Intermolecular Interactions as Controlling Factor for Water Sorption

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J. Phys. Chem. B 2007, 111, 8868-8878

Intermolecular Interactions as Controlling Factor for Water Sorption into Polymer Membranes A. Gugliuzza,*,† G. De Luca,† E. Tocci,† L. De Lorenzo,†,‡ and E. Drioli†,‡ Research Institute on Membrane Technology (ITM-CNR), Via Pietro Bucci, Cubo 17/C, I-87030 Rende (CS), Italy, and Department of Chemical Engineering and Materials, UniVersity of Calabria,Via Pietro Bucci 17/C, I-87030 Rende, Italy ReceiVed: March 5, 2007; In Final Form: May 16, 2007

A multidisciplinary approach was used for delineating the mechanisms controlling water sorption into modified block co-poly-(ether/amide) (PEBAX) membranes. In particular, incorporation of aromatic sulfonamide (KET) into the polymer matrix led to a nonlinear increase of water sorption in the membrane. The modification in sorption was accompanied by a nonlinear behavior in membrane surface energies. Infrared analysis revealed a different availability and accessibility of free polar groups supporting the formation of hydrogen bonding as a function of modifier concentration. A combination of both experimental and theoretical procedures was used to analyze the molecular processes of water sorption on PEBAX membranes. Molecular dynamics (MD) and quantum chemical (QC) calculations demonstrated that the formation of KET-KET dimers in the polymeric matrix led to a decrease in the interaction energy between water and modifiers. In addition, no variations in the dipole moments of water-dimer structures were found in comparison to a single KET and water-KET molecule. The formation of water-dimer complexes at higher concentration of modifier decreases the number of the dipole moment, thus preventing the polarization of polymer chains.

1. Introduction Functional membranes exhibiting perm-selective properties represent an important target for membrane technology.1 In recent decades, the introduction of pendant groups in the polymer chains allowed improved membrane separation features with respect to those of unmodified analogs.2 Indeed, changes in polymer chemistry or packing density are primarily responsible for modified membrane performances because of their enhanced diffusivity or solubility selectivity.3 Another outstanding approach used for tailoring membranes with controlled performance is to mix raw polymers with specific functional molecules.4 Flexible membranes obtained from the same polymer were easily yielded according to the specific applications.5,6 Recently, the changes in the affinity of the membranes to a particular molecule were demonstrated to be successful in the perm-selective process because of controlling interactions at the membrane-feed interface.7 This means that the affinity between membrane and permeating molecules can be directed by selecting for chemical moieties favoring selective intermolecular interactions.7 However, identifying the kind and optimal ratio of the chemical functionalities to be incorporated into the membranes is not an easy task. A deepened understanding of the phenomena, which govern interaction processes between membrane and molecules to be separated, could facilitate the selection of the materials on the basis of structural models. This means that a macroscopic phenomenon should also be interpreted at the molecular level to identify chemical groups, such as charges involved in * To whom correspondence should be addressed. Tel: +39 (0984) 492026. Fax: +39 (0984) 402103. E-mail: [email protected]; homepage: www.itm.cnr.it. † Research Institute on Membrane Technology. ‡ University of Calabria.

competitive molecular interactions. This approach evaluates the local molecular geometries and correlated properties in the embedding chemical environment.8 In this work, the membranes were based on a block co-poly(ether/amide) [80PTMO/PA12, PEBAX2533] functionalized by the N-ethyl-o/p-toluensulfonamide (KET) modifier, (Scheme 1). The latter was blended with the polymer at different concentrations, and dense membranes were formed. Contact angle measurements were performed to estimate the occurrence of changes in surface free energies which are responsible for the different water sorption onto the membrane. Furthermore, membrane affinity was estimated for all membranes by quantifying the difference of the solubility parameters between the membranes and penetrants. In particular, variations in surface free energy are caused by a different availability and accessibility of specific functional groups of both the modifier and polymer segments, respectively.9 Surface analysis correlated to permeation experiments highlighted the key role of the surface characteristics in the interacting process with water.5 Energy dispersive X-ray analysis (EDX) and infrared analysis yielded information about the modifier distribution through the polymer matrixes and relative changes in chemical environments as the modifier content increased. Attenuated total reflection (ATR) analysis yielded important indications about the possible mechanisms which can affect the availability and accessibility of hydrogen donor and acceptor groups. Molecular dynamic (MD) and quantum-chemical (QC) tools were combined to establish the modifier-water interactions. The distribution of the modifier molecules throughout the polymer matrixes was evaluated from slides obtained from MD calculations, performed on modified PEBAX boxes. Modifier geometries were identified and were used for following QC calculations.Thelatterprovidedspecificinformationaboutintermolecular interactions such as water-modifier, modifier-modifier, and

10.1021/jp071776q CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007

Intermolecular Interactions for Water Sorption

J. Phys. Chem. B, Vol. 111, No. 30, 2007 8869

SCHEME 1: Molecular Structures of PEBAX and o/p-NEthyl-toluenesulphonamide

modifier-water-modifier; in addition, corresponding interaction energies of the above complexes were estimated. The subject of this combined experimental and theoretical study was the assessment of the local geometries of the complexes, which can affect the availability of hydrogen donor and acceptor groups belonging to the modifier molecules, yielding different hydrogen-bonding strengths. In addition, an important evaluation was related to the constraining effects of the polymer segments on the stability of modifier-water complexes. With this respect, the existence of direct interactions between two or more modifier molecules and the identification of the possible structures embedded within the matrixes were indicated as possible causes of changes in the sorption measurements. An overview of each approach is subsequently reported, and the results of each investigation are compared and discussed. 2. Methodology 2.1. Materials and Membrane Preparation. A block copoly(ether/amide) 80PTMO/PA12 (PEBAX2533, Atofina) was dissolved with the modifier N-ethyl-o/p-toluensulphonamide (KET) in a mixture of n-butanol/n-propanol (99,5%, Carlo Erba) 3/1 v/v. Modifier concentrations ranged from 30 to 70 wt %. The polymer solutions were cast to obtain thin membranes. The films, air-dried for 4-5 days at room temperature, were stored in an oven at 40 °C for 3 days and under vacuum at room temperature for 7 days to remove traces of solvent. The layer thickness, measured using a digital gauge (Carl Mhar D 7300 Esslingen a. N.), ranged from 20 to 40 µm ( 1.5 µm. 2.2. Membrane Surface Free Energy and Solubility Parameter. Membrane surface free energies and relative components were estimated by static contact angle experiments. The technique adopted consisted of the sessile drop method using a CAM 200 contact angle meter (KSV instrument LTD, Helsinki, Finland). The probe liquids were ultrapure water (filtered through a USF ELGA plant), glycerol (Fluka AG, 88%), and di-iodomethane (Aldrich, 99%). The droplets were deposited on the membrane surface by using a microsyringe with an automatic dispenser, while the images were captured with a digital camera allowing static contact angles to be measured at time zero. Mean values of contact angle for three different liquids were obtained by averaging 12-16 different measurements which were carried out at various positions of two to three specimens of each membrane. The Lifshitz-van der Waals γLW [mJ/m2], polar γAB [mJ/ 2 m ], acid (electron acceptor) γ+ [mJ/m2], and base (electron donor) γ- [mJ/m2] components of the surface free energy γ [mJ/m2] were calculated from mean values of the contact angles for each sample, according to the Good et al. equations.9 The difference in solubility parameters (∆δ, 103 J1/2/m3/2) was calculated for each membrane and penetrant according to these relations:

∆δ )

( ) ( ) γm 0.75

3/4

-

γl 0.75

3/4

(1)

where γm [mJ/m2] is the overall surface free energy of the membrane and γl [mJ/m2] is the overall surface free energy of the liquid. 2.3. Sorption Value Estimation. Water vapor sorption (S) was derived from the ratio between the permeability (P) and diffusion coefficients (D) according to the diffusion-solution model PdDS, where P is the permeability coefficient measured in steady state and D is the diffusion coefficient measured in flux transient. The measurements were performed at water vapor activity p/p0 ) 0.9 to avoid condensation during the experiment. The procedure is described in more detail elsewhere.4 2.4. Infrared Characterizations. Infrared spectra were collected from the samples at a pixel size of 6.25 × 6.25 µm over 570 × 570 µm sampling area using a Spectrum Spotlight chemical imaging instrument by Perkin-Elmer Instruments. Fourier transform infrared (FT-IR) chemical imaging maps were extracted by comparing the spectrum exhibiting the highest modifier content with the other ones. In addition, a micrometer torque (UATR crystal Diamond/ZnSe, Spectrum One System by Perkin-Elmer Instruments) was used to obtain ATR spectra which were collected from different points of the sample surfaces using the same pressure. The depth of penetration was up to 1.66 µm, and the spectra were recorded at a resolution of 4 cm-1. 2.5. EDX Analysis. Distribution of the modifier throughout the polymer surface was evaluated using EDX analysis (Quanta200, FEI COMPANY). The distribution of sulfur atoms was probed for by monitoring the blend homogeneity. 2.6. Molecular Dynamic (MD) Simulation. The amorphous atomistic bulk structures of the copolymer PEBAX2533 were constructed and simulated by using three-dimensional cubic periodic boundary conditions and by using the commercial software Insight II-Discover of Accelrys.10 COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) force field was used for all simulations.11-12 The calculations were performed on SGI Onyx workstation. The structure of each single chain of the copolymer PEBAX2533 was modeled by alternating the comonomers polyamide-12 (PA-12) and poly(tetramethylene oxide) (PTMO) soft segment, respecting the experimental relative weight percentages of 20 wt % of PA-12 and of 80 wt % of PTMO.13 At first, the structure of polyamide-12 (PA-12) and poly(tetramethylene oxide) (PTMO) comonomers were built up using the BUILDER module of Insight II10 and were subjected to energy minimization. All the atoms in the copolymer chains were treated explicitly. Then, a single chain of the copolymer of the required length and composition was constructed using the POLYMERIZER module of Insight II10 as detailed in ref 14. A polymerization degree of 8 consisting of a total of 24 comonomers of polyamide PA-12 and 224 of PTMO was estimated taking into account the dimension of a typical simulation box side (40-50 Å) and the experimental density of pure PEBAX2533, that is, 1.01 g‚cm-3.13 To minimize chain end effects, each simulation box contained only one minimized copolymer sequence rather than several confined to the same volume, which would lead to increased density of chain ends. Also, the use of single-chain polymers to represent bulk amorphous systems is common and has been proven to be quite accurate in replicating the behavior of experimental polymeric systems.15-17 Initial starting copolymer configurations were generated using the method of Theodorou and Suter on the basis of the rotational isomeric state theory.18 To prevent the generation of high-energy configurations, the look-ahead feature of the AMORPHOUS_CELL module was used with a value of 6, and the maximum number

8870 J. Phys. Chem. B, Vol. 111, No. 30, 2007 of the look-ahead configurations was set to 128. To avoid the overlapping of polymer chains and possible catenations, a high number of argon molecules was included in each cell with the argon molecules acting as small obstacles. Also, KET in the mixture of ortho:para 1:1 w/w was added to the pure copolymer to make the models, each with three different copolymer/ modifier compositions: 90-10, 70-30, and 40-60 w/w, respectively. The choice of the three compositions was considered by the corresponding different sorptive behavior, which has been experimentally exhibited by the membranes. The limit of 60 wt % of KET cannot be exceeded because of the limitation of the AMORPHOUS_CELL module for computing more that 9500 atoms. Since the objective was to simulate chains of adequate length and considering the high number of modifier molecules corresponding to 70 wt % of KET, its concentration had to be limited to 60%. The initial density of the models, chosen lower than the experimental one, and the introduction of spacer molecules were sufficient to generate catenation-free structures. The cells were refined by removing the argon molecules in three steps. Cycles of energy minimizations and dynamic runs with a downscaled force field parameter (conformational energy terms and the nonbonded energy terms) were performed after each removal. The resulting packing models, at reduced densities without spacer molecules, needed to be slowly compressed from a density (about 20-10%) slightly below the experimental density to the real one via NPT (constant number of particles N, pressure P, and temperature T)-MD runs. The cells were pressurized at 300 K via NPT-MD simulations with increasing values of pressure at a density which was greater than the experimental one. The cells were refined by employing three temperature cycle NVT (constant number of particles N, volume V, and temperature T) runs (annealing). This procedure consisted of heating the system from 300 to 700 K. The last temperature is well above the glass-transition temperature (Tg) of the polymer. Then, the system was cooled back to 500, 400, and finally 298 K with NVT-MD simulations alternating energy minimizations. The duration of the NVT dynamics simulations at each temperature was 5000 fs. Further equilibration and density adjustment of the polymer system was achieved through a final 300 picosecond (ps) MD run, a time which was found to be sufficient for systems reaching an almost constant value of total energy. In all runs, the simulation conditions used were (a) minimum image boundary condition to make the system numerically tractable and to avoid symmetry effects and (b) a cutoff distance of 15 Å with a switching function in the interval of 13.5-15 Å. Through the dynamics, the Andersen pressure control method was used.19,20 Three models for each composition were constructed. The side length of the bulk models was 33 Å for the polymer with 10 wt % of KET, 36 Å for 30 wt % of KET, and 43 Å for 60 wt % of KET. 2.7. Quantum Chemical (QC) Procedure. Density functional calculations using B3LYP functional21 were here used. All the density functional theory (DFT) calculations were performed using the NWChem code.21,22 In this package, the hybrid functional B3LYP in conjunction with several linear combinations of Gaussian-type orbitals was implemented. The basic sets used were 6-31G* for carbon, oxygen, nitrogen, and hydrogen, whereas the Cristiansen, Ross, and Ermler relativistic effective core potential was used for the sulfur atom.22 Coulomb, exchange-correlation potentials, and energies were integrated numerically on a grid with medium accuracy. All the molecular structures, studied at quantum level, were fully optimized using the modified Fletcher-Powell minimization algorithm.23

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Figure 1. Membrane surface properties estimated for all membranes: (a) degree of liquid water wetting and electron donor component γ[mJ/m2] of the overall surface free energy γ [mJ/m2] vs KET content in the polymer matrix; (b) membrane affinity (∆δ), expressed as difference of the membrane-water solubility parameters, and water sorption (ln S) as a function of the KET content.

Optimization of the geometries in various quantum chemical procedures is generally carried out at a medium/low level of theory; then, single-point calculations on the minima are performed at a higher level of theory. Instead, in this work, the energies were obtained at the same level of theory as that used for the geometry optimizations. The convergence criteria in the optimizations were the maximum gradient and the gradient of the mean square root with thresholds of 10-4 and 10-3 au, respectively. The energy convergence threshold for the selfconsistent field (SCF) procedure was set to 10-6 au, while the root-mean-square of the electron density was set to 10-5 au. No level shifting was used to obtain convergence of SCF energy. In the self-consistent field procedure, the DIIS option was used.22 The Hessian of the optimized geometries was also analyzed to test if these were the real minima. Results and Discussion 3.1. Experimental Evidence. 3.1.1. EValuation of the Surface Character. The amphiphilic KET structure produced remarkable modifications of the surface characteristic of the membranes. The membranes exhibited a gradual increase in hydrophilicity up to 50 wt % of KET, whereas a dramatic reduction in wetting degree was appreciated at 70 wt %. Contact angle experiments evidenced changes in the water droplet spreading on the different membrane surfaces because of the formation of attractive and

Intermolecular Interactions for Water Sorption repulsive intermolecular interactions between the probing water and the polymer surface (Figure 1a). The membrane surfaces with 50 wt % of KET, having rich domains of polar moieties, participated in favorable interactions with water droplets. As the concentration increased, the availability of free groups was reduced. By using the Good and van Oss approach, both the polar [γ-/+/AB (mJ/m2)] and nonpolar [γLW (mJ/m2)] components of the overall surface free energy γ (mJ/m2) were estimated for all membranes, respectively.5,7 With this regard, the electron donor component γ- (mJ/m2) is a useful semiquantitative parameter expression of hydrophilicity of the membrane surface. This thermodynamic magnitude yields the amount of hydrophilic domains distributed on the surface. In Figure 1a, a clear maximum value of the γ- (mJ/m2) was found in correspondence to the minimum of water contact angle with 50 wt % of KET. A dramatic decreased in γ- (mJ/m2) was observed with increasing concentrations of KET. This implies that the amount of the modifier polar moieties increased, facilitating the membrane-water molecular interactions, as the concentration of modifier increased up to 50 wt%. At higher concentrations, notwithstanding that the amount of polar moieties of the modifier was increased, their accessibility on the membrane surface was drastically reduced. This produced a decrease in the attractive interactions between membranes and water. 3.1.2. Membrane Affinity and Water Solubility. Membrane affinity is well expressed by the difference in the solubility parameter (∆δ, 103 J1/2/m3/2) between the membrane surface and water molecules (Figure 1b). This parameter takes into account the overall polar and nonpolar components of the surface free energy γ (mJ/m2). Small differences in ∆δ mean high affinity between the two systems, whereas large differences reveal low affinity. The ∆δ minimum value was estimated for membranes containing 50 wt % of KET, where the availability of -NH moieties of the modifier were the highest, as confirmed below using infrared spectroscopy. A further increase in modifier content seemed to cancel this positive effect, lowering ∆δ because of a reduction in favorable intermolecular interactions (Figure 1b). The water sorption derived from the solution-diffusion model was related to changes in the ∆δ parameter. An increase in the water uptake was estimated as the membrane exhibited the highest predisposition to interact favorably with the polar penetrant. Thus, a direct proportionality between hydrophilic domains, affinity between the considered systems, and water sorption was elucidated (Figure 1a, b). As a result, these experimental achievements suggest the accessibility of polar moieties as a key factor for interpreting the changes in the water sorption into the modified PEBAX membranes. 3.1.3. Infrared Analysis. To validate the above hypothesis derived from the evaluation of the membrane surface character, water affinity and solubility infrared analysis was performed. A previous evaluation of the hydrophilic domain distribution through the membranes was necessary to evaluate the homogeneity and compatibility of the systems considered in this work. PEBAX/KET-based dense membranes exhibited macroscopically substantial homogeneous areas, as largely confirmed by Spectrum Spotlight FT-IR images (Figure 2a) and EDX analysis (Figure 2b). In the first case, infrared maps yielded information about the molecular composition and the chemical moiety distribution across the films. The maps were built up by comparing the spectrum with the highest content in modifier with the other ones. Each pixel represents an individual


Figure 2. Modifier distribution through the 50 PEBAX/KET membrane: (a) map of chemical imaging FT-IR spectra collected at a pixel size of 6.25 × 6.25 µm over 570 × 570 µm sampling area; (b) EDX analysis.

spectrum, and the color intensity shows the potential areas of chemical difference. Moreover, EDX analysis confirmed also a substantial uniform distribution on the length scale of the sulfur atom and, therefore, of the substituted sulfonamide molecules on the membrane surfaces, confirming good compatibility and affinity of the blends. ATR vibrational spectroscopy yielded precious indications on the relative changes in supramolecular chemistry, revealing the sensitivity of specific chemical moieties to inter- and intramolecular aggregations because of various hydrogenbonding possibilities. It is well-known that local geometries can affect the hydrogen-bonding strength because the distances between hydrogen donor and acceptor groups can be changed and, therefore, the electronic distributions can be modified. By comparing the spectra of the PEBAX/KET membranes with those of the pure polymer membrane and the pure modifier, significant changes in intensity bands and vibrational frequencies were appreciated and the disappearance of specific bands was observed at the highest KET content (Figure 3). The presence of different chemical environments was revealed by multiple and shouldered broad bands occurring in the regions of N-H, CdO, and SO2 vibrational modes. The infrared frequencies, associated to the chemical groups that are sensitive to hydrogen bonding, exhibited more or less shifted values as a function of the modifier content in the polymer matrix. In detail, the ATR spectra can be analyzed in two sequences: in Figure 3a and 3b, the effects of the modifier on the polymer chemical environment are highlighted. In Figure 3c and 3d, the specific information referring to the typical vibrational modes of the modifier was assessed. N-H stretching vibrations, located in the range of 3287-3382 cm-1, were found

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Figure 3. ATR spectra collected by UATR crystal Diamond/ZnSe: vibrational modes estimated for pure polymer, pure modifier, and membranes charged by KET (30-70 wt %) from 650 to 4000 cm-1 at resolution 4 cm-1.

for all samples. The spectra of the membranes containing KET, in all different concentrations, exhibited a further free νN-H vibration centered at 3499 cm-1. The band associated to this stretching mode became more significant and was shifted to higher frequency values for membranes with 50 wt % of modifier (Figure 3a). Another chemical moiety sensitive to strength and magnitude of hydrogen bonding is the carbonyl group CdO. A lowering of 12.28 cm-1 in νCdOester was estimated for the membrane with 70 wt % of KET with respect to the pure polymer (Figure 3b). Differently, the stretching of the CdOamide occurred at somewhat higher frequencies than that estimated for the pure polymer membrane, resulting in more weakly bonded carbonyl groups (Figure 3b). Concerning the vibrational bands ascribed to the stretching of ether group, changes in the profile and intensity of the related bands were appreciated for membranes with 70 wt % of modifier (Figure 3c). Concerning the stretching of the SO2 moiety, significant changes in the frequency values were appreciated when the KET content was equal to 70 wt %. At this concentration, the νasSO2-NR2 resulted in shifting from 1315 cm-1 to 1264 cm-1. Also, the vibrational mode associated to the νs-SO2-NR2 and located at about 1154 cm-1 was not detectable for membrane with 70 wt % of KET (Figure 3c). The band associated to the

wagging δN-H of the sulfonamide linkage disappeared from the spectrum collected on this membrane (Figure 3d). Out-of-plane -CH wagging and out-of-plane sextant ringbending vibrations are usually located between 910 and 660 cm-1.24 The pure modifier as well as both the membranes with 30 and 50 wt % of KET exhibited multiple intense bands indicative of the type of substitution on the ring, located at about 857, 814, 806, 710, 688, and 661 cm-1. In the spectrum collected on the membrane at 70 wt % in KET, the out-of-plane -CH wagging appeared attenuated and shifted at lower frequencies, whereas significant changes occurred in the triple bands typical of the ring-bending vibrations, resulting in a strong and intense band located at 707 cm-1 (Figure 3d). As a result, the appearance of N-H stretching (Figure 3a) and the changes in the intensity of the bands of carbonyls (Figure 3b) could be ascribed to different packing of the polymer chains. Various polymer packing can be supposed as a function of the KET content. Specifically, a polymer packing with many free N-H groups is plausible at 30 and 50 wt % of KET. Differently, membranes with 70 wt % of modifier exhibited a packing where the free N-H groups disappeared. Furthermore, the significant changes observed in the vibrational modes involving the νsSO2-NR2 and δN-H of the sulfonamide linkage indicated that the modifier structures were blocked. This suggests that the sulfonamide linkage is involved in intermolecular interactions,

Intermolecular Interactions for Water Sorption where the amine and oxygen groups of the modifier are linked with another modifier or with the polar moieties of the polymer chains (Figure 3c, 3d). By comparing the spectra collected on the pure modifier and the membranes with 70 wt % of KET, the shift of the νs-SO2NR2 frequency and the disappearance of δN-H are due to high concentration of the modifier but also to the constraining effect of the polymer. In fact, the νs-SO2-NR2 mode is located at higher frequencies and the bending δN-H is remarkably evident for the pure liquid KET. The analysis of the δ out-of-plane of the aromatic rings of KET (Figure 3d) indicated that at the highest concentration, a geometrical constraint such as pi-pi staking of the aromatic rings could be responsible for preventing vibrations. The reason for the changes in the polymeric packing is obviously attributed to the amount of KET in the membranes. Nevertheless, how the modifier works is to be assessed. This requires the identification of the crucial intermolecular interactions involving the modifier molecules. Specifically, is there a direct interaction between two or more modifiers in the polymer membranes? What are the kinds of interactions and the geometry of the KET molecules forming these interactions? Therefore, a theoretical (MD and QC) analysis can begin to provide answers to these questions. 3.2. MD Simulations. 3.2.1. Identification of Intermolecular Interactions at Short Range. Molecular dynamics (MD) simulations is a powerful technique for computing the equilibrium and dynamical properties of polymeric materials. MD simulations yielded indications about the modifier distribution in the polymer membranes by evaluating the polymer-modifier as well as the modifier-modifier distances. Bulk equilibrated models of PEBAX with three different amounts of KET were prepared and cut into slides with a dimension of about 8-9 Å along the z-axis (Figure 4a, b). The distribution of the modifier molecules inside the box was visualized, and intermolecular distances were indicated. In Figure 4c, the number of KET dimers found in the boxes with N‚‚‚H‚‚‚O bond lengths smaller than 3 Å is reported. Furthermore, the number of modifiers, exhibiting distances from the PEBAX functional groups smaller than 3 Å, was also reported. The first check was performed on the distribution of KET molecules in the polymeric matrix. In models with 10 wt % of KET, the molecules were randomly dispersed in the bulk of the copolymer. Because of the reduced number of KET molecules in the boxes containing the 30 wt %, few dimers forming hydrogen bonds were found. The interactions between both the amine and sulfur groups of two molecules of KET are present in relevant numbers in the models with 60 wt % of modifier, confirming a large presence of dimers, as shown in Figure 4c. KET molecules were found to be close to the amide, the carboxyl residues, the ether, and the ester groups of the PEBAX (Figure 4c). Independently of modifier concentrations, the number of modifiers close to the ether group of PTMO segments was larger. No distances less than 3 Å between -SO2 groups and the amide moiety of the polymer were found. The number of proximal modifiers rose with KET concentrations more than the number of modifiers close to polymeric groups. In other words, the distances between KET and copolymer segment chains changed slightly with increasing modifier content, as expected for the distances from the ether moieties. All data were in qualitative agreement with the indications extracted from the infrared analysis (Figure 3). Particularly, a

J. Phys. Chem. B, Vol. 111, No. 30, 2007 8873 proportional shift of the vibrational stretching νCONH was not observed in correspondence to the significant shift of the νasSO2-NR2. This was confirmed by the lack of bond lengths between SO2‚‚‚CONH moieties as reported in the histogram (Figure 4c). As a consequence, the shift of the νas-SO2-NR2 should be ascribed to interactions between modifier molecules. Three different dimers linked together by hydrogen bonding were extracted from the model containing 60% of KET and were subjected to density functional calculations to obtain the corresponding stable wave function and interaction energies. 3.3. QC Models. 3.3.1. Density Functional Electronic Structure Calculations. From a theoretical point of view, the study of hydrogen or nonbonding interactions by using the density functional theory (DFT) can be considered a relevant problem. Although some DFT functionals do not correctly describe nonbonding interactions, others take these into account properly.25 Hybrid functionals, such as X3LYP 26 and B3LYP,21 have also yielded reasonable results in the study of long-range interactions and hydrogen interactions.27 Various quantitative studies on covalent and noncovalent H-bonds have defined the optimized N‚‚‚H‚‚‚O bond lengths smaller than 2 Å as a conventional hydrogen interaction.28-31 In this work, in agreement with the previous statement, the intermolecular interactions were also defined as conventional hydrogen interactions, if smaller than 2 Å, without the need of further characterizations.32-35 Since the probability of finding two or more modifiers in a small volume of polymer should be large at high modifier concentrations, comparisons between the structures of single KET and relative dimers were performed. From this analysis, some deductions were achieved. The direct interaction between modifier dimers and water may be responsible for the nonlinear sorption. In addition, the dipole moments of KET molecules did not change with respect to the water-modifier and water-dimer complexes. Consequently, the number of dipoles does not change with increasing KET concentration, resulting in no modifications in the polarization of the polymer chains. 3.3.2. Modifier Geometries. The analysis of the most stable water-modifier geometries was done according to the following sequence. (a) Monomer-Water. At first, the fully optimized structures of the [H2O‚‚‚(o)-KET] system were determined to evaluate the most stable interactions between water and modifier (Figure 5a, b). Similar minima were also obtained for the isomer of KET substituted in the para position. In the first geometry (Figure 5a), the water molecule makes two hydrogen interactions (bridge conformation) with the amine hydrogen and with the oxygen atom of the SO2 moiety of the modifier. In the second geometry, the water interacts with both the oxygen atoms of the sulfonamide linkage by long-range interactions (Figure 5b). The first structure is more stable than the second one showing a difference in energy of 5.5 kcal/mol. (b) Monomer-Monomer. The second step of DFT calculations was focused on the minimization of the dimer geometries. Since the local minima of dimers are affected by the choice of the starting geometry, all the initial geometries were extracted from the equilibrated MD models. The extracted MD (o-KET)2 dimer was fully optimized, and the resulting geometry is displayed in Figure 5c. The ortho-para and para-para dimers were also optimized in a similar way (Figure 5d, e). Figure 5f shows the minimum obtained from the starting geometry derived by the symmetric inversion of a monomer. With this regard, the difference between the energy of the KET


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Figure 4. (a) (p-KET)2 and (b) (o-KET)2 dimers extracted from slides of an amorphous box at 60 wt %. The polymer chain is depicted in black, and the additive is depicted in gray. (c) Number of interactions involving hydrogen between modifier-polymer and modifier-modifier at a distance of e3 Å.

dimer and twice the energy of the corresponding monomer defines the interaction energy Eint (kcal/mol), while the difference between the energies of fully optimized geometries and the starting MD geometries yields the EMD-DFT quantity (kcal/ mol), both reported in Table 1. The optimized ortho-ortho structure, obtained from the MD geometry, was the most stable. In addition, the small EMD-DFT value confirms that no pronounced geometrical distortions were found between the (oKET)2 embedded in the bulk polymer and the corresponding DFT minimum.

All the DFT minima confirmed the formation of intermolecular hydrogen interactions, involving the N-H and the SO2 moieties (Figure 5c-f), being in qualitative agreement with the indication extracted from the infrared analysis (Figure 3c, d). At high modifier content, the remarkable shift to lower frequencies and the disappearance of the significant bands, ascribed to typical vibrational modes of N-H and SO2 groups, suggest a N‚‚‚H‚‚‚O interaction between two molecules of modifier.



Figure 5. (a, b) Density functional minima of water-monomer; (c-f) dimers; (g, h) water-dimer. Acceptor and donor hydrogen distances were reported and expressed in angstroms Å.

(c) Monomer-Water-Monomer. The most stable optimized DFT dimer was selected and a new optimization in the presence of water was carried out [H2O‚‚‚(o-Ket)2] (Figure 5g). Comparing the geometries reported in Figure 5a and Figure 5g, the water molecules seemed to be located at similar positions, although small differences in the intermolecular lengths can be appreciated. In Figure 5g, two modifiers formed hydrogen bonding between the amine group positioned on the first molecule (I)

and one oxygen of the SO2 belonging to the second modifier (II). In addition, the water molecule formed a bridge conformation, involving both the bonded oxygen atom and the amine moiety of the same modifier (II). Differently, long-range interactions characterized the structure with the phenyl groups in opposite directions (Figure 5f, h). The two modifiers were linked together between the amine (II) and the oxygen of the sulfonamide residue (I). Although this last geometry was never observed in the MD equilibrated bulk


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Figure 6. (a) Starting geometry of [(H2O)‚‚‚(o-KET)2] complex and a second water molecule. (b) Density functional minima of [(H2O)2‚‚‚(oKET)2] without constraint and (c) with constraint. Acceptor and donor hydrogen distances were reported and are expressed in angstroms Å.

TABLE 1: Interaction Energies Related to Dimers and Difference Energies between Stable MD and DFT Structures dimer

Eint (kcal/mol)

EMD-DFT (kcal/mol)

(o-KET)2 (p-KET)2 (o-KET)2a (o-KET)-(p-KET)

-12.2 -11.6 -11.4 -7.7

-39.8 -62.1

a

-118.1

figure 5c 5d 5f 5e

Obtained by symmetry.

box, the QC analysis of this structure was aimed at demonstrating how the choice of local minima was important for the achievements because of the changes in the number and length of short- and long-range interactions. (d) Water-Monomer-Water-Monomer. The effects of a second water molecule on the stability of the monomer-watermonomer complex, that is, [(H2O)2‚‚‚(o-KET)2], were examined. Both the initial and optimized internuclear distances of the [(H2O)2‚‚‚(o-KET)2] are displayed in Figure 6a and b. The Cartesian coordinates of the initial position of water were selected as those found in the [H2O‚‚‚(o)-KET] minimum (Figure 6a). In the absence of polymer chains, the N-H‚‚‚O-S-O hydrogen interactions between the two modifiers were broken, and the second water molecule moved toward the monomer (I), as shown in the optimized complex (Figure 6b). Thus, two separated monomers 2‚[H2O‚‚‚(o)-KET] were yielded, each of which interacted with only one water molecule [N-H‚‚‚OH‚‚‚O-S-O]. Each water molecule is bound with only one

modifier making a bridge conformation similar to Figure 5a; thus, in vacuum, the two water molecules separated the modifiers. The interaction energy of [(H2O)2‚‚‚(o-KET)2] was equal to -4.5 kcal/mol. (e) Polymer-Water-Monomer-Water-Monomer. The restraint of the polymer matrix was simulated at the QC level by defining a harmonic constraint (spring) along the length of the N-H‚‚‚O-S-O bond.21 The spring constant (k) was selected to obtain a minimum of its energy equal to 6.1 kcal/mol. This value corresponds to half of the (o-KET)2 dimer interaction energy, reported in Table 1. The equilibrium length (ro) between the hydrogen and oxygen atoms equals that of the optimized length of the N-H‚‚‚OS-O bond found in the (o-KET)2 dimer (Figure 6c). Because of the geometry constraint, an additional energy term has to be considered in the total energy expression. This further contribution implies that the optimized distances between the considered atoms will be in the proximity of ro but never exactly that. The full QC optimization of the [(H2O)2‚‚‚(o-KET)2] system yielded another stable geometry, where the N-H‚‚‚O-S-O interaction between the two modifiers is now preserved (Figure 6c). Although the geometry constraint used cannot be the best choice to represent the polymer restrain at QC level, the simple spring constraint was selected to evaluate if the polymer had, or not, a significant role. If relevant effects of the polymer are demonstrated, more complicated approaches can be used.36 The effects of the polymeric chains appeared significantly decisive. Indeed, in this case, the second water molecule preferred to bind



TABLE 2: Dipole Moments and Dipole Difference in Debye Calculated by DFT for the KET Monomer and Dimer without and with Water monomer

µ (D)

dimer

µ (D)

∆µ (D)

o-KET [H2O‚‚‚(o-KET)]

4.32 4.69

[(o-KET)2] [H2O‚‚‚(o-KET)2] [(H2O)2‚‚‚(o-KET)2]

7.18 6.14 5.33

2.86 1.45 0.64a

a Difference calculated between [(H2O)2‚‚‚(o-KET)2] and [H2O‚‚‚(oKET)].

to the oxygen of the free sulfonamide moiety (II) instead of breaking the N-H‚‚‚O-S-O bond between the modifiers I and II (Figure 6c). This water molecule did not form a bridge conformation between the hydrogen of the amine group and an oxygen of SO2. The geometry constraint changed the interaction between water and modifier molecules. In fact, the interaction energy of this system, Figure 6c, is equal to -2.3 kcal/mol and is reduced by 50% with respect to the complex in Figure 6b. Similar results were also obtained considering a spring with the same k value and an equilibrium length ro equal to the distance between the center of mass of the two monomers. The comparison between the interaction energies shows that a second molecule of water approaches less favorably to the [H2O‚‚‚(o-KET)2] complex. In other terms, the modifiers were joined by polymeric chains, and consequently they change their interaction with water molecules negatively. Thus, a decrease in the electronic interaction between water and KET is expected, as large amounts of modifier are embedded within the polymer segments. 3.3.3. Dipole Moment Calculation. Another possible aspect, which can affect the sorption of water into the modified PEBAX membranes, is represented by the polarization of the polymer chains caused by the dipole moments of the modifier. For all stable geometries, including the constrained dimer [(H2O)2‚‚‚(o-KET)2], the module of the dipole moment was calculated from the values of the electronic and nuclear coordinates (Table 2). In particular, the interaction of water with (o)-KET did not modify the dipole moment. On the contrary, a substantial increase in the dipole moment was estimated when moving from the monomer to the dimer without water. However, a remarkable reduction of this dipole moment was estimated as one/two water molecules interacting with the (oKET)2 dimers, lowering the dipole moment value to that of the single KET. In the last column of Table 2, the dipole difference (∆µ) between the dimer and monomer is reported, with and without water molecules. Because of the high values of dipole moments, large polarization effects of the polymeric functional groups should be expected; therefore, the segment chains could bind more water molecules according to the PEBAX polarizability. It is well-known that a number of dipoles corresponds to a specific number of modifier molecules. By doubling this number, the dipoles should proportionally increase, if dimers are not forming. The theoretical analysis showed that the dimerwater complex is a stable structure exhibiting a dipole moment almost equal to that of the monomer. Thus, if a doubling of the number of the modifiers takes place, the proportional increase in the dipole moments cannot occur. Consequently, no effects on water sorption because of a polarization of the polymer segments are possible. Concerning the questions about the geometry and the interaction between the modifiers reported in the end of section 3.1.3, the found structures could be considered the starting point interpreting the water sorption at different levels. Indeed, these

structures and related clusters could promote changes in polymer packing and in the direct water sorption as well as in the induced polarization of the polymer segment chains. The proposed mechanisms can occur simultaneously. Summarizing, the means by which KET binds with itself over short and long ranges (Figure 5c-f) was established. The NH‚‚‚O-S-O bond, shown in the mentioned figures, indicates how more molecules can be assembled in clusters affecting the polymer packing and hydrophilic/hydrophobic domain formation. Conclusion The water dissolution in modified polymer membranes was assessed by using different experimental and theoretical tools, focusing on the effects of the modifier content. Water sorption in PEBAX membranes containing a substituted aromatic sulfonamide was evaluated as a function of its content. Experimentally, an increase in water uptake was estimated up to a modifier content of 50 wt %. Further slight increases in concentration produced dramatic decreases in water dissolution. As largely confirmed by infrared analysis and surface energy properties, the decrease in water affinity of the polymer matrix was ascribed to the accessibility and availability of the polar head of the modifier. The chemical group accessibility and availability can be attributed to both the changes in polymer packing and to direct intermolecular interactions involving modifier molecules. The key indication derived from theoretical analysis highlighted the geometries involving two linked modifiers and established the intermolecular interaction N-H‚‚‚O-S-O underlying the polymer influence on this interaction. This information is significant because it explains how a second water molecule interacts less with the [H2O‚‚‚(o-KET)2] complex than a separate o-KET. In addition, the dipole moments of [H2O‚‚‚(o-KET)2] and [(H2O)2‚‚‚(o-KET)2] complexes are almost equal to the dipole moment of the o-KET and [H2O‚‚‚(oKET)]. This means that the increase in modifier molecule number does not produce a corresponding increase in the overall dipole moment and, consequently, in the polymer polarization. The established intermolecular interaction indicated the way by which the KET can be assembled in clusters that could be responsible for changes in the polymer packing and in the hydrophilic/hydrophobic domains. Experimental and theoretical approaches suggest, therefore, plausible explanations of the sorption phenomenon that can be controlled as a function of the final utilization of modified PEBAX membranes. A reciprocal validation of experimental evidence and theoretical structural models was possible, since the information extracted from multiapproach evaluations provided similar interpretations. Acknowledgment. This work was supported by the European Commission 6th Framework Program Project MULTIMATDESIGN Computer aided molecular design of multifunctional materials with controlled permeability properties, Contract Number: NMP3-CT-2005-013644. The authors are gratefully to INSTM/CINECA for computational support (Superprogetto di calcolo 2005). References and Notes (1) Pandey, P.; Chauhan, R. S. Prog. Polym. Sci. 2001, 26, 853. (2) Nagai, K.; Freeman, B. D.; Cannon, C.; Allcock, H. R. J. Membr. Sci. 2000, 172, 167.

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Intermolecular Interactions as Controlling Factor for Water Sorption

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