Measurement and Correlation of Activity, Density, and Speed of Sound

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

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Measurement and Correlation of Activity, Density, and Speed of Sound for Binary Mixtures of 1‑Propanol + Poly(Propylene Glycol) 400, 725, and 1025 Hemayat Shekaari,* Mohammed Taghi Zafarani-Moattar, and Saeid Faraji Department of Physical Chemistry, University of Tabriz, Tabriz 5166616471, Iran ABSTRACT: The improved isopiestic method was used to measure 1-propanol activity data for several binary mixtures of 1-propanol + poly(propylene glycol) 400 (PPG400)/ poly(propylene glycol) 725 (PPG725)/poly(propylene glycol) 1025 (PPG1025) at 298.15 K. The effect of polymer molar mass was studied on the solvent activity and vapor pressure of the studied systems. The results indicate that solvent activity increases with the increasing of the polymer molar mass. These data have been correlated with different activity models including Flory−Huggins (FH), modified Flory−Huggins, NRTL, NRF-NRTL, Wilson, and NRF− Wilson models. The obtained values of standard deviations for the models represent that modified Flory−Huggins model have good agreement with the experimental data. The apparent specific volume, excess specific volume, isentropic compressibility, isentropic compressibility increments, and apparent specific isentropic compressibility quantities were obtained with use of density and speed of sound data in the 1-propanol + poly(propylene glycol) 400/poly(propylene glycol) 725 systems at T = 288.15 to 318.15 K which supplies the strong solute−solvent interactions and more compatibility between 1-propanol with PPG400 rather than the other polymers.

1. INTRODUCTION The binary mixtures of poly(propylene glycol) (PPG), one of the most used polymers in the industry, in organic solvents are extensively used in formulations of polyurethanes, rheology modifier in solid tires, automobile seats, foams, membranes, and in talc separation from talc-carbonate ore.1−4 The design, optimization, and development of process, including polymers mixtures, thermodynamic properties, such as vapor−liquid equilibrium (VLE) and volumetric properties, are needed. These data have valuable results to understand the interactions between the components of the mixtures in polymer−solvent systems and deviation from ideal solutions.5 Different research groups measured the thermodynamic properties of polymers mixtures in several organic solvents.6,7 Despite the importance and extensive application of the PPG in industry there are limited thermodynamic data for this polymer in organic solvents. In this regard, vapor−liquid equilibrium gives useful information about activity, osmotic coefficient, and the vapor pressure of the polymer solutions. The use of activity model is essential to obtain and modelling of solvent activity data in polymer mixtures. The experimental determination of solvent activity data in the mixtures, several techniques, such as freezingpoint depression, boiling point elevation, osmotic pressure measurement, the isopiestic method,8 and vapor-pressure osmometry (VPO), have been employed.9 Each of the above techniques has positive and negative characteristics. Among them, the isopiestic method is one of the common experimental techniques for measuring the solvent activity and osmotic coefficient for nonvolatile solutes in mixtures. Because it is one of the easiest methods which is based on variation of mixture © XXXX American Chemical Society

composition by transferring solvent mass by vaporation, when connected through the vapor space to approach equilibrium.9 Recently, the solvent activity data for the binary mixtures of alcohols, including methanol, ethanol, 2-propanol, 1-butanol, and acetonitrile with PPG with different molar masses, have been determined using the isopiestic method at 298.15 K.10,11 The vapor pressure osmometry (VPO) method was also applied to measure the solvent activity and vapor pressure of various aqueous and nonaqueous mixtures of PPG400 at 318.15 K.12 To the best of our knowledge, the thermodynamic properties of PPG400/PPG725/PPG 1025 in 1-propanol have not been reported in the literature. Studies on the volumetric and compressibility properties of the mixtures give the useful information about the nature and structure of the intermolecular interactions occurring in the alcohol + polymer mixtures.13 In literature, measurement of densities and speeds of sound have been reported for the PPG1025 and PPG400 in the aqueous and nonaqueous solvents13,14 to determine the apparent specific volume, excess specific volume, isentropic compressibility, isentropic compressibility increments, and apparent specific isentropic compressibility at different temperatures.15 However, for the binary mixtures of 1-propanol + PPG400 and + PPG725 there is no density and speed of sound data in the literature. In continuing of our previous works, the current study is done on the vapor−liquid equilibria (VLE) behavior of binary mixtures 1-propanol + PPG with different molar masses to Received: June 25, 2017 Accepted: October 20, 2017

A

DOI: 10.1021/acs.jced.7b00581 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Descriptions of the Used Chemicals at Experimental Pressure (P = 86.6 kPa)a material

PPG400

provenance

Fluka

CAS number

purity (in mass fraction)

25322-69-4

T/K

ρ/(kg·m−3)

u/(m·s−1)

288.15

1011.860 1011.814 1003.929 1003.914 995.937 995.914 987.935 1015.645 1007.136 999.967 991.831 1011.563 807.837 799.597 799.521 791.399 792.022 783.121 784.123

1400.58

298.15 308.15

PPG725

Aldrich

PPG1025

Riedel-deHaen

1-propanol

Merck

25322-69-4

71-23-8

0.998

318.15 288.15 298.15 308.15 318.15 298.15 288.15 298.15 308.15 318.15

CaCl2 a

Merck

10043-52-4

1366.70 1333.64 1300.55 1388.59 1354.15 1321.10 1137.31 1242.34 1205.33 1170.36 1137.31

0.995

Standard uncertainties (u) for each variables are u (ρ) = 0.2 kg·m−3; u (u) = 0.5 m·s−1; u (T) = 0.03 K; u (p) = 0.5 kPa

To determine isopiestic equilibrium molalities, the masses of isopiestic flasks in equilibrium were measured by an analytical balance (Shimadzu, 321−34553, Shimadzu Co., Japan) with a precision of ±1 × 10−7 kg as described previously.24,25 The density and speed of sound of the solutions at different temperatures were measured with the density and speed of sound analyzer (Anton Paar DSA 5000, Austria) that proportional temperature of an apparatus kept the samples temperatures with an uncertainty of 0.03 K using Peltier device built in the densimeter. The degassed double distilled water and dry air was used to calibrate the apparatus at 298.15 K. The density of a known molality of aqueous NaCl was used to test the apparatus given by Pitzer et al.26 Uncertainty of the measurement is ±0.2 kg·m−3 for density and 0.5 m·s−1 for speed of sound.

describe the nature of the structural interaction between the solvent and solute in these mixtures. In the present research, the solvent activity and vapor pressure data for 1-propanol + PPG400, PPG725, and PPG1025 binary mixtures were measured using the improved isopiestic method at 298.15 K. The findings were correlated with the Flory−Huggins(FH),16 modified Flory−Huggins,17 and some of the local composition models, such as NRTL,18 NRF−NRTL,18 Wilson,19 and NRF−Wilson20 equations. The density and speed of sound data were also measured for 1-propanol + PPG400 and PPG725 binary mixtures to obtain the apparent specific volume, excess specific volume, isentropic compressibility, isentropic compressibility increments, and apparent specific isentropic compressibility at different temperatures.

3. RESULTS AND DISCUSSION 3.1. Activity Results. The solvent activity is considered as one of the important thermodynamic properties for calculations of vapor−liquid equilibria and deep understanding about the nature and structure of intermolecular interactions in solute + solvent mixtures. The vapor−liquid equilibria behavior in polymer + alcohol systems is studied with the use of improved isopiestic method, which in this method chemical potentials in reference and polymer solutions have been equal at equilibrium. Based on the activity solvent measured in reference and polymer mixtures, they should also have the similar values. In the present study, the activity of 1-propanol in binary mixtures, such as 1-propanol + PPG400/PPG725/PPG1025, was measured by using the improved isopiestic method. The experimental solvent activity data is calculated for 1-propanol + CaCl2 with the help of fourth-order polynomial eq 1 relating to reference molality mr:

2. EXPERIMENTATION 2.1. Materials. PPG400, PPG725, and PPG1025 were obtained from Fluka, Sigma-Aldrich, and Riedel-deHaen, respectively. The calcium chloride (G R, minimum 0.995 in mass fraction) were dried in an electrical oven at about 110 °C for 24h prior to use. 1-Propanol with the purity of minimum mass fraction 0.998, poly(propylene glycol) 400, 725, and 1025 without more purification were employed. The CAS number, purity, density, and speed of sound of the used chemicals are given in Table 1.21−23 2.2. Apparatus. The isopiestic method8 was used to measure of solvent activity in the studied solutions. The apparatus contained a five-leg manifold is attached to round-bottom flasks. Two flasks consisted of the standard (CaCl2) two flasks contained polymer solutions, and the central flask was used as an alcohol reservoir. The isopiestic apparatus was slowly evacuated several times to remove the air and degas the solutions. Then isopiestic apparatus was immersed in a bath with a constant temperature at least 120 h for equilibrium using a temperature controller (Julabo, MB, Germany) with standard uncertainty of 0.1 K. After equilibrium was reached the air is admitted to the isopiestic apparatus while it was still in the bath.

as = 1 + b0(mr ) + b1(mr )2 + b2(mr )3 + b3(mr )4

(1)

Equation coefficients for 1-propanol + CaCl2 derived from the literature5 are as follows: b0 = −0.012 ± 0.001, b1 = −0.1 ± 0.01, b2 = 0.06 ± 0.01, b3 = −0.012 ± 0.003. B

DOI: 10.1021/acs.jced.7b00581 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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The activity data for 1-propanol + CaCl2 has obtained with standard deviation of about 0.001, and based on, the activity values are reported with three decimal point for polymer + alcohol solution. The obtained activities are given in Table 2 and Table 2. Experimental Isopiestic Weight Fraction of Polymer (W2), Weight Fraction of Reference (WCaCl2), Vapor Pressure of Solution, pexp (kPa), Vapor Pressure Depression, Δp (kPa), and 1-Propanol Activity, a1 for the 1-Propanol (1) + PPG400 (2)/PPG725 (2)/PPG1025 (2) at T = 298.15 Ka WCaCl2 0.0000 0.0543 0.0661 0.0668 0.0743 0.0863 0.0880 0.0917 0.1024 0.1137 0.1170 0.1230 0.1272 0.1333 0.1373 0.0000 0.0489 0.0576 0.0700 0.0783 0.0820 0.0916 0.1095 0.1296 0.1327 0.1505 0.0000 0.0442 0.0690 0.0855 0.0866 0.0966 0.1161 0.1177 0.1336 0.1366 0.1471

W2

a1

pexp/kPa

1-propanol (1) + PPG400 (2) 0.0000 1.000 2.78 0.1219 0.975 2.71 0.1460 0.965 2.68 0.1538 0.964 2.68 0.1727 0.958 2.66 0.1913 0.948 2.64 0.1959 0.947 2.63 0.2092 0.943 2.62 0.2297 0.934 2.59 0.2532 0.924 2.57 0.2607 0.921 2.56 0.2636 0.916 2.54 0.2707 0.912 2.53 0.2811 0.907 2.52 0.2940 0.903 2.51 1-propanol (1) + PPG725 (2) 0.0000 1.000 2.78 0.1243 0.978 2.72 0.1449 0.972 2.70 0.1741 0.962 2.67 0.1932 0.955 2.65 0.2056 0.952 2.65 0.2203 0.946 2.63 0.2648 0.927 2.58 0.3109 0.910 2.53 0.3131 0.907 2.52 0.3482 0.892 2.48 1-propanol (1) + PPG1025 (2) 0.0000 1.000 2.78 0.1322 0.982 2.73 0.1959 0.963 2.68 0.2266 0.954 2.65 0.2379 0.948 2.63 0.2644 0.939 2.61 0.3003 0.922 2.56 0.3078 0.920 2.56 0.3311 0.907 2.52 0.3426 0.904 2.51 0.3582 0.895 2.49

Δp/kPa 0.00 0.07 0.10 0.10 0.12 0.14 0.15 0.16 0.18 0.21 0.22 0.23 0.24 0.26 0.27

Figure 1. Comparison of solvent activity (a1) of 1-propanol in 1propanol (1) + PPG400 (2) ⧫, 1-propanol (1) + PPG725 (2) ■, and 1propanol (1) + PPG1025 (2) ▲ and 2-propanol activity in 2-propanol (1) + PPG400 (2) ◊ and 2-propanol (1) + PPG1025 (2) Δ, which are taken from refs 4,11 systems plotted against weight fraction of polymer (W2) at T = 298.15 K (, modified Flory−Huggins model).

1-propanol + CaCl2 solutions are given to two decimal points shown in Table 2. ⎛p ⎞ (B − V S0)(pexp − pS0 ) exp lnaS = ln⎜⎜ 0 ⎟⎟ + RT ⎝ pS ⎠ 0

(2)

p0s

where, as, B, R, T, V s, pexp, and are the activity, second virial coefficient of alcohol vapor, global gases constant, absolute temperature, molar volume of solvent, vapor pressure of solution, and pure solvent, respectively. The constants of B, V0s, and p0s for 1-propanol at 298.15 K are given in Table 3, and indicated as follows:

0.00 0.06 0.08 0.11 0.13 0.13 0.15 0.20 0.25 0.26 0.30

103·B(m 3·mol−1) = − 2.913427, 105·V 0 s(m 3·mol−1) = 7.51175, p0 s (kPa) = 2.785

Table 3. Physical Properties of 1-Propanol at 298.15 K T/ K

alcohol 0.00 0.05 0.10 0.13 0.14 0.17 0.22 0.22 0.26 0.27 0.29

1-propanol a

298.15

106·V*s/m3·mol−1 7.5117

a

103·B/m3·mol−1

p0s/kPa

−2.9134

2.78a

b

b

Ref 5. Ref 27.

Vapor pressure depression (Δp) is another important thermodynamic property which is directly attributed to the solute−solvent interactions and can be computed using the eq 3.

Δp = ps0 − pexp

(3)

The obtained values for the vapor pressure depression of the 1propanol in 1-propanol + PPG400, PPG725, and PPG1025 mixtures are given in Table 2 and indicated in Figure 2. The obtained results state that the activity and vapor pressure of 1-propanol in the studied systems increase with the increasing of polymer molar mass. Correlation of Data. Several models have been suggested for the VLE description of polymer solutions, and the correlation between experimental solvent activity data in this study. Presented models, such as Flory- Huggins (FH),16 modified Flory−Huggins,17 NRTL,18 NRF−NRTL,18 Wilson,19 and NRF−Wilson,20 have been explained as follows.

a

Standard uncertainties (u) for each variables are u (W2) = 0.0001; u (a1) = 0.001; u (T) = 0.1 K; u (p) = 0.01 kPa.

shown in Figure 1. Also, the comparison of the activities of 1propanol at studied systems in this work and 2-propanol activities in the same polymer based on previous works are shown in Figure 1. The vapor pressure of 1-propanol solution, p was determined by the following relation by using solvent activity data. Because of meaningfulness of corresponding activity data to only three decimal points, the calculated vapor pressure data for C

DOI: 10.1021/acs.jced.7b00581 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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to molar volume from solvent correlated with the equation of r2 = (Mp/ρp)/(Ms/ρs), where ρp and ρs are density of polymer and solvent respectively. Derived interaction parameter for the studied systems is χ12, and it is reported in Table 4. For the present study, the interaction parameter indicates that solvent activity increases with the increasing of molar mass of polymer. It also obtained different values of χ12 in various molar masses of polymer. The next model is the modified Flory−Huggins17 which the solvent activity data were fitted using the suggested equation by Bae et al.17 which indicate the correlation of χ12 concentration dependency. The equation can be written as follows: ⎛ 1⎞ d ln a1 = ln φ1 + ⎜1 − ⎟(1 − φ1) + 1 − f (1 − φ1) r2 ⎠ ⎝

Figure 2. Experimental data of vapor pressure depression, (Δp = p0s pexp), for 1-propanol (1) + PPG400 (2) ▲, 1-propanol (1) + PPG725 (2) ■, and 1-propanol (1) + PPG1025 (2) ⧫ systems plotted against weight fraction of polymer (W2) at T = 298.15 K (, modified Flory− Huggins model).

(1 − φ1)2

where d and f are adjustable parameters of the modified Flory− Huggins equation. The parameters of this equation have been given in Table 4. Also, NRTL,18 NRF−NRTL,18 Wilson,19 and NRF−Wilson20 models have been used for the correlation of activity data, which are sum of combinatorial and residual contributions in the investigated systems. In all of the models, the Freed Flory− Huggins equation28 for the expression of combinatorial contribution and also the above proposed models were used for the expression of residual contribution. Using the standard deviation for all of presented models, the agreement between experimental and calculated data have been indicated in Table 4.

The activity data of solvent are fitted using the Flory−Huggins equation,16 indicating the relation between experimental data with the use of the following model: ⎛ 1⎞ ln a1 = ln ϕ1 + ⎜1 − ⎟(1 − ϕ1) + χ12 (1 − ϕ1)2 r2 ⎠ ⎝

(5)

(4)

where, φ1, indicates volume fraction of solvent, χ12, is the interaction parameter of Flory−Huggins for the system, r2 is the segments of polymer is expressed as molar volume from polymer

Table 4. Values of Parameters, χ12, d, f, α, τ12, τ21, E21, and E12 (J·mol−1) for the Activity Models in (1-Propanol (1) + PPG400 (2)/ PPG725 (2)/PPG1025 (2)) Systems at T = 298.15 K

Flory−Huggins χ12 102σ modified Flory−Huggins d f 102σ NRTL α τ12 τ21 102σ NRF−NRTL α τ12 τ21 102σ Wilson α 103 E21 10−3 E12 102σ NRF−Wilson α 10−3 E21 103 E12 102σ

1-propanol (1) + PPG400 (2)

1-propanol (1) + PPG725 (2)

1-propanol (1) + PPG1025 (2)

−0.3100 0.1439

−0.3810 0.3534

−0.3380 0.1661

−0.2530 0.8420 0.1427

−2.1940 −18.916 0.1140

−0.6290 −3.2160 0.1000

0.1090 −6.2420 −6.2420 0.1509

−0.0034 0.0400 −5.8710 0.9352

−0.0004 −7.7840 0.0008 0.5000

−0.0250 0.7310 0.7600 0.1430

−0.0053 1.4000 1.4330 0.1774

−0.0025 1.1200 1.1200 0.1340

−0.0150 0.1719 −1.7540 0.1473

−0.0020 −2.7500 −3.2600 0.1691

−0.0016 −2.7500 −2.6320 0.1340

−0.0200 1.7550 −1.1430 0.1431

−0.0035 −3.2600 −1.7610 0.1691

−0.0021 2.6350 −4.5690 0.1341

D

DOI: 10.1021/acs.jced.7b00581 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Apparent Specific Volume, Vφ (mol·kg−1), Density, ρ (kg·m−3), Excess Specific Volume, VE (m3·kg−1), Apparent Specific Isentropic Compressibility, κs,φ (Pa−1·m3·kg−1), Isentropic Compressibility, κs (Pa−1), Isentropic Compressibility Increments, Δκs (Pa−1), Speed of Sound, u (m·s−1), Values for the 1-Propanol + PPG400 (2)/PPG725 (2) Binary Mixtures Against the Polymer Weight Fraction (Wp) at Different Temperatures and the Experimental Pressure (P = 86.6 kPa)a Wp

a

ρ/kg·m−3

u/m·s−1

0.0809 0.1340 0.3525 0.5769 0.8490

821.906 830.318 859.204 881.650 902.464

1250.79 1255.77 1275.36 1291.60 1306.73

0.0809 0.1340 0.3525 0.5769 0.8490

813.765 822.239 851.015 873.402 894.148

1214.56 1220.23 1241.09 1257.64 127270

0.0809 0.1340 0.3525 0.5769 0.8490

805.596 814.036 842.713 865.038 885.730

1179.95 1186.02 1207.18 1223.92 1239.22

0.0809 0.1340 0.3525 0.5769 0.8490

797.270 805.671 834.273 856.532 877.194

1147.19 1153.26 1173.74 1190.47 1206.02

0.0677 0.2505 0.3451 0.4868 0.9105

818.681 843.460 854.145 867.392 896.928

1249.11 1265.26 1273.04 1283.08 1305

0.0677 0.2505 0.3451 0.4868 0.9105

810.512 835.471 846.159 859.420 888.971

1212.86 1231.01 1238.98 1249.37 1272.14

0.0677 0.2505 0.3451 0.4868 0.9105

802.388 827.378 838.072 851.350 880.930

1178.27 1197.36 1205.45 1215.93 1239.19

0.0677 0.2505 0.3451 0.4868 0.9105

794.125 819.145 829.852 843.147 872.777

1145.44 1164.09 1172.32 1182.87 1206.42

103VE/m3·kg−1

103Vφ/mol·kg−1

1013κs,φ/Pa−1·m3·kg−1

1-propanol (1) + PPG400 (2) T = 288.15 K −4.6535 0.9548 −4.6659 0.9542 −4.7064 0.9539 −4.736 0.9546 −4.7622 0.9552 T = 298.15 K −4.6988 0.9597 −4.7115 0.9591 −4.7526 0.9607 −4.7827 0.9617 −4.8093 0.9626 T = 308.15 K −4.7448 0.9661 −4.7577 0.9661 −4.7995 0.9684 −4.8301 0.9695 −4.8571 0.9705 T = 318.15 K −4.7919 0.9742 −4.805 0.9744 −4.8476 0.9766 −4.8787 0.9778 −4.9062 0.9787 1-propanol (1) + PPG725 (2) T = 288.15 K −4.6325 0.9793 −4.6684 0.9769 −4.6832 0.9763 −4.7011 0.9783 −4.7390 0.9799 T = 298.15 K −4.6781 0.9850 −4.7149 0.9826 −4.7300 0.9824 −4.7483 0.9848 −4.787 0.9868 T = 308.15 K −4.7226 0.9907 −4.7603 0.9893 −4.7757 0.9893 −4.7943 0.9918 −4.8337 0.9941 T = 318.15 K −4.7696 0.9979 −4.8081 0.9966 −4.8238 0.9966 −4.8428 0.9993 −4.8831 1.0017

1010 κs/Pa−1

1010Δκs/Pa−1

5.6661 5.6999 5.7623 5.8454 5.9357

9.7273 9.5906 9.1258 8.7816 8.4798

−0.1906 −0.2995 −0.8031 −1.1865 −1.4910

5.7207 5.7415 5.8759 5.9982 6.1192

10.1177 9.9669 9.468 9.1039 8.7875

−0.2700 −0.4419 −1.0302 −1.4238 −1.7064

5.8459 5.8676 6.0545 6.1975 6.3328

10.5201 10.3577 9.8299 9.4452 9.1107

−0.3187 −0.5281 −1.1494 −1.5594 −1.8548

6.0078 6.0525 6.2946 6.4441 6.5812

10.9335 10.7625 10.2122 9.807 9.4526

−0.3638 −0.5825 −1.1763 −1.6051 −1.9345

6.1887 6.2207 6.2251 6.3016 6.4401

9.7788 9.3703 9.1966 8.9853 8.5434

−0.0307 −0.1802 −0.3032 −0.3793 −0.5122

6.2650 6.2959 6.3359 6.4419 6.6198

10.1726 9.7232 9.5386 9.3133 8.8425

−0.1030 −0.4294 −0.5648 −0.6601 −0.8285

6.3845 6.4441 6.5038 6.6317 6.8362

10.5772 10.0942 9.8985 9.6601 9.1605

−0.1474 −0.5588 −0.7023 −0.7984 −0.9818

6.5536 6.6767 6.7339 6.8696 7.0865

10.9936 10.487 10.2791 10.0267 9.4973

−0.1822 −0.5838 −0.7498 −0.8586 −1.0740

Standard uncertainties (u) for each variable are u (Wp) = 0.0001; u(ρ) = 0.2 kg·m−3; u(u) = 0.5 m·s−1; u(T) = 0.03 K; u(p) = 0.5 kPa.

Freed Flory−Huggins Combinatorial Term. This term is

ln γ1Comb = ln

presented as an extended theory from Flory−Huggins models in

φ1 x1

+ (1 − r1/r2)φ2 + α(1/r1 − 1/r2)2 φ2 2 (6)

expressions powers of a nonrandomness factor (α), which is

the contribution for the excess entropy associated with random mixing is allocated by first and second terms on the right−hand

presented as follows: E

DOI: 10.1021/acs.jced.7b00581 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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The results of fitting are correlated with the experimental data given in Table 4. The standard deviation (σ) was calculated by using the following equation:

side of eq 6 and is equal as the expression in Flory−Huggins theory. The third term as the correction to the Flory−Huggins theory may be understood as the local composition effect from the chained segments in a polymer. φi =

rn i i r1n1 + r2n2

⎛ ∑nDat (a − a )2 ⎞1/2 cal i = 1 exp ⎟ σ = ⎜⎜ ⎟ n Dat ⎝ ⎠

(7)

where nDat is the number of experimental data. Using the eq 12, it was concluded that the modified Flory−Huggins17 Model was the appropriate model for expressing the experimental solvent activity data (aexp). Figure 1 indicates the measured 1-propanol activity data and the calculated values with the use of modified Flory−Huggins for the studied systems in this work. 3.2. Volumetric Results. In this study, the density and speed of sound data of binary mixtures for 1-propanol + PPG400/ PPG725 are measured at T = 288.15 to 318.15 K and listed in Table 5. Volumetric and compressibility properties, such as apparent specific volume (Vφ), excess specific volume (VE), isentropic compressibility (Ks), isentropic compressibility increments (ΔKs), and apparent specific isentropic compressibility (Ks,φ) were determined for investigated systems by using these data. The apparent specific volumes (Vφ) of studied systems in this work at dilute region were calculated by the use of the following equation:15

where, ni and ri are the number of moles and segment of the component i, respectively. NRTL Residual Term. This term is written in the form of the following equation: ⎛ ⎞ τ21exp(− ατ21)2 τ12exp(− ατ12) 1 ⎟ ln γ1NRTL = φ2 2⎜⎜ + 2 2⎟ r1 ( exp( )) ( exp( )) φ + φ − ατ φ + φ − ατ ⎝ 1 ⎠ 21 12 2 2 1

(8)

In this equation, parameters α and τij have been obtained from fitting the experimental data. NRF−NRTL Residual Term. This term is used in the form of the following equation: ⎛ τ21exp(− ατ21)2 1 ln γ1NRF − NRTL = φ2 2⎜⎜ 2 r1 ⎝ (φ1 + φ2exp(− ατ21)) +

⎞ τ12exp(− ατ12) ⎟ + (φ1 − 1)(φ2τ12 + φ2τ21) 2⎟ (φ2 + φ1exp(− ατ12)) ⎠

(9)

Vϕ = (1 + Wp)/Wpρ − 1/Wpρ0

where the NRF−NRTL parameters α and τij are fitted to the experimental data. Wilson Residual Term. Using eq 10, Wilson Residual term is expressed. ⎛ ⎛ E ⎞⎞ 1 ln γ Wilson = ln⎜φ1 + φ2exp⎜− 21 ⎟⎟ ⎝ CRT ⎠⎠ ⎝ Cr1 1 ⎛ E21 ⎜ 1 − φ1 + φ2exp − CRT + φ1⎜ E21 ⎜ φ1 + φ2exp − CRT ⎝

(

(

(

)

) (

⎟ ⎟ ⎠

( )

(

(13)

where ρ and ρ0 are the densities of the mixtures and 1-propanol, respectively, and Wp, weight fraction of polymer (kg polymer per kg of solvent). The results are presented in Table 5, as well as the comparison between the systems at various temperatures were shown in Figure 3. According to this Figure, apparent specific volume (Vφ) for PPG400 less than PPG725 representing the weaker solute + solvent interactions in the PPG725.

)) ⎞⎟

⎛ E12 E12 ⎜ exp − CRT − φ2 + φ1exp − CRT + φ2⎜ E12 ⎜ φ2 + φ1exp − CRT ⎝

(

(12)

)) ⎞⎟ ⎟ ⎟ ⎠

(10)

where R and T are the gas constant and absolute temperature, and Eij are the parameters of eq 10. NRF−Wilson Residual Term. This term is expressed with the help of the following equation: ⎛ ⎛ E ⎞⎞ 1 ln γ Wilson = ln⎜φ1 + φ2exp⎜− 21 ⎟⎟ ⎝ CRT ⎠⎠ ⎝ Cr1 1 ⎛ E21 ⎜ 1 − φ1 + φ2exp − CRT + φ1⎜ E21 ⎜ φ1 + φ2exp − CRT ⎝

(

(

(

)

)) ⎞⎟

⎛ E12 E12 ⎜ exp − CRT − φ2 + φ1exp − CRT + φ2⎜ E12 ⎜ φ2 + φ1exp − CRT ⎝

(

) (

(

⎛ E E ⎞ + φ2 2⎜ 12 + 21 ⎟ ⎝ CRT CRT ⎠

Figure 3. Comparison of apparent specific volume, (Vφ), for 1-propanol (1) + PPG400 (2) and 1-propanol (1) + PPG725 (2) systems plotted against weight fraction of polymer (Wp) (− −, PPG400; ..., PPG725; ⧫, T = 288.15 K; ■, T = 298.15 K; ●, T = 308.15 K; ▲, T = 318.15 K).

⎟ ⎟ ⎠

( )

)) ⎞⎟ ⎟ ⎟ ⎠

The limiting apparent specific volume, V0φ, of the polymer in investigated solutions was obtained by use of eq 14.15

(11)

where C is a parameter that represents the effective coordination number which is equal to 10, and the Wilson and NRF−Wilson parameters, Eij, are fitted to the experimental data. The values of r for solvent equal 1 and for polymer were obtained from the ratio of molar volume of polymer to that of the solvent at 298.15 K.

Vϕ = V ϕ0 + Bv Wp + CvWp2

(14)

where Bv and Cv are depending on solute−solvent interactions and temperature and are considered as empirical parameters. Table 6 gives the parameters of this equation. F

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Table 6. Limiting Apparent Specific Volume and the Parameters, V0φ, Bv, Cv, and Standard Deviation, σ, of Eq 14 for 1-Propanol (1) + PPG400 (2)/PPG725 (2) Systems at T = 288.15 K to 318.15 K T/K 288.15 298.15 308.15 318.15 288.15 298.15 308.15 318.15

106 V0φ/m3·kg−1

Bv/m3·kg−1

Cv/m3·kg−1

1-propanol (1) + PPG400 (2) 0.9552 −0.0050 0.0060 0.9589 0.0056 −0.0014 0.9651 0.0111 −0.0056 0.9732 0.0110 −0.0059 1-propanol (1) + PPG725 (2) 0.9796 −0.0111 0.0126 0.9851 −0.0094 0.0125 0.9905 −0.0036 0.0085 0.9976 −0.0029 0.0082

102σ 0.003 0.003 0.017 0.012 0.076 0.086 0.076 0.077

Figure 5. Isentropic compressibilities, (KS), of 1-propanol (1) + PPG400 (2) and 1-propanol (1) + PPG725 (2) systems plotted against weight fraction of polymer (Wp) (− −, PPG400; ..., PPG725; ⧫, T = 288.15 K; ■, T = 298.15 K; ▲, T = 308.15 K; ●, T = 318.15 K).

Another specific volumetric property is excess specific volume (VE) which can be calculated for the studied mixtures by the use of the following equation:15 ⎛ ⎞ ⎛1⎞ 1 ⎜ Wp 1⎟ + VE = ⎜ ⎟ − ρ0 ⎟⎠ ⎝ ρ ⎠ 1 + Wp ⎜⎝ ρp

in PPG400 are less than values of PPG725 at different temperatures. The experimental isentropic compressibility increments, ΔKs,15 were obtained using the following equation: 1 ΔK s = K s − (WpK sp + K s0) 1 + Wp (17)

(15)

where ρp is pure polymer density and Wp is weight fraction of polymer. The obtained negative values for excess specific volume in the studied systems as shown in Table 5 became more negative with the increasing of temperature and for PPG400 in comparison to PPG725 indicated in Figure 4.

where Ksp and Ks0 are the values of isentropic compressibility of the polymer and 1-propanol, respectively, which are given in Table 5. In Figure 6, the variation of this quantity has been

Figure 4. Obtained values of excess specific volume, (VE), for 1propanol (1) + PPG400 (2) and 1-propanol (1) + PPG725 (2) systems plotted against weight fraction of polymer (Wp) (− −, PPG400; ..., PPG725; ⧫, T = 288.15 K; ■, T = 298.15 K; ●, T = 308.15 K; ▲, T = 318.15 K).

Figure 6. Comparison of isentropic compressibility increment, (ΔKS), of 1-propanol (1) + PPG400 (2) and 1-propanol (1) + PPG725 (2) systems plotted against weight fraction of polymer (Wp) (− −, PPG400;..., PPG725; ⧫, T = 288.15 K; ■, T = 298.15 K; ●, T = 308.15 K; ▲, T = 318.15 K).

3.3. Compressibility Results. Isentropic compressibility (Ks) was obtained for investigated binary mixtures using the solutions density and speed of sound data with the help of Laplace Newton equation15 as follows: 1 Ks = 2 uρ (16)

indicated for binary mixtures of 1-propanol + PPG400 and + PPG725 in against to polymer weight fraction (Wp). The results show the more negative values of ΔKS for PPG400 in comparison to PPG725 at different temperatures. The apparent specific isentropic compressibility was calculated using the density and Ks measurments for the studied systems in this work by the use of the following equation:15

where u is speed of sound of binary mixtures. The values of isentropic compressibility are presented in Table 5 and their values also are plotted in Figure 5. These values are increasing with the increase of temperatures and decreasing with the increase of polymer weight fractions. The obtained values for Ks

K sφ =

(1 + Wp)K s ρWp

−

K s0 ρ0 Wp

(18)

where Ks and Ks0 are the isentropic compressibility of the mixture and 1-propanol, respectively. The results are given in Table 5 and G

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also shown in Figure 7. The obtained positive values of Ksφ indicate that the solvent molecules around the polymer

Article

AUTHOR INFORMATION

Corresponding Author

*Tel: +98 4133393094; Fax: 98 4133340191; E-mail: [email protected]. ORCID

Hemayat Shekaari: 0000-0002-5134-6330 Funding

We are grateful to University of Tabriz Research Council for the financial support of this research. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 7. Comparison of apparent specific isentropic compressibility, (KSφ), of 1-propanol (1) + PPG400 (2) and 1-propanol (1) + PPG725 (2) systems plotted against weight fraction of polymer (Wp) (− −, PPG400;..., PPG725; ⧫, T = 288.15 K; ■, T = 298.15 K; ●, T = 308.15 K; ▲, T = 318.15 K).

molecules have greater compressibility. These values are more than for the PPG725 compared with the PPG400 values. The findings of volumetric and compressibility properties generally show that solute−solvent interactions and structural effect in PPG400 systems is stronger than the other polymers.

4. CONCLUSIONS The thermodynamic properties, including VLE, volumetric, and compressibility, for binary 1-propanol + PPG400, 725, and 1025 mixtures were measured. The activity and vapor pressure of the studied systems increase with higher molar mass of the polymer which indicating strong solute−solvent interaction between PPG400 and 1-propanol rather than other polymers. The correlation of the experimental activity data were evaluated with the use of Flory−Huggins (FH), modified Flory−Huggins, NRTL, NRF−NRTL, Wilson, and NRF−Wilson activity models. The corresponding standard deviations for all of this models supply that the modified Flory−Huggins model has good agreement with the experimental data. The volumetric and compressibility results of the binary investigated mixtures (1propanol + PPG400/PPG725) were used to determine the apparent specific volume, excess specific volume, isentropic compressibility, isentropic compressibility increments, and apparent specific isentropic compressibility at different temperatures. The excess specific volume and isentropic compressibility increments quantities are more negative for PPG400 compared to PPG725 which showing more compatibility of 1-propanol with PPG400. The obtained values for the apparent specific volume, isentropic compressibility, and apparent specific isentropic compressibility are positive, that increase with the increasing of temperature. In this work, the effect of the polymer molar mass on the activity and vapor pressure of 1-propanol was investigated. By increasing the molar mass of the polymers, the effect of the packaging decreases and as a result, the activity and vapor pressure increases. The compression of the polymer decreases with increasing molecular mass, which results in easier 1propanol penetration into the polymer structure, which increases the activity of 1-propanol in the polymer. H

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I

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