Prediction of the Solubility of Chloroform in Acrylate Polymer Mixtures

In this paper, the presence of hydrogen bonding in chloroform-acrylate polymer mixtures was demonstrated by observation of 1H and 13C NMR chemical shi...
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J. Phys. Chem. B 2001, 105, 3143-3149

3143

Prediction of the Solubility of Chloroform in Acrylate Polymer Mixtures with Inclusion of the Hydrogen-bonding Effect Bao-guo Wang,† Takeo Yamaguchi,* and Shin-ichi Nakao Department of Chemical System Engineering, UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan ReceiVed: September 16, 2000; In Final Form: February 5, 2001

In this paper, the presence of hydrogen bonding in chloroform-acrylate polymer mixtures was demonstrated by observation of 1H and 13C NMR chemical shifts. Comparison of the NMR chemical shifts in polymer solutions with their low molecular weight analogues showed the effect of steric hindrance on hydrogen bonding. Using the data obtained by NMR analysis, this work correlates the proton chemical shift with the fraction of associated hydrogen in chloroform, which is related to the polymer steric hindrance effect on molecular association. A lattice-fluid hydrogen bonding and equation of state (LFHB-EOS) model enables correct prediction of chloroform solubility in poly(acrylate)s due to the inclusion of hydrogen bonding and its equation of state nature. This initial investigation is helpful for understanding intermolecular interaction for relatively weak hydrogen-bonded polymer solutions.

Introduction Hydrogen bonding in polymer solutions has attracted particular attention in recent years because of its importance in the understanding of intermolecular interactions, which often affect physical properties in polymer mixtures.1-5 Studies have indicated that hydrogen bonding affects phase equilibrium behavior;6 e.g., chloroform shows abnormal thermodynamic properties in its vapor pressure, as well as in the heat and volumes of mixing with poly(propylene glycol dimethyl ether).7,8 Moreover, it also reduces molecular mobility in polymer systems.9 Using the hydrogen-bonding interaction, well-known as a general interaction force second in strength to the chemical bond, many promising materials have been developed, such as liquid crystalline polymers10,11 and miscible polymer blends,12,13 with modern analysis techniques playing an important role in these processes. In particular, based on the results obtained with Fourier transform infrared (FT-IR) spectroscopy of hydrogen bond formation and rupture, a thermodynamic theory has been developed for association polymer blends14-16 that has permitted good predictions for association blending behavior. The hydrogenbonding interaction, unlike ordinary van der Waals interactions, has a stronger interaction and a much longer lifetime, with the hydrogen-bonding energy spanning the range from -5 to approximately -155 kJ/mol. For this reason, FT-IR analysis suffers from a limitation for strong hydrogen-bonding situations such as polymer blends including hydroxyl groups. FT-IR spectra only show a small shift or a small change in peak shape for some weak hydrogen-bonding systems, thus resulting in a practical difficulty in obtaining the equilibrium constant. Nevertheless, an analogous method is expected to be usable for a polymer solution with relatively weak hydrogen bonds. The nuclear magnetic resonance (NMR) technique provides a good alternative for quantitatively measuring hydrogen bonding because of its high sensitivity. * Fax: +81-3-5841-7227. E-mail: [email protected]. † Present address Department of Chemical Engineering, Tsinghua University, Beijing, 100084, The People’s Republic of China.

In general, three theoretical approaches have been proposed to describe association solution thermodynamics: chemical, quasi-chemical, and perturbation.17 The lattice-fluid hydrogen bond (LFHB) model was recently derived in such a way that hydrogen bonding was introduced into the formalism of the original lattice-fluid theory,8,18 using an equation of state (EOS). The hydrogen-bonding contribution to the free energy can be calculated by counting the hydrogen bond arrangements and their energy in a given system. This theory has been successfully applied to predict phase behavior of organics, polymer blends, and mixtures of solvent and polymers.3,18,19 Formation of hydrogen bonding in a polymer solution is generally affected by the following factors:16 steric hindrance, decrease in rotational freedom, and the entropy change on hydrogen-bond formation. In particular, polymer chain connectivity might reduce the accessibility of a functional group in a polymer relative to its low molecular weight analogue. For this reason, a parameter is included in the LFHB-EOS model, expressing the steric hindrance effect. So far, no way has been reported to determine this parameter, except for fitting from vapor-liquid equilibrium data. Chloroform is a commonly used solvent in industrial processes, also infamous as an environmental pollutant. To remove chlorinated compounds from emissions, a pore-filling membrane was developed in our previous study, and it showed an excellent separation performance.20,21 Prediction of solubility and diffusivity has fundamental significance in developing a membrane design method, which helps to develop quality separation materials for removal of volatile organic compounds.22 Chloroform can associate with low molecular weight proton acceptor solvents, and NMR spectra show a downfield shift as apparent proof of hydrogen bonding.23 However, to our knowledge, no direct evidence has been published to demonstrate hydrogen bonding in chloroform with polymers: a representative of weak hydrogen-bonding systems. In this study, 1H and 13C NMR were employed to confirm the presence of hydrogen bonding in chloroform-acrylate polymer mixtures and to compare the chemical shifts with those

10.1021/jp003313p CCC: $20.00 © 2001 American Chemical Society Published on Web 03/23/2001

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from acetates. Using the results of NMR spectra, the proton chemical shift was correlated with the fraction of associated hydrogen in chloroform, calculated with the LFHB-EOS model, a parameter related to the steric hindrance effect was determined and adopted to predict chloroform solubility in poly(acrylate)s. Finally, various models, UNIFAC-FV,24 GCLF-EOS,25 and LF-EOS,26 were separately employed to calculate tetrachloromethane solubility to compare a mixture without hydrogen bonding with that of associated solutions. Theory The lattice-fluid hydrogen bonding and equation of state (LFHB-EOS) model is a useful tool to calculate polymer solution behavior including the hydrogen-bonding effect. This model introduces an association term into lattice-fluid theory,8,26 by assuming that the canonical partition function is separable into two terms: physical (van der Waals) and chemical (hydrogen-bonding) interaction. The LFHB-EOS model determines the fraction of associated groups on the basis of the total number of lattice sites, excluding the contribution from empty sites. The total fraction νHB of hydrogen-bonded pairs in the mixture can be expressed as

νHB ) Σνij rN )

νij ) Nij/rN

(1)

∑k rkNk ) N∑k rkxk

(2)

Here, N and Nij are the total number of molecules and the number of hydrogen-bonded pairs in the mixture, respectively. r is the average segment length of a molecule. With an equation of state, the characteristic quantities of reduced pressure, temperature, and density P ˜ , T˜ , F˜ are related to the average segment length r and the fraction νij of hydrogen bonds formed in the mixture:

{

[ (

˜ + T˜ ln(1 - F˜ ) + F˜ 1 F˜ + P 2

1

m

-

r

n

∑i ∑j νij

)]}

) 0 (3)

Solvent activity can be expressed by the following formula for a polymer solution without self-association:

+ ln aHB ) ln aLF ln apure 1 1 1 physical chemical

( )

ln aLF 1 ) ln φ1 + 1 r1

[

r1 φ + r1F˜ φ22X12 + r2 2

P ˜ 1(ν˜ - ν˜ 1) - (F˜ - F˜ 1) T˜ 1 m

ln

aHB 1

) r1

n

(4)

(ν˜ -1)

+ ln

(1 - F˜ )

(1 - F˜ 1)

(ν˜ 1-1)

νid

n

m

∑i ∑j νij - ∑i

d1i

ln

νi0

-

∑j

]

a1j

Figure 1. Hydrogen-bonding structure between chloroform and poly(acrylate)s.

poly(acrylate)s have a common electronegative functional group, -COO-, in their side chain, as proton acceptor. Hydrogen bonding may occur between the carbonyl or the ester group and the hydrogen atom of chloroform as shown in Figure 1, whereas no self-association can occur among chloroform molecules, nor among the polymers. The total number of donors is the sum of chloroform molecules, N1, and the total number of acceptors is 2aN2, the parameter a is the number of crossassociation sites. With the help of the equation of state, this study calculates the fraction of hydrogen bonding pairs involving hydrogen-carbonyl, V11, and hydrogen-ester, V12, by the following equations:

rν11 ) (1/2){(x1 + ax2 + A11 - rν12) [(x1 + ax2 + A11 - rν12)2 - 4ax2(x1 - rν12)]1/2} (7) rν12 ) (1/2){(x1 + ax2 + A12 - rν11) [(x1 + ax2 + A12 - rν11)2 - 4ax2(x1 - rν11)]1/2} (8) x1 and x2 are the mole fraction of solvent and polymer, respectively. A1j is defined in the following formula:

( )

0 G1j A1j ) rν˜ exp RT

G0ij ) E0ij + PV0ij - TS0ij

F˜ (5) F˜ 1

νia ln ν0j

(6)

Here dki is the number of donor groups of type i and aki is the number of acceptor groups of type j in each molecule of type k. These parameters are related to the polymer configuration, reflecting the steric hindrance effect on hydrogen bonding. The subscript 1 represents solvent and 2 represents polymer, φ denotes the volume fraction. For formation of a hydrogen bond, a mixture is required containing a proton donor and an acceptor. In this case, chloroform provides the hydrogen atom as proton donor, and

i ) 1, j ) 1,2

(9) (10)

To compare the results with conventional chemical equilibrium theory, this study redefined the fraction of hydrogenbonded pairs based on the amount of acceptor or donor in a component. For instance, in the case of chloroform and poly(acrylate) mixtures, the ratio of associated hydrogen to the amount of hydrogen in chloroform is written as

fHB ) + ln

j ) 1, 2

NHB r1νHB ) N1 1 - (r2/r)x2

νHB ) ν11 + ν12 (11)

NHB and N1 are the number of hydrogen-bonded hydrogen and the total number of hydrogens in chloroform, respectively. In NMR measurements, the change of the chemical shift represents intermolecular interaction, which is proportional to the fraction of hydrogen-bonded protons in chloroform molecules. For both low molecular weight solvent mixture and polymer solution, the given proton chemical shift corresponds to the same amount of associated hydrogen in chloroform. Therefore, we can correlate the NMR results with the fraction of associated hydrogen and investigate the polymer steric hindrance effect on forming hydrogen bonds by comparing with the analogous solvent mixture. In calculating solubility for the poly(acrylate) solutions studied, the following parameters were needed: two sets of hydrogen-bonding parameters corresponding to each of the

Chloroform Solubility in Acrylate Polymers

J. Phys. Chem. B, Vol. 105, No. 15, 2001 3145

TABLE 1: Molecular Parameters of Lattice-Fluid Theorya component chloroformb tetrachloromethanec methyl acetate ethyl acetated poly(methyl acrylate) poly(n-butyl acrylate) poly(lauryl acrylate)

P* (MPa)

T* (K)

F* (kg/m3)

476 381 450 452 493.3 404.3 167.0

499 535 459 468 593.9 570.9 509.7

1709 1790 1012 1052 1263.3 1123.4 750.2

a Values were calculated based on the group-contribution method,28 unless otherwise noted. b Reference 18. c Reference 26. d Reference 27.

associations, and molecular characteristic parameters in latticefluid theory. The number of cross-association sites related to the steric hindrance effect can be determined by correlating the 1H NMR chemical shift with the calculated fraction of associated hydrogen in chloroform. With the help of vapor-liquid equilibrium data of chloroform and acetate solutions, this work determined the parameters for the hydrogen-carbonyl and hydrogen-ester pairs by calculating the vapor pressure using the LFHB-EOS model. At present, sixty sets of solvent parameters, involving characteristic pressure P*, temperature T* and density F* of a closed-packed compound for lattice-fluid theory are known,27 and corresponding parameters for polymers can be estimated with a recently developed group-contribution method.28 Table 1 lists the lattice-fluid characteristic parameters of the pure components. Experimental Section Materials. Chloroform and ethyl acetate (EA) were purchased from Wako Pure Chemical Ind., methyl acetate (MA) and propyl acetate (PA) were provided by Aldrich Chemical Co., and used without further purification. Pure polymer samples used were poly(methyl acrylate) (PMA), poly(n-butyl acrylate) (PBA), and poly(lauryl acrylate) (PLA), purchased from Scientific Polymer Products, Inc. The molecular weights (MW) of PMA, PBA, and PLA were 30 700, 100 000, and 50 000, respectively. Chloroform Vapor Sorption. Sorption experiments were performed with various chloroform vapor pressures, and the polymer sample was kept at 25 °C. Beforehand, polymer samples were dried in a vacuum-dryer at 50 °C for 24 h, and the chloroform was degassed by the freeze and thaw method as previously described.29 NMR Measurements. The polymers were vacuum-dried at 50 °C for more than 5 days to completely remove toluene used as a preservation solvent; no toluene resonance appeared in the NMR spectra. A Mercury 300 NMR made by Varian Co. was used in this work. A double-tube method was employed to measure the 1H and 13C NMR chemical shifts of chloroform in poly(acrylate)s. A sample of chloroform-poly(acrylate) mixture was placed in the outer tube. An inner tube with dimethyl sulfoxide-d (DMSO-d), used to lock the magnetic field, was immersed in the sample solution. Tetramethylsilane (TMS) was used as a standard. Chloroform has a characteristic peak at 7.26 ppm for 1H and 77.2 ppm for 13C NMR spectra. The chemical shift of chloroform was measured with various polymer compositions from 4-20% (wt) to investigate molecular association at ambient temperature. For comparison with low molecular weight analogues, mixtures of chloroform and acetates with various compositions were also measured. Using the following expression, this study determined the acceptor concentration in the mixture:

c)

2dwp MW

(12)

Figure 2. Variation of 1H NMR chemical shift with acceptor concentration in chloroform solution.

Here, wp is the polymer weight in 1 mL of sample mixture, and d indicates the number of repeat units in a polymer molecule, each unit has two acceptors. The value of d is 1 for a solvent. Results and Discussion Evidence of Hydrogen Bonding in Chloroform-Acrylate Polymer Mixtures. This study used chloroform as a probe molecule to examine the hydrogen-bonding interaction between low molecular weight solvents and poly(acrylate)s. The hydrogen atom of chloroform interacts with oxygen atoms in a functional group, -COO-, in two ways: hydrogen-ester and hydrogen-carbonyl. They are clearly distinguished in our calculation, each hydrogen bond has specific interaction energies30 and equilibrium constants, and the observed chemical shift of chloroform in the NMR spectra includes the two combined effects. As can be seen in Figure 2, the change in the proton NMR chemical shift increases almost linearly with acceptor concentration, all data obtained in chloroform and acetate mixtures almost lie on a straight line, as do those of the polymer solutions. The 1H NMR shift for the low molecular weight analogue mixtures is bigger than that in polymer solutions. Figure 3 illustrates a similar tendency with the 13C NMR results; a bigger shift in scale than that for proton NMR permits us to compare the chemical shifts for various polymer solutions in detail. The downfield chemical shift, a characteristic phenomenon for hydrogen bonding,30 confirms the presence of hydrogen bonding in chloroform-acrylate polymer mixtures. Because this study employs a double-tube method for measurement, disturbance from DMSO-d used to lock the magnetic field is completely avoided, chloroform only interacts with poly(acrylate)s. Certainly, physical interaction (van der Waals) exists in the mixtures as a universal intermolecular force, weaker than hydrogen bonding, and generally causes no obvious chemical shift in NMR spectra in this case. Therefore, the proton chemical shift of chloroform in the NMR spectra demonstrates the change of the hydrogen atom state, due to the influence from poly(acrylate)s with the hydrogen-bonding interaction. Only one structure of hydrogen bond for chloroform -C-H...B: appears in the mixtures studied, thus producing a chemical shift in the

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Wang et al. TABLE 2: Hydrogen-Bonding Interaction Parameters donor (i) acceptor (j) Eij0 (kJ/mol) Sij0 [J/(mol.K)] Vij0 (cm3/mol) C-H C-H

CdO -O-

-8.12 -4.92

-10.45 -9.74

-0.85 -0.85

Figure 3. Variation of 13C NMR chemical shift with acceptor concentration in chloroform solution.

proton NMR that is parallel to the changes in the carbon NMR. This behavior has been published for chloroform NMR chemical shifts measured in a variety of solvents.23 Because of the steric hindrance effect on formation of hydrogen bonding in a polymer solution, the chemical shift in the studied polymer solutions is smaller than that of chloroform in acetates, although they have the same acceptor concentration for hydrogen bonding. The length of the side chain in the three poly(acrylate)s is different, the number of -CH2- groups is 0, 3, and 11 in PMA, PBA, and PLA, respectively. This measurement was performed in a dilute polymer solution where each of the polymer molecules is surrounded by a large number of chloroform molecules, thus no significant difference in NMR chemical shift is observed for various polymers. However, such a difference might be expected in corresponding concentrated polymer solutions. Prediction of Phase Equilibrium in Low Molecular Weight Mixtures. The LFHB-EOS model was originally developed to describe phase behavior of low molecular weight solvent mixtures; the number of donors or acceptors in a molecule can be clearly counted, and the steric hindrance effect is generally negligible. For this reason, the hydrogen-bonding parameters Eij0, Vij0, and Sij0 in the LFHB-EOS model are the only adjustable variables, and vapor-liquid equilibrium data can help to determine these parameters by the least-squares method. Once these parameters are determined, they can be used as constant parameters both in low molecular weight compounds and in polymer systems, based on the consideration of group contributions. The studied chloroform-poly(acrylate) systems contain two kinds of hydrogen-bonding pairs: hydrogen-ester and hydrogencarbonyl. Hydrogen-bonding parameters for the former have been published and successfully used in the chloroform-poly(ethylene oxide) system,18 whereas those for the latter are not available. This work determines them by fitting phase equilibrium data of chloroform-ethyl acetate with the LFHB-EOS model and reexamines the hydrogen-ester hydrogen-bonding parameters using chloroform-acetone vapor pressure data. Table 2 shows the parameters obtained in this work. Figure 4 illustrates the comparison of the calculated results of the chloroformethyl acetate mixture with published experiments, and good

Figure 4. Determination of hydrogen-bonding parameter for hydrogencarbonyl pair by fitting VLE data of chloroform-ethyl acetate mixture.

Figure 5. Confirmation of hydrogen-bonding parameter by comparing predicted results with VLE data of chloroform-methyl acetate mixture.

agreement is shown. To confirm the validity of these parameters, methyl acetate was also employed as a model compound; prediction from the LFHB-EOS model is plotted in Figure 5. These common parameters represent the nature of hydrogen bonding, and predicted results are generally consistent with the measured results. In addition, other studied solvent mixtures of acetone and methyl ethyl ketone in chloroform show the same result. Therefore, the group-contribution method can be regarded as a valuable way to deal with hydrogen-bonding systems, both low molecular weight solvent and polymer can use the same parameters for an association pair. To elucidate the effect of hydrogen bonding on phase behavior, calculations from the LF-EOS model without including the hydrogen-bonding term are also plotted in Figures 4 and 5; predictions obviously underestimate the experimental results. This can be attributed to ignoring the hydrogen-bonding effect. Hydrogen bonding increases the intermolecular interaction, and

Chloroform Solubility in Acrylate Polymers

Figure 6. Correlation of the fraction of associated hydrogen in chloroform, obtained by the LFHB-EOS model, with proton NMR chemical shift measured at ambient temperature.

chloroform solubility increases as a result. Some previous research has also demonstrated the same tendency.6,31,32 Correlation of Hydrogen Bonding with NMR Measurements. In a low molecular weight solvent mixture, all molecules can obtain enough space to form and break hydrogen bonds, and no steric hindrance effect is found. Therefore, the number of cross-association sites is the total of hydrogen atoms in chloroform, and all parameters in the LFHB-EOS model are available. The fraction of associated hydrogen in chloroform, as defined in eq 11, can be calculated corresponding to a fixed chloroform composition. As can be seen in Figure 6, the 1H NMR chemical shift linearly increases with the fraction of associated hydrogen, for chloroform in both methyl acetate and ethyl acetate mixtures. When the LFHB-EOS model is used to calculate chloroform solubility in poly(acrylate)s, the polymer steric hindrance effect gives rise to difficulty in determining the number of cross-association sites. This work employed NMR analysis to observe the proton chemical shift in chloroform molecules, the value of the 1H NMR chemical shift represents the amount of associated hydrogen atoms. For this reason, we can reasonably assume that the polymer mixture has the same relationship of proton chemical shift and the fraction of associated hydrogen as that for low molecular weight analogues. In this case, using the relationship obtained from chloroform in acetates, the fraction of associated hydrogen in a poly(acrylate) solution can be calculated from the corresponding proton NMR chemical shift. Figure 6 illustrates the relationship of 1H NMR chemical shift and the fraction of associated hydrogen, for chloroform in both acetates and poly(acrylate)s, all data almost lie on a straight line through the origin. This work correlates the results of NMR measurements with the cross-association parameter in the LFHB-EOS model, which is related to the polymer steric hindrance effect on hydrogen bonding. The cross-association parameter is used to replace the adjustable entropy parameter in polymer systems, thus the identical hydrogen-bonding parameters Eij0, Vij0, and Sij0 remain available both in low molecular weight compounds and in polymer solutions. Therefore, all parameters of the LFHB-EOS model for a polymer solution are obtained and this model permits the calculation of chloroform solubility in poly(acrylate)s.

J. Phys. Chem. B, Vol. 105, No. 15, 2001 3147 Calculation of Solubility of Chloroform in Poly(acrylate)s. Using the LFHB-EOS model, this study calculated chloroform solubility in poly(acrylate)s, and the results are plotted in Figure 7. With the increase in chloroform activity, chloroform solubility in PMA increases gradually, the predicted results agree well with measurements, as shown in Figure 7a, this is attributed to the correct estimation of hydrogen bonding in the calculation. Figure 7b illustrates that chloroform solubility measured in the PBA mixture approximately agrees with that calculated from the LFHB-EOS model, even though a small underestimation exists at low concentration. Prediction of chloroform solubility in PLA gives an exception for this work, as shown in Figure 7c; the calculated results obviously underestimate the experimental data, although the hydrogen-bonding effect has been included in the model. From the comparison of calculated results of the LFHB-EOS model with experiment, Figure 7 illustrates that predicted accuracy decreases with polymer side-chain length. PMA has the shortest side-chain among the three polymers studied and the model provides the best prediction. By contrast, the sidechain length of PLA is the longest; calculation for the PLAchloroform mixture obviously deviates from the measurements. Before the solubility of solvent in polymer with the LFHBEOS model is calculated, an equation of state first needs to be resolved, and the calculated solubility includes the effect of the polymer P-V-T relationship on phase equilibrium. In this study, the lattice-fluid parameters for the polymer, used in solving the equation of state, were obtained with a groupcontribution method, for lack of reliable P-V-T data to determine these parameters. For this reason, an error in the lattice-fluid parameters may cause failure in the solubility calculation, such as for PLA with its long side-chain. Furthermore, this study investigates tetrachloromethane solubility in PBA to demonstrate the applicability of the LFHBEOS model to a system containing no hydrogen bonding. In this mixture, tetrachloromethane has no hydrogen atom, which is an essential condition as proton donor to associate with the -COO- group in PBA; no molecular association occurs, and physical (van der Waals) interaction dominates the polymer solution phase equilibrium. As a result, the hydrogen-bonding term in the LFHB-EOS model loses its meaning; only the latticefluid term remains in the expression, called the LF-EOS model. Owing to its fundamental statistical thermodynamic basis, predictions from the LF-EOS model are in good agreement with experimental results. As a comparison of the LF-EOS model with the general theory, calculations from the GCLF-EOS and UNIFAC-FV models, which are suitable for describing polymer solution phase behavior without molecular association, are also plotted in Figure 8, and show acceptable accuracy. The LFHBEOS model covers a wider range of polymer solution phase behavior, including not only the ordinary situation but also molecular association mixtures. This study provides a method to determine the parameters in the LFHB-EOS model, thus making it more useful in application. Conclusions Using 1H and 13C NMR measurements, this study has demonstrated the presence of hydrogen bonding in chloroformacrylate polymer mixtures, and shown the effect of steric hindrance on hydrogen bonding, by quantitatively comparing the NMR chemical shift in polymer solutions with their low molecular weight analogues. This study also investigated the relationship of NMR chemical shift and the fraction of associated hydrogen and correlated these data with the help of low

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Figure 8. Solubility of tetrachloromethane in poly(n-butyl acrylate) and comparison of the predictions of various models with experimental data.

molecular weight analogue results. In this way, the parameter in the LFHB-EOS model related to the effect of steric hindrance on hydrogen bonding was determined and employed to successfully predict chloroform solubility in acrylate polymers. Vapor-liquid equilibrium data of low molecular weight solvent mixtures were used to determine hydrogen-bonding parameters, and these parameters are transferable to polymer solutions according to the concept of group contributions. Acknowledgment. We thank Dr. Minori Hayashi for his help in NMR measurements and also Japan Science and Technology Corp. (JST) and Research Institute of Innovative Technology for the Earth (RITE) for providing financial support. References and Notes

Figure 7. (a) Prediction of chloroform solubility in poly(methyl acrylate) from the LFHB-EOS model. The fraction of associated hydrogen in chloroform was determined by NMR chemical shift data. (b) Prediction of chloroform solubility in poly(n-butyl acrylate) from the LFHB-EOS model. The fraction of associated hydrogen in chloroform was determined by NMR chemical shift data. (c) Prediction of chloroform solubility in poly(lauryl acrylate) from the LFHB-EOS model. The fraction of associated hydrogen in chloroform was determined by NMR chemical shift data.

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