Pore size distribution calculation from 1H NMR signal and N2 adsorption–desorption techniques

Physica B 407 (2012) 3797–3801

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Pore size distribution calculation from 1H NMR signal and N2 adsorption–desorption techniques Jamal Hassan a,b,n a b

Department of Applied Mathematics and Sciences, KU, United Arab Emirates Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

a r t i c l e i n f o

abstract

Article history: Received 27 February 2012 Received in revised form 13 May 2012 Accepted 15 May 2012 Available online 9 June 2012

The pore size distribution (PSD) of nano-material MCM-41 is determined using two different approaches: N2 adsorption–desorption and 1H NMR signal of water confined in silica nano-pores of MCM-41. The first approach is based on the recently modified Kelvin equation [J.V. Rocha, D. Barrera, K. Sapag, Top. Catal. 54(2011) 121–134] which deals with the known underestimation in pore size distribution for the mesoporous materials such as MCM-41 by introducing a correction factor to the classical Kelvin equation. The second method employs the Gibbs–Thompson equation, using NMR, for melting point depression of liquid in confined geometries. The result shows that both approaches give similar pore size distribution to some extent, and also the NMR technique can be considered as an alternative direct method to obtain quantitative results especially for mesoporous materials. The pore diameter estimated for the nano-material used in this study was about 35 and 38 A˚ for the modified Kelvin and NMR methods respectively. A comparison between these methods and the classical Kelvin equation is also presented. & 2012 Elsevier B.V. All rights reserved.

Keywords: Pore size distribution MCM-41 NMR Nitrogen absorption-desorption Kelvin equation

1. Introduction Nano-materials play an important role in many applications of science and technology. There is an increasing interest in using these materials in different fields ranging from chemistry, medicine, and biochemistry to electrical engineering. The characterization of the pores of these materials is an essential step before any application. Thus it is important to have a very fast, reliable and straightforward method for characterization of these materials. With gases such as nitrogen, nitrogen adsorption–desorption (NAD) or mercury intrusion porosimetry is the conventional way for calculating the pore size distribution (PSD) of porous materials [1]. These methods usually underestimate the real pore sizes especially for mesoporous materials (pore sizes in the range of ˚ [2,3]. Nuclear Magnetic Resonance (NMR) studies have 20–50 A) been carried out previously to characterize different materials (silica gel, controlled pore glass, zeolites, etc.) [4–7]. In addition, a number of NMR techniques have been used: spin–lattice relaxation T1, spin–spin relaxation T2 and NMR diffusion measurements [8–10] have been utilized for determining PSD in porous materials. These methods need prior information regarding the interaction

n

Correspondence address: Department of Applied Math and Sciences, KU, United Arab Emirates. Tel.: þ 971 2 4018094; fax: þ 971 2 4018099. E-mail address: [email protected] 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.05.063

between the solid and the liquid used and also the relaxation parameters that often are not available. On the other hand, NMR has a unique advantage in studying the freezing phenomena of confined water. This is because T2 of water is much larger (  a few seconds) than that of solid ice (  6 ms). This will ensure that the NMR signal below 273 K, the freezing temperature of bulk water, will arise essentially from the non-frozen confined water in the sample. This idea was used previously for estimating the PSD of materials [11–17]. These studies indicated the importance of using NMR for calculation of large pores; however limited studies are found for small pores (  30 nm). In this work we assess the usefulness of using NMR measurements for determination of the PSD for small pores (  30 nm) and to compare the result of this technique with that of NAD measurements. The melting point depression of liquid in confined geometries is utilized to obtain the PSD of a porous material. This is done by using the 1H NMR signal of unfrozen water versus temperature of hydrated sample mesoporous material MCM-41 which is fully saturated with water.

2. Experimental The method described in refs. [18–20] for the synthesis of MCM-41 is used to prepare the material needed for this work. The final product of the material needs to be hydroxylated. This is done by immersing the product inside deionized water and

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letting it stay for about 1 week in an open glass vial. To prepare fully saturated samples of MCM-41 with water, an amount of MCM-41 powder is immersed in deionized water inside two different small glass vials. The samples are then equilibrated at room temperature for 2 days. In order to force water to enter the pores (air leaving the pores), two different methods are used. In the first method, one of the glass vials containing the sample is placed in a high-speed centrifuge at 15,000 rmp. The centrifugation process is repeated several times. In the second method the other glass vial, containing the sample, is connected to a vacuum system and carefully pumped out till small bubbles are observed leaving the powder through the water. This is an indication that water is replacing the air inside the pores. This process is continued till no further air bubbles are seen leaving the immersed powder. The product, in both batches, is placed into two different filter papers to let them dry under ambient condition (for about 12 h) so that most of the excess water evaporates. The existence of some quantity of bulk water in the sample is also important as it ensures the observation of the bulk melting temperature and provides us with a calibration point for the melting curve of water within the pores. The samples are packed into 4 mm (ID) Magic Angle Spinning rotors and sealed with Viton O-rings along with Zirconia caps (from Wilmad LabGlass company). A standard 901 pulse sequence of 4 mm with repetition time of 10 s is used. The 1H NMR spectrum is taken, for each of these samples, at different temperatures corresponding to bulk water freezing point, 273, and 20 K below it (253 K). The results show that the sample prepared using centrifugation has larger amount of water as a bulk compared with the other one. The data presented in this study is for the sample prepared with the vacuum system which has some amount of bulk excess water outside the pores. The bulk water has no influence on the freezing depression DT of the pore water [21]. The experimental data is taken using a Bruker DMX 500 spectrometer of magnetic field of 11.7 T. The 1H NMR spectra are measured, every 2 K, in the range of temperature between 210 and 275 K. The temperature is controlled using a temperature controller of type BVT3000 provided with the spectrometer. The accuracy of the temperature determination is within 0.5 K and calibrated using pure methanol [22]. The temperature of the sample is lowered from room temperature to 210 K and the NMR spectra are recorded in the heating run. An equilibrium time of about 15 min is allowed at each temperature before collecting data. NAD measurements were carried out using a volumetric adsorption equipment (AUTOSORB-1MP, from Quantachrome Instruments) at 77 K with an outgas temperature at 473 K. X-ray diffraction patterns for the sample used in this study were recorded on a Rigaku D/M-2200T automated diffractometer ˚ (Ultimaþ) using Cu Ka radiation (l ¼1.5406 A).

The Kelvin radius Rk is given by the following equation (which from now on will be referred to as the classical Kelvin equation):[25] Rk ¼

K ab lnðP=P o Þ

3.1. PSD determination and NAD measurements The pore radius Rp of the material under study is the sum of the Kelvin radius Rk and the thickness of the initially adsorbed layer tads of nitrogen gas on the pore surface [22]: ð1Þ

There are different suggested methods to obtain tads from experimental relative pressure (P/Po). In this study, the following equation is used which is more suitable for cylindrical pores such

ð3Þ

Kab is the adsorption constant, which is equal to 2g V/RT, where g is the surface tension of liquid nitrogen, 8.88  10  3 (J/m2), VL is the molar volume of the liquid nitrogen, 3.468  1025 (A˚ 3/mole), R is the ideal gas constant, 8.3143  1020 (J A˚ 2/F m2 mole) and T is the absolute temperature of adsorption, 77 K; thus ˚ Kab ¼9.62 A[26]. In a recent study on MCM-41 [27] a correction factor fc is added to the classical Kelvin equation which gives an optimal match between experimental and simulated isotherm curves. ˚ for the Therefore, the modified-Kelvin radii Rk, expressed in A, adsorption and desorption branches, respectively, are given by Rk ¼

K ab þf c 2lnðP=P o Þ

Rk ¼

K ab þf c lnðP=P o Þ

ð4Þ

Finally, to determine the PSD, an expression for dV/dRp versus dRp is needed which can be written as
dV dV d P=P o dRk
¼ ð5Þ dRp dRk dRp d P=P o where dV/d(P/Po) is determined by numerical differentiation of the NAD data with respect to d(P/Po). The last two terms in the product, on the right hand side of Eq. (5), can be expressed in terms of d(P/Po) using Eq. (3) or (4). Thus the final expression is given as     dV dV P P
ln2 ¼a ð6Þ dRp Po Po d P=Po where a is a constant (a ¼0.98 A˚  1 if Eq. (3) is used, a ¼ 2 A˚  1 if the adsorption part of Eq. (4) is used and a ¼1 A˚  1 if the desorption part of Eq. (4) is used). The PSD of the porous material can be obtained by plotting dV/dRp (Eq. (6)) versus Rp (Eq. (1) and (3) or (1) and (4) depending on whether classical Kelvin or modified Kelvin pore radii are used, respectively). 3.2. PSD determination from NMR The melting point depression DTm of a liquid in a confined geometry is given by the Gibbs–Thompson equation[28]

DT m ¼ T m T m ðrÞ ¼

3. Theoretical background

Rp ¼ Rk þt ads

as those of MCM-41 [24]. Thus the tads value in A˚ is determined by  0:3968 60:65 ð2Þ t ads ¼ 0:03071logðP=P o Þ

4sT m r DHf r

ð7Þ

where Tm is the normal melting point of the bulk liquid, Tm(r) is the melting point of the same liquid confined in a confinement r, s is the surface energy at the liquid–solid interface, DHf is the bulk enthalpy of fusion and r is the density of the solid. In the above equation the contact angle between solid, water and the pore wall is assumed to reach p radians. The equation can be written, for a particular liquid, as T m T m ðrÞ ¼

k r

where k is a constant whose value depends on the liquid.

ð8Þ

J. Hassan / Physica B 407 (2012) 3797–3801

Most porous materials have interconnected pores with different pore sizes and distributions. If these materials are saturated with a liquid which is then cooled, this will produce a distribution of melting temperatures that depends (according to Eq. (8)) on the PSD. NMR is a powerful technique that can be used to monitor the amount of unfrozen water versus temperature. These measurements can then be utilized to determine the PSD of the porous material under study. The pore volume V(r) is a function of pore diameterr. The volume of pores with diameter between r and r þ Dr is (dV/dr)Dr. If the pores are filled with the liquid, the melting temperature of the liquid Tm(r) is related to the PSD by dV dV dT m ðrÞ ¼ dr dT m ðrÞ dr

ð9Þ

The second term on the right-hand-side of the above equation can be obtained from Eq. (8) [dTm(r)]/(dr)¼(k)/(r2). Thus the following equation will be obtained: dV dV k ¼ dr dT m ðrÞ r 2

ð10Þ

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Again, Eq. (8) will be used in Eq. (10) to obtain the final expression for (dV/dr) as dV dV ½T m T m ðrÞ2 ¼ dr dT m ðrÞ k

ð11Þ

The first term, on the right-hand side of Eq. (11), can be obtained from the 1H NMR signal of the volume of non-frozen water with temperature. This enables us to find the PSD of the material by plotting dV/dr (from Eq. (11)) versus r (from Eq. (8)).

4. Results and discussion Fig. 1 shows the small angle XRD pattern of as-synthesized (upper graph A) and calcined MCM-41 (lower graph B). The sample before calcination shows an extra peak at 2y ¼2.21, which is likely attributable to the presence of different amounts of template material inside different pores [29,30]. The calcined sample (Fig. 1B) shows well-resolved peaks typical of the hexagonal pattern in highly ordered MCM-41 [20]. The peaks can be indexed according to a honeycomb lattice [31–33] as in MCM-41. It is obvious that the final calcination process results in an enhancement of the 100 peak intensity. This is indicative of

Fig. 1. Small angle X-ray diffraction patterns of as-synthesized (A) and calcined (B) MCM-41 used in this study. Five peaks can be seen in (B), an indication of the high order in the MCM-41.

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improvement in the long-range ordering of the pores in MCM-41 [34] via removal of the template during the calcination stage. The calcined sample is used for this study and the surface area is estimated [35] to be equal to 1126 m2/g with the BET model [36]. Fig. 2 shows the NAD isotherm of the sample. The data shows three distinct regions; the initial linear increase of the curve is indicative of monolayer–multilayer adsorption on the pore walls, the steep increase represents capillary condensation within the pores, and the final part of the curve represents multilayer adsorption on the outer surface of the powder. The sharp step in the isotherm for the sample studied implies uniformity in the pore size [37]. The adsorption isotherm for the MCM-41 sample, shown in Fig. 2, is of type IV with no hysteresis as observed previously [38]. Spin–spin relaxation T1 of silanol protons on the surface of MCM-41 is about 2.3 s [39]; thus a long repetition time (10 s) is used between radio frequency pulses in the NMR measurements. Since this value is about 3T1, which is smaller than the typical value (5T1) used in NMR measurements, a quantitative error is expected for the total signal measurement (about 4–5%). At each temperature the 1H NMR spectrum shows a broad component and a narrow component. The former is attributed to the solid part (protons from silanol groups on the surface of the pores) and the latter is attributed to the proton of water inside the pores. To find the water signal, a Lorentzian line is fitted (using Origin pro V7 software) to the narrow part of the spectra. The areas under the curves of the Lorentzian lines, at different temperatures, are calculated and corrected using Currie’s law, i.e., the NMR signal intensity measured at temperature T was corrected by multiplication by the ratio T/Tm, with Tm ¼ 275 K. The area under the Lorentzian curve represents the intensity of the water signal inside the pore. Fig. 3 shows intensity, corrected according to Currie’s law, versus temperature for the sample used in this study. The intensity represents the volume of unfrozen water pore enclosed in the pore size of MCM-41. A decrease in the signal intensity is noticed around 273 K, which represents the bulk water freezing point, and between this and around 230 K which represents freezing of the pore water [40]. To calculate the PSD from NAD data, Eqs. (1)–(3) and (5), (6) are used (for the classical Kelvin equation) or Eqs. (1), (2), (4)–(6) are used (for the modified Kelvin equation). Either part of Eq. (4) can be used, as the selection of branch, adsorption or desorption, is the subject of discussion for many researchers. Some of them

Fig. 3. 1H NMR signal intensity versus temperature of water enclosed in the pores of MCM-41.

Fig. 4. Pore size distribution of MCM-41 used in this work from the classical Kelvin equation (solid circles), the modified Kelvin equation (open circles) and 1H NMR (solid triangles).

Fig. 2. Nitrogen adsorption-desorption isotherm of the calcined sample of MCM-41 used in this study.

justify the selection of the adsorption part [24] or the desorption branch [27,41]. In this study, the desorption part of NAD data is used for determining the PSD (for the modified Kelvin equation) ˚ and the result is shown in Fig. 4. The correction factor, fc ¼4.9 A, appearing in Eq. (4) is determined using the proposed method described in Ref. [27] to our data. There is no considerable difference in the estimation of the pore size from both branches of NAD data when the material does not exhibit hysteresis (Fig. 3), but the selection of isotherm branch is critical if the material shows hysteresis. For example, SBA-15, which has similar pores to those of MCM-41, but larger in size, exhibits hysteresis in its isotherm data. The PSD results of this material using both isotherm branches show a considerably larger gap of about ˚ being higher for the desorption branch [27]. 10 A, The PSD (Fig. 4) shows pore distribution with a peak at around 27 A˚ (filled circles) using the classical Kelvin equation (without using the correction factor) and at around 38.5 A˚ (open circles) using the modified Kelvin equation. Both curves exhibit a narrow ˚ It is known that the pore size, calculated distribution of about 5 A.

J. Hassan / Physica B 407 (2012) 3797–3801

with the classical Kelvin equation, underestimates the real pore size, especially for smaller mesoporous pores [3]. Thus the PSD obtained using the modified Kelvin equation is more reliable and is expected to represent a closer estimation to the actual pore size of this material. PSD is estimated from 1H NMR data (Fig. 3) using Eqs. (8) and (11) and the result is presented in Fig. 4, (solid triangles). ˚ is taken from Ref. [23]. The value of the constant (k ¼494.8 K/A) The PSD from NMR is centered at about 35 A˚ with a distribution of about 7–9 A˚ (wider than in the previous methods). A broader peak ˚ This is probably due to the slow increase is seen around 55–70 A. of the NMR intensity beyond 260 K and before the bulk water melting point at 273 K (Fig. 3). In general, the NMR method gives a relatively good agreement with the NDA method. This confirms the feasibility of using it for the PSD of small pores, but care should be taken for the branch used in the NDA if the isotherm data shows any hysteresis which is characteristic of the material and only depends on the nature of the pores in the material under study.

5. Conclusions Two different techniques, nitrogen adsorption–desorption and NMR, are used to determine the pore size distribution of nanosilica material MCM-41. PSD results from the Kelvin equation and its modified version are compared with the NMR method. The result shows the feasibility of the latter method in estimating the PSD for small size mesoporous materials. Care should be taken in comparing the results and in the selection of which isotherm data branch is to be used in samples that exhibit hysteresis in their gas adsorption–desorption.

Acknowledgments The author would like to thank Dr. Claude Lemaire (Department of Physics and Astronomy, University of Waterloo, Canada) for valuable assistance in the NMR measurements of this work. References [1] J. Rouquerol, G. Baron, R. Denoyel, H. Gieshe, J. Groen, P. Klobes, P. Levitz, A.V Neimark, S. Rigby, R. Skudas, K. Sing, M. Thommes, K. Unger, Pure Appl. Chem. 84 (1) (2012) 107. [2] J.C. Groen, M.C. Doorn, L.A.A. Peffer, in: D.D. Do (Ed.), Adsorption Science and Technology, Proceedings of the 2nd Pacific Basin Conference, Brisbane, Australia; P229, 2000.

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