Viscosity at the Nanoscale: Confined Liquid ... - ACS Publications

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Viscosity at the Nanoscale: Confined Liquid Dynamics and Thermal Effects in Self-Recovering Nanobumpers Yaroslav Grosu,*,†,‡,§ Alberto Giacomello,∥ Simone Meloni,∥ Luis González-Fernández,‡ Miroslaw Chorazewski,⊥ Monika Geppert-Rybczynska,⊥ Abdessamad Faik,‡ Jean-Marie Nedelec,† and Jean-Pierre Grolier† †

Université Clermont Auvergne, CNRS, SIGMA Clermont, ICCF, F-63000 Clermont-Ferrand, France CIC Energigune, Albert Einstein 48, Miñano, Alava 01510, Spain § Laboratory of Thermomolecular Energetics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Pr. Peremogy 37, 03056 Kyiv, Ukraine ∥ Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, via Eudossiana 18, 00184 Rome, Italy ⊥ Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland

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‡

S Supporting Information *

ABSTRACT: Understanding the effect of liquid viscosity in nanoconfinement is of paramount importance from both the fundamental and practical points of view. In particular, unexpected dynamic phenomena are ubiquitous in a broad range of nanofluidic applications. In this work, we used state-of-the-art highpressure (P,V,T) calorimetry for direct observation of pressure, volume, temperature, and thermal effects during controlled intrusion/extrusion of liquids in nanoporous materials. It was discovered that the liquid extrusion pressure and the accompanying thermal effects can be controlled by changing solely the liquid viscosity. Such knowledge allowed us to propose the {nanoporous material + nonwetting liquid} system as a self-recovering nanobumper and to clarify the parameters for its optimization. Experimental results were interpreted in terms of confined classical nucleation theory as the slowdown of bubble expansion in the nanopores because of the high liquid viscosity. The present results are of practical value for designing energy storage/dissipation devices based on intrusion/extrusion cycles, as well as of fundamental importance for understanding the effect of viscosity in nanoconfined liquids.

1. INTRODUCTION Understanding the behavior of fluids at the nanoscale is a great interdisciplinary challenge, with potential applications in biology,1 electronics,2 energy,3−5 and more.6 In particular, the forced intrusion of a nonwetting liquid into nanopores can be used for energy storage (molecular springs) or dissipation (shock absorbers/bumpers).7−13 This process (see Scheme S1) is accompanied by a large volume variation corresponding to the occupation of the porous cavities by the liquid (mechanical energy storage in the form of solid−liquid interfacial energy) and, typically, endothermic effects (thermal energy storage). Heterogeneous lyophobic systems (HLSs) consisting of porous materials and nonwetting liquids have several important advantages as compared to competing energy storage/ dissipation technologies, including the possibility to accumulate/release mechanical energy at constant pressure,8,9,14 which is not achievable with other methods of energy storage, for example, with compressed air energy storage; the ability to sustain unprecedented frequencies of compression-decompression cycles, inaccessible to classical shock absorbers;10,15,16 the possibility to be scaled down to few tens of nanometers, as in © XXXX American Chemical Society

most cases, the system is in the form of a suspension; the possibility to combine mechanical and thermal energy storage because of the pronounced and controlled effect of negative17−19 or positive19 thermal expansion; and the high energy density12−14 and durability.10,15,20 The reversibility of intrusion upon decompression defines the applicability of a HLS for energy storage or dissipation. If upon decompression, extrusion of a nonwetting liquid from the pores takes place at pressures close to the pressure of intrusion, such systems act as “molecular springs” and can be used for energy storage.9,14,21,22 There are several systems based on microporous materials, which have been reported to exhibit negligible or even zero hysteresis.21−24 If, on the contrary, upon decompression, a nonwetting liquid remains trapped inside the pores or extrudes at pressures considerably lower than the intrusion pressure, such systems Received: February 26, 2018 Revised: May 31, 2018

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DOI: 10.1021/acs.jpcc.8b01959 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

nanopores as a triggering mechanism of nonwetting liquid extrusion from the nanopores. In particular, here we focused on the intrusion/extrusion of water, glucose, and ionic liquid solutions into/from C8 silica, a material with an average porous diameter of 8 nm. C8 has been chosen because it is of interest for technological applications, for example, dissipation of mechanical and thermal energy, and we show that by changing the viscosity of the liquid one can transform a shock absorber into a bumper and vice versa. Moreover, the size of C8 pores is large enough that the experimental results can be interpreted on the basis of continuum theories of liquids. Systems with much smaller pores, whose mouth has a size comparable with that of solutes (glucose and ionic liquid), might act as molecular f ilters. This poses specific additional problems connected to the fact that the composition of the solution inside the pores would differ from the nominal value. We leave for future work the intriguing problem of the interplay between viscosity and pore size and focus on the general aspect of viscosity on intrusion/extrusion into/from porous systems.

can be used for energy dissipation (bumpers and shock absorbers).25−37 Since the introduction of the concept,7,38 different aspects of HLSs have received considerable attention,8−69,96,97 some focusing on the investigation of the principles and mechanisms of their operation51,55−59 and others on the development of prototypes.16,39,40 Despite this research effort, the phenomena responsible for hysteresis in intrusion/extrusion cycles are not fully understood. In particular, the operational dynamics (speed or frequency of cycling) and effect of viscosity on hysteresis has been so far very challenging to address. It was shown that, depending on the hydrophobic porous material, the rates of compression and decompression may strongly60 or negligibly15,16,27 affect the intrusion and extrusion pressures. By means of molecular dynamics (MD) simulations, Liu and Cao52 demonstrated that extrusion of water in carbon nanotubes is rate-dependent (and geometry-dependent). The frequency dependence of hysteresis was investigated by means of advanced MD simulations in the context of confined classical nucleation theory (CNT);61 it was shown that, for cylindrical pores, the extrusion pressure is expected to be more sensitive to the cycling frequency (loading rate) than the intrusion pressure. There is, however, a limited number of studies addressing the effect of viscosity of highly confined nonwetting liquids other than water on hysteresis. Recently, Sun et al.62 reported a rate dependence of the intrusion pressure in HLSs formed by a mesoporous material and several liquids. However, it was not possible to investigate the effect of viscosity on extrusion pressure as all the liquids remained trapped inside the pores after intrusion. Han et al.36 studied the intrusion of an aqueous solution of glycerin depending on the compression rate and concentration. Also in this case, the irreversible intrusion prevented to analyze the effect of viscosity on extrusion. Zhang et al.37 demonstrated that, for ZSM-5 zeolite mixed with glycerol solutions, extrusion depends on the temperature, and, among other factors, it might be related to the viscosity of the nonwetting liquid. The effect of viscosity on liquids flowing under nanoconfinement is widely discussed in the literature.90−95 Transition from viscous to elastic behavior was demonstrated when the thickness decreases below three to four molecular layers.92 Shear thinning for monolayer and bilayer water was reported.93 The increased and viscosity-independent flow rates were reported through carbon nanotube membrane, hydrophobicity being mainly responsible for the observed effects.94 In ref 95, it was argued that the increased flow rates are not only due to water slip effect on a hydrophobic surface but also due to shear thinning. Although the very rich rheological behavior of nanoconfined liquids has been widely investigated, in the present work we address the different problem of the thermally activated formation of a gas/vapor phase inside the nanopores. Here, we target the effect of viscosity on the dynamics of intrusion and extrusion of nonwetting liquids in nanopores focusing, in particular, on the dependence of the extrusion pressure on viscosity. To this aim, we investigated the (high-pressure) intrusion/extrusion of three liquids with similar surface tensions and contact angles but with viscosity differing by orders of magnitude into/from nanoporous silica gels grafted with octylsilanes. These experiments were coupled with in situ calorimetry. The results are discussed in terms of the dynamics of bubble nucleation induced by the hydrophobicity of

2. MATERIALS AND METHODS 2.1. Materials. Here, we consider three nonwetting liquids, namely distilled water, 55 wt % sucrose aqueous solution (referred as “sucrose solution” in the text), and 12 wt % aqueous solution of 1,3-dimethylimidazolium glutamate ionic liquid (referred as “ionic liquid solution”). It is important to remark that the aqueous solutions we employed are characterized by very low molar fractions of sucrose and ionic liquid (6 and 1 mol %, respectively). Therefore, by Raoult’s law, the vapor pressure of these solutions is expected to present the corresponding small deviations from the vapor pressure of water; therefore, the effects we describe in the following are likely to be due to the only property that varies significantly among the three systems, that is, the viscosity (see below). Pure sucrose was purchased from Sigma-Aldrich and was mixed with distilled water directly to obtain the 55 wt % sucrose aqueous solution. An aqueous solution of 1,3dimethylimidazolium glutamate ionic liquid (12 wt %) was custom-purchased from IoLiTec-Ionic Liquids Technologies GmbH, Germany. A commercial mesoporous silica gel, SymmetryPrep C8, in the shape of 7 μm granules grafted with octylsilanes with a density of 2.1 groups/nm2 according to the data provided by the supplier (WATERS), was used for all the experiments of intrusion/extrusion. The average pore diameter of this silica gel is 8.4 nmFigure S1; the pore volume is 0.53 cm3/g. The porosity of the material can be represented by randomly intersecting spheres. 2.2. Methods. 2.2.1. High-Pressure Calorimetry. An ST7M transitiometer from BGR-Tech was used for recording the PV isotherms at different temperatures in the pressure range of 0.1−30 MPa and for simultaneously measuring the associated thermal flows according to the experimental procedure given in a previous work.47 The compression−decompression cycles were performed at 1 MPa/min rate. The values of intrusion/ extrusion pressure correspond to the pressures at which half of the total porosity is filled/emptied during the first cycle at a given temperature. The experiments were performed at 295, 330, 345, and 370 K. For the ionic liquid solution, experiments at 295 K are not presented as, at this low temperature, handling of the solution for the preparation of the experiment resulted to be impossible for its very high viscosity. B


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The Journal of Physical Chemistry C The viscosity measurements were carried out by means of a DHR-1 rheometer (TA Instruments) equipped with 25 mm diameter parallel plates geometry. The viscosity was measured in temperature ramp between 25 and 100 °C at 2 °C/min, with an angular frequency (ω) of 1 rad/s and an oscillation strain (γ) of 5%. The choice of these parameters was done by analyzing the behavior of the ionic liquid solution as a function of both the angular frequency and the oscillation strain and selecting the values that ensured that the final measurement was carried out in the Newtonian region. The protocol for these preliminary tests is as follows: first, measuring the viscosity of the material at a fixed angular frequency (ω = 5 rad/s) for strains ranging from 0.0125 to 125% and, second, selecting the strain value within the Newtonian region. This brought us to select γ = 5% oscillation strain. With this value of γ, the viscosity was finally measured for angular frequencies varying from 0.1 to 100 rad/s, which allowed us to select a proper frequency value. Surface tension and contact angle were measured with a DSA 100S Krüss tensiometer, following the experimental procedure described elsewhere.75,76 For surface tension, the pendant drop method was used. For each substance and temperature, the measurements were repeated several times. The uncertainty of temperature measurements for the surface tension experiment was ±0.1 K. The typical uncertainty of surface tension determination with this setup is ±0.1 mN·m−1; in our case, the standard deviation of the mean value (from all points) was below this value. The liquid densities, which are a necessary input data for the determination of surface tension, were measured with an Anton Paar DMA 5000 M densimeter with an uncertainty 90°) and that the variation of θY among the liquids and with temperature is within 3°. The trend is similar to that observed on the pellets; however, as expected for a liquid deposited on a corrugated surface, the absolute values are noticeably lower compared to the ones measured with roughness. 3.2. High-Pressure Intrusion/Extrusion Experiments. 3.2.1. Intrusion. The behavior of {WC8 + water}, {WC8 + sucrose solution}, and {WC8 + ionic liquid solution} systems under high-pressure cycling is demonstrated in Figure 1. For all the systems, a pronounced step of intrusion is observed at pressures of 15−19 MPa. The intrusion pressures at a given temperature are very similar for the three systems, within approximately 2 MPa (Figure 2). The Kelvin−Laplace equation, here written with cos θY as the unknown variable, is useful to obtain an estimate of the Young contact angle θY from the intrusion pressure cos θY = −PintA p /σL

(1)

In eq 1, we assumed that the gas pressure is negligible with respect to the liquid pressure. The pore geometry, which is the same for all the systems, enters eq 1 via the perimeter length L and the projected area Ap of the cavity mouth. Although deviations from the macroscopic Kelvin−Laplace eq 1 might occur in nanoscale confinement,61 they become significant for pores smaller than those considered here.77 In addition, any such effect is expected to be analogous for all the considered liquids. We are thus entitled to estimate the Young contact angle via eq 1. In general, because the three liquids have similar intrusion pressure and surface tension σ (Figure S2) and the pores have the same distributions of L and Ap for the three systems, eq 1 predicts that also the contact angles should be very close. In more quantitative terms, we estimate the ratio L/ Ap ≈ 108 m−1, plugging in eq 1 the data of water at ambient temperature, σ = 0.072 N/m and θY = 105°, which is a reasonable estimate for the Young contact angle of water with a silanized surface.78 Choosing a different reference contact angle would not change the agreement between the three systems, their trend with temperature, and the dependence of extrusion pressure on viscosity discussed below. The resulting contact angles are plotted in Figure S4 (bottom) and show that the data are within 3° from each other and their values decrease with temperature. 3.2.1.1. High-Pressure Calorimetry. We also measured the heat flux during the intrusion process at 370 K for water, sucrose, and ionic liquid solutions. One immediately notices a qualitative difference between the two liquids, with intrusion being endothermic for water and exothermic for the ionic liquid solution (Figure 3). No detectable calorimetric response was recorded for the sucrose solution within the precision of the

3. RESULTS AND DISCUSSION 3.1. Liquids Characterization. Three nonwetting liquids were chosen with similar surface tensions and contact angles but considerably different viscosities. Figure S2 reports the temperature dependence of the surface tensions of the three liquids in air. It can be seen that all the three liquids have surface tensions in a rather narrow range deviating from each other no more than 3% at the temperatures under investigation. At the same time, the difference of viscosity between pairs of liquids is more than 2 orders of magnitude (Figure S3), spanning an overall range of 6 orders of magnitude. As expected, the ionic liquid solution has the highest viscosity, followed by sucrose solution and water. The apparent contact angles measured on WC8 pellets by goniometry measurements are shown in Figure S4. The very large values correspond to a hydrophobic behavior. More importantly, these measurements indicate that the three systems have, essentially, the same wettability properties and a similar decrease with temperature. C


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Figure 2. Temperature dependence of the intrusion and extrusion pressures for {WC8 + water}, {WC8 + ionic liquid solution}, and {WC8 + sucrose solution} as recorded in the isothermal intrusion/ extrusion cycles of Figure 1. The error bars are smaller than the symbols.

Figure 3. Thermal effects upon compression process of {WC8 + water} and {WC8 + ionic liquid solution} at 370 K. The arrow indicates the direction of the endothermic calorimetric signal (heat flux < 0). The thermal flux of {WC8 + sucrose solution} falls below the instrument precision (case not shown in the figure).

medium, and high viscosities. This trend in the flux transfer is striking because one would expect the quasi-static intrusion process to be endothermic, as reported in previous studies.11,22,46−48,63 The sign of the heat flux upon intrusion of lyophobic nanopores is due to the fact that the sum of the partial derivatives of entropy with respect to the three interface areas (LV, SV, and SL) is positive Σ(∂S/∂A)T,V = ∂(σ cos θY)/ ∂T,98,99 and so is the reversible heat transfer δQrev = TΣ(∂S/ ∂A)dASL when intrusion (dASL > 0) is considered. In the present experiments, both σ and θY have similar values and dependence on temperature for the three systems, meaning that this reversible part of heat transfer is not expected to change the sign when the intruding liquid is changed; we remark that this is different than the case discussed, for example, in ref 100 where different systems with different wetting properties are considered. However, intrusion also implies an irreversible, exothermic process in which the liquid intrudes the pores dissipating mechanical energy by viscosity δQirr < 0. To use an electrical analogue, an HLS undergoing intrusion is similar to a resistor through which a constant electrical current flows, which dissipates a power that is proportional to the resistance W = I2R. Because the present experiments happen at constant flow rate (I), which is imposed by the volumetric variations of the piston, the higher the liquid viscosity (R, in the analogy), the larger the heat production rate

Figure 1. PV isotherms at different temperatures for (a) {WC8 + water}, (b) {WC8 + ionic liquid solution}, and (c) {WC8 + sucrose solution}. Lines indicate cycles performed at the normal rate. Red symbols indicate cycles attempted after a 12 h pause following intrusion. Extrusion is always observed for case (a), which allows for the cycle to close, never for case (b), and only for sufficiently high temperatures for case (c).

equipment used. Our results show a correlation between the viscosity of the liquid and heat flux, with the sign of the latter changing from positive to neutral to negative for liquids at low, D


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The Journal of Physical Chemistry C by friction (W). Overall, the sum δQrev + δQirr can have positive (endothermic) or negative (exothermic) sign, depending on the relative importance of the reversible and irreversible terms.30 In the present case, viscous dissipation is expected to be 4000 larger for the ionic liquid solution than for water, which seems to account for the change of sign reported in Figure 3. It should be noted that in ref 71, exothermal effects of intrusion and extrusion were also considered as dynamic ones and were related with internal friction during confined liquid displacement. However, to our knowledge, the present experiments are the first account of the possibility of changing the sign of the thermal flux by changing the liquid properties, more specifically, viscosity, without changing the porous material and its wetting properties. This information can be useful in designing shock absorbers, which indeed require the dissipation of mechanical energy.70 3.2.2. Extrusion. The extrusion process presents the most striking differences among the three liquids. For water, extrusion was observed at all the tested temperatures and at relatively large pressures, ca. 2 MPaFigure 1a. The ionic liquid solution never extrudedFigure 1b. The behavior of the sucrose solution was intermediate, with extrusion happening only at higher temperatures; at 295 K, no extrusion was recorded even after waiting for 12 h (Figure 1c). At 330 K, partial extrusion was observed in the experiments performed at standard intrusion/extrusion rates (1 MPa/min): successive cycles had lower and lower extruded volumes at the end of the extrusion phase, connected with an increasing amount of liquid trapped inside the pores. This partial entrapment may be ascribed to the fact that only a fraction of the pores, presumably the smaller ones, is capable of extruding during the limited duration of the experiment; at the next cycle, less pores are available for intrusion, which results in a decreased ΔV. Only after a 12 h waiting time at ambient pressure, it was possible to fully extrude the sample, as seen from the comparison between the first intrusion/extrusion cycle and the last one performed after this long waiting time (red dots in Figure 1c). At 345 K, extrusion was almost complete (minor deviations from the first cycle), and at 370 K, it was complete. A clear trend is observed in Figure 4 concerning the effect of viscosity on the extrusion pressure: Pext has a negative logarithmic dependence on η, completely inhibiting extrusion for the highest viscosities. With waterthe liquid with the lowest viscositycomplete extrusion is observed after the decompression stage at all the temperatures (Figure 1a), which is in agreement with previous studies on the present porous system.20 With the ionic liquid solution, which has the highest viscosity, there is no extrusion in the whole temperature range even after keeping the system for a long time at atmospheric pressure (7 days). Finally, as already described above, the sucrose solution demonstrates an intermediate behavior (Figure 1c), with no extrusion at room temperature, partial extrusion at intermediate temperaturesfull extrusion achieved only after 12 h waiting timeand complete extrusion at 345−370 K corresponding to lower viscosities. The full extrusion at ambient conditions after adequate waiting time demonstrates a potential of creating self-recovering bumpers based on the liquids/solutions of suitable viscosity, which after the impact absorb a large amount of energy (remain compressed) but recover their initial state after a sufficiently long dwell time. In the following, we interpret the results of extrusion experiments and the effect of the viscosity of liquids in the

Figure 4. Dependence of the extrusion pressure on the viscosity for {WC8 + water} (black), {WC8 + ionic liquid solution} (red), and {WC8 + sucrose solution} (green). The reported temperatures are 295, 330, 345, and 370 K. The grey region indicates the experimental viscosity range at which no extrusion is observedPext is arbitrarily set to zero. The dashed line and the corresponding equation are a guide to the eye to underscore the logarithmic dependence of the extrusion pressure on viscosity. The error bars are smaller than the symbols.

framework of CNT. (Note: It should be noted that alternatively extrusion dynamics was discussed in the framework of percolation theory.56−59) In particular, we follow ref 83, where an explicit expression for the nucleation rate of a bubble of vapor from a viscous liquid was derived based on the previous work by Blander and Katz84 and by using the Rayleigh−Plesset expression for the bubble dynamics.85 In this case, the nucleation rate per unit volume reads J=

kBTσ 3 η|Pext|

ρ0 exp( − β ΔΩ†)

(2)

where β = 1/(kBT) is the inverse thermal energy (kB is the Boltzmann constant), η is the dynamic viscosity, ρ0 is connected to the number density of liquid and vapor, and ΔΩ† is the free-energy barrier for nucleation. We preliminarily note that the nucleation rate J is inversely proportional to the viscosity, which implies that, at the same thermodynamic conditions (P and T), the rates are expected to vary as the inverse ratio of the viscosities. This seems consistent, for example, with the data at 330 K, for which the viscosities are in the proportions 1:15:4000 for water, sucrose, and ionic liquid solutions, respectively, and the extrusion times are below 1 min for water, below 12 h for sucrose, and above 7 days for the ionic liquid solution. To analyze in greater detail eq 2, let us suppose that, for the heterogeneous nucleation case relevant for this experiment, the expression for the prefactor does not change or at least it preserves the same functional dependence on η. The freeenergy barrier in the confined case can be computed, for example, from confined nucleation theory79−82 or from atomistic simulations,55,86 and has the generic expression ΔΩ† = PextVc + σ(ALV + cos θYASV), where Vc is the critical bubble volume and the surface contribution to the free-energy barrier depends on the areas ALV and ASV of the liquid−vapor and solid−vapor interfaces, respectively, and consistently with eq 1, we made the assumption that the gas pressure is negligible as compared to Pext. In fixed-time experiments, such as those considered here, the pressure at which extrusion, that is, bubble nucleation, occurs is determined by the imposed rate J. By E


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dynamic loadings or high frequencies, as well as for the fundamental understanding of the nonwetting liquid behavior under nanoconfinement.

inverting eq 2, it is thus possible to obtain an implicit expression for the extrusion pressure Pext

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PextVc + kBT ln|Pext| ⎡ ⎛ ⎞ J ⎟ + σ(A = −kBT ln η − ⎢kBT ln⎜⎜ LV ⎢ 3⎟ ⎝ ρ0 kBTσ ⎠ ⎣ ⎤ + cos θYASV )⎥ ⎥ ⎦

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b01959. Pore size distribution for C8 porous silica; temperature dependences for surface tension, viscosity, and contact angle for water, ionic liquid solution, and sucrose solution; and scheme for the intrusion/extrusion process (PDF)

(3)

where the second term on the right-hand side is independent of η. For nucleation occurring at sufficiently large Pext, that is, away from bulk liquid−vapor coexistence, which is the case of the present experiments, the linear term on the left-hand side of eq 3 dominates and a dependence of the extrusion pressure on the logarithm of the viscosity is found, PextVc ∝ −kBT ln(η). This prediction can be now compared with the experimental data shown in Figure 4, which, indeed, show a linear trend of Pext versus ln(η). A further confirmation of this simple theory is that the slope is independent of the liquid in agreement with the experimental results. The shift between the water and the sucrose solution curves, instead, indicates that the other terms in eq 3 depend on the nature of the liquid, for example, via ρ0. We remark that the dependence on η is a dynamic effect connected to the viscous slowing down of the bubble expansion implied by the Rayleigh−Plesset equation; accordingly, this weak dependence is encoded in the prefactor of eq 2 and not exponentially in the free-energy barriers: these are thermodynamic quantities unaffected by the dynamics. The fair agreement between the simple theoretical prediction and the experimental data of Figure 4 suggests that the critical volume Vc only weakly depends on the pressure (cf. ref 89).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yaroslav Grosu: 0000-0001-6523-1780 Alberto Giacomello: 0000-0003-2735-6982 Jean-Marie Nedelec: 0000-0002-8243-6849 Jean-Pierre Grolier: 0000-0002-6524-8731 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.G., L.G.F., and A.F. would like to thank the Department of Industry, Innovation, Commerce and Tourism of the Basque Government for funding the ELKARTEK CIC Energigune2017 research program. M.C. and M.G.-R. are grateful for the financial support based on decision no. 2016/23/B/ST8/02968 from the National Science Centre (Poland). S.M. would like to thank the Sapienza University of Rome (Italy) for financial support via the grant “Porous Lyophobic Crystalline Materials for Mechanical Energy Storage”, no. RG11715C81D4F43C.

4. CONCLUSIONS In this work, we investigated the effect of viscosity on the intrusion/extrusion dynamics of a nonwetting liquid in nanopores. For this purpose, three liquids with similar surface tensions and contact angles but different viscositieswater, sucrose solution, and an ionic liquid solutionwere subjected to high-pressure intrusion/extrusion cycling into/from nanoporous grafted silica. Low viscous liquids, water and sucrose solution at high temperature, showed complete extrusion. High viscous solutions, the ionic liquid solution, remained trapped in the pores for an observation time of 7 days at any temperature in the range considered. Liquids at intermediate viscosity, the sucrose solution at intermediate temperatures, can completely recover after a 12 h waiting time. It was also demonstrated that by increasing the viscosity, the sign of the thermal flux of intrusion can be changed from endothermic to exothermic. An explanation of the present calorimetric results based on the viscous dissipation (throttling effects at the nanoscale) was proposed. Overall, these observations can be used to design and create self-recovering bumpers with an enhanced capacity of dissipating energy. Experiments showed a logarithmic dependence of the extrusion pressure on viscosity, which was explained within the framework of CNT as a dynamic effect connected to the viscous slowing down of bubble expansion during extrusion. These pieces of information are essential for the development of energy storage/dissipation applications based on intrusion/extrusion cycles that are expected to work under

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