Article pubs.acs.org/jced
Determination and Correlation of Poly(vinylpyrrolidone) Solubility in Subcritical 1,1,1,2-Tetrafluoroethane Jun-su Jin,* Lin-tao Guo, Cheng-wei Chang, and Hong Meng* Beijing Key Laboratory of Membrane Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China ABSTRACT: Poly(vinylpyrrolidone) (PVP) is most widely used in the process of preparing a drug carrier by subcritical or supercritical fluids impregnation technology, and the design and operation conditions of the subcritical or supercritical fluids impregnation technology are based on the equilibrium solubility of PVP in subcritical or supercritical fluids. In this work, the solubility of PVP with molecular weights of 24 000 and 58 000 in subcritical 1,1,1,2-tetrafluoroethane (R134a) was measured at temperatures from 313 to 333 K and at pressures of 5.0, 7.0, 9.0, 11.0, 13.0, 15.0, and 18.0 MPa. The solubility of PVP in SCCO2 and subcritical R134a at the same experimental temperature and pressure conditions was also compared by calculating the enhancement factor (δ), finding that the solubility of PVP in subcritical R134a is much higher than that in SCCO2. Six semiempirical models (Chrastil, Adachi and Lu, Kumar and Johnston, Sung and Shim, Mendez-Santiago and Teja, and Bartle) were used to correlate PVP solubility in subcritical R134a, and the enthalpy values of PVP, including ΔHtotal, ΔHsub, and ΔHsol, were estimated through the Chrastil’s and the Bartle’s models.
1. INTRODUCTION In recent decades, the subcritical or supercritical fluid impregnation technology has developed a new method to prepare polymeric carriers to increase the solubility of drugs which exhibit poor solubility in water,1,2 and carbon dioxide is the most commonly used fluid in this subcritical or supercritical fluid impregnation technology.3 However, most polymer carriers are polar solutes, and the solubility of them in supercritical CO2 (SCCO2) is poor because the dipole moment of CO2 is zero Debye.4 In addition, SCCO2 impregnation technology requires a greater equipment investment and operational risk due to its comparatively high critical pressure (7.38 MPa). These disadvantages result in the limitation of its applications in impregnation reaction, separation, and material preparation processes; consequently, looking for a suitable replacement for SCCO2 is one of the key points for the development of subcritical or supercritical fluid impregnation technology.5−7 1,1,1,2-Tetrafluoroethane (R134a) is one of several widely used refrigerants. R134a is nonexplosive, nonirritating, apyrous, innocuous, nonozone-depleting, noncorrosive, colorless, and tasteless. Meanwhile, the dipole moment of R134a is 2.06 D, so it is also a good solvent for polymers;5,8,9 especially, the subcritical state of R134a with critical pressure of 4.06 MPa is easier to achieve, which may reduce experimental and operational costs of subcritical R134a (sub-R134a) impregnation and pharmaceutical particle preparation processes. Moreover, the boiling point of R134a is 246.9 K at atmospheric pressure, which means that it can be discharged with negligible solvent residues in the solutes.10,11 Therefore, R134a can represent a suitable alternative of SCCO2 in subcritical or supercritical fluid impregnation technology. © 2017 American Chemical Society
Poly(vinylpyrrolidone) (PVP) with molecular weights of 24 000 and 58 000 is widely used as materials in the preparation of polymer carriers by subcritical or supercritical fluid impregnation technology, and the solubility of some drugs in aqueous solutions can be increased by injecting them into polymer carriers by subcritical or supercritical fluids;12−15 however, the fundamental equilibrium solubility of PVP in subR134a has never been reported to date, which has hindered the industrial process of subcritical or supercritical fluid impregnation technology. In this work, the solubility of PVP with molecular weights of 24 000 and 58 000 in sub-R134a was measured by the static method at temperatures of 313, 323, 333 K and pressures from 5.0 to 18.0 MPa. The effects of temperature, pressure, and solute molecular weights on solubility were investigated. In addition, the enhancement factor (δ) was defined and calculated to compare the solubility of PVP in SCCO2 and sub-R134a at the same experimental temperature and pressure condition. Six semiempirical models, including Chrastil’s model,16 Adachi and Lu’s (A−L) model,17 Kumar and Johnston’s (K−J) model,18 Sung and Shim’s (S−S) model,19 Mendez-Santiago and Teja’s (M-S−T) model,20 and Bartle’s model21 were used to correlate the experimental data.
2. EXPERIMENT AND SEMIEMPIRICAL MODELS 2.1. Materials. R134a (mass purity more than 99.9%, CAS 811-97-2) was supplied by DuPont Company. PVP Received: May 15, 2017 Accepted: August 11, 2017 Published: August 24, 2017 3368
DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
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Figure 1. Schematic diagram of the experimental apparatus: 1, R134a cylinder; 2, R134a entrance control valve; 3, low-temperature cooling liquid circulation pump; 4, R134a storage tank; 5, entrance control valve; 6, double-plunger pump; 7, buffer tank entrance valve; 8, buffer tank; 9, highpressure equilibrium cell; 10, calibrated pressure gauge; 11, thermocouple; 12, decompression sampling valve; 13, two U-shape tubes; 14, glass surge flask; 15, rotating flow meter; 16, wet-gas flow meter.
((C6H9NO)n, Mn = 24 000 and 58 000, mass purity more than 98.0%, CAS 9003-39-8) was obtained from Aladdin Chemistry Co., Ltd., and the dispersity of PVP with molecular weights of 24 000 and 58 000 is 1.49 and 1.6022 which was measured by a GPC instrument (Waters, 1525 GPC) in the Analysis and Test Center of Beijing University of Chemical Technology. Deionized water was used in this experiment. All chemicals in this work were used without further purification. 2.2. Apparatus and Procedure. A static experiment device as shown in Figure 1 was applied in this work, which had been described in our previous work23,24 with the same measurement method adopted by other literature.25−27 First, about 5.0 g of PVP was loaded in the high-pressure equilibrium cell (9) of 10 mL, and two pieces of diaphragm were placed at the end of the high-pressure equilibrium cell to prevent physical entrainment of the undissolved solute. After the high-pressure equilibrium cell was connected to the experimental channel and the low temperature cooling liquid circulation pump was turned on (3) to decrease the temperature of the R134a storage tank (4) below room temperature, R134a in the cylinder (1) flowed to the R134a storage tank because of the temperature difference between storage tank and cylinder. Next, R134a was heated in the R134a storage tank and then was pressured by the doubleplunger pump (6) and entered into the high-pressure equilibrium cell through the buffer tank (8) until the highpressure equilibrium cell reached the experimental pressure. A thermocouple thermometer (11, with an accuracy of ±0.1 K) and a calibrated pressure gauge (10, with an accuracy of ±0.1 MPa), were used to measure temperature and pressure of the high-pressure equilibrium cell, respectively. After 60 min, unscrewing the decompression sampling valve (12), subR134a saturated by PVP flowed into two U-shape tubes (13), in which the dissolved PVP was deposited for sequence analysis and the discharged R134a was measured by a wet-gas flow meter (16, with an accuracy of ±0.01 L). The suitable dissolving time was determined to guarantee the accuracy of the experimental solubility of PVP in sub-R134a at 323 K and 18.0 MPa. The solubility of PVP with different molecular weights in sub-R134a varying with different dissolving time was shown in Figure 2. It can be found that the solubility data retained a rising trend when the dissolving time ranged from 20 to 60 min. After 60 min, the solubility data remained stable, which means the system achieved balance. So, 60 min was adopted in this work. 2.3. Analytical Method. The solute deposited in the two U-shaped tubes was dissolved with deionized water. The
Figure 2. Dissolving time of PVP in sub-R134a at 323 K and 18.0 MPa: ●, 24 000; ▲, 58 000.
absorption wavelength at 205 nm of PVP with different molecular weights was detected by ultraviolet spectrophotometer (Purkinje, model TU-1810), and calibration curves of PVP with molecular weights of 24 000 and 58 000 were established with regression coefficients higher than 0.9992. Each experimental solubility data point at the same experimental temperature and pressure condition was determined at least three times to ensure the accuracy was better than ±5.9% in this work. 2.4. Semiempirical Models. The density-based semiempirical models are widely used because physical property data of polymer are normally not available. In this work, six semiempirical models (Chrastil,16 A−L,17 K−J,18 S−S,19 M-S− T,20 and Bartle21) shown in Table 1 were used to correlate the experimental solubility data. In the Chrastil and the A−L models, S is the mass solubility of the solute in sub-R134a, which can be calculated using eq 1. S=
yρM 2 M1(1 − y)
(1)
where y is the mole fraction of the solute in sub-R134a; ρ (g· L−1) is the density of sub-R134a; and M1 and M2 are the molecular weights of sub-R134a and solute, respectively. As shown in Table 1, the adjustable parameter B0 of the Chrastil model is a function of total heat ΔHtotal (kJ·mol−1) of 3369
DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
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Table 1. Six Semiempirical Models models
expressions B0 T
ref
Chrastil
ln S′ = A 0 ln ρ +
A−L
ln S′ = (A 0 + B1ρ + C1ρ2 ) ln ρ +
K−J
B2 T
ln y = A 2ρ +
(
B3 T
+ C0
16
) ln ρ +
ln y = A3 +
M-S−T
T ln(yP) = A4 ρ + B4 T + C4
Bartle
ln y P
P
5
ref
+ E1
)+
+ D3 B5 T
T(K)a
17
313
19
21
323
the solute, which is the sum of heat of solvation ΔHsol (kJ· mol−1) and heat of sublimation enthalpy ΔHsub (kJ·mol−1), and is defined as −ΔHtotal/R; the adjustable parameter B5 of the Bartle’s model can be applied to calculate the ΔHsub (kJ·mol−1) of PVP by eq 2; where R is the gas constant and typically taken as 8.314 J·mol−1·K−1. ΔHsub = −B5R
P(MPa)a
R134a
CO2
R134a
CO2
δ
1.36 1.56 1.69 1.80 1.91
5.00 5.22 5.65 6.03 6.18
1.41 1.65 1.89 2.09 2.31
5.47 5.59 5.82 6.07 6.19
1.52 1.75 2.03 2.34 2.68
5.93 6.17 6.28 6.29 6.32
0.41 0.47 0.51 0.55 0.59
3.56 3.57 3.67 3.74 3.78
0.44 0.51 0.57 0.62 0.67
4.34 4.35 4.53 4.75 4.94
0.48 0.55 0.62 0.70 0.78
4.98 5.04 5.11 5.15 5.21
Mn = 24 000
20
+ C5
y·107 (mol·mol−1)a
ρ (g·L−1)b
18 C3 T
S−S
ref
D1 T
+ C2
( ) = A (ρ − ρ
Table 2. Solubility Comparison of PVP in sub-R134a and SCCO222 under the Same Pressure and Temperature
333
(2)
3. RESULTS AND DISCUSSION 3.1. Solubility of PVP in Sub-R134a. The experimental solubility data of PVP with molecular weights of 24 000 and 58 000 in sub-R134a are listed in Table 2, which also illustrates those solubility data of PVP in SCCO2.22 The density of subR134a is obtained from the National Institute of Standards and Technology Web site.28 From Table 2, the solubility of PVP in sub-R134a is ranged from 4.64 × 10−7 to 16.94 × 10−7 mol· mol−1 for a molecular weight of 24 000 and 1.15 × 10−7 to 4.07 × 10−7 mol·mol−1 for a molecular weight of 58 000, respectively. Figure 3 shows the solubility curves of PVP with molecular weights of 24 000 and 58 000 in sub-R134a. From the tendency of the curves, it can be found that at the same temperature, the solubility increased with the pressure increasing, which could be explained by the increase of solvent density and the enhancement of molecular interaction between the solute and solvent molecules. In addition, PVP solubility increases with rising temperature at a given pressure because in this case the dominant factor influencing PVP solubility is the solute vapor pressure, which increases with temperature increasing and results in the increase of PVP solubility in sub-R134a. The solubility data in Table 2 also shows that under the same experimental temperature and pressure condition, the solubility of PVP decreases when its molecular weights increase, and the tendency of solute solubility is the same as those reported in the literature.24,29 On the one hand, this can be attributed to the fact that the interactions between solute molecules become stronger with increasing molecular weights, which makes it much more difficult for the solute to dissolve; on the other hand, both phenomena can be explained by entropythe Gibbs free energy (ΔG) of a single polymer chain and the steric hindrance of the polymer increase with increasing molecular weight.30 According to Flory’s theory (eq 3), the chaos degree of solute molecule (ΔS), decreases with increasing ΔG. Therefore, the solute solubility decreases with increasing molecular weights. ΔG ΔS − = (3) RT R
313
323
333
5.0 7.0 9.0 11.0 13.0 15.0 18.0 5.0 7.0 9.0 11.0 13.0 15.0 18.0 5.0 7.0 9.0 11.0 13.0 15.0 18.0
1176.7 1189.0 1200.2 1210.5 1220.1 1229.1 1241.5 1137.0 1151.9 1165.2 1177.3 1188.3 1198.5 1212.5 1093.7 1112.2 1128.2 1142.4 1155.1 1166.8 1182.7
5.0 7.0 9.0 11.0 13.0 15.0 18.0 5.0 7.0 9.0 11.0 13.0 15.0 18.0 5.0 7.0 9.0 11.0 13.0 15.0 18.0
1176.7 1189.0 1200.2 1210.5 1220.1 1229.1 1241.5 1137.0 1151.9 1165.2 1177.3 1188.3 1198.5 1212.5 1093.7 1112.2 1128.2 1142.4 1155.1 1166.8 1182.7
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 Mn = 58 000
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
4.64 5.76 6.80 8.15 9.55 10.86 11.82 5.15 6.42 7.71 9.22 11.00 12.70 14.31 5.94 7.49 9.01 10.80 12.76 14.7 16.94 1.15 1.30 1.46 1.68 1.87 2.06 2.23 1.38 1.65 1.91 2.22 2.58 2.95 3.31 1.75 2.06 2.39 2.77 3.17 3.61 4.07
Standard uncertainties are u(T) = ± 0.1 K, u(P) = ±0.1 MPa, u(y) = ±6.8 × 10−9 mol·mol−1. bρ is the density of pure R134a and CO2 at different experimental temperatures and pressures, which is obtained from the NIST fluid property database. a
3.2. Comparison of Solubility of PVP in SCCO2 and Sub-R134a. To compare the solubility of PVP in SCCO2 and sub-R134a under the same temperature and pressure condition (temperatures of 313, 323, 333 K, pressures of 9.0, 11.0, 13.0, 15.0, and 18.0 MPa), the solubility enhancement factor (δ) is defined as eq 4 and listed in Table 2. 3370
DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
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temperature and pressure condition. The enhancement factor of PVP ranges from 5.00 to 6.32 for a molecular weight of 24 000, and from 3.56 to 5.21 for a molecular weight of 58 000, respectively. On the one hand, PVP as a polar solid solute is more easily dissolved in sub-R134a with more polarity than SCCO2; on the other hand, solvent density is a key factor of its ability to dissolve solvent, and the increase of solvent density can make its dissolve ability increase. As shown in Table 2, the density of sub-R134a is higher than that of SCCO2 under the same experimental temperature and pressure condition, therefore the solubility of PVP in sub-R134a is more than that in SCCO2. 3.3. Prediction of Solubility and Thermodynamic Enthalpy. The average absolute relative deviation (AARD) is proposed to compare the correlation results of the models. The formula is as follows: AARD(%) =
AARD′(%) =
yin R134a yin CO2
n
∑
|ycal − yexp | yexp
1
(5)
where ycal is the solubility value correlated by model; yexp is the experimental solubility value; and n is the number of experimental data points. The values of AARD (%) and adjustable parameters for PVP with molecular weights of 24 000 and 58 000 were listed respectively in Table 3. It was found that the S−S model (AARD value of 1.99%) is better than other models for a molecular weight of 24 000, and the A−L model (AARD value of 0.80%) is better than other models for a molecular weight of 58 000. In this work, the statistical test method is carried out to evaluate the effects of the number of adjustable parameters on correlation precision for each model. The AARD′ (%) was established using the following equation:
Figure 3. Experimental solubility of PVP for (a) 24 000 and (b) 58 000 in sub-R134a as a function of pressure at different temperatures: ■, 313 K; ●, 323 K; ▲, 333 K.
δ=
100 n
100 n−z
n
∑ 1
|ycal − yexp | yexp
(6)
where z is the number of adjustable parameters in each model; n, ycal and yexp are the same as in eq 5. The values of AARD′ (%) of the M-S−T, the S−S, and the A-L models are listed in Table 4. The differences of AARD′ (%) between these models with different numbers of adjustable parameters are statistically significant (variance analysis; p = 0.0542 > 0.01). The result indicates that the model correlation precision has no relation to the number of adjustable parameters, and mainly depends on
(4)
where yin R134a is the solubility of PVP in sub-R134a and yin CO2 is the solubility of PVP in SCCO222 at the same experimental temperature and pressure condition. It was shown in Table 2 that the solubility of PVP in subR134a is more than that in SCCO2 at the same experimental
Table 3. Correlated Results of Semiempirical Models for Solubility of PVP in sub-R134a models
Mn
Chrastil
24 000 58 000 24 000 58 000 24 000 58 000 24 000 58 000 24 000 58 000 24 000 58 000
A−L K−J S−S M-S−T Bartle
AARD (%)
adjustable parameters A0 A0 A1 A1 A2 A2 A3 A3 A4 A4 A5 A5
= = = = = = = = = = = =
16.394; B0 = −6.194 × 103 g·K·L−1; C0 = −98.079 g·L−1 13.396; B0 = −6.482 × 103 g·K·L−1; C0 = −76.554 g·L−1 −5.933 × 102; B1 = 0.131 L·g−1; C1 = −3.019 × 10−5 L2·g−2; D1 = −6.331 × 103 g·K·L−1; E1 = 3.419 × 103 g·L−1 −8.626 × 102; B1 = 0.194 L·g−1; C1 = −4.586 × 10−5 L2·g−2; D1 = −6.767 × 103 g·K·L−1; E1 = 4.955 × 103 g·L−1 0.013 L·g−1; B2 = −6.319 × 103 K; C2 = −9.976 0.011 L·g−1; B2 = −6.511 × 103 K; C2 = −7.715 −45.459 L·g−1; B3 = 2.113 × 104 K·L·g−1; C3 = −1.558 × 105 K; D3 = 3.557 × 102 −8.723 L·g−1; B3 = 6.877 × 103 K·L·g−1; C3 = −5.515 × 104 K; D3 = 66.558 9.614 K·L·MPa·g−1; B4 = 26.470 MPa; C4 = −2.359 × 104 K−1·MPa−1 8.755 K·L·MPa·g−1; B4 = 25.572 MPa; C4 = −2.275 × 104 K−1·MPa−1 −0.030 L·g−1; B5 = −1.222 × 104 K; C5 = 14.493 −0.027 L·g−1; B5 = −1.241 × 104 K; C5 = 14.909 3371
4.53 2.68 3.51 0.80 3.69 2.29 1.99 2.21 7.36 5.79 8.85 6.75
DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
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solvent molecules for PVP with lower molecular weights are much stronger than that for PVP with higher molecular weights. Therefore, the solubility of PVP with lower molecular weights in R134a is much higher, which is consistent with the experimental phenomenon of this work. The thermodynamic enthalpy of PVP (ΔHtotal, ΔHsol and ΔHsub) can be calculated by the Chrastil and the Bartle models. The value of ΔHtotal can be obtained by −B0R; while that of ΔHsub is through −B5R. Thus, the value of ΔHsol can be obtained by subtracting ΔHsub from ΔHtotal. The thermodynamic enthalpy of PVP with molecular weights of 24 000 and 58 000 are listed in Table 5, which can help the research on phase equilibrium of PVP in sub-R134a.
Table 4. AARD′ (%) of Four Semiempirical Models for Solubility of PVP in sub-R134a AARD′ (%) Mn
M-S−T
S−S
A−L
24 000 58 000 mean
8.58 6.75 7.67
2.45 2.73 2.59
4.60 2.02 3.31
the function description of solvent density in each model expression. Usually, the M-S−T model is used to prove the selfconsistency of the experimental data. From the expression of the M-S−T model, when T ln(yP) − B4T is plotted versus the density of the solvent, the mole fraction (y) is a straight line, as shown in Figure 4, which shows that the solubility increased
Table 5. Thermodynamic Enthalpy of PVP Mn
ΔHtotala (kJ·mol−1)
ΔHsubb (kJ·mol−1)
ΔHsol (kJ·mol−1)
24 000 58 000
51.5 53.9
101.6 103.2
−50.1 −49.3
a ΔHtotal is the total enthalpy of the solute, which was calculated by the Chrastil model. bΔHsub is the sublimation enthalpy of the solute, which was calculated by the Bartle model.
4. SUMMARY The solubility of PVP with molecular weights of 24 000 and 58 000 in sub-R134a is obtained by the static method for the temperatures of 313, 323, and 333 K and in the pressure range from 5.0 to 18.0 MPa. The solubility range is from 4.64 × 10−7 to 16.94 × 10−7 mol·mol−1 for PVP with a molecular weight of 24000 and 1.15 × 10−7 to 4.07 × 10−7 mol·mol−1 for PVP with a molecular weight of 58 000. Six density-based semiempirical models (Chrastil, A−L, K−J, S−S, M-S−T, and Bartle) are used to correlate the solubility data, and the adjustable parameters and AARD for each model are calculated, respectively. The values of the total heat of solution, the enthalpies of sublimation, and solvation of PVP in sub-R134a are 51.5 kJ·mol−1, 101.6 kJ·mol−1, −50.1 kJ·mol−1 for a molecular weight of 24 000 and 53.9 kJ·mol−1, 103.2 kJ·mol−1, −49.3 kJ·mol−1 for a molecular weight of 58 000.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Tel: +86-10-64434788. Fax: +86-10-64436781. ORCID
Jun-su Jin: 0000-0002-8329-1442 Funding
Figure 4. Solubility of PVP for (a) 24 000 and (b) 58 000 in subR134a correlated by the M-S−T model at temperatures of (313 K, 323 K, 333 K); ■, experimental data; , calculated results.
This research was financially supported by the funds awarded by National Natural Science Foundation of China (No. 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.
with increasing density and most of the experimental data were in the vicinity of a straight line. Therefore, the self-consistency of the experimental data is satisfactory. Moreover, the values of A0, A2, and A4 correlated by the models of Chrastil, K−J and M-S−T represent the number of solvent molecules that associate with one solute molecule. Meanwhile, the values of A0, A2, and A4 for PVP with lower molecular weights are higher than those with higher molecular weights, which proves that the interactions between solute and
Notes
The authors declare no competing financial interest.
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REFERENCES
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DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
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DOI: 10.1021/acs.jced.7b00434 J. Chem. Eng. Data 2017, 62, 3368−3373
