Experimental Determination and Modeling of Solubility of

Article pubs.acs.org/jced

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

Experimental Determination and Modeling of Solubility of Polyacrylamide in Subcritical 1,1,1,2-Tetrafluoroethane Junsu Jin,* Mingjie Qu, Hailun Wang, and Hong Meng*

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 09/27/18. For personal use only.

Beijing Key Laboratory of Membrane Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China ABSTRACT: To promote the application of subcritical 1,1,1,2-tetrafluoroethane (R134a) technology in polymers, the solubility of polyacrylamide (PAM) with molecular weights 5000000, 7000000, and 14000000 g·mol−1 were measured in subcritical R134a at pressures ranging from 7.0 to 18.0 MPa and temperatures between 313 and 333 K by the static method. The effects of experiment conditions (pressure and temperature), solvents, and molecular weights of PAM on the solubility of PAM in subcritical R134a were investigated and the enhancement factor (δ) of solvents was defined and calculated. Six semiempirical models were used to correlate the experimental solubility data, and the obtained adjustable parameters can be used to predict the solubility of PAM in subcritical R134a at other temperatures and pressures in the range of experimental conditions. Furthermore, the total enthalpy, solvation enthalpy, vaporization enthalpy and partial molar volume of PAM in subcritical R134a were calculated by the Christal, Bartle, and K-J models, respectively. fluids.11,12 However, the research on solute solubility in subcritical R134a is relatively less than that in SCCO2. In view of the application of two these solvents in the polymer processing, it is necessary to enrich the solubility data of polymer solute in subcritical R134a and compare the dissolving capacity of subcritical R134a and supercritical SCCO2. In this work, the solubility of polyacrylamide (PAM) with molecular weights 5000000, 7000000, and 14000000 g·mol−1 in subcritical R134a were measured at pressures ranging from 7.0 to 18.0 MPa and temperatures between 313 and 333 K. The effects of experiment conditions (pressure and temperature), and molecular weights on the solubility of PAM in subcritical R134a were investigated. The enhancement factor (δ) of solvents was defined and calculated to evaluate the dissolving capacity of subcritical R134a and supercritical SCCO213 for PAM at the same pressure and temperature. Six semiempirical models, including Chrastil model,14 Kumar and Johnston (K-J) model,15 Adachi and Lu (A-L) model,16 Sung and Shim (S-S) model,17 Mendez-Santiago and Teja (M-S-T) model,18 and Bartle model,19 were used to correlate the solubility data of PAM with three different molecular weights in subcritical R134a. In addition, the values of the thermodynamic properties of PAM, including total enthalpy (ΔHt), solvation enthalpy (ΔHsolv), vaporization enthalpy (ΔHvap), and partial molar volume (V̅ 2) were obtained through model calculation. This study can not only enrich the solubility database of polymers in subcritical R134a but also promote the application of subcritical R134a technology in the polymer processing industry.

1. INTRODUCTION In recent years, the applications of polymers have been widely involved and greatly enriched in various aspects of human life by the utilization of plastic, fiber, rubber and other polymer products. However, the deep developments of polymers were limited because of serious environment pollution and much raw material waste in the process of polymers production. Supercritical or subcritical fluid technology as a green chemical technology may solve these problems, and it has been successfully applied in functional polymer material preparation, polymer modification, polymer processing, and so on.1−5 Supercritical carbon dioxide (SCCO2) is the most commonly used supercritical fluid due to its low critical temperature (304.2 K), moderate critical pressure (7.38 MPa),6 and the advantages of low price, nontoxicity, and noncorrosiveness. Using SCCO2 technology can make up for some defects in polymers production process, such as larger amount of consumption of organic solvent, difficult separation of organic solvents, and serious environmental pollution.7 However, SCCO2 is a nonpolar solvent (0 D), which has a little limitation of weak ability to dissolve polar solute. It was found that subcritical 1,1,1,2-tetrafluoroethane (R134a), with dipole moment of 2.1 D, has been chosen as another solvent in polymer processing.8−10 The critical pressure of R134a is 4.06 MPa, which is much lower than that of SCCO2. Subcritical R134a has stronger dissolving capability than SCCO2 for polar solutes at lower operation pressure, which means subcritical R134a technology may have higher production efficiency with lower equipment and operation costs. Furthermore, R134a is nonflammable, nonexplosion, nontoxicity, nonirritant, noncorrosion, and nonozone-depleting. In recent years, many scholars have sought to obtain the solubility data of polymers in supercritical or subcritical © XXXX American Chemical Society

Received: April 20, 2018 Accepted: September 12, 2018

A

DOI: 10.1021/acs.jced.8b00316 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

2. EXPERIMENTAL SECTION 2.1. Materials. PAM (CAS 9003-05-8) with three different molecular weights (5000000, 7000000, 14000000 g·mol−1) was supplied by Macklin Chemistry Co. Ltd. The mass purity of PAM was 98.5%. R134a (CAS 811-97-2) with mass purity of 99.9% was purchased from DuPont Company. All chemicals used in this work were analytically pure and without further processing. 2.2. Apparatus and Procedure. In this work, the solubility of PAM in subcritical R134a were measured by the static method. Figure 1 shows the schematic diagram of static

Figure 2. Determination of equilibrium time at 323 K, 13.0 MPa for PAM with (▲) Mn = 5000000 g·mol−1, (●) Mn = 7000000 g·mol−1, (■) Mn = 14000000 g·mol−1.

Figure 1. Schematic diagram of the experimental apparatus (1, R134a cylinder; 2, exit control valve; 3, low-temperature cooling liquid circulation pump; 4, temperature control box; 5, entry control valve; 6, doubleplunger pump; 7, exit control valve; 8, surge flask; 9, high pressure equilibrium cell; 10, pressure gauge; 11, thermocouple thermometer; 12, decompression-sampling valve; 13, two U-shape tubes; 14, glass surge flask 15, rotating flow meter; 16, wet gas flow meter).

(5000000, 7000000, and 14000000 g·mol−1) in subcritical R134a were measured and shown in Table 1 at experimental temperatures (313, 323, and 333 K) and pressures (7.0 MPa, 9.0 MPa, 11.0 MPa, 13.0 MPa, 15.0 MPa, and 18.0 MPa). It could be seen that the solubility ranges of PAM in subcritical R134a were 7.80 × 10−10−20.58 × 10−10 mol·mol−1 with the molecular weight of 5000000 g·mol−1, 5.20 × 10−10−13.84 × 10−10 mol·mol−1 with the molecular weight of 7000000 g·mol−1, and 1.88 × 10−10−6.21 × 10−10 mol·mol−1 with the molecular weight of 14000000 g·mol−1, respectively. To clarify the effects of temperatures, pressures, and molecular weights on the solubility of PAM in subcritical R134a, the solubility data of PAM in subcritical R134a were depicted in Figure 3. It is concluded that the solubility of PAM in subcritical R134a increased with pressure when the temperature was constant because of increasing dissolving capacity of R134a with the increasing density. The influence of temperature on solubility showed that PAM solubility in subcritical R134a also increased with the temperature when the pressure was constant. The density of subcritical R134a decreases and the vapor pressure of PAM increases with temperature increasing and the increasing vapor pressure of PAM was the determinant that results to the PAM solubility increasing. It could be also concluded that the solubility of PAM in subcritical R134a decreased with the increasing of PAM molecular weights. It could be explained by the changes of the entropic value of PAM and the intermolecular interaction, which had been introduced in details in our previous work.13 3.2. Comparison of Dissolving Capacity of Subcritical R134a and SCCO2 for PAM. To compare the dissolving capacity of SCCO2 and subcritical R134a for PAM at the same experimental conditions, the enhancement factor (δ) of solvents was calculated by eq 1. y δ = in R134a yin CO (1)

apparatus. The schematic diagram of this apparatus had been described in details in our previous work.20,21 Before the experiment, a low-temperature cooling liquid circulation pump transported R134a from the cylinder into the temperature control box to prevent blocking of pipeline by gas R134a. For each experiment, about 2 g of PAM was loaded into high pressure equilibrium cell with an effective volume of 10 mL. The volume of loaded PAM should account for more than threequarters of the equilibrium cell. Both ends of high pressure equilibrium cell were equipped with stainless steel sintered disks to prevent the undissolved PAM flowing out with R134a. The system reached equilibrium after the equilibrium time and then the dissolved solid solute in subcritical R134a separated from R134a through the decompression-sampling valve and deposited in the two U-shaped tubes. UV spectrophotometer (TU1810) determined the concentration of PAM dissolved in pure water, which standard curve had been presented in our previous work.13 The volume of R134a was calculated by the wet gas flow meter with an uncertainty of 0.01 L. The determination of the equilibrium time is essential for solubility measurement to ensure PAM and subcritical R134a reaching equilibrium. The solubility of PAM in subcritical R134a at 323 K, 13.0 MPa was tested when the equilibrium time ranged from 20 to 70 min. Solubility changes of PAM with different equilibrium time were presented in Figure 2. Experimental results indicated that the system could reach equilibrium for more than 50 min. Therefore, all the solubility measurements in this work conducted for 60 min. In this work, each experiment repeatedly conducted at least thrice and each solubility data obtained was an average of three replicated sample measurements, which is reproducible with the relative uncertainty within ±5%.

2

where yin R134a is the solubility of PAM in subcritical R134a; yin CO2 is the solubility of PAM in SCCO2 at the same temperature and pressure. The solubility data of PAM with three different molecular weights (5000000, 7000000, and 14000000 g·mol−1) in two

3. RESULTS AND DISCUSSION 3.1. Experimental Solubility of PAM in Subcritical R134a. Solubility of PAM with three different molecular weights B



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Table 1. Solubility of PAM in Subcritical R134a and Comparison with That in SCCO213 at Same Experimental Conditions ρb (g·L−1) −1

Mn (g·mol ) 5000000

a

T (K) 313

323

333

7000000

313

323

333

14000000

313

323

333

a

P (MPa) 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0

R134a 1189.0 1200.2 1210.5 1220.1 1229.1 1241.5 1151.9 1165.2 1177.3 1188.3 1198.5 1212.5 1112.2 1128.2 1142.4 1155.1 1166.8 1182.7 1189.0 1200.2 1210.5 1220.1 1229.1 1241.5 1151.9 1165.2 1177.3 1188.3 1198.5 1212.5 1112.2 1128.2 1142.4 1155.1 1166.8 1182.7 1189.0 1200.2 1210.5 1220.1 1229.1 1241.5 1151.9 1165.2 1177.3 1188.3 1198.5 1212.5 1112.2 1128.2 1142.4 1155.1 1166.8 1182.7

1010yc (mol·mol−1) CO2

in R134a

492.75 685.58 744.41 781.32 820.39 286.12 505.69 637.96 701.08 758.11 235.91 359.16 507.26 605.60 688.34 492.75 685.58 744.41 781.32 820.39 286.12 505.69 637.96 701.08 758.11 235.91 359.16 507.26 605.60 688.34 492.75 685.58 744.41 781.32 820.39 286.12 505.69 637.96 701.08 758.11 235.91 359.16 507.26 605.60 688.34

7.80 ± 0.040 8.95 ± 0.018 9.99 ± 0.007 11.23 ± 0.025 12.40 ± 0.012 13.64 ± 0.034 8.52 ± 0.011 9.74 ± 0.041 12.11 ± 0.028 13.38 ± 0.008 15.20 ± 0.012 16.72 ± 0.018 11.22 ± 0.029 13.27 ± 0.020 14.69 ± 0.027 16.80 ± 0.016 19.34 ± 0.009 20.58 ± 0.013 5.20 ± 0.010 6.00 ± 0.024 6.72 ± 0.021 7.61 ± 0.014 8.37 ± 0.010 9.25 ± 0.019 5.58 ± 0.022 6.71 ± 0.026 8.10 ± 0.019 9.05 ± 0.030 10.34 ± 0.021 11.40 ± 0.014 7.57 ± 0.010 8.98 ± 0.020 9.93 ± 0.008 11.32 ± 0.012 12.96 ± 0.013 13.84 ± 0.017 1.88 ± 0.045 2.24 ± 0.029 2.58 ± 0.024 2.96 ± 0.022 3.23 ± 0.025 3.65 ± 0.014 2.41 ± 0.032 2.77 ± 0.017 3.45 ± 0.023 3.84 ± 0.013 4.34 ± 0.012 4.78 ± 0.008 3.47 ± 0.044 4.06 ± 0.032 4.47 ± 0.024 5.09 ± 0.014 5.85 ± 0.014 6.21 ± 0.018 a

in CO213

δ

2.34 2.99 3.33 3.88 4.02 2.61 3.67 4.36 5.01 5.83 3.26 4.32 5.39 6.45 7.72 1.55 1.94 2.13 2.35 2.60 1.69 2.35 2.92 3.51 3.90 2.16 2.89 3.65 4.44 5.24 0.59 0.82 0.97 1.05 1.10 0.71 1.03 1.21 1.45 1.63 0.98 1.25 1.59 1.80 2.29

3.82 3.34 3.37 3.20 3.39 3.73 3.30 3.07 3.03 2.87 4.07 3.40 3.12 3.00 2.67 3.87 3.46 3.57 3.56 3.56 3.97 3.45 3.10 2.95 2.92 4.16 3.44 3.10 2.92 2.64 3.80 3.15 3.05 3.08 3.32 3.90 3.35 3.17 2.99 2.93 4.14 3.58 3.20 3.25 2.71

Standard uncertainties u are u(T) = ±0.1 K, u(P) = ±0.2 MPa, u(y) = ±5%. bρ is the density of subcritical R134a and SCCO2, which is obtained from the NIST fluid property database. cy is the equilibrium mole fraction of the solute in subcritical R134a. a

different solvents at the same experimental conditions and δ value of solvents were also shown in Table 1. As shown in Table 1, the solubility values of PAM in subcritical R134a were

more than that of PAM in SCCO2 at the same experimental conditions, and the values of δ were in the range of 2.64−4.16, which indicated that the subcritical R134a had better dissolving C



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interaction between solvent and PAM. It could be seen from the molecular structure of R134a and PAM that hydrogen bonds could be formed between them, while there is not a hydrogen bond between PAM and CO2. The hydrogen bonds formed between solute molecules and solvent molecules could lead to the increase of solubility,26 which results in the solubility of PAM in subcritical R134a is more than the solubility of PAM in SCCO2. The density of solvents is the third reason for the difference in the solubility of the two solvents. It could be seen in Table 1 that the density of R134a ranges from 1128.2 to 1241.5 g L−1 and that of CO2 ranges from 235.91 to 820.39 g L−1 under the same experimental conditions. The density of R134a was much more than that of CO2 at the same temperature and pressure, and results in the solubility of PAM in subcritical R134a is more than the solubility of PAM in SCCO2.27 In summary, the subcritical R134a has a stronger ability to dissolve PAM than SCCO2 under the same experimental conditions. 3.3. Models Correlation. The study on phase equilibrium was essential for solubility study, which could reduce experiment measurements through correlating the experimental solubility data or directly predicting solubility data. The semiempirical models were the widely used method for correlating the solubility of solutes in supercritical or subcritical fluid. In this work, six semiempirical models were used to correlate the solubility data of PAM in subcritical R134a and the model expressions were shown in Table 2. Table 2. Expressions of Six Semi-Empirical Models Used in This Work model name

model expression

Chrastil

ln S = A1 ln ρ + B1/T + C1

K-J

ln y = A 2 ln ρ + B2 /T + C2

A-L

ln S = (A3 + B3ρ + C3ρ2 )ln ρ + D3/T + E3

S-S

ln y = (A4 + B4 /T )ln ρ + C4 /T + D4

M-S-T

T ln(yP) = A5ρ + B5T + C5

Bartle

ln(yP /Pref ) = A 6(ρ − ρref ) + B6 /T + C6

The average absolute relative deviation (AARD) estimated the accuracy of different models, which expressed as follows. AARD(%) =

100 n

n

∑ 1

|ycal − yexp | yexp

(2)

where yexp is the experimental solubility of PAM in subcritical R134a; ycal is the calculated PAM solubility using semiempirical models at the same temperature and pressure; n is the number of experimental points. According to the expressions of six different models, M-S-T model was selected to investigate the self-consistency of PAM solubility in subcritical R134a between the experimental and calculated values by plotting the linear relationship between T ln(yP) − B5T and the density of solvent. The results were shown in Figure 4, and it could be seen that the experimental values of PAM solubility in subcritical R134a were in the vicinity of the straight line of calculated values and increased with the density of R134a. Therefore, the experimental data of PAM in subcritical R134a had satisfactory self-consistency. The results of the solubility analysis of PAM in subcritical R134a by the six semiempirical models including parameters and ARRD of different models were shown in Table 3. It could

Figure 3. Experimental solubility of PAM for (a) Mn = 5000000 g·mol−1, (b) Mn = 7000000 g·mol−1, (c) Mn = 14000000 g·mol−1 in subcritical R134a at ■, 313 K; ●, 323 K; ▲, 333 K.

capacity for PAM than SCCO2 at the same temperature and pressure. The results of the dissolving capacity of subcritical R134a and SCCO2 in this work were consistent with most studies on solubility of different solutes.21−23 There are many reasons for subcritical R134a having better dissolution ability for PAM than SCCO2, and the first point is the polarity of solvents. The dipole moment of R134a (2.1 D) is more than that of CO2 (0 D), which leads to better dissolution ability for PAM in subcritical R134a.24,25 Therefore, R134a with more polarity has better ability to dissolve PAM. The second point is molecular D



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Table 3. Correlated Results of Semi-Empirical Models for the Solubility of PAM in Subcritical R134a models Chrastil

K-J

A-L

Mn (g·mol−1) 5000000 7000000 14000000 5000000 7000000 14000000 5000000 7000000 14000000

S−S

5000000 7000000 14000000

M-S-T

Bartle

5000000 7000000 14000000 5000000 7000000 14000000

AARD (%)

adjustable parameters A1 = −76.42; B1 = −5.61 × 103; C1 = 12.89 A1 = −77.73; B1 = −5.68 × 103; C1 = 13.09 A1 = −76.56; B1 = −6.63 × 103; C1 = 13.32 A2 = 11.89; B2 = −5609.60; C2 = −87.26 A2 = 12.10; B2 = −5673.94; C2 = −88.88 A2 = 12.32; B2 = −6625.80; C2 = −88.37 A3 = 4.96 × 103; B3 = −5.76 × 103; C3 = −8.60 × 102; D3 = 0.187; E3 = −4.34 × 10−5 A3 = 5.82 × 103; B3 = −5.84 × 103; C3 = −1.01 × 103; D3 = 0.221; E3 = −5.10 × 10−5 A3 = 4.08 × 103; B3 = −6.81 × 103; C3 = −7.04 × 102; D3 = 0.151; E3 = −3.40 × 10−5 A4 = 3.90 × 102; B4 = −1.61 × 105; C4 = −55.47; D4 = 2.20 × 104 A4 = 4.16 × 102; B4 = −1.70 × 105; C4 = −59.37; D4 = 2.32 × 104 A4 = 4.75 × 102; B4 = −1.90 × 105; C4 = −67.25; D4 = 2.59 × 104 A5 = −1.39 × 104; B5 = 8.41; C5 = 5.87 A5 = −1.41 × 104; B5 = 8.17; C5 = 5.91 A5 = −1.50 × 104; B5 = 10.16; C5 = 5.95 A6 = 5.94; B6 = −1.09 × 104; C6 = 2.53 × 10−2 A6 = 5.67; B6 = −1.10 × 104; C6 = 2.55 × 10−2 A6 = 7.67; B6 = −1.20 × 104; C6 = 2.57 × 10−2

4.07 4.23 4.52 4.07 4.23 4.54 3.32 3.28 3.34 2.46 2.38 2.44 5.65 5.87 6.52 7.06 7.22 7.72

(ΔHt), solvation enthalpy (ΔHsolv), vaporization enthalpy (ΔHvap) and partial molar volume (V̅ 2) of PAM in subcritical R134a were calculated by the Chrastil, Bartle, and K-J models. Table 4 and Table 5 listed the calculation results. Table 4. Total, Solvation, And Vaporization Enthalpy of PAM in Subcritical R134a Mn (g·mol−1)

ΔHt(kJ·mol−1)

ΔHvap(kJ·mol−1)

ΔHsolv(kJ·mol−1)

5000000 7000000 14000000

46.64 47.22 55.12

90.62 91.45 99.77

−43.98 −44.23 −44.65

The ΔHt could be calculated by the adjustable parameters of Chrastil model and was expressed as eq 3. ΔHt = −B1R

Figure 4. Solubility of PAM for (a) Mn = 5000000 g·mol−1, (b) Mn = 7000000 g·mol−1, (c) Mn = 14000000 g·mol−1 in subcritical R134a correlated by M-S-T model (▲, experimental results; −, calculated results).

(3) −1

where ΔHt (kJ·mol ) is the total enthalpy of solution for PAM in subcritical R134a; B1 is the adjustable parameter of Chrastil model; R is the molar gas constant, and its value is 8.314 J·(mol·K) −1. The ΔHvap could be calculated by the adjustable parameter of Bartle model and was expressed as eq 4.

be concluded that the AARD of six models were in the range of 2.38−7.72%, and the S-S model had the best prediction accuracy in the six semiempirical models for the solubility of PAM in subcritical R134a. The AARD values of the S-S model correlating solubility of PAM with molecular weight 5000000, 7000000, and 14000000 g·mol−1 in subcritical R134a were 2.46%, 2.38%, and 2.44%. Therefore, the S-S model could be chosen to calculate the solubility of PAM in subcritical R134a at other temperature and pressure conditions within the scope of the experimental operation. 3.4. Calculation of Thermodynamic Properties. The thermodynamic properties which were total enthalpy of solution

ΔH vap = −B6 R

(4) −1

where ΔHvap (kJ·mol ) is the vaporization enthalpy of PAM in subcritical R134a; B6 is the adjustable parameter of Bartle model. ΔHt is the sum of the ΔHsolv and the ΔHvap So, the ΔHsolv could be calculated by eq 5. ΔHsolv = ΔHt − ΔH vap

(5)

−1

where ΔHsolv (kJ·mol ) is the solvation enthalpy of PAM in subcritical R134a. E



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Table 5. Partial Molar Volume of PAM in Subcritical R134a V̅ 2 (mL·mol−1) T/K 313

323

333

P/ MPa

Mn = 5000000 g·mol−1

Mn = 7000000 g·mol−1

Mn = 14000000 g·mol−1

7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0 7.0 9.0 11.0 13.0 15.0 18.0

−143.95 −142.60 −141.39 −140.28 −139.25 −137.86 −159.87 −158.04 −156.42 −154.97 −153.65 −151.88 −127.26 −125.46 −123.90 −122.54 −121.31 −119.68

−148.17 −146.79 −145.54 −144.39 −143.34 −141.90 −165.84 −163.94 −162.26 −160.76 −159.39 −157.55 −125.89 −124.11 −122.57 −121.22 −120.00 −118.39

−168.73 −167.16 −165.74 −164.43 −163.23 −161.60 −162.32 −160.46 −158.81 −157.34 −156.01 −154.20 −122.42 −120.69 −119.19 −117.88 −116.69 −115.12

The V̅ 2 (mL·mol−1) could be calculated by the Kumar and Johnston model:15 ij P vp yz PV2 jij V2̅ zyz − jj ln y = −C1 + lnjjjj 2 zzzz + ln ρr j κ RT zzz RT k T { ρr = 1 k ρc RT {

(6)

P2vp

where y is the solubility expressed by the molar fraction; is the vapor pressure of solute; V2 and V̅ 2 are the molar volume and the partial molar volume of the solute, respectively. κT = [(1/ρ)(∂ρ/ ∂P)T,y] is the isothermal compressibility, which could be calculated by density-pressure plot by retrieving the NIST Website. ρr = ρ/ρc is the reduced density of R134a. P and T are the operating pressure temperature, respectively. C1 is the constant. Since the value of V̅ 2 is much larger than that of V2, the third term in eq 6 could be considered as a constant; therefore, eq 6 could be derived and simplified as following: ij V̅ yz ln y = C0 − jjj 2 zzz ln ρr j κ RT z k T { ρr = 1

(7)

Since the ratio of V̅ 2 to κT is essentially independent of ρr, eq 7 implied that there is a linear relationship between ln y and ln ρr (See Figure 5). The V̅ 2 could be calculated by the slope of eq 7.

Figure 5. Plots of lny versus ln ρr for PMA (a) Mn = 5000000 g·mol−1, (b) Mn = 7000000 g·mol−1, (c) Mn = 14000000 g·mol−1. (■, 313 K; ●, 323 K; ▲, 333 K).

4. CONCLUSIONS In this work, the solubility of PAM in subcritical R134a were determined by static method and the solubility of PAM in subcritical R134a are more than that in SCCO2 at the same temperatures and pressures, which indicates that subcritical R134a has better dissolving capacity for PAM than SCCO2. All six semiempirical models correlated PAM solubility in subcritical R134a within 8% AARD, and the S-S model was chosen to calculate the solubility of PAM in subcritical R134a at other temperature and pressure conditions within the scope of the experimental operation. In addition, the thermodynamic properties, which were total enthalpy of solution (ΔHt), solvation enthalpy (ΔHsolv), vaporization enthalpy (ΔHvap), and partial molar volume (V̅ 2) of PAM in subcritical R134a were calculated. All the solubility data, thermodynamic properties data, and

model adjustable parameter values will contribute to understand and study phase equilibrium and thermodynamic phenomena between PAM and subcritical R134a and also provide basic data for the application of subcritical R134a in polymer process.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +86-10-64434788. Fax: +86-10-64436781. *E-mail: [email protected]. ORCID

Junsu Jin: 0000-0002-8329-1442 F



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Funding

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This research was financially supported by the funds awarded by National Natural Science Foundation of China (Grant Nos. 21476008 and 51473013). The authors are grateful to the support of this research from the Mass Transfer and Separation Laboratory in Beijing University of Chemical Technology. Notes

The authors declare no competing financial interest.

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Experimental Determination and Modeling of Solubility of

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