Temperature Dependence of Nanoconfined Water Properties

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Temperature Dependence of Nanoconfined Water Properties: Application to Cementitious Materials Patrick Alain Bonnaud, Hegoi Manzano, Ryuji Miura, Ai Suzuki, Naoto Miyamoto, Nozomu Hatakeyama, and Akira Miyamoto J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00944 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 15, 2016

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The Journal of Physical Chemistry

Temperature Dependence of Nanoconfined Water Properties: Application to Cementitious Materials Patrick A. Bonnaud,∗,† Hegoi Manzano,‡ Ryuji Miura,† Ai Suzuki,† Naoto Miyamoto,† Nozomu Hatakeyama,† and Akira Miyamoto† New Industry Creation Hatchery Center, Tohoku University, Sendai, Miyagi, Japan, and Molecular Spectroscopy Laboratory, Universidad del Pa`ıs Vasco UPV/EHU, Bilbao, Spain E-mail: [email protected] Phone: +81-22-795-7233. Fax: +81-22-795-7235

To whom correspondence should be addressed NICHe-Tohoku University ‡ Universidad del Pa`ıs Vasco/EHU

∗ †

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Abstract Nanoconfined water exhibits peculiar properties with respect to the bulk that plays a crucial role in damage processes affecting concrete sustainability. We employed molecular simulation techniques to investigate water physical properties in calcium-silicatehydrate nanopores and compare them with bulk water. We considered systems opened to and isolated from the environment to characterize the effect of the density and the fluid order, respectively. On freezing conditions, we found that the most disruptive effect in nanopores of cement paste arises from the hydraulic pressure. Upon heating, the water expansion in the closed porosity is the most disruptive process. Combining thermodynamic, structural, and dynamical data, we found liquid-liquid transitions in the temperature range 180-195 K. Lowering further the temperature, we found from translational mean square displacements glass transitions at ∼170 K for all systems, except for bulk water in the open system, where the transition was located at ∼155 K. Confinement effects on diffusion coefficients in our molecular models are also in very good agreement with experimental data. These findings underscore the importance of accounting for the molecular nature of water to investigate temperature-induced damage mechanisms in cement and concrete.

Introduction Despite its geometrical and chemical simplicity, water has a complex collective behavior 1 that is significantly perturbed in the vicinity of surfaces. 2–4 When surfaces confine water like in small pores, physical properties are even more strongly modified. We find confined water in nature (e.g., living organisms, earth chemical reactions, hydration and reactivity of mineral surfaces), 4,5 in industrial applications (e.g., nanofiltration, catalysis, phase separation), 6–8 and in widespread used building materials like cement and concrete. Through the hydration reaction, 9 the mix of aggregate, sand, cement and water produces concrete, which is a complex, composite material. The main component, the Calcium-

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silicate-hydrate (or C-S-H with C−CaO; S−SiO2 ; H−H2 O), is an inosilicate-like disordered phase resulting from cement hydration that acts as glue (binding phase) in concrete. C-SH can be conceptualized as a disordered aggregation 10,11 of nanoplatelet particles of 5-50 nm in apparent width. 12,13 Aggregation is driven by strong cohesive forces arising from charged, geometrically anisotropic particles. As a consequence, hydrated cement pastes exhibit a multiscaled porous network 14 in which water can adsorb, desorb, and undergo physical changes, playing a crucial role by affecting the overall behavior of the material. 14,15 The mechanical properties of calcium-silicate-hydrates limit the stiffness and strength of concrete structures 16–18 and determine up to a great extent the durability of the material. Since concrete and its related industry are responsible for 5-7% of global CO2 emissions, 19 confined water is therefore critical for concrete sustainability. In the past few years, molecular modeling and simulations were proven very useful in better understanding the role of water on the physical behavior of the ”fully dense” C-S-H phase (i.e., the phase constituting C-S-H nanoplatelet particles). Youssef et al. 20 showed that in such a strong hydrophilic confinement interlayer water (i.e., water in the ∼0.5 nm space between C-S-H layers) adopts a glassy behavior at room temperature. Using molecular dynamics in combination with a reactive force field (ReaxFF), Manzano et al. 21 demonstrated that this ultra-confined space between C-S-H layers with high hydrophilicity promote the dissociation of water molecules to form hydroxyl groups inducing changes in the molecular structure from a layer-like arrangement to a three-dimensional network. By investigating mechanical properties, Hou et al. 22 found that this water dissociation into hydroxyl groups is accompanied by a degradation of mechanical properties. Further studies by Manzano et al. 23 using the same simulation techniques as in Ref. 21 pointed out the role of water as a lubricant in such interlayer space under shear conditions (i.e., in the interlayer region, the denser the water is, the more important the lubricating effect is). Similarly, Hou et al. 24 found that increasing the water content within C-S-H gradually transforms a gel into a layered structure (depolymerization of silicates) affecting mechanical properties of the phase.

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Moreover, the C-S-H phase exhibits a wide range of chemical compositions denoted by the C/S ratio, which varies from ∼1 to ∼2.4 with a mean value around ∼1.7. 25 To reflect this, Abdolhosseini Qomi et al. 26 generated various molecular structures having different chemical compositions and validating them against experiments. In particular, they showed a decrease of hardness and indentation modulus with increasing the C/S ratio. Hou et al. 22,27 further investigated the effect of the chemical composition and found a degradation of the Young’s modulus and the tensile strength for the highest C/S ratios as well as anisotropic mechanical properties because of the layered organisation of ”fully dense” C-S-H. Variations in the C/S ratio (i.e., the substrate chemistry) affect also water structural properties and water dymamics is close to supercooled liquids and glassy phases. 28 Beyond the interlayer space (.1 nm), the C-S-H phase exhibits a gel porosity with widths between approximately 1 and 10 nm, 14 which is strongly dependent of the phase mesostructure. Bonnaud et al. 29 recently investigated by molecular simulations cohesion forces among C-S-H particles at the origin of this mesostructure and found a strong effect of particle aspect ratio and crystallographic misorientation on cohesion forces. While the upper bound (10 nm) is still challenging to access in molecular simulations, Bonnaud et al. 30,31 investigated the lower bound for various relative humidities (RH) and temperatures. In a first investigation, 30 they demonstrated that changes of the water content induced by variations of RH at room temperature in the smallest gel pores affect cohesion between C-S-H particles (i.e., the more water there is, the less cohesive the material is). Furthermore, they highlighted the role of calcium ions as being the origin of cohesion within the C-S-H phase. In their second investigation 31 at the molecular scale, they explored calcium-silicate-hydrate mechanical properties at high temperatures. The results highlighted the critical role of confined water within C-S-H and between particles separated by about 1 nm. Upon temperature driven water desorption, C-S-H particles densified due to shrinkage, inducing an increase in the mechanical properties in fair agreement with experimental works. 32 In the related experimental temperature range 100-200℃, a water loss from the interparticle space was shown, once again in agreement with

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experiments. 33 When temperature was raised, computed pore pressures between C-S-H particles exhibited a transition temperature (located at an experimental temperature ∼112℃) below which cohesion was increased in the material and above which cohesion was decreased. This result is in qualitative agreement with maximum hardness 32 (∼200℃) and maximum macroscale compressive strength 34 (∼200-300℃) observed experimentally. The aforementioned work was based on grand canonical Monte Carlo simulations to equilibrate the water content in the nanoporous C-S-H structure with an environment defined by its temperature and chemical potential. In other words, water molecules entered and left the porous structure driven by laws proportional to the Boltzmann factor 35 to reach an equilibrium state. Such conditions correspond to a pore directly in contact with the environment or connected to a porous network with a very high permeability. In the remainder of this work, we called this model open pore. Permeability of a cement paste is strongly related to the amount of mixing water used during cement hydration and commonly defined by the water-to-cement ratio (W/C). The higher the W/C is, the higher the permeability in cement is. 36 Temperature also affects permeability as shown experimentally, 37 where higher permeabilities were found in high performance concrete samples (W/C= 0.30) subjected to high temperatures (≤600 K). Note that the previous finding is in good agreement with the previous observation of particle shrinkage in simulation when temperature is raised. 31 Overall, the previous work constitutes a higher bound (high permeability) for the behavior of pore solution in a cement paste. In this work, we investigated the lower bound (no permeability) by considering a closed pore model, where exchanges of water molecules were prohibited (constant water content/density). We also extended the simulation work to low temperatures (down to 100 K) for both models. In such a way, by combining results in the open and closed pore models, we got valuable molecular-scale information to better understand freezing-thaw damages in cement pastes, which is critical for cement-based infrastructures. Indeed, with the open pore model we simulated effects due to hydraulic pressure (densification of water) and with the closed pore model

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we simulated pressures induced by an increase of the fluid order (or crystallization pressure if the crystal phase is formed in the porous network). Previous experimental, theoretical, and modeling studies 15,38–42 showed a competition between these two pressures. Depending on experimental conditions, one pressure is dominant over the other. Furthermore, structural and dynamical properties were also investigated, since they provide useful information about the state of confined solutions (water and calcium ions) in C-S-H nanopores as a function of temperature. In the remainder of this article, we first present methods used to build our molecular models and to simulate our systems. Then, we show results on thermodynamic and dynamical properties. Finally, we discuss the results and their implications for cement durability in extreme conditions.

Methods Molecular model of a C-S-H nanopore We performed molecular simulations on a previously designed molecular model of a calciumsilicate-hydrate nano slit pore. 30,31 It has been used with success to estimate the effect of water on cement mechanical properties at ambient 30 and high temperatures. 31 This model is built using the molecular structure of calcium-silicate-hydrate suggested by Pellenq et al. 18 as a basic unit. Note that in the remainder of this work, we follow the notation in cement chemistry denoting CaO as C, SiO2 as S, and H2 O as H such as calcium-silicate-hydrate becomes C-S-H. In the mentioned C-S-H structure, two silicate-rich layers are explicitly described in the simulation box. The calcium-to-silicon ratio of this structure is C/S = 1.65, similar to the mean value found using energy dispersive X-ray analysis 43,44 of hardened Portland cement pastes (C/S=1.70). Surface charge of this C-S-H molecular structure arises from ionized silanol groups in the silica chains; we used the PN-TrAZ force field 30 to reflect this with σ=-0.73 C.m−2 . The surface charge is compensated by calcium counterions to maintain the electroneutrality. The original molecular model is enclosed in a triclinic 6


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box of (a, b, c) = (1.33 nm, 2.95 nm, 2.37 nm) with the following angles (α, β, γ) = (92.02°, 88.52°, 123.58°). The C-S-H nano slit pore is built by duplicating Pellenq’s molecular model along the x-direction. Then, the two silicate-rich layers were separated by a distance of 1 nm. This, added to the space between C-S-H layers in the bulk model (interlayer porosity of ∼0.483 nm), implies an effective pore width of Heff. ∼ 1.483 nm (see Supporting Information for details). The resulting molecular model is enclosed in a triclinic box of (a, b, c) = (2.66 nm, 2.95 nm, 3.37 nm) with previously mentioned angles. Fig. 1 shows molecular configurations taken from the open pore set of simulations for various temperatures. Note that the subscript ‘w’ was added to atoms and ions belonging to the fluid so that (i ) oxygen atoms and hydrogen atoms of water molecules are labelled Ow and Hw , respectively; (ii ) calcium counterions are labelled Caw . Silicon atoms, oxygen atoms, and calcium ions in the C-S-H molecular structure are labelled Si, O, and Ca, respectively.

Interatomic Potential, Monte Carlo simulations, and Molecular Dynamics To describe interactions among atoms in the C-S-H molecular structure and the pore solution (water molecules and calcium counterions), we used classical potentials combining dispersionrepulsion interactions (short-range interactions) with electrostatic interactions (long-range interactions). We used the PN-TrAZ method 45 to derive potential parameters. Ref. 30 provides full details of the potential parameters used to model these interactions. For interactions between water molecules, we employed the rigid-SPC model 46,47 in order to simulate a large number of water molecules (Nwater per simulation box ∼440 molecules for the lowest temperatures) in a reasonable amount of time. In the course of the simulation, dispersionrepulsion interactions were summed within a cutoff radius of Rcut ∼ 1.2 nm. The Ewald summation technique was employed to account for the long-range component of the electrostatic interactions with parameters κ ∼ 2.4 nm−1 and kmax = 5. In this work, we defined a closed pore model and an open pore model corresponding to 7



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molecular simulations in the canonical ensemble and the grand canonical ensemble, respectively. In the canonical ensemble the number of atoms and molecules (Ntotal ), the volume of the system (V ), and the temperature (T ) are constants. In the grand canonical ensemble the volume V of the system is constant and is in equilibrium with an infinite reservoir of water molecules of defined chemical potential µwater and temperature T . 35 The chemical potential is related to fugacity (fwater , pressure of the infinite reservoir of water if it were an ideal gas) and temperature (β = 1/kB T ) by µwater = ln(βfwater Λ3water )/β, where p Λwater = βh2 /(2πmwater ) is de Broglie thermal wavelength, h is Planck’s constant, and

mwater is mass of a water molecule. In the open pore (grand canonical ensemble), only the number of water molecules is allowed to fluctuate in the simulation box as calcium counterions are treated in the canonical ensemble: each ion is allowed to move while the number of ions remained constant. As these ions compensate the surface charge of the silicate-rich layers, this ensures that the system remains electroneutral. For both sets of simulations (closed/open pore), silicate-rich layers are kept fixed (rigid) in the course of the simulation to reduce computing time. Then the adsorbate/substrate interactions were computed using an energy grid. The potential energy is calculated at each corner of each triclinic element (la , lb , lc ) = (0.02 nm, 0.02 nm, 0.02 nm) with the following angles (α, β, γ) = (92.02°, 88.52°, 123.58°). In the course of simulations, grid values are interpolated in a linear fashion to provide an accurate estimate of the energy. Such a procedure has been shown to simulate adsorption in mesoporous media of complex morphology and/or topology without a direct summation over matrix species during Monte Carlo runs. 48 Periodic boundary conditions were used along the a, b, and c directions. As starting point we defined a reference thermodynamic state at T0 = 300 K and fwater = P0 (T0 ), where P0 is the saturating vapor pressure (the pressure at which for a given temperature we are at the bulk liquid-gas equilibrium), corresponding to thermodynamic conditions for which rigid-SPC water potential parameters were developed. 46 At room temperature, we can reasonably assume that the pressure of the gas reservoir is Pwater = fwater

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(ideal gas). For the rigid-SPC water model, this pressure is P0SPC (T0 = 300 K) = 4.4 kPa. 49 We seek to characterize the effect of temperature on confined water properties in C-S-H nanopores. Therefore, starting from the latter reference state, for each set of simulations (closed/open pore) we increased (resp. decreased) the temperature with a step of δT = 5 K. For each new simulation point at Tn = Tn−1 ± δT , the final configuration of the previous simulation point (Tn−1 ) was taken as the initial configuration. The temperature range is chosen so that (i ) during heating the system is passing through the liquid-gas transition temperature for confined water (T0confined ) and goes up to 575 K, which is ∼20 K below the critical temperature (Tc ) for the rigid-SPC water potential (∼593.8-596 K), 50 (ii ) during freezing the system is passing through the bulk melting temperature of the rigid-SPC water SPC model, which was reported to be Tmelt ∼ 190.5 K for an external pressure of 100 kPa, 51 and

goes down to 100 K in order to ensure that the bulk crystallization temperature of rigid-SPC SPC SPC water is reached (Tfreeze ), which should be very close to Tmelt , as well as the confined crystalSPC, confined ). 96 computations were done for each set of simulations lization temperature (Tfreeze

(closed/open pore). Previous experimental work on porous silica gels 52 showed that in a pore of ∼1.5 nm the freezing temperature Tfreeze is reduced by ∆T ∼ 27 K. By analogy with the aforementioned hydrophilic material, we expect in our C-S-H pore of ∼1.483 nm a freezing temperature depletion of ∆T > 27 K, C-S-H being more hydrophilic than silica gels and calcium counterions being in the pore solutions. Nevertheless, only few molecular simulation studies reported ice nucleation like, for example, the work of Matsumoto et al. 53 for bulk water and the work of Han et al. 54 for confined water in hydrophobic nano slit pores. For the former, a density slightly lower than bulk water at room temperature (ρwater = 0.96 g.cm−3 ) was used to increase the degree of supercooling as well as the nucleation rate. 53 It still necessitated several simulations to observe a nucleation event. For the latter, a water bilayer confined in a hydrophobic slit pore was considered. 54 Therefore, very specific conditions were used to obtain water crystallization. Generally, considered volumes are so small in simulations that the probability of having an event either by homogeneous nucleation

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or by heterogeneous nucleation is extremely low. Even experimentally, Sun and Scherer 40 predicted for cementitious materials (mortars) that only one nucleus able to form ice would appear at −1℃ in a cube of ∼35 cm side. Again, Sun and Scherer 41 found in thermoporometry experiments on cementitious materials that the so-called unfrozen layer (the layer close to the confining surface where the fluid structure is strongly modified over several molecular diameters) is about 1.0-1.2 nm thick leading them to the conclusion that no freezing would occur in pores with diameters ≤ 4.5 nm, at least down to −40℃. Therefore, we did not expect the formation of ice in our work since the pore size is ∼1.483 nm, but rather the formation of a glass. Note also that beyond 300 K, we increased the temperature (heating). In such a way, we performed a desorption of the water content. At room temperature and for varying relative humidities, it is well known that for pores large enough an hysteresis between water adsorption and water desorption can exist. 14,30,55,56 Here, we showed in Fig. S2 of Supporting Information that water contents during the adsorption path (cooling of our systems) and the desorption path (heating of our systems) are very similar with a capillary condensation occuring at a temperature (∼332.5 K) very close to the cavitation temperature (∼340 K). We even showed that excess potential energies as well as pore pressures are also very similar between heating and cooling. Therefore, in the remainder of this work, when we analyzed data at intermediate and high temperatures, we considered that properties were the same during adsorption (cooling) and desorption (heating). Finally, using last configurations of well-equilibrated systems in Monte Carlo simulations, we employed the DL POLY Simulation Package (version 2.19) to perform Molecular Dynamics simulation runs (MD). 57 Independently of the original set of simulations (closed/open pore), MD runs were carried out in the canonical ensemble; the temperature in the simulation box was maintained using a Nos´e-Hoover thermostat 58,59 with a relaxation time of 1.0 ps. Standard deviations for each temperature of our sets of simulations (closed/open pore) as well as bulk data for the same thermodynamic conditions have been reported in Fig. S6 of Supporting Information. Largest standard deviations and overlaps between adjacent sim-

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ulation points were found at high temperatures and for systems containing just a few water molecules like in the open pore model. Overlaps between standard deviations of neighbor simulation points remain at low temperatures. Nevertheless, averages remain very close to targeted temperatures. MD trajectories were integrated using the leapfrog integrator algorithm with a time step of 1 fs. Integration of the rotational part of equations of motion for rigid-SPC water molecules was done with the quaternion algorithm. 60 After an equilibration run of 2 ns, we performed a sampling run of 50 ns with a sampling rate of 1 ps. If water (Ow and Hw atoms) and calcium counterions (Caw ) were free to move in the course of the simulation, Si, Ca, and O atoms of the silica-rich layers were kept frozen. As in Monte Carlo simulations, periodic boundary conditions were used. The PN-TrAZ potential functions for the dispersion-repulsion interactions in the Molecular Dynamics simulations were fitted with n-m interaction potentials available in DL POLY: n m r0 r0 E0 , m −n Uij = n−m rij rij

(1)

where E0ij is the well-depth of the interaction potential between an atom i and an atom j, r0 is the distance between the two atoms when the potential energy is minimum Uij = −E0ij , and n and m are power values for the repulsion and dispersion terms. We showed in Supporting Information results of the fit of PN-TrAZ potential functions with n-m interaction potentials. A good agreement is obtained with the best accuracy in the well-depth region of the potential. Furthermore, previous work on amorphous, porous silica 55 also showed that such a change in mathematical form for interaction potentials does not affect significantly the potential energy and the structure of water. Potential parameters for MD are summarized in Tab. 1. As in Monte Carlo simulations, the Ewald summation technique was employed to take into account the long-range part of electrostatic forces in MD simulations.

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Table 1: n-m potential parameters for Molecular Dynamics simulations resulting from the fit of PN-TrAZ potentials used in Monte Carlo simulations. Fluid species Hw

Ow

Caw

C-S-H species O Si Ca O Si Ca O Si Ca

E0 × 104 [Ha] 1.9588 0.1513 1.0568 2.5602 0.2833 1.5472 0.9750 0.1355 0.6374

r0 [a0 ] 5.6633 7.1144 5.6316 6.9800 8.1669 6.8511 7.3694 8.2844 7.1690

n 8.16281 12.0680 8.36479 11.5515 15.0758 11.3548 13.9288 17.1895 14.3334

m 8.16279 7.35114 8.36435 7.3271 6.8112 7.6490 6.8068 6.4881 6.7356

Results and discussion Thermodynamic properties of confined water In this work, we sought to understand nanoconfined water behavior in C-S-H as a function of temperature, where gas-liquid and liquid-solid (ice or glass) phase transitions may occur. To investigate wether or not confined water in our porous C-S-H model undergoes phase transitions (gas-liquid and/or liquid-solid), we followed two thermodynamic properties: the excess potential energy (excess of energy with respect to the reference state defined above) and the pore pressure. Potential energy (or the excess potential energy) gives a useful indication of the occurrence of a first-order phase transition like for the gas-liquid or the liquid-solid phase transition. For example, liquid-ice phase transition was previously characterized by a drop (resp. a jump) in potential energy at the freezing (resp. melting) temperature. 53,54,61,62 The pore pressure computed as a function of temperature gave us useful information on the mechanical behavior of the nanopore. Indeed, the two sets of simulations designed above helped us to discriminate the more drastic disruptive effect between the hydraulic pore pressure and the pore pressure induce by the increased order of the fluid (or crystallization pressure in case of liquid-ice phase transition).

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Excess potential energy We reported in Fig. 2 excess potential energies as a function of temperature (from 100 K to 575 K) for the closed and the open pore sets of simulations. As previously defined, the reference state is taken at 300 K and we computed the total, the fluid-fluid, and the fluid-solid contributions to the excess potential energy with ∆U (total) = U (T ) − U (300K), ∆U (fluid-fluid) = U ff (T ) − U ff (300K), and ∆U (fluid-solid) = U fs (T ) − U fs (300K), respectively, where U , U ff , and U fs are the total, the fluid-fluid, and the fluidsolid contributions to the potential energy and summarized in Tab. 2. For comparison, we also reported in Fig. 2 and Tab. 2 values for bulk water in a closed system (CS), where water density is constant (equivalent to simulations in the closed pore), and values for bulk water in an open system (OS), where density is a function of temperature (equivalent to simulations in the open pore). For bulk water, the obtained potential energy per water molecule (∼ −41.5 kJ/mol) is close to the experimental potential energy derived from the heat of vaporisation at 298 K (∼ −41.8 kJ/mol). 46 Note that for bulk water, where only fluid-fluid contributions are considered, the potential energy at the reference state is negative, i.e., cohesive behavior originates from fluid-fluid interactions. In contrast, for confined water in C-S-H and for both sets of simulations, the fluid-fluid contribution to the potential energy (including water) is positive above 300 K. In fact, cohesion is ensured by fluid-substrate interactions that keep negative the potential energy. Table 2: Potential energies at the reference state (300K) computed in Monte Carlo simulations for the closed and the open pore models as well as for the closed and the open systems.

Potential energy contributions Total [kJ/mol] Fluid-Fluid [kJ/mol] Fluid-Solid [kJ/mol]

C-S-H nanopore OP CP −144929.10 −144740.35 50227.93 50700.11 −195157.03 −195440.45

Bulk water OS CS −19225.80 −19235.14 — — — —

In the closed pore (or closed system; Fig. 2a), we observed that total excess potential energies are decreasing from 575 K to 100 K. Two regimes are observed. At high and in14


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termediate temperatures, total excess potential energies have a non-linear behavior lasting down to 215 K and down to 190 K for confined water in C-S-H and for bulk water, respectively. The non-linear decrease is steeper for bulk water showing that confinement affects the ability of water to reduce its potential energy in this temperature range. Under the transition temperature, total excess potential energies follow a linear behavior down to 100 K. The slope for bulk water (∼14.54 kJ/mol/K) is steeper than for confined water (∼12.83 kJ/mol/K) meaning again that confinement is hindering the ability of water to reduce its potential energy when temperature is decreased. As a consequence, if a nucleation event had occurred (freezing), it would have first appeared in the bulk phase in fair agreement with previous experiment on water freezing in porous silica 52 and with theory. 39 In other words, confinement induces a depletion of the freezing temperature. Focusing on fluid-fluid and fluid-solid contributions to the total excess potential energy, we observed that the fluid-fluid part contributes mainly to changes in the total excess potential energy (on average ∼81%) and is at the origin of the observed transition in the total behavior. The fluid-solid part contributes less to the excess potential energy (on average ∼19%) and slightly decreases while going down to 100 K. Nevertheless, no change of the behavior is observed. For the open pore (or open system; Fig. 2b) and as for the closed pore set of simulations, the total excess potential energy is decreasing non-linearly down to a transition temperature located at ∼200 K and ∼215 K for confined water in C-S-H and bulk water, respectively. Above this temperature, a jump in total excess potential energy (∼5×103 kJ/mol) is found at ∼340 K for confined water in C-S-H corresponding to the liquid-gas transition in confinement through a cavitation process. Indeed, the displacement of a meniscus cannot take place during water desorption due to the molecular model design and the use of periodic boundary conditions. Note that for bulk water, we stopped recording data at 315 K since the simulation box is completely empty above that temperature (gas state). Again, the decrease of the total excess potential energy is faster for bulk water than for confined water in C-S-H. Water is affected by the confining C-S-H substrate and, therefore, cannot reduce its potential energy

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as fast as for its bulk counterpart. Under the transition temperature and as for the closed pore model, we found a linear regime with a slope for bulk water (∼19.68 kJ/mol/K) steeper than for confined water in C-S-H (∼18.51 kJ/mol/K). Interestingly, while for the closed pore model the transition temperature for confined water is higher than the bulk water one, in the open pore model the transition temperature for bulk water is higher than the one for confined water. Water density is constant in the closed pore and only an increase of the fluid order can change properties under freezing. Water densification is the main effect in the open pore. Therefore, the potential energy transition temperature is advanced when only the fluid order is increased (constant density) under freezing, while the transition temperature for confined water is delayed when water can densify. Like for the closed pore set of simulations, the fluidfluid part is mainly responsible for the behavior of the total excess potential energy with an average contribution of ∼74%. The observed jump in the total potential energy is due solely to the fluid-fluid part, since it originates from the liquid-vapor phase transition. The linear behavior at low temperatures ( 0.06 × 10−5 cm2 .s−1 ). In the open pore, in-plane self-diffusivities are nearly constant from 450 to 575 K (1.74 < 1000/T < 2.22) and with values ∼0.6 × 10−5 cm2 .s−1 . As can be seen in Fig. 1, at such temperature range only few water molecules (in the first water layer) are adsorbed at pore surfaces (the pore is not full of water). These in-plane self-diffusivities reflect water dynamical behavior in the vicinity of pore surfaces, where structural and dynamical properties are significantly affected with respect to the bulk. Since C-S-H is a strong hydrophilic substrate, water mobility is reduced. From 450 to 340 K (2.22 < 1000/T < 2.94), the adsorbed water layer at the pore surface is becoming thicker and thicker. More water molecules are less affected by the substrate, since they are located farther from the pore surface. So, in-plane self-diffusivities increase smoothly with the thickening of the adsorbed water layer. The diffusivity jump at 340 K (1000/T ∼ 2.94) is due to cavitation (i.e., the sudden pore emptying). Water self-diffusivity in our C-S-H open nanopore of Heff. ∼ 1.483 nm cannot exceed ∼2.5×10−5 cm2 .s−1 . Below 340 K, water in-plane self-diffusivity decreases and reach particularly low values down to ∼190 K (1000/T ∼ 5.26). Note also that in the range 320-340 K (2.94 < 1000/T < 3.125), water density in the open pore model is lower than in the closed pore model (see Fig. S8 in Supporting Information) allowing higher water mobility and, therefore, higher self-diffusion coefficients. Beyond 340 K (1000/T < 2.94), in-plane self-diffusivity of water in the closed pore model is always higher than in the open pore model. Indeed, in the former case the pore is full of water, while in the latter case water content decreases with most of the remaining water molecules in the

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vicinity of pore surfaces with a strongly hindered dynamics. Furthermore, we used in Fig. 4 the same plot scheme as in the work of Chen et al. 71 In such approach, the authors were able to characterize dynamic crossover phenoma in bulk water. 71 More particularly, they ran long MD simulations of bulk water (TIP4P-Ew model) and extracted self-diffusion coefficients in the temperature range 200-260 K. On the basis of these data, they found a crossover between an Arrhenius behavior and a Vogler-Fulcher-Tammann (or VFT or super-Arrhenius) behavior at TL ∼ 215±5 K. The aforementioned trend was also found in the α-relaxation time (taken from the fit of self-intermediate scattering functions using the relaxing cage model). 71 The bulk melting temperature of the TIP4P-Ew water model was reported to be ∼244 K. 72 Assuming that the bulk crystallization temperature is very close to the melting temperature, the transition lies ∆TL = Tfreeze − TL = 34-24 K lower than the freezing point. Regarding the rigid-SPC/E water model, earlier simulation of bulk water at a density of 1.0 g.cm−3 found TL ∼ 212 K 73 (∆TL ∼ 3 K), while simulations of confined water in a cylindrical silica nanopore of 1.5 nm in diameter and for a density of 1.0 g.cm−3 exhibited TL ∼ 215±5 K 74 (−5 ≤ ∆TL ≤ 5 K). The two aforementioned results show that the crossover temperature in simulations is nearly independent of confinement effects down to a pore size of 1.5 nm at constant water density. Experimentally, the transition temperature TL for water has been observed in water films less than 500 nm thick (TL ∼ 228 K), 75 in silica-based nanopores (TL ∼ 215-250 K), 76–79 clays (TL ∼ 185 K), 80 and cement (TL ∼ 145−231 K), 81–83 which is generally around the freezing point of pure supercooled water, 84 233 K (−17 ≤ ∆TL ≤ 88 K). Here, we have chosen to refer to the freezing point of pure supercooled water, since conditions are very close to molecular simulations, where impurities leading to heterogeneous nucleation are not considered. The crossover temperature TL was interpreted as a liquid-liquid transition (or fragile (super-Arrhenius) to strong (Arrhenius) transition), and it is attributable to intrinsic water properties, 71 or to confinement effects on the cooperative rearrangements of water. 82,83,85 Note the presence of this transition in other glass-forming systems. 71,86–88 Furthermore, Chen et al. approximated the water glass

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transition temperature (Tg ) by the ideal glass transition (Tg, id. ) as defined in the VoglerFulcher-Tammann (VFT) model. They found Tg ∼ 190 K. 71 For cement, on one side, Quasi Elastic Neutron Scattering experiments (QENS) in white cement showed the glassy nature of water around TL ∼ 231 K (∆TL = 2 K) and the presence of a large amount of immobile water. 81 On the other side, Broadband Dielectric Spectroscopy in tricalcium silicate pastes have identified several water relaxation processes. 82,83 For the one attributed to C-S-H pores of 1-3 nm, the glassy nature of water was found around TL ∼ 145 K (∆TL = 88 K). Similarly to Chen et al., we fitted our data in Fig. 4 with a VFT model,

DH2 O =

D0V F T

exp

B − T − Tg, id.

(6)

for large and intermediate temperatures, where D0V F T , B, and Tg, id. are, respectively, the self-diffusivity at the high temperature limit, a quantity related to the activation barrier energy, and the ideal glass transition at which the VFT model diverges, 89 and an Arrhenius model, DH2 O = D0 exp

Ea − kB T

(7)

for low temperatures, where D0 and Ea are the self-diffusion at infinite temperature and the activation energy of the diffusion process, respectively. Fitting relsuts are summarized in Tab. 3. For bulk water, we found crossover temperatures located at ∼185 K and ∼180 K for the closed and the open system, respectively. For confined water, we found crossover temperatures located at ∼195 K and ∼190 K for the closed and the open pore, respectively. Note also the additional crossover between two Arrhenius regimes in the case of the closed pore model (∼175 K). Since for the rigid-SPC water model the freezing temperature is ∼190.5 K, the range where we found our simulated crossover temperatures is −4.5 ≤ ∆TL ≤ 5.5 K. It is in fair agreement with the previously mentioned experimental and simulation studies. 71,72,74,81–83 It is worth noting that usually simulation works like Ref. 73 or Ref. 74 study

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Table 3: Arrhenius and Vogler-Fulcher-Tammann (VFT) parameters obtained by fitting self-diffusion coefficient of water in Fig. 4.

Model Bulk water (CS) Bulk water (OS) Confined water (CP) Confined water (OP)

T [K] T ≥ 185 T < 185 T ≥ 180 T < 180 T ≥ 195 195 > T ≥ 175 T < 175 330 ≥ T ≥ 190 T > 190

Arrhenius D0 Ea [cm2 .s−1 ] [kJ/mol] — — 1267.85 35.48 — — 1.66 24.42 — — 46.67 32.48 0.47 27.24 — — 3078.12 40.46

VFT D0V F T 2 −1

[cm .s ] 63.84 × 10−5 — 115.04 × 10−5 — 28.23 × 10−5 — — 47.67 × 10−5 —

B [K] 467.37 — 627.16 — 550.67 — — 667.35 —

Tg, id. [K] 128.84 — 110.27 — 126.33 — — 121.19 —

water diffusivity as a function of temperature for a constant density. Here, we show that even when the density varies as a function of temperature (water densifies when lowering the temperature in the open system/pore), the transition between a super-Arrhenius behavior and an Arrhenius behavior is still observed. Even more interesting, we observed that our simulated liquid-liquid transition temperatures (TL ) falls in the temperature range where we already observed transitions in excess potential energies and order parameters (e.g., bulk water in the closed and open system and confined water in the open pore). Therefore, what we observed in thermodynamics, structural, and dynamics properties of bulk and confined water is an overall signature of the liquid-liquid transition. As mentioned before, Chen et al. 77 found an ideal glass transition located at 190 K, which is 54 K lower than the freezing point of TIP4P-Ew bulk water. Other simulations of rigidSPC/E bulk water located the ideal glass transition at ∼125 K, 73 which is 90 K lower that SP C/E

SP C/E

the freezing point of SPC/E water (Tf reeze ∼ Tm

= 215 K 51 ). Experimentally, the ideal

glass transition was found to be at 118 K in less than 500 nm thick water films, 75 ∼114.5 K in a silica based molecular sieve, 76 187 K in nanoporous silica, 77 165 K in partially saturated Vycor (a mesoporous silica), 78,79 and 223 ± 1 K in white cement, 81 which is respectively

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115 K, 118.5 K, 46 K, 68 K, and 10 K lower than the freezing point of pure supercooled water (233 K). 84 In this study, we found ideal glass transitions ∼61.7 K and ∼80.2 K lower than the bulk freezing temperature of rigid-SPC water for the closed system and the open system, respectively. For confined water, the ideal glass transition is located ∼64.2 K and ∼69.3 K lower than the bulk freezing temperature for the closed and the open pore models, respectively. Note that for confined water the ideal glass transition is very similar for both models. Our simulation results are in reasonably good agreement with both simulation and experimental data considering the wide scattering of values (difference with respect to the freezing point in the range 10-118.5 K). We found the least agreement with experimental data of Zhang et al. in white cement 81 and the best agreement with experimental data of Zanotti et al. in partially hydrated mesoporous silica. 78,79 In our simulations, the lower location of the ideal glass transition in the open system model with respect to the closed system model is explained by the rise of water density when lowering the temperature. Indeed, it disturbs strongly the hydrogen bond network and, therefore, delays the formation of a glass phase. In addition, we observed from our bulk and confined data that the more dense the water is, the lower is the ideal glass transition temperature. Comparing ideal glass transition temperatures for closed system and for closed pore models, we observed almost identical values (∆T ∼ 2.5 K) even if water density is higher in the bulk than in the pore (∼7-11%). In that case, the density difference is compensated by confinement effects (pore walls disturbing water structure (density profile oscillations in Fig. S12 in Supporting Information) and dynamics) leading to similar temperature values. Comparing the open system and the open pore models, the larger temperature difference (∆T ∼ 10.9) is chiefly attributable to high water densities (>1.0 g.cm−3 ) and the larger density difference between bulk and confined water (∼14%) at low temperatures (Fig. S8 in Supporting Information). In that case, effects due to confining surfaces on water properties are not sufficient to compensate the density difference between bulk and confined water resulting in a lower ideal glass transition for the bulk. For bulk water in the Arrhenius regime, we found activation energies in the range 24-35

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kJ/mol. Our simulation values of activation energy correspond to 38-55% of the computed value based on molecular simulations of bulk SPC/E water at a density of 1.0 g.cm−3 , Ea ∼ 65 kJ/mol. 73 Nevertheless, the aforementioned value is closer to the average experimental activation energy for self interstitial water diffusion in bulk ice, ∼58.54 kJ/mol 90 and the activation energy for crystal diffusion in 500 nm thick films of ice, 59 kJ/mol. 75 Moreover, Smith et al. 75 found on the basis of experimental results an activation energy of 170 kJ/mol for water diffusion in amorphous ice produced by water deposition on a low-temperature substrates (

Temperature Dependence of Nanoconfined Water Properties

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