4-(N,N-Dimethylamino)pyridine, DMAP, and glycidyl methacrylate, GMA, were Fluka products. Poly(vinyl alcohol) with nominal weight average molecular weight, M_w, of 35,000 g/mol (degree of deacetylation: 98%) was a Sigma product. The photoinitiator, 1-[4-(2-hydroxyethoxy)-phenyl]-2-hydroxy-2-methyl-1-propane-1-one, was supplied by Ciba. Dimethyl sulfoxide, DMSO, acetone, HCl, and NaOH were purchased from Carlo Erba. All chemicals were reagent grade and used without further purification. Water was Milli-Q purity grade (18.2 MΩ cm), produced with a deionization apparatus (PureLab) from USF. Dialysis membranes (cut off 12,000 g/mol) were purchased from Medicell International Ltd. and prepared according to standard procedure.

PVA was grafted with a methacrylate moiety according to the procedure described by Hennink [60,61] and Anseth [62]. Typically, 10 g of PVA with M_w of 35,000 g/mol was dissolved in 250 mL of DMSO added with 5 g of DMAP. After displacement of oxygen by purging N₂ for 1 h, GMA was added in the 1:100 molar ratio with the polymer repeating units and left for 48 h under stirring in the darkness. DMAP was neutralized by the addition of concentrated hydrochloric acid to prevent alkaline hydrolysis of the methacrylic ester. Samples with stoichiometric degree of substitution, DS, of 1% were prepared.

After completion, the reaction mixture was dialyzed against water to purify the derivative of PVA and to exchange DMSO with water. The PVA-MA samples with DS lower than 2% are soluble in water. After dialysis the samples were precipitated very slowly by adding acetone up to a volume ratio of 50:50 (v/v). The precipitate was collected, finely broken up, and finally dried. The experimental DS value, determined by ¹H NMR [25], was 1.0 ± 0.1%.

Typically a 9% (w/v) aqueous solution of PVA-MA was added with the photoinitiator at a concentration of 3 g/L. The mixture was irradiated in a photoreactor with a power of 12 Watt at 365 nm (Photochemical Multirays Reactor, Helios Italquarz) for 5 min. The system was left for 12 h at 25 °C. After this equilibration period, the gel was set, and extensive washings were carried out to remove the excess of reactants. Hydrogel samples were prepared in three replicas to average out possible differences and heterogeneities occurring in the gels. Polymer hydrogels at a working concentration of 8% (v/v) were transparent.

Freeze-dried PVAMA1 hydrogels were re-hydrated with 99.9% pure D₂O (Aldrich) at the maximum swelling degree, corresponding to a polymer volume fraction, Φ₂, of 0.08 (v/v), by equilibrating the wet samples over-night in capped containers. For elastic neutron scattering experiments the D₂O hydration degree of the sample was 0.4 (w/w).

Incoherent elastic neutron scattering experiments were carried out at the backscattering spectrometer IN13 [63] at the ILL facility. The instrumental resolution of 9 μeV was determined by calibrating the instrument with vanadium. Data were corrected for the absorption and normalized with respect to vanadium scattering, using the software package LAMP available at ILL. Measurements were performed at controlled temperature from 270 to 320 K in a range of scattering vectors, Q, from 0.2 to 4 Ǻ⁻¹. The thickness of the sample was 0.1 mm. At this level multiple scattering effects are deemed negligible.

The elastic incoherent neutron scattering was analyzed as a function of Q and temperature. At a particular temperature and in the Gaussian approximation, the Q-dependence of the elastic scattering law S(Q, ω = 0) is given by (1) S ( Q , 0 ) = K ⋅ exp ( − 〈 u 2 〉 ⋅ Q 2 6 )where the mean-square amplitude <u²> is the full amplitude of the atomic displacements during the time resolution of the experiment, dominated by the values of the ¹H-atoms in the sample, and K is a constant. For the Gaussian approximation to be valid, either all ¹H-atoms must be dynamically equivalent and vibrate harmonically [64] or the values of Q should be (2) Q ⋅ 〈 u 2 〉 2 ≤ 1

We verified a posteriori that, for our systems, the condition of Equation 2 is fulfilled limiting the analysis at Q < 2 Ǻ⁻¹. The mean squared hydrogen displacement of the polymer moiety in the hydrogel was therefore obtained by Equation 3 (3) ( d { ln [ S ( Q , 0 ) ] } d ( Q 2 ) ) Q → 0 = − 〈 u 2 〉 6derived from Equation 1, for Q values lower than 1.9 Ǻ⁻¹ [65].

QENS experiments were carried out at the ISIS pulsed neutron facility (Rutherford Appleton Laboratory, Chilton, UK) using the time-of-flight inverted-geometry backscattering spectrometer IRIS [66]. The instrument was operated in the 002 pyrolytic graphite configuration which provides a Q-range from 0.44 to 1.83 Ǻ⁻¹ with an energy window from −0.35 to 1.2 meV and an energy resolution of 17 μeV. Raw data were corrected for absorption and detector efficiencies and normalized using the standard software package GUIDE available from ISIS. Aluminium flat cells of 0.02 cm thickness were used for all measurements and corrections for multiple scattering were not applied since at this level multiple scattering effects are deemed negligible.

Measurements were performed at 283, 303 and 313 K. Samples were weighed before and after measurements and weight variations within 10% were observed. The instrumental resolution, R(Q,ω), was determined running a vanadium slab.

Assuming purely incoherent scattering, the experimental dynamical structure factor, S_exp(Q, ω), was fitted according to Equation 4 (4) S exp ( Q , ω ) = R ( Q , ω ) ⊗ S inc ( Q , ω ) + bkgwhere the instrumental resolution is convoluted with the incoherent dynamical structure factor, S_inc(Q, ω), written as: (5) S inc ( Q , ω ) = A ( Q ) ⋅ ⌊ p t ⋅ S inc , pol ( Q , ω ) + ( 1 − p t ) ⋅ S inc , D 2 O ( Q , ω ) ⌋with: (6) S inc , pol ( Q , ω ) = [ EISF ( Q ) ⋅ δ ( ω ) + ( 1 − EISF ( Q ) ) ⋅ L pol ( Q , ω ) ]and (7) S inc , D 2 O ( Q , ω ) = ⌊ p a ( Q ) ⋅ L D 2 O , 1 ( Q , ω ) + ( 1 − p a ( Q ) ) ⋅ L D 2 O , 2 ( Q , ω ) ⌋

The bkg term of Equation 4 is a background. The A(Q) term of Equation 5 accounts for an overall Debye-Waller behavior, assuming a common average Debye-Waller factor for all hydrogens in the sample [42]. In this model, Equation 5, the incoherent dynamical structure factor is described by a linear combination of polymer and solvent contributions, with weights given by pt and (1 − pt) factors, respectively. The pt factor resulted independent on Q and T in the fitting procedure, with a value of 0.72 ± 0.06. This value compares well with the stoichiometric polymer contribution to the cross section in the PVAMA hydrogel, pt_st. The fraction of the incoherent cross section due to the polymer in our sample, i.e., pt_st, is equal to 0.62, taking into account of the experimental hydration degree and of the residue composition of the polymer scaffold. The pt value, about 10% greater than pt_st, indicates that some solvent molecules are bound with the polymer and display a similar dynamics behavior. The polymer contribution to the dynamical structure factor, S_inc,_Pol(Q, ω), Equation 6, contains an elastic term, EISF, i.e., the elastic incoherent structure factor, and a quasi-elastic term, given by the Lorentzian function L_Pol. The purely elastic term accounts for the arrested dynamics of the polymer in the percolating network. The contribution of the solvent, S_inc,_D2O(Q, ω), Equation 7, is described by the Lorentzian functions L_D2O,1 and L_D2O,2, with Q-dependent weights pa and (1 − pa), respectively. This treatment of the quasielastic scattering of the solvent is in agreement with the results of QENS and MD simulations studies [44,67], indicating that QENS data of water can be analyzed in term of two motional components. The broader Lorentzian function, L_D2O,2, is related to local structural fluctuations within water clusters, the narrower Lorentzian function, L_D2O,1, accounts for the slower water diffusion. Assuming a random-jump diffusion motion of the solvent, the dependence on Q of the width of the narrower Lorentzian allows us to obtain a microscopic diffusion coefficient [68]. The value of the diffusion coefficient of the solvent, D, at the investigated temperatures is calculated by Equation 8 (8) Γ D 2 O , 1 = D Q 2 1 + D τ Q 2where Γ_D2O,1 is the broadening of the Lorentzian L_D2O,1 and τ is the residence time between jumps. The diffusion coefficient values do not show differences respect to the corresponding values of the bulk solvent, within the accuracy of measurements. This result is in agreement with the finding of QENS measurements, carried out on PVAMA hydrogel microparticles, PVAMA5, synthesized from a PVA-MA polymer with a degree of substitution of methacryloyl groups equal to 5% [26]. The analysis of QENS spectra of PVAMA5 microparticles at the maximum degree of swelling in H₂O showed a limited influence on the dynamic behavior of bound water. The PVAMA1 hydrogel of this study, obtained from PVA-MA with a degree of substitution of 1%, has a polymer network with a lower degree of cross-linking in comparison to PVAMA5 hydrogel. Therefore, a lower effect on the dynamic behavior of bound water (and in the QENS spectrum) has to be expected for the PVAMA1 system. A deeper investigation of the solvent dynamics in the hydrogel needs the use of H₂O and deuterated polymer moiety. The work related to the synthesis of such hydrogels is in progress. In the present study we focus on the polymer component, performing the QENS experiments in D₂O.

The PVAMA hydrogels are prepared by means a photoiniziated radical polymerization in aqueous solution of methacryloyl grafted PVA-MA chains. This reaction forms polymethacrylate (PMA) chains and generates a three-dimensional polymer network, since the PVA chains are inter-connected via PMA chains till to percolation. Chart 1 shows a scheme of junction in PVAMA networks.

Here we study a hydrogel system obtained by PVA-MA with M_w of 35,000 g/mol, corresponding to an average polymerization degree of about 800, and a degree of substitution of methacryloyl groups equal to 1%. Neutron scattering experiments were carried out on samples of this hydrogel and a corresponding molecular model was developed for the MD simulations.

The starting configuration consisted of a central PMA chain of eight residues, in an all-trans conformation, connecting seven looping PVA chains, each of 100 residues, and two PVA end chains of 50 residues, in an all-trans conformation. The model topology is shown in Chart 2.

An equal population of randomly distributed d and l enantiomers was used for PVA residues, in agreement with the atacticity of PVA. The polymer scaffold was then hydrated with a shell of water of thickness suited to introduce a solvent content corresponding to the experimental polymer volume fraction, Φ₂, of 0.08 and the system was compressed to the correct final density by means of a preliminary MD simulation applying a ‘pressure bath’ of 1 atm with the Berendsen's pressure coupling algorithm [69], a procedure already applied for the simulation of self cross-linked PVA hydrogel networks [52]. MD simulation runs at controlled pressure and at 313 K, using the Berendsen's temperature coupling algorithm [69], for 1 ns and then in the NVT ensemble for about 4 ns were performed to equilibrate the system. The following 1 ns trajectory of the NVT run was used for analysis. The equilibration of the system in the NVT MD run, at T = 313 K, was checked by following the time behavior of the root mean squared deviation of all N polymer atoms, RMSD: (9) RMSD ( t + t 0 ) = [ 1 M ∑ i = 1 N m i ‖ r i ( t + t 0 ) − r i ( t 0 ) ‖ 2 ] 1 / 2

The reference structure was the starting polymer configuration (t₀ = 0) of the NVT run. The RMSD was calculated after roto-translational fit on the backbone atoms of the PMA chain. In the trajectory interval used for analysis, the value of RMSD was stable, with a drift lower than 20% of the RMSD standard deviation.

During this equilibration phase, a few PVA chain formed entanglements with periodic images of other polymer sections, leading to the percolation of the network in one dimension.

The NVT MD run at 293 K was carried out after the NVT MD run at 313 K. The starting configuration at 293 K was the last configuration of the NVT MD run at 313 K. The RMSD for the MD run at 293 K was calculated using as reference structure the starting polymer configuration at 293 K. Finally, the NVT MD run at 283 K was carried out after the NVT MD run at 293 K. The starting configuration at 283 K was the last configuration of the NVT MD run at 293 K. The RMSD for the MD run at 283 K was calculated using as reference structure the starting polymer configuration at 283 K. The equilibration of the system in the NVT MD runs at 293 and 283 K required about 2 ns. The longer equilibration time of the run at 313 K was adopted due to a preliminary major rearrangement of the model. The following MD runs, at the lower temperatures, did not require this starting evolution, and had a shorter equilibration phase.

In the final configuration, the cubic simulation box (with size of 8.484 nm) contained a polymer network of 800 PVA and 8 PMA residues hydrated by 18,308 water molecules, for a polymer concentration of 9.9% (w/w).

Calculations were carried out on the IBM Linux Cluster 1350 at the CINECA Supercomputing Center (Bologna, Italy). MD simulations were performed by GROMACS software, version 3.2.1 [70,71]. The GROMOS 45A3 force field [72,73] was used and the 45A4 ethanol model [74] was considered for the atomic partial charges of PVA residues. Water was simulated by the single-point charged (SPC) intermolecular potential model [75]. The same force field, using the united atom convention for CH and CH₂ groups, was selected in a previous MD simulation study of PVA hydrogels [55]. Production runs were carried out in the NVT ensemble, with the leap-frog integration algorithm [76] using a time step of 0.5 fs. Temperature was controlled at 313, 293 and 283 K by the Berendsen's temperature coupling algorithm [69]. Non-bonding interactions were treated as described in a previous work [59]. The total simulation time, including equilibration, was about 6 ns at 313 K, 3 ns at 293 K and 3 ns at 283 K. The configurations were saved every 0.1 ps.

MD simulations of a water box with the same size of the hydrogel model, containing 20,265 molecules, were carried out in the same simulation conditions to obtain the bulk water properties for a comparison. A trajectory of 400 ps for each temperature was calculated for the water box at 313, 293 and 283 K.

In the following of this Section we report some information about the procedures used for the trajectory analysis.

The hydrogen bond (HB) was studied by analyzing the trajectory for the occurrence of this interaction, adopting as geometric criteria an acceptor-donor distance (A…D) lower than 0.3 nm and an angle Θ (A…H-D) higher than 120°. The intramolecular HB was analyzed even by integration of the radial distribution function between the hydrogen and oxygen atoms of PVA, g_H-O(r), according to Equation 10 (10) n H B = N o V ∫ 0 R min 4 π r 2 g H − O ( r ) d rwhere n_HB, N_O, V are the average number of HB's per PVA residue, the total number of PVA residues and the volume of the simulation box, respectively. R_min is the first minimum distance of the gH-O(r). This procedure allowed us to separate the contribution to the intramolecular hydrogen bonding of near-neighboring and of more distant residues, by proper selection of the exclusion number in the calculation of the radial distribution function. The average number of HB's per PVA residue, calculated by means of Equation 10 including all residues, had the same value, within errors, as that obtained by direct trajectory analysis.

Polymer-water HB's formed by polymer OH group acting as a H acceptor and HB's formed by OH group acting as a H donor were separately evaluated by integration of the radial distribution functions between PVA oxygen and water hydrogen atoms, gO-HW(r), and between PVA hydrogen and water oxygen atoms, g_H-OW(r), respectively, according to Equations 11 and 12 (11) n ACC = N H W V ∫ 0 R min 4 π r 2 g O − H W ( r ) d r (12) n D O = N O W V ∫ 0 R min 4 π r 2 g O − O W ( r ) d r

In Equations 11 and 12, n_ACC and n_DO are the average number of HB formed as acceptor and donor per PVA hydroxylic group, respectively. The total average number of HB's per water molecule, calculated as sum of n_ACC and n_DO, had the same value, within errors, than that obtained by direct trajectory analysis.

The coordination number of an atom X by atoms Y was evaluated by integration of the corresponding radial distribution function, Equation 13 (13) n X − Y = N Y V ∫ 0 R min 4 π r 2 g X − Y ( r ) d rwhere N_Y and R_min are the number of Y atoms in the simulation box of volume V and the first minimum distance in g_X-Y (r), respectively.

The dynamics of HB was evaluated by studying the normalized time autocorrelation function C_HB(t): (14) C H B ( t ) = 〈 S i j ( t 0 ) S i j ( t + t 0 ) 〉 〈 S i j ( t 0 ) S i j ( t 0 ) 〉where the state variable s_ij has a value of 1 or 0 depending on the existence or nonexistence of an HB between a selected donor-acceptor pair ij. t₀ and t in Equation 14 range from 0 to half of the simulation time considered for analysis. The function s_ij(t + t₀) is set to 1 if the HB between ij is found to be present in the time steps t₀ and t₀ + t, even if the same HB can be interrupted in some intermediate time. This definition of C_HB(t) corresponds to the intermittent HB autocorrelation function, described by Rapaport [77] and Luzar [78], where the correlation of a particular donor-acceptor pair is evaluated irrespective of possible prior bond breaking and reforming events. With this choice the correlation time, τ_HB, estimates the average lifetime of interaction for the ensemble of HB pairs, within the time window of the analyzed trajectory time. The correlation time, τ_HB, was obtained by integration of C_HB(t) in a time window about 10 times τ_HB.

Water diffusion coefficient, D_W, was obtained from the long-time slope of the mean squared displacement, Equation 15 (15) D W = 1 6 lim t → ∞ d d t 〈 | r ( t ) − r ( 0 ) | 2 〉where r(t) and r(0) correspond to the position vector of the water oxygen at time t and 0, respectively, with an average performed over both time origins and water molecules. The mean squared displacement was calculated in a time-window equal to the average lifetime of the hydrogen bonds (HB) between PVA hydroxylic groups and water. The diffusion coefficient value was obtained from the slope of the mean squared displacement vs. time in the second half of the explored time window, when the double log plot of the mean squared displacement vs. time displayed a linear behavior with a slope of 1.

The <u>² value, obtained by elastic neutron scattering measurements as described in Section 2.2.2, was compared with the mean squared displacement (MSD) of the backbone carbon atoms calculated from the MD simulation trajectory according to Equation 16 (16) MSD ( t + t 0 ) = 〈 ‖ r i ( t + t 0 ) − r i ( t 0 ) ‖ 2 〉 iwhere i is a backbone carbon atom and the average is performed over all backbone carbon atoms of the model. The MSD was calculated for a t value equal to 70 ps, corresponding to the time resolution of the neutron scattering experiment. This MSD value is hereafter named MSD₇₀. The error of MSD₇₀ was estimated by the standard deviation of the ensemble average of carbon atoms. To increase the statistics, we sampled over 14 time intervals of 70 ps in the last ns trajectory. The final RMS₇₀ value is the average of these 14 values.

The graphic visualization was done using the molecular viewer software package VMD [79].

One of the aims of the simulation study of polymer networks is to obtain a structural description of the system. By means of fully-atomistic molecular dynamics simulations we can focus the junction domain and include the inter- and intra-molecular interactions that influence its characteristics in the modeling.

In the PVAMA1 hydrogel, the DS of methacryloyl groups is very low, namely 1% of PVA residues, therefore the polymer component is mainly PVA. However, the particular junction topology of this system leads to a network structure different from that of PVA hydrogels obtained by self-crosslinking of telechelic PVA macromers [52]. In telechelic PVA hydrogels, the junction is strictly three-functional and the distribution of chains in the network can be quite homogeneous, even considering the chain end effects and the polydispersity of the starting macromers. The network structure in PVAMA hydrogels is based on 2N-functional junctions (see Chart 1) formed by PMA segments with N methacrylate residues, where N can assume several values since the polymerization degree of PMA chains is not controlled in the synthesis of the hydrogel [25].

In each 2N-functional junction, 2N PVA strands are connected and the network is formed when a same PVA chain participates to different junctions, thus jointing different cross-links. This kind of junction topology causes a large heterogeneity at a nanoscopic level in the chain density distribution, with a higher chain density in the surrounding of cross-links and a lower chain density in the regions including only PVA. The structural heterogeneity causes also a dynamical heterogeneity of the polymer network, as highlighted by the simulation. In this respect, even the different water affinity of PVA and PMA, hydrophilic and hydrophobic, respectively, contributes to increase the local heterogeneity of this hydrogel.

The picture of the junction domain obtained in the simulation study is reported in Figure 1, showing a snapshot of the MD trajectory at 313 K.

The PMA cross-linking chain, formed by eight PMA repeating units, is in the core of this structure and two PVA chains exit from each PMA residue, for a total of 800 PVA residues. This model describes a network portion in a surrounding of about 5 nm from the junction. The sterical development of the network in the hydrogel can be represented as an ensemble of elements similar to that shown in Figure 1, interconnected by means of one or more PVA chains.

We investigated the intramolecular connectivity of the polymer system in the junction domain as a function of temperature, by selectively analyzing the radial distribution function between oxygen atoms of PVA, the major polymer component, and the intramolecular hydrogen bonding. [Figure 2(a)] reports the radial distribution function between PVA oxygen atoms, g_O-O(r), calculated including only the contribution of near neighboring residues, namely the radial distribution function between the oxygen atoms of the i and i + 1 residues of PVA.

The peak at about 0.27 nm shows the contribution to the first coordination shell of PVA oxygen atoms by adjacent residues and a decreasing of this contribution at increasing temperature is observed. The behavior of the g_O-O(r)s at higher distances seen in [Figure 2(a)], determined by the average conformational features and configuration constraints of adjacent residues, is not influenced by temperature, as reported for other vinyl polymers [85]. The temperature effect on the long range intramolecular connectivity is shown in [Figure 2(b)], where the radial distribution function between the oxygen atoms of i and i + j PVA residues, with j > 5, is reported. In this case, a lowering of the g_O-O(r) in the whole range of distances can be observed at increasing temperatures, denoting a relaxation and a loosening of the structure with temperature. The same kind of analysis was carried out on the radial distribution function between oxygen and hydrogen atoms of PVA hydroxyl groups, g_O-H(r), to investigate the intramolecular hydrogen bonding. By integration of the g_O-H(r), the average number of HBs per PVA residue was calculated, by distinguishing the contribution of near-neighboring and more distant residues. The results, reported in Table 1 together with the average self-coordination number of PVA oxygen atoms obtained from the g_O-O(r)s, indicate that the system evolves toward a less structured chain arrangement at increasing temperature.

The local mobility of the system in the surrounding of the junction was investigated by analyzing the torsional dynamics of the polymer backbone, governed by the possibility of transitions between different conformations of the chain dihedral angles. In a vinyl chain the dihedral angles defined by the backbone carbon atoms are all equivalent, therefore the description of the polymer conformation in the network can be performed in term of a single dihedral angle, θ, for PVA and for PMA, by considering two dihedrals per residue. The PVA and PMA components were separately analyzed and in the case of PVA the five residues nearest to the junction were excluded. We monitored the backbone dihedrals throughout the simulation to detect the transitions between rotational states. In PVA chains, the transitions occurred between the trans state (θ = 180°) and one of the gauche states (θ = ±70°), as the cis barrier was never crossed during the simulations.

The average lifetime of rotational state, <τ_rot>, was estimated by means of Equation 17 (17) 〈 τ rot 〉 = 1 N DIHE ∑ i = 1 N DIHE t SIM ( N TRANS , i + 1 )where N_DIHE, t_SIM and N_TRANS,i are the number of dihedral angles which perform transitions, the simulation time interval considered in the analysis and the number of transitions of the i-th dihedral angle, respectively. In Equation 17 the single term of the summation represents the time-average lifetime of rotational state for the i-th dihedral angle, τ_rot,i, then the average is performed on the mobile chain dihedral angles. The torsional dynamic behavior of PVA in the polymer network as a function of temperature is summarized in Table 2, where the fraction of mobile dihedrals, f_DIHE, and the <τ_rot> values are reported.

These findings show that the increase of temperature activates a higher number of dihedrals whereas the local torsional dynamics is, on average, less affected. By comparing the <τ_rot> values in Table 2 with the value of <τ_rot>, equal to 161 ps, obtained in the MD simulation of a telechelic PVA network at 323 K [52], we can conclude that, although the network structure is different, the local dynamics of the PVA component in these two hydrogels is quite similar.

The torsional mobility of the PMA chain is almost completely hindered and only the two external dihedrals can perform transitions, with τ_rot,i values of about 200 ps, irrespective of temperature. Therefore, the torsional dynamic behavior of the polymer in the surrounding of the junction of PVAMA1 hydrogel is strongly heterogeneous, with a very low mobility of the cross-linking chain and an activation effect by temperature acting only on the PVA moiety.

At the aim to evaluate the local dynamics of the polymer in the network, the root mean squared fluctuation (RMSF) of atomic positions for each backbone carbon atom was determined: (18) RMS F i = 〈 ( r i ( t ) − 〈 r i 〉 ) 2 〉 t

The results are shown in Figure 3, where the RMSFs are reported as a function of the atom location in the polymer system (see Chart 2).

Empty squared symbols indicate atoms belonging to the PMA cross-linking chain. Figure 3 displays the dynamic heterogeneity of the junction domain. This heterogeneity is enhanced at the highest temperature. The system averaged RMSF increases at increasing temperature, as showed by values in the last column of Table 2.

We investigated the interaction between water and the two polymer components of the network, PVA and PMA, from both a structural and dynamic point of view. The analysis of polymer-water radial distribution functions and hydrogen bonding provided an averaged description of the network's hydration as a function of temperature. The study of polymer-water HB time autocorrelation function and of water mobility in the first hydration shell revealed the time scale of this interaction.

Figure 4 shows the radial distribution functions between hydroxyl PVA and water atoms, g_O-OW(r), g_H-OW(r), g_O-HW(r), at 283, 293 and 313 K. By integration of the g(r)s, as described in Section 2.3.2, we obtained the average water coordination number of PVA oxygen and the average HB capability of PVA with water.

The results, reported in Table 3, show a slightly increasing water affinity of PVA at increasing temperature.

The accessibility of water to the PMA cross-linking chain is described by Figure 5.

The radial distribution function between backbone carbon atoms of PMA and water oxygen atoms is reported in [Figure 5(a)]. From this curve we calculated the average number of water molecules per PMA residue inside a spherical domain of radius r centred on the PMA residue, N_OW(r), shown in [Figure 5(b)]. The results in [Figure 5(a,b)] indicate a swelling of the junction domain at increasing temperature. It is noteworthy that the temperature induced swelling effect begins at distances greater than about 0.9 nm. This result indicates that the low water affinity of the hydrophobic PMA residues is not affected by temperature, since at r > 0.9 nm from the PMA core only PVA residues are found. [Figure 5(c)], showing the radial distribution function between backbone carbon atoms of PMA and PVA, provides the complementary information to [Figure 5(a)]. In the distance range between about 0.8 and 2 nm the g(r)s of [Figure 5(a)] increase with temperature and, correspondingly, those in [Figure 5(c)] decrease; a behavior which describes the network swelling.

The polymer-water HB time autocorrelation function, C_HB(t), at the investigated temperatures is shown in [Figure 6(a)], together with the C_HB(t) of bulk water in the inset. The decay of the polymer-water C_HB(t) is strongly slowed, indicating a damping of water dynamics in the surrounding of PVA.

[Figure 6(b)] displays the results of an analysis of water mobility in the 0.35 nm thickness shell from the polymer. The solvent molecules included in this analysis correspond to the first hydration shell of polymer, since 0.35 nm is the distance of the first minimum in [Figure 4(a)]. We labeled the water molecules staying within a 0.35 nm distance from the polymer in the configuration at time t₀ and then we calculated the fraction of these water molecules, F_W0.35, jet residing inside the 0.35 nm shell at t > t₀. The F_W0.35(t) time decay, reported in [Figure 6(b)], is caused by the exchange of the water molecules in the first hydration shell with the more external water molecules, due to the diffusion motion of the solvent. The first information of [Figure 6(b)] is the kinetic effect of the temperature on water mobility, in agreement with the temperature behavior of the polymer-water hydrogen bond lifetime. In Table 3 we report the half-time of the hydration shell refresh, τ_1/2, obtained from the curves in [Figure 6(b)], and the average lifetime of PVA-water HB's, τ_HB, at the investigated temperatures. The increase of temperature enhances the water mobility in the surrounding of the polymer, with a decrease of both these times. The second information of [Figure 6(b)] is provided by the greater than 0 value of F_W0.35(t) at long times, indicating that some water molecules are confined within the first hydration shell. The fraction of these not exchangeable water molecules, reported in Table 3, decreases at increasing temperature. It is noteworthy that the value of τ_1/2 is always higher than the corresponding τ_HB (see Table 3) and that the C_HB(t) curves in [Figure 6(a)] can almost completely de-correlate in the investigated time window, whereas the corresponding F_W0.35(t) functions stabilize to a higher finite value. These findings indicate that a few water molecule moves along the polymer contour without leaving the shell. Indeed, such a dynamic behavior allows the de-correlation of C_HB(t), a function monitoring the HB between specific polymer-water pairs, but not the complete decay of the F_W0.35(t) function.

The interaction with the polymer network modifies the water dynamics, as shown by the behavior of the water diffusion coefficient, D_W, and of the hydrogen bonding between solvent molecules. The analysis of water properties was carried out by selecting the solvent molecules in different domains, depending on the distance from the polymer. The domain I includes water molecules within 0.6 nm, the distance corresponding to the second minimum of the g_O-OW(r), in [Figure 4(a)]. The domain II considers water molecules at distances from 0.6 to 2 nm. The remaining water molecules form the domain III. [Figure 7(a)] shows the ratio D_W/D_bulk for the three domains, being D_bulk the diffusion coefficient of bulk water, and Figure 7(b) reports the population of each water domain, as a function of temperature.

A supercooling effect on water molecules in domain I, including about 12% of total water, can be observed at each temperature. Moreover, the inversion of population of domain II over domain III at 313 K, shown in [Figure 7(b)], is in agreement with the network swelling at increasing temperature. The average lifetime of HBs between water molecules in the different domains, obtained by integration of the corresponding C_HB(t)s, is reported in Table 4, together with the values obtained for bulk water.

Data in Tables 3 and 4 indicate a polymer-induced slowing effect on the dynamics of the water. This effect involves solvent molecules which belong to the first and second coordination shell of the polymer, forming the domain I.