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Water Sorption Thermodynamics in Glassy and Rubbery Polymers: Modeling the Interactional Issues Emerging from FTIR Spectroscopy Giuseppe Scherillo,† Michele Galizia,† Pellegrino Musto,‡ and Giuseppe Mensitieri†,* †

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

‡

S Supporting Information *

ABSTRACT: Water sorption thermodynamics has been effectively investigated in rubbery and glassy polymers using, respectively, an equilibrium lattice fluid model, originally introduced by Panayiotou et al. [Panayiotou, C.; Tsivintzelis, I.; Economou, I.G. Ind. Eng. Chem. Res. 2007, 46, 2628], accounting for hydrogen bond (HB) interactions in the system (i.e., the nonrandom hydrogen bonding, NRHB, model), and an extension of this model to a nonequilibrium glassy state (i.e., nonequilibrium thermodynamics for glassy polymers (NETGP)) that follows the same line of thought adopted originally by Doghieri and Sarti [Doghieri, F.; Sarti, G.C. Macromolecules 1996, 29, 7885] to develop the NETGP approach. NRHB and NETGP-NRHB models have been used to interpret water sorption thermodynamics respectively in polycaprolactone and in polyimides. Model predictions in terms of self- and cross-HB established in the system are compared with quantitative information gathered from in situ infrared spectroscopy experiments, exploiting the wealth of information provided by proper elaboration of spectroscopy data by means of 2D correlation techniques.

1. INTRODUCTION Sorption thermodynamics of low molecular weight compounds in polymers represents a subject of primary interest both from a fundamental and a technological perspective. The applications where this subject has a major impact are countless, ranging from membranes for gas mixtures separation to drug delivery, from barrier structures for food packaging to durability and aging issues in polymer-based composite materials. Of particular interest in this context is water sorption thermodynamics, both from a fundamental point of view and for its practical implications. In fact several polymer matrices, when exposed to a humid environment, absorb significant amounts of water which adversely affect most physicomechanical properties. Occurrences of molecular interactions between water molecules and the polymeric substrate are often associated with sorption and it is, therefore, necessary to gain an insight at the molecular level in order to reach a fundamental understanding of the underlying thermodynamic behavior. Absorbed water molecules in polymer matrices do establish different types of interactions with the matrix (different “states” of water molecules) and, in turn, a range of different effects on physical properties are expected to be associated to each of them. As a consequence the water uptake alone is not a reliable predictor of possible effects on physical properties of the resin. Addressing these issues is needful to elucidate the plasticization mechanisms by which water affects in many ways the performances of polymer matrices. In this respect, in recent years, a number of investigators recognized the potential of applying spectroscopy-based techniques, and in particular several experimental efforts have been put forward to address the issue of the state of water molecules in epoxies. Among the spectroscopic techniques which have been used for this purpose, the most effective are nuclear magnetic resonance (NMR), dielectric, and Fourier transform infrared (FTIR) © 2012 American Chemical Society

spectroscopies. The results obtained by these experimental approaches are still inconclusive and sometimes conflicting.1−11 However, the apparently contradictory results obtained by these spectroscopic techniques may be partly due to the characteristic time scale of each probing method. Notable examples of these approaches are the study of water sorption thermodynamics based on time-resolved FTIR spectroscopy.12−19 In particular, the latter technique provides several appealing features: that is, the very high sampling rate, the sensitivity and accuracy of the quantitative analysis, and, above all, the wealth of information at the molecular level contained in the vibrational spectrum. Several efforts have been devoted in the past decade by our group to gather information on water/ polymer mixtures from infrared spectroscopy, exploiting also the enhancement of spectral resolution by spreading peaks over the second dimension and the establishment of unambiguous assignments available from two-dimensional correlation spectroscopy.17,20−28 In fact transmission FTIR spectroscopy analysis performed on samples placed in cells at controlled humidity and temperature, allows the identification of proton acceptor (PA) and proton donor (PD) groups, present on the polymer backbone and on water molecules, involved in specific interactions assessing quantitatively the amount of the adducts formed due to self- and cross-hydrogen bonding. In fact, in several polymer/water systems the different “species” of water present determining the number of hydrogen atoms involved in Special Issue: Giulio Sarti Festschrift Received: Revised: Accepted: Published: 8674

September 1, 2012 November 8, 2012 November 8, 2012 November 8, 2012 dx.doi.org/10.1021/ie302350w | Ind. Eng. Chem. Res. 2013, 52, 8674−8691

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Panayiotou and Vera (PV) further improved it by introducing a compressible LF model accounting for the presence of hole sites.39 In the PV model nonrandomness is assumed for contacts between mers of the components of the mixture, the holes distribution being still taken as random (free volume random distribution hypothesis). Later, You et al.40 and Taimoori and Panayiotou41 extended this approach allowing for the nonrandomness of all the possible couple of contacts, also including those involving the hole sites, still adopting a nonrandom quasichemical approximation. Yeom et al.42 and Panayiotou et al.43−48 then modified this nonrandomness approach including also the contribution of HB interactions, factorizing the configurational partition function in an approach that is similar to the one followed in the case of the PS model to extend the random SL model to include the specific interactions. In the following we will refer to the nonrandom model accounting for HB interactions, proposed by the group of Panayiotou in references 43 46, and 48, as the “nonrandom lattice fluid hydrogen bonding” (NRHB) model. This model will be the one used in the present contribution to interpret water sorption behavior in rubbery polymers displaying specific HB interactions. In fact, water molecules as well as macromolecules can establish specific self-interactions between their proton donor and proton acceptor groups. Water self-interactions can occur both in the polymer−penetrant mixture and in the water vapor phase in equilibrium with it. In addition, specific crossinteractions can occur in the water−polymer mixture between water molecules and polymer backbones. NRHB has already been used to describe the vapor−liquid equilibrium of binary polymer−solvent systems, where functional groups of the polymer can self-associate and cross-associate with the solvent molecules, providing a flexible approach for considering association in mixtures with complex hydrogen bonding behavior. In particular, Tsivintzelis at al.49 reported on the use of NRHB for the case of mixtures of poly(ethylene glycol), poly(propylene glycol), poly(vinyl alcohol), and poly(vinyl acetate) with several solvents, including water: NRHB provided in all cases good correlations of the experimental sorption isotherms. Modeling thermodynamics of water sorption in glassy polymers displaying possible HB interactions is characterized by a 2-fold theoretical complexity: a need to account for the out-of-equilibrium state of the glassy system and a need to account for the occurrence of specific interactions. Available theories dealing with sorption thermodynamics of penetrants in a nonequilibrium glassy polymer neglect the possible occurrence of specific interactions or account for them in a rather simplistic way. These theories start from the experimental evidence that polymers in the glassy state display physical properties which significantly differ from those of the same polymer in the rubbery state, in terms, among others, of both mechanical properties (e.g., dramatic decrease of moduli at the glass transition temperature, Tg), and thermodynamic properties (glassy polymers are in a nonequilibrium state characterized by a tendency to physical aging which determines a time-dependent density). Consistently, sorption thermodynamics differs substantially from the case of rubbery polymers, and modeling should properly account for nonequilibrium state. A first successful and simple way to describe the sorption of low molecular weight penetrants within glassy polymers is represented by the so-called dual sorption model.50,51 Sorption

specific interactions have been identified and evaluated quantitatively.17,20−28 On the basis of these findings several theories have been proposed to interpret water sorption thermodynamics in polymers accounting for all molecular details associated to this process. In fact several sorption modes and related states of absorbed water molecules have to be considered which frequently occur simultaneously: bulk dissolution, hydrogen bonding (HB) interaction between hydrophilic groups of the polymer and water, clustering of water molecules and adsorption onto the surface of excess free volume microvoids in glassy matrices. Models for penetrant sorption in rubbery and glassy polymers in the presence of possible specific interactions have been developed starting from existing frameworks not accounting for these interactions. We provide here a brief literature survey focused on lattice fluid theories which are of specific interest for the present contribution. In the last two decades theoretical models have been proposed concerning equilibrium rubbery polymer−penetrant mixtures displaying HB interactions as well as approaches addressing the issue of mixtures of low molecular weight penetrants and nonequilibrium glassy polymers which do not display specific interactions. However, to the best of our knowledge, no model accounting, at the same time, for interactions and nonequilibrium glassy nature of the system has yet been operatively used in order to treat systems endowed with hydrogen bonding, although theoretical developments potentially able to provide a description of sorption thermodynamics in glassy polymers−penetrant systems exhibiting specific interactions have been proposed.29,30 A class of theoretical approaches describing sorption thermodynamics of low molecular weight compounds in rubbery polymers for systems exhibiting HB interactions, is that extending available mean-field lattice fluid (LF) models to include the effect of possible self- and cross-interactions. In particular, Panayiotou and Sanchez (PS)31 have modified the original Sanchez−Lacombe (SL) lattice fluid equation of state theory32−34 to account for the formation of HB interactions, assuming that the configurational partition function can be factorized in two separate contributions: one related to meanfield interactions and one accounting for the effects of specific interactions. The first contribution can be expressed, in principle, by using any available mean-field LF theory. In the specific case of the PS model this mean-field contribution is represented by a relatively simple compressible lattice fluid, random mixing, model, while the effect of HB interactions is accounted for by using a combinatorial approach first proposed by Veytsman.35,36 The mean-field contribution adopted in the PS model is based on a simplified statistical framework, in which the arrangement of r-mers and holes is assumed to be at random. Actually, in the case of nonathermal contacts between different kind of r-mers and/or holes, such an assumption is likely to be incorrect. 37 On the basis of the pioneering work of Guggenheim,38 several theories have been developed to deal with nonrandomness distribution of contacts in LF models, first tackling the cases in which the occurrence of specific interactions is not accounted for. The basic concept consists in factorizing the partition function into an ideal random contribution and in a nonrandom contribution that is obtained by treating each kind of contact as a reversible chemical reaction (quasichemical approximation). Guggenheim developed the theory for a lattice fluid system without holes and 8675

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the macroscopic nature of the chosen order parameter which allows a good precision in its measurement. To simplify the approach and to not deal with complex dynamic evolution of nonequilibrium polymer density, the system can be considered as being in a pseudoequilibrium (PE) state, in the sense that the two-phase equilibrium is attained between an external pure penetrant phase with the polymer phase that is assumed to be in a kinetically locked nonequilibrium state. The same authors further developed, however, the theory to take also into account issues related to the kinetics of structural evolution of the glassy system. Such a model results in a powerful tool to predict the solubility of low molecular weight compounds in polymers where specific interactions are not present. Later, theoretical descriptions of sorption thermodynamics of glassy polymer−penetrant systems exhibiting specific interactions have been proposed based on extension of “statistical associating fluid theory”(SAFT)29 and of NRHB,30 although, to the best of our knowledge, these approaches were never actually applied to treat experimental data for systems exhibiting HB interactions. Very recently, to account for HB interactions in water/glassy polymer mixtures, we have developed and applied an extension of the NRHB model to nonequilibrium glassy polymers,28 that has been performed following the same line of thought originally introduced by Doghieri and Sarti59 to extend equilibrium equation of state theories. We will refer to this model as NETGP−NRHB. In this contribution we present an integrated approach that, by combining a detailed experimental gravimetric and spectroscopic analysis of polymer/water systems with theoretical approaches based on compressible lattice fluid theories, allows the understanding of water sorption thermodynamics in rubbery and glassy polymers. FTIR spectroscopy is exploited to gather quantitative and qualitative information concerning the chemical groups involved in specific interactions evidencing the cross- and self-hydrogen bonding established in the water− polymer mixtures. The quantitative assessment of the different water species is obtained by properly combining spectroscopic and gravimetric data. The indications obtained from spectroscopic analysis on the chemical groups involved in the formation of HB have been used to guide the construction of the thermodynamic model for the chemical potential of water in the mixture, providing the type of specific interactions for which to be accounted. The theoretical analysis is based on the NRHB and NETGP−NRHB models, respectively, for the case of rubbery and glassy polymers. In particular, these models have been used to interpret qualitatively and quantitatively experimental gravimetric and spectroscopic data for water sorption in polycaprolactone (PCL) and in polyimides (PIs) with different fluorine content. In particular theoretical predictions of the amount at sorption equilibrium of self-HB interactions among water molecules and of cross-HB established between water molecules and polymer backbones as a function of water mass fraction in the polymer−water mixture are compared with the values determined experimentally. In fact PCL has been chosen as an example of rubbery polymer while PIs, characterized by different levels of fluorination and, in turn, different level of specific interaction with water molecules, as an example of glassy polymer. Beside serving the purpose of illustrating the details of the procedures for the experimental and theoretical analyses, these systems are also of practical interest. PCL is relatively hydrophobic and,

of penetrants is assumed as being contributed by two “populations”: one is made of penetrant molecules molecularly dispersed in the bulk of the polymer matrix, assumed to behave like an equilibrium rubbery system, and the other is made of penetrant molecules adsorbed onto the surfaces of the frozen microvoids. Accordingly, the model is in the form of the sum of two contributions: the first is typically based on a mean-field equilibrium approach, such as Flory−Huggins theory52,53 or, in the limit of small penetrant concentration, Henry‘s law, while the second one is in the form of a Langmuir-type adsorption contribution. Although rather successful in supplying a physically sound framework to interpret sorption in glassy polymers, the dual sorption approach is suitable for correlation purposes but it is not predictive. More recently, many efforts have been devoted to the development of a theoretical framework grounded on rational nonequilibrium thermodynamics aimed at extending the equilibrium mixture theories suitable for rubbery polymers to the nonequilibrium glassy polymer−penetrant mixtures, by introducing order parameters, that quantify the departure from the equilibrium conditions at fixed pressure and temperature and act as internal state variables. The concept of order parameter has been often used to describe the thermodynamic properties of nonequilibrium systems: after its introduction by Donder54 it was extensively used to describe glassy systems by Staverman,55 Gibbs and Di Marzio,56 Astarita et al.,57 Wissinger at al.,58 and Doghieri et al.59 The basic idea is that, in addition to the external state variables describing the state of a system at equilibrium, such as pressure, temperature, and concentration, a set of order parameters is needed to give an appropriate description of the state for a nonequilibrium polymer−pentrant system. For example, Wissinger and Paulaitis (WP)58 assumed as an order parameter the polymer fractional free volume at glass transition temperature, considering its value as “frozen in” at the value it takes at Tg for all the temperature values below Tg. Despite its capability to reproduce reasonably well the sorption isotherms of CO2 in polymethyl methacrylate and polystyrene, the WP approach failed in reproducing hysteresis phenomena during desorption runs, as well as swelling-enhanced sorption capacity of the polymer matrix. To overcome this difficulty, Conforti et al.60 proposed a model that makes use, as order parameter, of the number of holes per polymer mass in the mixture, in a lattice fluid framework. On the basis of experimental information on the different volumetric behavior of the polymer−penetrant system during the sorption and desorption process, this model is able to describe the typical sorption−desorption hysteresis of glassy systems using two adjustable parameters.61 The need for experimental information on the volumetric behavior of the polymer−penetrant system to estimate the value of the order parameter represents a major drawback for the effective use of such a model in a predictive fashion. In the last two decades, Doghieri and Sarti59 have proposed the use, as order parameter, of the density of the polymer in the mixture which plays the role of a true internal state variable. On the basis of a rigorous rational thermodynamic treatment, they developed a procedure aimed at extending equilibrium statistical thermodynamics theories to nonequilibrium glassy systems. This theory, reported generically as “nonequilibrium thermodynamics for glassy polymers” (NETGP),62 has been successfully applied to many binary and ternary polymer− penetrant glassy systems. The approach takes advantage from 8676



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Scheme 1

of the bubble were adjusted in order to achieve a stable bubble. The screw speed was set at 40 rpm. Polyimides. The molecular structures of the three investigated polyimides are reported in Scheme 1. The PMDA−ODA was obtained by thermal imidization of its polyamic acid precursor, Pyre ML RK692 from IST (Indian Orchard, MA). This precursor, supplied as a 12 wt % solution in N-methyl-2-pyrrolidone/xylene mixture (80/20 wt) had a molecular weight of Mw = 1.0̇105 g/mol. The 6FDA−ODA and 6FDA−6FpDA polyamic acid precursors were synthetized from the respective dianhydride and diamine monomers [(hexahydrofluoroisopropylidene) diphthalic anhydride (6FDA), 4,4′diaminodiphenyl ether (ODA), 4,4′-(hexafluoroisopropylidene) dianiline (6FpDA)], according to the procedure described elsewhere.68 The monomers were purchased from Sigma-Aldrich (St. Louis, MO). Films (20/30 μm thick ) were prepared by spreading the polyamic acid solution on a glass support, using a calibrated Gardner knife. The films were dried 1 h at room temperature and 1 h at 80 °C, allowing the solvent evaporation. Finally, the casted samples were cured in a stepwise manner at 100, 150, 200, 250, and 290 °C for 1 h at each temperature. 2.2. FTIR Spectroscopy. A vacuum tight FTIR cell was used to perform the time-resolved acquisition of FTIR spectra during the sorption experiments. Data collection on the

among biodegradable polymers, exhibits low water solubility,63,64 which results in a relatively good barrier to moisture. In view of its properties, it is an interesting polymer for use in biodegradable food packaging and to make scaffolds for tissue engineering. These applications motivate the interest in understanding water sorption thermodynamics in PCL. On the other hand, sorption of water in PIs may affect their performances in both membrane applications and coating of electronic devices by modifying, respectively, gas separation properties and the dielectric constant.65−67 In fact, the reduced level of moisture absorption and of the value of dielectric constant typical of fluorinated polyimides is of particular relevance.

2. MATERIALS AND METHODS 2.1. Materials. PCL. A film grade thermoplastic PCL, CAPA FB100, was used, supplied by Solvay Warrington (Cheshire, WA4 6HB, United Kingdom), with a mean molecular weight of Mw = 80000. The material was processed by using a film blowing equipmen, obtaining a film with a thickness of around 40 μm. Film blowing was performed on lab scale equipment (Collin E 20T, Germany). The temperatures of the four heating sections of the extruder barrel and of the die (80/100/ 120/110/110), the velocity of the takeoff rolls, and the volume 8677



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⎤ ⎡⎛ x − x ⎞ 2 0⎟ f (x) = (1 − Lr )H exp −⎢⎜ (4 ln 2)⎥ ⎦ ⎣⎝ w ⎠ H + Lr x−x 2 4 w0 +1

polymer films exposed to water vapor at constant relative pressures was carried out in the transmission mode. The cell was connected through service lines to a water reservoir, a turbo-molecular vacuum pump, pressure transducers, and a Pirani vacuometer. Full details of the experimental setup are reported elsewhere.17 The FTIR spectrometer was a Spectrum GX from PerkinElmer (Norwalk, CT), equipped with a Ge/KBr beam splitter and a wide-band deuterated triglycine sulfate (DTGS) detector. The instrumental parameters for data collection were as follows: resolution = 4 cm−1; optical path difference (OPD) velocity = 0.5 cm/s; spectral range, 4000−400 cm−1. A single data collection per spectrum was performed, which took 2.0 s to complete in the selected instrumental conditions. Spectra were acquired in the single-beam mode for subsequent data processing. Automated data acquisition was controlled by a dedicated software package for time-resolved spectroscopy (Timebase, from Perkin-Elmer). In the case of the PCL/water system, sorption tests were performed at 25, 30, and 37 °C, by increasing in a stepwise manner, at each temperature, the relative pressures of water vapor, p/p0, where p0 is the vapor pressure of water at the test temperature. In the case of PIs/water systems, instead, the experiments were carried out only at 30 °C. For PCL and PIs, a sorption test was also performed on a thin polymer sample, to identify the functional groups in the polymer backbone which form cross interactions with penetrant molecules. In the case of PCL, a little amount of polymer was dissolved in tetrahydrofuran (THF) to obtain a dilute solution (1 wt %). A drop of solution was then cast on a KBr support, and the solvent was allowed to evaporate. The supported film of PCL (whose thickness is about 1 μm) was then introduced in the FTIR cell, and a sorption test was performed at 65 °C, just above the melting point of the polymer. In the case of PIs, thin samples (1−3 μm) were prepared by a two-step spin coating process, using a Chemat KW4A apparatus equipped with an automatic fluid dispenser. Spinning conditions were 700 rpm for 12 s in the first step and 1500 rpm for 20 s in the second step. Thin samples were then cured using the same procedure of thicker ones. The free-standing films obtained by following this procedure were introduced in the FTIR cell to perform sorption experiments. 2.3. FTIR Data Analysis. Full absorbance spectra (i.e., polymer plus sorbed water) were obtained using as background the cell without sample at the test conditions. The spectra representative of absorbed water were obtained by using as background the single-beam spectrum of the cell containing the dry film. Spectra obtained with this procedure are referred to as “difference spectra”. This allows one to eliminate the interference of the polyimide spectrum in the regions of interest. It is explicitly noted that this data processing approach is equivalent to the more general difference spectroscopy method provided that no changes in sample thickness take place during the measurement.24 This has been verified in the present case. Curve fitting analysis was performed by a Levenberg− Marquardt least-squares algorithm.69 The peak function used throughout was a mixed Gauss−Lorentz line shape of the form:70

(

)

(1)

where x0 is the peak position; H is the peak height; w is the fullwidth at half height (fwhh) and Lr is the fraction of Lorentz character. To keep the number of adjustable parameters to a minimum, the baseline and the number of components were fixed, allowing the curve-fitting algorithm to optimize the fwhh, the position of the individual components, and the band-shape (Lr parameter). 2-Dimensional correlation spectroscopy (2D-COS) analysis71 was performed on an evenly spaced sequence of 20 spectra collected with a sampling interval of 12 s. To this aim, the software Matlab was used to process the spectra. For the notation adopted to identify the peaks in the correlation spectra, refer to ref 24. 2.4. Gravimetric Measurements. The equipment used to determine the weight gain of samples exposed to a controlled humidity environment is analogous to that used for the spectroscopic measurements, with an electronic microbalance D200 from Cahn Instruments (Madison, WI), in place of the FTIR sorption cell. The microbalance provides a sensitivity of 0.1 μg with an accuracy of ±0.2 μg. Gravimetric sorption isotherms were collected in a stepwise manner, at the same temperatures as for spectroscopic experiments and at different vapor activities: in each case, the activity was estimated as the relative pressure p/p0, where p0 is the vapor pressure at experimental temperature. Full details about the experimental procedure are given elsewhere.26

3. THEORETICAL BACKGROUND 3.1. Nonrandom Lattice Fluid Hydrogen Bonding (NRHB) Model. Analysis of thermodynamics of sorption of water in rubbery polymers is performed in the present contribution using a LF theory including the effect of possible self- and cross-interactions in polymer−penetrant systems. In particular, we consider here the “nonrandom lattice fluid hydrogen bonding” (NRHB) theory developed by Panayiotou et al.,43−48 based on the factorization of the configurational partition function in two separate contributions: one related to mean-field interactions and one accounting for the effects of specific (HB) interactions. The first contribution is constructed starting from the idea that the partition function related to mean-field interactions can be further factorized into an ideal random contribution and in a nonrandom contribution that is obtained treating each kind of contact as a reversible chemical reaction (quasichemical approximation38): nonrandomness of all the possible couple of contacts between mers of the components of the mixture as well as hole sites is assumed.41 The second contribution, accounting for the effect of HB interactions, is formulated by using a combinatorial approach first proposed by Veytsmann.35,36 We focus here on the phase equilibrium between a binary rubbery polymer−water mixture and pure water in a vapor phase, since the polymer is assumed to be not soluble within the gaseous phase. Establishment of this equilibrium implies the equality of the chemical potentials of water in the two coexisting phases. According to the NRHB model, the water 8678



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HB occurring between the proton donor groups of water molecules and the proton acceptor groups present on the PCL backbone, normalized as well per mass of amorphous phase of am PCL (i.e., nwp 12 /m2 ). Further details are available in the Supporting Information (see description S5 in Table S1). (d) Equations for the nonrandom factors for the distribution of contacts in the lattice. In particular, the state variables Γ00 and Γ11 appear in the equations, that are, respectively, the nonrandom factors for the distribution of an empty site around another empty site and of molecular segments of penetrant around a molecular segment of the penetrant itself, in the two phases at equilibrium (see ref 46). Further details are available in the Supporting Information (see descriptions S6 and S7 in Table S1). This model has been used to fit experimental sorption isotherms of water in PCL, assuming as fitting parameters k12, 0wp E0wp 12 , and S12 . The solution of this system of equations supplies, at fixed values of pressure and temperature, the density of the two phases, the values of Γ00 and Γ11 variables in the two phases, the concentration of penetrant in the polymer− penetrant mixture, the number of each type of hydrogen bonds in the vapor phase and in the water−polymer mixture, that is, wp Nv11, Nwp 11 , and N12 . It is important to note that, as for any theory based on EOS, one needs to know the scaling parameters for pure water and pure polymer. In fact, for the case of PCL, lattice fluid scaling parameters for pure polymer (i.e, ε*h2, ε*s2 and v*sp,02; see descriptions S1 and S8 in Table S1 in the Supporting Information and ref 46 for the meaning of these terms) have been determined by the fitting of PVT data for PCL using the NRHB EOS equation, while lattice fluid scaling parameters for water (i.e., ε*h1, ε*s1 and v*sp,01; see descriptions S1 and S8 in Table S1 in the Supporting Information and ref 46 for the meaning of these terms), E011 and S011 have been taken from the literature49 and are assumed to be the same in the water vapor and in the 0wp 0w 0wp water/polymer mixtures (i.e., E0w 11 = E11 and S11 = S11 ). Further details are available in ref 26. It is important to note that the NRHB model is based on the LF framework which is suitable for totally amorphous rubbery polymers and does not account for the presence of crystalline domains. For the sake of interpretation of experimental water sorption isotherms in semicrystalline PCL, in the present contribution, crystals are modeled as being impervious and to compare data with model predictions the overall solubility measured in the semicrystalline samples has been rescaled to obtain that of the pure amorphous PCL, accounting for the presence of the impervious crystalline fraction. It has been, hence, assumed that the presence of crystals does not alter the thermodynamic behavior of the amorphous domains.26 That this is the approach of choice when swelling data are not available and when the crystalline phase is not supposed to absorb penetrant has been thoroughly discussed by Morbidelli et al.72 3.2. Nonequilibrium Theory for Glassy Polymers Nonrandom Lattice Fluid Hydrogen Bonding (NETGP− NRHB) Model. In this section we summarize the approach that we have adopted28 to extend the NRHB model to the case of glassy polymers with the purpose of constructing a nonequilibrium thermodynamic model for sorption of penetrants in glassy polymers endowed with cross- and self-HB interactions. Full details of this development are reported in ref 28. With the aim of building a theoretical framework to interpret sorption thermodynamics of low molecular weight compounds

chemical potential in the polymer−water mixture and in the pure water phase is expressed as the sum of a LF and a HB contribution:31 μ1 = μ1,LF + μ1,HB

(2)

The expressions of water chemical potential in both phases is coupled with the proper expressions for the equation of state (EOS) of both phases. Here and in the following we will consider only binary mixtures, with subscript ‘1’ referring to water and subscript ‘2’ referring to polymer. Relevant parameters of the model are (1) k 12 (or equivalently, ψ12 = 1 − k12), that is, the mean-field lattice fluid interactional parameter which measures the departure from the geometric mean of the mixing rule for the characteristic energies of the lattice fluid: * = (1 − k12) ε11 *ε22 * ε12

(3)

A brief description of the parameters appearing in eq 3 is available in the Supporting Information (Table S3). (2) E0ij, S0ij and V0ij representing, respectively, the molar internal energy of formation, the molar entropy of formation, and the molar volume change upon formation of hydrogen bonding between the proton donor group of type i and the proton acceptor group of type j. E011 and S011 have been taken as being the same both in the vapor and in the polymer mixture phase and are available from the literature.49 In the present context, V012 and V011 have been taken to be equal to zero according to the assumption made by the authors of NRHB in recent publications.49 When necessary, in the following, superscript “v” and “wp” will be used to indicate that we specifically refer, respectively, to the water vapor or to the water/polymer phases. In summary, the set of equations to be solved to determine the water solubility in PCL according to the NRHB model is the following: (a) Equivalence of chemical potentials of penetrant in the gas POL phase (μGAS 1 ) and polymer phase (μ1 ). (see eq 2). Further details are available in the Supporting Information (see descriptions S1, S2, and S4 in Table S1). (b) EOS for the vapor and for the polymer mixture phases. Further details are available in the Supporting Information file (see descriptions S3 and S4 in table S1). (c) Equations for the number of hydrogen bonds established in the two phases at equilibrium with Nij representing the total number of hydrogen bonding interactions between proton donor groups of type i and proton acceptor groups of type j. On the basis of polymer chemical structure (absence of PD group on the polymer backbone) we infer that self-HB only occurs between water molecules, both in the pure water vapor and in the polymer−water mixture. Hence Nv11 and Nwp 11 are the only number of self-HB to be considered. Moreover, based on the outcomes of the spectroscopic analysis, it can be deduced that only one type of PA group is present on the polymer backbone and one type of PD group is present on a water molecule. As a consequence, considering that the polymer is not present in the vapor phase, Nwp 12 is the only variable related to cross-HB, that occurs between water and polymer molecules in the polymer−water mixture. In the following, the variables that we will consider when comparing model with experiments are actually a slight reformulation of the Nij. In fact, referring to the polymer−water phase, it will be considered in the analysis the number of moles of water self-HB per mass of amorphous am phase of PCL (i.e., nwp 11 /m2 ) and the number of moles of cross 8679



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contact with an external phase of pure penetrant, reaches a phase pseudoequilibrium (pseudoequilibrium attribute is used here since the mixture is itself in a pseudoequilibrium glassy state). In the hypothesis that the polymer is insoluble in the external (EXT) penetrant phase (i.e., n2 in the polymer− penetrant mixture has a fixed value), it can be demonstrated73 that the thermodynamic condition for phase PE is still dictated by

in nonequilibrium glassy polymers, several procedures have been proposed in the literature which consist in extending equilibrium theories for sorption in rubbery polymers to the case of glassy polymers.59,73,74 In particular, we briefly report here on the NETGP approach elaborated by Doghieri and Sarti.59,73 In fact, in this contribution, to extend equilibrium NRHB model, we specifically follow the same line of thought introduced by Doghieri and Sarti59,73 to deal with sorption thermodynamics of low molecular weight penetrants in nonequilibrium glassy polymers. The NETGP approach is rooted on the thermodynamics endowed with internal state variables. In this framework, for a nonequilibrium glassy polymer/penetrant mixture, in the case of a spatially uniform phase, the constitutive class identifying the state for the extensive properties is considered to be the following set of variables: temperature (T), pressure (p), number of moles of penetrant (n1), number of moles of polymer (n2) and density of the polymer in the mixture (ρ2).73 ρ2 is an order parameter measuring the departure from the equilibrium state and actually, in this approach, plays the role of a true internal state variable of the system. Accordingly,75 the rate of variation of ρ2 is a function of the state, that is, dρ2 dt

= f (T , p , ω1 , ρ2 )

μ1POL,PE (T , p , ω1PE , ρ2, ∞) = μ1,EXT (T , p)

where the superscript PE has been used here to underline the fact that the value of the mass fraction of penetrant which satisfies the condition given by eq 9 is, actually, a PE value. The chemical potential of the penetrant in the polymer− penetrant mixture under the existing nonequilibrium conditions appearing in eq 9 is obtained as μ1POL,PE =

dt

(4)

≅0

(5)

ρ2 = ρ2, ∞ ≠ ρ2EQ (T , p , ω1)

(6)

The af f inity, Aρ2, to the internal state variable defined as

⎛ ∂G ⎞ ⎟⎟ A ρ2 = ⎜⎜ ⎝ ∂ρ2 ⎠T , p , n , n 1

(7)

2

is equal to zero at true equilibrium, that is, when ρ2 = ρEQ 2 , and is instead different from zero in nonequilibrium condition as it is the PE condition dictated by eqs 5 and 6. Here G is the Gibbs energy of the system. For nonswelling penetrants ρ2,∞ can be simply considered as being equal to the value it takes for the pure polymer, ρ02. Conversely, when penetrants induce a non- negligible swelling, the value of ρ2,∞ needs to be retrieved from dilation measurements on the mixture or, at low pressures, can be calculated using the simple expression:76 59,73

ρ2, ∞(p) = ρ20 (1 − kswp)

∂G ∂n1

T , p , ρ2 , n2

(10)

where the derivative on the right hand side of eq 10 has to be evaluated at ρ2 = ρ2,∞ and n1 = nPE 1 . The nonequilibrium expressions for G to be used in eq 10 can be retrieved59,73 from the forms provided by several statistical thermodynamics theories, ranging from lattice fluid theories59 to perturbation theories.76 We adopted this same line of thought, and related procedures, to extend the NRHB model to glassy polymers. Again, we have to select order parameters to be used as true internal state variables which contribute to define the thermodynamic state of the nonequilibrium system. In this latter instance, the evolution kinetics of order parameters are material properties that are a function of the thermodynamic state of the system, which include the order parameters themselves. The specific property of interest dictates the choice of how many order parameters, and of what type, have to be introduced as internal state variables as well as the expression for their evolution kinetics. As discussed in literature,57 at least two order parameters are needed for thermodynamic description of properties below the glass transition temperature (T g ). The different alternatives among possible order parameters to be used as internal state variables are not equivalent in view of the fact that the different evolution kinetics are not interchangeable.59 To extend to nonequilibrium the equilibrium statistical thermodynamics NRHB theory, the general expression derived for it from the developments of statistical thermodynamics, before the application of the minimization conditions that mark the equilibrium state, has been taken28 as nonequilibrium Gibbs energy. In such a case, the internal state variables to be selected for the description of the nonequilibrium state naturally emerge as the set of variables for which the minimization procedure is performed to obtain the equilibrium expression for G. In the case of the NRHB model, polymer density, number of HBs, and effective number of nonrandom contacts can all be selected as internal state variables. At equilibrium their value is only related to the equilibrium state variables through the minimization conditions for G. Conversely, in nonequilibrium conditions, their values are dictated by the evolution kinetics that, consistently with theory of internal state variables, must depend only on the actual state of the system.

where ω1 is the mass fraction of penetrant. Although ρ2 is, in the general formulation, a time-dependent property characterized by a thermodynamically consistent kinetic expression,73 in the applications of the model to polymer systems well below glass transition temperature, it is frequently assumed that f takes a value close to zero due to the very slow relaxation kinetics of glassy polymers and ρ2 is assumed to take a constant nonequilibrium value, referred to as ρ2,∞. This value has not to be confused with the equilibrium value, i.e. ρEQ 2 , and it cannot be determined by using an equilibrium EOS. It is, hence, generally assumed that the polymer mixture is in a pseudoequilibrium (PE) state for which: dρ2

(9)

(8)

where ksw is the swelling coefficient that can eventually be used as a fitting parameter in interpreting sorption isotherms. The kinetically hindered polymer−penetrant mixture, when in 8680



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mixture density has been evaluated on the basis of the available experimental value of polymer PE density, as ρ2,∞/ω2. The NETGP−NRHB model has been used to fit experimental sorption isotherms of water in PIs, assuming as fitting parameters k12 and A0wp 12 (Helmholtz energy of formation of water/polymer HB). In fact, since experimental sorption isotherms were determined only at one temperature (30 °C), it was not possible to use as fitting parameters E012 and S012. The solution of this system of equations supplies, at fixed values of pressure and temperature, the density of the water vapor phase, the values of N̲ NR rs variables in the two phases, the concentration of penetrant in the polymer−penetrant mixture and the number of each type of hydrogen bonds in the vapor phase and in the water−polymer mixture. The latter are, for the wp investigated systems, simply Nv11, Nwp 11 , and N12 : in fact, self-HB are formed only between water molecules in view of the absence of proton donor on PIs backbones and, as confirmed by FTIR spectroscopy (see section 4.1.3), only one type of cross-HB is likely to form, that is, the one between the only type of PA group present on PIs and H atoms of water molecules. Also in this case NRHB EOS parameters for pure water and pure polymer are needed. This information is not available for PMDA−ODA since, as discussed later, it was not possible to perform PVT measurements in the molten state due to polymer degradation. For the case of 6FDA−ODA and 6FDA− 6FpDA, lattice fluid scaling parameters for the pure polymer (i.e., εh2 * , εs2 * , and vsp,02 * ) have been determined by the fitting of PVT data using EOS equation of the NRHB model (see ref 28), while lattice fluid scaling parameters for water (i.e., ε*h1, ε*s1 and vsp,01 * E011, and S011) have been taken from the literature.49 Further details are available in ref 28.

As already discussed, in the original NETGP approach the only internal state variable is the polymer density, ρ2. In the case of the NETGP−NRHB model, beside ρ2, two additional sets of order parameters are introduced as internal state variables, that is N̲ ij and N̲ NR (we adopt here underlined rs symbols to put in evidence the fact that they actually represent a set of variables). The generic component of the set N̲ ij represents the number of HB interactions between proton donor groups of type i and proton acceptor groups of type j, while the generic component of the set N̲ NR rs , which are related to the Γii introduced before, represents the effective number of nonrandom contacts in the compressible lattice between the mers of kind r and the mers of kind s. In fact, it is explicitly noted that the vector variable N̲ NR rs contains only a subset of independent NNR as determined by the material balance rs equations (see ref 46 and description S7 in Table S1 in the Supporting Information file). We need to introduce expressions for the evolution kinetics of the internal state variables. Regarding ρ2, the approach traces the same development of NETGP, while in the case of N̲ ij and N̲ rsNR it is assumed, to simplify the matter, that an “instantaneous” evolution kinetics holds for these internal state variables. As a consequence, the HB contacts, N̲ ij, and the nonrandom contacts, N̲ NR rs , are the ones which the system would exhibit at equilibrium at the current values of pressure, temperature, concentration and polymer density. A detailed discussion of the model development and presentation of results in terms of expression of water chemical potential in the polymer−water phase can be found in ref 28. From the previous discussion, we realize that A Nij =

∂G ∂Nij

=0

for each i and j

T , p , n1, n2 , ρ2 , Nrs ≠ ij , N̲ rsNR

4. EXPERIMENTAL RESULTS 4.1. FTIR Spectroscopy. 4.1.1. Absorbance and Difference Spectra. Well-defined bands appear in the absorbance spectra of samples upon sorption of water witnessing the multiplicity of water species present in the PCL and PIs. As an example, Figure 1 shows a comparison of the absorbance spectra of dry PMDA−ODA with that of the same polyimide after sorption equilibration at a p/p0 = 0.6. As highlighted in Figure 1, in three different regions of the spectrum appear the characteristic bands of absorbed water, that is, in the 3800− 3200 cm−1 range (O−H stretching modes, νOH), in the 1680−

(11a)

A NrsNR =

∂G ∂NrsNR

=0

for each r and s

NR T , p , n1, n2 , ρ2 , N̲ pq ≠ rs , N̲ ij

(11b)

while we still have that A ρ2 =

∂G ∂ρ2

≠0 T , p , n1, n2 , N̲ rsNR , N̲ ij

(11c)

In summary, the set of equations to be solved to predict, in PE conditions, sorption isotherms of a low molecular weight penetrant in a glassy polymer exhibiting HB interactions is made of (1) the equation expressing the equivalence of penetrant chemical potential in the gas phase (μGAS 1 ) and polymer phase (μPOL 1 ). Further details are available in the Supporting Information (see descriptions S9 and S11 in Table S2); (2) minimization conditions for N̲ ij and N̲ NR rs for the polymer phase and for the penetrant vapor phase. Further details are available in the Supporting Information (see descriptions S5, S6, and S7 in Table S1); (3) NRHB EOS for the vapor phase. Further details are available in the Supporting Information (see description S3 in Table S1). Differently from NRHB, in NETGP−NRHB the EOS of the polymer−water phase is not used to evaluate the mixture density whose value is now obtained by the intrinsic evolution history of nonequilibrium glassy systems. In particular, the

Figure 1. FTIR spectra in the 4000−400 cm−1 range for the PMDA− ODA polyimide in the dry state (black trace) and after equilibration at p/p0 = 0.6 (blue trace). Sample thickness = 20 ± 0.5 μm. 8681



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1570 cm−1 region (in-plane deformation, δHOH), and as a very broad absorption centered at around 500 cm−1 (libration modes, i.e., hindered rotation of the H2O molecule). Analogous features are also found in the absorbance spectra of the other samples. The spectrum of sorbed water can be isolated by use of difference spectroscopy.24 In this context the OH stretching region is of particular interest. Figure 2 shows a comparison of

two polymers. The more significant difference is the red shift of the PCL components at 3630 and 3546 as compared with that of the analogous components for PMDA−ODA, which clearly indicates a stronger HB interaction in the case of the PCL− water system. With the aim of identifying the different water species that are present and of quantifying their concentration, a curve fitting analysis of the νOH profiles can therefore be attempted. This issue will be discussed in detail in a following section, on the basis of the additional information gathered from 2D-FTIR spectroscopy and of the information that can be gathered from absorbance spectra on the effective involvement in HB interaction of proton acceptor groups present on polymer backbones. 4.1.2. 2D-COS. Beside determining difference spectra at sorption equilibrium conditions, time-resolved data were also collected in situ during sorption/desorption tests. As an example in Figure 4 are reported the difference spectra relative

Figure 2. Difference spectra (wet − dry) normalized for the sample thickness, representative of water absorbed in the three investigated polyimides in the 4000−3000 cm−1 wavenumber range for the three investigated PIs. Spectra denoted as wet were collected at equilibrium at p/p0 = 0.6.

the difference spectra (wet − dry) for the three investigated PIs at water sorption equilibrium at p/p0 = 0.6. As expected on the basis of the different chemical structure, the spectra evidence significant differences in terms of total amount of sorbed water that decreases considerably with an increase in the fluorine content. The complex, well-resolved band-shape appears to be qualitatively similar in all three PIs and indicates the occurrence of distinct water species involved in H-bonding interactions. Difference spectra were also collected in the case of the PCL/water system. In particular, Figure 3 shows a comparison of the difference spectra in the νOH region for the PMDA− ODA/water and PCL/water systems collected at equilibrium at p/p0 = 0.6. The overall shape of the profiles are very similar in the two samples and, as will be discussed in detail later, is indicative of the presence of the analogous water species in the

Figure 4. Difference spectra (wet − dry) in the 4000−2800 cm−1 interval, collected at increasing times during the sorption of H2O vapor into the PMDA−ODA film (p/p0 = 0.4, T = 30 °C). Collection time increases as indicated by the arrow.

to the stretching modes, as collected at different times during a typical sorption experiment (p/p0 = 0.4) of water vapor in PMDA−ODA. These data can be used to precisely monitor the diffusion kinetics.24,77−80 Moreover, such a set of dynamic spectra collected in a sequential order during the sorption or desorption process, can be transformed, in the generalized 2D correlation spectroscopy scheme,71 into a set of 2D correlation spectra by cross-correlation analysis. This technique, referred to as 2D-FTIR correlation spectroscopy (2D-COS), introduced by Noda et al.,71,81 is an extremely useful and effective tool to investigate in detail the behavior of polymer/penetrant systems from an interactional standpoint. In fact, among the main advantages of this technique we recall:71 (i) the simplification of complex spectra with numerous overlapped peaks improving the resolution by spreading the data over a second frequency axis, (ii) the establishment of unambiguous assignments through correlation of bands, and (iii) probing the sequential order of spectral intensity changes that occur during the measurement providing information about the dynamics of the evolving system. In particular, a great wealth of information is gathered from asynchronous spectra. We recall that a peak in the asynchronous spectrum at [ν1, ν2] corresponds to two IR signals changing at different rates, while when two signals change at the same rate a zero intensity is obtained, thus providing the characteristic resolution enhancement and the specificity of the asynchronous pattern. On the basis of the so-

Figure 3. Comparison of difference spectra (wet − dry) representative of absorbed water in PMDA−ODA (red trace) and PCL (blue trace) in the 4000−3000 cm−1 wavenumber range. The absorbance scale refers to the PCL spectrum. Spectra denoted as wet were collected at equilibrium at p/p0 = 0.6. The red trace is reported in full scale to facilitate the comparison. 8682



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called Noda rules,71,81 the sign of the asynchronous peaks supplies information about the sequence of changes of the two correlated IR signals. It is explicitly noted here that, for all the investigated samples, the overall pattern is exactly coincident in sorption and desorption experiments, but with the sign reversed. In Figure 5 are reported the asynchronous correlation

sorption test, the concentration of the species absorbing at 3660−3570 cm−1 increases faster than the concentration of the species absorbing at 3616−3456 cm−1, while on desorption, the opposite occurs. Very close patterns are found for the case of PMDA−ODA and 6FDA−ODA (Figure 5A,B) pointing to the presence of the same interacting species. Conversely, in the case of 6FDA-6FpDA, two additional correlation peaks are observed at [3660−3700 cm−1] and [3570−3700 cm−1], indicating the presence of a further component at 3700 cm−1 which evolves at the same rate as the doublet at 3616−3456 cm−1 (no correlations observed at the respective frequencies) and at a slower rate compared to the doublet at 3660−3570 cm−1. Full details of this analysis are reported in ref 24, 27. To provide the vibrational assignment of the signals identified so far, the molecular environment of the water molecules needs to be specified by identifying the active site(s) of the polymer. The discussion is therefore postponed after the analysis of the polyimide spectrum. The same type of analysis has been conducted also in the case of PCL. Figure 6 shows the asynchronous 2D-COS

Figure 6. 2D-FTIR correlation spectrum (asynchronous) obtained from the time-resolved spectra collected at 25 °C during water desorption experiment at p/p0 = 0.8 on PCL.

spectrum obtained at 25 °C from desorption test of water from PCL (p/p0 = 0.8). This map is very similar to the one found for PMDA−ODA/water (Figures 5), pointing to a similarity of water species present in the two systems. In the case of PCL/water system the 2D-COS analysis suggests again the presence of a couple of signals at 3635−3550 cm−1 and a couple of signals at 3595−3465 cm−1, the two couples exhibiting different dynamics: the couple of signals at 3595−3465 cm−1 increases faster than the two peaks at 3635− 3550 cm−1, while on sorption the opposite occurs. Also in this case, the 2D-COS findings point to the occurrence of two distinct water species. 4.1.3. The Active Sites on Polymers. The sites of interaction on the polymer backbones were identified by investigating the perturbation of the polymer spectrum induced by the presence of absorbed water. This analysis was performed on thin films (see section 2.2). Spectroscopic evidence of the involvement of imide carbonyls as proton acceptor (PA) groups in H-bonding interactions with absorbed water is provided by a red shift of both the νas(CO) and the νs(CO) modes observed for the PMDA−ODA and the 6FDA−ODA polyimides (see Figure

Figure 5. 2D-FTIR correlation spectrum (asynchronous) obtained from the time-resolved spectra collected at 30 °C during the water sorption experiment at p/p0 = 0.6 on the (A) PMDA−ODA polyimide; (B) 6FDA−ODA polyimide; (C) 6FDA−6FpDA polyimide.

maps, obtained for the three investigated PIs from the timeresolved FTIR spectra collected in situ during water vapor sorption tests at p/p0 = 0.6. The whole of the 2D results suggests the presence of a couple of signals at 3660−3570 cm−1 and a couple of signals at 3616−3456 cm−1. The two components of each couple change at the same rate, but the two couples exhibit different dynamics. These findings can be interpreted by assuming the occurrence of two distinct water species, based on the general observation that a single water molecule produces two OH-stretching modes (in-phase at lower frequency and out-of-phase at higher frequency). In particular, the signs of the correlation peaks indicate that, in a 8683



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7A,B). The red shift of the ν(CO) peaks is to be related to the lowering of the force constant of the CO bond caused by

Figure 8. Carbonyl stretching region of dry PCL at 30 °C (semicrystalline PCL) and at 65 °C (molten PCL).

evident in the dry PCL sample (see Figure 8), because the polymer is now totally amorphous. The red shift of the ν(C O) peak upon water sorption at 65 °C proves, also in the case of PCL, the involvement of carbonyls as PA groups in HB interactions with water. In Figure 9 it is evidenced the shift of

Figure 7. The carbonyl stretching region at sorption equilibrium at different p/p0 values: (A) PMDA-ODA; (B) 6FDA-ODA.

the H-bonding. Similar conclusions about the involvement of CO groups in HB interactions with water can be also drawn for the case of 6FDA−6FpDA, although in this case the peakshifts are barely detectable as a consequence of the very limited amount of absorbed water (data not shown). In the case of the PMDA−ODA and the 6FDA−ODA polyimides, in principle, also the ether oxygen could act as proton acceptors toward water molecules. However, the spectroscopic evidence allows us to conclude that their involvement in H-bonding, if any, can be safely neglected. In fact, the prominent band that originates from the ether linkage of the ODA unit (associated with the asymmetric stretching vibration of the C−O−C bond,82,83 at 1244 cm−1 in PMDA− ODA and at 1246 cm−1 in 6FDA−ODA) remains completely unperturbed even at the highest concentrations of absorbed water (no shift in the absorbance spectra). The above conclusion is also supported by earlier investigations by CPmass NMR spectroscopy.84 In the case of PCL, this analysis is complicated by the interference of the carbonyl stretching peak associated to the crystalline phase that is centered at 1725 cm−1 while that of the amorphous phase is centered at 1735 cm−1 (see Figure 8). Since water is expected to penetrate only within the amorphous domains and, in turn, to interact only to carbonyls located on the amorphous polymer backbones, experiments on thin films aimed at assessing involvement of carbonyls as PA in HB interactions with water molecules were performed at 65 °C, that is, right above the melting temperature of PCL. In fact, in this case a single peak associated with carbonyl stretching is

Figure 9. Shift of the carbonyl stretching peak at equilibrium (p/p0 = 0.4).

the carbonyl stretching peak occurring on sorption of water, at equilibrium at 65 °C and at p/p0 = 0.4. Also in this case, spectroscopic evidence leads to exclude the involvement of ether groups as PA. 4.1.4. Identification of HB Interactions. On the basis of the spectroscopic results, likely structures can be put forward for the H-bonding aggregates that are formed in the investigated systems. In detail, in all the three PIs, the couple of water signals at 3660−3570 cm−1, can be associated, respectively, to the out-of-phase and in-phase stretching modes of water molecules bound to imide carbonyls via a HB interaction (see structure I in Figure 10). The other two peaks, also identified in all the three PIs at 3616 and 3470 cm−1, can be ascribed to the water molecules interacting with another water molecule Hbonded to a carbonyl, that is, self-associated water that form (predominantly) dimers (see structure II in Figure 10), the feature at 3616 cm−1 being assigned to a νOH localized primarily on the noninteracting O−H bond, whereas the 3470 cm−1 band being ascribed (predominantly) to the stretching mode of the interacting O−H bond. To simplify the notation, we will refer to these two types of water molecules respectively as “monomeric” water belonging to the “first shell” and “dimeric” water belonging to the “second shell”. 8684



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Figure 11. Water vapor sorption isotherms as measured gravimetrically for the three investigated polyimides. Curves connecting the data points are to be intended for eye guidance only.

omitted here for the sake of brevity and can be found in ref 27. We discuss here in some detail the procedure adopted in the case of PCL, since it differs from the case of PIs and has not yet been published. In general, for PCL, owing to the invariance of the water species present, the following relationship can be assumed to hold: Figure 10. Schematic representation of the H-bonding interactions in the investigated water/polyimide systems. Atoms color codes: white = H; gray = C; red = O, blue = N; cyan = dummy. The structures represented are those of the 6FDA−ODA and the 6FDA−6FpDA polyimides. Also indicated, are the frequencies of the stretching vibrations of the O−H bonds for the different water species.

CTOT = Cm + Cd =

A′ A m′ + d εm·L εd ·L

(12)

where CTOT is the total water concentration, Cm and Cd are, respectively, the concentration of monomeric and dimeric water molecules, A′m and A′d are the corresponding integrated absorbances of the component associated to monomeric and dimeric water molecules, εm and εd are the associated molar absorptivities, and L is the sample thickness. If we now choose two analytical peaks characteristic of the species to be quantified, that is, at 3546 cm−1 for the monomer and at 3493 cm−1 for the dimer, we may write, rearranging eq 12:

Only in the case of the 6FDA−6pDA is a signal present at 3700 cm−1. It has been attributed27 to water molecules whose hydrogen atoms are not involved in H-bonding, and in particular, on the basis of the results of 2D-COS, to a water molecule in a self-associated environment that realizes the Hbonding interaction through its oxygen atom as a proton acceptor (see structure III in Figure 10). Further details of the previous analyses can be found in refs 24 and 27. An analogous interpretation can be provided for the PCL/ water system on the basis of the outcomes of the spectroscopic analysis. In particular, the couple of water signals at 3635−3550 cm−1, can be associated, to water molecules bound to ester carbonyls via a HB interaction while the other two peaks, identified at 3595 and 3465 cm−1, can be ascribed to selfassociated water that forms of (predominantly) dimers. 4.1.5. Quantitative Evaluation of Water Species and of Self- and Cross-HB. Toward a quantitative assessment of the concentration of the different water species present in the investigated systems, a least-squares curve fitting analysis of the difference spectra collected in the OH stretching region has been performed guided by the results of the 2D-COS analysis. Combining the results of curve fitting analysis with gravimetrically determined sorption isotherms, it has been possible to determine the molar absorptivity of one peak representative of each water species (e.g., in the case of 6FDA−ODA, of the peak 3568 cm−1 for water molecules interacting with carbonyls and of that at 3495 cm−1 for the water molecule that form self-HB with another water molecule H-bonded to the carbonyl). Once the molar absorptivities are known, it is possible to obtain a quantitative evaluation of the concentration of each species of water. The gravimetric sorption isotherms used in the calculations for the case of polyimides are reported in Figure 11 while those for the case of PCL are reported later. Full description of the procedure adopted to perform the calculation of the molar absorptivities in the case of PIs are

A A3546 ε · = ε3546 − 3493 3546 C TOT C TOT ε3493·

(13)

where A3546 = A3546 ′ /L and A3493 = A3493 ′ /L. Thus, by reporting A3546/CTOT vs A3463/CTOT a linear plot is obtained from which it is possible to evaluate ε3546 from the intercept on the ordinate axis and ε3493 from the slope. Figure 12 shows this plot as constructed on the basis of diagram of data collected at water sorption equilibrium in PCL at several values of p/p0 at 25 and 30 °C. Once the molar absorptivities have been evaluated, concentration of the two water species (monomeric or “first shell” water and dimeric or “second shell” water) can be

Figure 12. Diagram of A3546/CTOT vs A3493/CTOT. Data collected at water sorption equilibrium at several values of p/p0 at 25 and 30 °C. 8685



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Figure 13. Concentration of water present in the first- and in the second-shell layers as a function of the relative vapor pressure of the sorption test. (A) PMDA−ODA; (B) 6FDA−ODA; (C) 6FDA−6FpDA; (D) PCL. Curves connecting the data points are to be intended for eye guidance only.

reflected in the total amount of established cross H-bonding. In fact, to calculate the moles of cross H-bonding (nwp 12 ) from the concentration of first shell water as evaluated spectroscopically, it is necessary to assume a specific stoichiometry for the water− carbonyl adduct. Thus we may introduce an “upper bound” experimental value corresponding to the 1:2 stoichiometry and a “lower bound” corresponding to a 1:1 stoichiometry. The “lower bound” is coincident with the concentration of first shell water while the “upper bound” is twice this value. As an example, in Figure 14 are reported, in the case of 6FDA−

evaluated straightforwardly. In Figure 13 are reported the results of these calculations for the three PIs and for PCL. With the aim of comparing these results with the predictions of the NRHB and NETGP−NRHB model, data on concentration of the different water species need to be reelaborated to evaluate the number of self- and cross-HB established within the polymer−water mixture, that is the outcome of the models. Hence, we need to determine the number of moles of water self-HB normalized per mass of wp /m2am, m2am representing the mass of the polymer (n11 amorphous phase for PCL and nwp 11 /m2 for PIs) and the number of moles of cross HB occurring between the proton donor groups of water molecules and the proton acceptor groups present on the polymer backbone, normalized per mass am for PCL and nwp of polymer (nwp 12 /m2 12 /m2 for PIs). The calculation is rather straightforward in the case of dimeric water. In fact, in this case, a 1:1 ratio can be safely assumed to occur 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. In the case of monomeric water it has been assumed, in schematizing the possible interactions in Figure 10 (see structure I), that each water molecule belonging to the first shell establishes only one hydrogen bond with the PA group of the polymer (i.e., 1:1 stoichiometry). However, it is explicitly noted that the possibility exists for a single water molecule to form two Hbonding interactions with two distinct carbonyls (i.e., a 1:2 stoichiometry) thus “bridging” two functional groups. In this arrangement, each H2O would still produce two peaks (a symmetric and an antisymmetric ν(OH) vibration), and the interpretative arguments presented so far would remain valid. The spectroscopic analysis does not allow, at present, to discriminate between 1:1 and 1:2 stoichiometry, and it is even possible that, in the actual system, both arrangements occur. As a matter of fact, although this bridging should be statistically favored due to the large excess of carbonyl groups with respect to absorbed water, actually the formation of these bridges requires specific conformations for juxtaposed carbonyls to be bridged. Although the stoichiometry of the water−carbonyl adduct will not affect the absolute concentration of first shell water as evaluated from the νOH band profile, it will certainly be

wp Figure 14. Calculated values for nwp 11 /m2 and for n12 /m2 as a function mass fraction present at sorption equilibrium in the 6FDA−6FpDA/ water system.

6FpDA, the values calculated for nwp 11 /m2 and those calculated for nwp 12 /m2 as a function of the water mass fraction present at sorption equilibrium in the system. In the latter case, both “upper bound” (1:2 stoichiometry of water/polymer interaction) and the “lower bound” (1:1 stoichiometry of water/ polymer interaction) values are plotted.

5. COMPARISON WITH THEORETICAL PREDICTIONS 5.1. PIs/Water Systems. Interpretation of water sorption thermodynamics has been limited to 6FDA−ODA and 6FDA− 6FpDA. In fact, since PMDA−ODA degrades in the proximity of its glass transition temperature, it was not possible to perform PVT characterization at high pressure in the rubbery state that is needed to evaluate the equation state scaling 8686



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Table 1. NRHB Parameters for Pure Polyimides and Pure Water

a

component

εs* [J/mol]

εh* [J/(mol K)]

vsp,0 * [cm3/g]

E0w 11 [J/mol]

S0w 11 [J/(mol K)]

3 V0w 11 [cm /mol]

6FDA−ODA 6FDA−6FpDA watera

5988.5 5471.1 5336.5

4.3186 3.8652 −6.506

0.5736 0.5174 0.9703

−16100

−14.7

0

From ref 49.

parameters of pure polymer, that is, ε*h , ε*s , and v*sp,0. The values estimated for scaling parameters of pure 6FDA−ODA and 6FDA−6FpDA are reported in Table 1. For the case of water, the three LF parameters and the two hydrogen bonding parameters have been taken from literature49 and are reported in Table 1 as well. Finally, it has been assumed that the volume change upon formation of water self-hydrogen bonding, V0w 11 , is equal to zero. Further details are given in ref 28. In the implementation of NETGP−NRHB model, the swelling coefficient, ksw, has been assumed to be equal to zero in view of the small amount of sorbed water. Regarding the HB contributions, in line with the assumptions made by 0wp Tsivintzelis et al.49 in applying the NRHB model, V0wp 11 and V12 have been both taken as being equal to zero. Consequently, only two fitting parameters are needed to fit water sorption isotherms in polyimides, the mean-field polyimide/water interaction parameter, ψ12 = (1 − k12), and the molar Helmholtz energy of formation of polymer/water HB interaction, A0wp 12 . It is recalled here that, since experimental sorption data were available only at one temperature (30 °C), it was impossible to separate the contributions of molar internal energy of formation of cross-HB interaction from the entropic one, they being lumped in the parameter A0wp 12 . On the basis of the spectroscopic analysis, it has been assumed that four proton acceptor groups (i.e., carbonyl groups) are present per repeating unit of the polymers and that two equivalent proton donor groups and two equivalent proton acceptor groups are present on each molecule of water.46 In Figure 15 panels A and B are reported the best fitting curves provided by the NETGP−NRHB model for water sorption isotherms, respectively, for 6FDA−ODA and 6FDA− 6FpDA along with experimental data. Best fitting parameters are reported in Table 2. The NETGP−NRHB model supplies a good fitting capability of sorption isotherms in both polyimides,. As expected in view of the similar chemical structure of the polymer proton acceptor groups involved in the HB interactions, the parameter A0wp 12 takes close values for the two polyimides. Using the parameters determined from the best fitting of the sorption isotherms, the NETGP−NRHB model has been used to predict the amounts of the different types of hydrogen bonding adducts formed at equilibrium in the polyimide−water mixtures. In Figure 16A,B model predictions are compared with the experimental data for the case of 6FDA−ODA and of 6FDA−6FpDA. In particular are compared, as a function of water mass fraction at sorption equilibrium with water vapor at different values of p/p0, the moles of self-HB occurring between the proton donor and the proton acceptor groups of water molecules, normalized per mass of polymer (i.e., nwp 11 /m2) and the moles of cross-HB occurring between the proton donor groups of water molecules and the proton acceptor groups present on polymer backbone, again normalized per mass of polymer (i.e., nwp 12 /m2). In the latter case both “lower bound” values (i.e., calculated assuming 1:1 stoichiometry of the

Figure 15. (A) Fitting of experimental water sorption isotherms for (A) 6FDA−ODA; (B) 6FDA−6FpDA. Continuous line represents fitting curve provided by NETGP−NRHB.

Table 2. NETGP−NRHB Parameters for Polyimide−Water Mixtures As Obtained from Data Fitting of Experimental Sorption Isotherms system

ψ12

A0wp 12 [J/mol]

6FDA−ODA/water 6FDA−6FpDA/water

0.787 0.869

−12 400 −12 100

carbonyl/water adduct) and the “upper bound” values (i.e., calculated assuming 1:2 stoichiometry of the carbonyl/water adduct) are reported. The NETGP−NRHB model provides an excellent agreement with values calculated on the basis of FTIR spectroscopy analysis in the case of water self-HB and, quite interestingly, an excellent agreement with values for cross-HB as evaluated assuming a 1:2 stoichiometry. However, this cannot be taken as a definite proof that bridges actually provide the prevailing contribution to cross-HB interactions, in view of the rather crude assumptions on which the modeling of HB statistics is rooted, that do not allow to discriminate between different kinds of cross-HB established between water and PA groups present on the macromolecule. 5.2. PCL/Water System. The NRHB model has been used to interpret water sorption thermodynamics in PCL. As already mentioned, the concentration of water has been normalized to the fraction of amorphous phase of the polymer, assuming that the solubility in the crystalline phase is negligible and that the presence of crystals do not alter the thermodynamic behavior of the amorphous domains. In applying the NRHB approach, we have imposed that the volume change upon formation of water 8687



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As evident in Figure 17, where are reported best fitting curves provided by the model for water sorption isotherms in

Figure 17. Fitting of experimental water sorption isotherms for PCL. Continuous lines represent fitting curves provided by NRHB.

PCL along with experimental data at 25, 30, and 37 °C, the NRHB model provides a good fitting of experimental data. Best fitting parameters are reported in Table 4. Figure 16. (A, B) Comparison of predictions of NETGP−NRHB model with experimental results for (A) 6FDA-ODA and (B) 6FDA6FpDA. 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 dry polymer as a function of water mass fraction and (2) moles of hydrogen bonding between absorbed water molecules and proton acceptor groups on the polymer backbone in the polymer/water mixture per gram of dry polymer (points evaluated from spectroscopic experiments assuming both 1:1 and 1:2 of the carbonyl/water adduct are reported).

Table 4. The NRHB Mean-Field Interaction Parameter and Cross-HB Parameters for the PCL−Water System, As Obtained from Data Fitting of Experimental Sorption Isotherms k12

E012 [J/mol]

S012 [J/(mol K)]

−0.1152 ± 0.005

−11130 ± 200

−6.13 ± 0.1

Once the model parameters were determined from the fitting of the gravimetric data, the NRHB model was used to predict quantitatively the amount present in the polymer/water mixture, in equilibrium with a water vapor phase, of self-HB formed by water molecules and of cross-HB established between carbonyls and water molecules at 25 and 30 °C. As can be inferred from Figure 18, the moles of HB established at 30 °C within the polymer/water mixture, normalized by the mass of amorphous polymer, are reported as a function of the water mass fraction; also in this case the model provides a reasonable estimate of the number of hydrogen bonds formed,

self-HB and water/polymer cross-HB are zero (both in the water/polymer mixture and in the vapor phase in contact with it), according to the assumption made by the authors of NRHB in recent publications.49 Application of NRHB to the PCL/ water system and its use for fitting of gravimetric sorption isotherms are thoroughly discussed in recent publication by Scherillo et al.26 and we briefly recall the results to focus then on the comparison of model predictions with the results of spectroscopic analysis. Fitting parameters for NRHB model to be determined from experimental sorption isotherms of water 0wp in PCL are k12, E0wp 12 , and S12 . Lattice fluid scaling parameters for pure PCL (i.e., ε*h2, ε*s2, and v*sp,02) have been determined by the fitting of PVT data for PCL using the NRHB model for pure fluids and their values are reported in Table 3. Lattice fluid Table 3. NRHB EOS Parameters for Pure PCL. ε*h , ε*s , and v*sp,0 Have Been Obtained by Fitting PVT Data Using the NRHB Model for Pure Fluids component

ε*h [J/mol]

ε*s [J/(mol K)]

v*sp,0 [cm3/g]

PCL

5876 ± 50

3.824 ± 0.01

0.8873 ± 0.005

Figure 18. Comparison of predictions of the 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 dry polymer as a function of water mass fraction and (2) moles of hydrogen bonding between absorbed water molecules and proton acceptor groups on the polymer backbone in the polymer/water mixture per gram of dry polymer (points evaluated from spectroscopic experiments assuming both 1:1 and 1:2 of the carbonyl/water adduct are reported).

0wp scaling parameters for water (i.e., ε*h1, ε*s1, and v*sp,01), E0w 11 = E11 49 0w 0wp and S11 = S11 have been taken from the literature and are the same as already reported in Table 1. On the basis of the spectroscopic analysis, it has been assumed that a one proton acceptor group (i.e., carbonyl group) is present per repeating unit of the polymer and that two equivalent proton donor groups and two equivalent proton acceptor groups are present on each molecule of water.46

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reaching a good agreement with values for cross-HB evaluated in the hypothesis of the 1:2 stoichiometry of the carbonyl− water adduct. However, the same caution as for the case of polyimides, should be applied in drawing conclusions about actual involvement of a single water molecule in bridging two PA groups present on macromolecules.

CONCLUSIONS The NRHB equilibrium model and the NETGP−NRHB approach that represents its extension to the nonequilibrium glassy state, have been proven to provide a consistent framework to interpret water sorption thermodynamics in rubbery and glassy polymers, accounting for HB interactions. The capability of these theoretical approaches has been verified by studying the water sorption thermodynamics in polycaprolactone and in three polyimides. In fact, beside showing a good fitting capability of sorption isotherms, models are able to supply quantitative predictions for self- and cross-HB established within the polymer/water mixture in contact with a water vapor phase that compare well with the results of the analyses performed by in situ infrared spectroscopy. An extensive experimental analysis of PCL/water and PIs/ water systems has been conducted, exploiting the wealth of information that can be obtained by re-elaborating spectroscopic data collected dynamically with a 2D-COS technique. Information on the type and amount of water species present in the systems as well as on the proton acceptor groups of the polymer backbone that actually take part to the HB interactions has been reliably gathered from experiments. This information has been used to tailor the structure of the models in terms of the number of interacting groups to be accounted for in the HB contribution to the expression of the chemical potential of water. Quite interestingly, the models are consistent with the occurrence, as a main contribution to cross-HB, of a single water molecule bridging between two PA groups present on the macromolecules, although this consistency cannot be taken as a definite proof in view of the level of accuracy used in modeling to describe the HB statistics in the mixture. Important implications of this approach that combines gravimetric and spectroscopic measurements with modeling of sorption thermodynamics accounting for HB formation, certainly are in terms of assessing the plasticization efficiency of water in different polymers. In fact, once the fitting parameter have been determine, NRHB model provide a useful theoretical framework able to predict glass transition temperature of water/polymer mixtures. ASSOCIATED CONTENT

S Supporting Information *

Relevant equations for NRHB and NETGP−NRHB models and related descriptions (Tables S1 and S2); list of symbols (Table S3) related to these equations and not explicitly indicated in the manuscript. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +39-081-7682512. Fax: +39-081-7682404. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 8689



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