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Positron Probing of Liquid-Free Volume to Investigate AdsorptionDesorption Behaviour of Water in Two Dimensional Mesoporous SBA-3 Priya Maheshwari, Marek Gorgol, Agnieszka Kierys, and Rados#aw Zaleski J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04317 • Publication Date (Web): 19 Jul 2017 Downloaded from http://pubs.acs.org on July 22, 2017

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The Journal of Physical Chemistry

Positron Probing of Liquid-free Volume to Investigate Adsorption-Desorption Behaviour of Water in Two Dimensional Mesoporous SBA-3 Priya Maheshwaria,*, Marek Gorgolb, Agnieszka Kierysc, Radosław Zaleskib,* a

Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai-400 085, India Maria Curie-Sklodowska University, Institute of Physics, Department of Nuclear Methods, Pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland c Maria Curie-Sklodowska University, Faculty of Chemistry, Department of Adsorption, Pl. M. Curie-Sklodowskiej 3, 20-031 Lublin, Poland b

*Corresponding authors: [email protected] (P. Maheshwari); [email protected] (R. Zaleski)

Abstract Transport of fluids through channels and cavities of nano/mesoporous materials is of paramount importance in various fields of science and industry. The transport properties can be well derived from the adsorption-desorption behaviour of fluids. Positron annihilation lifetime spectroscopy (PALS) allows probing adsorption-desorption of water from two dimensional mesopores of SBA-3. In situ study of the size of evolving water-free volumes during successive stages of adsorption and desorption is a sensitive way to elucidate the course of pore filling and emptying. The changes of positron annihilation parameters indicate that adsorption of water is mediated through the formation of isles on the surface of the pore walls and these, in turn, develop into water plugs. Subsequently, these plugs grow and consecutively join together when the distance between them decreases to ca. 1 nm until the complete capillary condensation occurs. Akin to adsorption, desorption of water from the pores involves formation of cavities capped with water plugs. The final stage of desorption shows the presence of water trapped in micropores in the pore walls. The linear dependence between the volume of water and the intensity of the waterrelated positronium component allows to estimate the amount of water in the system. The study highlights an approach to understand adsorption-desorption mechanism of liquids in mesopores by probing liquid-free volumes using ortho-positronium.

Introduction Adsorption-desorption behaviour of liquids in nanoscale environment plays a crucial role in state-of-the-art technologies like adsorption, catalysis, nanofiltration, separation and nanofluidics.1,2 Liquids confined in nanodomains affect the course of many physical, geological and biological processes.3,4 Understanding the transport mechanism of liquids through the nanochannels and cavities of porous matrices is useful not only for understanding the

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fundamental processes but also for designing porous materials for aforementioned engineering applications. There are numerous experimental5-7 and theoretical8-11 studies on the liquid transport mechanism in nano-sized pores in various materials. These studies reveal that macroscopic concepts of capillary condensation and evaporation are also suitable for the description of processes in the nano- and mesoscale.12,13 Experiments show that temperature14-16, pore size17,18, morphology and surface coverage14,15 strongly influence the kinetics of transport. On the microscopic scale, interactions between a liquid molecule and other adjacent liquid molecules or the surface of a pore wall also influence the transport mechanism and kinetics.19 The transport characteristics of liquids at nano/mesoscale can be derived from the kinetics of liquid uptake and release from the pores as well as from its adsorption-desorption isotherms. The studies on kinetics shows that spontaneous imbibition of liquids in the pores depends on surface roughness and/or wettability.20 However, when the porous material is exposed to humid environment, the water uptake mechanism can be different from the spontaneous imbibition. The rate of water uptake depends on the relative pressure. At the low relative humidity, water molecules adsorb on the inner walls of the pores, while at the high relative humidity, molecules condense at the pore entrances, and subsequently they migrate into the pore interiors as a condensate.21 Yanagihara et al. have measured the kinetics of water uptake and release during stepwise changes of the relative humidity.16 They revealed the effect of hydrophilicity of the pore surface, temperature and magnitude of a stepwise change in relative humidity on the adsorption-desorption isotherms and relaxation rates. The adsorption of liquids in pores modifies their surface state and this can influence subsequent adsorption of liquids.22 A considerable degree of complexity of the adsorption-desorption mechanism demands its in-depth knowledge. Therefore, understanding it also in terms of molecules distribution inside the pores at various stages of adsorption-desorption processes is very important since it provides a deeper insight into the transport characteristics of liquids at nano/mesoscale. The mechanism of adsorption-desorption of a vapour onto porous matrices possessing pores of different size and shape has been extensively studied 7, 23-25 and modelled.19, 26 These studies mainly consist in measurements of the amount or fraction of liquid filling the pores as a function of relative vapour pressure, the so-called sorption isotherm. The different shapes and hystereses of the isotherm are correlated with various mechanisms of adsorption-desorption of the liquid in the pores. The phenomena like cavitation or pore blocking have been invoked to explain the observed hysteresis.27-29 These phenomena depend on the pore structure as well as interaction of adsorbate with the pore surface.22 Thommes et al. have shown that the shape/type of hysteresis loop depend on the mechanism of adsorption-desorption, which in turn is related to the pore size and shape.23 The adsorption-desorption isotherms are usually determined by standard analytical techniques like volumetric/gravimetric methods. Information deduced from these techniques is an indirect implication of the proposed mechanisms of the studied phenomena. The interpretation of experimental isotherms would be much more reliable if structural parameters like free volume disappearance or formation during adsorption and desorption, respectively, were also known. Therefore, a direct method that can provide a


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microscopic picture of the adsorption-desorption phenomena is needed to understand the kinetics of transport of liquids in the mesopores. Over the past years, positron annihilation lifetime spectroscopy (PALS) has emerged as a powerful and sensitive technique for porosimetry measurements in various kinds of materials.3035 The positron’s sensitivity to free volumes allows probing pore systems in solids. The free volumes like open or closed pores, voids in the skeleton of the matrix of a porous material and intergrain spaces act as trapping sites for ortho-positronium (o-Ps) (the bound state of positron and electron with parallel spins). In contrary to short-lived para-positronium (p-Ps) (Ps with antiparallel spins), o-Ps decays by three photon mode and is sufficiently long-lived (~142 ns) to be sensitive to competitive decay modes. Mainly, in the presence of matter, it can seek out an electron of opposite spin from the surroundings and annihilate through the faster two-photon mode. This process is known as pick-off annihilation. The probability of pick-off depends on the size of the trapping site. In consequence, the o-Ps pick-off lifetime can be used to evaluate free volume size. The great advantage of the o-Ps probe is the ability to track in situ changes of free volume size and concentration during adsorption-desorption process and this way provide unique information that can help in revealing the underlying mechanism of the studied phenomena.36-39 In this study, PALS was used to investigate adsorption-desorption behaviour of water in two dimensional mesoporous silica SBA-3. Confined water can be found in many real life systems from geological to biological in nature, where it controls their properties and functioning.40 In recent years, water confined in inorganic matrices like porous silica (e.g. MCM41), alumina, and zeolites has acquired great relevance for pharmaceutical applications.41,42 Understanding of fundamental processes, which govern the kinetics of adsorption-desorption and transport of water in nano/meso length scales, is useful for the development of these applications. The mechanism of water adsorption and desorption in pores can be better revealed through a direct observation of free volume changes in the system during these processes. Our study consists in probing the evolution of free volumes at various stages of adsorption and desorption of water in the mesopores of SBA-3 using PALS. This aims at elucidating the mechanism of adsorption and desorption of water in mesopores.

Experimental SBA-3 synthesis The procedure of SBA-3 synthesis was adapted from the literature except that dodecyltrimethylammonium bromide (C12TAB, Aldrich) was used as a structure directing agent (surfactant).43 The synthesis was based on the use of tetraethyl orthosilicate (TEOS) (0.048 mol) as the silica source, with hydrochloric acid (0.434 mol) as the catalyst and an aqueous solution of surfactant (6.6×10-3 mol in 112 g H2O). The as-synthesized SBA-3 powder was calcined at 550oC in air for 5 h.



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Measurements The porosity of the sample was determined by the measurements of nitrogen adsorptiondesorption at 77 K using a volumetric adsorption analyzer ASAP 2020 V4.01 (Micromeritics, Norcros, GA) in the range of the relative pressure from 10-6 to 1. Prior to the adsorption measurements, samples were outgassed under high vacuum at 473 K for 18 h. The specific surface area (SBET) was calculated by using the Brunauer–Emmett–Teller (BET) equation in the relative pressure range of p/p0 = 0.02–0.18. The total pore volume (Vp), was obtained from the volume of adsorbed N2 at p/p0 = 0.995. The pore size distribution (PSD) was calculated by the non-local density functional theory (NLDFT) method for cylindrical pore geometry using the software provided by Micromeritics (models N2—Tarazona NLDFT, Esf = 30.0 K).44-46 The micropore volume of the sample was calculated using αs-plot method whereas the specific micro and external surface area were calculated using t-plot [cyt].47,48 Adsorption data of nitrogen for macroporous silica gel Li-Chrospher Si-100049 as a reference adsorbent were used in the αs-plots calculations. Ultrahigh purity H2O (18.2 MΩ cm at 298 K) was used in all water related experiments. The water adsorption-desorption were measured at 297.1 K using a Quantachrome Autosorb 1 automated gas sorption system in the p/p0 relative pressure range from 0.02 to 0.9. Prior to the adsorption measurements, samples were outgassed under high vacuum at 473 K for 18 h. The SBA-3 sample (0.26 g) in the sandwich configuration (sample-positron source-sample) was placed in the loosely capped container, which in turn was mounted in the sealed vacuum/pressure chamber (Supplement, Appx.1). The chamber was initially evacuated to p < 10-4 Pa and the sample was heated to 473 K. These conditions were maintained for ca. 12 h. Prior to the sorption measurements, water was outgassed four times by freezing, pumping and thawing cycles. Next, the chamber was filled with water vapour (without air) and the desorption run was carried out. The vapour flow was regulated using Pfeiffer RVC controller with EVR gas dosing valve. This setup allowed to register the vapour flow through the valve, which was used for estimating the volume of water introduced to or removed from the chamber.50 The water vapour pressure was lowered from the saturated vapour pressure (p/p0 = 1) in 50-300 Pa steps (depending on the rate of water release from the sample) until water was completely removed (p/p0 ≈ 0). A positron annihilation lifetime spectrum was collected for ca. 7 h after each pressure change. Afterwards, the heating of the sample under high vacuum was repeated. The subsequent adsorption run consisted in the analogous measurements at stepwise increasing pressure. Additionally, highstatistics spectra were collected for ca. 35 h for dry, partially hydrated (p/p0 = 0.27) and fully hydrated (p/p0 = 1) SBA-3. All the measurements were performed at room temperature (stabilized in range 23-24oC by air conditioning). The fast-slow delayed coincidence spectrometer was used in PALS measurements. Its scintillation detectors were equipped with BaF2 crystals with size of Ø1”×1” and Ø1”×1.5” for


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start and stop branch, respectively. The detectors were placed in the immediate vicinity of the chamber at right angles to each other. The time base of the spectrometer for high-statistics (ca. 4×107 counts) measurements was 0.5 µs for both the fully and partially hydrated samples and 2 µs for the dry sample. The spectra for the pressure dependence (ca. 8×106 counts) were measured at the intermediate time base 1 µs. The stop energy window was widely opened (ca. 200-600 keV) to collect as large as possible number of three-quanta annihilation events, which contribute to the intensities of long-lived components. Additionally, the start energy window covered approximately half of the Compton plateau in addition to the 1274 keV photopeak to assure the highest possible counting rate (over 300 cps). This was necessary to minimize the chance of temperature and pressure instabilities during the measurement. The resolution function for such energy windows could be approximated by two Gaussians of intensities ca. 95.5%/4.5%, and FWHM ca. 290 ps/430 ps, respectively. The analysis of the registered spectra was performed using LT program.51 Six components, which originate from annihilation of p-Ps (1), free positrons (2) and o-Ps (3-6), were necessary to fit the spectrum of dry SBA-3 with reasonable accuracy (χ2 ≤ 1.02). In the further analysis of the adsorption and desorption runs, the lifetime of the p-Ps component was fixed to τ1 = 125 ps to prevent scatter of the results caused by its mixing with the resolution function. It resulted in stabilization of the free positrons lifetime at τ2 ≈ 440 ps. However, even then the scatter of the lifetime of the longest-lived o-Ps component (τ6) was unacceptably large due to its very low intensity (< 2 %). Therefore, it was fixed at the average value τ6 = 60 ns. The pressure dependences obtained this way were readable, but still noisy. Fortunately, the lifetime τ3 did not exhibit a clear pressure dependence extending beyond its uncertainty, and thus τ3 was also fixed to its average value 1.17 ns. This approach allowed to obtain relatively smooth dependences even with the lifetime distribution σ5 of the fifth component (τ5) that was assumed in the final analysis. The analysis of the high-statistics spectra was performed by MELT program52, which allows to calculate distribution of lifetimes without assuming the number of components a priori.

Results and discussion Porosity The low-temperature nitrogen adsorption-desorption measurements on two dimensional mesoporous SBA-3 appear to be of the type I isotherms, which is the characteristic for microporous materials according to IUPAC (Fig. 1a).53 The specific surface area, which was fitted from the data, gives the Brunauer–Emmett–Teller (BET) surface area of 1030 ± 30 m²/g. The total pore volume estimated from the single point adsorption is 0.506 cm³/g. The αs-plot and t-plot were calculated from the nitrogen adsorption isotherms (Supplement, Appx.2). The αs-plot reveals that SBA-3 contains micropores. The t-plot gives an estimation of the micropore area of 499 m2/g and the micropore volume of 0.212 cm3/g. The corresponding pore size distribution of SBA-3 (Fig. 1b) derived from the adsorption branch of isotherm using the NLDFT method



indicates the presence of micropores. From the PSD it may be concluded that in SBA-3 two groups of pore of the diameter below 2 nm are present. The pores of size on the borderline between mesopore and micropore ranges with the PSD peak centred at ca. 2 nm are also present in the studied SBA-3.

b) dV/dlogD (cm3g-1)

Quantity Adsorbed (cm3g-1 STP)

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2

1

0 0.4 0.6 0.8 1

2

4

6

8

D (nm)

Fig. 1 Nitrogen adsorption–desorption isotherms of SBA-3 (a) and the corresponding pore size distribution (b). The adsorption and desorption branches are represented by triangle pointing right and left, respectively.

Lifetime and free volume size distributions To identify kinds of free volumes present in SBA-3 at various hydration levels, pore size distributions were calculated from the lifetime distributions received as a result of MELT analysis.54 The calculation was performed for dry, partially hydrated (p/p0 = 0.27) and completely hydrated (p/p0 = 1) SBA-3. The Extended Tao-Eldrup (ETE) model55 was used to obtain the relation between lifetime and free volume size. The assumptions of the model had to be adjusted for each case. 1. Cylindrical geometry of pores was assumed for dry SBA-3. This is an obvious choice for its primary mesopores, which are known to have honeycomb-like structure of long cylindrical channels. However, it should be remembered that the size of more spherical-like free volumes can be slightly underestimated. Except the choice of the pore geometry, the ETE model requires to assume the ∆ value, which is an empirically adjusted parameter. It is related to the electron density of pore walls and in the case of porous silica, was found to be ca. 0.18 nm.56,57 2. The assumptions required to perform the calculations for partially hydrated SBA-3 are the most difficult to determine, because the location of water is not known. As a first approximation, cylindrical geometry was retained. It would correspond to a scenario, in


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which water forms a layer on the surface of the pores. In such case, the ∆ parameter was set to 0.166 nm, which is commonly used for water.58,59 3. The cylindrical shape of pores is not appropriate for o-Ps, when the pores are completely filled. Instead, we expect “digging” of spherical bubbles. Therefore, spherical geometry was used in the calculations. Since, o-Ps locates preferably in water, ∆ = 0.166 nm was chosen. The free volume size distributions based on the above assumptions were calculated using the relation 60: dV dI dτ ∝ dD dτ dD

(1)

Fig. 2 Distribution of o-Ps lifetimes (left) obtained using MELT analysis and free volume size distributions (right) calculated using ETE model in dry (red), partially (green) and fully (blue) hydrated SBA-3. The lifetime and free volume size distributions for dry, partially hydrated and fully hydrated SBA-3 are shown in Fig. 2. The dry SBA-3 shows four o-Ps components indicating the presence of various kinds of free volumes. Another o-Ps components appear in the initial stage of the adsorption process, followed by reduction of their number in the final stage of adsorption. In the case of dry SBA-3, the two long-lived o-Ps components; τ6 > 80 ns and τ5 = 20-35 ns are attributed to large intergranular spaces and mesopores, respectively. The PSD shows the presence of a relatively narrow (FWHM = 0.23 nm) distribution of pores with diameter centred at ca. 1.9 nm, which dominates in the system. The two short-lived components, τ4 = 8-12 ns and τ3 = 3-5 ns with small intensities, can be ascribed to micropores in SBA-3. The micropore of sizes 0.7 nm and slightly above 1 nm surprisingly well coincide with the ones obtained from nitrogen adsorption (Fig.1b). There is practically no component related to the bulk silica. Most likely it has low intensity due to small thickness of silica walls and, therefore, was not resolved



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from the free positron component that has exceptionally long lifetime in the highly porous material. Large dispersion of lifetimes in this component confirms the above hypothesis. The tail of the free positron component, which possibly originates from o-Ps, is shown in Fig. 2. Partial hydration of SBA-3 (p/p0 = 0.27) results in the intensity reduction of the long-lived components in favour of the short-lived ones. Practically, the continuous distribution of lifetimes is visible in the range of micropores and silica skeleton. It indicates that free volumes in a variety of sizes are present in the system. Two characteristic peaks appear around 1 and 3 ns. These are the only components left, which become slightly shorter with a narrow distribution, when water completely fills the pores (p/p0 = 1). The longer one with τ4 ≈ 2 ns coincides well with the lifetime observed in bulk water.61 However, no component with lifetime ca. 1 ns is present in the bulk water spectra. Therefore, it has to be the characteristic of the SBA-3-water binary system. The most probable origin of this component is the water-silica interface. Some contribution from micropores, which are either initially closed or capped because they are too deep or/and too small to host water molecules, is also expected. The interpretation of the origin of the components is summarized in Fig.3.

Fig. 3 Scheme presenting the origin of the particular o-Ps components (3-6) in dry (a), partially hydrated (b) and fully hydrated (c) SBA-3. The red arrow indicates that the origin of the 6th component is mostly migration of o-Ps outside mesopores. The detailed analysis of free volume changes during adsorption and desorption of water is required to understand the mechanism of adsorption-desorption of water in the SBA-3 pore system. These changes are reflected in the variation of lifetime, its distribution and intensity of oPs components. Therefore, free volume changes can be discussed interpreting these quantities.


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Water adsorption and desorption course by PALS The introduction of water into the mesopores results in the modification of free volume sizes during various stages of adsorption and desorption. Positron annihilation lifetime (PAL) spectra collected at various relative pressures reflect the evolution of different free volumes in the system. As it was shown in previous section, the lifetime of an individual o-Ps component is related to the size of free volume where o-Ps annihilates. Therefore, it can be used to evaluate the water-free volume size during the adsorption and desorption process. On the contrary, the volume of a particular group of pores or smaller free spaces is correlated to both intensity and lifetime. However, its dependence on the lifetime is weaker than the one on the intensity. In consequence, if the change of a lifetime is not large, the intensity related to this lifetime is a good estimate of the volume of that group of pores. Four to six o-Ps components can be extracted from the PAL spectra measured as a function of pressure. However, the exact number of components present in the system at a given pressure could not be determined with certainty. Moreover, the MELT analysis showed that wide lifetime distributions, which cannot be exactly reconstructed by LT, are present in the part of the spectra. Therefore, an approximation had to be made to achieve dependences smooth enough to allow interpretation of the experimental data. For this purpose, each of the PAL spectra was fitted assuming the minimum number of components to obtain satisfying fit (χ2 ≤ 1.02). This approach applied to the spectra with moderate number of counts usually results in the smaller number of components than the one found by MELT. Possible distortions in the LT results can be estimated by comparing them to the corresponding MELT results (Supplement, Appx.3). Additionally, lifetimes of two extreme o-Ps components (τ3 and τ6) were fixed based on their average values to get smaller scatter of the observed results.



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Fig. 4 o-Ps lifetimes (τn) and intensities (In) in SBA-3 as a function of relative pressure of water vapour during adsorption (triangle pointing right) and desorption (triangle pointing left). Dispersion (σ5) of τ5 during adsorption and desorption is shown by corresponding hollow triangles

Lifetimes and Intensities The lifetimes, intensities and dispersion of o-Ps components at various pressures during adsorption and desorption of water are shown in Fig. 4. The number of components decreases with the increasing pressure, which indicates the disappearance of some free volumes in the system. The two long-lived o-Ps components (6-th and 5-th) disappear at a relative pressure 0.2 and 0.4, respectively. In contrary, the intermediate-lived and short-lived o-Ps components (4-th and 3-rd, respectively) are present in the whole pressure range. The presence of water in the


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pores has clearly a greater impact on the o-Ps intensities, in particular I5 and I4, than on the lifetimes. Except I6, which is too small to observe its details, all other components show an intensity hysteresis in different pressure regimes. The discussion of the pressure dependence of the PAL parameters allows to reconstruct the course of water adsorption and desorption in the SBA-3 pore system.

Longest-lived o-Ps component The contribution of the longest-lived o-Ps component, which corresponds to o-Ps annihilation in intergranular spaces in SBA-3 (Fig. 3), is only I6 ~ 2%. Since water is primarily confined in mesopores, no significant change in the free volume size corresponding to this component is expected with the change in pressure until p/p0 approaches one. Therefore, fixing the lifetime of this component (τ6) during the numerical analysis to reduce uncertainty in other parameters is well justified. Most likely the average value 60 ns is underestimated due to the difficulty in extracting this component from the background of random coincidences. However, fixing τ6 at almost two times greater value obtained from MELT influences other components very slightly (the most sensitive is τ5, but it elongates by less than 1 ns and the change of I5 does not exceed its uncertainty range). Similar to τ6, the intensity of this component (I6) is expected to be constant until the pressure close to p0 is reached. Surprisingly, it decreases fast with pressure and reaches zero at much lower pressure (p/p0 ≈ 0.2) than I5, which is related to mesopores. It indicates that virtually all oPs that annihilate in intergranular spaces do not form there. The surface of mesopores is approximately hundred times larger than that of intergranular spaces (including mesopore entrances). Therefore, the vast majority of o-Ps is formed in the mesopores. A small fraction of these o-Ps can reach the end of a mesopore and migrate to intergranular spaces.62 According to this interpretation, the disappearance of the longest-lived component is not caused by water filling intergranular spaces, but rather by water blocking the entrances to the mesopores (no more o-Ps are able to escape from the mesopores).

Medium-lived o-Ps component The medium-lived o-Ps component is related to the free volume inside the mesopores of SBA-3 (Fig.3). This component dominates in the dry system (I5 = 27 %), where τ5 is ca. 23 ns. It corresponds to the diameter of 1.8 nm, as given by the ETE model for cylindrical geometry and ∆ = 0.18 nm. The adsorption-desorption of water in the mesopores is expected to cause changes in the size of the free volume (i.e. water-free space). This, in turn, should be reflected in τ5. However, this direct relationship is not preserved even at slightly elevated pressures (p/p0 > 0.06). In this pressure range a lognormal distribution of τ5 has to be assumed to obtain good fits. It indicates that the free volume sizes become less uniform due to the presence of water. In consequence, a single value is no longer a good approximation to describe the pore size. Instead, a quite wide PSD has to be considered, which is in agreement with the results of MELT analysis.



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Its evolution is reflected by the changes of both τ5 and σ5. During adsorption, the small decrease in τ5 and a much more pronounced increase in σ5 are observed, but these changes are almost within the uncertainty ranges. During desorption, the slight decrease in τ5 in the relative pressure range 0.3-0.2 is questionable due to large uncertainties when the intensity of the component is small, but the increase from 19 to 24 ns on further reduction in pressure is much more reliable. Simultaneously, σ5 follows the same behaviour as during adsorption. The increase in σ5 with the increase in water content reveals that the evolution of free volumes of diversified sizes occurs during adsorption as well as desorption. On the other hand, τ5 is shorter for the desorption run in comparison to the adsorption one. This indicates the smaller average size of water-free volumes or/and greater electron density of the free volume wall. In the ETE model electron density is represented by the ∆ parameter, which is larger for silica and smaller for water (see “Lifetime and free volume size distributions”). The o-Ps lifetime in two different free volumes of the same size but smaller or larger electron density would result in longer and shorter lifetime, respectively. Thus, it is possible that during adsorption the pore wall is more “loose” than during desorption. It would happen if water molecules initially adsorb on the protruding places on a wall, while during desorption last molecules remain in cavities (e.g. micropores). The intensity (I5) of the medium-lived component decreases with the increase in pressure during adsorption and subsequently vanishes at p/p0 ≈ 0.4. This is ascribed to successive filling of mesopores with water until the whole pore volume gets occupied. The intensity I5 exhibits a prominent hysteresis in the whole pressure range. Desorption is shifted towards lower p/p0 by ca. 0.1, which is in good agreement with the gravimetric sorption experiment.17 Noteworthy is that I5 at zero pressure after desorption differs by as much as 4% from the value observed before adsorption. Certainly this does not reflect a fraction of pores blocked by water, because bulk water hardly remains in the system at this pressure. This is indicated by the intensity (I4) of the water-related component, which is close to its zero-pressure value already below p/p0 = 0.2. An alternative is that during desorption, water remains in micropores even at low pressure due to hydrophilic nature of the pore surface. Undoubtedly, a fraction of micropores has entrances open to mesopores, analogously to described previously for mesopores interconnected to intergranular spaces. In consequence, it is highly probable that o-Ps formed in the open micropores migrates to the adjacent mesopore and annihilate with lifetime characteristic for mesopores. However, this oPs fraction cannot contribute to I5 when micropores are blocked by water molecules and migration is suppressed. Instead of considering o-Ps migration, the difference in I5 during adsorption and desorption can be explained in terms of the surface roughness. The intensity of a component related to mesopores depends on their surface area, which in turn depends on the roughness.63,64 Therefore, the greater intensity of the medium-lived o-Ps component during adsorption than during desorption indicates the rough and smooth surface, respectively. Most likely this is the consequence of protuberances (water isles) formation during adsorption and surface flattening, which is caused by water molecules remaining in cavities, during desorption.


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This hypothesis is confirmed by recovery of I5 to its original value (i.e. ca. 27%) after heating the sample to 473 K under high vacuum. Therefore, the shift of the pressure dependence of I5 is possibly not only along p/p0 axis, but also along vertical axis, at least in the pressure range from 0 to 0.2. It should be emphasized that the pressure dependences of both lifetime and intensity suggest that water localization is different during the initial phase of adsorption than during the final phase of desorption (p/p0 = 0-0.2). Namely, water forms protuberances or remains in cavities, respectively.

Intermediate-lived o-Ps component The component with the intermediate lifetime (τ4 ~ 5-8 ns) originates most likely from the micropores in the sample. However, the o-Ps, which annihilated in mesopores before reaching full thermalization, can also give some contribution to this component (Fig.3). The occupation of excited levels in a potential well greater than that described by Boltzmann distribution for these o-Ps leads to the lifetime shortening. In consequence, their lifetime, which would be τ5 when thermalized, can become even close to τ4. The decrease in τ4 from ca. 6 to 3 ns with the increase in pressure during mesopore filling (i.e. when I4 > 0 at p/p0 < 0.4) can be ascribed to several factors: 1. decrease of the micropore size caused by their partial blockage by water molecules, 2. increase of the contribution from bubbles in water, where o-Ps lifetime is shorter than in micropores, when pores are getting filled, 3. possible increase of the thermalization time, what causes even greater lifetime shortening, due to the different interaction of o-Ps with the mesopore surface when water is adsorbed than with dry surface. These factors can contribute only when pores are not completely filled. However, τ4 keeps decreasing (from ca. 3 to 2 ns) also above p/p0 = 0.4. Similar effect was observed in the case of n-heptane adsorption.38,65 At the relative vapour pressure p/p0 = 1, τ4 is close to the lifetime observed for the bubble in bulk liquid water.61 The intensity of this o-Ps component (I4) is a good approximation of the water content in the system. It nearly mirrors I5, which confirms that most of the bulk water (i.e. in clusters large enough to host an o-Ps bubble) is located in the mesopores. The hysteresis loop seen in I4 is the most similar to the hysteresis loop seen for conventional adsorption-desorption isotherm among all the parameters of PAL spectra. Its stepwise run indicates capillary condensation during adsorption and evaporation from the pores during desorption at relative pressures ca. 0.3-0.4 and 0.3-0.2, respectively. The sharp intensity changes confirm the fairly uniform size of mesopores. Above these steps this component dominates in the spectra with constant intensity ca. 20%. This



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plateau indicates that amount of water is virtually pressure independent there. Most likely all the free volumes in SBA-3 are occupied by water in the pressure range of the plateau. The intensity I4 exhibits a distinct hysteresis in the relative pressure range 0.2-0.4. It can be explained on various levels (i.e. percolation theory, molecular dynamics, density functional theory or dynamic mean field theory).26,66 It is noteworthy that I4 desorption run is steeper than adsorption one, which exhibits more smooth transition from small to large slope in the pressure range 0.2-0.3. The origin of the intermediate-lived o-Ps component from confined water can be verified by comparing it with the amount of water introduced into the sample. Although the used setup was not designed to do an exact measurement of the volume of water vapour introduced into the chamber at subsequent pressures, it can be estimated from the vapour flow. Unfortunately, this method seems to fail in giving absolute values. On the other hand, the conditions of water adsorption during the PALS experiment cannot be accurately reproduced by the standard adsorption experiment (Supplement, Appx.4). However, the most reliable parameter describing the water adsorption, which should be common for both experiments, is the volume of adsorbed water in completely filled pores. Therefore, the data obtained from the vapour flow are normalized to this volume at the possibly high relative pressure (VH2O = 0.24 cm3/g at p/p0 = 0.83) (Fig. 5). It should be remembered that the result obtained this way can be inaccurate and gives only the qualitative information.

Fig. 5 Volume of water adsorbed in SBA-3 as a function of water vapour relative pressure during adsorption (triangle pointing right) and desorption (triangle pointing left) obtained by vapour flow measurement normalized with respect to the volume obtained from water adsorption measurements (Supplement , Appx. 4). Spline lines are provided for convenience.


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In a similar way to I4, the pressure dependence of the volume of water (VH2O) shows three steps: linear increase (p/p0 = 0-0.3), sharp step (p/p0 = 0.3-0.4) and plateau (p/p0 > 0.4). Nevertheless, there are some differences between the variations of I4 and VH2O. The initial increase of volume is much steeper and its plateau is not as flat as in the case of the intensity. These differences are reasonable under the assumptions that: 1. Below the condensation pressure, water forms mostly small clusters of molecules, whose volume is not large enough to host an o-Ps bubble. 2. The o-Ps intensity cannot increase indefinitely, but eventually reaches saturation. In bulk water, o-Ps intensity ca. 23% was found.67 Thus, I4 ≈ 20% in the binary system, where an additional short-lived o-Ps component (I3 ≈ 5%) exists, seems to be very close to the saturation value. In consequence, o-Ps fraction cannot increase even if some additional water is placed in intergranular spaces. Still, some deviation of the ratio between I4 and I3 is expected if the ratio between the amount of silica and water changes in the binary system. However, ca. 15% increase of the volume of water, which occurs above condensation in the mesopores, is not significant enough to noticeably change the ratio between the intensities. The pressure dependence of the volume of desorbed water is shifted from the adsorption run, forming a hysteresis loop. Quite interesting is that the hysteresis can be seen at pressures both below and above the condensation-evaporation step. The low pressure part of the VH2O(p/p0) dependence is not reliable enough to draw conclusions from it (Supplement, Appx.4), but the hysteresis above the step may indicate the existence of intergranular spaces, which are accessible only through mesopores (the blocking effect). The agreement between I4 and VH2O can be directly verified by plotting their mutual function (Fig. 6). Characteristic s-shaped dependency is visible for both adsorption and desorption. Its flat ends depict both the ranges described previously, where I4 does not follow volume changes (i.e. water clusters being too small to host o-Ps bubble and the intensity saturation). However, there is a wide range (VH2O = 0.07-0.18 cm3/g) where dependence between the intensity and the volume of water is almost linear. A shift between the adsorption and desorption dependences is visible, but still their agreement is quite good. This relation between the intensity and the volume of water allows to determine the amount of bulk water in a binary system just by PALS measurement. This is a very convenient and non-invasive method, especially, if the history of a sample is not known.



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20

15

10

5

0 0

0.05

0.1

0.15

0.2

0.25

VH2O (cm3/g)

Fig. 6 Intensity of the intermediate-lived component as a function of the volume of water adsorbed in SBA-3 during adsorption (triangle pointing right) and desorption (triangle pointing left). Fitted polynomials were added as an eye-guide.

Shortest-lived o-Ps component The lifetime (τ3) of the shortest-lived o-Ps component is difficult to determine. In dry SBA-3, this component originates mostly from the bulk silica skeleton, which has the form of thin (~1 nm) walls. Therefore, the component has a very small intensity of ca. 1.5%, which makes it hardly separable from other more intense components. At complete pore filling by water, the shortest o-Ps component is ascribed to the free volumes present at the interface of water and silica (Fig.3). Its intensity reaches 5-6%, which would be enough to properly fit this component. Unfortunately, lifetimes of both the short-lived components (τ3 and τ4) are too close to each other above p/p0 = 0.4, when the mesopores are completely filled, and again separating them is a problem. The adsorption of water in the mesopores should not significantly affect the small contribution from bulk silica. Therefore, we can assume that any variation in the shorter component with changing pressure is caused by the increasing contribution from free volumes at the interface. However, both the lifetimes related to bulk silica and the interface are very similar. Once the interface is formed, the location of the water molecules adjacent to silica does not depend on the insignificant changes of the external pressure (up to p0). In consequence, size of the free volume on the interface is not expected to vary with the change of p/p0. Therefore, fixing τ3 to 1.17 ns, which corresponds to the interface, seems to be justified. It considerably reduces the uncertainty of other parameters, which in turn helps in the interpretation of the results. However, it should be remembered that this approximation most likely causes a distortion of the results at low pressure. The intensity (I3) of this component has a very small contribution at low pressure but it increases with pressure up to the capillary condensation (p/p0 = 0.3). This reveals greater contribution from the interfacial free volumes, when larger surface area is covered by water. At higher relative


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pressures (> 0.3), I3 becomes constant indicating that water covers almost the whole surface of pore walls. The I3 increase at low pressure during desorption process may indicate the presence of water confined in micropores even after desorption is completed.

Free volume The most interesting from our point of view is water distribution at various stages of adsorption and desorption. This can be derived from the size and the volume of water-free space in mesopores that are provided by PALS almost directly as the parameters of the medium-lived component (i.e. τ5, σ5 and I5). However, information describing o-Ps formation and annihilation in water-free spaces is not straightforward for reasoning. Pore size distributions, like the ones presented in the “Lifetime and free volume size distributions” section, are much more convenient for a qualitative estimation of the water adsorption-desorption course. Additionally, their parameters can be used in a quantitative discussion of these processes. A PSD can also be reconstructed from a component, for which lifetime dispersion is assumed in LT analysis. However, it should be remembered that the PSDs obtained this way can be distorted if the lognormal shape of lifetime distribution, which is assumed a priori, differs significantly from the shape of the real distribution. Another possible source of distortions can come from the assumptions used in the model calculations (i.e. shape of free volume and parameter ∆), which have to be chosen based on a hypothetical course of the process. Classic description of capillary condensation in perfectly cylindrical pores says that molecules adsorbed on a surface form layers or isles until the Kelvin radius, which inter alia depends on adsorbate pressure, equals pore radius. Then rapid condensation in the whole volume occurs at a given pressure. In real systems pore radii differ not only between pores but also along the same pore. Most likely it results in formation of “plugs” in narrower sections.19 This seems to be supported by the comparison of interaction energy between water molecules (44-45 kJ/mol) and H-bond formation energy for surface bonded silanol (11.7 kJ/mol).68 However, the large spread of both water 69 and water-silanol group 70 interaction energies determined by various methods makes it questionable. Still, heterogeneous distribution of silanol groups on silica surface causes that, undoubtedly, there are sites preferred by water molecules,71 where isles begin their growth. From the viewpoint of o-Ps even a water isle can also be considered as a “plug”. This is so because the pore contraction caused by a water isle acts as an energy barrier for o-Ps. Thus, the isle is sufficient to prevent further propagation of o-Ps if it is large enough, which requires only several water molecules in pores of diameter ca. 2 nm. Based on these considerations, the assumptions of the model used for calculation of the approximate size distribution of water-free pore volume from the lifetime distribution of the medium-lived o-Ps component were formulated: 1. Geometry. In addition to pick-off in the pore walls, the o-Ps lifetime is shortened due to pickoff annihilation in the plugs at the ends of free-space, where o-Ps is trapped. It follows that a cylindrical free space of the radius of the original pore and limited by two plugs to the length



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L is assumed. The curvature of the plugs is neglected. Also, water molecules that can possibly be adsorbed on pore walls are not taken into account. Both these approximations may lead to the underestimation of the length of a water-free space. 2. Material of the walls. The cylinder walls are considered to be made of silica. According to this, the probability of both the intrinsic annihilation and the pick-off annihilation in the walls is the inverse of the lifetime observed for open pores (calculated for the high statistic spectrum of dry SBA-3). No assumption of ∆ is required. The plugs (i.e. the cylinder bases) are considered to be made of water. The probability of pick-off annihilation in them is calculated using the ETE model with ∆ = 0.166 nm. This value would be smaller in the case of water isles instead of full plugs, what can cause an overestimation of the calculated length.

Fig. 7 Length distributions of hypothetic gaps in water-filled mesopores for selected pressures during adsorption and desorption. The pore diameter is fixed in the described model, thus the lifetime distribution is reflected in the pore length distribution (PLD) alone. The PLDs obtained from the lifetime distributions of the medium-lived component for selected pressures are presented in Fig. 7. The “gaps” between the water plugs (including large isles) have the length distribution reaching to several nanometers


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with maximum at ca. 2 nm at p/p0 ≈ 0.1. Initially, a shift of PLDs towards smaller lengths is visible during the first stage of adsorption. Further changes consist in the decrease in the concentration of gaps of all sizes. Most likely such evolution of PLD is a consequence of shortening of all gaps until they reach minimum length, below which they collapse (i.e. water plugs on their ends merge). The tendency of changes is similar for desorption. In this case, it can be a consequence of the following scenario: water filling the pores splits into separate plugs, which initially have minimal possible size (similar to adsorption). Then, more small gaps are formed and simultaneously the length of existing ones increases with the decrease in pressure, what is observed as vertical “growth” of the PLDs. It seems that the number of gaps reaches saturation at a certain pressure (p/p0 ≈ 0.2) and further changes consist in the increase of their size (possibly due to their interconnection). At this stage PLDs shift towards larger lengths.

Fig. 8 Total water-free pore volume (V), length of the cylinder (gap) at maximum of PLD (L@max) (full symbols) and full width at half maximum of its distribution (FWHM) (open symbols) calculated from the medium-lived o-Ps lifetime at various relative vapour pressures during adsorption (triangle pointing right) and desorption (triangle pointing left). Fitted polynomials serve as an eye-guide.



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Reliable determination of the evolution of PLD with pressure requires quantitative information describing the shape of PLDs. The total water-free pore volume, i.e. the area under a PLD (V), length of the gap at maximum of a PLD (L@max) and full width at half maximum of a PLD (FWHM) were chosen as the parameters providing such information (Fig. 8). The most probable length of the gap (L@max) clearly changes at low relative pressure, but this tendency becomes very weak at p/p0 > 0.15. The pressure dependence of FWHM is even weaker due to the lack of significant changes in low pressure range. This behaviour is common for both adsorption and desorption, but during desorption the gaps seems to be slightly smaller, as can be concluded from both L@max and FWHM values. It is worth noticing that FWHM decreases with decreasing p/p0 at the beginning of water removal from pores, which is opposite to all other dependencies. According to this, it may be assumed that some large water-free volumes open in addition to the sub-nanometre gaps during the initial phase of desorption. It is quite natural that V follows the similar behaviour as I5, i.e. the decrease at low pressures during adsorption (p/p0 < 0.3) and desorption (p/p0 < 0.2) is relatively slow, while the decrease during condensation or evaporation stage is clearly sharper (Fig. 8). More interesting is the lack of difference in V between adsorption and desorption for p/p0 < 0.2, which was clearly seen in I5. This allows to formulate an explanation of the I5 hysteresis in this pressure range alternative to the one presented in the “Medium-lived o-Ps component” section. Instead of the differences in the surface roughness during adsorption and desorption, the I5 hysteresis can originate from the differences in L@max and FWHM, which are both smaller during desorption. It is possible because the term dτ/dD in Eq.(1) has the bell-shaped dependence on D.72 In the case of the gap length this term becomes dτ/dL (Supplement, Appx. 5) with maximum around 0.8 nm. In consequence, the same total volume of pores of size 1 nm and 2 nm will result in the small and large o-Ps intensity, respectively. In such case, the water-free volume in the mesopores at corresponding pressures below 0.2 would be approximately the same during adsorption and desorption. This is not consistent with the estimated volume of water, which shows hysteresis in this range (Fig. 5) also. Nevertheless, it could be possible if not full plugs, but isles only partially blocking a pore clearance are formed during adsorption, while full plugs completely closing the pore clearance remain during desorption. In both cases the section of the pore is inaccessible to o-Ps, but the amount of water required to form the cluster blocking the same length of a pore is greater during desorption.

Conclusions Positron annihilation lifetime spectroscopy enables an innovative approach to study the adsorption-desorption behaviour of water in the two dimensional mesoporous SBA-3. This technique provides a free-volume perspective to probe the course of water adsorption and desorption. Several o-Ps components are identified in the PAL spectra of water–SBA-3 binary system. These components are characterized by lifetime and intensity that are related to the size and concentration of free volumes, respectively. Therefore, the changes in PAL spectra can be


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interpreted in terms of evolving free volumes of different types: intergranular spaces, mesopores, micropores, o-Ps bubbles in liquid water and free spaces on water-silica interface. This perspective allows to propose the most probable mechanism of adsorption and desorption of water in the pore network of ordered silica SBA-3. Course of adsorption-desorption of water. During the initial stage of adsorption at low pressure, water forms isles on the inner walls of the pores. These isles are mainly concentrated around silanol groups, which are pervasive on the silica surface of SBA-3. The number and size of these isles are initially small and the large fraction of pore volume is free of water. With the increase of pressure in the system, more and more isles occupy free spaces in the pores. This is reflected in the decrease in the average length of the water-free cylinder and, consequently, the total pore volume. The presence of isles also reduces the probability of o-Ps escape from the mesopores into the intergranular spaces. The decreasing pore volume is correlated with the increasing contribution from the water-silica interface. This indicates more and more coverage of the pore surface by water and suggests that a complete surface coverage is not achieved until capillary condensation occurs. When the relative pressure is above 0.3 and capillary condensation starts, the isles become large enough to completely close the pore clearance, i.e. form plugs inside pores. These plugs consisting of liquid water are large enough to host o-Ps bubbles, whose concentration reflects the amount of water in the system. Condensation occurs in the narrow relative pressure range (ca. 0.3-0.4). It is observed as the constant replacement of water-free volume by bulk water. Presumably, the new plugs formation is no longer the dominating process at this stage. Instead, the size of every existing cavity between plugs systematically decreases with pressure and the cavity collapses when its size drops below several tens of nanometre. No further significant changes in PAL spectra with pressure are detected when the concentration of water-free volumes drops to zero. The course of water desorption from the pores is similar to its adsorption, i.e. it is mediated mainly through the formation of cavities. When the capillary evaporation starts, water-free cylinders limited by water plugs at their ends (i.e. the cavities), appear in water columns filling the pores. Further pressure decrease in the range 0.3-0.2 results in continued breaking of the plugs and, consequently, increase in the concentration of the cavities. Simultaneously, the size of existing cavities increases. The water plugs are too small to host o-Ps bubbles below relative pressure of 0.2. Formation of new cavities becomes inferior to their growth and joining together in this stage. Eventually, all water plugs evaporate from the mesopores. Unlike during adsorption, water remains confined in micropores at low relative pressure. Complete removal of water from the pores requires heating SBA-3 in vacuum. The presented interpretation follows mostly from the fact that the concentration of free volumes decreases fast with pressure increase, but their size distribution is only slightly affected. This is specific to the plug-cavity distribution of water and can be hardly interpreted in terms of the layer-by-layer adsorption mechanism. In the latter case the size of water-free volume is expected to systematically decrease and approach zero along with the concentration. Moreover, this



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mechanism gives no convincing explanation why neither the size distribution increases when water is introduced to the system nor the concentration of the interfacial free volumes increases during whole condensation stage. These effects can be interpreted in terms of the plug-cavity mechanism as heterogeneity of the isles/plugs distribution and successive coverage of the pore surface along with plugs growth, respectively. Strengths and limitations. The free volume perspective provided by PALS gives a new insight into the mechanism of water adsorption and desorption. This sensitive way to measure in situ the size distribution of water-free space in the pores is still unique in adsorption studies. Additionally, this technique brings otherwise inaccessible information about the subnanometer free volumes, which are related to the micropores, bulk adsorbate and adsorbate-adsorbent interface. On this basis, the current state of knowledge of o-Ps behaviour in porous materials allows to elucidate the course of adsorption and desorption. The gravimetric techniques usually provide much less information about the system. Moreover, they are based on models in much greater extent than the presented study to explain the mechanism of pore filling/emptying. In this regard, the ability to probe in situ both open and closed free volumes having a wide range of sizes can provide almost direct information about the phenomena. For example, the cavitation phenomenon during desorption, whose presence was only deduced, is revealed with great certainty in the present work. However, there are certain limitations of this technique, which pose some difficulties in interpreting the results. Several assumptions are required to analyse the positron annihilation lifetime spectra (i.e. the number of components, the value of the ∆ parameter, and the freevolume shape). Inaccuracy or simplification in each assumption can distort the results (e.g. the parameters describing the micropore related component at low pressure are uncertain due to simplification in the number of components and a necessity to fix its lifetime). In addition, o-Ps behaviour in the studied porous material is complex due to its migration between different kinds of pores, what primarily distorts the volumes calculated from the intensities related to these pores. Apart from all these complexities and limitations in analysing and interpretation of PALS results, some effects and their implications (e.g. the wide size distribution of water-free spaces implying plug-cavity water arrangement) can be ascertained for sure. Prospects for further research. Confirmation of the hypothesis of water confinement in micropores even in high vacuum and revealing its details requires additional studies by PALS as well as supplementary techniques. High statistics measurements at low pressure can be performed using a digital PAL spectrometer to achieve a possibly good time resolution. Simultaneously, the accuracy of the measurement of the volume of water in the system should be improved. Additionally, removal of the confined water during heating should be noticeable by both PALS and calorimetric techniques. The presence of the water in micropores or other modifications of the pore surface should be detectable by nuclear magnetic resonance or infrared spectroscopy. However, such measurements require the precise control of the conditions of a sample and, in consequence, a specialized or dedicated experimental setup.


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The presented study opens multiple prospects for further research on the adsorption and desorption mechanism using PALS. Validity of the plug-cavity distribution in pores of different sizes and shapes can be verified. It would be interesting to study if the surface of more hydrophobic character results in similar course of adsorption and desorption. The presented method also provides the possibility to monitor the kinetics of water introduction and removal from pores by probing the water-free volume and the amount of bulk water. Finally, the control over the level of pore filling and the knowledge of the water distribution allows to study the behaviour of water clusters of various size (e.g. as a function of temperature).

Supporting Information 1. Appendix 1: Description of the pressure system used for adsorption and desorption measurement 2. Appendix 2: αs- plot and t-plot of nitrogen adsorption isotherms on SBA-3 obtained from the adsorption branch. 3. Appendix 3: Discussion on results obtained using LT and MELT analysis. 4. Appendix 4: Comparison of the volume of water adsorbed in SBA-3 obtained from the vapour flow measurement and standard water adsorption experiment. 5. Appendix 5: The estimation of water-free volume as a function of the water-free gap length using ETE model related term.

References 1. Sparreboom, W.; Berg, A. van den and Eijkel, J. C. T. Principles and Applications of Nanofluidic Transports. Nat. Nanotechnol. 2009, 4, 713-720. 2. Schoch, R. B.; Han, J.; Renaud, P. Transport Phenomena in Nanofluidics. Rev. Mod. Phys. 2008, 80, 839-883. 3. Zhou, R.; Huang, X.; Margulis, C. J.; Berne, J. B. Hydrophobic Collapse in Multidomain Protein Folding. Science 2004, 305, 1605-1609. 4. Wheeler, T. D.; Stroock, A. D. The Transpiration of Water at Negative Pressures in a Synthetic Tree. Nat. Lett. 2008, 455, 208-212. 5. Lee, J. W.; Shim, W. G.; Moon, H. Adsorption Equilibrium and Kinetics for Capillary Condensation of Trichloroethylene on MCM-41 and MCM-48. Microporous Mesoporous Mater.2004, 73, 109-119.



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