Article pubs.acs.org/jced
Sorption of Benzene, Dichloroethane, Dichloromethane, and Chloroform by Poly(ethylene glycol), Polycaprolactone, and Their Copolymers at 298.15 K Using a Quartz Crystal Microbalance Abhijeet R. Iyer, Jonathan J. Samuelson, Gregory F. Barone, Scott W. Campbell,* and Venkat R. Bhethanabotla* Department of Chemical & Biomedical Engineering, University of South Florida, Tampa, Florida 33620-5350, United States ABSTRACT: Solubilities of benzene, 1,2-dichloroethane, chloroform, and dichloromethane in poly(ethylene glycol) (PEG), polycaprolactone (PCL), and several PEG/PCL diblock copolymers at 298.15 K are reported. Activity versus weight fraction data were collected using a quartz crystal microbalance and are adequately represented by the Flory−Huggins model.
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INTRODUCTION There are several methods of organic vapor sensing; among them, the quartz crystal microbalance (QCM) technique, first introduced by King,1 offers high sensitivity, thus allowing for the use of thinner polymer films, which results in shorter equilibration times. Previously reported results from our laboratory were obtained using a QCM in a static apparatus.2−5 Here we report data obtained using a QCM in a newly designed flow system. In particular, we present solubilities of benzene, 1,2-dichloroethane, chloroform, and dichloromethane in the homopolymers polycaprolactone (PCL) and poly(ethylene glycol) (PEG) as well as three PEG/PCL diblock copolymers at 298.15 K. The copolymers are PEG(5000)/ PCL(1000), PEG(5000)/PCL(5000), and PEG(1000)/ PCL(5000), where each number in parentheses represents the molecular weight of that segment of the polymer. PCL is the leading biodegradable compound approved by the U.S. Food and Drug Administration (FDA) for drug delivery systems, implants, adhesion barriers, and tissue engineering.6 The rate of biodegradation of PCL is low because of the polymer’s strong crystalline nature, though it can be improved by copolymerization with PEG. 7 The study of these copolymer−solvent interactions is of interest for processing and applications. Activity−weight fraction data for benzene in PEG at 365 K for benzene weight fractions ranging from 0.06 to 0.47 were reported by Panayiotou and Vera8. Hao et al.9 reported data for benzene in PEG at 297.5 K for benzene weight fractions between 0.86 and 0.98 as well as for chloroform in PCL at 333.15 K for chloroform weight fractions in the range of 0.08− 0.62. Booth et al.10 reported data for chloroform sorption in PEG with weight fractions ranging from 0.029 to 0.811; the data exhibited a marked inflection consistent with phase © 2017 American Chemical Society
separation. No data for PEG/PCL copolymers have been reported in the literature.
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EXPERIMENTAL SECTION Materials. PEG and PCL were obtained from Sigma-Aldrich with weight-average molecular weights of 2000 and 14 000, respectively. PEG(5000)/PCL(5000), PEG(1000)/ PCL(5000), and PEG(5000)/PCL(1000) diblock copolymers were obtained from Polysciences, Inc. Benzene, dichloromethane, chloroform, and 1,2-dichloroethane were obtained from Sigma-Aldrich with 99.9% purity and were used with no further purification. The 5 MHz quartz crystals utilized in this study (1 in. diameter, 0.013 in. thickness, AT-cut) were supplied by Phillip Technologies (Greenville, SC) and exhibited good piezoelectric and mechanical properties. The crystals were well-polished and had gold-coated electrodes. Their operating range was 4.976− 5.020 MHz, with resistances of approximately 10 Ω. Apparatus and Procedure. The working apparatus consisted of a stream of solvent vapor diluted with nitrogen to arbitrary concentration passing over a QCM oscillated to its resonant frequency. The experiment and data collection were automated by a custom LabView script running on a computer connected to the main apparatus. A schematic diagram of the experimental apparatus is shown in Figure 1. A size-300 tank (T1) of prepurified-grade nitrogen gas fed two MKS1179A mass-flow controllers (MFC1 and MFC2),
Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 31, 2017 Accepted: June 9, 2017 Published: June 23, 2017 2755
DOI: 10.1021/acs.jced.7b00120 J. Chem. Eng. Data 2017, 62, 2755−2760
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Figure 1. Schematic diagram of the quartz crystal microbalance apparatus. Legend: T1, nitrogen tank; MFC1 and MFC2, mass-flow controllers; FV1A−4A and FV1B−4B, solenoid valves; I1−4, solvent impingers; HX1 and HX2, chillers; HX3, heat exchanger; FS1, 5 MHz quartz crystal.
which were computer-controlled to produce flows ranging from (0 to 100) sccm in increments of 10 sccm that summed to 100 sccm to maintain a constant flow. The flow through MFC1 was routed through one of four impingers (I1−4) by two banks of normally closed solenoids (FV1A−4A and FV1B−4B) that were activated by computer-controlled relays so that only one flow path was open at a given time. The nitrogen gas bubbled through a reservoir of solvent in each impinger, and the equilibrated bubbler vapor stream was diluted by the MFC2 diluent flow; the impingers were meanwhile kept at a constant temperature by a NESLAB RTE 740 recirculating chiller (HX1). In this way, up to 10 different isothermal concentrations of solvent vapor for four different solvents could be produced by automated software. The vapor was routed through a cell containing a 5.00 MHz QCM oscillated to its resonant frequency via a PLO-10i phaselock oscillator (Maxtek), and the frequency, measured by an HP5334B frequency counter, was logged via computer. The cell was kept at a constant temperature by another NESLAB RTE 17 recirculating chiller (HX2), and the vapor entering the cell was also preheated via a separate heat exchanger (HX3). Frequency−time data were logged, and a running list of the last 50 data points was stored; when the slope of the frequency versus time regression line was within a 95% confidence interval of 0 and the standard deviation of the frequency data was less than 0.9 Hz, the system was considered to be at equilibrium, and the average and standard deviation were reported. These data were then used to calculate weight fractions; if the Butterworth−van Dyke equivalent resistance was below 20 Ω, the data were considered reliable in representing true weight fractions. Crystals used in the experimentboth new and reused were cleaned prior to spin-coating of the polymer or copolymer by means of Soxhlet extraction for 6 h with 1,2-dichloroethane followed by 1 h of sonication in hydrochloric acid. The crystals were then rinsed clean with purified water and dried under a stream of nitrogen before plasma cleaning for 15 min on both sides. A polymer film was then applied to the clean crystals by means of spin-coating with a solution of the polymer in chloroform (for PEG(1000)/PCL(5000)) or toluene (for all others) to a frequency shift Δf 0 of 1000−5000 Hz between the uncoated and coated crystals. For each of the four solvents, the polymer was purged with nitrogen until the frequency stabilized
before the application of gradually increasing concentrations of solvent vapor at constant flow. The frequency shift Δf between the purged crystal and the crystal with sorbed solvent was used in conjunction with Δf 0 to obtain the weight fraction w1 via the Sauerbrey equation:11 w1 =
Δf Δf + Δf0
(1)
where Δf 0 is the frequency shift due to the mass of polymer film and Δf is the frequency shift due to the mass of sorbed solvent. Solvent activities a1 were determined from a1 =
⎡ P − P s(T ) 1 ⎢ exp B11 P1s(T ) RT ⎢⎣ y1P
+
P(1 − y1)2 (2B13 − B11 − B33) ⎤ ⎥ RT ⎥⎦
(2)
where y1 is the mole fraction of the solvent in the combined gas stream passing over the crystal, P is the total pressure, Ps1(T) is the solvent vapor pressure at the cell temperature T, B11 is the second virial coefficient of the pure solvent, B33 is the second virial coefficient of nitrogen, and B13 is the second virial cross coefficient. Second virial coefficients were estimated using the Tsonopolous equation.12 The binary interaction coefficient for benzene + nitrogen was taken from Meng and Duan.13 A binary interaction coefficient for nitrogen + chloroform was extracted from second virial cross coefficient data in Dymond and Smith14 and was also applied to nitrogen + 1,2-dichloroethane and nitrogen + dichloromethane. The vapor pressures Ps1 were obtained using the Antoine equation: log10(P1s/bar) = A −
B (T /K) + C
(3)
where T represents the cell temperature. The values of the constants15 A, B, and C are given in Table 1. The mole fraction y1 in eq 2 was obtained from a mass balance around the point at which the bubbler and diluent flows combine: 2756
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σa1
Table 1. Values of the Coefficients Used To Calculate Solvent Vapor Pressures
a1
Antoine parameter
benzene
dichloroethane
chloroform
dichloromethane
A B C
4.01814 1203.835 −53.226
4.58518 1521.789 −24.67
4.20772 1233.129 −40.953
4.52691 1327.016 −20.474
y1 =
σ d ln P1s(T ′) d ln P1s(T ) σT ′ + σT + V dT ′ dT V
(4)
σΔf
where y1B is the mole fraction of solvent in the gas stream leaving the impinger and V31 and V32 are the volumetric flow rates of nitrogen passing through mass-flow controllers MFC1 and MFC2, respectively. The value of y1B was obtained under the assumption that the solvent vapor and nitrogen reached equilibrium in the impinger and is a trial-and-error solution of the following expression:
Δf0
y1B =
P1s(T ′) P
σw1 =
w1 1 − w1
w1 1 − w1
⎜
σΔf
⎞
0⎟
Δf0 ⎠
2
(7)
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RESULTS Experimental Data. The solvent weight fractions as functions of solvent activity for the four solvents in PEG, PCL, PEG(1000)/PCL(5000), PEG(5000)/PCL(5000), and PEG(5000)/PCL(1000) at 298.15 K are given in Tables 2−5. As noted earlier, the software that controls the experiment is capable of generating 10 concentrations of each solvent. On the basis of specific evidence from our own data, the lowest eight, five, and four data points are reported for 1,2-dichloroethane, chloroform, and dichloromethane, respectively, as at higher solvent activities a second phase with different properties is formed. This will be discussed later; for all of the data reported in Tables 2−5, only a vapor phase and a single polymer phase are present at equilibrium. Plots of solvent activity versus weight fraction for each solvent are shown in Figures 2−5. Close inspection of these figures reveals that with the exception of benzene, the variation of the weight fraction with the PCL/PEG ratio at constant activity is not monotonic. For the halogenated solvents, the weight fractions at constant activity are lowest for PEG and increase with increasing PCL/PEG ratio, reaching a maximum for the PEG(1000)/PCL(5000) copolymer, then decreasing slightly for the PCL homopolymer. Data Correlation. The data were correlated by fitting the experimental solvent activity−solvent weight fraction data to the Flory−Huggins model:
P(1 − y1B )2 (2B13 − B11 − B33) ⎤ RT ′
( )⎛⎝ (1 + ) +
where σΔf and σΔf 0 are the uncertainties in the frequency shifts Δf and Δf 0, respectively. The resulting uncertainties in the weight fractions are 0.0006 or less.
1 ⎡ P − P s(T ′) exp⎢ RT1 ′ B11 + ⎣
(6)
where σV is the uncertainty in the volumetric flow rate V (=V31 + V32) and σT and σT′ are the uncertainties in cell and impinger temperatures, respectively. The values of σT and σT′ are 0.01 and the uncertainty in the volumetric flow rate is 1%. As a result, the uncertainties in the activities are less than 1.5%. The uncertainty in the weight fraction, σw1, is given by
y1B V31 V31 + (1 − y1B )V32
=
⎥⎦ (5)
Ps1(T′)
where is the solvent vapor pressure at the temperature of the impinger, T′. Equilibrium in the impingers was verified by gas chromatography for the solvents benzene and chloroform. Known masses of solvent were injected into a sealed container of nitrogen at atmospheric pressure and known temperature. The mole fraction of the solvent, y, was calculated, and the relative percent area of the solvent peak, A, was obtained by injection into an Agilent GC 7890A gas chromatograph. The calibration curve was linearized by plotting 1/(y − 1) versus (100 − A)/A with coefficients of determination of 0.9995 or better. Vapor samples from the apparatus during normal operation were collected, and the relative percent areas were used to calculate mole fractions, which were then compared to values calculated by assuming equilibrium was reached in the impingers. The results deviated by average absolute relative deviations of 2.6% for chloroform and 1.2% for benzene. The assumption that equilibrium was achieved in the impingers was subsequently used in all of the calculations. If the effect of gas nonideality in error estimation is neglected, the uncertainty σa1 in calculated solvent activity is given by
Table 2. Experimental Data for the Weight Fraction w1 of Benzene in PCL, PEG(1000)/PCL(5000), PEG(5000)/PCL(5000), PEG(5000)/PCL(1000), and PEG at 298.15 K as a Function of the Benzene Activity a1 w1 a1
PCL
PEG(1000)/PCL(5000)
PEG(5000)/PCL(5000)
PEG(5000)/PCL(1000)
PEG
0.070 0.136 0.205 0.267 0.330 0.392 0.448 0.509 0.565 0.620
0.007 0.016 0.025 0.033 0.042 0.052 0.062 0.075 0.092 0.110
0.009 0.016 0.025 0.033 0.042 0.051 0.061 0.072 0.085 0.098
0.007 0.013 0.018 0.024 0.030 0.036 0.042 0.049 0.057 0.066
0.005 0.010 0.016 0.021 0.027 0.034 0.041 0.048 0.057 0.067
0.001 0.002 0.004 0.005 0.006 0.008 0.009 0.011 0.013 0.015
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Table 3. Experimental Data for the Weight Fraction w1 of Dichloroethane (DCE) in PCL, PEG(1000)/PCL(5000), PEG(5000)/PCL(5000), PEG(5000)/PCL(1000), and PEG at 298.15 K as a Function of the DCE Activity a1 w1 a1
PCL
PEG(1000)/PCL(5000)
PEG(5000)/PCL(5000)
PEG(5000)/PCL(1000)
PEG
0.069 0.133 0.202 0.263 0.326 0.388 0.444 0.505
0.014 0.029 0.043 0.059 0.074 0.092 0.112 0.134
0.017 0.034 0.051 0.067 0.084 0.101 0.119 0.138
0.013 0.026 0.037 0.048 0.059 0.073 0.090 0.120
0.010 0.021 0.031 0.042 0.054 0.067 0.082 0.101
0.003 0.006 0.009 0.012 0.016 0.020 0.024 −
Table 4. Experimental Data for the Weight Fraction w1 of Chloroform in PCL, PEG(1000)/PCL(5000), PEG(5000)/ PCL(5000), PEG(5000)/PCL(1000), and PEG at 298.15 K as a Function of the Chloroform Activity a1 w1 a1
PCL
PEG(1000)/PCL(5000)
PEG(5000)/PCL(5000)
PEG(5000)/PCL(1000)
PEG
0.079 0.153 0.228 0.293 0.358
0.038 0.073 0.108 0.143 0.193
0.044 0.085 0.121 0.154 0.199
0.033 0.062 0.091 0.126 −
0.028 0.055 0.082 0.112 −
0.008 0.016 0.025 0.038 −
Table 5. Experimental Data for the Weight Fraction w1 of Dichloromethane (DCM) in PCL, PEG(1000)/PCL(5000), PEG(5000)/PCL(5000), PEG(5000)/PCL(1000), and PEG at 298.15 K as a Function of the DCM Activity a1 w1 a1
PCL
PEG(1000)/PCL(5000)
PEG(5000)/PCL(5000)
PEG(5000)/PCL(1000)
PEG
0.106 0.196 0.282 0.352
0.031 0.061 0.092 0.123
0.039 0.072 0.101 0.128
0.034 0.064 0.098 −
0.024 0.046 0.069 0.097
0.008 0.016 0.025 −
Figure 3. Comparison of activity versus weight fraction for dichloroethane in PCL ( ◆ ), PEG(1000)/PCL(5000) ( ■ ), PEG(5000)/PCL(5000) (×), PEG(5000)/PCL(1000) (▲), and PEG (●) at 298.15 K. Solid curves refer to fits to eq 10.
Figure 2. Comparison of activity versus weight fraction for benzene in PCL (◆), PEG(1000)/PCL(5000) (■), PEG(5000)/PCL(5000) (×), PEG(5000)/PCL(1000) (▲), and PEG (●) at 298.15 K. Solid curves refer to fits to eq 10.
ϕ ϕ NGE = N1 ln 1 + N2 ln 2 + χϕ1ϕ2(N1 + rN2) RT x1 x2
where xi is the mole fraction (1 = solvent, 2 = polymer), ϕi is the volume fraction, r = V2/V1 is the ratio of molar volumes, Ni is the number of moles, and χ is used here as an adjustable parameter. The volume fraction of component i is given by
(8) 2758
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Table 6. Molar Masses (M) and Molar Volumes (V) of the Solvents and Polymers species
M/g·mol−1
V/cm3·mol−1
Solvents benzene dichloroethane chloroform dichloromethane PCL PEG(1000)/PCL(5000) PEG(5000)/PCL(5000) PEG(5000)/PCL(1000) PEG
78.11 98.95 119.37 84.93 Polymers 14000 6000 10000 6000 2000
92.41 78.97 80.17 64.02 12216.40 5195.40 8530 5038.80 1666.67
⎛ 1⎞ ln a1 = ln ϕ1 + ⎜1 − ⎟ϕ2 + χϕ2 2 ⎝ r⎠
Values of χ were obtained by minimizing the sum of the squares of the differences between the experimental and calculated activities and are given for each solvent−polymer system in Table 7, along with the average difference between the
Figure 4. Comparison of activity versus weight fraction for chloroform in PCL (◆), PEG(1000)/PCL(5000) (■), PEG(5000)/PCL(5000) (×), PEG(5000)/PCL(1000) (▲), and PEG (●) at 298.15 K. Solid curves refer to fits to eq 10.
Table 7. Parameters Used in the Flory−Huggins Model and Average Deviations between Experimental and Calculated Weight Fractions
Figure 5. Comparison of activity versus weight fraction plot for dichloromethane in PCL ( ◆), PEG(1000)/PCL(5000) ( ■ ), PEG(5000)/PCL(5000) (×), PEG(5000)/PCL(1000) (▲), and PEG (●) at 298.15 K. Solid curves refer to fits to eq 10.
ϕi =
Vx i i ∑j Vjxj
(10)
system
χ
Δw1
benzene + PEG benzene + PEG(5000)/PCL(1000) benzene + PEG(5000)/PCL(5000) benzene + PEG(1000)/PCL(5000) benzene + PCL DCE + PEG DCE + PEG(5000)/PCL(1000) DCE + PEG(5000)/PCL(5000) DCE + PEG(1000)/PCL(5000) DCE + PCL chloroform + PEG chloroform + PEG(5000)/PCL(1000) chloroform + PEG(5000)/PCL(5000) chloroform + PEG(1000)/PCL(5000) chloroform + PCL DCM + PEG DCM + PEG(5000)/PCL(1000) DCM + PEG(5000)/PCL(5000) DCM + PEG(1000)/PCL(5000) DCM + PCL
2.641 1.274 1.244 0.945 0.895 2.162 0.989 0.871 0.632 0.714 1.477 0.335 0.222 −0.039 0.045 1.670 0.621 0.317 0.266 0.385
0.001 0.001 0.001 0.001 0.002 0.001 0.002 0.003 0.003 0.001 0.002 0.001 0.002 0.003 0.004 0.001 0.002 0.001 0.003 0.001
experimental weight fraction and that calculated from the Flory−Huggins model. The model represents experimental weight fractions to within an average between 0.001 and 0.004. It was noted earlier that for a number of runs the formation of a second polymer-containing phase occurred at higher solvent weight fractions than reported here. Figure 6 shows the phase behavior of chloroform + PEG as determined by Booth et al.10 at 298 K. Our data for this system, including an additional data point not reported in Table 4, are shown for comparison. It is clear from Figure 6 that a second polymercontaining phase begins to form for chloroform weight fractions exceeding 0.038. The current technique, as can be seen in Figure 6, is capable of determining that a second phase is formed. However, the resulting activity−weight fraction
(9)
The molecular weights and molar volumes for the homopolymers, copolymers, and solvents are given in Table 6. The molar volumes for the homopolymers and solvents were calculated from known densities and molecular weights. For the copolymers, the specific volume was assumed to be a weightfraction average of the specific volumes of the homopolymers. The molar volume was then calculated from the specific volume by multiplying by the molecular weight of the copolymer. From eq 8, the following expression for the solvent activity a1 can be derived: 2759
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ORCID
Venkat R. Bhethanabotla: 0000-0002-8279-0100 Notes
The authors declare no competing financial interest.
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(1) King, W. H. Piezoelectric Sorption Detector. Anal. Chem. 1964, 36, 1735−1739. (2) Wong, H. C.; Campbell, S. W.; Bhethanabotla, V. R. Sorption of Benzene, Dichloromethane, and 2-Butanone by Poly(methyl methacrylate), Poly(butyl methacrylate), and Their Copolymers at 323.15 K Using a Quartz Crystal Balance. J. Chem. Eng. Data 2016, 61, 3877− 3882. (3) Wong, H. C.; Campbell, S. W.; Bhethanabotla, V. R. Sorption of benzene, toluene and chloroform by poly(styrene) at 298.15 and 323.15 K using a quartz crystal balance. Fluid Phase Equilib. 1997, 139, 371−389. (4) Wong, H. C.; Campbell, S. W.; Bhethanabotla, V. R. Sorption of benzene, tetrahydrofuran and 2-butanone by poly(vinyl acetate) at 323.15 K using a quartz crystal balance. Fluid Phase Equilib. 2001, 179, 181−191. (5) Wong, H. C.; Campbell, S. W.; Bhethanabotla, V. R. Sorption of Benzene, Dichloromethane, n-Propyl Acetate, and 2-Butanone by Poly(methyl methacrylate), Poly(ethyl methacrylate), and Their Copolymers at 323.15 K Using a Quartz Crystal Balance. J. Chem. Eng. Data 2011, 56, 4772−4777. (6) Woodruff, M. A.; Hutmacher, D. W. The return of a forgotten polymerPolycaprolactone in the 21st century. Prog. Polym. Sci. 2010, 35, 1217−1256. (7) Pitt, C. G.; Jeffcoat, A. R.; Zweidinger, R. A.; Schindler, A. Sustained drug delivery systems. I. The permeability of poly(epsiloncaprolactone), poly(DL-lactic acid), and their copolymers. J. Biomed. Mater. Res. 1979, 13, 497−507. (8) Panayiotou, C.; Vera, J. H. Thermodynamics of PolymerPolymer-Solvent and Block Copolymer-Solvent Systems I. Experimental Measurements. Polym. J. 1984, 16, 89−102. (9) Hao, W.; Elbro, H. S.; Alessi, P. Polymer Solution Data Collection, Part 1: Vapor_Liquid Equilibrium; Chemistry Data Series, Vol. XIV, Part 1; DECHEMA: Frankfurt, Germany, 1992. (10) Booth, C.; Gee, G.; Holden, G.; Williamson, G. R. Studies in the thermodynamics of polymer-liquid systems. Polymer 1964, 5, 343− 370. (11) Sauerbrey, G. Verwendung von Schwingquarzen zur Wägung dünner Schichten und zur Mikrowägung. Eur. Phys. J. A 1959, 155, 206. (12) Tsonopoulos, C. An empirical correlation of second virial coefficients. AIChE J. 1974, 20, 263−272. (13) Meng, L.; Duan, Y.-Y. Prediction of the second cross virial coefficients of nonpolar binary mixtures. Fluid Phase Equilib. 2005, 238, 229−238. (14) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures: A Critical Compilation; Clarendon Press: Oxford, U.K, 1980. (15) NIST Chemistry WebBook; NIST Standard Reference Database Number 69; National Institute of Standards and Technology: Gaithersburg, MD; http://webbook.nist.gov/chemistry/ (Antoine parameters retrieved Aug 24, 2016). (16) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1998.
Figure 6. Comparison of literature data10 and experimental data for activity vs weight fraction for chloroform in PEG at 298.15 K.
measurements are not quantitatively correct because the second phase appears to be a viscous liquid whereas the technique assumes that the polymer film is a solid extension of the quartz crystal. Resistance measurements support this claim, as large resistances indicate viscoelastic effects in the polymer film. For the runs shown here, the resistance was approximately 10 Ω for the single-phase measurements but over 200 Ω after the second phase began to form. The conclusion is that the present technique is accurate as long as the polymer is inertially coupled to the piezoelectric surface and does not exhibit viscoelasticity to a significant extent. As a result, we have reported measurements only for the cases where the resistance is very small, on the order of 10 Ω. Many of the systems included here are expected to exhibit phase splitting, as the Flory−Huggins model leads to phase instability when16 χ≥
2 1⎛ 1 ⎞ ⎜1 + ⎟ 2⎝ r⎠
(11)
where r = V2/V1 is the ratio of molar volumes. This condition is met by about half of the systems examined here.
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CONCLUSION Solubilities of benzene, 1,2-dichloroethane, chloroform, and dichloromethane in poly(ethylene glycol) (PEG), polycaprolactone (PCL), and their copolymers (PEG/PCL) at 298.15 K are reported in the form of activity versus weight fraction data and are represented by the Flory−Huggins equation to within experimental accuracy. The QCM technique is shown to identify when phase splitting occurs, and only data for which a single polymer-containing phase exist are reported here, as the technique is inapplicable when viscoelastic effects are present, as when phase splitting occurs.
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
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DOI: 10.1021/acs.jced.7b00120 J. Chem. Eng. Data 2017, 62, 2755−2760
