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Predicting Equilibrium Sorption of Neutral Organic Chemicals into Various Polymeric Sorbents with COSMO-RS Kai-Uwe Goss* Department of Analytical Environmental Chemistry, UFZ—Helmholtz Centre for Environmental Research, Permoserstrasse 15, D-04318 Leipzig, Germany, and Institute of Chemistry, University of Halle Wittenberg, Kurt Mothes Strasse 2, D-06120 Halle, Germany
bS Supporting Information ABSTRACT: There is an increasing use of polymers in analytical chemistry as sorbents for organic chemicals in sampling, cleanup, and chromatography. In order to find the optimal polymer for a given purpose, one needs to know the equilibrium partition constants of the chemicals of interest in a wide range of polymers. COSMOtherm, a quantum-chemically based software, is designed to predict such equilibrium partition constants based only on the molecular structure as input information. In this work, literature data for such equilibrium partition constants were collected for a wide range of different polymers and used to evaluate the performance of COSMOtherm. The results show good agreement between the predicted and experimental data from water and air for most of the tested polymers. The relative preference of analytes to sorb in a given polymer represented by the molecular structure of a monomer can be predicted without any calibration. If absolute values for the partition constants are required, then a few experimental values are needed to establish a log-linear regression between the model output and the experimental values. COSMOtherm appears to be a helpful tool for selecting the best sorbent polymer for a given task or for designing new polymers. The present evaluation is limited to chemicals with a rather simple structure. Further evaluation with complex chemicals that possess multiple functionalities is still warranted.
T
here are a multitude of applications where knowledge about the sorption equilibrium of organic chemicals between air or water, on the one hand, and polymers, on the other hand, is desired. Examples are the sorption of analytes from environmental samples into solid-phase extraction materials or passive samplers,13 the sorption of contaminants into polymer coatings of chemical sensors,4 the chromatographic separation of analytes, or the sorption of flavors into food packaging.5 Existing methods for predicting sorption into polymers are mostly empirical.6,7 Thus, these methods are limited to polymers whose sorption properties have been experimentally characterized and to sorbates from specific compound classes for which a calibration/ evaluation is available. An example of such an empirical method is the linear solvation energy relationship (LSER) approach by Abraham and co-workers.2,811 This method is very accurate and has a very wide applicability with respect to the sorbates, provided that a thorough calibration was done for the air/polymer or water/polymer system and experimentally determined descriptors are available for the sorbates. Unfortunately, both conditions are often not fulfilled. Also, like other empirical and semiempirical methods, the LSER approach requires a separate calibration for each polymer using a diverse and large experimentally determined data set. The COSMO-RS method, a combination of the quantum-chemical dielectric continuum solvation model (COSMO) with a statistical thermodynamics treatment of surface interactions (COSMO-RS), can provide sorption equilibrium data for any sorbate in any partition system that has a defined molecular structure. For partitioning into polymers, only r 2011 American Chemical Society
the molecular structure of the repeat units has to be known. With this information and some limited calibration, COSMO-RS should be able to predict the polymer partitioning of any neutral organic sorbate based on its molecular structure. Thus, this method potentially has a much wider applicability than other methods in the field. The goal of the current study is an evaluation of the COSMO-RS method, as implemented in the commercial COSMOtherm software, with respect to its ability to predict the partitioning of diverse sets of organic chemicals into various polymers.
’ METHOD For the selected sorbates, calculations were started with a search for low-energy conformations (performed with COSMOconf, version 2.1). This was followed by BP-TZVP gas-phase and COSMO calculations with the TURBOMOLE program (version 6.0, TURBOMOLE, a development of the University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 19892007, TURBOMOLE GmbH, since 2007 available from www.turbomole. com) for the complete set of conformations with full geometry optimization in the gas phase and in the conductor reference state (COSMO). This results in 3D images of the molecules with a color-coded surface, where the color represents the ability of the molecule to interact with its neighbors by electrostatic Received: March 23, 2011 Accepted: May 23, 2011 Published: June 13, 2011 5304
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Analytical Chemistry interactions. The gas-phase energies and COSMO files of the sorbates that resulted from the TURBOMOLE calculations were then used in the COSMOtherm software (version C21_0111, COSMOlogic GmbH & Co. KG, Leverkusen, Germany, 2010) for calculating the free energies of sorption at infinite dilution based on statistical thermodynamics. In contrast to the fundamental treatment of the electrostatic interactions, the also relevant van der Waals interactions are covered in a simple empirical approach by the software. For further details on the COSMO-RS theory, see refs 12 and 13. Note that polymer swelling at high sorbate concentrations cannot be taken into account by the software. This limitation is not relevant though when the polymers are used for analytical purposes, as is the focus here. The polymers were represented by molecular fragments (a monomer or an oligomer), which are shown in Figure 1. For the quantum-chemical calculations performed by TURBOMOLE, these truncated molecules were end-capped with a CH3 group. In the subsequent COSMOtherm calculations, these groups were disregarded. This was done by choosing appropriate weighting factors (see the COSMOtherm manual for details). COSMOtherm calculations treat the polymer as a liquid of monomer repeat units that can move independently from each other. Thus, only sorption to amorphous regions of a polymer that is above its glass transition temperature can be predicted. This is not a severe limitation: sorption into crystalline polymer regions is not expected to take place anyway, and sorption into glassy polymers is slow because of very small diffusion coefficients, so that for many practical purposes it is not relevant. Apart from the absorption process that is studied here, the surface or interface of crystalline, glassy, and rubbery polymers may serve as an adsorbent as well but was not further studied here because of the limited number of experimental data available for this specific process. There are various reasons why COSMO-RS as well as other predictive tools cannot predict absolute partition coefficients for the polymers: (a) Free-volume differences between polymers and liquids and between polymers of different densities cannot be assessed by the software. (b) For the calculations, it is assumed that the sorbing polymer lacks any crystalline or glassy regions. (If the actual polymer contains nonquantified crystalline or glassy regions but the experimental sorption coefficients were normalized to the total amount of polymer, then this will result in a systematic offset for all chemicals between the experimental and predicted results.) (c) The combinatorial term in the free energy of partitioning is not well-defined for the polymers. To adjust for all of these effects, the use of a calibrated log-linear regression between the predicted and experimental values for each individual polymer is necessary in order to receive good absolute predictions. Here such calibrated regressions are presented. The focus of the evaluation lies on the ability of COSMO-RS to correctly predict the relative partitioning of a diverse set of organic compounds into polymers with various structures and functional groups.
’ RESULTS AND DISCUSSION First tested was how sensitive the COSMOtherm predictions were to the molecular structures that were chosen to represent the polymers. It was found that correlation statistics [r2 and rootmean-square error (rmse)] between the predictions and the experimental values were hardly influenced by (a) different conformations of the monomers, (b) activation/deactivation of
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Figure 1. Molecular structure of the polymer structures used for COSMOtherm calculations.
the methyl end groups, (c) switching on or off of the combinatorial term, and (d) using one or several repeat units of the polymer. However, the predicted absolute results and thus the correlation parameters (slope and intercept) did depend on these factors. The respective 3D information for the molecular structures chosen here to present the studied polymers is provided by the author upon request. All calculations were done 5305
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Table 1. Statistical Comparison of Logarithmic Experimental Sorption Constants (K in L/kg) or Capacity Factors (Dimensionless) and COSMOtherm Predictions system
slope
atactic polypropylene/air at 100 °C
0.92 ( 0.01
PDMS/air at 25 °C PDMS/water at 25 °C
0.90 ( 0.02 0.81 ( 0.02
intercept
r2 0.93
0.20
43
0.92 ( 0.08 0.31 ( 0.07
0.94 0.95
0.52 0.44
128 146 106
rmse
n
poly(ethylene glycol)/air at 60 °C
1.18 ( 0.04
0.86
0.33
PDMS 5% with diphenylsiloxane/air at 60 °C
0.85 ( 0.02
0.93
0.16
106
PDMS with 65% diphenylsiloxane/air at 60 °C
0.89 ( 0.03
0.91
0.18
106
bis(cyanopropyl)siloxane þ 9:1 methylsilarylene/air at 60 °C
1.03 ( 0.02
0.94
0.19
106
50% poly[(cyanopropyl)phenyldimethylsiloxane]/air at 60 °C
0.98 ( 0.02
0.93
0.18
106
35% poly[(dimethylmethyl)trifluoropropylsiloxane]/air at 60 °C
0.65 ( 0.03
0.83
0.22
106
OV202/air at 25 °C SXCN/air at 25 °C
1.02 ( 0.06 0.94 ( 0.06
0.86 0.85
0.32 0.29
49 51
SXFA/air at 25 °C
0.51 ( 0.05
0.74
0.37
36
SXPYR/air at 25 °C
1.08 ( 0.07
0.87
0.27
38
ZDOL/air at 25 °C
0.86 ( 0.06
0.84
0.33
43
FPOL/air at 25 °C
0.95 ( 0.27
0.24
0.69
24
PMCPS/air at 25 °C
0.80 ( 0.7
1.42 ( 0.16
0.83
0.30
32
PMAPS/air at 25 °C
0.62 ( 0.09
1.60 ( 0.24
0.64
0.44
32
PMiPCAS/air at 25 °C CSVAL/air at 25 °C
0.85 ( 0.06 0.88 ( 0.07
1.12 ( 0.14 1.00 ( 0.18
0.87 0.83
0.24 0.35
32 32
cellulosestarch/water at 25 °C calcd as dry glucose
0.73 ( 0.03
1.30 ( 0.09
0.93
0.24
57
cellulosestarch/water at 25 °C calcd as glucose with 20% (w/w) water
1.02 ( 0.04
1.66 ( 0.11
0.93
0.24
57
polyurethane/air at 15 °C
1.08 ( 0.03
0.70 ( 0.12
0.91
0.46
101
polyurethane/air at 95 °C
1.01 ( 0.04
1.01 ( 0.09
0.86
0.34
89
poly(epichlorohydrin)/air at 80 °C
0.67 ( 0.06
0.86
0.15
25
poly(ɛ-caprolactone)/air at 80 °C
0.69 ( 0.06
0.84
0.14
25
with the combinatorial term switched off, as was recommended in the COSMOtherm manual. The results are presented in the following way: Table 1 contains the regression parameters for regression in the form of y = slope x þ intercept between the logarithmic experimental partition constant (y) and the COSMOtherm-predicted logarithmic partition constant (x). In some cases, the experimental values from the literature have been reported as gas chromatography (GC) retention capacity factors, which only provide a relative information; i.e., these values are proportional to the absolute partition constants. In these cases, only the slope and not the intercept (which would be meaningless) of the regression between the experimental values and the COSMOtherm predictions is reported in Table 1. Table 1 further contains r2 of the regression, the number of experimental data, n, and the rmse from a comparison of the experimental values with those calculated from the regression model using the COSMOtherm predictions as x values. Tables with all numerical values as well as graphics are provided in the Supporting Information for all polymers. For chemicals that may ionize in water (e.g., phenols), predictions were always performed for the neutral species. Hydrocarbon Polymers. Sorption into hydrocarbon polymers without any functional groups like polyethylene and polypropylene can be expected to be similar to sorption into the liquid phases of larger alkanes such as hexadecane. The experimental data in ref 14 indeed show partitioning into various alkane phases (C28, C32, and C36) and hydrocarbon polymers with different branching to be very similar. The remaining
systematic differences between the absolute values for various polymers are likely due to different densities, resulting in different free volumes.6 Here, the experimental data for sorption in atactic polypropylene14 were chosen for comparison with COSMOtherm predictions using hexadecane as the polymer surrogate. The results show a very good agreement with rmse of only 0.2 log units (Table 1 and the Supporting Information). Poly(dimethylsiloxane) (PDMS). PDMS is another rather nonpolar phase besides the hydrocarbon polymers. The existing large experimental data collections8,15 allow validation of the PDMS/air and PDMS/water partitioning systems (see Figure 2 for the PDMS/water results). The overall statistics for the prediction of PDMS partitioning are very good, with no clear difference between the PDMS/air and PDMS/water systems (Table 1). The experimental values had been measured at pH 3,16 so that one can exclude any influence of ionic phenol species on the measured partitioning. Checking the surface potential of the PDMS molecule that was used in COSMOtherm and that resulted from TURBOMOLE calculations revealed a significant negative surface charge connected to the oxygen atoms, which makes it attractive for hydrogen-bond donors such as the phenols. The LSER that was used in the work by Sprunger et al.8 to evaluate the same experimental data set supports the existence of such a significant hydrogen-bond acceptor function. Thus, COSMOtherm correctly predicts the polarity difference between PDMS and an alkane phase. Stationary Phases in GC. The following polymers, which are representative of the diversity of commercially available stationary phases in GC, were used for validation (all data from ref 17; 5306
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Analytical Chemistry
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Figure 2. Experimental versus predicted partition coefficients exemplarily shown for the two largest data sets: PDMS/water (left) and polyurethane/air partitioning (right).
molecular structures are shown in Figure 1): PDMS with 5% diphenylsiloxane (DB-5), PDMS with 65% diphenylsiloxane (Rtx-65), 9:1 bis(cyanopropyl)siloxane þ methylsilarylene/air 60 °C (HP-88), 50% poly[(cyanopropyl)phenyldimethylsiloxane] (DB-225), 35% poly[(dimethylmethyl)trifluoropropylsiloxane] (DB-200), and poly(ethylene glycol). In general, there was a very good correlation between the predicted and experimental values at 60 °C. The rmse lies in the range of 0.20.3 log units, which is, in fact, lower than what is typical for simple solvent systems. This might be due to the experimental data set that is biased toward simple analytes without any complex structures. Sensor Polymers. The following polymers that are of potential interest as sensor coatings have been characterized for their sorption behavior:9,10 poly[bis(cyanopropyl)siloxane] (SXCN), poly(oxy[methyl(4-hydroxy-4,4-bis(trifluoromethyl)but-1-en1-yl)silylene]) (SXFA), poly(oxy[methyl(3,3,3-trifluoroprop-1yl)silylene]) (OV-202), poly(oxy[methyl(3-(N-methyl-N-4pyridylamino)propyl)silylene]) (SXPYR), ZDOL, FPOL, poly[methyl(2-carboxy(D-valinyl-tert-butylamide)propyl)siloxane] (CSVAL), poly[methyl(aminopropyl)siloxane] (PMAPS), poly[methyl(cyanopropyl)siloxane] (CMCPS), and poly[methyl(isopropylcarboxylic acid)siloxane] (PMiPCAS). The molecular structures are shown in Figure 1. For most of these polymers, a good correlation between the predicted and experimental sorption values was found (see Table 1 and the Supporting Information). For two of them, PMAPS and FPOL, however, the agreement was worse than average. For PMAPS, the sorption of hydrogen-bond-donor compounds (i.e., the alcohols) was strongly overestimated by COSMOtherm because the prediction considers the amine group in PMAPS to be a strong hydrogenbond acceptor, which is plausible. The experimental data suggest though that PMAPS is an even weaker hydrogen-bond acceptor than CSVAL.10 Judging from the molecular structures reported in the literature (see Figure 1), this seems very unrealistic considering the electron-withdrawing influence that the carbonyl oxygen in CSVAL has. A possible explanation would be protonation of the amine group in PMAPS, which would then reduce its hydrogen-bond-acceptor ability. In contact with water, one would certainly expect that CSVAL should be protonated because pKb values of primary amines generally are on the order of 56. The experiments had been conducted in dry air, but it seems likely that the polymer had the opportunity to become
protonated during handling prior to the experiments. For the polymer FPOL, the hydrogen-bond-acceptor compounds such as ketones or nitro compounds are underestimated by the COSMOtherm calculations. It is not clear whether this is also due to a misrepresentation of the actual polymer by the molecular structure reported in the original work or just an inferior performance of COSMOtherm. The polymer ZDOL is reported to have a molecular weight of 2000.9 This defines the concentration of the end-standing hydroxyl groups in the polymer. The COSMOtherm calculations were found to be sensitive to this information. The correct concentration of OH groups was represented by the mixing of monomers with and without OH groups in the appropriate proportion. Cellulose/Starch Swollen with Water. Hung et al.18 found no significant difference between the cellulose/water and starch/ water partition experiments. Similarly, COSMOtherm calculations for cellubiose and D-glucose were almost identical. Here the results of COSMOtherm calculations for D-glucose are compared with the combined experimental values for cellulose and starch. From the experimental results, two outliers (diethyl phthalate and dibutyl phthalate) were excluded. Their experimental values deviated by more than 1 log unit from the predicted values. In fact, these data are also not internally consistent within the experimental data set. If the experimental value for dimethyl phthalate is assumed to be correct and used as a starting point, then one can receive extrapolated values for diethyl phthalate and dibutyl phthalate by using CH2 increments taken from the experimental data for alkylbenzenes. These extrapolated values for the phthalates are very close to the COSMOtherm predictions. Hence, the reported values for diethyl phthalate and dibutyl phthalate were discarded as experimental artifacts. For the remaining values, a very good correlation between the predictions and experimental values is found. The predictions using dry glucose or glucose with 20% (w/w) water as the sorbing phase show the same goodness of fit only differing in the regression parameters. Interestingly, the inclusion of water in the calculations not only is a more realistic representation of the experimental conditions but also brings the slope much closer to the theoretical value of unity. Polyurethane (Polyether). The urethane unit within the polyurethane structure exhibits an hydrogen-bond-donor function. However, the experimental sorption data for polyurethane reveal no hydrogen-bond-donor function for the polymer at all 5307
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Analytical Chemistry when evaluated with an LSER model.2 This indicates that the hydrogen-bond-donor function in the polymer is completely occupied by internal hydrogen bonding. It was interesting to see whether COSMOtherm predictions would reproduce this behavior correctly. For 15 and 95 °C, a good correlation between the experimental and predicted polyurethane/air partitioning data was found (Table 1 and Figure 2). Strong hydrogen-bondacceptor molecules like 1,4-dioxane, dimethyl phthalate, and others did not show a pronounced deviation. Poly(epichlorohydrin) and Poly(E-caproplactone) at 80 °C. These two polymers differ considerably in their molecular structure from the other polymers tested. The agreement between the experimental and predicted partitioning is very good. However, the slope of the regression line is much smaller than the theoretical value of unity. The results for all tested polymers can be summarized as follows: for most polymers, a very good agreement between the experimental and predicted partition constants was observed (rmse between
