Local Structure and Dynamics of Water Absorbed in Poly(ether imide

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Local Structure and Dynamics of Water Absorbed in Polyetherimide: A Hydrogen Bonding Anatomy Antonio De Nicola, Andrea Correa, Giuseppe Milano, Pietro La Manna, Pellegrino Musto, Giuseppe Mensitieri, and Giuseppe Scherillo J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b00992 • Publication Date (Web): 23 Mar 2017 Downloaded from http://pubs.acs.org on April 4, 2017

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The Journal of Physical Chemistry

Local Structure and Dynamics of Water Absorbed in Polyetherimide: A Hydrogen Bonding Anatomy Antonio de Nicola1, Andrea Correa2, Giuseppe Milano1,3*, Pietro La Manna3, Pellegrino Musto3*, Giuseppe Mensitieri3, 4 and Giuseppe Scherillo4. *Corresponding Authors 1.

Department of Chemistry and Biology “Adolfo Zambelli”, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy

2.

Department of Chemical Sciences, Federico II University of Naples Via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy 3

Institute on Polymers, Composites and Biomaterials, National Research Council of Italy, Via Campi Flegrei 34, 80078 Pozzuoli (NA), Italy 4

Department of Chemical, Materials and Production Engineering, Piazzale Tecchio 80, 80125 Naples, Italy

ACS Paragon Plus Environment

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ABSTRACT: Hydrogen Bonding (HB) interactions play a major role in determining the behavior of macromolecular systems absorbing water. In fact, functional and structural properties of polymer-water mixtures are affected by the amount and type of these interactions. This contribution aims at a molecular level understanding of the interactional scenario for the technologically relevant case of the polyetherimide-water system. The problem has been tackled by combining different experimental and theoretical approaches which, taken together, provide a comprehensive physical picture. Relevant experimental data were gathered by in-situ FTIR spectroscopy while Molecular Dynamics (MD) and statistical thermodynamics approaches were used as modelling theoretical tools. It was found that, among the possible interaction configurations, some are strongly prevailing. In particular, water molecules preferentially establish water bridges with two carbonyl groups of the same PEI repeating unit. Water selfinteractions were also detected, giving rise to a ‘second shell’ species in the prevalent form of dimers. The population of the different water species was evaluated spectroscopically and a remarkable agreement with theoretical predictions was found.

Introduction The sorption of water molecules and their interactions within synthetic polymers is a subject of considerable interest from both technological and fundamental points of view. This interest is witnessed by the increasing number of studies, involving several experimental characterization techniques1-9 and molecular simulations10-13 appearing in the current literature. In fact, polymerwater interactions have a considerable impact on material performances since, in typical environmental conditions, water can be absorbed even in moderately hydrophobic polymers. Issues related to water sorption are hygro-thermal aging, polymer plasticization, depression of the glass transition temperature (Tg) and, in some cases, hydrolytic degradation14. These have significant technological implications for long term durability of glassy polymer matrices for composites,14 for the use of polymers to realize membranes for separation of liquid and gaseous mixtures containing water,15-17 for the development of water barrier polymers for packaging applications18 and for the utilization of polymer matrices as humidity sensor or as gas sensor in a humid environment.19. All these effects are closely related to the type and amount of Hydrogen Bonding (HB) interactions that are established within the system. In a series of previous


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contributions we have investigated several glassy polymer-water systems20-23 showing how the information gathered from infrared vibrational spectroscopy, combined with gravimetric measurements, can lead to a quantitative estimation of the amount of different water species as well as of self and cross HB interactions. These experimental results were successfully interpreted using a compressible lattice fluid thermodynamic model (the so called Non Equilibrium Theory for Glassy Polymers with Non Random Hydrogen Bonding, NETGPNRHB), accounting for both HB interactions

24-25

and non-equilibrium nature of glassy

polymers22 . The previous approaches can be combined with the wealth of information provided by Molecular Dynamics (MD) simulation to gather further insight into the physical picture of the investigated systems. In fact, MD results can be directly correlated with the spectroscopic outcomes and with the predictions of the thermodynamic model. Approaches based on atomistic MD simulations have been used to investigate HB interactions in water-polymer systems. Relevant examples are the investigation of water inclusion and transport in Nafion analysis of static and dynamic properties of HBs in water-Kapton systems

33

26-32

, the

and the study of

pressure effects on water-PEI systems34,35. Simulation with empirical potentials allowed to study amorphous polyaniline (PANI) structures: water absorption and diffusion in PANI ES,36 thermal conductivity,37 and water absorption in PANI EB.38 Using the proposed scheme and the corresponding procedure, atomistic models of amorphous PANI-HCl structures were generated and studied at different doping levels.39 A multiscale modeling scheme for gas-sensitive conducting polymer devices is described. The scheme is used to describe the effect of humidity in the sensor response.40 Polyamide water interactions have been intensively studied by means of molecular dynamics simulations by several groups. In particular, Müller-Plathe and coworkers


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reported all atom MD studies about water influence on the local structure41 and mobility enhancement induced by water sorption of Polyamide 6,6 (PA66).42 Later, using MD simulations, Eslami and Müller-Plathe studied water influence on local structure of nanoconfined PA66 and water solubility in PA66 using grand canonical ensemble MD simulations.13,

43

Aromatic PA in cross linked structures have been studied to investigate the properties and molecular features of hydrated membrane for reverse osmosis,44 interactions of PA membranes with calcium alginate gels in water solutions45 and water sorption and permeation in the presence of ions in models of PA membranes for desalinization.46 On these premises, we propose here a multidisciplinary investigation of water sorption in a high performance glassy polymer based on FTIR spectroscopy, MD simulation and statistical thermodynamics modeling. The aim is to achieve a thorough molecular-level understanding of the technologically relevant case of the polyetherimide (PEI)-water system. PEI is an amorphous engineering thermoplastic with excellent mechanical properties that, due to its high Tg (≅ 489 K), finds application up to elevated temperature. Ether groups provide chain flexibility and good melt flow properties coupled to stiffness and high heat resistance imparted by aromatic imide groups, thus promoting the use of PEI as a matrix for fiber reinforced composites.47-49 In addition, PEI is the material of choice for several separation processes18,

50--58

, thanks to its

excellent chemical, mechanical, thermal and transport properties and to its durability.59-61 The adopted multidisciplinary approach allowed us to identify the prevailing HB interactions established in the PEI-water system. In particular, it has been demonstrated that water molecules preferentially establish water bridges with two carbonyl groups of the same PEI repeating unit. No significant involvement of PEI ether groups in HBs with water emerged. In addition, water self-interactions were identified that give rise to a ‘second shell’ species in the prevalent form of


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dimers. The population of these different water species was evaluated spectroscopically and a remarkable agreement with the theoretical predictions was found. 2. Materials and Methods 2.1 Materials Totally amorphous PEI films was a commercial grade product, kindly supplied by Goodfellow Co., PA, USA in the form of a 50.0 µm thick film. To obtain film thicknesses suitable for FTIR spectroscopy, the original product was first dissolved in chloroform (15 % wt/wt concentration) and then cast onto a tempered glass support. The solution was spread by a calibrated Gardner knife, which allows one to control the film thickness in the range 10 – 40 µm. The cast film was dried 1 hr at room temperature and 1 hr at 80°C to allow most of the solvent to evaporate, and at 120°C under vacuum over night. At the end of the drying protocol the film was removed from the glass substrate by immersion in distilled water at 80°C. Thinner films (3.0 – 1.0 µm) were prepared by a two-step, spin-coating process performed with a Chemat KW-4A apparatus from Chemat Technologies Inc (Northridge, CA). Spinning conditions were 12 s at 700 rpm for the first step and 20 s at 1500 rpm for the second step. The spin-coated films were dried in the same conditions as for the thicker films and freestanding samples were removed in distilled water at room temperature. 2.2 Wide Angle X-ray scattering XRD analysis has been carried out using a PANalytical X'pert Pro diffractometer, equipped with a PIXcel 1D detector, using a Ni-filtered Cu Kα radiation under the following operative conditions: voltage = 40kV, current = 40 mA, angular range = 5-60 °2θ, resolution = 0.0066 °, counting time per step = 39 s. 2.3 FTIR spectroscopy A custom designed vacuum tight FTIR cell, was used to acquire time-resolved FTIR spectra during the sorption experiments. Data collection on the polymer films exposed to water vapor at a constant relative pressure (i.e ratio of pressure of pure water to the vapor pressure of water at the test temperature, p/p0) was carried out in the transmission mode and sorption kinetics was monitored up to the attainment of sorption equilibrium. The cell, positioned in the sample compartment of the spectrometer, was connected through service lines, to a water reservoir, a


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turbo-molecular vacuum pump and pressure transducers. Full details of the experimental setup are reported in62-63 . 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. 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). Full absorbance spectra (i.e. polymer plus absorbed water) were obtained using as background the cell without sample at the test conditions. The spectra representative of water absorbed at equilibrium were obtained by using as background the singlebeam spectrum of the cell containing the dry polymer film. 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.64 This has been verified in the present case. Details of curve fitting analysis of spectra representative of water absorbed at equilibrium within the two polymers are reported later when discussing the results of FTIR analysis. 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 several temperatures (303.15, 318.15, 333.15 and 343.15 K) 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.65


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2.5 Polymer Model The OPLSAA force-field66-69 has been used for the full atomistic model of PEI. Only a slight tuning of single point charges has been done to preserve the electro-neutrality of the system. In the Scheme 1, the chemical structure of a repeating unit of PEI chain, together with the different atom types, are reported. For the simulations presented in the present work, we have built PEI chains containing 12 repeating units. Each chain is terminated by using a phenyl group and a hydrogen atom. Validation of the OPLS-AA force field employed in the manuscript is provided in the Supporting Information, Section 3. In the mixed PEI/water systems, the SPC model70 for the water molecule has been adopted. A full list of bonded and non bonded interaction parameters is reported in section 2 of Supporting Information.

Scheme 1. Chemical structure of PEI repeating unit. Different atom types are indicated by corresponding labels. For sake of clarity, all hydrogen atoms are omitted except the ones used for the labeling. Non bonded interactions over two consecutive bonds are excluded.

2.6 Simulation Details MD simulations having a hybrid particle-field representation of the molecular models (MDSCF) aimed to equilibrate PEI pure amorphous systems have been performed by using OCCAM code,71 following the procedure reported by De Nicola et al.,72 were run in NVT ensemble at constant temperature of 570 K. The temperature was controlled by using the Andersen thermostat73 with a collision frequency of 7 ps-1, a time step of 1 fs was employed in all simulations and a density field density update has been performed every 0.1 ps. More information about the relaxation procedure can be found in reference simulation method employed there can be found in references.

72

and the basics of the

74-75

MD all atom simulations of both systems, PEI and PEI+water, have been performed by using GROMACS76 5.0.4. For the pure PEI system, a preliminary short equilibration (1 ns) in NVT


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ensemble, starting from the relaxed structure obtained by MD-SCF simulations, was performed before productions run performed in the NPT ensemble. A time step of 2 fs has been used for all simulations. For the non-bonded interactions a cut-off of 1.1 nm has been used, while the coulomb long range electrostatic interactions have been treated by generalized reaction field77 with a dielectric constant εrf = 5 and a cut-off of 1.1 nm. The temperature of the systems has been kept constant at 303.15 K by using Berendsen thermostat78 with a time coupling τ = 0.1 ps. The pressure has been kept constant at 1.01325 bar by Berendsen barostat78, using a time coupling τ = 0.1 ps. In Table 1, the compositions of all simulated systems are reported in terms of ω, that represents the mass ratio of water (i.e. mass of water divided by total mass of polymer/water mixture). Table 1. System composition Simulation

No. water

No. atoms

Box Volume

ω

3

(nm )

molecules

Time (ns)

I

0

22680

251.2396

-

120

IIa

86

22938

251.6076

0.0042

198

IIIa

100

22980

251.6675

0.0048

200

IVb

120

23040

251.9438

0.0057

200

VIb

150

23130

252.4120

0.007

200

VIIb

220

23340

253.4763

0.01

240

a

Five independent MD simulations starting from different configurations have been performed. b For systems with more water molecules included two independent MD simulations starting from different configurations have been performed. For all systems a constant number of 27 PEI chains has been considered. The temperature has been kept constant at 303.15 K.


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3. Results and Discussion 3.1. FTIR spectroscopy 3.1.1. Absorbance, difference and two-dimensional correlation spectra For the analysis of water absorbed in PEI, the normal modes of the water molecule in the ν(OH) frequency range (3800 – 3200 cm-1) are of particular interest. A second region potentially useful for the spectroscopic analysis, that is, the δ(HOH) bending range (1680 – 1550 cm-1) 64, is not available in the present case because of the exceedingly low signal intensity and for the interference of the PEI spectrum which fully saturates this frequency interval (see Figure S4, Supplementary Information). Spectra collected in the 3800 – 3200 cm-1 range, after attainment of phase equilibrium of a PEI film exposed to water vapor at different p/p0 values are reported in Figure 1A and Figure 1B.

Figure 1. Absorbance (A) and difference spectra (B) of a PEI film 37.7 µm thick equilibrated at different relative pressures of water vapor. Green trace: dry film; blue: p/p0 = 0.1; black: p/p0 = 0.2; red navy: p/p0 = 0.3; purple: p/p0 = 0.4; dark green: p/p0 = 0.5; red: p/p0 = 0.6.

In particular, Figure 1A reproduces the as-collected traces, while Figure 1B displays the profiles obtained after spectral subtraction of the dry-sample spectrum (green trace in Figure 1A); these are representative of the spectrum of absorbed water. The ν(OH) band exhibits a fine structure where at least three maxima can be recognized at 3651, 3561 and 3475 cm-1. The above


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results are consistent with previous reports on several polyimides differing for their molecular structure 64 and can be analogously interpreted. The maximum at 3475 cm-1 was demonstrated to be a derivative-type feature due to the red-shift of the PEI peak originally centered at 3485 cm-1. The shift occurs as a consequence of H-bonding formation with water and is not related to the spectrum of absorbed water; accordingly, it is to be disregarded in the curve fitting analysis (vide infra). The other two maxima are indicative of the presence of distinct H2O species whose molecular environment is sufficiently dissimilar to produce a wide change in the respective vibrational response. Difference spectra, as those reported in Figure 1B, can also be collected as a function of time rather than at equilibrium, which affords a precise evaluation of the sorption/desorption kinetics, to be reported in a forthcoming contribution of this series. Two-dimensional correlation spectroscopy (2D-COS)23,

64, 79,80

was performed on the time-

resolved measurement carried out at p/p0 = 0.6 on both the sorption and the subsequent desorption run (kinetic data reported in Figure S7, Supporting Information). The results relative to the sorption test, summarized in Table 2, are consistent with those previously reported for different polyimides64. The asynchronous map, which provides the highest enhancement of resolution, displays analogous features in sorption and desorption measurements (see Figure 2A and Figure 2B). It exhibits the presence of four distinct components at 3655, 3611, 3562 and 3486 cm-1; these components are arranged pair-wise: the two signals centered at 3655 and 3562 cm-1 evolve synchronously and at a different rate with respect to the couple at 3611 – 3486 cm-1 that is also synchronously correlated. In particular, according to the sign of the cross-peaks, and taking into account the Noda correlation rules 80, in the sorption experiment the doublet at 3655 – 3562 cm-1 grows faster than the doublet at 3611 - 3486 cm-1. The asynchronous map relative to


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the desorption test (Figure 2B) is coincident with that for sorption in terms of peaks’ shape but with all signs reversed. This points to opposite dynamic relationships, i.e. on desorption, the doublet at 3611 -3486 cm-1 decreases at a faster rate with respect to the doublet at 3655 - 3562 cm-1. Figure 2A and Figure 2B provide also information on the band-shape of the components 81. Thus, the peaks at 3655, 3611 and 3562 cm-1 are comparably narrow, while the component at 3486 cm-1 is much broader. The above findings are reasonable when one considers that a single water molecule produces two OH-stretching modes (in-phase at lower frequency and out-ofphase at higher frequency). Thus, the two couples of signals suggest the presence of two distinct water species.

Figure 2. 2D-COS Asynchronous maps obtained from the time-resolved spectra collected in the sorption (A) and in the desorption experiment (B) at p/p0 = 0.6.

Table 2. Correlation peaks in the asynchronous spectrum obtained from the sorption test at p/p0 = 0.6. ν1 (cm-1)

ν2 (cm-1)

signa

rate of change

3611

3655

-

3611 < 3655

3486

3655

-

3486 < 3655

3562

3611

+

3562 > 3611

3486

3562

-

3486 < 3562


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a

The sign refers to the cross-peaks in the lower side of the spectrum, with respect to the main diagonal. The sign of the cross-peaks in the upper side can be deduced on the basis of the anti-symmetric character of the matrices.

3.1.2 Identification of the interacting sites on the polymer backbone: thin-film spectroscopy For identifying the active site on the polymer backbone, it is necessary to detect the perturbation brought about by the probe molecule on the spectrum of the matrix. This requires films in the thickness range 1.0 – 3.0 µm, so as to keep the whole spectrum within the range of absorbance linearity. These films were prepared ad hoc by a spin-coating process: the relative spectrum is represented in Figure S5A, Supporting Information. Figures S5B and Figure S5C compare the spectrum of the dry sample (blue trace) with that of the sample equilibrated at p/p0 = 0.6 in the two frequency ranges that display the strongest variation. The effects are small, yet well within the detectability limits of the interferometric sampling used in the present study. Previous reports82 demonstrated that shifts of such a magnitude are best investigated by subtraction spectroscopy. Figure 3A reports the difference spectra in the frequency range 1820 1660 cm-1, obtained by subtracting the spectrum of the fully dried sample from those of the same sample equilibrated at different relative pressures of water vapor. These difference spectra display the typical first-derivative features associated with peak shifts; in particular, the negative lobe that precedes the positive indicates a red shift, i.e. a lowering of the peak frequency in the sample spectrum (wet film) with respect to the reference spectrum (dry film). The effect is evident for both peaks occurring in the present interval, according to the nature of the relative vibrations (symmetric and anti-symmetric stretching modes of the imide carbonyls). The twolobe profiles are symmetric (i.e. the positive and the negative components have comparable intensities) and grow progressively with water concentration. Furthermore, the effect is fully reversible, as demonstrated by the black trace of Figure 3A, Figure 3B and Figure 3C, which refers to the difference spectrum obtained by considering the sample equilibrated at p/p0 = 0.6


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and subsequently dried. These results confirm that the observed shifts, albeit small, are not an artifact but actually originate from the molecular interactions between the proton acceptors on the polymer backbone and the water molecules. The red-shift of the two ν(C=O) modes demonstrates the involvement of the imide carbonyls as proton acceptors in H-bonding. In fact, the observed effect is a direct consequence of the electron-density withdrawing by the proton which, in turn, causes a lowering of the C=O force constant.

Figure 3. Difference spectra of a PEI film 3.0 µm thick equilibrated at different relative pressures of water vapor. Red navy trace: p/p0 = 0.1; light blue: p/p0 = 0.2; purple: p/p0 = 0.3; blue: p/p0 = 0.4; red: p/p0 = 0.5; violet: p/p0 = 0.6. A): 1820 – 1660 cm-1 range; B): 1420 – 1300 cm-1 range; C): 1320 – 1180 cm-1 range. In Fig. 3C the absorbance spectra of the dry sample (blue trace) and of the sample equilibrated at p/p0 = 0.6 (red trace) are also reported for comparison purposes.

In the 1420 – 1300 cm-1 range a first-derivative profile centered at 1359 cm-1 is accompanied by the appearance of a fully resolved peak at 1391 cm-1. This feature is apparently due to an intensity increase rather than a peak-shift. The shift takes place in the opposite direction with respect to those of the carbonyl modes (it is a blue-shift, the positive lobe comes first). The band involved, at 1359 cm-1, has been demonstrated by previous literature reports and a recent normal coordinate analysis

64, 83,84

to be a complex vibration containing a significant contribution from

the in-plane deformation of the N−C=O unit in the imide ring. Accordingly, the blue-shift is


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accounted for by the well-known stiffening effect produced by H-bonding on the relative forceconstant 85. No reliable interpretation is presently available for the component emerging at 1391 cm-1. In the 1320 – 1180 cm-1 range the difference spectra display a complex pattern which can be interpreted in terms of two opposite and closely lying shifts: a blue-shift of a component centered at around 1280 cm-1 coupled with a red-shift of a second band at lower frequency. The possible interference between the two effects makes it difficult to define exactly the original peak positions; however, both shifts are considerably lower than those observed in the previously considered frequency ranges. Below 1240 cm-1 the difference spectra approach zero. The interpretation of these features demand a positive assignment of the complex spectral profile in the region of interest. The absorbance spectrum (Figure 3C, blue trace) exhibits two prominent bands centered at 1275 and 1238 cm-1. The band at higher frequency displays a multicomponent structure, while that at 1238 cm-1 has a quasi-resolved component on the right side. Aryl ethers show a characteristic band in the 1270 – 1230 cm-1 region attributed to the C─O─ stretching vibration.86 In particular, diphenylether displays a single, intense and symmetric peak at 1244 cm-1; polyetherimides other than PEI (i.e. PMDA-ODA, 6FDA-ODA) display a single band at 1244 cm-1 which clearly correspond to the above normal mode.

82

(a comparison between the

spectra of PEI and PMDA-ODA in the 1320 – 1180 cm-1 interval is reported in Figure S6, Supporting Information). In the absence of reliable group-frequency correlations, the only way to deepen the spectral interpretation in the fingerprint region is to rely on a full normal coordinate analysis (NCA) based on quantum chemistry methods rooted on Density Functional Theory (DFT).


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A detailed account of the DFT/NC Analysis is reported in Section 6 of the Supporting Information. The relevant conclusion is that the complex band observed at 1275 cm-1 does not involve the C─O─C stretching, which, instead, significantly contributes to the bands observed at 1238 and 1215 cm-1 (see PED in Table S8, Supporting Information). Thus, the observed shifts are to be associated with the phenyl and the imide ring structures, while the C─O─C unit remains completely unaffected. In summary, although in principle, ether oxygens may participate to H-bonding interactions with water, the experimental results demonstrate their involvement to be negligible, if any.

3.1.3. Water species identification In the light of the results discussed so far, a likely interpretation of the ν(OH) band of sorbed water is as follows: the two sharp peaks at 3655 – 3562 cm-1 are assigned, respectively, to the νas and the νs modes of isolated water molecules interacting with the PEI carbonyls, while the second doublet at 3611 – 3486 cm-1 originates from water molecules self-interacting with the above species. More specifically, the absence of a characteristic sharp component in the high frequency side (~ 3690 cm-1) which is a readily detectable signature of “free” O─H bonds in the complex C=OH–O–H 87, coupled with the evidence provided by 2D-COS for the presence of only two H2O species, indicates that in the present system the amount of H2O molecules forming a single H-bonding interaction with an imide carbonyl is negligible, if any. The stoichiometry of the carbonyl-to-water interaction is thus 2:1, i.e., of the type –C=OH–O–HO=C–. Concerning the self-associated species, the component at 3611 cm-1 originates (predominantly) from the “free” O─H bond, while the 3486 cm-1 band is due to the O─H bond linked to the water


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molecule interacting with the imide groups. Water-to-water H-bonding, with the associated distribution of bond-lenghts, accounts for the characteristic breadth of the 3486 cm-1 component. A schematic representation of the two aggregates identified spectroscopically, with the indication of the peak-frequencies they produce, is reported in Scheme 2.

Scheme 2. Schematic representation of the two water species hypothesized in the PEI/H2O system. The isolated water molecules represented in the right side of Scheme 2, can be envisaged as a “core-hydration” species, i.e. the first hydration layer of penetrant (first shell) in the multilayer adsorption model of Brunauer, Emmet and Teller (BET) 88, while the selfassociated water molecules (right-side) are representative of the second-shell hydration layer.

3.1.4. Population analysis To quantify the population of the two water species identified spectroscopically, we relied on a least-squares curve fitting (LSCF) analysis of the spectral profiles in the ν(OH) region; typical results are represented in Figure 4, relative to the sample equilibrated at p/p0 = 0.6. A satisfactory reproduction of the experimental profile was achieved by considering three components, albeit 2D-COS spectroscopy resolved a fourth one at 3611 cm-1. The latter is not amenable to LSCF analysis because of the absence of any fine structure in the peak at 3655 cm-1.


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Quantitative analysis of the ν(OH) profile requires the evaluation of the molar absorptivity , , of the analytical signals. This was achieved by coupling the Beer-Lambert expression for the total concentration of sorbed water with the mass-balance relationship89:

(1)

(2)

which can be rearranged as

(3)

Figure 4. Curve fitting analysis of the spectrum representative of water sorbed in PEI (p/p0 = 0.6). The figure displays the experimental profile (red trace), the best-fitting curve (blue trace) and the resolved components (black traces). The inset represents the calibration curve for evaluating the absorptivities of the analytical peaks.

In equations 1 – 3 A is the integrated absorbance, C the volumetric concentration, L the sample thickness and the subscripts fs, ss and tot denote, respectively, first-shell, second-shell and total. Ctot vs p/p0 was obtained by an independent gravimetric measurement. The density of PEI20 (1.2683 g/cm3), assumed invariant with H2O sorption, was used to convert gravimetric weight ratios into volumetric concentration values.


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Equation 3 predicts a linear correlation between / and / with a negative slope equal to the absorptivity ratio and the intercept equal to . Selecting the analytical signals at 3562 cm-1 for the first-shell species and at 3468 cm-1 for the second-shell, we obtained the expected correlation (see inset of Figure 4) and the values of 34.5 km/mol for and 89.7 km/mol for . The absorptivity ratio (0.38) compares favorably with a previously reported estimate of 0.39.82 The absolute concentration of the two water species, calculated from the respective Lambert-Beer relationships (i.e., C fs = A fs / Lε fs ; C ss = Ass / Lε ss ) is reported in Figure 5A as a function of p/p0. It is found that Cfs exceeds Css, indicating that in the explored p/p0 range the predominant species is the monomer and the self-associated aggregate is likely to be the dimer. However, while the Cfs curve seems to approach a plateau for p/p0 values exceeding 0.7, the Css curve shows a pronounced upward concavity, suggesting an intersection of the two curves somewhere above the explored p/p0 range. When the concentration of selfinteracting species offsets that of the carbonyl-bound species, aggregates of more than two water molecules start to form, and the intersection point is generally regarded as the onset of the clustering process. 20, 22, 81, 82 For the present system, extrapolating the Cfs - Css curves, clustering appears to occur at p/p0 = 0.67.


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Figure 5. A): Cfs and Css as a function of relative pressure of water vapor. B) Concentration of interacting imide groups, Cfs and 2 x Cfs as a function of p/p0.

The spectroscopic data collected on thin films and discussed in the preceding section also afford the quantitative evaluation of the proton acceptors, i.e., the carbonyl groups involved in Hbonding. The analysis relies on the red-shift of the carbonyl bands (in particular, the νas at 1722 cm-1) which is the result of the superposition of two unresolved components due to the noninteracting and the interacting imide groups. It is possible to eliminate the contribution of the non-interacting imides by use of difference spectroscopy and using the fully dried sample as reference spectrum. In this way, the band due to interacting imides is isolated and can be used to quantify the population of this species.64, 81, 90 More specifically, the difference spectrum can be expressed as:

∙

(4)

where the subscripts d, s and r refer, respectively to the difference, the sample (wet film) and the reference (dry film) spectra and K is the subtraction factor. Assuming the invariance of the sample thickness, the subtraction factor can be expressed as64, 81, 90

:

! 1

(5)

where f, b and tot indicate, respectively, the non-interacting (free) imide groups, the imide groups H-bonded to H2O molecules, and their total population. The criterion to correctly choose the subtraction factor K has been discussed in detail in 64. In Figure 5B the concentration of firstshell water is compared to the concentration of interacting imide groups: the Cfs curve lies well below that of the imide but when the Cfs values are multiplied by a factor of two the two curves


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coincide. This result nicely confirms the stoichiometry of the PEI/H2O complex as was postulated on the basis of the spectroscopic analysis (Scheme 2, left structure).

3.2. MD simulations 3.2.1. MD Relaxation of Polymer Models The relaxation of PEI atomistic model has been obtained using a procedure based on Molecular Dynamics to generate well-equilibrated system of full atomistic polymer melts. The models employed are based on soft potentials having non bonded interactions described by density fields derived by Self Consistent Field (SCF) theory (MD-SCF).74-75 Such procedure has been proven to provide all-atom structures, also for large molecular weight models, that are indistinguishable from those obtained by long MD simulations.72, 91, 92 The procedure based on previous studies of some of us adopted for PEI is reported and validated in the Supporting Information section. Initial positions of water molecules in PEI matrix, for all water concentrations, have been obtained by using the software Packmol.93 Water molecules have been placed by trial random insertions at a random orientation. Trials were accepted if the minimum distance between water and polymer atoms was larger than 0.2 nm. Using configurations obtained in this way, preliminary NPT simulations have been performed for at least 150 ns well beyond density and energy convergence. Later, to avoid any bias towards the initial position of water molecules, the water-water and water-polymer non-bonded interaction potentials have been reduced, for each system. In particular, the non-bonded parameters of water (Lennard-Jones and charges) have been reduced from their whole value to about half with a rate of 5⋅10-7 for time step (2 fs), for a total simulation time of 4 ns. The resulting systems have been simulated for 50 ns in NVT


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ensemble to allow the water molecules to freely explore the configurations space. Then, all nonbonded parameters have been restored to their default values in once and after energy minimization all systems have been equilibrated for 100 ns in the NPT ensemble. After this equilibration procedure, production runs of at least 200 ns (simulation time is reported in Table 1) have been performed. From the mean square displacement (MSD) of water molecules, it can be estimated that, by 200 ns, on average, each water molecule has a displacement of about half box size and larger (about 1.3 times) than the radius of gyration of a PEI chain. The system size (27 PEI chains) assures a good statistic also for systems at lower water concentrations. In this case the number of water molecules is not lower than 86. However, to improve the statistics for the systems at lower water concentration (systems II and III, with 86 and 100 water molecules) results were averaged over production runs of five independent simulations. For systems IV-VII having from 120 to 200 water molecules results are averaged over two independent simulations.

3.2.2. Hydrogen Bonded Water Species in PEI MD simulations have been performed to analyze in detail hydrogen bond features from calculated trajectories, to be compared with the indications emerging from FTIR spectroscopy in conjunction with DFT calculations. In the Scheme 3, the nomenclature for potential hydrogen bond acceptor sites is shown. Carbonyl oxygen atoms are indicated in the following as AC1, while ether oxygen and imidic nitrogen atoms as AC2 and AC3, respectively.


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Scheme 3: Nomenclature used to identify potential hydrogen bond acceptor sites. Carbonyl oxygen atoms are indicated in the following as AC1. Ether oxygen and imidic nitrogen atoms are indicated as AC2 and AC3, respectively.

In Figure 6A the time behavior of percentages the different possible species hydrogen bond species are reported for one of the two independent MD simulations of system VI (see Table 1). In agreement with the interpretation provided by FTIR, dominant hydrogen bond acceptors are AC1 (about 96% of total bonds), a snapshot of a typical water first shell (fs) configuration interacting with carbonyl oxygen atoms is depicted in Figure 6B. Lower, but still relevant values are obtained for second shell hydrogen bound water molecules (about 25%, see ss in Figure 8). AC2 and AC3 acceptors have been counted, in agreement with FTIR analyses, as 4 and 1% of total bonds i.e. about two order of magnitudes less than for AC1.


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Figure 6. (A) Time behaviour of percentage hydrogen bonds for the three possible acceptors calculated in one of the 2 independent simulations system VII ( ω = 0.01). Snapshots showing of H-bonded water molecules for three different acceptors: (B) AC1; C) AC2; D) AC3. (see Scheme 3 for the definition of each hydrogen bond acceptor group). In agreement with FTIR analyses AC2 and AC3 populations are very low.

The hydrogen bond counting is based on geometrical criteria. In particular, according to literature prescriptions, a hydrogen bond is counted when two geometrical conditions are both satisfied. First, the distance A-O between potential acceptors (A) on PEI chains (AC1, AC2 and AC3 groups) and the oxygen of water molecules (O) must be shorter or equal to 0.3 nm. The second condition is that the angle θA-H-O must be larger than 120°.94 The black curves are the rolling averages behaviour obtained using previous 100 points.


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In Figure 7 are reported the time behaviour of hydrogen bond percentage (calculated with respect to the sum of fs and ss bonds) for fs and ss water molecules. Second shell water molecules are identified by considering for each configuration only those molecules bonded to polymer bonded water molecules and excluding water molecules forming hydrogen bonds with other free water molecules. This kind of analysis confirms the occurrence of ss molecules. MD simulations, consistently with FTIR, identify two main hydrogen bonded species having water molecules hydrogen bonded with carbonyl oxygen atoms (fs) and second shell water (ss) bonded to fs. These results can be rationalized by considering the larger propensity of carbonyl oxygen to favorable electrostatic interactions with water hydrogen. Indeed, carbonyl oxygen brings a larger negative charge (-0.700 ecu see Table 1 OC atom type) and more steric accessibility with respect to ether oxygen (-0.170 OS atom type) and imidic nitrogen (-0.140 N atom type) atoms. More quantitative comparisons between MD simulations and FTIR population analysis, also as function of water content, will be given in the next section. MD calculations can also provide information about the hydrogen bonding dynamics. In particular, evaluation of hydrogen bond lifetime is worth to be investigated in order to better understand the microscopic picture of water dynamics. The dynamics of the hydrogen bonds was analyzed by evaluating the continuous time autocorrelation function (ACF) defined as in ref. 96

95,

.


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Figure 7. (A) Time behaviour of percentage hydrogen bonds for the first and second shell. Snapshots of the two different hydrogen bond type are reported. (B) typical conformation of first shell. (C) water molecule forming a second shell. Hydrogen bond conditions on distance and angle are the same used to identify the species of Figure 8.

Quite interestingly, the ACF(t) vs time curves could not be fitted by a single exponential decay, indicating the superposition of multiple dynamic processes. In particular, the longer lifetime was of the order of 2 ns and 0.1 ns, respectively for the system at lowest water concentration (system II, containing 86 water molecules) and for the system at highest water content (system VII, 220 water molecules). A similar range of lifetimes has been reported in other simulation analyses, indicating also values in excess of 1 ns for interacting glassy


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polymers95. The results of our MD simulations are consistent with the observation of discrete peaks in the FTIR spectra of absorbed water, since the characteristic time-scale of FTIR experiment is of the order of few ps. More detailed account of this analysis will be reported in a forthcoming contribution.

3.2.3. Population analysis The absolute concentration of the two water species, Cfs and Css, reproduced from the MD simulations performed at five different water concentrations, compare very well with results obtained by FTIR spectroscopy (see Figure 8A). As evident in Figure 8B, MD simulations performed at different water concentrations (Figure 8B empty symbols) confirm the presence of two different water species and provide a good reproduction of the behaviour of concentration of interacting C=O groups, obtained spectroscopically from the concentration of first-shell water or from direct evaluation of interaction carbonyl groups. The analysis of water configurations obtained from MD simulations can give further details and a molecular interpretation of the results. In particular, analyses of simulations show that most of fs water molecules form two hydrogen bonds, bridging two different carbonyl oxygen atoms, each one belonging to a different imide group. The fraction of bridging fs water molecules as function of water content, according to the findings reported in Figure 8B, is close to one in all composition range (relative plots are reported in the Supporting Information, Section 7). A further analysis of MD simulations has been focused on the type of water bridges. fs water molecules can be classified as intramolecular or intermolecular bridges. In particular, at all water concentration the most frequent species are intramolecular bridges (see


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Figure 9A) where water molecules form hydrogen bonds with two successive carbonyl oxygen on the same PEI chain, as depicted in Figure 9B.

Figure 8. (A) Concentration Cfs (first shell) and Css (second shell) as a function of mass fraction of water in the water-PEI mixture: comparison of the results of FTIR spectroscopy with outcomes of MD simulations. (B) Concentration of interacting C=O of imide groups from FTIR spectroscopy performed on thin films, experimentally determined Cfs and 2xCfs, compared with the concentration of interacting C=O of imide groups calculated from MD simulations, as a function of mass fraction.

Interchain water bridges (a typical snapshot is depicted in Figure 9C) are present at lower extent going from a fraction about 0, at the lowest water concentration, to a fraction ~ 0.3 of all bridged molecules at the highest water concentration analysed by MD simulations.


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Figure 9. (A) H-Bond fractions, as function of ω, for the acceptor AC1 forming first shell hydrogen bonds with successive acceptors along the same chain (intrachain) or hydrogen bonds formed with acceptors of two different chains (interchain). Snapshot of: (B) intrachain hydrogen bond, and (C) interchain hydrogen bond. The two different chains are reported in blue and green, respectively.

An explanation of this behaviour can be obtained on a geometrical basis. In figure 10 several geometrical distributions involving the two different intra and intermolecular bridging sites are compared. As shown in Figure 10A in the case of intramolecular bridging, due to stiff constrains (two successive carbonyl groups are separated by a single phenyl ring), the distance between the two bridged acceptors (O····O) is shorter and more tightly distributed than for intermolecular


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bridged pairs. A similar behaviour is obtained for angles between two bridged carbonyl groups in the case of intramolecular and intermolecular acceptors (see Figure 10B). More information is contained in Figures 10E and Figure 10F where two dimensional histograms, showing the most populated pairs of O····O distance and angles between carbonyl bonds are reported for the two different water bridged sites. From the 2D plots of Figures 10E and Figure 10F the very localized and constrained nature of the site, in the case of intramolecular bridging, is apparent. As consequence of these constraints in the acceptor geometries hydrogen bond features, in intramolecular and intermolecular bridged sites, are different. Differences in hydrogen bonds geometries are compared in Figure 10C and figure 10D. In particular, the comparison in Figure 10C shows that in the case of intramolecular bridge the distance between the carbonyl oxygen atoms and oxygen of water is shorter (distribution has a peak at ~ 0.29 nm) and more narrow than the one obtained for intermolecular bridging sites. A similar behaviour is obtained comparing the angle θA-H-O (where A is hydrogen bond acceptor i.e. the carbonyl oxygen atom) in the two cases (Figure 10D). In a way similar than for acceptor sites, the 2D histograms reporting the most frequent pairs of distances and angles (Figure 10G and Figure 10H), show a more constrained and tight hydrogen bonding in the case of intramolecular bridges.


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Figure 10. Distributions of: (A) distance r between AC1 acceptors of intramolecular bridge (green) and intermolecular bridge (blue). (B) angle θ between AC1 acceptors for intermolecular and intramolecular bridges. The angles have been calculated considering the scalar product of vectors formed by OC---->CO atoms. Distribution of distances (C) and angles (D) of AC1 acceptors involved in hydrogen bridges calculated for intrachain and interchain. Bidimensional map pair (r, θ) of distances between AC1 acceptors involved in bridges (E) intrachain, (F) interchain, and hydrogen bonds for intrachain (G) and interchain (H). At each colour is assigned the corresponding occurring frequency.


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The peculiar chemical structure of PEI chain allows to form intrachain hydrogen bonds between two consecutive carbonyl groups, as reported in the Figure 10B. Differently, in the case of Kapton having the same HB acceptors of PEI, a different topology does not allow the formation of intrachain hydrogen bonds.33 In particular, MD simulations of Brown and coworkers33 show that about 75 % of water molecules are involved in hydrogen bonds with polymer chains, and, in most of the cases water molecules form ss HB with another water molecule or intermolecular bridges and, differently from the case of PEI, no intrachain bridges are formed.

3.3 Modelling sorption thermodynamics of water in glassy PEI A modelling approach of sorption thermodynamics of low molecular weight compounds in amorphous glassy polymers, accounting for the establishment of self- and cross-HB interactions, has been proposed a few years ago by our group.22 This model has been recently used to describe the thermodynamics of glassy PEI – water20 and we briefly recap here those results for the sake of comparison with the experimental outcomes of FTIR investigation and with MD simulations presented above. The modelling approach is based on extending the equilibrium Non Random Hydrogen Bonding (NRHB) theory to the case of out-of-equilibrium glassy polymers. We will refer in the following to this non-equilibrium model as Non Equilibrium NRHB Theory for Glassy Polymers (NETGP-NRHB). Details on this approach are illustrated in the Supplementary Information, Section 4. It is worth of mention here that, in view of the out of equilibrium glassy state of the system, the density of polymer evolves with time. In fact, polymer density, whose value is not dictated by an Equation of State, changes according to an intrinsic kinetics and is considered, in the framework of the NETGP-NRHB model, as an internal state variable (see


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Supplementary Information). In view of the small amount of sorbed water and because the test temperatures are much lower than the glass transition temperature (Tg) of the neat polymer (489.15 K), it has been assumed

20

that the polymer is ‘frozen’, in the time frame of sorption

experiments, in a fixed pseudo-equilibrium glassy state, characterized by a polymer density assumed to be time invariant and, for each temperature, equal to the starting density of the neat 0 polymer, ρ2 .

The experimental sorption isotherms of water in PEI originally reported in our previous contribution 20, at four values of temperature (303.15, 318.15, 333.15 and 343.15 K), are reported in Figure 11. In constructing the HB interactional part of the NETGP-NRHB model, one needs to define the types of Proton Donor and Proton Acceptor groups available for interaction as well as their number on each water molecule and PEI repeating unit. This information has been gathered from FTIR analysis. In particular, for the present system, the discussed spectroscopic results point to the establishment of only one type of cross-HB interaction occurring between water hydrogens (acting as proton donors) and the carbonyl groups (acting as proton acceptor) of PEI. Moreover, FTIR results indicate that self-HB interactions occur only between water molecules. In detail, the model assumes the presence of two proton donors and two proton acceptors for each water molecule. It would have been certainly possible to account for all possible HB interactions when constructing the structure of the thermodynamic model, independently of the outcomes of vibrational spectroscopy analysis. However, this would unavoidably increase the number of model parameters, thus affecting the reliability of their estimates. That is why we preferred to guide the selection of really significant interactions on the basis of the spectroscopic results.


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The experimental data have been obtained by contacting the polymer with water vapor at several relative pressures (i.e. ratio of pressure to water vapor pressure at a certain temperature) and measuring the amount of water absorbed at pseudo-equilibrium by gravimetric method. Values of density of pure PEI at the investigated temperatures, of the EoS scaling parameters for pure PEI and of the EoS scaling parameters and of the self HB parameters for pure water in the NETGP-NRHB model, have been taken from a previous contribution20 and their values are reported in Supporting Information, Section 4.

Figure 11. Water sorption isotherms in PEI determined gravimetrically at several temperatures. Continuous lines are curves obtained by concurrent best fitting of all data with NETGP-NRHB model.

NETGP-NRHB model has been used to perform a concurrent fitting of the four experimental isotherms (see Figure 11), using as fitting parameters the energy and entropy of formation of 0 wp

0 wp

water-polymer cross-HB ( E12 , S12 , see Supplementary Information for more details) and the


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mean field interaction parameter (ψ12 , see Supplementary Information for its definition). The 0 wp

volume of formation of water-polymer cross-HB ( V12 , see supplementary Information for more details) is instead assumed to be identically equal to zero, following the previous literature.97 The best fitting values of the parameters are reported in Table 3. 95% confidence intervals of the fitting model parameters reported in the table were evaluated using the Jacobian method, implemented by built-in functions of the Matlab® software (combination of nlinfit and nlparci routines). As evident in Figure 11, the model provides a good interpretation of gravimetric data. 0 wp Table 3. NETGP-NRHB fitting parameters for PEI-water mixture (note that the value of V12 has been imposed to be 0 according to 97).

ψ12

0.879 ± 0.005

E120 wp

S120 wp

V120 wp

[J/mol]

[J/(mol∙K)]

[cm3/mol]

-13264 ± 200

-6.107 ± 0.100

0

As side result of the fitting procedure, the model provides also predictions for the amounts of self (i.e.1-1) and cross (i.e. 1-2) HB interactions occurring in the PEI-water mixtures. In particular we have determined: a) the moles of HB self-interactions involving only water molecules, in terms of moles of 1-1 interactions per gram of amorphous PEI, n11 / m2 , and b) the moles of HB cross-interactions between water molecules and carbonyl groups of PEI, in terms of moles of 1-2 interactions per gram of amorphous PEI, n12 / m2 . It is to be noted here that while the model provides information in terms of concentration of hydrogen bonds, the MD simulations and FTIR spectroscopy deliver results in terms of concentration of water molecules. Hence, for the sake of comparison, one needs to recalculate the outcomes of MD simulations and FTIR spectroscopy to obtain the estimated values of n11/m2 and of n12 / m2 . While in the case of


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n11/m2 only a change of dimensions is performed on Css to pass from a volumetric to a unit mass concentration, in the case of n12 / m2 the value of Cfs has also to be multiplied by a factor of 2 to account for the 1:2 stoichiometry of the H2O / C=O adduct. NETGP-NRHB predictions, for a temperature of 303.15 K, are compared in Figure 12 with the corresponding results obtained from FTIR spectroscopy and with the outcomes of MD simulations. The agreement is satisfactory in the whole range of water concentrations.

Figure 12. Comparison of the predictions of the NETGP-NRHB model for the amount of selfand cross-HBs with the outcomes of FTIR spectroscopy and of MD simulations.

4. Conclusions The state of water in glassy PEI has been thoroughly analyzed by combining experimental and theoretical approaches, specifically investigating HB interactions. FTIR spectroscopy, coupled with gravimetric measurements, has provided the basis for an analysis of the system, supplying quantitative information on water concentration as well as on the amount and type of hydrogen bonds. A comprehensive physical picture of the system has been obtained by coupling these


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experimental results with the analyses performed by Quantum Chemistry calculations, MD simulations and statistical thermodynamics modelling. Two water populations were identified, one consisting in water molecules bridging two consecutive intrachain carbonyls of PEI (first shell, fs, water) and one consisting in water molecules interacting with fs water molecules (second shell, ss, water). No significant involvement of PEI ether groups in HB with water molecules emerged from the performed analysis. FTIR spectroscopy provided quantitative estimates of the amounts of cross- and self-HB as a function of overall water concentration. These estimates were found to be in good agreement with MD simulations as well as with the predictions of a non-equilibrium compressible lattice fluid model (NETGP-NRHB). The proposed methodology, based on a thorough validation of theoretical tools against robust experimental protocols, highlights the potential of a multidisciplinary approach for an in-depth investigation of hydrogen bonding in polymers and polymer mixtures.


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Supporting Information Available Details on the MD-SCF approach, on the atomistic model of PEI and on relaxation procedure for amorphous PEI are reported. The NETGP-NRHB thermodynamic model for mixtures of low molecular weight compounds and glassy polymers, endowed with HB interactions, is described. Supplementary FTIR spectra are reported. Details on Quantum Chemistry / Normal Coordinate Analysis are presented. Finally, an additional plot is presented, reporting H-Bond fraction of first-shell water molecules involved in bridge, single bond and two single bonds.

This information is available free of charge via the Internet at http://pubs.acs.org

AUTHOR INFORMATION

Corresponding Authors Giuseppe Milano – e-mail: [email protected]; ph.: 0039 089 969567 Pellegrino Musto – e-mail: [email protected]; ph.: 0039 081 7682512

ACKNOWLEDGMENT G. Milano wishes to thank the HPC team of Enea (http://www.enea.it) for using the ENEAGRID and the HPC facilities CRESCO (http://www.cresco.enea.it) in Portici.


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TOC Graphic


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Scheme 1. Chemical structure of PEI repeating unit. Different atom types are indicated by corresponding labels. For sake of clarity, all hydrogen atoms are omitted except the ones used for the labeling. Non bonded interactions over two consecutive bonds are excluded. 24x8mm (300 x 300 DPI)



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Scheme 2. Schematic representation of the two water species hypothesized in the PEI/H2O system. The isolated water molecules represented in the right side of Scheme 2, can be envisaged as a “corehydration” species, i.e. the first hydration layer of penetrant (first shell) in the multilayer adsorption model of Brunauer, Emmet and Teller (BET) 88, while the self-associated water molecules (right-side) are representative of the second-shell hydration layer. 55x25mm (300 x 300 DPI)


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Scheme 3: Nomenclature used to identify potential hydrogen bond acceptor sites. Carbonyl oxygen atoms are indicated in the following as AC1. Ether oxygen and imidic nitrogen atoms are indicated as AC2 and AC3, respectively. 22x7mm (300 x 300 DPI)



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Figure 1. Absorbance (A) and difference spectra (B) of a PEI film 37.7 µm thick equilibrated at different relative pressures of water vapor. Green trace: dry film; blue: p/p0 = 0.1; black: p/p0 = 0.2; red navy: p/p0 = 0.3; purple: p/p0 = 0.4; dark green: p/p0 = 0.5; red: p/p0 = 0.6. 36x11mm (300 x 300 DPI)


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Figure 2. 2D-COS Asynchronous maps obtained from the time-resolved spectra collected in the sorption (A) and in the desorption experiment (B) at p/p0 = 0.6 47x18mm (300 x 300 DPI)



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Figure 3. Difference spectra of a PEI film 3.0 µm thick equilibrated at different relative pressures of water vapor. Red navy trace: p/p0 = 0.1; light blue: p/p0 = 0.2; purple: p/p0 = 0.3; blue: p/p0 = 0.4; red: p/p0 = 0.5; violet: p/p0 = 0.6. A): 1820 – 1660 cm-1 range; B): 1420 – 1300 cm-1 range; C): 1320 – 1180 cm-1 range. In Fig. 3C the absorbance spectra of the dry sample (blue trace) and of the sample equilibrated at p/p0 = 0.6 (red trace) are also reported for comparison purposes. 36x9mm (300 x 300 DPI)


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Figure 4. Curve fitting analysis of the spectrum representative of water sorbed in PEI (p/p0 = 0.6). The figure displays the experimental profile (red trace), the best-fitting curve (blue trace) and the resolved components (black traces). The inset represents the calibration curve for evaluating the absorptivities of the analytical peaks. 42x26mm (300 x 300 DPI)



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Figure 5. A): Cfs and Css as a function of relative pressure of water vapor. B) Concentration of interacting imide groups, Cfs and 2 x Cfs as a function of p/p0. 44x16mm (300 x 300 DPI)


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Figure 6. (A) Time behaviour of percentage hydrogen bonds for the three possible acceptors calculated in one of the 2 independent simulations system VII (ω = 0.01). Snapshots showing of H-bonded water molecules for three different acceptors: (B) AC1; C) AC2; D) AC3. (see Scheme 3 for the definition of each hydrogen bond acceptor group). In agreement with FTIR analyses AC2 and AC3 populations are very low. 96x92mm (300 x 300 DPI)



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Figure 7. (A) Time behaviour of percentage hydrogen bonds for the first and second shell. Snapshots of the two different hydrogen bond type are reported. (B) typical conformation of first shell. (C) water molecule forming a second shell. Hydrogen bond conditions on distance and angle are the same used to identify the species of Figure 8. 137x189mm (300 x 300 DPI)


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Figure 8. (A) Concentration Cfs (first shell) and Css (second shell) as a function of mass fraction of water in the water-PEI mixture: comparison of the results of FTIR spectroscopy with outcomes of MD simulations. (B) Concentration of interacting C=O of imide groups from FTIR spectroscopy performed on thin films, experimentally determined Cfs and 2xCfs, compared with the concentration of interacting C=O of imide groups calculated from MD simulations, as a function of mass fraction. 49x20mm (300 x 300 DPI)



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Figure 9. (A) H-Bond fractions, as function of ω, for the acceptor AC1 forming first shell hydrogen bonds with successive acceptors along the same chain (intrachain) or hydrogen bonds formed with acceptors of two different chains (interchain). Snapshot of: (B) intrachain hydrogen bond, and (C) interchain hydrogen bond. The two different chains are reported in blue and green, respectively. 249x620mm (300 x 300 DPI)


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Figure 10. Distributions of: (A) distance r between AC1 acceptors of intramolecular bridge (green) and intermolecular bridge (blue). (B) angle θ between AC1 acceptors for intermolecular and intramolecular bridges. The angles have been calculated considering the scalar product of vectors formed by OC---->CO atoms. Distribution of distances (C) and angles (D) of AC1 acceptors involved in hydrogen bridges calculated for intrachain and interchain. Bidimensional map pair (r, θ) of distances between AC1 acceptors involved in bridges (E) intrachain, (F) interchain, and hydrogen bonds for intrachain (G) and interchain (H). At each colour is assigned the corresponding occurring frequency. 152x234mm (300 x 300 DPI)



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Figure 11. Water sorption isotherms in PEI determined gravimetrically at several temperatures. Continuous lines are curves obtained by concurrent best fitting of all data with NETGP-NRHB model. 77x59mm (300 x 300 DPI)


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Figure 12. Comparison of the predictions of the NETGP-NRHB model for the amount of self- and cross-HBs with the outcomes of FTIR spectroscopy and of MD simulations. 78x61mm (300 x 300 DPI)



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Local Structure and Dynamics of Water Absorbed in Poly(ether imide

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