Static field gradient NMR studies of water diffusion in mesoporous silica

Max Weigler a, Edda Winter a, Benjamin Kresse a, Martin Brodrecht b, Gerd Buntkowsky b and Michael Vogel *a
aInstitut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany. E-mail:
bEduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany

Received 6th March 2020 , Accepted 9th June 2020

First published on 10th June 2020

NMR diffusometry is used to ascertain the pore-size dependent water diffusion in MCM-41 and SBA-15 silica over broad temperature ranges. Detailed analysis of 1H and 2H NMR stimulated-echo decays reveals that fast water motion through voids between different silica particles impairs such studies in the general case. However, water diffusion inside single pores is probed in the present approach, which applies high static field gradients to enhance the spatial resolution of the experiment and uses excess water in combination with subzero temperatures to embed the silica particles in an ice matrix and, thus, to suppress interparticle water motion. It is found that the diffusion of confined water slows down by almost two orders of magnitude when the pore diameter is reduced from 5.4 nm to 2.1 nm at weak cooling. In the narrower silica pores, the temperature dependence of the self-diffusion coefficient of water is well described by an Arrhenius law with an activation energy of Ea = 0.40 eV. The Arrhenius behavior extends over a broad temperature range of at least 207–270 K, providing evidence against a fragile-to-strong crossover in response to a proposed liquid–liquid phase transition near 225 K. In the wider silica pores, partial crystallization results in a discontinuous temperature dependence. Explicitly, the diffusion coefficients drop when cooling through the pore-size dependent melting temperatures Tm of confined water. This finding can be rationalized by the fact that water can explore the whole pore volumes above Tm, but is restricted to narrow interfacial layers sandwiched between silica walls and ice crystallites below this temperature. Comparing our findings for water diffusion with previous results for water reorientation, we find significantly different temperature dependencies, indicating that the Stokes–Einstein–Debye relation is not obeyed.

1 Introduction

Water diffusion in porous media is of fundamental importance in both nature and technology.1 It enables biological and geological processes and defines applications, e.g., in heterogeneous catalysis and drug delivery. Therefore, many scientific studies ascertained translational motion of water in various confinements.2–18 It was found that the mobility of water is usually significantly reduced in nanosized spaces, although there are notable exceptions.19,20 Despite important insights from simulation studies,19–32 a comprehensive understanding of the dependence of water diffusion on the properties of the confinement is, however, still lacking to this day, limiting knowledge-based optimization of applications.

To gain detailed knowledge about the diffusion behaviors of confined waters, it is necessary to employ matrix materials with controllable pore parameters. Therefore, many workers investigated water confined to MCM-41 or SBA-15 silica, which feature well-defined cylindrical pores with adjustable diameter d in the nanometer range.33 Furthermore, it is important to ascertain mechanisms for water transport in confinement. For this purpose, comparisons of short-range and long-range motions are useful. Finally, it is advisable to observe water properties in broad temperature ranges. In particular, the supercooled regime of water attracted considerable interest in recent years because it is widely believed to host the origin of the anomalous properties of this liquid.34 Explicitly, this temperature range was proposed to encompass a liquid–liquid critical point associated with a phase transition between high-density (HDL) and low-density (LDL) liquid phases of water.35

Neutron scattering works studied translation motion of confined waters on length scales of ∼1 nm. For MCM-41 confinements, it was observed that the self-diffusion coefficient D of water is smaller in narrower pores.3 Moreover, a fragile-to-strong dynamical crossover from non-Arrhenius to Arrhenius behavior was reported when cooling through ca. 225 K and related to the proposed HDL–LDL transition.4,5 Similar dynamical crossovers were also found in various approaches to the rotational motion of confined waters, but the interpretation of this phenomenon remains highly controversial.36–39

In NMR studies, pulsed (PFG) or static (SFG) field gradients were applied to probe diffusion of confined waters on length scales of ∼1 μm. For MCM-41 materials, some workers reported that water diffusion, even in very narrow pores with diameters below 2 nm, is hardly slower than in the bulk.12,13 Moreover, they took a kink in the temperature dependence of the diffusion coefficients D near 225 K as support for the second critical point hypothesis. Other NMR approaches, by contrast, observed that water diffusivity is reduced by more than an order of magnitude in silica pores with diameters of a few nanometers.9,10,17

These results exemplify our incomplete and sometimes controversial knowledge about the diffusion of water in nanosized confinements. Partly, this deficiency is caused by non-trivial effects, which interfere with straightforward interpretations of diffusion data for confined waters. In NMR studies using MCM-41 or SBA-15 silica particles, one should consider that diffusion is anisotropic in cylindrical pores.9,10 Moreover, it is necessary to take into account that the length scale of the diffusion measurements is similar to the size of the silica particles so that exchange between water species inside and outside of the pores can impair the interpretation of experimental results.17,18 Also, in PFG and SFG approaches to heterogeneous materials, an exchange of magnetization, explicitly, cross relaxation, between mobile and immobile spin species can hamper an interpretation of signal decays in terms of water diffusion.15 Finally, the pore-size dependent freezing of water in confinement needs to be considered in temperature-dependent diffusion studies. While crystallization is completely suppressed in severe confinements, fractional freezing occurs at pore-diameter dependent melting points Tm in wider confinements and results in a coexistence of frozen water fractions in the pore centers and unfreezable water fractions at the pore walls below these temperatures.40–43 Thus, it is essential to determine the relevance of all these effects for the experimental findings and to overcome possible obstacles.

Here, we use 1H and 2H SFG NMR to ascertain water diffusion in mesoporous silica. These SFG approaches, as compared to the PFG counterparts, allow us to apply stronger field gradients and, thus, to probe diffusion on smaller length scales and in broader dynamic and temperature ranges.44 We employ MCM-41 and SBA-15 materials to systematically vary the pore diameter and, hence, to ascertain the role of the confinement size. In particular, we consider silica pores where partial crystallization does and does not occur. Furthermore, we use samples with capped and open pore exits, respectively, to analyze the relevance of interfering contributions from water motion between different silica particles. Both types of samples differ with respect to the presence of excess water, which freezes and embeds the silica particles in an ice matrix at subzero temperatures. Moreover, we exploit that comparison of findings for 1H and 2H probe nuclei informs about the relevance of cross relaxation effects. Finally, the present results for water diffusion are compared with previous ones45 for water reorientation in exactly the same confinements to gain insights into the transport mechanism.

2 NMR background

In SFG NMR,6 a magnetic field with a static gradient g along the z axis is applied, B(z) = B0 + gz. Then, the Larmor frequency depends on the nuclear position according to ω(z) = γ(B0 + gz), where γ is the gyromagetic ratio of the observed nucleus. Correspondingly, the frequency changes as a result of water diffusion in the gradient field. This time dependence can readily be probed in stimulated-echo (STE) experiments, which employ a three-pulse sequence, 90° − te − 90° − tm − 90° − te, to correlate the resonance frequencies during two evolution times te, which are separated by a mixing time tm. Specifically, water diffusion causes a decrease in the height of the produced echo signal when the length of tm or te is extended in the measurement.

For free diffusion, the STE decays depend on the self-diffusion coefficient D according to6

S(tm,te) ∝ exp(−Dq2td).(1)
where image file: d0cp01290d-t1.tif and q = γgte. Since these parameters are controlled in the SFG experiment, the STE decays enable straightforward determination of the diffusion coefficient D. In analogy with the momentum transfer in scattering experiments, the value of q determines the length scale ld on which diffusion is probed.6,7,46 For the setup and sample characteristics of the present study, ld can be varied in a range of ∼0.1–10 μm for 1H, while the experimental length scales are a factor of 6.5 larger for 2H due to the smaller gyromagnetic ratio.

Porous media, however, do not allow free diffusion, but rather cause anisotropic diffusion. Explicitly, it is often useful to distinguish diffusion coefficients parallel (D) and perpendicular (D) to the pore axes. In such circumstances, the STE decays are given by6,7

image file: d0cp01290d-t2.tif(2)
Here, Dan(θ) = D[thin space (1/6-em)]cos2[thin space (1/6-em)]θ + D[thin space (1/6-em)]sin2[thin space (1/6-em)]θ describes the combined contributions from parallel and perpendicular displacements for a given angle θ between pore axis and field gradient and the integral considers the powder average over the random orientations of the silica particles in our samples and, hence, over the pore orientations θ.

If there are ideal cylindrical pores, which have a pore diameter much smaller than ld and a pore length much larger than ld, NMR diffusometry will not probe displacements perpendicular to the pore axis, i.e., D = 0, but it will merely detect that along this axis. This means that the SFG experiment observes one-dimensional diffusion characterized by D and eqn (2) simplifies to6,7

image file: d0cp01290d-t3.tif(3)
While this ideal case may be met in studies on perfect MCM-41 or SBA-15 materials, deviations can occur in experimental practice. For example, D > 0 will be found if the pores are bent or their walls penetrable.9,10 Moreover, a finite perpendicular component can result when, due to limited pore lengths, the water molecules exit their initial pore, move in the space between different silica particles, and enter a new pore in the same or another silica particle.

When analyzing SFG STE measurements, it is further necessary to consider that, in addition to molecular diffusion, spin relaxation can attenuate the echo signal. Therefore, when fitting S(tm,te) data, we multiply the above equations by the factor

image file: d0cp01290d-t4.tif(4)
to take into account spin–lattice (T1) relaxation during the mixing time tm and spin–spin (T2) relaxation during both evolution times te. In doing so, we exploit that the T1 and T2 relaxation times can be determined in independent measurements and fixed in this analysis. Nevertheless, these spin relaxation effects limit the maximum lengths of the mixing and evolution times, imposing a lower bound to the accessible diffusivities. Still, diffusion coefficients of confined water down to D = 10−13 m2 s−1 can be measured in our specifically designed SFG setup, which allows for very high gradient strengths g.

We note in passing that limited sizes of silica particles can cause deviations from the Gaussian displacement statistics assumed in eqn (2) and (3). Specifically, when the particle sizes are of the same order of magnitude as the probed displacements, a significant fraction of water molecules reaches the pore exits, where they are expected to experience enhanced backward correlations. Moreover, non-Gaussian behavior can arise due to molecules, which either exit or enter a pore on the time scale of the experiment so that their diffusion speeds up or slows down, respectively. However, any non-Gaussianity resulting from these effects is too weak to be probed in the present studies, see below.

3 Experimental

3.1 Sample preparation and characterization

The preparation and characterization of the used mesoporous silica was described in some detail in previous works.45,47 Briefly, we followed a standard protocol33,48 to synthesize the MCM-41 materials. In doing so, we varied the pore diameter d by utilizing template molecules with different numbers of carbon atoms in their alkyl chains, explicitly, n = 10–16. Strictly speaking, MCM-41 silica denoted as C10, C12, C14, and C16 were produced in one series of preparations45 and MCM-41 C14* in another.47 Both syntheses used the same protocol but slightly different parameters. In addition, we utilize SBA-15 silica purchased from Sigma-Aldrich.

The prepared and purchased mesoporous silica were characterized by Brunauer–Emmett–Teller (BET) analysis, scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). BET analysis, which is detailed in the ESI, yielded the pore diameters and pore volumes, see Table 1. As expected, for MCM-41 materials, the pore diameter increases from C10 (d = 2.1 nm) to C16 (d = 3.0 nm) and SBA-15 silica has the widest confinements (d = 5.4 nm). We note that, for the latter two samples, the present values differ slightly from the previous ones,45 which were extracted from less elaborate analysis (MCM-41 C16) or provided by the supplier (SBA-15). SEM images revealed that the MCM-41 silica come along as nearly spherical particles.45 Exemplary images in the ESI show that the typical particle sizes range from ∼300 nm to ∼1000 nm, where particles with narrower pores (MCM-41 C10) tend to be, on average, larger than that with wider ones (MCM-41 C16). DSC measurements provided us with the freezing and melting temperatures of water confined to these mesoporous silica, see Table 2. Consistent with literature results,40–43 the phase behavior strongly depends on the pore diameter. In sufficiently wide silica pores, partial crystallization occurs but shifts to lower temperatures when the pore diameter is reduced. This depression of the freezing/melting point can be explained based on the time-honored Gibbs–Thomson equation, when an effective pore radius is used to consider the existence of an unfreezable water layer at the pore wall.40–43 In the narrow pores of MCM-41 C10, by contrast, the DSC thermograms do no longer yield evidence of any ice formation.

Table 1 Pore diameters and pore volumes of the prepared MCM-41 and purchased SBA-15 materials as obtained from nitrogen adsorption and desorption isotherms45
Sample Pore diameter (nm) Pore volume (cm3 g−1)45
C10 2.1 0.34
C12 2.4 0.49
C14 2.8 0.70
C14* 2.8 0.68
C16 3.0 0.69
SBA-15 5.4 0.58

Table 2 Freezing (Tf) and melting (Tm) temperatures of H2O in the studied MCM-41 and SBA-15 materials as obtained from DSC measurements with cooling and heating rates of 5 K min−1 (ref. 45)
Sample Freezing: Tf (K) Melting: Tm (K)
C12 209 210
C14 215 219
C16 222 226
SBA-15 246 257

The water filling of the mesoporous silica was also described in some detail in previous works.45,47 In short, to prepare samples with open pore ends, the silica materials were carefully dried in high vacuum49 before a filling factor of ca. 100% was adjusted by adding appropriate amounts of water. To obtain samples with capped pore ends, large quantities (∼1000%) of excess H2O or D2O (purchased from Sigma-Aldrich) were supplied so as to embed the silica particles in spanning ice matrices at subzero temperatures. Fig. 1 shows a schematic diagram of the studied samples. The water-loaded SBA-15 and MCM-41 materials were filled into NMR tubes, which were subsequently flame sealed to avoid water losses. Prior to use in measurements, the samples were stored for several days to ensure that water filling is in thermal equilibrium.

image file: d0cp01290d-f1.tif
Fig. 1 Schematic diagram of the studied samples. Lengths are not drawn to scale. Roughly micrometer-sized silica particles feature aligned cylindrical pores, which are filled with water. The pore diameters are adjusted in the range 2.1–5.4 nm. Depending on the amount of excess water, the silica particles are surrounded by air or embedded in an ice matrix so that the pore exits are open and capped at subzero temperatures, respectively. While interparticle motion is possible for open pores, it is suppressed for capped ones.

3.2 NMR measurements

For 1H and 2H NMR diffusion measurements, we used two similar specifically designed SFG setups, which feature superconducting coils in anti-Helmholtz arrangement to produce a magnetic field with very high static gradients. Further details of the SFG setups can be found in the literature.44 The 1H SFG measurements were carried out at various positions in the magnetic gradient field. They are characterized by Larmor frequencies of ω/(2π) = 91–162 MHz and gradient strengths of g = 45–176 T m−1. It was assured that the obtained self-diffusion coefficients of water do not depend on the used position, see ESI. The 2H SFG experiments were done at a Larmor frequency of ω/(2π) = 25 MHz and a field gradient of g = 146 T m−1.

The 1H and 2H SFG NMR data were recorded using the STE pulse sequence with an appropriate phase cycle, which removes all but the STE signal.50 The temperature was controlled employing liquid-nitrogen cryostats. The temperature accuracy was better than ±1 K and the temperature stability better than ±0.5 K. All measurements were performed from low to high temperatures to avoid uncontrolled crystallization during data acquisition.

4 Results

4.1 Open pore exits vs. capped pore exits

Since displacements probed by NMR diffusion studies are comparable to the sizes of the MCM-41 and SBA-15 particles, it is important to first determine to which extent the measurements probe water diffusion inside the particles and water motion between the particles, respectively. For this purpose, we compare findings for open and capped pore exits, see Fig. 1. In samples with open pore ends, the silica particles are surrounded by empty voids so that fast interparticle water motion can occur. In samples with capped pore ends, by contrast, the silica particles are embedded in a spanning ice matrix at the studied temperatures, preventing interparticle exchange.9

Fig. 2 shows 1H SFG STE decays S(tm) for H2O in MCM-41 C14* with open and capped pore exits, respectively. As expected for diffusive motion, the decays of both samples occur at shorter mixing times tm when the evolution time te and, thus, the spatial resolution is increased. Relating to their shape, deviations from exponential behavior are evident, indicating that the model of free diffusion, which was used in several studies on water diffusion in mesoporous silica, does not apply. The nonexponentiality is particularly striking when inspecting S(tm) data for long evolution times te, which decay prior to an onset of spin–lattice relaxation damping. Thus, our results are clear evidence for an anisotropic nature of water diffusion.

image file: d0cp01290d-f2.tif
Fig. 2 Normalized 1H SFG STE decays S(tm) for H2O in MCM-41 C14* (d = 2.8 nm) for various evolution times te: (a) sample with capped pore ends at 250 K (g = 57 T m−1) and (b) sample with open pore ends at 260 K (g = 176 T m−1). The lines are global fits of the data for all used evolution times te to eqn (1), (2), or (3), each supplemented by spin–lattice relaxation damping, eqn (4): (dotted lines) free diffusion, (dashed lines) anisotropic diffusion, and (solid lines) one-dimensional diffusion.

In view of these shortcomings of the model of free diffusion, we distinguish between diffusion parallel (D) and perpendicular (D) to the pore axes in all further analyses. Fitting the STE decays to this model of anisotropic diffusion, see eqn (2), yields D > 0 and D ≈ 0 for open and capped pore exits, respectively. As both types of samples were prepared from the same batch of silica particles, this discrepancy with respect to the existence of a finite perpendicular component results from the fact that water motion through the interparticle space is possible for the former samples, but suppressed for the latter.

Since fits to eqn (2) yield D ≈ 0 for capped pore ends, we reanalyze the S(tm) data of this sample with the model of one-dimensional diffusion, see eqn (3), where a perpendicular component does not exist from the outset. In Fig. 2, we observe that this approach yields good interpolations of the nonexponential decays for all evolution times te. This finding indicates that the utilized MCM-41 C14* silica material has well-defined cylindrical pores, in particular, pore bending and wall permeability are negligible. Moreover, it implies that there are no significant deviations from Gaussian displacement statistics, which would arise due to distorted diffusion at the pore exits. Analogous results are obtained when we analyze the SFG STE decays recorded for the other used MCM-41 and SBA-15 silica. Thus, our detailed analysis of the decay shape indicates that water diffusion inside single pores can be probed when high field gradients are applied to reduce the experimental length scale ld or, equivalently, enhance the spatial resolution and excess water is used to cap the pore exits at subzero temperatures. By contrast, water motion outside the silica particles will interfere with a straightforward interpretation of NMR diffusion data, if no specific measures are taken.

The temperature-dependent self-diffusion coefficients of H2O in MCM-41 C14* with open and capped pore ends are displayed in Fig. 3. Exploiting knowledge from the above shape analysis, the data for open and capped exits result from fits of S(tm) decays to eqn (2) and (3), respectively. A comparison of D reveals that water transport is slower for capped than open pore ends. This discrepancy is larger when water is more mobile at higher temperatures so that a larger fraction of molecules reach an exit and have the chance to escape from the pore on the experimental time scale. These findings support the above conclusion that interparticle motion can strongly affect NMR diffusion studies on confined water if no measures for suppression are taken.

image file: d0cp01290d-f3.tif
Fig. 3 Self-diffusion coefficients of H2O in MCM-41 C14* (d = 2.8 nm). For the sample with open pore ends, diffusivities parallel (D) and perpendicular (D) to the pore axis are compared, as obtained from fits to the model of anisotropic diffusion. For the sample with capped pore ends, D of the model of one-dimensional diffusion is displayed. The lines are literature data for (solid line) bulk H2O51 and (dotted line) H2O in open MCM-41 pores with a diameter of d = 1.8 nm, both obtained from fits to the model of free diffusion.12,13

For MCM-41 C14* with open pore exits, water diffusivities in parallel and perpendicular directions differ by roughly two orders of magnitude, see Fig. 3. Interestingly, the interparticle-motion impaired D values of this sample agree with diffusion coefficients obtained in previous studies of water motion in silica pores with open ends,12,13 implying that water motion outside the silica pores also strongly affected the literature results. Therefore, unlike the authors of those studies, we caution to take a reported crossover in the temperature dependence of these literature data near 225 K as an evidence for the existence of a liquid–liquid critical point.12,13 For MCM-41 C14* with capped pore ends, water diffusion is about an order of magnitude slower in the confinement than in the bulk. The pore-size dependence of this slowdown will be studied in more detail below.

In the ESI, we further explore the discrepancies between samples with open and capped exits and the relevance of the generalized scattering vector q = γgte, which determines the experimental length scale ld. Unlike the other evaluations, this additional analysis does not use global fits, but rather individual fits of STE decays for various evolution times te and field gradients g. It is found that the diffusion coefficients D significantly depend on the used generalized scattering vector for open ends. By contrast, they are largely independent of the experimental parameters for capped ends. Explicitly, D for open exits approaches the constant value for capped exits only when we exploit the high field gradients of our SFG setup to reach low inverse generalized scattering vectors q−1 ≈ 0.2 μm and, hence, a spatial resolution high enough to probe diffusion inside the silica particles, while it is a factor of about five higher for q−1 > 1 μm typical of PFG approaches, i.e., when the experimental length scale ld is larger than the silica particle sizes so that there are contributions from interparticle motion. In view of the questionable interpretation of results for open pore exits, we will exclusively utilize samples with capped pore exits in the following studies.

4.2 1H NMR vs.2H NMR

Next, we perform 2H SFG NMR studies of D2O diffusion in MCM-41 C14* pores with capped ends. Fig. 4 shows S(tm) for various evolution times te and S(te) for several mixing times tm, both measured at 260 K. Consistent with the outcome of the above 1H SFG NMR approach, we observe that the model of free diffusion fails to describe the nonexponential nature of the S(tm) and S(te) decays, while one-dimensional diffusion yields good global interpolations of both data sets.
image file: d0cp01290d-f4.tif
Fig. 4 Normalized 2H SFG STE decays for D2O in MCM-41 C14* (d = 2.8 nm) at 260 K (g = 146 T m−1): (a) S(tm) for various evolution times te and (b) S(te) for various mixing times tm together with results obtained from the Hahn-echo sequence, which correspond to tm = 0. In both panels, the lines are global fits to eqn (1) or eqn (2) supplemented by spin–lattice or spin–spin relaxation dampings: (dotted lines) free diffusion and (solid lines) one-dimensional diffusion.

In Fig. 5, we display the diffusion coefficients D obtained from global fits of 2H SFG STE decays at various temperatures to the model of one-dimensional diffusion. We see that D2O diffuses slightly slower than H2O in MCM-41 C14*. This is in agreement with expectations based on the mass difference between heavy and light waters, in particular, the diffusivities of bulk D2O and H2O have a similar ratio.51,52 Moreover, we observe that our SFG data are in harmony with prior PFG findings for water diffusion in silica pores with similar diameter and capped exits, which were analyzed in terms of anisotropic diffusion.9,10 These consistencies further corroborate the validity of our results. For example, we would expect stronger differences between 1H and 2H data if the STE decays were not caused by water diffusion but rather by cross relaxation between different spin species because the latter effect depends on the strengths of dipolar spin couplings and, hence, substantially differs for protons and deuterons with diverse gyromagnetic ratios.

image file: d0cp01290d-f5.tif
Fig. 5 Self-diffusion coefficients D of H2O and D2O in MCM-41 C14* (d = 2.8 nm) with capped pore ends at T > Tm from fits to the model of one-dimensional diffusion. For comparison, literature data are included for (solid line) D of bulk H2O,51 (dotted line) D of bulk D2O,52 both from free diffusion fits, and (dashed line) D of H2O in capped MCM-41 pores with a diameter of d = 3.0 nm, as obtained previously from interpolations with the model of anisotropic diffusion.9

4.3 Pore-diameter dependence of water diffusion

Having assured the validity of our approach, we are in the position to compare water diffusion in confinements of various sizes. For this purpose, we perform 1H SFG STE experiments on H2O in MCM-41 and SBA-15 pores with diameters in the range 2.1–5.4 nm. For all samples, we ensure capped pore ends and fit S(tm) data for various evolution times te globally to the model of one-dimensional diffusion. In Fig. 6, we see that, near 270 K, the resulting diffusion coefficients D strongly decline when the pore size is reduced. Compared to the bulk value, the diffusivity is decreased by a factor of ∼2 in pores with a diameter of d = 5.4 nm, while it is diminished by two orders of magnitude for d = 2.1 nm.
image file: d0cp01290d-f6.tif
Fig. 6 Self-diffusion coefficients D of H2O in MCM-41 silica with capped pore ends and various pore diameters, as obtained from fits to the model of one-dimensional diffusion. The arrows indicate the melting temperatures Tm of water in the respective silica confinements. Accordingly, completely filled and half filled symbols distinguish situations where all confined water is liquid at T > Tm from those where confined water is partially frozen at T < Tm. The solid lines are interpolations of the diffusion coefficients for d = 2.1 nm and d = 2.4 nm with an Arrhenius law, yielding the same activation energy of Ea = 0.40 eV for both pore diameters. For comparison, the dotted line indicates self-diffusion coefficients of bulk H2O.51

Concerning the temperature dependence of D, we see in Fig. 6 that the diffusion coefficients obey the Arrhenius law in narrow pores,

image file: d0cp01290d-t5.tif(5)
while there are significant deviations in wide pores. In detail, D is well described by an Arrhenius law with an activation energy of Ea = 0.40 eV for d = 2.1 nm. When increasing the pore diameter to 2.4 nm, the diffusion coefficients become overall larger, but the activation energy remains unchanged. By contrast, the temperature dependence of D is discontinuous for d ≥ 2.8 nm. Specifically, the diffusion coefficients drop at the pore-size dependent melting temperatures Tm of water in these wider confinements, which are indicated by arrows in Fig. 6.

To explain these findings, it is important to recall that, unlike water in narrow pores, water in wide pores undergoes fractional freezing in the studied temperature range. Above Tm, all water is liquid so that NMR diffusion studies observe molecules that explore the whole pore volumes. Upon partial freezing, two-phase systems arise, which comprise solid (ice) fractions in the pore center and liquid (water) fractions near the pore wall.40–43,53 Below Tm, NMR diffusometry merely probes the liquid fractions because the solid fractions have too short T2 relaxation times. Thus, the experimental results in this temperature range characterize water motion in thin unfreezable layers sandwiched between ice crystallites and silica walls, leading to reduced diffusivity. In other words, D drops when ice in the pore center forms and further restricts the space available for the diffusion of water to an interfacial layer. When we further consider the fact that the thickness of the unfreezable water layer is essentially independent of the pore diameter,40–43,53 these arguments also rationalize the observation that D does no longer depend on the value of d in the two-phase regimes below the respective Tm values, see Fig. 6.

These findings show that genuine information about the temperature dependence of the diffusion of confined water is available when narrow pores with capped exits are used. This situation is met in our studies on H2O in MCM-41 C10 silica particles featuring capped pores with a diameter of 2.1 nm. In Fig. 6, we see for this sample that water diffusion follows an Arrhenius law with an activation energy of Ea = 0.40 eV from 270 K all the way down to 207 K. Hence, our NMR diffusion data do not support the conjecture that there is a fragile-to-strong dynamical crossover related to a liquid–liquid phase transition near 225 K, which was proposed in previous studies on water diffusion in mesoporous silica.12,13

4.4 Water diffusion vs. water reorientation

Finally, we compare translational and rotational dynamics of confined water. For bulk liquids, both aspects of motion are usually linked by the Stokes–Einstein–Debye (SED) relation:54
image file: d0cp01290d-t6.tif(6)
Here, DT and DR are the translational and rotational diffusion coefficients, respectively, and RH is the hydrodynamic radius of the diffusing molecule. Furthermore, it is exploited that DR is related to the rotational correlation times τ[small script l] describing the rotational correlation functions of the Legendre polynomials of rank [small script l], P[small script l](cos[thin space (1/6-em)]θ). Altogether, the SED relation predicts DTτ[small script l]−1. When performing SED analyses for confined liquids, it is advisable to determine translational and rotational dynamics in identical matrices. Therefore, we exploit that the MCM-41 and SBA-15 silica of the present work on water diffusion were also employed in previous approaches to water reorientation.45,47 There, it was found that the rotational motion of confined water is largely independent of the pore diameter d and very similar for capped and open ends. Furthermore, it was observed that differences between H2O and D2O are minor.

Fig. 7 compiles translational diffusion coefficients and rotational correlation times of water in silica pores with various diameters. Specifically, results of the present 1H SFG measurements of H2O diffusion, shown as D−1, are compared with findings of previous 2H NMR studies on D2O reorientation, which yielded correlation times τ2.45 To enable straightforward comparison, the respective axes are scaled such that the D−1 and τ2 data will coincide in the whole temperature range if the SED relation is valid, the hydrodynamic radius amounts to RH = 1.35 Å, and differences between H2O and D2O are negligible. We observe that this SED approach allows us to match D−1 and τ2 for wide pores with d = 5.5 nm at T > Tm, where water dynamics should be most bulk-like, whereas it fails in the general case. In particular, translational motion has a significantly weaker temperature dependence than rotational motion for pore diameters of d = 2.1 nm and d = 2.4 nm so that the D−1 and τ2 traces intersect in the used representation.

image file: d0cp01290d-f7.tif
Fig. 7 Comparison of rotational45 and diffusive motions of confined water. Identical mesoporous silica with pore diameters of 2.1, 2.4, and 5.4 nm, respectively, were used to investigate both modes of motion. The reorientational dynamics is characterized by correlation times τ2 from previous 2H NMR studies on D2O in MCM-41 and SBA-15 confinements.45 They mark the peak positions of broad distributions of correlation times in these materials and are essentially independent of the pore diameter, as indicated by the orange bar. Moreover, they are consistent with correlation times obtained from dielectric susceptibility peaks for both H2O and D2O in silica pores.47,55,56 The diffusive motion is characterized by reciprocal diffusion coefficients D−1 from the present 1H SFG measurements. The ordinates are scaled such that the D−1 and τ2 data will coincide in the whole temperature range if the SED relation is valid and the hydrodynamic radius amounts to RH = 1.35 Å. The dashed lines are interpolations with an Arrhenius law, see Fig. 6.

For the moment, the origin of this discrepancy between diffusion and reorientation dynamics of water confined to narrow silica pores remains elusive. One may speculate that (i) we utilized erroneous D−1 or τ2 values. This can be excluded because the used diffusion coefficients agree with literature data for capped pores,9,10 see Fig. 5, and the used correlation times are in harmony with findings of various approaches to water reorientation in mesoporous silica.36–39 Also, one may suspect that (ii), here and there, the silica pores have defects, which act as additional barriers against the long-range transport, while these bottlenecks hardly delay the short-range motion. However, if this scenario applied, water diffusion should be slower than is expected from water reorientation in the whole temperature range, at variance with intersecting D−1 and τ2 traces. Moreover, one may conjecture that (iii) a two-phase nature of confined water affects diffusion and reorientation differently, because large displacements, unlike local rotation, involve motion not only in liquid regions but also around or through solid regions. This is very unlikely since there is also a discrepancy between translation and rotational dynamics when fractional freezing does not occur in narrow confinements or at high temperatures. Finally, as 1H NMR diffusion studies, strictly speaking, report on proton displacements, one may propose that (iv) the failure of the SED relation is caused by proton transport, which occurs independent of water diffusion in a Grotthuss-like mechanism. In silica confinements, this effect may be particularly important because the acidic silanol groups lead to low pH values, which facilitate fast proton hopping. However, an additional mechanism for proton transport should result in diffusion that is enhanced with respect to reorientation, at variance with our observation that D−1 values are much too large compared to τ2 data at higher temperatures.

To shed further light on the relevance of the Grotthuss mechanism, future 1H NMR diffusion studies on confined water at various pH values may be worthwhile. Unfortunately, 17O NMR approaches, which could settle this question, have turned out to be unfeasible even though we have used the SFG method to apply strong field gradients. Reasons for this are the low diffusion coefficients of water in narrow pores at subzero temperatures in combination with the inferior NMR properties of 17O nuclei, including a low gyromagnetic ratio γ and, in particular, very short T1 and T2 relaxation times, which severely limit the length of the accessible diffusion times.

5 Conclusion

MCM-41 and SBA-15 silica proved very useful to systematically investigate water dynamics in nanosized confinements. As these materials feature well-defined cylindrical pores with adjustable diameters, they are ideally suited, in particular, for pore-size dependent studies. While these benefits of a series of specifically prepared mesoporous silica particles were exploited to analyze water reorientation in previous work,45 they were used to ascertain water diffusion in the present contribution.

Performing NMR field-gradient measurements, we determined self-diffusion coefficients of water molecules, strictly speaking, of water protons, over broad dynamic and temperature ranges. This NMR method probes displacements on length scales ld of about 0.1–10 μm, which are much larger than the diameters, but similar to the lengths of the silica pores. These circumstances can hamper a straightforward interpretation of the experimental data. Explicitly, the small pore diameters interfere with analyses in terms of three-dimensional free water diffusion and the limited pore lengths mean that the experimental results may be governed by fast motion of unconfined water between different silica particles.

While both these effects were not considered in previous NMR works,12,13 we presented an improved NMR approach. Specifically, we used the model of anisotropic rather than free diffusion for the data analysis, i.e., we distinguished displacements parallel (D) and perpendicular (D) to the pore axes. Furthermore, we determined the relevance of intra- and interparticle water motions by comparing findings for various experimental length scales ld and for open and capped pore exits. Both types of samples differ with respect to the absence and presence of an ice matrix that encompasses the silica particles and suppresses water motion through their interstices. Finally, we exploited that the SFG method, as compared to the PFG counterpart, allowed us to apply stronger field gradients and, thus, to extend the dynamic range towards slower diffusion and smaller displacements.

For a detailed analysis of the diffusion behavior, we measured STE decays S(tm) for various evolution times te and, hence, for different spatial resolutions. We found that the model of anisotropic diffusion enables global fits of the STE data. In particular, unlike the model of free diffusion, it well described the pronounced nonexponential shape of S(tm). The fit results revealed that water transport is significantly faster for open than for capped pore ends. Moreover, they yielded D > 0 and D ≈ 0 for the former and latter samples. These observations showed that water motion between the silica particles strongly affects NMR diffusion studies on samples with open pore exits, while this dynamics is suppressed for capped ones. This result was confirmed when analyzing the dependence of the experimental results on the experimental length scale ld in more detail. Hence, NMR data may not be interpreted in terms of water diffusion inside single pores unless it is shown that water exchange between different pores is negligible. In the present NMR study, a detailed analysis of STE decays and a comparison of 1H and 2H data indicated that one-dimensional water motion along the axes of cylindrical silica confinements is probed when the pore exits are capped and high field gradients applied, enabling reliable determination of the related diffusion coefficient D.

Exploiting these capabilities of 1H and 2H SFG NMR diffusometry, we found that confined water shows slower diffusion than bulk water. Meaningful analysis of the pore-size dependence requires that all confined waters are liquid and, hence, it is restricted to weak cooling. At such temperatures, we observed that the diffusion coefficient D of water continuously decreases when reducing the pore diameter from d = 5.4 nm to d = 2.1 nm. In detail, the diffusivities of confined and bulk waters differ by two in the widest pores and by two orders of magnitude in the narrowest ones.

As for the temperature dependence of water diffusion in silica confinements, we noticed that possible partial crystallization has a strong impact. When all water is completely unfreezable in sufficiently narrow silica pores, D follows an Arrhenius law with an activation energy of Ea = 0.4 eV. We determined that the Arrhenius behavior extends over broad temperatures intervals well across ∼225 K. Thus, our data did not yield any evidence for the existence of a fragile-to-strong transition related to a proposed liquid–liquid phase transition at this temperature, at variance with findings in previous NMR diffusion studies, which used pores with comparable diameter, but open exits.12,13 Fractional freezing inside sufficiently wide silica pores resulted in a peculiar non-continuous temperature dependence of water diffusion. Specifically, D dropped at the respective melting temperatures Tm. This observation can be rationalized when we consider that the water molecules can explore the whole pore volume above Tm, while liquid and solid water phases coexist inside the pores below this temperature and, hence, water diffusion is restricted to narrow interfacial layers sandwiched between silica walls and ice crystallites. In other words, D drops when ice forms in the pore centers and further restricts the pore volumes, which are accessible to water diffusion, consistent with the observed strong pore-size dependence of the diffusivity of confined water.

Finally, we compared findings for the diffusion and reorientation of confined water. In wide silica pores and, hence, for most bulk-like water behavior, we observed that the SED approach successfully links both aspects of water motion near ambient temperature, while the SED relation breaks down upon fractional freezing, which strongly affects diffusive motion, but hardly alters rotational dynamics. In narrow silica pores, we found that water reorientation has a much stronger temperature dependence than water diffusion, indicating that the SED fails in the whole studied temperature range. Considering several possible scenarios, it turned out that the origin of this discrepancy remains elusive. Therefore, it may be worthwhile to study the relevance of proton motion independent of water diffusion in more detail in future work.

Conflicts of interest

There are no conflicts to declare.


Financial support of the Deutsche Forschungsgemeinschaft (DFG) in the framework of Forschergruppe FOR 1583 through grants Bu-911/18-2 and Vo-905/8-2 is gratefully acknowledged.


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Electronic supplementary information (ESI) available: BET and SEM characterizations of the pore-size and particle-size distributions of the studied MCM-41 and SBA-15 silica; dependence of the diffusion coefficients D on the length scale of the diffusion measurements. See DOI: 10.1039/d0cp01290d

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