Time-Resolved Fourier Transform Infrared Spectroscopy, Gravimetry

Article pubs.acs.org/JPCB

Time-Resolved Fourier Transform Infrared Spectroscopy, Gravimetry, and Thermodynamic Modeling for a Molecular Level Description of Water Sorption in Poly(ε-caprolactone) Pellegrino Musto,*,† Michele Galizia,‡ Marianna Pannico,† Giuseppe Scherillo,‡ and Giuseppe Mensitieri‡ †

Institute of Chemistry and Technology of Polymers, National Research Council of Italy, via Campi Flegrei, 34, 80078 Pozzuoli, Italy Department of Chemical, Materials and Production Engineering, University of Naples Federico II, p.le Tecchio 80, 80125 Naples, Italy

‡

S Supporting Information *

ABSTRACT: Sorption of water in poly(ε-caprolactone) (PCL), with specific focus on the hydrogen-bonding interactions, has been analyzed by combining ab initio calculations, macroscopic thermodynamics modeling, and relevant features emerging from spectroscopic and gravimetric measurements. Fourier transform infrared (FTIR) data, analyzed by difference spectroscopy, two-dimensional correlation spectroscopy, and least-squares curve-fitting analysis associated with gravimetric determination of water sorption isotherm provided information on the system’s behavior and on the molecular interactions established between the polymer and the penetrant. A consistent physical picture emerged pointing to the presence of two spectroscopically discernible water species (first-shell and second-shell layers) that have been quantified. Water molecules are present in the form of dimers within the polymer equilibrated with water vapor up to a relative humidity of 0.65. At higher humidities, clustering of water sorbed molecules starts to take place. The multicomponent ν(OH) band representative of absorbed water has been interpreted with the aid of ab initio calculations performed on suitably chosen model systems. The outcomes of spectroscopic analyses were interpreted at a macroscopic level by modeling the thermodynamics of water sorption in PCL based on a nonrandom compressible lattice theory accounting for hydrogen-bonding (HB) interactions. Starting from the fitting of the gravimetric sorption isotherm, the model provided quantitative estimates for the amount of selfand cross-HBs which compare favorably with the FTIR results. molecules, rather than by intrinsic rates of ester cleavage.7 In turn, water access to the ester bonds is strongly affected by a series of factors including polymer hydrophobicity, crystallinity, and molecular weight. Elucidating water sorption thermodynamics in polycaprolactone is therefore a subject of considerable interest in developing intelligent design of devices and implants based on this polymer. Accurate thermodynamic modeling of PCL−water mixtures has to be rooted in a deep understanding of the system at a molecular level, with particular focus on the specific interactions which, in the present case, are of the hydrogen-bonding type. When the molecular-level information is unavailable or incomplete, thermodynamic models fail to provide a sound interpretation of the relevant phenomena. Our line of reasoning is to build macroscopic thermodynamics of the system at hand based upon the insights afforded by the spectroscopic analysis. On one hand, the latter supplies the underlying physical picture needed to properly model interactional issues, and on the other, provides the experimental data to validate the model predictions.

1. INTRODUCTION The interaction between water and polymeric materials has raised considerable interest both from a technological and a fundamental standpoint, witnessed by the steadily increasing number of studies appearing in the literature on the subject.1−6 From an end-properties perspective, water diffusion plays a central role in any of the countless applications requiring outdoor exposure. In fact, at the relative-humidity levels generally found in the environment (40−80%), water vapor is readily absorbed even in moderately hydrophobic polymers and exerts its action of an efficient plasticizer, causing a general deterioration of several physicomechanical properties. For biocompatible polymers like poly(ε-caprolactone) (PCL), the way these materials interact with water is even more relevant, controlling their biodegradation and the ease with which they can be integrated within a living organism.7 The superior rheological and viscoelastic properties of PCL over many resorbable-polymers boosted a renewed interest in this material7 in the field of tissue engineering. Of particular relevance is the realization of a large range of scaffolds and of longer-term degradable implants with tailored degradation kinetics. The degradation process, which is a key issue, is mainly governed by the accessibility of ester bonds to water © 2014 American Chemical Society

Received: March 5, 2014 Revised: May 30, 2014 Published: June 3, 2014 7414

dx.doi.org/10.1021/jp502270h | J. Phys. Chem. B 2014, 118, 7414−7429

The Journal of Physical Chemistry B

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limits and often prevents the resolution of the different components of a generally complex band profile. It is worth noting here that each water species produces two distinct vibrational modes in the OH stretching region [in-phase and out-of-phase ν(OH)], which further complicates the analysis. Another limitation of the infrared technique arises from the intensity enhancement of the ν(OH) bands upon the establishment of the interaction. This poorly predictable effect poses serious problems to the quantitative analysis; some ways to circumvent this difficulty have been proposed in the literature.6,18 Researchers have adopted two different approaches to investigate water sorption by infrared spectroscopy: attenuated total reflection−Fourier transform infrared (ATR-FTIR)19−23 and transmission FTIR.2−6,16−18 the two sampling techniques share the same electromagnetic probe and molecular information but are by no means equivalent in terms of response. ATR-FTIR samples a thin surface layer (0.1−2.0 μm) of a polymer film in intimate contact with an internal reflection element. The penetrant diffusion is unidirectional, as it occurs from the top surface of the film to the bottom, by means of a reservoir of liquid water contacted with the top surface. The intensity of the infrared signal depends (among other variables) on the concentration gradient in the thickness direction. Because of the sampling requirements, the film is always supported. In transmission FTIR, the film is contacted with water vapor at a selected pressure. The film is generally free-standing, and the diffusion occurs from both sides. The intensity of the signal is proportional to the average concentration of penetrant in the film, irrespective of any concentration gradient in the thickness dimension. This allows a direct comparison with gravimetric measurements. When careful control of vapor pressure in the diffusion chamber was unavailable, some authors ran the measurement in the desorption mode after equilibration of the sample in liquid water.13 It has been noted that the spectrum of sorbed water as collected with the two above methods in many cases does not coincide, and this occurs also for the present system; the reasons for such a discrepancy will be touched upon. In the present contribution, time-resolved FTIR measurements have been performed at different relative pressures of water vapor to investigate the H2O diffusion into semicrystalline PCL with the aim of a quantitative characterization of the system at the molecular level. An additional aim of the study was to deepen the vibrational interpretation, which still needs to be definitively clarified. To achieve these goals, the spectral data have been analyzed by different and complementary approaches, namely, difference spectroscopy, least-squares curve fitting (LSCF), and 2-D correlation spectroscopy (2DCOS), which allowed us to isolate the spectrum of the sorbed penetrant and helped improve the resolution of the complex band profiles. Taken together, the above techniques provided information on the nature, number, and dynamic behavior of the water species present in the system under scrutiny. This information was exploited in the development of a method for quantifying the population of the water species, based on the evaluation of the respective molar absorptivities. The analytical methodology, which is claimed to be of general applicability, relies on coupling the spectroscopic data with careful gravimetric measurements carried out in the same conditions of temperature and vapor pressure. The interpretation of the observed spectroscopic effects was facilitated and deepened by

The molecular-level characterization of the system requires the identification of the species present in terms of number, structure, stoichiometry, and possibly population. It may be safely stated that this level of understanding is far from established: conflicting and/or incomplete accounts have been reported in the literature. For example, in an early study of water diffusion in polyesters by FTIR spectroscopy, Sammon and co-workers8 found that the ν(OH) band of water had a complex shape which was resolved with four different components. Accordingly, four types of H-bonding with different hydrophilic groups of the polymer were proposed, denoted as weak, moderately weak, moderately strong, and strong. No further details on the structures of these aggregates were given. A quantitative analysis was also proposed, which appears to be impaired by the uncertainty on the number and the nature of the molecular species. A common theme of these investigations concerns the occurrence of water clustering, that is, whether or not sorbed molecules self-interact to form larger aggregates with a mobility and diffusivity different from that of the isolated molecules and depending on the cluster size. Thus, water clustering was proposed in the early studies of Zimm et al.9 and Barrie et al.10 on the basis of gravimetric diffusion measurements, as well as in the contributions of Errede11 and Woo and Piggott.12 Davis and Elabd reported on water diffusion in PMMA as investigated by gravimetric and spectroscopic techniques. They concluded that clustering takes place at water activities higher than 0.5, whereas dimeric species predominate at lower activity values. These authors detected a doublet in the ν(OH) region at 3610 and 3550 cm−1, which they associated with “free” and H-bonded O−H bonds, respectively. A further, broad component at lower frequency (between 3460 and 3200 cm−1) was ascribed to selfinteracting penetrant molecules.5 In a series of papers culminating in a comprehensive review article,6 Marechal and co-workers established that the hydration mechanism depends on the nature of the polymer substrate and on the overall water content in the sample. In cases of relatively hydrophilic media, both the interactions with the matrix and the degree of selfassociation of the penetrant change in going from the early stages of the sorption process onward. Clearly, in these instances the situation is even more complicated; however, according to these authors, it is still amenable to at least a semiquantitative analysis.4 In more hydrophobic systems with limited water solubility, a single hydration mechanism was recognized throughout the whole diffusion process. More recently, Iwamoto and co-workers reported on the interactions of water in polymers and developed an approach to identify Hbonding aggregates of different types by use of low molecular weight model compounds dissolved in inert solvents; they referred to their method as hydrophobic isolation infrared spectroscopy (HIIR).13 The results obtained by these authors are relevant in the context of the present contribution and will be considered in detail when discussing and interpreting our data. Although many techniques have been employed to investigate water−polymer systems (solid-state NMR, Raman, neutron scattering, light scattering),14,15 FTIR spectroscopy has been demonstrated to be among the most powerful. This is due to the method’s sensitivity toward H-bonding detection and to its sampling flexibility, which makes it relatively straightforward to develop in situ, time-resolved measurements.16,17 However, even FTIR has its own drawbacks, represented by a considerable band broadening in the analytical range, which 7415



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Finally, a sorption test was also performed on a much thinner sample to identify the functional group(s) in the polymer backbone directly involved in the interaction with the penetrant. To this end, a dilute solution (1 wt %) of PCL in THF was prepared and cast as a single drop on a KBr substrate. After complete solvent removal, the supported PCL film (about 1.0 μm thick) was introduced in the FTIR cell and a sorption test was performed at 65 °C, which is slightly higher than the melting point of the crystalline domains of PCL. 2.3. Gravimetry. Water sorption measurements were performed at 30 °C using a quartz spring balance. Prior to the sorption test, the sample was dried overnight under vacuum at the experimental temperature: once a constant weight was attained, water vapor was introduced in the system and differential sorption experiments were performed by increasing water vapor activity in a stepwise manner. Full details on the experimental procedure are given elsewhere.25 2.4. FTIR Data Analysis. Full absorbance spectra (i.e., PCL plus absorbed water) were obtained using a background collected on the cell with no sample inside, at the test conditions, i.e., at the same relative pressure of water vapor used for the sorption measurement. The spectra representative of absorbed water were obtained by using the difference spectroscopy (DS) technique,26 i.e.

comparison with the results of quantum chemistry calculations performed by use of a hybrid density functional theory (DFT) functional. The ab initio simulation of the vibrational spectra were found to be in good agreement with the experiment, confirming the predictive capabilities of the chosen model chemistry and supporting the proposed molecular structure of the H-bonding aggregates. The outcome of the spectroscopic analysis in terms of population of penetrant species represents the background information that we have used to tailor and test a predictive thermodynamic model for the PCL−water system. In particular, our thermodynamic analysis has been based on the use of a nonrandom compressible lattice model available in the literature,24 able to cope with issues related to cross- and selfhydrogen bond formation (non-random hydrogen-bonding theory, NRHB). In fact, on the basis of the physical picture emerging from the vibrational analysis and information available from gravimetric sorption isotherms, water selfinteractions and hydrogen-bonding cross-interactions between water molecules and the carbonyl groups of the polymer backbone have been accounted for explicitly in the model. A satisfactory quantitative agreement has been obtained between theoretical predictions and experimental results in terms of concentration of water species present in the mixture.

Ad = A s − kA r

2. EXPERIMENTAL SECTION 2.1. Materials. PCL (CAPA FB100) was supplied by Solvay Warrington (Cheshire, WA4 6HB, U.K.) as a 100% resin in the form of 3 mm pellets, with a weight-average molecular weight M̅ w of 80 000 D. To obtain a film 100 ± 1 μm thick, the material was processed by compression molding (T = 110 °C, p = 120 bar). The resulting film had a density of 1.158 g/cm3 and a crystallinity degree of 58% (DSC). 2.2. FTIR Spectroscopy. A stainless steel, vacuum tight cell equipped with ZnSe windows was accommodated in the sample compartment of a suitably modified FTIR spectrometer to perform the time-resolved acquisition of the spectra during the sorption experiments. Data collection on the polymer films exposed to water vapor at constant temperature and different relative pressures was carried out in the transmission mode. The sorption cell was directly connected through service lines to a water reservoir, a turbo-molecular vacuum pump, a pressure transducer [MKS Baratron 121 (Andover, MA); full scale, 100 Torr; resolution, 0.01 Torr; accuracy, ±0.5% of the reading] and a Pirani vacuometer. Full details of the experimental setup are reported elsewhere.17 Before each sorption measurement, the sample was dried under vacuum overnight at the test temperature in the same apparatus used for the test. The FTIR spectrometer was a Spectrum 100 from PerkinElmer (Norwalk, CT), equipped with a Ge/KBr beam splitter and a wide-band deuterated triglycine sulfate (DTGS) detector. The transmission spectra were collected with the following instrumental parameters: resolution, 2 cm−1; optical path difference (OPD) velocity, 0.5 cm/s; spectral range, 4000−600 cm−1. Spectra were acquired in the single-beam mode using a dedicated software package for time-resolved spectroscopy (Timebase from PerkinElmer). Differential sorption tests were performed at 30 °C by increasing stepwise the relative pressures of water vapor p/p0 within the range 0−0.75. Moreover, an integral sorption test was performed in the p/p0 range of 0−0.6.

(1)

where A is the absorbance and the subscripts d, s and r denote, respectively, the difference spectrum, sample spectrum (“wet” specimen), and the reference spectrum (“dry” specimen). k is an adjustable parameter which allows compensation for thickness differences (if any) between the sample and the reference spectra. It was experimentally verified that negligible thickness changes take place during sorption; therfore, the k values were consistently taken as unity. The DS procedure allows us to eliminate the interference of the polymer spectrum in the regions of interest, i.e., the 3800−3100 cm−1 range [ν(OH)] and the 1670−1580 cm−1 range [δ(HOH)]. Separation of multicomponent bands into individual peaks was achieved by a least-squares curve fitting algorithm based on the Levenberg−Marquardt method.27 The peak function used throughout was a mixed Gauss−Lorentz line-shape of the form ⎡⎛ x − x ⎞ 2 ⎤ 0 ⎟ f (x) = (1 − Lr )H exp −⎢⎜ (4 ln 2)⎥ ⎣⎝ FWHH ⎠ ⎦ H + Lr x−x 2 4 FWHH0 + 1

(

)

(2)

where x0 is the peak position, H the peak height, fwhh the fullwidth at half height, and L the fraction of Lorentz character. In order to keep the number of adjustable parameters to a minimum, the baseline and the number of components and the band-shape (L parameter) were fixed, allowing the curve-fitting algorithm to optimize the fwhh, height, and position of the individual components. The minimum number of components was determined by visual inspection and by a second-derivative analysis of the experimental profiles. The experimental spectra for 2D-COS analysis were preprocessed to avoid the occurrence of artifacts due to baseline instabilities and other nonselective effects.28 The frequency region of interest (3900−3200 cm−1) was truncated and subjected to a linear baseline correction, followed by offset to zero absorbance. Generalized 2D-IR analysis was performed 7416



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by a computer program written in house within the MATLAB environment (Mathworks, Natick, MA), which also provided the tools for the graphical representation of the correlation spectra (contour plots, 3D images). The algorithm proposed by Noda relying on the Hilbert transform29 was employed, which offers a robust and efficient method for the numerical evaluation of the correlation intensities. The 2D correlation analysis was performed on an evenly spaced sequence of 25 spectra collected at a constant sampling interval of 3 s. It was found that considering shorter time intervals does not improve the quality and resolution of the resulting correlation spectra. The notation adopted to identify the peaks appearing in the correlation spectra is that described in ref 26. 2.5. Computational Methods for Conformational Searching and Normal Coordinate Analysis. All the molecular mechanics (MM) calculations were performed using the MM+ force field, which is an extension of the popular Allingher’s MM2.30,31 The potential energy surface of the model compound was explored by a conformational search algorithm adopting the Monte Carlo multiple minimum (MCMM) scheme32 for systematic variations of the selected dihedrals. All MM computations were made with the program suite Hyperchem Pro6, from Hypercube Inc. (Gainesville, FL). Quantum chemistry calculations were performed using the unrestricted density functional theory.33 In particular, the hybrid method referred to as B3LYP was used, in combination with the standard 6-31G(d) basis set. This method includes Becke’s three-parameter exchange functional coupled with the Lee−Yang−Parr correlation functional. After geometry optimization, a normal coordinate analysis at the same level of theory was performed, comprising the calculation of the Hessian matrix (F) by analytical evaluation of the first and second derivatives of the potential energy with respect to the Cartesian displacement coordinates. The F matrix was then transformed in terms of mass-weighed coordinates and diagonalized to obtain the corresponding eigenvalues (normal frequencies) and eigenvectors (displacement vectors, L matrix). Finally, a transformation into a set of nonredundant internal coordinates of both the F and L matrices was accomplished to characterize the normal modes in terms of their potential energy distribution (PED), expressed in normalized form.34 (PED)jk =

FjjLjk2 ∑i FiiLik2

Figure 1. FTIR spectrum of PCL in the dry state (red trace) and after equilibration in water vapor at p/p0 = 0.6 (blue trace).

1670−1580 cm−1, respectively). Suppression of the polymer interference by difference spectroscopy allows us to isolate the spectrum of the penetrant in both the frequency intervals. This analysis is reported in Figure 2A,B for the sample equilibrated at different relative pressures of water vapor. The gradual increase of the signal intensity is evident; the δ(HOH) band is featureless, which reflects the lower sensitivity of this mode toward H-bonding formation. This characteristic would make the bending peak more suitable for analytical purposes (no significant changes in molar absorptivities between the different water species), but the advantage is offset by an intensity decrease with respect to the stretching modes of about 1 order of magnitude. This worsens the signal-to-noise ratio and lowers the quantitative accuracy. The ν(OH) band is more complex: it displays two well-resolved maxima at 3629 and 3547 cm−1. A LSCF analysis was attempted by using the minimum number of components (two) identified visually and by second-derivative spectroscopy, but it was unsuccessful, irrespective of the model adopted for band-shape simulation (Gaussian, Lorentzian, or a linear combination of the two, see Experimental Section). This suggests the occurrence of further components in the lower-frequency side; failure of secondderivative spectroscopy in identifying the low-frequency bands is to be ascribed to their considerable fwhh coupled with the closeness between the peaks’ maxima. 3.2. Two-Dimensional Correlation Spectroscopy. To improve the resolution in the ν(OH) range we turned to bidimensional correlation spectroscopy, which has been demonstrated to be very effective in investigating molecular interactions in H-bonding systems.26 The resolution enhancement brought about by this technique originates from the spreading of the spectral data over a second frequency axis, coupled with the vanishing of the asynchronous correlation intensity for signals evolving at the same rate.29 In addition, 2DCOS spectroscopy can provide valuable information about the dynamics of the evolving system. 2D-COS spectroscopy is a perturbative technique whereby a system initially at equilibrium is subjected to an external stimulus: a correlation analysis is performed on the spectral response of the system by measuring the covariance of two correlated signals (peak absorbance, in the present case) as a function of a third common variable related to the perturbing function (time, in the present case). Thus, the time-evolution of the stretching band of sorbed water was considered for the analysis, which is represented in Figure 3 in terms of overall band area as a function of sorption time. It is noted that the process is relatively fast (it can be considered complete after 50 s) and can be very accurately described in terms of Fick’s

· 100 (3)

where the PED (in %) refers to the contribution of the jth internal coordinate to the kth normal mode, Fjj the jth diagonal force constant, and Ljk the corresponding element of the L matrix. Only the diagonal terms of the F matrix are considered. DFT and normal coordinate analysis (NCA) calculations were performed by the Gaussian 03 program package35 (Gaussian Inc., Pittsburgh, PA) run on a HP system model Integrity rx2620 (UNIX OS), equipped with two parallel Itanium processors. The results were visualized with the GaussView graphic interface. PED calculations were carried out with the aid of the VEDA program.36

3. RESULTS AND DISCUSSION 3.1. Absorbance and Difference Spectra. In Figure 1, the spectrum of PCL equilibrated at a relative pressure of water vapor of 0.6 is compared with the spectrum of dry PLC. The characteristic features of sorbed water are readily identified in the ν(OH) and in the δ(HOH) ranges (3800−3100 cm−1 and 7417



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Figure 2. Difference spectra in the stretching region (3800−3100 cm−1) and in the bending region (1670−1580 cm1) for different relative pressures of water vapor (from 0.1 to 0.75).

intensity changes in the sampling interval. Conversely, the asynchronous spectrum displays a peak at [v1, v2] when the two corresponding IR signals change at different rates and zero intensity if they change at the same rate. This provides the characteristic resolution enhancement and the specificity of the asynchronous pattern.26,28,29,39 Moreover, the sign of the peaks supplies information about the sequence of changes of the two correlated signals, according to the so-called Noda’s rules.29 Those of interest in the present context are the following: (i) In the synchronous spectrum, the sign of a cross-peak is positive if the correlated signals change in the same sense (they both increase or decrease) and is negative otherwise. (ii) If an asynchronous cross-peak located at coordinates v1, v2 is positive, the intensity change at v1 is accelerated with respect to that at v2. If the cross-peak is negative, the opposite relationship between the rates of change holds true. (iii) This remains valid as far as the synchronous spectrum at v1, v2 is positive; otherwise, the above relationships are to be reversed. The synchronous spectrum obtained by 2D-COS analysis of the sequence of spectra shown in the inset of Figure 3 is reported in Figure 4, while the asynchronous spectrum is

Figure 3. Integrated absorbance (3720−3000 cm−1) of the H2O spectrum as a function of sorption time. Measurement performed at 30 °C at p/p0 = 0.6. Solid dots represent the experimental data points; the continuous line is the least-squares best-fitting of the data with eq 4. The inset displays the time evolution of the H2O spectra.

equation.37,3 The data represented in Figure 3 yield a diffusivity value of 4.93 × 10−7 cm2/s, in excellent agreement with the value reported by Yoon et al. based on gravimetric measurements (2 × 10−7 cm2/s).38 From a phenomenological point of view, the response function of the system can be suitably simulated by a twocomponent exponential of the form (see Figure 3) A(t ) = A1(1 − e−k1t ) + A 2 (1 − e−k 2t )

(4)

which allows us to directly relate the dynamic behavior of the system to one of the cases that have been most extensively investigated.26,29 If we assume the two components to be related to the distinct species involved in the diffusion process, it turns out that the synchronous spectrum [Φ(v 1 , v 2 )] and the asynchronous spectrum [Ψ(v1, v2)] can be expressed as follows:29 Φ(ν1 , ν2) =

A(ν1)A(ν2) 1 · T k1 + k 2

2A(ν1)A(ν2) k1 − k 2 Ψ(ν1 , ν2) = · πT k1 + k 2

(5)

Figure 4. 2D-COS synchronous map obtained from the time-resolved spectra collected during the sorption experiment at p/p0 = 0.6 (sequence shown in the inset of Figure 3).

(6)

where A(v1) and A(v2) represent the initial absorbance of the peaks centered at v1 and v2, respectively, and T is the time lapse. Equations 5 and 6 clarify the meaning of the correlation spectra, which can be summarized as follows: in the synchronous map, the main diagonal (power spectrum) conveys information about the signals that are more sensitive to the applied perturbation. The cross-correlation peaks at offdiagonal positions reflect any couple of signals undergoing

represented in Figure 5 both as a color-map and as a threedimensional representation, which is possibly easier to read. In the same figure is also shown the 1-D spectrum with the location of the components identified by the analysis. The 2DCOS results are summarized in Table 1. The synchronous map does not provide significant enhancement of resolution, displaying only the two components already identified in the frequency spectrum plus the relative 7418



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Figure 5. 2D-COS asynchronous map obtained from the time-resolved spectra collected during the sorption experiment at p/p0 = 0.6 (sequence shown in the inset of Figure 3).The map is represented as an intensity−color diagram (A) and as a 3-D image (C); (B) presents the frequency spectrum with the position of the components identified by 2D-COS analysis.

occurrence of two couples of signals centered at 3635−3550 cm−1 and at 3595−3465 cm−1: the two signals of each doublet evolve with the same rate, but the dynamics of the two doublets is different. In particular, according to the sign of the crosspeaks, in the sorption experiment, the couple at 3635−3550 cm−1 grows faster than that at 3595−3465 cm−1. The above findings are sound when one considers that a single water molecule produces two OH-stretching modes (out-of-phase at higher frequency and in-phase at lower frequency) and are suggestive of the presence of two distinct water species. Of the four identified signals, three are sharp and the fourth is considerably broader. In particular, the components of the doublet at 3635−3550 cm−1 display a comparable fwhh, whereas for the couple at 3595−3465 cm−1 the band at lower frequency is much broader than its high-frequency counterpart. This suggests that in the H2O molecules responsible for the former doublet, the two O−H bonds are equivalent (i.e., the original C2v symmetry is retained), while the species producing the 3595−3465 cm−1 pattern displays two hydrogens with a substantially distinct chemical environment (more on this later). Finally, we note that the asynchronous spectrum obtained in the desorption experiment is exactly coincident with that of Figure 5 as for the overall pattern, but the sign of all peaks is reversed. This implies that, on desorption, the doublet at 3595−3465 cm−1 evolves (decreases) faster than that at 3635−3550 cm−1. We will see in the forthcoming paragraphs that this result brings relevant implications in the analysis of the diffusion process. 3.3. Interacting Site(s) on the Polymer Backbone. For a positive assignment of the components identified in the spectrum of absorbed water, we need to recognize the functional groups of the polymer backbone involved in the H-bonding interactions with the penetrant. This will allow us to propose a likely structure for the H-bonding adduct. Two

Table 1. Position, Sign, and Type of the Correlation Peaks Appearing in the Synchronous and Asynchronous Spectra Synchronous ν1 (cm−1)

ν2 (cm−1)

3628 3549 3628

3628 3549 3549

signa

+ + + Asynchronous

ν1 (cm−1)

ν2 (cm−1)

signa

typeb

3595 3550 3465 3465

3635 3595 3635 3550

− + − −

C C C C

typeb

trend

A A C

↑ ↑↑ rate of change 3595 3550 3456 3465

< > <
110°.41 For water as proton donor and the R2CO group as acceptor, a mean D value of 2.840 Å (2.69−3.11 Å)42 and a d value of 1.900 (1.73−2.23 Å)42 were evaluated over 2485 different structures, all of which are characterized by a pronounced directionality (θ > 130°). The out-of-phase and in-phase ν(OH) modes of H2O in the structure shown in Figure 9B are shifted downward with respect to the isolated molecule by −41 and −63 cm−1, respectively, while the δ(HOH) vibration is shifted to higher frequency by +26 cm−1 (see Table 3). These effects are characteristic of water acting as proton donor and represent the signature for the occurrence of H-bonding in the structure shown in Figure 9B. The experimentally observed frequencies for isolated water molecules are 3756, 3657, and 1595 cm−1,42

respectively, to be compared with the values 3635, 3550, and 1632 relative to the frequencies of the same normal modes measured in the PCL/H2O system. Toward a comparison between the calculated and the experimental effects, one must consider the highly anharmonic character of the ν(OH) vibrations; thus, the frequency shift due to the H-bonding interaction is customarily calculated considering the mean stretching vibration (i.e., (vop − vip)/2) in place of the single frequency values.26 Accordingly, the observed shift is (3604 − 3707 = −103) cm−1, while the calculated shift is (3591 − 3643 = −52) cm−1. For the bending mode, the experimental shift is +41 and the calculated is +26. Concerning the acceptor, the ν(CO) is theoretically predicted to be red-shifted by −26 cm−1, as compared to an experimental Δν value of −15 cm−1. The ν(C−O)/δ(O−C O) mode is correctly predicted to shift at higher frequency (+13 cm−1), although only the direction is experimentally available for this mode. According to the QM picture, the ν(CO) moves downward because of the weakening of the CO force constant (from 13.185 to 12.902 mdyn/Å; see Table 4), which in turn is a consequence of the redistribution of the electron density caused by the interacting proton. In contrast, the (C)C−O force constant is predicted to increase from 6.162 to 6.648 mdyn/Å, and this effect is caused by an 7422



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increased participation of the sp3 oxygen to the −C(O)−O− resonance system to compensate for the withdrawing of electron density from the sp2 oxygen by the proton. Thus, while the bond order of the CO linkage decreases as a consequence of H-bonding formation, the bond order of the C−O linkage increases, which explains the opposite directions observed and calculated for the shifts of the relative normal modes. The bond lengths show analogous trends: when the interaction takes place, the CO bond is elongated by about 0.6% (see Table 4), while the C−O bond decreases by 1.0%. As for the proton donor, the H−O bond involved in the interaction is elongated by about 0.7% and the relative force constant decreases from 8.03 to 7.77 mdyn/Å; the other O−H bond is only marginally affected. The same analysis carried out with the second-lowest-energy minimum identified in the conformational search produced essentially coincident results. The interaction of water with the sp3 oxygen has been simulated also: the resulting complex, represented in Figure 9C, is again consistent with the requirements of H-bonding formation for the specific donor/acceptor pair. In particular, the D parameter is 2.94 Å, to be compared to a value of 2.93 Å reported in ref 42, while d is equal to 1.99 Å. The interaction retains a significant directionality character (θ = 165.3°) as is generally observed for H-bonding.42−45 The three H2O vibrations are predicted to occur at 3667, 3526, and 1658 cm−1, i.e., −35, −49 and +11 cm−1 with respect to the reference state (isolated H2O molecule). A comparison of the above shifts with those found for the structure shown in Figure 9B indicates the formation of a weaker H-bonding interaction in the structure shown in Figure 9C. However, the hypothetical possibility of the sp3 oxygen to act as an acceptor is confirmed. Considering the vibrations of the donor, it is found that the ν(CO) is predicted to absorb at 1757 cm−1 (Δν = +11) while the ν(C−O)/δ(O−CO) vibration is calculated at 1147 cm−1 (Δν = −21), which is just the opposite of what is experimentally observed. The above comparison rules out the direct involvement of the sp3 oxygen in the interaction and demonstrates that the observed blue-shift of the ν(C−O)/ δ(O−CO) mode is a second-order effect due to the carbonyl−water interaction. It is noted that whereas the theoretical analysis correctly predicts the modes perturbed by the interaction as well as the directions of the observed shifts, the extent of these shifts is underestimated by a factor of about two for the donor and is overestimated 1.7 times for the acceptor. This discrepancy can be partly related to the highly anharmonic character of the vibrations involved in the case of the donor but is less justified for the acceptor. As we will discuss in more detail later, the actual origin of the disagreement lies in the fact that the real configuration of the adduct is more complex than that shown in Figure 9B. 3.5. Interpretation of the Experimental Spectrum of Sorbed Water. Putting together the information discussed so far, we are now in position to propose the interpretation of the spectrum of sorbed water reported in Figure 2A. The two sharp peaks at 3635−3550 cm−1 are assigned to the νas and the νs modes, respectively, of a single water molecule interacting with the carbonyl groups of PCL. In a series of papers46,47 Iwamoto and co-workers investigated the H-bonding interactions of water with polymers and low-molecular weight model compounds. In particular, these authors were interested in interpreting the complex pattern displayed by the interacting water in the ν(OH) range. By systematically changing the H2O/CO molar ratio, they were able to obtain systems in

which the prevailing aggregate had a 1:1 stoichiometry, a 1:2 stoichiometry, or intermediate situations. According to their notation, the species present were −CO···H−O−H, −C O···H−O−H···OC−, or both. The 1:1 complex exhibits a very sharp peak at 3688 cm−1 which is well-resolved from the remaining spectral features and represents a readily detectable signature of the latter species. The second peak associated with the 1:1 complex lies at 3563 cm−1 and is fully overlapped with the corresponding mode of the 1:2 complex which absorbs at 3638 and 3543 cm−1. The nature of the vibrations is quite different for the two complexes. In the 1:1 adduct, the local symmetry of the H2O molecule is suppressed and the highfrequency peak is mostly associated with the vibration of the free O−H bond, whereas the 3563 cm−1 peak is prevailingly due to the interacting O−H. However, a certain degree of mechanical coupling still persists; therefore, the two modes can be described as out-of-phase and in-phase stretchings, respectively. In the 1:2 adduct, the local symmetry of the water molecule is retained and the two modes can be classified as νas(OH) and νs(OH), respectively. The nonequivalence of the two O−H bonds in the 1:1 complex is reflected in the considerable difference of fwhh for the two modes, which exhibit close band-shape in the case of the 1:2 adduct. Returning to the system under investigation, we made the following observations: (i) No evidence was found for the presence of a sharp component at around 3690. (ii) The 2DCOS analysis indicated that in the PCL/H2O system the water species producing the signals at 3635−3550 cm−1 have two equivalent O−H bonds, that is, these species retain the original C2v symmetry. It is concluded that H2O molecules forming a single H-bonding interaction with a PCL carbonyl do not exist. Each water molecule directly interacting with the polymer substrate, “the core hydration”, has both O−H groups involved in H-bonding with two carbonyls. This conclusion is in accord with those of Iwamoto et al. on the state of water in poly(methyl methacrylate) and poly(vinylacetate).47 The doublet at 3595−3465 cm−1 is to be ascribed to self-associated water. In particular, the sharp feature identified by 2D-COS at 3595 cm−1 is localized primarily on the noninteracting O−H bond, whereas the broad band at 3465 cm−1 is attributed (predominantly) to the ν(OH) vibration of the interacting O− H bond. Here again, mechanical coupling persists and the two modes are more accurately classified as νop(OH) and νip(OH), respectively. Both the position and the breadth of the 3465 cm−1 component are characteristic of self-associated water. A schematic representation of the two water species identified by the spectroscopic analysis is reported in Scheme 1. Scheme 1. Schematic Representation of the Two Water Species Identified in the PCL−H2O System

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It is apparent that the proposed structure of the H2O/PCL adduct (Scheme 1A) is more complex than that considered for the ab initio−normal-coordinate analysis (Figure 9B). However, we found a more realistic model (i.e., with two PHEX groups bound to a single water molecule) exceedingly difficult to handle in terms of geometry optimization and the resulting structures scarcely reliable. In spite of the adopted simplification, we believe the computational results to be qualitatively meaningful to rationalize the observed spectral effects and to exclude the direct involvement of the sp3 oxygen in the Hbonding interaction. The simplified molecular structure is likely responsible for the discrepancies between the calculated and the observed peak-shifts for both the donor and the acceptor groups (see Tables 2 and 3). 3.6. Estimating the Population of Water Species. For the present system, the curve-fitting process represents an essential part of the quantitative analysis. It is therefore worth discussing in some detail the criteria adopted to develop the starting model to be refined by the optimizing algorithm. The results of 2D-COS analysis were taken as a guide to establish the number of components and the starting peak positions. However, the number of components detected by 2D-COS represents a “true” or limiting value, but a peak was included in the curve-fitting model only if it could be discerned in the frequency spectrum by visual inspection and/or secondderivative analysis. Thus, for the peak at 3630 cm−1, which according to 2D-COS analysis comprises two components, only a single peak was included in the model because of the absence of any resolution. In the lower-wavenumber side, a further band at 3259 cm−1 not identified by 2D-COS analysis, likely because of its very low intensity, was included in the LSCF model to improve the fitting. It was tentatively ascribed to the first overtone of the bending fundamental, 2δHOH, possibly enhanced by Fermi resonance with the neighboring band at 3465 cm−1. As demonstrated in Figure 10a, very satisfactory simulation of the experimental data points was achieved; the results of the LSCF analysis are summarized in Table 5. The quantitative analysis relies on coupling spectroscopic and gravimetric data collected in closely matching conditions.

The isolated water molecules represented in Scheme 1A coincide with the first hydration layer of penetrant (first shell) in the frame of the multilayer adsorption model of Brunauer, Emmet, and Teller (BET),48 whereas the self-associated water molecules (Scheme 1B) are representative of the second-shell hydration layer. To complete the interpretation of the band profile of sorbed water, we explicitly note that it invariably displays a feature at around 3440 cm−1 which resembles a partly resolved component (see Figure 2A and inset of Figure 3). This feature was present and even more pronounced in the difference spectra reported in refs 46 and 47, and was assigned to the hydrated CO groups; a quantitative analysis based on the intensity of this supposed component was also put forward. Our interpretation differs from that of the above authors. In our view, the feature at 3440 cm−1 does not represent an actual maximum but is a derivative-type feature appearing in the difference spectrum as a consequence of the downward shift of the 3438 cm−1 peak of PCL (the first overtone of the ν(CO) fundamental) after water sorption. The effect is similar to that represented in Figure 7A for the ν(CO) vibration but amplified twice (roughly) because of overtone nature of the vibration involved. According to this interpretation, the feature was considered to be an artifact and neglected in the subsequent curve-fitting analysis (see Figure 10).

Figure 10. Curve fitting analysis of the spectrum representative of water sorbed in PCL (p/p0 = 0.6). The figure displays the experimental profile, the best-fitting curve, and the four resolved components.

Table 5. Relevant Spectral Parameters Obtained from LSCF Analysis

It is explicitly noted that the FTIR spectra discussed so far differ from those in previous literature reports22,23 where the spectrum of water sorbed in PCL was collected by ATR-FTIR spectroscopy. The shape and, above all, the relative intensity of the ν(OH) water band in these works are unrealistic and incompatible with the present data. In particular, the band shown is the strongest of the whole spectrum (it is more intense than the carbonyl fundamental), whereas in our case it is barely detectable and comparable to the carbonyl overtone, which is about 3 orders of magnitude weaker than the respective fundamental (see Figure 1). Furthermore, the bandshape reported in refs 22 and 23 resembles the characteristic profile of liquid water and is considerably different from that in Figure 2A and in the inset of Figure 3. Our interpretation is that the above authors sampled a layer of liquid water formed between the PCL film and the ATR optical element. In any event, in the light of the data discussed herein, the ATR spectrum reported in refs 22 and 23 cannot be considered representative of water molecules sorbed in PCL.

peak 1

peak 2

peak 3

a

7424

p/p0 = 0.20

p/p0 = 0.30

p/p0 = 0.50

p/p0 = 0.60

p/p0 = 0.75

position (cm−1) fwhh (cm−1) area (cm−1) La position (cm−1) fwhh (cm−1) area (cm−1) La position (cm−1) fwhh (cm−1) area (cm−1) La

3632

3632

3632

3631

3631

72.4 3.28 0 3546

72.7 4.94 0 3546

72.8 8.39 0 3546

72.6 10.14 0 3546

72.0 12.46 0 3546

58.0 1.96 0.47 3493

59.3 2.99 0.47 3493

63.2 5.29 0.47 3493

65.6 6.59 0.47 3494

69.4 8.50 0.47 3494

148.0 1.77 0.21

150.1 2.80 0.21

163.8 5.73 0.21

174.2 8.04 0.21

193.8 13.30 0.21

R2

0.997

0.998

0.998

0.999

0.999

Fixed parameter. dx.doi.org/10.1021/jp502270h | J. Phys. Chem. B 2014, 118, 7414−7429


Article

The overall correlation between the two data sets is demonstrated in Figure 11, relative to the sorption isotherms

Figure 11. Integrated absorbance of the ν(OH) and the δ(HOH) bands as a function of the total water concentration as evaluated gravimetrically.

Figure 12. A3546/Ctot as a function of A3491/Ctot.

is of general applicability, provided that carefully collected spectroscopic and gravimetric data are available. From the knowledge of the absorptivity values, the concentration of water species is readily obtained as

evaluated with the two techniques. The linear correlation through the origin between the integrated absorbance and the total water concentration in the sample, both in the OH stretching and in the HOH bending ranges, demonstrates the Beer−Lambert behavior of the system, thus allowing reliance on band intensities to monitor the species concentration. The linearity is slightly worse for the δ(HOH) signal (correlation coefficients R2 are 0.995 and 0.960 for the ν(OH) and δ(HOH) signals, respectively) likely because the intrinsic intensity of the former signal is lower by more than 1 order of magnitude with respect to the latter. If we label the water molecule interacting with the carbonyls as (H2O)fs (subscript standing for first shell; see Scheme 1, structure A) and the self-interacting water molecule as (H2O)ss (for second shell; see Scheme 1, structure B), from the Beer− Lambert relationship, and taking into account the mass balance (Cfs + Css = Ctot), we may write A fs A + ss = C tot εfs ·L εss ·L (7) which can be rearranged as A fs A ε = εfs ·L − ss fs C tot C tot εss

Css =

C tot A fs εss A ss εfs

+1

;

Cfs = C tot − Css (9)

Equation 9 shows that only the absorptivity ratio is needed to quantify the species and that the sample thickness, a relevant source of uncertainty in the evaluation, especially for thin samples (≤1 μm), does not appear explicitly in the formula. The method remains applicable even when gravimetric data are unavailable, in which case the concentrations follow directly from the respective Lambert−Beer relationships (i.e., Cfs = Afs/ Lεfs; Css = Ass/Lεss). Figure 13 reports the total concentration of sorbed water along with those of first shell and second shell species as a

(8)

In the above equations, A is the absorbance area of the analytical peak (cm−1), L the optical path (sample thickness, cm), C the concentration (mol/cm−3), and ε the molar absorptivity (cm/mol; later transformed into the customary units km/mol). The subscripts have the already stated meaning. Equation 8 predicts that a plot of Afs/Ctot versus Ass/Ctot is linear, with a negative slope equal to the molar absorptivities’ ratio εfs/εss and the intercept equal to εfsL. As analytical peaks, we selected the component at 3546 cm−1 for the (H2O)fs species because the peak at 3630 cm−1 is actually made of two unresolved components and the band at 3491 cm−1 for (H2O)ss; Ctot was the water concentration evaluated gravimetrically. The plot of Figure 12 conforms to the theoretical prediction; the molar absorptivities evaluated therefrom are εfs = 72.2 km/mol and εss = 98.2 km/mol. The close agreement between the predicted and the observed behavior confirms the soundness of the proposed molecular model and the reliability of the quantitative method. The latter

Figure 13. Ctot, Cfs, and Css as a function of the relative pressure of water vapor.

function of the relative pressure of water vapor. It is apparent that the two above concentrations lie within the experimental uncertainty for most of the relative pressure range investigated (seven data points over nine). This coincidence strongly suggests that from p/p0 = 0 to 0.65 all absorbed water is present in the form of dimers. At the highest p/p0 values (>0.7), Css significantly offsets Cfs, which may occur only if aggregates of more than two water molecules start to form. Thus, the 7425



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two separate contributions: the first related to mean field interactions and the second accounting for specific H-bonding interactions. In turn, the mean field contribution is expressed as the sum of an ideal random mixing contribution and a nonrandom mixing contribution, the latter being constructed by treating each kind of contact as a reversible chemical reaction, according to the quasichemical approximation.50 Nonrandomness is assumed for all the possible couples of contacts between mers of the components of the mixture as well as hole sites of the lattice.51 The second contribution, related to H-bonding interactions, is formulated in NRHB model by using the combinatorial approach proposed by Veytsman.52,53 Expressions for water chemical potential in the PCL−water mixture and in the pure water vapor phase in contact with it are both supplied by the NRHB model, which also provides equations for equilibrium density of the mixture and pure water vapor as well as for the amount of self- and cross-HB formed at equilibrium in the mixture and in the water vapor phase. The volumetric water fraction present within the amorphous PCL domains when phase equilibrium establishes between pure water vapor and polymer−water mixture, at a fixed pressure and temperature, is ruled by the equality of the chemical potentials of water in the two phases. It is assumed that no polymer is present in the vapor phase; thus, no equality of chemical potential of polymer in the two phases needs to be imposed. Relevant parameters of the model are i) the mean field lattice fluid interaction parameter k12 which quantifies the departure from the geometric mean of the mixing rule for the characteristic mean field energies of the lattice fluid, i.e.

departure point between the Css and Cfs curves unambiguously defines the onset of the clustering phenomenon, whereby we define clustering as the occurrence of aggregates comprising more than two water molecules. Extrapolation of the curves of Figure 13 indicates that the concentration of high-order aggregates becomes even more predominant approaching the water vapor pressure (p/p0 = 1). In the light of the above results, we may also interpret the sequence of events as revealed by 2D-COS analysis (see Table 1). The two water species display different dynamics: on sorption, the concentration buildup of the first-shell layer is accelerated with respect to that of the second-shell layer; on desorption, the opposite behavior is observed. This is exactly what one would intuitively expect for a molecular system as that depicted in Scheme 1. In the usual assumption of a crystalline phase impervious to the penetrant, which diffuses only through the amorphous phase, we calculated that, at the onset of clustering, 0.094 mmol/cm3 of water (Cfs) are directly interacting with the carbonyls, which corresponds to 0.188 mmol/cm3 of H-bonded carbonyls. Taking into account the crystallinity degree of PCL and the densities of the crystalline and amorphous phases (1.200 and 1.021 g/cm3, respectively), we can evaluate the molar concentration of carbonyls in the amorphous phase and conclude that only 4.0% of these are H-bonded to water, which means that the onset of the clustering phenomenon is not to be ascribed to a saturation effect. 3.7. Macroscopic Thermodynamics of PCL−Water Mixture Accounting for HB Interactions. Modeling of water sorption thermodynamics in PCL has been performed assuming that water is absorbed only within the amorphous regions and that the crystalline domains are impervious to water. Moreover, the amount of crystallinity is taken as not being affected by absorbed water. In addition, the possible presence of interphases made of amorphous domains with a restricted mobility determined by the constraint exerted by the crystalline regions has also been neglected. In fact, invoking the arguments proposed by Bonavoglia et al.49 to address this issue, it is explicitly considered here that the presence of crystals does not alter the thermodynamic behavior of the amorphous domains. As a consequence, in comparing experimental data with model predictions, the overall solubility measured in the semicrystalline sample has been simply rescaled to the sole amorphous phase, accounting for the presence of the impervious crystalline fraction. On this basis, in the following, water sorption will be analyzed by referring to the water mass fraction relative to the sole amorphous phase, i.e., wam 1 , defined as −1 ⎛ w am ⎞ w1am = ⎜1 + tot ⎟ w1 − 1 ⎠ ⎝

* = (1 − k12) ε11 *ε22 * ε12

(11)

where subscripts 1 and 2 refer to the penetrant and polymer species, respectively and ii) the parameters E0ij and S0ij which represent the molar internal energy of formation and the molar entropy of formation of hydrogen bonding between the proton donor group of type i and the proton acceptor group of type j, respectively. In the case at hand, because only data at one temperature are examined, the parameters E0ij and S0ij are lumped in the single parameter G0ij, which represents the molar Gibbs energy of ij HB formation. In fact, because V0ij is assumed to be always equal to zero (further on this point later), one can take Gij0 = Eij0 − TSij0

(12)

To interpret sorption isotherm using the NRHB model, the findings of vibrational spectroscopy investigation have been used as a guide to identify the type of H-bonding interactions occurring in the PCL−water system. In fact, self-interactions occur only between water molecules and are indicated as 11 interactions, because they are established between a proton donor of type 1 (i.e., a hydrogen atom of a water molecule) and a proton acceptor of type 1 (i.e., the oxygen atom of a water molecule). It is worth noting that, according to the previous literature on NRHB model,54 two equivalent proton donor groups and two equivalent proton acceptor groups are assumed to be present on each molecule of water. As indicated by the discussed vibrational spectroscopy analysis, cross interactions occur between a hydrogen atom of a water molecule (i.e., a proton donor of type 1) and a carbonyl group on the polymer backbone (i.e., a proton acceptor of type 2) and are indicated as 12 interactions. Each of these two H-bonding interactions is characterized, in principle, by three parameters, i.e., energy of

(10)

am

where w is the mass fraction of amorphous phase of polymer and wtot 1 the mass fraction of absorbed water referred to whole semicrystalline PCL, that is, the value determined experimentally by gravimetric measurements. An equation of state (EOS) approach, accounting for possible self- and cross- interactions (hydrogen bonding) in rubbery polymer−penetrant systems, has been used to model water sorption thermodynamics in the amorphous regions of PCL. In detail, the adopted model is the “non-random lattice fluid hydrogen bonding” (NRHB) model24 in which the polymer−penetrant mixture is idealized as a compressible lattice. The configurational partition function is factorized in 7426



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Table 6. NRHB-EOS Parameters for Pure Water and PCL, As Obtained by Fitting PVT Data to NRHB Model for Pure Fluidsa component

εh* (J/mol)

εs* (J/(mol K))

vsp,0 * (cm3/g)

E011 (J/mol)

S011 (J/(mol K))

water PCL

5336.5 5876 ± 50

−6.506 3.824 ± 0.01

0.970 34 0.8873 ± 0.005

−16 100 −

−14.7 −

a Error ranges for PCL parameters represent the 95% confidence intervals estimated through Jacobian analysis in correspondence to the set of optimized fitting parameters.

formation, entropy of formation, and volume change upon formation of the bond. In particular, the values of E011 and S011, reported in Table 6, have been taken from literature and are assumed to be the same both in the vapor and in the polymer mixture phase.55 As anticipated, both V012 and V011 have been assumed to be equal to zero, as suggested by Tsivintzelis and Kontogeorgis.56 This assumption is not relevant for the case at hand and only matters when the exact value of the volume of the system has to be predicted. Where required for the sake of clarity, in the following, superscript v and wp will be used to indicate that we specifically refer to the water vapor or water− polymer phases, respectively. In summary, to interpret experimental sorption isotherm of water in PCL with the NRHB model, the only fitting 0wp parameters are k12, E0wp 12 , and S12 . As anticipated, because experimental sorption isotherm was determined at only one temperature, actually it is not possible to estimate independ0wp ently E0wp 12 and S12 , and they are in fact lumped in a single parameter, G0wp , that represents the Gibbs energy associated 12 with the formation of water−polymer HB. It is important to note that, as for any theory based on EOS, EOS parameters for pure water and pure polymer are also needed. In fact, for the case of pure PCL, lattice fluid scaling parameters (i.e., ε*h2, ε*s2, and v*sp,02; see ref 54 for the meaning of these terms) have been determined by fitting of PVT data available for PCL55 using the EOS from the NRHB model applied to pure compounds, whereas lattice fluid scaling parameters for pure water (i.e., ε*h1, ε*s1 and v*sp,01; see again ref 54 for the meaning of these terms), have been taken from the literature.56 The scaling parameters for pure water and PCL are listed in Table 6. As reported in Figure 14, the NRHB model provides a good interpretation of experimental sorption isotherm. The best-

Table 7. NRHB Fitting Parameters (Mean Filed Interaction Parameter and Gibbs Energy Associated to the Formation of Water−Polymer HB) for the System PCL−Water at 30°Ca k12

G0wp 12 (J/mol)

−0.119 ± 0.005

−9300 ± 200

a

One proton acceptor group has been considered on the PCL backbone, as resulted from FTIR experiments. Error ranges represent the 95% confidence intervals estimated through Jacobian analysis in correspondence to the set of optimized fitting parameters.

compared with the outcomes of vibrational spectroscopy. With the aim of comparing experimental results with the predictions of the NRHB model, it is to be noted that from vibrational spectroscopy analysis one obtains information on concentration of the different water species (i.e., (i) amount of water molecules directly interacting with the polymer substrate, “the core hydration”, with both O−H groups involved in H-bonding with two carbonyls and (ii) amount of the so-called “secondshell” water molecules). Conversely, NRHB model predictions supply values for the amount of water self-HBs (i.e., 11) and water−polymer cross-HBs (i.e.,12). Consequently, to perform a comparison, spectroscopic data need to be re-elaborated to evaluate the amount of self- and cross-HBs established within the polymer−water mixture. In fact, one needs to determine the number of moles of water self-HB normalized per mass of am polymer (nwp and mam representing the mass of the 11 /m2 2 amorphous phase of PCL) and the number of moles of crossHB occurring between the proton donor groups of water molecules and the proton acceptor groups present on the polymer backbone, normalized per mass of amorphous polymer am (nwp 12 /m2 ). In the case of “second-shell” water, a 1:1 ratio can be assumed to hold between the number of water molecules forming the “second shell” and the number of self-HB that they establish with water molecules interacting with carbonyls. Conversely, as by the structure reported on the left in Scheme 1, the vibrational spectroscopy analysis indicates that a single water molecule belonging to the “first shell” does form two Hbonding interactions with two distinct carbonyls (i.e 1:2 adduct), thus “bridging” two functional groups. It follows that the moles of cross H-bonding (nwp 12 ) can be calculated simply by doubling the moles of first shell water as evaluated spectroscopically. In Figure 15 theoretical predictions are compared with results obtained from vibrational spectroscopy analysis. NRHB wp model predictions overestimate to some degree n12 and wp underestimate n11 . Tentatively, these deviations could be attributed to the relevant assumption, made in constructing the model, that the polymer displays an ideal biphasic morphology (amorphous domains and impervious crystalline regions) with no amorphous interphases with intermediate rigidity. Actually, these regions, if present, could be endowed with a different thermodynamic behavior as compared to the one for bulk rubbery amorphous polymer. Moreover, there is some evidence that not all the carbonyls present in the

Figure 14. Fitting of experimental water sorption isotherm in PCL. Continuous line represents fitting curve provided by NRHB.

fitting values determined for the two NRHB parameters (i.e., k12 and G0wp 12 ) are reported in Table 7. Once the values of the two parameters have been gathered from the fitting of experimental sorption isotherm, the NRHB model can be used to provide quantitative predictions on the amount of self HB interactions between water molecules and of mutual HB interactions between carbonyl group of PCL and water molecules. These theoretical results could then be 7427



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Article

ASSOCIATED CONTENT

S Supporting Information *

Initial configuration of the donor−acceptor complexes, atom numbering schemes for the molecular systems considered, and definition of internal coordinates for the investigated molecular systems. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +39-0818675202.

Figure 15. Comparison of predictions of NRHB model with experimental results for PCL at 30 °C. Data and model predictions are reported as a function of water mass fraction in terms of (1) moles of water self-hydrogen bonding in the polymer−water mixture per gram of amorphous dry polymer as a function of water mass fraction and (2) moles of hydrogen bonding between absorbed water molecules and proton acceptor groups on polymer backbone in the polymer−water mixture per gram of amorphous dry polymer.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Thanks are due to Mr. G. Orefice for his assistance in performing the time-resolved FTIR experiments. Financial support from the National Research Council of Italy (CNR) in the frame of the project “Ricerca a Tema Libero” is gratefully acknowledged.

amorphous domains are actually available for interaction with water molecules, likely because of steric or mobility reasons.

■

4. CONCLUSIONS The diffusion of water in PCL was investigated by coupling gravimetric and spectroscopic measurements. The timeresolved FTIR data were analyzed by several techniques (difference spectroscopy, 2D-COS, LSCF analysis) which provided detailed and complementary information on the system’s evolution. It is demonstrated that the specific Hbonding interactions formed in the system can be selectively monitored by FTIR spectroscopy coupled with its more advanced data-analysis tools. In particular, two water species were identifieda first-shell, core-hydration layer and a second-shell layerwhich were quantified by evaluating the molar absorptivities of the two species. Spectroscopic analysis of the sorption isotherm showed that the dimer represents the largely predominant species up to p/p0 values of 0.65; at higher values of relative pressure, clustering starts to occur. The complex band profile of absorbed water in the O−H stretching region was interpreted in terms of normal modes contributions with the aid of ab initio calculations performed on representative model systems. These were able to capture the main features of the experimental spectra and the perturbations brought about by the interactions of the polymer substrate with the penetrant. In the light of the ab initio−normal-coordinate analysis, it was possible to exclude the direct involvement of sp3 oxygen in H-bonding interaction with water. In terms of dynamic behavior, it was shown that on sorption, the concentration buildup of the first-shell layer is accelerated with respect to that of the second-shell, whereas the opposite occurs on desorption, according to an intuitive evolution of the proposed molecular model. Finally, water sorption thermodynamics was interpreted using a nonrandom compressible lattice model accounting for HB interactions (NRHB model). Good fitting results were obtained for the gravimetric sorption isotherm at 30 °C. Quantitative estimates provided by the model for the amount of self- and cross-HBs compare reasonably well with the outcomes of the vibrational spectroscopy analysis.

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