

source (country)

purification method

Merck (Germany) Merck (Germany)

crystallization

>99.5

fractional crystallization

>99.5

analytical method calibration curve calibration curve

Figure 1. Practical approach for determination of phase composition of binary and ternary solution of PEG−salt ATPS.43

purification method, final mole fraction purity, and analytical method are shown in Table 1. 2.2. Apparatus and Procedure. In order to prepare the binary (PEG 1500 + water; dipotassium tartrate + water) and ternary (dipotassium tartrate + PEG 1500 + water) solutions, ten grams of specific amounts of PEG 1500/dipotassium tartrate and distillated deionized water were mixed in a 15 mL scaled tube. All binary and ternary solutions were prepared by mass using an analytical balance (A&D; model GF300; Japan) with an accuracy of ±10−4 g. The solutions were freshly prepared and stirred vigorously due to the high viscosity of the PEG 1500 and the glass tube was provided with an external jacket and put in a thermostatic bath (Member, Germany, model INE400) to keep the temperature constant within ±0.1 K. To ensure complete miscibility, retention was allowed at a desired temperature for some hours. The phase compositions were obtained by measuring the physical properties of refractive index (nD) and density (ρ) of binary (PEG + water, dipotassium tartrate + water) and ternary (dipotassium tartrate + PEG + water) systems at 298.15 K using a CETI refractometer (Belgium) with an accuracy of 0.0001 nD and an Anton Paar oscillation U-tube densitometer (model: DMA 500) (DMA 500) with a precision of ±10−4 g.cm−3. It was calibrated with double-distilled water and air. The calibration equations were calculated beforehand. Duplicate data measurement was utilized and the mean values of the parameters were recorded. Using eq 1, this data was correlated as

various binary solution,26−38 and ternary solution,39,40 and excess thermodynamic properties,41,42 of the above-mentioned solutions have been reported. According to the related studies in the literature, the excess thermodynamic properties of binary or ternary system including PEG (solid state; molecular weight ≥1000) are rare. However, Graber et el.22 was the only study that reported the excess molar volumes (VE) of unsaturated solutions of sodium nitrate + poly(ethylene glycol) 4000 + water for different compositions at six temperatures between 288.15 and 313.15 K. Consequently, the current study reported the experimental values of the refractive index, density, and viscosity of PEG 1500, water, and dipotassium tartrate ternary systems and also studied the corresponding binary solutions at 298.15 K and atmospheric pressure. Deviations from ideality have been studied with refractive index deviations, excess molar volumes, viscosity deviations, apparent specific volumes, and excess Gibbs energy of activation. To derive the binary coefficients and estimate the standard deviation between experimental and calculated results, the binary and ternary excess molar volumes and the changes in refractive indices were fitted to the Redlich−Kister equation, while the Cibulka equation was applied to the ternary solutions.

2. MATERIALS AND METHODS 2.1. Material. Poly(ethylene glycol) with an average MW of 1500 g.mol−1 and dipotassium tartrate with a minimum purity of 99.5% by mass were obtained from Merck (Darmstadt, Germany). Without further purification, the polymer and salt were used in addition to distilled deionized water. The chemical name, CAS number (CAS), source, initial mole fraction purity,

Z = a0 + a1w1 + a 2w2 + a3w12 + a4w22 + a5w1w2 B

(1)



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Table 2. Value of the Coefficients Observed from eq 1 at 298.15 K and 0.1 MPa nD ρ/ g.cm−3

a0

a1

a2

a3

a4

a5

R2

1.3327 0.9970

0.1239 0.5960

0.1269 0.1592

0.0661 0.2757

0.0201 0.0390

1.0000 1.0000

0.9998 0.9997

where the physical properties (density or refractive index) are represented by Z, w1 represents the mass fraction of the salt, and w2 represents the mass fraction of the polymer and the fitting parameters are denoted by a0 to a5. Figure 1 shows a practical approach for determination of the mass fraction of binary and ternary systems. Finally, an Anton Paar Lovis 2000 M viscometer of various capillary sizes (1.59−1.8 mm) with an accuracy of up to 0.5% was employed to measure the viscosities of the solutions.

Table 4. Experimental Refractive Index (nD), Density (ρ), and Mass Fraction (w) and Calculated Refractive Index Deviation (ΔnD), Molar Volume (Vm), and Excess Molar Volume (VE) of Dipotassium Tartrate (1) + Water (2) Solutiona at 298.15 K and 0.1 MPa

3. RESULTS AND DISCUSSION 3.1. Fitting Parameters of Calibration Equation. Table 2 indicates the obtained coefficients with six nominal values of a0, a1, a2, a3, a4, and a5 from eq 1. The refractive index and density of pure water at 298.15 K are 1.3327 and 0.9970, respectively. 3.2. Binary Systems. The refractive index, density, and viscosity for PEG + water and dipotassium tartrate + water solutions have been measured at different concentrations and at 298.15 K. The refractive indices and the densities of PEG (1) + water (2) are shown in Table 3. Table 4 shows the refractive

nD

ΔnD

ρ (g.cm3)

Vm (cm3.mol−1)

VE (cm3.mol−1)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

1.3327 1.3390 1.3457 1.3524 1.3591 1.3658 1.3725 1.3792 1.3859

0.0000 0.0066 0.0132 0.0198 0.0264 0.0329 0.0395 0.0460 0.0525

0.9970 1.0049 1.0127 1.0207 1.0290 1.0372 1.0457 1.0541 1.0620

18.069 18.859 19.739 20.720 21.819 23.066 24.485 26.124 28.047

0.000 0.043 0.095 0.151 0.210 0.283 0.362 0.459 0.587

K

Vm (cm3.mol−1)

VE (cm3.mol−1)

0.00 0.02 0.04 0.06 0.08 0.10 0.15 0.20 0.25 0.30 0.40

1.3327 1.3345 1.3374 1.3403 1.3432 1.3461 1.3533 1.3606 1.3678 1.3750 1.3895

0.0000 0.0027 0.0053 0.0080 0.0106 0.0132 0.0197 0.0261 0.0325 0.0387 0.0506

0.9970 1.0060 1.0196 1.0333 1.0469 1.0606 1.0947 1.1289 1.1630 1.1971 1.2654

18.069 18.243 18.342 18.453 18.574 18.706 19.090 19.557 20.118 20.786 22.529

0.000 0.028 0.013 0.004 0.001 0.005 0.042 0.123 0.252 0.434 0.991

s=

1 N−1

N

∑ (Q exp − Q cal)2 N =1

(3)

where Qcal indicates the adjusted property values, Qexp indicates the experimental property values, and N indicates the number of measurements. Table 5 clearly shows the coefficients and the deviation. The experimental viscosity (η) of PEG (1) + water (2) and dipotassium tartrate (1) + water (2) solutions at 298.15 K are shown in Table 6. Figure 2 shows a steady increase for the refractive index of an aqueous solution of PEG, by increasing the mass fraction of the polymer. In the same solution, there was a gradual increase in density because the polymer fraction grew larger (Figure 3). Furthermore, Figures 2 and 3 present the refractive indices and densities of dipotassium tartrate and water solution, respectively. This increase can be ascribed to the refractive index and density followed by the increase in dipotassium tartrate fraction. Graphically, the experimental densities and the refractive indices of the PEG + water and dipotassium tartrate + water agree with correlated data. Figure 4 is a plot of the results of variation of η as a function of PEG concentration at 298.15 K. For PEG + water, binary solution, an increase in the viscosity was observed with increasing mole fraction of PEG. A steady increase is illustrated for the viscosity of the PEG + water subsystem up to a PEG mass fraction of 40% w/w (Figure 4). At any amount above this value, the viscosity remains almost constant to pure PEG. The viscosity of dipotassium tartrate + water solution is also shown in Figures 4 and 5, respectively. Accordingly, there was an increase in viscosity with the increase in dipotassium tartrate mass fraction. Also, an experimental viscosity of the PEG + water and dipotassium tartrate + water agrees with the correlated data.

I

(2)

k=1 i=1

ρ (g.cm3)

equation. The standard deviation(s) for each adjustment45 was calculated using eq 3:

indices and densities of dipotassium tartrate (1) + water (2). In a bid to obtain the mathematical relationship between the properties and compositions of the solutions, both properties were adjusted to a polynomial mass fraction expansion model and the fitting lines were calculated by the following equation.44

∑ ∑ Aik . wik

ΔnD

Standard uncertainties u are u (wi) = 0.01, u (nD) = 0.0001, u (ρ) = 0.0001 g.cm3, u (ΔnD) = 0.0001, u (Vm) = 0.001 cm3.mol−1, u (VE) = 0.001 cm3.mol−1, u (T) = 0.05 K, and u (P) = 5 kPa.

a Standard uncertainties u are u (wi) = 0.01, u (nD) = 0.0001, u (ρ) = 0.0001 g.cm3, u (ΔnD) = 0.0001, u (Vm) = 0.001 cm3.mol−1, u (VE) = 0.001 cm3.mol−1, u (T) = 0.1 K, and u (P) = 5 kPa.

Q=

nD

a

Table 3. Experimental Refractive Index (nD), Density (ρ), and Mass Fraction (w) and Calculated Refractive Index Deviation (ΔnD), Molar Volume (Vm), and Excess Molar Volume (VE) of PEG (1) + Water (2) Solutiona at 298.15 K and 0.1 MPa w1

w1

−3

where Qis nD, η (mPa.s), or ρ in g.cm , Aik denotes the adjustment coefficients of the model, I indicates the number of components, wi accounts for the mass fraction of component i, and K is the polynomial degree. Adjustments were made to the refractive index and density, to obtain a third-order polynomial expansion model, and a second-order polynomial expansion C



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Table 5. Refractive Index (nD), Density (ρ), and Viscosity (η) Fitting Parameters (Aik) of PEG (1) + Water (2) and Dipotassium Tartrate (1) + Water (2) Solutions at 298.15 K and 0.1 MPa order (k) property

component (i)

nD

1 2 1 2 1 2

ρ/ g.cm−3 η/ mPa.s

nD

1 2 1 2 1 2

ρ/ g.cm−3 η/ mPa.s

(1)

(2)

PEG (1) + Water (2) −123.2125 1.0676 −243.2109 367.3355 −10.6004 11.7700 12.7518 −11.7549 319.2935 −519.9229 −76.0529 −160.8902 Salt (1) + Water (2) −648.0144 963.4355 336.9208 −21.6988 −5.0090 6.7078 7.6600 −6.6658 −28.6696 91.7479 −150.5447 58.8160

(3)

s

−122.8296 −122.7920

0.0001 0.0002

289.1307 237.6700

0.0490

−313.989 −313.8898

0.0003 0.0001

−25.8355 59.6960

0.0002

Table 6. Experimental Viscosity (η) and Mass Fraction (w) and Calculated Viscosity Deviation (Δη) of PEG (1) + Water (2)a, and Dipotassium Tartrate (1) + Water (2)b Solutions at 298.15 K and 0.1 MPa η (mPa.s)

w1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.02 0.04 0.06 0.08 0.10 0.15 0.20 0.25 0.30 0.40

PEG (1) + water (2) 0.894 1.045 1.537 2.234 3.220 4.545 6.263 8.370 10.788 dipotassium tartrate (1) + water (2) 0.894 0.929 0.965 0.998 1.040 1.090 1.191 1.313 1.460 1.590 1.910

Δη (mPa.s) 0.000 0.324 0.799 1.482 2.442 3.742 5.431 7.507 9.888

Figure 2. Refractive index (nD) against the mass fraction of the components (w): (orange ■), PEG (1) + Water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 2 are represented by dashed lines (- - -).

0.000 0.037 0.060 0.078 0.111 0.151 0.227 0.320 0.435 0.528 0.760

a Standard uncertainties are u(wi) = 0.01, u(η) = 0.005 η, u(Δη) = 0.005 η, u(T) = 0.05 K, and u(P) = 5 kPa. bStandard uncertainties are u(wi) = 0.01, u(η) = 0.005 η, u(Δη) = 0.005 η, u(T) = 0.05 K, and u(P) = 5 kPa.

The refractive indices deviation, excess molar volumes, excess Gibbs energy of activation for viscous flow (ΔG‡E) and viscosity deviations for binary and ternary solutions are excess properties studied in this work. The related results are shown in Tables 2, 3, 5, and 7. The refractive index deviation (ΔnD) is defined as46

Figure 3. Density (ρ) against the mass fraction of the components (w): (orange ■), PEG (1) + water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 2 are represented by dashed lines (- - -).

I

ΔnD = nD −

∑ xi. nDi i=1

(4) D



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To understand the intermolecular interactions in our binary solutions excess molar volume (VE), set as the deviation of ideality of density, was defined as follows:46 I

V E = Vm −

∑ xi. Vi

(5)

i=1

where Vm is the molar volume of the solution, Vi indicates the molar volume for the pure component i, and xi denotes the mole fraction of component i. The molar volumes of the solution were calculated from the experimental densities using46 I

Vm =

∑i = 1 Mixi ρ

(6)

where Mi is the molecular weight of the pure component i, xi denotes the mole fraction of the component i, and ρ indicates the experimental density values of the solution. In order to describe the molar volume of pure water the equation V3 = M3/ ρ3 is used, whereas those of dipotassium tartrate and PEG are ∞ ∞ shown by V1 = V∞ ⌀1 and V2 = V⌀2. In these two equations, V⌀1 and V∞ ⌀2 which are the apparent molar volumes at infinite dilution of dipotassium tartrate and PEG, must be computed on the basis of data on apparent molal volume (V⌀). The following equation shows the relation of the V⌀ of a binary solution with density

Figure 4. Viscosity (η) against the mass fraction of the components (w): (orange ■), PEG (1) + water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 2 are represented by dashed lines (- - -).

V⌀ =

(ρ − ρ ) Mi + w ρ miρw ρ

(7)

where mi is the molality of solute i, ρ is the density of the binary solution, and ρw is the density of water. In order to yield apparent molal volumes at infinite dilution V∞ ⌀ , the apparent molar volumes V⌀ of aqueous electrolyte solutions are extrapolated to zero concentration employing the Conway et al.47 equation V⌀ = V ⌀∞ + km1/2 + bm + cm3/2

In eq 8, there are two parameters b and c which are experimental and k is the limiting theoretical slope which is equal to 1.868 cm−3 L1/2 mol−3/2 at 298.15 K, respectively.48 Table 4 as shown the empirical data on the solutions of dipotassium tartrate in order to achieve values for V⌀. These values were fitted to eq 8 to obtain the value for V∞ ⌀ given in Table 7. Note that prior measurements of density on PEG + water should be performed to calculate the values of V∞ ⌀ for the polymer. Some of the researchers49,50 have proposed that the dependency of V⌀ on the molality of the polymer is a linear function specified by

Figure 5. Refractive index deviation (ΔnD) against the mass fraction of the components (w): (orange ■), PEG (1) + water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 13 are represented by dashed lines (- - -).

Table 7. Apparent Molal Volumes at Infinite Dilution of ∞ dipotassium tartrate (V∞ ⌀1) and PEG (V⌀2) at 298.15 K PEG dipotassium tartrate

3 −1 V∞ ⌀1 (cm .mol )

3 −1 V∞ ⌀2 (cm .mol )

86.23

1200.27 -

(8)

V⌀ = V ⌀∞ + hm

(9)

In eq 9, h is a constant which is empirical. Applying eq 7 and data in Table 3, we can obtain the values of V⌀ for the polymer. As mentioned before, these values were fitted to eq 9. We demonstrated the values of V∞ ⌀ obtained using this fit for PEG in Table 7. According to Figure 6 and the VE data in Tables 2 and 3, it can be observed that the VE contains positive values. In this case, the positive VE values represent a dilatation or loose packing of molecules in the solutions. Most probably, the different molecular sizes and shapes of dipotassium tartrate and PEG lead to interstitial accommodation in the solutions. At the

where nD is the refractive index of the solution xi represents the mole fraction of component i and the refractive index (for each pure component of the solution) is represented as nDi. Figure 5 shows the refractive indices deviations for PEG + water, dipotassium tartrate + water, binary system. There is a positive deviation from ideality in the refractive index deviation of all binary. The experimental data refractive index deviations present a maximum deviation of approximately 60% PEG mass fraction. E



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Figure 6. Excess molar volume (VE) against the mass fraction of the components (w): (orange ■), PEG (1) + water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 13 are represented by dashed lines (- - -).

Figure 7. Viscosity deviation (Δη) against the mass fraction of the components (w): (orange ■), experimental data of PEG (1) + water (2) at 298.15 K; (blue ⧫) dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 13 are represented by dashed lines (- - -).

same time, it may be necessary to consider the disruption of hydrogen-bonded structures upon mixing. As the mass fractions increase, the VE values will become more positive and increase for PEG + water and dipotassium tartrate + water systems. Meanwhile, the mass fraction of dipotassium tartrate indicated a greater influence than that PEG of on excess molar volume of the solution. The viscosity deviation (Δη) is defined as51

of this behavior was as expected, given that aqueous solutions of PEG routinely demonstrate viscosity values greater than those of aqueous solutions of electrolytes at the same concentration. Excess Gibbs energy of activation for viscous flow (ΔG‡E) was calculated through the equation51 n

ΔG‡ E = RT[ln(Vmη) −

I

Δη = η −

∑ xi. ηi i=1

∑ xi ln(Vi ηi)] i−1

(11)

where x, η, and V are the mole fraction, dynamic viscosity, and the mole volume, respectively. It can be seen in Table 8 and Figure 8 that the excess Gibbs energy of activation for viscous flow (ΔG‡E) values, for PEG + water and dipotassium tartrate + water binary system, are positive. In addition, excess Gibbs energy recorded a deviation from ideality which was positive. Experimental data excess Gibbs energy present a maximum deviation near to 60% PEG mass fraction. The apparent specific volumes of the polymer V⌀ in water, was obtained based on the equation below:29

(10)

where η is the viscosity of the solution, xi denotes the mole fraction of component i and the viscosity of each pure component of the solution is represented by ηi. Viscosity is a measure of the internal resistance of a liquid to shear or flow. It is an important physical character of fluid. Figure 7 shows the dependence of deviation of viscosity, Δη, on composition. Δη of all binary solutions have a positive deviation from ideality. If the solution in the flow process is more ordered than expected from ideality, it would have a positive Δη value. It has been shown by earlier studies that positive Δη are exhibited by solution with strong interactions between different molecules. The major contributing factor to the positive Δη values of aqueous PEG is the more efficient packing in the solution than in the pure PEGs.52−54 Also, this behavior can be attributed to the degree of self-association among the PEG molecules which are more than the degree of heteroassociation between PEG and the solvent molecules. Moreover, the interaction in solution is in relation with the Hbonding between the solute−solvent molecules. Consequently, by increasing the PEG mole fraction, the H-bonding between the solute and the solvent in the solutions is exchanged gradually by the intermolecular force between the PEG particles.3 Also, an increase in Δη was observed for dipotassium tartrate + water and PEG + water by increasing the mass fraction of dipotassium tartrate and PEG. This figure shows that the concentration of PEG had a greater influence than that of dipotassium tartrate on the magnitude of Δη. The occurrence

V⌀ =

1 ⎛1 1 − w⎞ ⎜⎜ − ⎟⎟ ρw ⎠ w⎝ρ

(12)

where the terms ρ, ρw, and w are used to represent the densities of the solution and solvent and mass fraction of PEG, respectively. Table 9 and Figure 9 show that the apparent specific volumes of PEG in water decreased when the polymer mass was increased by up to 5% (w/w). At low PEG concentrations, the apparent specific volumes of PEG in water decreased with increasing polymer mass fraction. On the other hand, beyond a polymer mass fraction of around 10−40% (w/w), the apparent specific volumes of PEG in water is independent of the polymer mass fraction. Furthermore, it was observed that for low concentration of PEG, the value of V⌀ decreases as the concentration of PEG increases and for a high concentration of PEG, the value of V⌀ is independent of the PEG concentration. F



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Table 8. Mass Fraction (w) and Calculated Excess Gibbs Energy of Activation for Viscous Flow (ΔG‡E) of PEG (1) + Water (2)a, and Dipotassium Tartrate (1) + Water (2)b Solutions at 298.15 K and 0.1 MPa

Table 9. Mass Fraction (w) and Polymer Apparent Specific Volumes of Polymer (V⌀) of PEG (1) + water (2)a at 298.15 K and 0.1 MPa w1

ΔG‡E (kJ mol−1)

w1

0.010 0.015 0.025 0.035 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400

PEG (1) + water (2) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.00 1.07 2.12 3.16 4.17 5.14 6.06 6.92 7.69 dipotassium tartrate (1) + water (2) 0.00 0.00 0.02 0.14 0.04 0.22 0.06 0.29 0.08 0.39 0.10 0.54 0.15 0.77 0.20 1.03 0.25 1.31 0.30 1.65 0.40 2.20

V⌀ (cm3. g

−1

)

0.881 0.867 0.856 0.851 0.845 0.848 0.848 0.847 0.848 0.847 0.848 0.849

a Standard uncertainties u are u (wi) = 0.01, u (V⌀) = 0.001 cm3. g −1, u (T) = 0.05 K, and u (P) = 5 kPa.

a Standard uncertainties u are u (wi) = 0.01, u (ΔG‡E) = 0.01 kJ mol−1, u (T) = 0.05 K and u (P) = 5 kPa. bStandard uncertainties u are u (wi) = 0.01, u (ΔG‡E) = 0.01 kJ mol−1, u (T) = 0.05 K and u (P) = 5 kPa.

Adjustments were made to the refractive index deviation and excess molar volumes to obtain the Redlich−Kister model for binary solutions, corresponding to55

Figure 9. Apparent specific volume of PEG in water (V⌀) against the mass fraction of component (w): (blue ⧫), PEG (1) + water (2) at 298.15 K and 0.1 MPa. (----), trendline.

K k Q ij = ww i j ∑ Ak (2wi − 1) k=0

where Qij denotes the excess property, wi and wj are the mass fractions of the components i and j in the binary solutions, and

(13)

Figure 8. Excess Gibbs energy (ΔG‡E) against the mass fraction of the components (w): (orange ■), PEG (1) + water (2) at 298.15 K; (blue ⧫), dipotassium tartrate (1) + water (2) at 298.15 K and 0.1 MPa. Values obtained from fitting to eq 13 are represented by dashed lines (- - -). G



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Ak is related to the fitting parameters, K being the order of the fit. Tables 3, 4, 6, and 8 show the refractive indices deviations, molar volumes, excess molar volumes, viscosity deviations, and excess Gibbs energy of activation, whereas the fitting parameters are shown in Table 10. Table 10. Refractive Index Deviation (nD), Excess Molar Volumes (VE), Excess Gibbs Energy (ΔG‡E), Viscosity Deviation (Δη), and Fitting Parameters (Aik) of PEG (1) + Water (2) and Dipotassium Tartrate (1) + Water (2) Solutions at 298.15 K and 0.1 MPa Order (k) excess property ΔnD VE/ cm3.mol−1 ΔG‡E/ kJ mol−1 Δη/ mPa.s ΔnD VE/ cm3.mol−1 ΔG‡E/kJ mol−1 Δη/ mPa.s

(0) 0.2597 3.6998

(1)

PEG (1) + water (2) 0.2347 0.1510 7.9713 9.2862

0.2430 6.6725

(3)

s

0.0540 4.3238

0.0001 0.0011

4.7820

0.2180

0.0002

116.7602 71.7990 Salt (1) + water (2) 0.1784 0.0830 13.8350 4.9510

10.7470

0.0005

0.0138 3.2440

0.0004 0.0001

35.5922 61.7890

(2)

18.6910

10.0902

2.5790

−12.1356

−10.5532

0.0002

3.8200

3.3670

0.0486

−0.8905

0.0001

3.3. Ternary System. At 298.15 K, measurements of the refractive index and density of the dipotassium tartrate + PEG + water ternary system were performed. The experimental properties are reported in Table 11 and the experimental data were adjusted to a model following eq 2 for the three components. Accordingly, using the obtained model in Figure 10, isolines were drawn. This illustrates the lines of constant densities and refractive indices of the ternary solution plotted against the mass fraction. For the sake of clarity in the figures, mass fraction is used for the reason explained above. Table 12

Figure 10. Experimental properties fitting for the dipotassium tartrate (1) + PEG (2) + water (3) system: (a) density in g.cm−3 and (b) refractive index at 298.15 K and 0.1 MPa.

Table 11. Experimental Refractive Index (nD) and Density (ρ) and Calculated Refractive Index Deviation (ΔηD), Molar Volume (Vm), and Excess Molar Volume (VE) of the Dipotassium Tartrate (1) + PEG (2) + Water (3) Systema at 298.15 K and 0.1 MPa w1

w2

nD

ρ (g.cm−3)

ΔnD

Vm (cm3.mol−1)

VE (cm3.mol−1)

0.02 0.05 0.10 0.15 0.20 0.02 0.05 0.10 0.15 0.20 0.02 0.05 0.10 0.15 0.05 0.02

0.02 0.02 0.02 0.02 0.02 0.05 0.05 0.05 0.05 0.05 0.10 0.10 0.10 0.10 0.20 0.20

1.3373 1.3415 1.3470 1.3532 1.3594 1.3412 1.3448 1.3512 1.3513 1.3644 1.3500 1.3502 1.3583 1.3701 1.3623 1.3619

1.0095 1.0260 1.0536 1.0811 1.1087 1.0144 1.0309 1.0584 1.0860 1.1135 1.0225 1.0390 1.0665 1.0941 1.0552 1.0387

0.0047 0.0086 0.0134 0.0188 0.0242 0.0086 0.0118 0.0175 0.0168 0.0290 0.0173 0.0170 0.0243 0.0353 0.0288 0.0289

18.553 18.794 19.251 19.786 20.410 19.052 19.318 19.824 20.416 21.106 19.958 20.275 20.875 21.576 22.571 22.123

0.076 0.130 0.251 0.413 0.620 0.104 0.164 0.296 0.471 0.695 0.158 0.228 0.380 0.580 0.389 0.293

Standard uncertainties u are u (wi) = 0.01, u (nD) = 0.0001, u (ρ) = 0.0001 g.cm−3, u (ΔnD) = 0.0001, u (Vm) = 0.001 cm3.mol−1, u (VE) = 0.001 cm−3.mol−1, u (T) = 0.05 K, and u (P) = 5 kPa. a

H



Article

shows the fitting parameters and calculated standard deviation for the ternary system. Quite a small number of studies have investigated the results of this solution.

concentrations of PEG or dipotassium tartrate. However, a differentiating factor can be observed between the two situations. When the concentration of PEG remained fixed, it was noted that the increase in VE from the low value for dipotassium tartrate of 2% (w/w) was more than 9 times that for the case when its concentration was increased to 20% (w/ w). In contrast, it was noted that VE only increased slightly when the concentration of PEG in the solution was increased from 2% (w/w) to 20% (w/w). This situation may indicate that the increase of dipotassium tartrate in the solution produces a greater perturbation (from the structural point of view of the dissolution than an increase in PEG. Similar behavior is also seen in the NaNO3 + H2O + PEG 4000 system reported by Graber et al.22 Figure 11a,b shows the calculated isolines against mass fraction corresponding to ternary excess molar volumes, and changes of refractive index, respectively. During the mixing process, as described by the breaking interactions among molecules in the pure components, dipotassium tartrate + PEG + water ternary system has positive excess volumes. It will reach a maximum around 0.695 cm3.mol−1, which is in accordance with the PEG + water and dipotassium tartrate + water binary systems. Upon measuring the ternary changes of refractive index, positive deviations from the ideal behavior over the whole composition range were obtained. Also, for the refractive index and density listed in Table 11, these properties showed both a slightly greater influence of mass % PEG compared with the concentration of dipotassium tartrate on the refractive index value of the ternary solutions. The opposite happens with density. The Cibulka equation56 for the excess properties was used to correlate the results of the ternary system dipotassium tartrate (1) + PEG (2) + water (3)

Table 12. Refractive Index (nD) and Density (ρ) Fitting Parameters (Aik) of Dipotassium Tartrate (1) + PEG (2) + Water (3) System at 298.15 K and 0.1 MPa order (k) property nD

ρ/g.cm−3

component (i)

(1)

(2)

(3)

s

1 2 3 1 2 3

4.5252 4.4022 −6.6907 1.5655 1.1788 0.9365

1.4033 3.6371 13.091 0.0277 −0.0101 0.0979

−3.9820 −12.2220 −5.0594 −0.0706 −0.0286 −0.0392

0.0002

0.0002

An excess study has been executed. Equations 4 and 5 were used to analyze and calculate the refractive index deviation and excess molar volume, respectively. Table 11 and Figures 10 and 11 also present the experimental and excess properties. By observing the values for the excess volume VE at a given temperature, it was found that VE increases with increasing

Q 123 = Q bin + w1w2(1 − w1 − w2)(C1 + C2w1 + C3w2) (14)

where Q bin = Q 23 + Q 13

(15)

The adjustment coefficients C1, C2, and C3 are shown in Table 13. Table 13. Refractive Index Deviation (ΔnD) and Excess Molar Volume (VE) Fitting Parameters of Dipotassium Tartrate (1) + PEG (2) + Water (3) System to the Cibulka eq 14 at 298.15 K and 0.1 MPa constant parameter VE/cm3.mol−1 ΔnD

C1

C2

C3

s

72.4493 1.3071

66.5242 −5.1587

−334.6522 −6.2548

0.0970 0.0001

Also, these excess properties have been fitted to the Redlich− Kister ternary third-order model, as follows57 Q 123 = Q 23 + Q 13 + w1w2w3(A + B(w1 − w2) + C(w1 − w3) + D(w2 − w3) + E(w1 − w2)2 + F(w1 − w3)2 + G(w2 − w3)2 + H(w1 − w2)3

Figure 11. Excess properties fitting for dipotassium tartrate (1) + PEG (2) + water (3) system: (a) refractive index deviation and (b) excess molar volume, in cm3.mol−1 at 298.15 K and 0.1 MPa.

+ I(w1 − w3)3 + J(w2 − w3)3 ) I

(16)



Article

Table 14. Refractive Index Deviation (ΔηD) and Excess Molar Volume (VE) Fitting Parameters of Dipotassium Tartrate (1) + PEG (2) + Water (3) System to the Redlich−Kister eq 16 at 298.15 K and 0.1 MPa excess property

A

B

C

D

E

F

G

H

I

J

S

ΔnD VE/cm3.mol−1

−609.47 −4063.26

1976.32 −11250.97

−1992.21 10012.99

−466.55 −27272.21

−101402.40 −406901.45

101589.60 408281.30

−3299.76 −24090.77

−1005.90 10496.87

2.10 837.67

−1475.30 −12033.27

0.0061 0.0500

where Q123 denotes the ternary excess fitted properties, Q23 denotes PEG + water, Q13 denotes dipotassium tartrate + water parameters at 298.15 K, reference is made to the binary fitted properties listed in Table 5 following eq 2, whereas w1, w2, and w3 are the mass fractions of the three components involved in the ternary solutions. The adjustment coefficients A, B, C, D, E, F, G, H, I, and J are shown in Table 14. Both refractive index deviation and excess molar volume indicate the nonideal trend with the composition in ternary dipotassium tartrate (1) + PEG (2) + water (3) solution.

water, and 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid. J. Chem. Eng. Data 2012, 57, 1165−1173. (5) Alcântara, L. A. P.; Amaral, I. V.; Bonomo, R. C. F.; da Silva, L. H. M.; da Silva, M. d. C. H.; Minim, V. P. R.; Minim, L. A. Partitioning of α-lactalbumin and β-lactoglobulin from cheese whey in aqueous twophase systems containing poly (ethylene glycol) and sodium polyacrylate. Food Bioprod. Process. 2014, 92, 409−415. (6) Lan, J. C.-W.; Yeh, C.-Y.; Wang, C.-C.; Yang, Y.-H.; Wu, H.-S. Partition separation and characterization of the polyhydroxyalkanoates synthase produced from recombinant Escherichia coli using an aqueous two-phase system. J. biosci. bioeng. 2013, 116, 499−505. (7) Madadi, B.; Pazuki, G.; Nasernejad, B. Partitioning of cefazolin in biocompatible aqueous biphasic systems based on surfactant. J. Chem. Eng. Data 2013, 58, 2785−2792. (8) Graber, T.; Andrews, B.; Asenjo, J. Model for the partition of metal ions in aqueous two-phase systems. J. Chromatogr., Biomed. Appl. 2000, 743, 57−64. (9) Spear, S. K.; Griffin, S. T.; Huddleston, J. G.; Rogers, R. D. Radiopharmaceutical and hydrometallurgical separations of perrhenate using aqueous biphasic systems and the analogous aqueous biphasic extraction chromatographic resins. Ind. Eng. Chem. Res. 2000, 39, 3173−3180. (10) Taboada, M.; Graber, T.; Asenjo, J.; Andrews, B. Drowning-out crystallisation of sodium sulphate using aqueous two-phase systems. J. Chromatogr., Biomed. Appl. 2000, 743, 101−105. (11) Zafarani-Moattar, M. T.; Hamzehzadeh, S.; Hosseinzadeh, S. Phase diagrams for liquid−liquid equilibrium of ternary poly (ethylene glycol)+ di-sodium tartrate aqueous system and vapor−liquid equilibrium of constituting binary aqueous systems at T = (298.15, 308.15, and 318.15) K: Experiment and correlation. Fluid Phase Equilib. 2008, 268, 142−152. (12) Zafarani-Moattar, M. T.; Hosseinpour-Hashemi, V.; Tolouei, S. Liquid−Liquid Equilibrium Data of the Ternary Systems Containing 1-Propanol/2-Propanol+ Dipotassium Tartrate/Potassium Sodium Tartrate+ Water at T= 298.15 K. J. Chem. Eng. Data 2013, 58, 1223−1228. (13) Abadía-Fenoll, F.; Garrido, M.; López-Lendínez, J.; Martos, R. C. A modification of the chromic tartrate silver impregnation technique for block impregnation of the central nervous system and paraffin wax embedding. J. Microsc. 1985, 137, 225−232. (14) Voříšek, J.; Sajdl, P.; Lojda, Z. Electron-cytochemical localization of phospho (enol) pyruvate carboxylase (EC 4.1. 1.31) in fungal cells. Histochemistry 1980, 67, 257−265. (15) Jue, C. K.; Lipke, P. N. Determination of reducing sugars in the nanomole range with tetrazolium blue. J. Biochem. Biophys. Methods 1985, 11, 109−115. (16) Nemati-Kande, E.; Shekaari, H.; Jafari, S. A. Liquid−Liquid Equilibrium of Some Aliphatic Alcohols+ Disodium Tartrate+ Water Aqueous Two-Phase Systems at 298.15 K. J. Chem. Eng. Data 2012, 57, 2336−2342. (17) Zafarani-Moattar, M. T.; Tolouei, S. Liquid−liquid equilibria of aqueous two-phase systems containing polyethylene glycol 4000 and di-potassium tartrate, potassium sodium tartrate, or di-potassium oxalate: Experiment and correlation. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2008, 32, 655−660. (18) Zafarani-Moattar, M. T.; Zaferanloo, A. Measurement and correlation of phase equilibria in aqueous two-phase systems containing polyvinylpyrrolidone and di-potassium tartrate or dipotassium oxalate at different temperatures. J. Chem. Thermodyn. 2009, 41, 864−871.

4. CONCLUSIONS The current study determined new experimental densities, viscosities, and refractive indices for the binary systems PEG + water, dipotassium tartrate + water, and for the ternary solution of dipotassium tartrate + PEG + water. To analyze the behavior of the solutions, the excess molar volumes, refractive indices deviations, viscosity deviations, apparent specific volumes, and excess Gibbs energy of activation for viscous flow were calculated from the experimental measurements. Refractive index deviation and viscosity deviations of all binary solutions had a positive deviation from ideality. Furthermore, the excess Gibbs energy had a positive deviation from ideality. Changes in the refractive index were positive also; the excess molar volumes were positive over the whole composition range. In conclusion, an investigation of the behavior of the ternary systems also showed a nonideal mixing behavior in the studied properties. Moreover, the binary and ternary excess molar volumes and changes in refractive indices correlated reliably with the Redlich−Kister equation while the Cibulka equation was applied successfully for the ternary solutions.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mohsen Pirdashti: 0000-0002-8862-0583 Abbas Ali Rostami: 0000-0002-3180-658X Notes

The authors declare no competing financial interest.

■

REFERENCES

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