This is the accepted version of the journal article: Wolanin, Julie; Michel, Lucas; Tabacchioni, D.; [et al.]. «Heterogeneous Mi- croscopic Dynamics of Intruded Water in a Superhydrophobic Nanoconfine- ment : Neutron Scattering and Molecular Modeling». Journal of physical chemistry B, Vol. 125, Num. 36 (September 2021), p. 10392-10399. DOI 10.1021/acs.jpcb.1c06791 This version is available at https://ddd.uab.cat/record/275365 under the terms of the license Heterogeneous Microscopic Dynamics of Intruded Water in a Superhydrophobic Nanoconfinement: Neutron Scattering and Molecular Modeling J Wolanin, L Michel, D Tabacchioni, J M Zanotti, J Peters, I Imaz, B Coasne, M Plazanet, Cyril Picard To cite this version: J Wolanin, L Michel, D Tabacchioni, J M Zanotti, J Peters, et al.. Heterogeneous Microscopic Dynam- ics of Intruded Water in a Superhydrophobic Nanoconfinement: Neutron Scattering and Molecular Modeling. Journal of Physical Chemistry B, 2021, 125 (36), pp.10392-10399. �hal-03332577� HAL Id: hal-03332577 https://hal.archives-ouvertes.fr/hal-03332577 Submitted on 2 Sep 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Heterogeneous Microscopic Dynamics of Intruded Water in a Superhydrophobic Nanoconfinement: Neutron Scattering and Molecular Modeling J. Wolanin,† L. Michel,† D. Tabacchioni,† J. M. Zanotti,‡ J. Peters,†,¶ I. Imaz,§ B. Coasne,† M. Plazanet,∗,† and C. Picard∗,† †Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France ‡Laboratoire Lon Brillouin, CEA, CNRS, Universit Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France ¶Institut Laue Langevin, 38042 Grenoble, France §Catalan Insitute of Nanoscience and Nanotechnology, Barcelona, Spain E-mail: marie.plazanet@univ-grenoble-alpes.fr; cyril.picard@univ-grenoble-alpes.fr 1 Abstract ergy harvesting 11 (with the goal to compete with high per- 44 formance biological selective nanochannels 3 ). 45 2 With their strong confining porosity and versatile surface Despite their significant impact at the macroscopic level, 46 3 chemistry, Zeolitic Imidazolate Frameworks – including the the molecular specificities of water near solid surface remain 47 4 prototypical ZIF-8 – display exceptional properties for vari- only partly elucidated. At the microscopic level, a large body 48 5 ous applications. In particular, the forced intrusion of water of experimental and numerical studies is available on the dy- 49 6 at high pressure (∼ 25 MPa) into ZIF-8 nanopores is of in- namics of water confined within wetting, i.e. hydrophilic, 50 7 terest for energy storage. Such a system reveals also ideal to nanoporous media. In this case, the strong molecular in- 51 8 study experimentally water dynamics and thermodynamics teractions with the hydrophilic surfaces combined with se- 52 9 in ultra-hydrophobic confinement. Here, we report on neu- vere in-pore confinement cause a decrease in water trans- 53 10 tron scattering experiments to probe the molecular dynam- lational diffusion coefficient – i.e. a slowing down of wa- 54 11 ics of water within ZIF-8 nanopores under high pressure up ter dynamics which gets more pronounced with tighter con- 55 12 to 38 MPa. In addition to an overall confinement-induced finement and/or stronger surface interactions. 12–16 In par- 56 13 slowing down, we provide evidence for strong dynamical tially wetting materials, available data on moderately hy- 57 14 heterogeneities with different underlying molecular dynam- drophobic materials such as carbon nanotubes suggest a 58 15 ics. Using complementary molecular simulations, these het- more complex scenario with strongly enhanced water trans- 59 16 erogeneities are found to correspond to different microscopic port as probed using permeability measurements. 17 While 60 17 mechanisms inherent to vicinal molecules located in strongly such faster transport can be rationalized by elucidating the 61 18 adsorbing sites (ligands) and other molecules nanoconfined very specific interactions between water and the host sur- 62 19 in the cavity center. These findings unveil a complex micro- face (weakened hydrogen-bond network, curvature-induced 63 20 scopic dynamics, which results from the combination of sur- friction decrease, etc.), 18 it does not necessarily imply an in- 64 21 face residence times and exchanges between the cavity sur- crease in the diffusion coefficient and associated faster self- 65 22 face and center. dynamics. As a matter of fact, even if the solid surface im- 66 pact is less pronounced with hydrophobic surfaces, a de- 67 creased self-diffusion coefficient with respect to that of bulk 68 23 Introduction water has been also reported in the literature by different 69 24 Interfacial and confined water has become a scientific field groups. 13,19 Nevertheless, in all these studies dedicated to 70 25 in itself at the crossroad of physics, chemistry and biology hydrophilic and so-called hydrophobic materials, the affin- 71 26 with significant implication for applied science such as in ity of water for the solid matrices is always strong enough to 72 27 geophysics, mechanical/fluid engineering, etc. 1,2 Such wa- promote a spontaneous water condensation within the pores 73 28 ter, which displays marked differences with its bulk counter- at a bulk vapor pressure lower than the saturation pressure. 74 29 part, is of importance for situations where physicochemical Beyond hydrophilic and moderately hydrophobic ma- 75 30 interactions with surfaces are at play: protein folding, bio- terials, the microscopic dynamics in superhydrophobic 76 31 logical nanochannels, nanofiltration/phase separation, catal- nanoporous solids – such as all-silica zeolites and some 77 32 ysis, etc. 1,3,4 Despite the microscopic origin and nanomet- Metal Organic Frameworks for which a pressure much larger 78 33 ric range of these physicochemical interactions, the impact than the water saturation pressure is needed to force wa- 79 34 of interfaces on the water structure and dynamics – with a ter into the porosity – remains to be elucidated. Despite 80 35 pronounced dependence on confinement size, geometry and a well-established non-wetting thermodynamic behavior, 20 81 36 chemistry – manifests itself at the macroscopic scale as illus- the molecular mechanisms ruling water transport in these 82 37 trated by considering water flow properties. 5–8 Hydrophilic, materials involve complex phenomena which are often over- 83 38 i.e. wetting, surfaces are typically characterized by a no slip looked in such superhydrophobic environment (residence 84 39 boundary condition while hydrophobic, i.e. non-wetting, steps, in-pore relocation, etc.). In particular, the elemental 85 40 surfaces are known to exhibit slippage. 9,10 Such slip bound- dynamical mechanisms remain almost unexplored using mi- 86 41 ary conditions are broadly considered as a mean to overcome croscopic experiments (e.g. neutron scattering, nuclear mag- 87 42 the permeability-selectivity trade-off in membrane science netic resonance). In this context, Zeolitic Imidazolate Frame- 88 43 such as for medical applications, water desalination, blue en- works (ZIF) are attractive candidates owing to their tunable 89 1 90 chemistry, variety of topology and nanoscale pore size. 21–24 water dominates the scattered intensity, therefore providing 152 91 ZIF-8 is made of tetrahedral zinc ions linked by imidazolate a measurement of the self-dynamics of water in the sam- 153 92 organic groups (see insert in Figure 1). These two different ple. Descriptions of the experimental environment together 154 93 moieties form a cubic structure of spherical cages, 11.6 Å in with calibration and adequate background measurements 155 94 diameter, interconnected by 3.4 Å narrow gates which fill are given in the Supporting Information (S2). In brief, an 156 95 with water at a pressure of the order of 25 MPa at room tem- optimized aluminium high pressure cell was designed 32 to 157 96 perature. The ZIF-8 structure, which is superhydrophobic, prepare a sub-millimetric uniform and dense layer of ZIF-8 158 97 presents local heterogeneities as regularly encountered in powder (BASF, Basolite R Z1200), with similar volume frac- 159 98 biological confinement. The large microporous volume of tions in intra-grain pores and inter-grain bulk voids. Mea- 160 99 ZIF-8 (∼ 0.4 cm3 /g) 25 is experimentally of interest to reach surements were performed under hydrostatic pressures of 161 100 – after intrusion – a significant content of confined water 4, 20, 28 and 38 MPa which are below and above the water 162 101 with respect to bulk water. While water within ZIF-8 has intrusion pressure of 25 MPa (see Figure 2a) at ambient tem- 163 102 been largely explored from a structural viewpoint, 22,26–29 its perature. 24 The two lower pressures correspond to a matrix 164 103 dynamics has received only very little attention. On the one empty of liquid whereas the two higher pressures corre- 165 104 hand, Han et al. 30 considered the impact of defects on the spond to a matrix filled with liquid of interest for the study 166 105 dynamics of gas water molecules in ZIF-8, on the other hand of water dynamics in this superhydrophobic framework. 167 106 Fraux et al. 28 reported a ten-fold decrease in liquid water The reproducibility of the measurements was assessed by 168 107 self diffusivity. Despite these pioneering works, we note that performing several short measurements during successive 169 108 the details of the molecular mechanisms leading to such a intrusion cycle from low to high pressure. 170 109 dynamics slowing down remain to be identified. 110 Here, we report on a coupled experimental and molecular 111 simulation investigation of the microscopic dynamics of in- Results and Discussion 171 112 truded water in superhydrophobic confinement. To the best We first investigate the water dynamics, using molecular 172 113 of our knowledge, we performed the first direct measure- simulation, from the mean square displacements (MSD) for 173 114 ment of the diffusion coefficient of liquid water in such su- bulk and confined water with respect to time (Figure 1). In 174 115 perhydrophobic environment by means of quasi-elastic neu- the long time limit t > 1 ns, the short-wave vector displace- 175 116 tron scattering (QENS). Our experiments are combined with ments (large distances) are dominated by translational mo- 176 117 a dual Grand Canonical Monte Carlo/molecular dynamics tion where both the O and H atoms diffuse over the same 177 118 simulation strategy which sheds light on the heterogeneous distance on a given time scale. While the Fickian regime is 178 119 dynamics of water confined in such hydrophobic environ- reached on a short time scale for bulk water (t ∼ 100 ps), we 179 120 ment. While we confirm the average slowing down of the found that much longer simulations are required to investi- 180 121 dynamics for confined water, careful analysis of our exper- gate this normal diffusion regime for confined water (typi- 181 122 imental data in the light of molecular simulations unveils a cally, t ∼ 10 ns). The diffusivity of water confined in ZIF- 182 123 complex microscopic dynamics related to two different dy- 8 at 300 K is found to be smaller than its bulk counterpart; 183 namical mechanisms: reduced dynamics for water located typically, DT ∼ 3.4 × 10−9 m2 /s for bulk water while DT 124 184 close to strongly adsorbing sites (ligands) and bulk-like wa- 125 ∼ 2.6 × 10−10 m2 /s for confined water. These two values 185 126 ter in the cavity center. obtained with the TIP4P water model being 30% larger than 186 the ones obtained with the SPC/E model (extended simple 187 127 Material and Methods point charge model) 28 . However, importantly, the ten-fold 188 decrease in the water self diffusivity between bulk and con- 189 128 The molecular simulation approach first involves Grand 129 Canonical Monte Carlo simulations to determine the number 130 of adsorbed water molecules as a function of pressure. Then 131 starting from configurations obtained at a pressure where the 132 ZIF-8 porosity is filled with water, we performed molecular 133 dynamics simulations to compare bulk and confined water 134 dynamics. A supercell consisting of a 2 × 2 × 2 ZIF-8 unit 135 cell (the cubic lattice parameter is approximately 1.7 nm) was 136 built to conduct these calculations. Periodic boundary con- 137 ditions were used along the 3 space directions to avoid fi- 138 nite size effects. Following previous works on water in ZIF, 139 the TIP4P ( Transferable Intermolecular Potential-4 Point) all- 140 atom model is used to describe the water molecule while 141 both a nominal and rescaled force field proposed by Am- 142 rouche et al. 31 is used to model the water/ZIF-8 molecular 143 interactions. All details on the molecular simulation strategy 144 can be found in the Supporting Information (S5). 145 QENS experiments were performed at Institut Laue- 146 Langevin (ILL, Grenoble) on the time-of-flight spectrometer 147 IN6-Sharp with an incident wavelength of 5.1 Å – leading Figure 1: Mean square displacements ∆r2 as obtained using 148 to an elastic energy resolution of 70 µeV (dynamics faster molecular dynamics for the O and H atoms of water in bulk 149 than ∼ 10 ps) over the momentum transfer q-range of 0.4-2 water (dashed lines) and confined in ZIF-8 (solid lines). The 150 Å−1 . Because of the large hydrogen incoherent cross section black dashed line is a guide to the eye to indicate the Fickian 151 for neutrons, the signal arising from hydrogen motions of regime where ∆r2 ∼ t. The insert shows the ZIF-8 structure. 2 190 fined values is independent of the force field or its scaling (as nal is therefore a direct measurement of the water dynamics 226 191 detailed in the Supplementary Information). in such superhydrophobic confinement. The limited ZIF-8 227 192 In the short time limit (t < 10-100 ps), for both bulk and compressibility, 34 which leads to minor deformations of the 228 193 confined water, the O and H mean square displacements matrix on the considered pressure range – essentially related 229 194 depart from each other due to rotational effects. Interest- to a slight dilation of the order of 0.5% occurring within the 230 195 ingly, while the mean square displacements for bulk water narrow pressure window associated to the filling process 35 – 231 196 is timescale independent in the sense that it exhibits a sin- is expected to not alter the liquid water dynamics within the 232 197 gle regime once rotational effects are no longer noticeable, pores after intrusion. The superimposition of signals mea- 233 198 the data for confined water indicate a heterogeneous dynam- sured at 28 MPa and 38 MPa confirms that once the matrix 234 199 ics with different regimes. In more detail, between the time is filled, the pressure increase does not alter the water dy- 235 200 range dominated by rotation/translation coupling (t < 100 namics, neither directly through a potential change of water 236 201 ps) and the normal Fickian regime (t ∼ 1-10 ns), a subdiffu- structure nor indirectly because of the flexibility of the ma- 237 202 sive regime where ∆r2 ∼ tα with α < 1 is observed. trix. The dynamical structure factor, S(q, ω ), in the inves- 238 203 At this stage it is useful to comfort these initial numeri- tigated energy range, can be approximated by the product 239 204 cal results with experimental values of the diffusion coeffi- of the Debye – Waller factor, accounting for the vibrational 240 205 cient DT . The confined water dynamics is extracted from motions, with the decoupled diffusive motions, such as rota- 241 206 the dynamical structure factor S(q, ω ). 33 The experimental tional, SR (q, ω ), and translational, ST (q, ω ), ones: 33 242 207 S(ω ) spectra (summed over the whole q-range) at the dif- 208 ferent investigated hydrostatic pressures are shown in Fig-  2 2  q hu i 209 ure 2b. The contribution from the ZIF-dry matrix, which S(q, ω ) = [ST (q, ω ) + SR (q, ω )] exp − (1) 210 is purely elastic, confirms the absence of QENS signal that 3 211 could arise from imidazole ring rotation on the investigated with hu2 i the mean-square vibrational amplitude of the hy- 243 212 time scale. Moreover, complementary measurements have drogen atoms. In a first approach, both translational and 244 213 been performed on the spectrometer IN13 (ILL), covering a rotational motions were described using a Lorentzian func- 245 214 shorter (∼ 100 ps) timescale than IN6-SHARP. The results tion of unconstrained half-width at half-maximum (hwhm), 246 show that the rotational motion of the 2-methyl-imidazole Γ. Γ T and Γ R refer to the translational and rotational mo- 215 247 rings is not influenced by the intrusion process (as it occurs tions, respectively. In the Fickian regime, the variation of Γ T 216 248 on a timescale that is included in the elastic line of the present is linear with q2 as Γ T = DTFick q2 where DTFick is the transla- 217 249 218 experiment). Details are presented in the Supporting Infor- tional self-diffusion coefficient. For the localized rotational 250 mation (S1). We also observe that spectra below Pint =25 MPa motion, the width is q-independent: Γ R = 2DR with DR 219 251 220 (4 and 20 MPa) are very similar as well as those above Pint (28 the rotational diffusion constant. Such a phenomenological 252 221 and 38 MPa). Below 25 MPa, only inter-grain water is present model relying on two Lorentzian functions provides a reli- 253 222 outside the ZIF-8 grains as the nanopores are empty. Thus, able description of the water dynamics under different ther- 254 223 the observed intensity increase between 20 and 28 MPa (Fig- modynamical conditions. We emphasize that the appropriate 255 224 ure 2c) provides evidence for the presence of water within background for each pressure condition is subtracted in or- 256 225 the nanopores above Pint . The obtained high-pressure sig- der to isolate successively the inter-grain and intra-grain wa- 257 high pressure low pressure inter-grain water + dry ZIF-8 grains inter-grain water intra-grain water Figure 2: (a) Experimental water intrusion/extrusion cycle at room temperature in a ZIF-8 material. V ( P) indicates the intruded and extruded volume V of water per g of ZIF material as a function of the exerted pressure P. (b) S(ω ) summed over q [from 0.4 to 2 Å−1 ] of the quasi-elastic spectra S(q, ω ) obtained for dry ZIF-8 (black), low-pressure water in contact with ZIF-8 (red) and high-pressure water intruded in ZIF-8 (blue). Inset: schematics of these three situations. (c) Zoom on the elastic peak showing the overall increase of the intensity upon water addition. 3 ulation, to a linear Fickian regime that extends much beyond 290 q2 ∼ 2 Å−2 . As detailed in the Supporting Information (S3), 291 the deviation from Fick’s law beyond this q value, marked by 292 the onset of a plateau for Γ T , provides a signature of the non 293 homogeneous behavior of intra-grain water, due to the influ- 294 ence of the discrete atomic structure surrounding water (also 295 highlighted in Figure 1 with the subdiffusive regime at short 296 times). To further analyze this departure from an effective 297 average behavior, a more rigorous model is needed to cover 298 and accurately describe both the Fickian and non-Fickian dy- 299 namical regimes. 300 Table 1: Numerical values of the extracted fitting parame- ters for the analysis 1. DTFick was calculated with the Fick’s law on the appropriate q-range. Analysis 1: eq. 1 DTFick ×10−5 [cm2 /s] DR [ps−1 ] Bulk water 2.01 ± 0.03 2.06 ± 0.01 ZIF-8: P<25 MPa 1.92 ± 0.04 2.09 ± 0.02 Figure 3: Half-width at half-maximum Γ T of the translational ZIF-8: P>25 MPa 1.22 ± 0.02 1.75 ± 0.02 contribution versus q2 for bulk water (black), low-pressure water in contact with ZIF-8 (red) and high-pressure water in- We performed therefore a deeper analysis based on a for- 301 truded in ZIF-8 (blue). Error bars are smaller than the sym- mal description of water translation through the use of the 302 bol size. The symbols refer to the results obtained with the jump diffusion model 33 coupled to isotropic rotational dif- 303 analysis 1 (Eq. 1). The dashed segments indicate the Fickian fusion in a sphere of radius R (equal to the OH distance in 304 regime where Γ T ∼ q2 . The solid lines are attributed to the re- a water molecule ∼ 1 Å). Each population will then be de- 305 sults obtained with the analysis 2 (Eq. 2) using the jump dif- scribed by the new fitting model: 306 fusion model. We note the presence of two solid blue lines as-  2 2  q hu i sociated to the heterogeneous behavior of the intruded high- S(q, ω ) = exp − S(q, ω ) T ⊗ R (2) pressure water obtained with the analysis 2. 3 with 307 258 ter dynamics. Moreover, we assume that inter-grain water is ! 259 identical at low and high pressures, as justified by the very 1 ΓT S(q, ω ) T ⊗ R = ⊗ 260 low-pressure dependence of the bulk translational diffusion π ω 2 + Γ2T 261 coefficient in the investigated pressure range (< 40 MPa). 36 ∞ !! More information on this analysis and curve fitting quality 1 Γi 262 263 are given in the Supporting Information (S2). The obtained A0 (q).δ(ω ) + ∑ A i ( q ). π ω 2 + Γ2i i =1 264 q2 dependence of Γ T is shown in Figure 3 (symbols) while the (3) 265 extracted parameters are given in Table 1. 266 The translational dynamics for bulk water and inter-grain where Γ T is defined within the jump-diffusion model: 308 267 water obey to Fick’s law for q2 < 3 Å−2 . The correspond- DTJump q2 ! 268 ing self-diffusion coefficients, of 2.01 × 10−9 m2 /s and 1.92 × ΓT = (4) 269 10−9 m2 /s respectively, are very close to each other, and in 1 + τDTJump q2 270 very good agreement with values found in the literature for 271 bulk water at 295 K 37 (incidentally we note that the MSD with τ the residence time, Ai (q) = (2i + 1) ji2 (qR) where ji is 309 272 value measured with the numerical TIP4P water model is the spherical Bessel function of order i and Γi = i (i + 1) DR . 310 273 70% larger than these experimental values). The water sur- As expected, a single water population only is not suffi- 311 274 rounding the grains is therefore only poorly influenced by cient to accurately fit our experimental data on the entire 312 275 the inter-grain boundaries on the time and space scales inves- (q, w) range. On the other hand, a good fit is obtained us- 313 276 tigated. The deviation from Fick’s law at large q is expected ing two water populations (ratio of 70/30 for fast and slow 314 277 because of the simplified model – single Lorentzian – used for population, respectively). Each of these two populations are 315 278 the rotational dynamics (instead of the full derivation taking described with the model given in Eqs. 2 and 3 (fitting curves 316 279 into account higher Lorentzian orders and coupling between are presented in the Supporting Information (S2)). The result- 317 280 the two relaxation dynamics – see Eq. 3 and in S3 for more ing fitting parameters are shown in Table 2. The fast popu- 318 281 details). lation is similar to bulk water while the slow population has 319 282 In contrast to inter-grain water, the translational dynamics a translational diffusion coefficient one order of magnitude 320 283 for intra-grain water follows Fick’s law up to q2 ∼ 2 Å−2 only. lower as inferred from the MSD obtained using molecular 321 284 In the low q Fickian regime, the confinement effect leads to a simulation (Figure 1). As detailed in the Supporting Infor- 322 285 decrease of both translational and rotational diffusion coef- mation (S3), at low q, the average dynamics of the two pop- 323 286 ficients with respect to their bulk counterpart. The slowing ulations is similar to the one presented in Analysis 1 with an 324 287 down measured experimentally is only of the order of 30% effective translational diffusion coefficient ∼ 30% than that of 325 288 with respect to the bulk values. Such a limited departure bulk water. This moderate deviation at low q is related to the 326 289 from the bulk dynamics should lead, for a single water pop- small proportion of the slow water population with respect 327 to the fast one. At high q, however, the slow water popula- 328 4 Table 2: Numerical values of the extracted fitting parameters of the confined water in ZIF-8: P>25 MPa for the Analysis 2 Analysis 2: eq. 2 DTJump ×10−5 [cm2 /s] τ [ps] DR [ps−1 ] ZIF-8: P<25 MPa 2.09 ± 0.05 0.55 ± 0.01 1.83 ± 0.01 ZIF-8: P>25 MPa: Population 1 1.87 ± 0.02 0.25 ± 0.05 2.18 ± 0.04 ZIF-8: P>25 MPa: Population 2 0.167 ± 0.007 2.55 ± 1.6 0.17 ± 0.01 329 tion, despite its limited proportion, becomes a leading term scattering function, f (q, t) (inverse time Fourier transform of 349 330 which contributes to the plateau observed for Γ T in Figure 3 S(q, ω )) extracted from molecular dynamics simulations for 350 331 in the framework of analysis 1. Furthermore, moving now bulk water conforms to the classical behavior expected for 351 332 to the temporal domain using the inverse time Fourier trans- Fickian diffusion. The superimposition of the curves plot- 352 333 form of the formal model Eq. 2 (see Supporting Information ted with respect to q2 t reveals that the rotational contribution 353 334 S4) for the two populations, the translational term expresses is restricted to a very short time scale. This is further con- 354 335 as the sum of two time-decaying exponentials. At long time firmed by the large value of DR ∼ 1 ps−1 obtained from the 355 336 this translational term should be controlled by the slower ex- fit of f – inset of Figure 4a – using the inverse time Fourier 356 337 ponential decay only associated to the slow population. This transform of the formal model Eq. 2 (see Supporting Infor- 357 338 means that at long time a Fickian regime with a diffusion co- mation S4). The dominant translational contribution of the 358 339 efficient of the order of 1.7 × 10−10 m2 /s is expected. This form exp(− DTJump q2 t) is characterized by a diffusion coeffi- 359 340 analysis of experimental data confirms, at long time, the ten- cient DTJump which agrees with the one inferred from MSD 360 341 fold decrease observed from numerical MSD and reveals, at calculations. In contrast, as previously observed from our 361 342 short time, that the heterogeneous dynamics of confined wa- experimental data and molecular simulation MSD, f (q, t) for 362 343 ter in ZIF-8 can be interpreted as the interplay between a slow confined water display a non-Fickian behavior which can be 363 344 and a main bulk-like water population. approximated again with the contribution of a fast and a 364 345 Attempting the same two-population decomposition us- slow population (ratio 60/40) – each of them modeled with 365 346 ing numerical data, a similar trend – even if to a less ex- the inverse time Fourier transform of Eq. 2 (see inset of 366 347 tent – is also observed when focusing on short time scales. Figure 4a). Nevertheless, DTJump for the fast population re- 367 348 As shown in Figure 4a, the self (incoherent) intermediate mains four times smaller than that for bulk water; this is a 368 Figure 4: (a) Self (incoherent) intermediate scattering function f (q, t) as a function of q2 t for different scattering vector q = | q | for bulk water (open circles) and for water confined in ZIF-8 (full dots). The color code is as follows: q = 0.7 Å−1 (red), q = 1.0 Å−1 (green), q = 1.5 Å−1 (blue), and q = 2.0 Å−1 (grey). Inset: f (q, t) according to t for bulk (open circle) and confined water (full dots). Dashed lines, bulk water: fit with a single water population using the inverse Fourier transform of Eq. 2 with DTJump = 4.2 × 10−9 m2 /s, τ = 0.9 ps and DR = 0.8 ps−1 . Full lines, confined water: fit with a fast and a slow population (ratio 60/40) with DTJump = 1.1 × 10−9 /3.4 × 10−10 m2 /s, τ = 0.25/20 ps and DR = 2/0.1 ps−1 (b) Contour plot showing the density of water in a ZIF-8 material as obtained using Grand Canonical Monte Carlo simulations. The density increases with color as follows: blue, green, yellow, orange and red. (c) Simulated density profiles ρ(r ) for the O and H atoms of water intruded in ZIF-8. r is the distance from the center of the ZIF cages shown in the contour plot in (b). The dashed line indicates the bulk density of water at room temperature.) 5 369 major difference with respect to experimental results. The 370 rotational diffusion coefficient of the slower population be- 371 ing 20 times smaller than the fast population, in qualitative 372 agreement with experimental results, the rotational contri- 373 bution extends to much longer time than for bulk water and 374 contributes to the separation of the curves observed in Fig- 375 ure 4a at large q2 t values. Interestingly, the functions f do 376 not present a linear asymptotic trend at long q2 t values that 377 would be expected in the presence of two distinct water pop- 378 ulations only. This means that such a basic yet efficient de- 379 composition to quantitatively analyze experimental and nu- 380 merical data does not fully reflect the heterogeneity of wa- 381 ter dynamics in such complex materials partly controlled by 382 residence times at surfaces (see Bousige et al. 38 for a recent 383 discussion on intermittent diffusion in complex nanoporous 384 media). 385 At the microscopic level, the strong variations of water 386 density as obtained from GCMC simulation (see Figure 4b 387 and Figure 4c) reveal and confirm a complex heterogeneous 388 water structure within the ZIF-8 porosity. These data, which 389 are consistent with previous molecular simulation in the 390 field, 22 show that water is adsorbed on specific sites, close 391 to the ligands at a distance about 0.4 - 0.5 nm from the pore 392 center [see marked density spots in Figure 4b], and in less ad- 393 sorbing sites located closer to the pore center [see less marked 394 density spots at a distance ∼ 0.2 nm]. Although these adsorb- 395 ing sites are hydrophobic enough to not trap water at ambi- 396 ent pressure, their relative affinity for the intruded water con- 397 tribute to the marked slowing down its dynamics observed at 398 long time. 399 For times much longer than the residence time, exchanges 400 between the different adsorbing sites contribute to the com- 401 plex heterogeneous dynamics and hence to the effective be- 402 havior accessible experimentally. Such a contribution from Figure 5: (a) Diffusion propagator G (r, t) as obtained us- 403 this molecular intermittence can be investigated by means ing molecular dynamics at room temperature for the O (red 404 of the diffusion propagator G (r, t) (inverse space and time lines) and H (blue lines) atoms of water confined in ZIF-8. 405 Fourier transform of S(q, ω )) which corresponds to the prob- The dashed line is a guide to the eye to indicate that the 406 ability that a molecule gets located at a position r at a time t data are estimated at increasing times t = 1, 5, 10 and 20 ps. 407 while being at r = 0 at a time t = 0. At short times (t < 10 ps), As discussed in the main text, the insert shows the differ- 408 G (r, t) shown in Figure 5a for both O and H atoms of con- ent contributions to the G (r, t) data for the O atoms at t = 409 fined water is monomodal and reflects local displacements 20 ps: all molecules in the ZIF-8 cage (red), molecules in the 410 (r ∼ 0.1 nm) which are similar to those found for bulk water cage center (blue) and molecules in strongly adsorbing sites 411 on the same time scale (although of a slightly smaller am- (green). (b) Rotational autocorrelation time θ (t)θ (0) showing 412 plitude in confinement). For larger times (t > 10 ps), the the change in a water molecule time at a time t = 0 and a time 413 propagator becomes bimodal for O and H atoms, therefore t later. The dashed and solid lines are for bulk water and wa- 414 indicating two characteristic translational modes coexisting ter confined at room temperature in ZIF-8. The insert shows 415 on the same time scale. We show in the insert of Figure 5a the same data for confined water but for different subpopu- 416 the propagators for the different water populations confined lations: molecules in the cage center (blue), molecules at the 417 in ZIF-8 (note the use of a log scale for improved visualiza- cage surface (purple), and molecules in strongly adsorbing 418 tion purpose). In more detail, we measured the propagator sites (green). 419 for molecules initially located at time t = 0 in the strongly 420 adsorbing sites close to the ZIF-8 ligands (see density con- 421 tour plot shown in Figure 4b) and that for molecules ini- we extracted the rotational relaxation time distribution for 434 422 tially located in the cavity center not directly in contact with water in the different regions of the ZIF-8 cavities to clarify 435 423 ZIF-8 ligand/surface. Such data confirm that the fast dif- more specifically the impact of the surface heterogeneities 39 436 424 fusion mode (i.e. subpeak in the propagator located at dis- (see Figure 5b). The timescale of rotational motions enables 437 425 tance r ∼ 3.5 Å) corresponds to molecules located within the indeed a more local analysis since molecules, over such a 438 426 cavity center while the slow diffusion model corresponds to short timescale, do not significantly exchange between dif- 439 427 molecules initially located in the strongly adsorbing sites. In- ferent sites. Owing to their intrinsically slow dynamics, the 440 428 terestingly, for both contributions, some molecules undergo rotational motion of the molecules located in the strongly ad- 441 429 displacements corresponding to the other mode. This is due sorbing sites is slower than for molecules in the pore center 442 430 to the fact that, during the characteristic time t = 10 ps con- again with a typical rotational relaxation time a few times 443 431 sidered here, some molecules leave the cavity center to mi- larger than for water in the pore center. Such a slow rota- 444 432 grate towards the strongly adsorbing sites and reciprocally. tional motion only applies to molecules in the strong adsorb- 445 433 Additionally to the analysis of the translational motions, ing sites. For molecules at the ZIF-8 cavity surface, away 446 6 447 from adsorbing sites, we indeed confirm that the relaxation (2) Kavokine, N.; Netz, R. R.; Bocquet, L. Fluids at the 488 448 time distribution is close to the one found for molecules in Nanoscale: From Continuum to Subcontinuum Trans- 489 449 the pore center. port. Annu. Rev. 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Adv. 2020, 6, 1–8. 521 Acknowledgement The authors thank the Institut Laue- Langevin (Grenoble, France) for the allocation of neutron (12) Bellissent-Funel, M.-C. Status of experiments probing 522 beam time. The neutron data set is available at DOI: the dynamics of water in confinement. Eur. Phys. J. E 523 http://10.5291/ILL-DATA.EASY-537. This work was sup- 2003, 12, 83–92. 524 ported by the French Research Agency (ANR LyStEn 15- CE06-0006, ANR TWIST 17-CE08-0003). Some of the com- (13) Siboulet, B.; Molina, J.; Coasne, B.; Turq, P.; Dufreche, J.- 525 putations in this paper were performed using the Froggy F. Water self-diffusion at the surface of silica glasses: ef- 526 platform of the GRICAD infrastructure (https://gricad.univ- fect of hydrophilic to hydrophobic transition. Mol. Phys. 527 grenoble-alpes.fr), which is supported by the Rhne-Alpes 2013, 111, 3410–3417. 528 region (GRANT CPER07-13 CIRA) and the Equip@Meso (14) Romero-Vargas Castrillón, S.; Giovambattista, N.; Ak- 529 project (reference ANR-10-EQPX-29-01) of the programme say, I. A.; Debenedetti, P. G. Evolution from surface- 530 Investissements dAvenir supervised by the French Research influenced to bulk-like dynamics in nanoscopically con- 531 Agency. We thank Claude Payre and Jérôme Giraud for high fined water. J. Phys. Chem. B 2009, 113, 7973–7976. 532 pressure equipment and the design of high pressure cell. We are grateful to David Farruseng who initiated fruitful collab- (15) Osti, N. C.; Cote, A.; Mamontov, E.; Ramirez-Cuesta, A.; 533 oration for this work. Wesolowski, D.; Diallo, S. Characteristic features of wa- 534 ter dynamics in restricted geometries investigated with 535 484 References quasi-elastic neutron scattering. Chem. Phys. 2016, 465, 536 1–8. 537 485 (1) Lynch, C. 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