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Langmuir 2008, 24, 4470-4472
Pore Size Distribution Measurements in Small Samples and with Nanoliter Volume Resolution by NMR Cryoporometry Alexander I. Sagidullin and Istva´n Furo´* DiVision of Physical Chemistry and Industrial NMR Center, Department of Chemistry, Royal Institute of Technology, Teknikringen 36, SE-10044 Stockholm, Sweden ReceiVed December 20, 2007. In Final Form: March 6, 2008 NMR cryoporometry is demonstrated to provide access to pore size and pore size distribution in small amounts of porous materials. With a conventional NMR spectrometer and probe, the detection limit for total pore volume is shown to be on the order of 100 nL with a volume resolution on the order of a few nanoliters.
Introduction There are many porous materials, both natural and artificial. Irrespective of their origin, their functions and applications are, to a large extent, defined by the size of pores they contain. A clear majority of porous systems do not possess pores of a single well-defined size; instead, there is a distribution of pore size and, often, pore shape. This distribution, together with pore interconnectivity, defines the porous structure. Hence the interest in methods for measuring pore size distribution (PSD).1,2 Conventionally, there are two dominant techniques for obtaining PSDs.1,3,4 The first one measures the adsorption (and, for a more complete characterization, also the desorption) of a gas onto the pore walls. Interpreted within the framework of suitable, though neither universal nor omnipotent, models, one can obtain measures of PSD, pore surface, and pore volume from the pressure dependence of the adsorbed amount of gas. The gases used can be either nitrogen, argon, or carbon dioxide. The second method, mercury intrusion porosimetry (MIP) observes instead the amount of liquid mercury that can be pressed into the pores by applying an external pressure. The pressure is required because mercury typically does not wet the pore walls and can therefore intrude into a pore if the external pressure exceeds the Laplace pressure that in turn depends on the size of pore access. Besides gas sorption porosimetry and MIP, there are some other, less well-known and less widespread techniques for characterizing porous structures. They exist and find applications because they are complementary: they may be used in systems where those other major tools cannot be applied, they may access pore sizes that those cannot reach, or they may provide more detail. For example, X-ray microtomography yields 3D images of porous networks with unparalleled detail.5-8 Nevertheless, its * Corresponding author. E-mail:
[email protected]. Tel: +46 8 7908592. Fax: +46 8 7908207. (1) Schu¨th, F.; Sing, K. S. W.; Weitkamp, J. Handbook of Porous Solids; Wiley-VCH: Weinheim, Germany, 2002; Vol. 1. (2) Sing, K. S. W. Colloids Surf., A 2004, 241, 3-7. (3) Lovell, S.; Shields, J. E.; Thomas, M. A.; Thommes, M. Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density; Kluwer: Dordrecht, The Netherlands, 2004. (4) Denoyel, R.; Llewellyn, P.; Beurroies, I.; Rouquerol, J.; Rouquerol, F.; Luciani, L. Part. Part. Syst. Charact. 2004, 21, 128-137. (5) Stock, S. R. Int. Mater. ReV. 1999, 44, 141-164. (6) Lindquist, W. B.; Venkatarangan, A.; Dunsmuir, J.; Wong, T. F. J. Geophys. Res. Solid Earth 2000, 105, 21509-21527. (7) Jones, A. C.; Sheppard, A. P.; Sok, R. M.; Arns, C. H.; Limaye, A.; Averdunk, H.; Brandwood, A.; Sakellariou, A.; Senden, T. J.; Milthorpe, B. K.; Knackstedt, M. A. Physica A 2004, 339, 125-130. (8) Arns, C. H.; Bauget, F.; Limaye, A.; Sakellariou, A.; Senden, T. J.; Sheppard, A. P.; Sok, R. M.; Pinczewski, W. V.; Bakke, S.; Berge, L. I.; Oren, R. E.; Knackstedt, M. A. SPE J. 2005, 10, 475-484.
high cost, its demand for sufficient contrast, and its approximately micrometer lower resolution renders it far less prevalent than either gas sorption or mercury porosimetries. In this paper we put the focus on NMR cryoporometry9-11 and, in particular, on one of its seemingly overlooked and potentially very useful aspects. NMR cryoporometry detects the pore-size-dependent shift of the melting and/or freezing points of pore imbibed materials. For detection, it exploits the huge difference between solid and liquid NMR signals. Among its advantages, some well exploited and some still nascent, one can name its relatively large size range, its ability to access the size distribution of liquid-filled pores, its shape sensitivity, and its promise to detect pore interconnectivity. Since NMR spectrometers are ubiquitous and since the experimental methodology is simple, NMR cryoporometry could evolve into a more common porometric method. The aspect we wish to draw attention to is the small size of samples NMR cryoporometry requires; as we demonstrate below, it can conveniently provide access to PSDs for sample masses of a milligram and below. Experimental The test samples used in this experiment consisted of sub-milligram amount controlled pore glasses (CPGs, from Millipore, Inc.) of 23.7 and 72.9 nm nominal pore diameters, respectively (see compositions in Table 1), with water employed as the probe liquid. These CPGs have been investigated previously by a variety of porosimetric techniques and are well-known to contain pores of narrow size distribution with a shape that is close to cylindrical.11 The grains (of ∼150 µm size) of CPGs were simply placed at the bottom of a conventional 5 mm NMR tube. Several microliters of water was carefully pipetted over the grains (see Table 1) and was imbibed into the pores by capillary pressure. The amount of added water was sufficient to saturate the pore volume and to provide an excess bulk where the latter had the role of internal temperature reference.11 Centrifugation (12 h, ∼1000 rpm) ensured that air plugs within the CPGs were suppressed. The 1H NMR cryoporometric experiments were carried out on a Bruker DMX500 spectrometer with 500 MHz resonance frequency equipped with a conventional 5 mm 1H-observe NMR probe. The detection of the liquid NMR signal and, in parallel, the suppression of signal from ice was performed by the Carr-Parcell MeiboomGill spin echo pulse sequence with four 180° radio frequency pulses and of 40 ms total echo time. The temperature was first increased in a few larger steps from far below (∼250 K) the bulk and pore (9) Strange, J. H.; Rahman, M.; Smith, E. G. Phys. ReV. Lett. 1993, 71, 35893591. (10) Hansen, E. W.; Schmidt, R.; Sto¨cker, M. J. Phys. Chem. 1996, 100, 11396-11401. (11) Petrov, O.; Furo´, I. Phys. ReV. E 2006, 73, 011608.
10.1021/la7039866 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/27/2008
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Langmuir, Vol. 24, No. 9, 2008 4471 Table 1. Sample Compositions
CPG nominal pore diametera (nm)
CPG porosityb (mL/g)
23.7 72.9
0.95 0.75
CPG mass in sample (mg)
total pore surface/ volume in samplec (m2/µL)
amount of added water (µL)
0.26 0.85
0.02/0.25 0.02/0.64
2.90 3.38
a As stated by the manufacturer; obtained by MIP. b As stated by the manufacturer and verified by other experiments.11 c Calculated from the specific pore volume and specific pore surface as stated by the manufacturer.
Figure 3. The temperature dependence of the integral intensity of the liquid NMR signal I(T) obtained for water in imbibed in a CPG with 72.9 nm nominal pore diameter (CPG729). The inset shows the PSD function calculated via eq 2 from I(T).
Figure 1. 1H NMR spectra recorded for water imbedded in a CPG with 72.9 nm nominal pore diameter at temperatures ∆Tm below the bulk melting point of water. The inset magnifies the spectrum at ∆Tm ) -0.7 K.
where K ) υγslT0/∆H is a material constant with the surface free energy of the crystal-liquid interface γsl, the molar volume υ, and the melting enthalpy of the pore-filling liquid ∆H as components. Unfortunately, γsl is not known by sufficient accuracy, and therefore the value of K is available instead from calibration experiments performed in systems with assumedly known pore sizes (and shapes). The values provided by two detailed calibrations performed in porous silica materials are K ) 26 K‚nm10 and K ) 24 K‚nm;12 hence, in the present study we evaluate our intensity data under the assumption of K ) 25 K‚nm. By assuming a particular pore shape, κ can be expressed by the pore diameter d. For cylinders, κ ) 1/d, from which one can derive a PSD as p(d) )
2K ∂I(T) (d)2 ∂T
(2)
As described in detail elsewhere,12 finite differences were taken instead of the derivative in eq 2. The ratios of the plateau intensities (above ∆Tm ) 0 K and below ∆Tm ) 0 K) in both figures fit well to the corresponding ratios of the added water to the pore-imbibed water (total pore volume) presented in Table 1.
Results and Discussion
Figure 2. The temperature dependence of the integral intensity of the liquid NMR signal I(T) obtained for water imbibed in a CPG with 23.7 nm nominal pore diameter (CPG237). The insert shows the PSD function calculated via eq 2 from I(T). The complete melting of the excess bulk is assigned as ∆Tm ) 0 K. freezing points, and then in 0.1 K steps until the point where all water in the samples was molten. The NMR spectra obtained at different temperatures are illustrated in Figure 1, and the temperature dependence of the integral intensity of the liquid signal I(T) for the two test samples is shown in Figures 2 and 3. Note the irregular spectral shape above the bulk melting point in Figure 1, which can be ascribed to two different signal components, one from the excess bulk water and one from the intrapore water, both subject to susceptibility broadening and shift. Information about pore size is then obtained through a modified form11 of the Gibbs-Thompson equation, which relates the shift of the melting temperature ∆Tm within a pore to the integral mean curvature of pore wall κ: ∆Tm ) -
υγslT0 2κ ∆H
(1)
The PSDs in Figures 2 and 3 were obtained via eq 2 for samples with a total pore surface area of 0.02 m2 (see Table 1). This total pore surface is ca. 3 orders of magnitude lower than that usually cited as the lower limit for gas sorption porosimetry.13,14 Similarly, routine MIP experiments are typically performed with approximately milliliter sample volumes, although there exist goodquality PSDs15 recorded with pore volumes on the order of 10 µL. Our total pore volumes (see Table 1) of 0.64 µL (CPG729) and 0.25 µL (CPG237) are almost 2 orders of magnitude lower than that value. As concerning volume resolution, the lower MIP limit cited by manufacturers (see, e.g., PoreMaster-60 from Quantachrome Instruments16) seems to be 3 × 10-2 µL. The volume resolution in our current experimental setup can be estimated from the spectra in Figure 1. There, the integral intensity obtained in the (12) Vargas-Florencia, D.; Petrov, O. V.; Furo´, I. J. Colloid Interface Sci. 2007, 305, 280-285. (13) Rouquerol, F.; Rouquerol, J.; Sing, K. S. W. Adsorption by Powders and Porous Solids; Academic Press: San Diego, CA, 1999. (14) Rouquerol, J.; Avnir, D.; Fairbridge, C. W.; Everett, D. H.; Haynes, J. H.; Pernicone, N.; Ramsay, J. D. F.; Sing, K. S. W.; Unger, K. K. Pure Appl. Chem. 1994, 66, 1739-1758. (15) Fantazzini, P.; Salem, A.; Timellini, G.; Tucci, A.; Viola, R. J. Appl. Phys. 2003, 94, 5337-5342. (16) Quantachrome Instruments Home Page. http://www.quantachrome.com (accessed Nov 2007).
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spectrum recorded at ∆Tm ) -0.7 K is about 10 times over the integral noise level. On the other hand, the integral intensity at ∆Tm ) -0.7 K is approximately 5% of the integral intensity recorded at ∆Tm ) -0.2 K, where the latter corresponds to the total pore volume of 0.64 µL. Hence, we can estimate that the volume resolution is approximately 0.5% of the total pore volume, which yields ∼3 nL. The spectra in Figure 1 were recorded by averaging the signal from 64 scans with a total experimental time of 7 min. Note that a fewer number of scans would not provide a large gain in total experimental time since the sample temperature must be equilibrated for a few (∼10) minutes after an upward temperature step. Hence, the total experimental time for recording the I(T) data was ca. 4 h for the CPG729 sample and ca. 7 h for the CPG237 sample. The total volume of our test samples was ca. 3 µL, and the total sensitive sample volume of the probe was ca. 0.3 mL, which renders the filling factor to ca. 1%.17 Hence, the NMR signalto-noise ratio could be increased by an order of magnitude or more by recording the signal in an NMR microprobe18 which, depending on the type and manufacturer, may have 5 µL of sensitive sample volume. Alternatively, adequate (as illustrated in Figure 1) signal-to-noise ratio could be achieved in samples with a total pore volume on the order of 10 nL and volume resolution on the order of 100 pL. (One should also note that the signal-to-noise ratio could be further improved by using custommade solenoidal microprobes or by performing experiments at higher magnetic fields.) As concerning the obtained PSDs, the resolution depends on the size of the temperature steps and the temperature spread within the sample. In the present setup, this latter quantity must be e0.03 to 0.04 K, which was established for somewhat larger sample volumes by 59Co NMR tests in K3Co(CN)6 solutions.19 The size of the temperature steps (0.1 K) was defined by the smallest step size of our current temperature regulator. Since the size of the temperature step is larger than the temperature spread, it is the former quantity that defines the apparent width of the phase transition of the excess bulk water (see Figures 2 and 3). The stability of temperature over a period of a few hours, of course, also plays a role; good stability requires, among other things, a good control of the room temperature. Our obtained PSDs indicate pore sizes slightly above the nominal values (17) Hoult, D. I.; Richards, R. E. J. Magn. Reson. 1976, 24, 71-85. (18) Lacey, M. E.; Subramanian, R.; Olson, D. L.; Webb, A. G.; Sweedler, J. V. Chem. ReV. 1999, 99, 3133-3152. (19) Levy, G. C.; Bailey, J. T.; Wright, D. A. J. Magn. Reson. 1980, 37, 353-356.
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provided by the manufacturer. This may reflect differences between the applied methods; the values in Table 1 were obtained by MIP, which is more sensitive to throat sizes, while NMR with its volume sensitivity reflects the size of volumes behind the access throats.15,20
Conclusions New materials are often prepared in small quantities. Similarly, small sample volumes are often a hindrance if one wishes to characterize systems obtained by preparation procedures that yield, for example, thin films.21 As we demonstrate above, porous materials that are available in small amounts can be readily characterized by NMR cryoporometry. The sample size we demonstrate above (less than a milligram of porous materials with less than a microliter of total pore volume) is also accessible by thermoporometry,22,23 a method that is closely related to NMR cryoporometry, but where the material mass that freezes or melts is detected by calorimetric means. While thermoporometry seems to be a more rapid method, NMR cryoporometry probably has a high upper size limit. NMR cryoporometry can also be combined by other NMR methods and by NMR imaging to provide additional information about the pores. NMR spectroscopy is conventionally perceived as an insensitive technique. This is indeed the case if NMR is compared to mass or optical spectroscopies. Nevertheless, during the past few decades, NMR sensitivity has increased dramatically, in part because of the increased magnetic field strength (500 MHz spectrometers are nowadays widespread) and in part because of improved electronics (such as digital receivers). This trend, continuing with the spread of cryoprobes,24 will make even more materials accessible by NMR cryoporometry. Acknowledgment. This work has been supported by the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation. LA7039866 (20) Vargas-Florencia, D.; Petrov, O.; Furo´, I. J. Phys. Chem. B 2006, 110, 3867-3870. (21) Vargas-Florencia, D.; Edvinsson, T.; Hagfeldt, A.; Furo´, I. J. Phys. Chem. C 2007, 111, 7605-7611. (22) Brun, M.; Lallemand, A.; Quinson, J. F.; Eyraud, C. Thermochim. Acta 1977, 21, 59-88. (23) Landry, M. R. Thermochim. Acta 2005, 433, 27-50. (24) Black, R. D.; Early, T. A.; Roemer, P. B.; Mueller, O. M.; Mogrocampero, A.; Turner, L. G.; Johnson, G. A. Science 1993, 259, 793-795.
