Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Sorption of Benzene, Dichloromethane, and n‑Propyl Acetate by Poly(methyl methacrylate)/ Polystyrene Copolymers at 323.15 K Using a Quartz Crystal Balance Howard C. Wong, Scott W. Campbell, and Venkat R. Bhethanabotla*
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Department of Chemical & Biomolecular Engineering University of South Florida Tampa, Florida 33620-5350, United States ABSTRACT: Solvent activity versus solvent weight fraction are reported for benzene, dichloromethane and n-propyl acetate in each of two different poly(methyl methacrylate)−polystyrene copolymers and for dichloromethane and n-propyl acetate in polystyrene homopolymer. Results were obtained at 323.15 K for low solvent weight fractions using a quartz crystal balance. A modified Flory−Huggins equation is used to interpret the data.
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INTRODUCTION
EXPERIMENTAL SECTION Materials. The polystyrene used here has a molecular weight of 233 000 (weight-average) and was purchased from Polysciences, Inc. It was used with no further purification. PMMA/PS (30:70), a random copolymer of poly(methyl methacrylate) and polystyrene, was 30 wt % poly(methyl methacrylate) and had a weight-average molecular weight of 270 000. It was obtained from Polysciences, Inc. Random copolymer PMMA/PS (49:51) was 49 wt % poly(methyl methacrylate) and had a viscosity average molecular weight of 175 000. It was synthesized8 at the University of South Florida via suspension polymerization and was characterized for molecular weight by viscometry and for composition by Fourier transform nuclear magnetic resonance spectroscopy. PMMA/PS copolymers were purified by dissolving in dichloromethane, then precipitating in excess methanol under constant stirring, followed by drying overnight in a vacuum oven at 353 K. Benzene, dichloromethane, and npropyl acetate solvents were obtained from Aldrich Chemical Co. All were HPLC grade and were at least 99.95% pure. They were used without additional purification except for degassing, for which the procedure described by Bhethanabotla and Campbell9 was followed. The quartz crystals used were purchased from Crystek Corporation and were of 5 MHz base frequency. Apparatus and Procedure. A complete description of the experimental apparatus and procedure was given earlier1 and comparisons of data obtained with the apparatus to existing literature data have been made.1,2,4 The polymer under investigation is deposited onto the surface of a quartz crystal
Development of thermodynamic solution models for solvent− polymer mixtures requires high quality experimental data for testing. Copolymer systems present an additional challenge both to modeling and experiment because the composition of the copolymer introduces an additional variable. It is a focus of our laboratory to measure solvent sorption in copolymers and in their constituent homopolymers, so as to provide internally consistent sets of data for model development and testing. In this last of a series of papers1−4 reporting the use of a static method to measure solvent activities in solvent + polymer binary systems, we present new sorption data for npropyl acetate and dichloromethane in a polystyrene (PS) homopolymer and for benzene, dichloromethane, and n-propyl acetate in two poly(methyl methacrylate)/polystyrene (PMMA/PS) copolymers. Results were obtained at 323.15 K for low solvent weight fractions using the same quartz crystal balance employed earlier.1−4 When combined with results presented earlier for benzene + polystyrene1 and for benzene, dichloromethane, and n-propyl acetate + poly(methyl methacrylate),3 a set of data for all three solvents in both homopolymers and two copolymers of different composition are available. Activities of n-propyl acetate in polystyrene (MW = 290 000) at 298.15 K and at 343.15 K were reported by Bawn and Wajid5 for solvent weight fractions between approximately 0.06 and 0.5. Activities of benzene in PMMA/ PS copolymer (MW = 12 060, 41.45% styrene) at 298.15 and 308.15 K were reported for benzene weight fractions between approximately 0.01 and 0.4 by Kang et al.6 Benzene + PMMA/ PS (MW = 270 000, 44% styrene) copolymer was also examined by Sé and Aznar7 at 343.15 K for benzene weight fractions ranging from approximately 0.2 to 0.5. © XXXX American Chemical Society
Received: January 29, 2018 Accepted: June 12, 2018
A
DOI: 10.1021/acs.jced.8b00094 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 1. Coefficients in the Vapor Pressure Equation (eq 3) and Second Virial Coefficients B11 for the Solvents, Used in the Activity Calculations solvent
A
B
C
D
B11/cm3 mol−1
benzene dichloromethane n-propyl acetate
−6.98273 −7.36864 −7.85524
1.33213 1.76727 1.43936
−2.62863 −3.34295 −4.30187
−3.33399 −1.43530 −3.04832
−1292 −678 −2127
jij σΔf + j Δf0 σw1 = k 1+
and then placed in a static sorption cell, where it is exposed to vapor of the desired solvent. A shift Δf 0 in frequency of the crystal occurs when the polymer film is deposited and an additional shift Δf occurs when solvent vapor is sorbed by the polymer. At equilibrium, the weight fraction w1 of solvent in the polymer is calculated from w1 =
Δf Δf + Δf0
(
(1)
2
{
)
(5)
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RESULTS Solvent weight fraction versus solvent activity are given for benzene, dichloromethane, and n-propyl acetate in Tables 2, 3
where B11 is the second virial coefficient of the solvent at the sorption cell temperature. Pressure P is the solvent vapor pressure at the solvent cell temperature and Psat 1 is solvent vapor pressure at the sorption cell temperature. The Wagner equation was used to calculate values of both Psat 1 and P:
Table 2. Experimental Weight Fractions w1 of Benzene (1) in PMMA−PS Copolymers (2) as a Function of Benzene Activity a1 at 323.15 Ka PMMA/PS (49:51)
(3)
where x = 1 − T/TC and where TC and PC are the critical temperature and pressure of the solvent. Second virial coefficients were estimated using the Tsonopoulos10 correlation and the constants A, B, C, and D in eq 3 were obtained from Reid et al.11 Table 1 provides the values for the solvents studied here. The solvent and sorption cell temperatures are maintained to ±0.01 and ±0.3 K, respectively. Upon neglecting the uncertainty in solvent cell temperature relative to that of the sorption cell temperature, the uncertainty in solvent activity σa1 is1 ij d ln P1sat yz z |σa1/a1| = jjj σT j dT zzz k {323.15K
w1 1 − w1
where σΔf and σΔf 0 are uncertainties in Δf and Δf 0. Uncertainties in Δf ranged from ±1 to ±5 Hz, depending on the solvent weight fraction. Maximum uncertainties in Δf 0 ranged from 15 to 30 Hz. For the worst case of thinnest film thickness, these uncertainties propagate to a maximum uncertainty in solvent weight fraction of 0.006. Previously,1 it was noted that sorption and desorption results would sometimes fail to superimpose with this type of measurement. Based on t tests comparing sorption and desorption runs, no hysteresis was indicated for the data reported here. It was not possible to perform a t test on the DCM + PS system due to there being only a single sorption and desorption run. However, the average difference in sorption and desorption weight fractions at equal activity was 0.003 for this system.
The range in Δf 0 values was 1525 to 3004 Hz and the average value was 2074 Hz. This corresponds to film thicknesses between roughly 0.3 and 0.6 μm. A separate solvent cell, which is at a lower temperature than the sorption cell, is used to generate solvent vapor. At constant sorption cell temperature, experiments proceed either in the direction of sorption (by increasing the solvent cell temperature) or desorption (by decreasing the solvent cell temperature). In either case, at equilibrium, the solvent activity in the polymer phase is obtained from ÄÅ ÉÑ Å −B Ñ P a1 = sat expÅÅÅÅ 11 (P1sat − P)ÑÑÑÑ ÅÅÇ RT ÑÑÖ P1 (2)
ji P zy lnjjj zzz = (1 − x)−1[Ax + Bx1.5 + Cx 3 + Dx 6] j PC z k {
y w1 σΔf0 z z 1 − w1 Δf0 z
PMMA/PS (30:70)
a1
w1
w1
0.283 0.340 0.408 0.485 0.528 0.575 0.624 0.675 0.731 sorption/desorption runs avg std dev in w1
0.065 0.078 0.097 0.121 0.135 0.151 0.170 0.192 0.217 3/3 0.004
0.066 0.079 0.098 0.122 0.135 0.152 0.170 0.191 0.215 2/2 0.001
a
Also included is the number of sorption and desorption runs and the average standard deviation in measurements of w1.
and 4, respectively. The number of sorption and desorption runs for each solvent + polymer combination are also shown. Weight fractions in Tables 2−4 are computed by averaging (at equal activity) all of the sorption and desorption runs, and the standard deviations reported in the tables indicate the spread in these values. All standard deviations are within the experimental uncertainty in solvent weight fraction. Direct comparison with results from other studies is difficult because of differences in temperature, copolymer composition and/or polymer molecular weight between investigations. A
(4)
where σT = is the uncertainty in sorption cell temperature. All three solvents have similar derivatives of log vapor pressure with the result that the uncertainty in solvent activity is approximately ±2%. The uncertainty in solvent weight fraction, σw1, is (to within the first order): B
DOI: 10.1021/acs.jced.8b00094 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 3. Experimental Weight Fractions w1 of Dichloromethane(1) in PS and PMMA−PS Copolymers (2) as a Function of Dichloromethane Activity a1 at 323.15 Ka PMMA/PS (49:51)
PMMA/PS (30:70)
PS
a1
w1
w1
w1
0.142 0.179 0.224 0.278 0.342 0.415 0.501 0.602 0.669 0.715 0.766
0.060 0.071 0.085 0.105 0.132 0.163 0.201 0.248 0.280 0.300 0.322
0.057 0.067 0.080 0.100 0.125 0.156 0.194 0.240 0.271 0.292 0.310
0.051 0.062 0.073 0.087 0.110 0.136 0.171 0.216 0.248 0.269 0.287
sorption/desorption runs avg std dev in w1
2/1 0.006
2/2 0.004
1/1 0.002
a
Also included is the number of sorption and desorption runs and the average standard deviation in measurements of w1.
Table 4. Experimental Weight Fractions w1 of n-Propyl Acetate(1) in PS and PMMA−PS Copolymers (2) as a Function of n-Propyl Acetate Activity a1 at 323.15 Ka
Figure 1. Cross-study comparison of activities a1 of n-propyl acetate (1) in PS as a function of n-propyl acetate weight fraction w1: ■ = Bawn and Wajid5, 298.15 K, ▲ = Bawn and Wajid5, 343.15 K, ● = present study, 323.15 K.
PMMA/PS (49:51)
PMMA/PS (30:70)
PS
a1
w1
w1
w1
0.284 0.351 0.429 0.474 0.524 0.577 0.632 0.694 sorption/desorption runs avg std dev in w1
0.065 0.077 0.095 0.108 0.123 0.142 0.163 0.190 2/2 0.002
0.063 0.074 0.095 0.107 0.121 0.140 0.162 0.191 2/2 0.002
0.066 0.077 0.098 0.111 0.127 0.145 0.166 0.194 2/2 0.003
Table 5. Molecular Weights Mi and Molar Volumes Vi of Solvents and Polymers species i
Mi/g mol−1
Vi/cm3 mol−1
benzene dichloromethane n-propyl acetate PMMA/PS (49:51) PMMA/PS (30:70) PS
78.11 84.93 102.13 175 000 270 000 233 000
92.41 64.44 118.88 157 200 247 700 220 700
Φ Φ NGE = N1 ln 1 + N2 ln 2 + Φ1Φ2(N1 + rN2) RT X1 X2
a
Also included is the number of sorption and desorption runs and the average standard deviation in measurements of w1.
[A Φ1 + BΦ2]
(6)
where Xi, Ni, and Φi are mole fractions, mole numbers, and volume fractions, respectively, of the solvent (i = 1) and polymer (i = 2). Parameter r is the ratio of molar volumes, V2/ V1, and A and B are parameters obtained by minimizing the sum of the squares of the differences between calculated and experimental activities. The volume fraction Φi of species i is expressed as
comparison of the results of Bawn and Wajid5 for n-propyl acetate + polystyrene to those reported here is reasonable because the polystyrene samples used in both studies had similar molecular weights and the two temperatures investigated by Bawn and Wajid bracket those of the present study. Bawn and Wajid’s results, as shown in Figure 1, indicate that temperature has little influence on the solvent-activity versus weight fraction curve in the range of 298−343 K. The results of the present study, recorded at a temperature nearly at the middle of this range, are in fairly good agreement with those of Bawn and Wajid. Data Correlation. A modified Flory−Huggins model that allows the χ parameter to vary linearly with volume fraction was used to fit the solvent activities. No attempt is made here to ascribe a theoretical significance to this modified model. It was chosen purely to provide a compact representation of the experimental data to within experimental uncertainties. The Gibbs excess energy is expressed by
Φi =
VX i i ∑j VjXj
(7)
The molar volume of polystyrene at 323.15 K was calculated as described by Wong et al.1 Specific volumes of the copolymers were assumed to be a weight fraction average of those of pure PMMA3,4 and PS and were converted to molar volumes using the given molecular weights. Molar volumes of the solvents were calculated using the modified Rackett equation.12 Molar volumes and molecular weights of all species are given in Table 5. C
DOI: 10.1021/acs.jced.8b00094 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 6. Parameters for Use in the Modified Flory−Huggins Equation (eq 8)a system benzene(1)-PMMA3 benzene(1)-PMMA/PS (49:51) benzene(1)-PMMA/PS (30:70) benzene(1)-PS1 dichloromethane(1)PMMA3 dichloromethane(1)PMMA/PS (49:51) dichloromethane(1)− PMMA/PS (30:70) dichloromethane(1)−PS n-propyl acetate(1)− PMMA3 n-propyl acetate(1)− PMMA/PS (49:51) n-propyl acetate(1)− PMMA/PS (30:70) n-propyl acetate(1)−PS
A
B
avg dev
χ
avg dev
0.791 0.673
0.305 0.317
0.0002 0.0003
0.531 0.448
0.007 0.005
0.724
0.315
0.0010
0.464
0.005
0.677 0.715
0.408 0.081
0.002 0.003
0.503 0.362
0.004 0.018
0.891
0.093
0.003
0.370
0.016
0.857
0.183
0.003
0.432
0.014
0.942
0.384
0.003
0.560 0.767
0.010 0.003
0.764
0.400
0.002
0.518
0.004
0.717
0.464
0.002
0.544
0.003
0.766
0.434
0.002
0.540
0.003
a
Deviation (avg dev) between experimental values of w1 and those calculated from eq 8. Also shown are parameter and resulting average deviation for A = B = χ.
Figure 3. Experimental activities a1 of dichloromethane (1) in PMMA, PS and PMMA−PS copolymers (2) as a function of dichloromethane weight fraction w1 at 323.15 K: ⧫ = PMMA3, ■ = PMMA/PS (49:51), ▲ = PMMA/PS (30:70), ● = PS. Solid curves are from the fits of eq 8.
Figure 2. Experimental activities a1 of benzene (1) in PMMA, PS, and PMMA−PS copolymers (2) as a function of benzene weight fraction w1 at 323.15 K: ⧫ = PMMA3, ■ = PMMA/PS (49:51), ▲= PMMA/ PS (30:70), ● = PS1. Solid curves are from the fits of eq 8.
Figure 4. Experimental activities a1 of n-propyl acetate (1) in PMMA, PS, and PMMA−PS copolymers (2) as a function of n-propyl acetate weight fraction w1 at 323.15 K: ⧫ = PMMA3, ■ = PMMA/PS (49:51), ▲ = PMMA/PS (30:70), ● = PS. Solid curves are from the fits of eq 8.
The solvent activity a1, derived from eq 6, is given by ÄÅ É Å 1 ÑÑ ln a1 = ln(Φ1) + ÅÅÅÅ1 − ÑÑÑÑΦ2 + [2(A − B)Φ1 + B]Φ22 ÅÇ r ÑÖ
Flory−Huggins equation, obtained from eq 8 by equating both A and B to χ, and the corresponding average deviation between model and data are shown in Table 6. For completeness, we include the results of the fits to previously published data for benzene + PS homopolymer1 and for all solvents with PMMA homopolymer.3 Table 6 indicates that the modified Flory−
(8)
Table 6 shows values of A and B obtained by regression for each solvent + polymer pair. Also included are resulting average deviations between experimental and calculated values of weight fraction w1. In addition, the result of fitting the D
DOI: 10.1021/acs.jced.8b00094 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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(7) Sé, R.A. G.; Aznar, M. Vapor-Liquid Equilibrium of Copolymer + Solvent Systems: Experimental Data and Thermodynamic Modeling with New UNIFAC Groups. Chin. J. Chem. Eng. 2008, 16, 605−611. (8) Narayan, S. Synthesis of Styrene Methyl Methacrylate Copolymer Standards. Master of Science Thesis, Department of Chemical Engineering, University of South Florida, December 1993. (9) Bhetanabotla, V. R.; Campbell, S. W. P-x Measurements for Ethanol - n-Heptane - Isobutanol at 303.15 K. Fluid Phase Equilib. 1991, 62, 239−258. (10) Tsonopoulos, C. An Empirical Correlation of Second Virial Coefficients. AIChE J. 1974, 20, 263−272. (11) Reid, R. C.; Prausnitz, J. M.; Poling, B. W. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, NY, 1987. (12) Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236−241.
Huggins model is capable of representing all of the data but that the Flory−Huggins equation is not, at least for systems containing dichoromethane. Comparisons of experimental activities and calculated solvent activities are shown in Figures 2 through 4. It is interesting to observe that results for the two copolymers are conformal to those of a polystyrene homopolymer when benzene and n-propyl acetate are solvents but are conformal to those of poly(methyl methacrylate) homopolymer when the solvent is dichloromethane.
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CONCLUSION Solvent activity at 323.15 K is reported as a function of solvent weight fraction for dichloromethane and n-propyl acetate in polystyrene and for benzene, dichloromethane, and n-propyl acetate in two poly(methyl methacrylate)/polystyrene copolymers. When supplemented with results for benzene + polystyrene1 and for benzene, dichloromethane and n-propyl acetate + poly(methyl methacrylate),3 a set of data for all three solvents in both homopolymers and two copolymers of different composition are now available. Solubilities of benzene and n-propyl acetate in the copolymers are similar to their solubilities in polystyrene, while those of dichloromethane in the copolymers are similar to its solubility in poly(methyl methacrylate).
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AUTHOR INFORMATION
Corresponding Author
*Author for correspondence E-mail:
[email protected]. ORCID
Venkat R. Bhethanabotla: 0000-0002-8279-0100 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to Suresh Narayan for synthesizing the PMMA/PS (49:51) copolymer used in this work.
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REFERENCES
(1) 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. (2) 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. (3) 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. (4) 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. (5) Bawn, C. E. H.; Wajid, M. A. High Polymer Solutions Part 7. − Vapour Pressure of Polystyrene Solutions in Acetone, Chloroform and Propyl Acetate. Trans. Faraday Soc. 1956, 52, 1658−1664. (6) Kang, S.; Huang, Y.; Fu, J.; Liu, H.; Hu, Y. Vapor-Liquid Equilibria of Several Copolymer + Solvent Systems. J. Chem. Eng. Data 2002, 47, 788−791. E
DOI: 10.1021/acs.jced.8b00094 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
