J. Phys. Chem. B 2008, 112, 3927-3930
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Water Diffusion in Nanoporous Glass: An NMR Study at Different Hydration Levels Domenico Majolino,* Carmelo Corsaro, Vincenza Crupi, Valentina Venuti, and Ulderico Wanderlingh Department of Physics, UniVersity of Messina, C.da Papardo, S.ta Sperone 31, P.O. Box 55, 98166 S. Agata, Messina, Italy ReceiVed: December 4, 2007; In Final Form: January 16, 2008
By pulsed field gradient nuclear magnetic resonance measurements, we investigated the translational diffusion of water confined in the 200 Å diameter pores of a sol-gel silica glass. The experiments, performed as a function of the hydration level, showed an enhancement of the self-diffusion coefficient when the water content corresponds to one or fewer monolayers. An explanation for this occurrence has been given in terms of a two-phase process involving a fast molecular exchange between the liquid and the vapor phase. Moreover, in partially filled pores, the surface water diffusion coefficient was measured, and was 4 times lower than the diffusion of liquid confined water in saturated spaces.
Introduction The dynamical and structural properties of water confined in a nanospace of mesoporous silica are of utmost interest in materials science and biological systems. For this reason, much work has been done to investigate the adsorption of water on the solid surfaces of randomly ordered porous glass such as Vycor, Britsorb, and aerogel, which have amorphous pore walls and random pore connectivity. As a general trend, the interesting modifications of the behavior of water with respect to the bulk phase are thought to be due to the strong competition between the geometrical confinement and specific interaction between H2O molecules and the solid surface.1-6 Through nuclear magnetic resonance (NMR) relaxation experiments, an enhanced relaxation rate, on the time scale of liquids confined in partially saturated open space of mesoporous matrices was observed.7-10 Essentially, this fact has been ascribed to interactions involving the probing molecules at the liquid-solid interface. Understanding the modifications from bulk liquid behavior caused by the porous medium provides a tool for characterization, crucial to various technologies such as catalysis and oil recovery. But in some cases, the confined liquid presents new characteristics that cannot be solely ascribed to a simple modification of bulk properties. In this paper, we present results of self-diffusion coefficient measurements, as obtained through NMR experiments, on a well-characterized porous silica glass filled with water at different hydration levels at ambient temperature, with the aim of obtaining information on the diffusive behavior at the very first layers of hydration water. Indeed, the range of investigated water content extends from saturated conditions down to submonolayer surface coverage of the wetting liquid. Going below one monolayer, a strong increase of H2O molecule selfdiffusion is observed. This experimental result will be discussed in the framework of a two-region model involving an exchange between the liquid and the vapor phase that forms, when there is a partial filling of the nanoporous matrix, two interpenetrating porous systems, a liquid one and a vapor one. This procedure * To whom correspondence should be addressed. Tel: +39 6765237. Fax: +39 090395004. E-mail:
[email protected].
allowed us to follow the liquid water dynamics down to the first monolayer. Experimental Methods The sol-gel synthesized porous silica glass used, GelSil, was transparent, rigid, high-purity xerogel with fully interconnected porosity. It is used as optical sensors, substrates for photovoltaic dyes, separation devices and catalyst supports. The internal surface of the cylindrical pores is naturally terminated with a variety of surface silanols (isolated, geminal, and vicinal) which are preferential adsorption sites for water molecules and other polar molecules which form a multiple hydrogen-bonded layer. This glass can be produced with different pore sizes, each having a narrow size distribution, amorphous walls, and random pore connectivity. It is more than 99% silica and can adsorb up to 120% of its dry weight in water vapor. In particular, we used GelSil monoliths with a pore-diameter distribution sharply peaked at 200 Å (5% of standard deviation), purchased from GelTech, Inc. The thickness and diameter of the disk-shaped samples were 2.8 and 6.3 mm, respectively. The disks presented the following specifications: bulk density equal to 0.611 g/cm3, density of the silica skeleton was 2.18 g/cm3, as measured with the pycnometric method,11 pore volume fraction equal to 0.72, pore volume was 1.178 cm3/g and finally the specific surface area was 215 m2/g. The hydrophilic character of the GelSil glass causes the adsorption of many organic substances onto the surface. For this reason, the samples were cleaned before use (for details on the usual procedure see ref 12). We also measured adsorption isotherms by gravimetric determination of water adsorbed into the nanoporous silica glass exposed to controlled humidity air at 22 ( 2 °C, to obtain quantitative information on the formation of H2O adsorbates. As far as the NMR measurements are concerned, different hydration levels, h ) grams H2O/grams dry glass, were reached by exposing the disks in a jar under controlled atmosphere at a percentage humidity %RH. The obtained h values were as follows: 0.07, 0.15, 0.25, 0.35, 0.42, 0.50, 0.86, 1.08, and finally 1.17. This last h value corresponds to the highest filling factor of the GelSil glass, i.e., full hydration. The filling factor is defined as volume H2O/available volume, V/V0. From now on,
10.1021/jp711433d CCC: $40.75 © 2008 American Chemical Society Published on Web 03/07/2008
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we will use the filling factor as a control parameter. After the desired weight was achieved, samples were sealed in the NMR tube and left to equilibrate for 24 h. After each measurement, the water content was checked again and found unchanged. The NMR experiments were performed at ambient pressure and temperature T ) 293 K by using a Bruker AVANCE NMR spectrometer, operating at 700 MHz. We have measured the self-diffusion coefficient of water through the pulsed gradient spin-echo technique 1H-PGSE. PGSE13 self-diffusion measurements are based on NMR pulse sequences which generate a spin-echo of the magnetization of the resonant nuclei. By the appropriate addition of pulsed field gradients (PFG) of duration δ, intensity g, and interval ∆, in the defocusing and focusing period of the sequence, the spin-echo intensity becomes sensitive to the translational motion along the gradient direction for the tagged molecules. In stochastic processes, such as thermally excited Brownian motion (self-diffusion), the spinecho intensity M(δg, ∆) is attenuated. The attenuation factor is given in terms of the mean square displacement of the diffusing molecules, along the gradient direction z, during the time interval ∆ by:
ψ(δg, ∆) )
M(δg, ∆) 1 ) exp - (γδg)2〈z2(∆)〉 2 M(0, ∆)
[
]
(1)
where γ is the gyromagnetic ratio of 1H and q)γδg, which has the dimension of an inverse length, is equivalent to the exchanged wave vector in a spectroscopy experiment, being a measure of the spatial scale probed, and is customary referred as q. In general, one may define a time-dependent self-diffusion coefficient D(∆) through the relation ) 2D(∆)∆ for the unidimensional case, from which the long-time limit lim∆f∞ D(∆) ) D is obtained. Hence, eq 1 can be written as follows: The experimental parameters used in the NMR pulse sequence
ψ(δg, ∆) ) exp[-Dq2∆]
(2)
were as follows: δ ) 0.25 ms, ∆ ) 5, 10, 20, and 100 ms, g ) 12 T/m. Isothermal water absorption/desorption measurements on GelSil surface have also been performed, using samples exposed to controlled humidity air at 20 °C by appropriate saturated salt solutions. Results and Discussion As far as the absorption/desorption measurements are concerned, the obtained isothermal curves are shown in Figure 1, where on the right side of the graph, we reported the filling factor values of GelSil glass, V/V0, corresponding to the obtained hydration levels, h. In the experiment, each point was left to equilibrate and monitored for several days. The up triangles represent the load process: increasing %RH starting from a 120 °C vacuum-dried sample, while the down triangles represent the unloading. As can be seen, the water intake is very little up to about RH ) 75%, then a step increase is present up to RH ) 85%, after which a hysteresis cycle takes place. The water surface coverage for RH ) 53, 75, and 85%, corresponds to 5.5, 10.5, and 120 µmol H2O/m2. These values, compared with the Kiselev-Zhuravlev14 concentration of silanol groups on fully hydroxylated silicas (7.6 µmol SiOH/m2), suggest that the first, and partially the second, monolayer of water is different from the rest of the water layers, this is probably due to chemical interactions between the silica and water. The observed hysteresis, very often present in porous systems, is due to capillary condensation.
Figure 1. Equilibrium absorption-desorption isotherms of water within GelSil glass. Load process: up triangles; unloading process: down triangles. Left scale is the hydration level, whereas right scale is the corresponding filling factor.
In Figure 2, we report the values of the confined water diffusion coefficients, as evaluated from the best-fit of the echo attenuation curves, for all of the measured ∆. As an example, in the inset of Figure 2, the fit for ∆ ) 20 ms is shown on a semilog scale, obtained with a single exponential, eq 2, plus a flat background accounting for non-diffusing 1H in silanol groups, for the obtained different filling factors, V/ V0. Looking at the inset, from the observed linear behavior, we can claim that only a single diffusing species is present in our system and that there is no evidence for confinement effects. The increase of the diffusion coefficient at low filling factor was already revealed in partially filled porous systems7,9,15 and is ascribed to the vapor phase that is present along with the fluid one. This means that a water molecule diffuses in the porous matrix with two different rates related to a fast diffusion in the vapor phase, Dv, and to a slower diffusion in the liquid phase, Dl. Since only one diffusing species appears to be present in our data, this indicates that a fast exchange takes place between the two phases during the measurement time, which is very feasible in our case, where the diffusion is sampled over tens of milliseconds. In order to analyze the obtained diffusion coefficients vs V/V0, it is necessary to average the water-diffusion coefficients Dv and Dl over the elapsed times spent in the two phases. These times are proportional to the number of molecules present in the two phases which, in turn, are proportional to the fraction of mass present in the liquid and vapor phase. So a Deff can be written as follows:
Deff )
1 (F V/V0Dl + FV(1 - V/V0)DV) FlV/V0 + FV(1 - V/V0) l (3)
where Deff is the observed diffusion coefficient, and FV and Fl are the densities in the vapor and liquid phase, respectively. We have also to note that the transport properties in porous materials are predominantly affected by the geometrical properties of the system. In particular, the diffusion coefficient in the pore space is reduced relative to its bulk value D0 due to tortuosity effects, according to the following general law:7,16,17
D)
D0 τ
(4)
where τ is the tortuosity factor that accounts for the greater distance that fluid must travel to navigate a path through the
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Figure 2. Effective water diffusion coefficients in GelSil matrix as a function of the filling factor. The continuous line is the theoretical best-fit by eq 5. The inset shows the echo attenuation curves for different hydration levels, h: 0.06 (circles), 0.23 (squares), 0.46 (up triangles), 0.80 (diamonds), and 1.03 (down triangles). The continuous lines are the monoexponential best-fits.
porous media than if it were to pass straight through. Before going on with the comments of our results, it is worth doing some observations. In two authoritative papers by Ardelean et al.9,15 on confined water in micrometer silica glass, the authors found, as above cited, a similar behavior of Deff vs the filling factor V/V0, with the presence of a minimum. In those articles, the geometrical restrictions were expressed by the authors through the Archie’s law Deff ) ΦmD0, where m is an empirical factor that takes into account the tortuosity of the total pore space (tortuosity effects), and Φ is instead the porosity of the system. Looking at this law, one can observe that it essentially holds for low porosity systems, in view of the fact that in the limit case of porosity approaching unity, the tortuosity does not play any role any more, as expected. The occurrence that Archie’s law works very well in the silica glass used by Ardelean, is, in fact, related to the low porosity value of the confining matrix. However, we tentatively applied this law to our data, but the analysis was totally inappropriate, likely due to the high porosity of GelSil glass, exactly in contrast to the previous case. Hence, in order to apply eq 3 to our measurements, we have to write the explicit dependence of Dv and Dl on the pore filling factor, V/V0. Here, some considerations must be made, since diffusion coefficients in heterogeneous media depend on the space-time scale over which the system is probed. Diffusion in the vapor phase is usually governed both by collisions among molecules, typical of the Einstein diffusion regime, and by collisions of molecules with liquid-vapor phase and/or with inner surfaces of the confining matrix which we often refer to as “pore walls”, characteristic of the Knudsen diffusion regime. In our case, molecule-wall collisions dominate since the vapor molecular average free path is much longer (on the order of cm) than the pores diameter (200 Å), hence the Knudsen contribution to diffusivity becomes the dominant one.
Thus Dv tends to DK, known as the Knudsen diffusion coefficient. Due to its low density, the contribution from the vapor phase is relevant only at small water content (V/V0 < 2), corresponding to no more than two water monolayers, and we can assume that the pore geometry remains unaffected and retains a constant value for Dv ) D0,K/τ. D0,K ) 1/3 ujd, where uj ) (8RT/πM)1/2 is the mean thermal speed, R is the gas constant, M is the molar mass, and d is the diameter of the pores.17 This term is usually defined in straight parallel nonoverlapping cylindrical pores of infinite length with diameter equal to the mean intercept length in the considered real pore structure. As far as diffusion in the liquid phase is concerned, our data reveal a linear dependence of Dl from the filling factor, which is equivalent to the growth of layers of water up to complete filling of the available volume. At full hydration, the found value of Dl ) 1.46 × 10-9m2/s provides a value for the tortuosity of τl ) 1.6 ( 5% when compared through eq 4 with bulk water diffusion Dbulk ) 2.3 × 10-9m2/s.18 As the pore filling decreases, the Dl does not go to zero but rather approaches a finite value which can be assigned to the surface diffusion coefficient, Ds, of water molecules in the first monolayer. This quantity is very important, as it can be useful for understanding the interaction between water and solid surfaces which is of fundamental interest in material sciences and biological systems. The diffusion coefficient of the water layer in contact with the solid surface is a matter of debate and commonly retained to be about 3-4× less than bulk coefficient, on hydrophilic surfaces.19 The linear increase of Dl with the increase of the filling factor could be attributed, according to the authors, to the increase of the cross-section available to the water molecules for navigating trough the cylindrical pores of GelSil. In fact, from the point of view of the PGSE technique only the axial contribution of the diffusion along the pores can be probed, since the radial
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component of such a diffusion is far beyond the spatial instrumental resolution. Then it appears natural that the axial diffusion is increased as more and more layers of water are added by increasing V/V0. From the above consideration we can write Dl ) [Ds + V/V0(D0,l - Ds)]and complete eq 3 in the form
Deff )
Flx‚[Ds + x(D0,l - Ds)] + FV(1 - x)‚DK Flx + Fv(1 - x)
(5)
where x stands for the filling fraction V/V0 and D0,l is the liquid water diffusion at full hydration, which we can refer to as “bulk” regime. In the calculations, the following parameters have been used: D0,l ) 1.46 × 10-9m2/s and FV)1.75 × 10-5g/ cm3, the latter value actually being slightly smaller than that in the case of saturation condition; it corresponds to a percentage relative humidity RH ≈ 70%. It is worth noticing, looking at Figure 2, that the theoretical curve described by eq 5, fits the effective diffusional data pretty well, considering that there are only two free parameters: Ds and DK. From the best-fit procedure we found Ds ) 0.4 × 10-9 m2/s and DK ) 0.18 × 10-5 m2/s. The best-fit parameters determination presents an error which is approximately 5%. We can observe that the obtained value of Ds is almost four times lower than D0,l, indicating a dramatic reduction of the water molecule diffusion when they are totally adsorbed on the pore surface of GelSil. This can be explained by taking into account the interactions with the hydrophilic inner surface of the GelSil pores which play the main role in the transport properties of confined water as the filling factor decreases. Also, the Knudsen diffusion coefficient DK reveals a slowing down of vapor diffusion compared to the reference value DK,0 which was equal to 0.33 × 10-5m2/s. It was estimated taking into account that when water molecules are in the vapor phase, mainly monomer and dimer structures contribute to the molar mass.20 We also calculated, in the vapor/Knudsen regime, the corresponding tortuosity factor τK ) 1.8 ( 5%. We can observe that this latter tortuosity factor is consistent with the value of τl ) 1.6, estimated in the liquid-phase region. This result mainly indicates that since the tortuosity factor is essentially related to the intrinsic geometrical properties of the porous structure, in our case it does not depend on the diffusion regime, Knudsen or bulk. This can be explained taking into account the wide size of pore diameter. In particular, the tortuosity factor in the Knudsen regime is slightly larger than in the liquid one. This observed difference could indicate that passing from the liquid phase to the vapor phase, as the filling factor decreases, not only the intrinsic geometrical confinement contributes to reducing the bulk translational water diffusion but also the liquidinner surface interactions.
Conclusions We have measured the translational diffusion coefficients of water confined within a hydrophilic silica glass as a function of the filling factor, through pulsed field gradient nuclear magnetic resonance (NMR) experiments. The obtained data have shown a strong dependence on the hydration level, which has been interpreted by a simple model based on an interphase exchange between vapor and liquid. In particular, as the pore filling decreases, Dl diminishes approaching a finite value assigned to the surface diffusion coefficient, Ds, of water molecules which are totally adsorbed on the hydrophilic surface of the glass. From the absorption/desorption measurements, we observed that a hysteresis cycle takes place. The obtained water surface coverage suggested that the first, and partially the second, monolayer of water is different from the others layers, likely due to chemical interactions between the silica and water. References and Notes (1) Gallo, P.; Ricci, M. A.; Rovere, M. J. Chem. Phys. 2002, 113, 342. (2) Gallo, P.; Rovere, M. J. Phys. Cond. Matter 2003, 15, 7625. (3) Webber, B.; Dore, J. J. Phys.: Condens. Matter 2004, 16, 5449. (4) Zangi, R.; Mark, A. E. J. Chem. Phys. 2004, 120, 7123; Zangi, R.; Engberts, J. B. F. N. J. Am. Chem. Soc. 2005, 127, 2272. (5) Kumar, P.; Buldyrev, S. V.; Starr, F. W. ; Giovambattista, N.; Stanley, H. E. Phys. ReV. E 2005 72, 051503; Kumar, P.; Starr, F. W.; Buldyrev, S. V.; Stanley, H. E. Phys. ReV. E 2007, 75, 011202. (6) Mallamace, F.; Broccio, M.; Corsaro, C.; Faraone, A. ; Liu, L.; Mou, C. Y.; Chen, S. H. J. Phys.: Condens. Matter 2006, 18, 2285; Mallamace, F.; Broccio, M.; Corsaro, C.; Faraone, A.; Liu, L.; Mou, C.Y.; Chen, S. H. J. Chem. Phys. 2006, 124, 161102. (7) D’Orazio, F.; Bhattacharja, S.; Halperin, W. P.; Gerhardt, P. Phys. ReV. Lett. 1989, 63, 43. (8) D’Orazio, F.; Bhattacharja, S.; Halperin, W. P.; Eguchi, K.; Mizusaki, T. Phys. ReV. B 1990, 63, 42. (9) Ardelean, I.; Mattea, C.; Farrher, G.; Wonorahardjo, S.; Kimmich, R. J. Chem. Phys. 2003, 119, 10358. (10) Valiullin, R.; Kortunov, P.; Karger, J.; Timoshenko, V. J. Chem. Phys. 2004, 120, 11804. (11) Eschricht, N.; Hoinkins, E.; Ma¨dler, F.; Schubert-Bischoff, P.; RohlKuhn, B. J. Colloid Interface Sci. 2005, 291, 201. (12) Crupi, V.; Majolino, D.; Migliardo, P.; Venuti, V. J. Phys. Chem. B 2002, 106, 10884. (13) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (14) Zhuravlev, L. T. Colloids Surf., A 2000, 173, 1. (15) Ardelean, I.; Farrher, G.; Mattea, C.; Kimmich, R. J. Chem. Phys. 2004, 120, 9809. (16) Massey, B. S. Mechanics of Fluids, 6th ed.; Chapman & Hall: London, 1989. (17) Geier, O.; Vasenkov, S.; Karger, J. J. Chem. Phys. 2002, 117, 1935. (18) Kimmich, R.; Stapf, S.; Makalakov, A. I.; Skirda, V. D.; Khozina, E. V. Magn. Reson. Imaging 1996, 14, 793. (19) Lee, S. H.; Rossky, P. J. J. Chem. Phys. 1994, 100, 3334. (20) Chylek, P.; Fu, Q.; Tso, H. C. W.; Geldart, D. J. W. Tellus 1999, 51, 304.
