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Langmuir 2008, 24, 7024-7030
AFM-Porosimetry: Density and Pore Volume Measurements of Particulate Materials Malin H. So¨rensen,*,† Juan J. Valle-Delgado,‡ Robert W. Corkery,† Mark W. Rutland,‡ and Peter C. Alberius† YKI, Institute for Surface Chemistry, Stockholm, Sweden, and Department of Chemistry, Surface Chemistry, Royal Institute of Technology, Stockholm, Sweden ReceiVed January 25, 2008. ReVised Manuscript ReceiVed March 20, 2008 We introduced the novel technique of AFM-porosimetry and applied it to measure the total pore volume of porous particles with a spherical geometry. The methodology is based on using an atomic force microscope as a balance to measure masses of individual particles. Several particles within the same batch were measured, and by plotting particle mass versus particle volume, the bulk density of the sample can be extracted from the slope of the linear fit. The pore volume is then calculated from the densities of the bulk and matrix materials, respectively. In contrast to nitrogen sorption and mercury porosimetry, this method is capable of measuring the total pore volume regardless of pore size distribution and pore connectivity. In this study, three porous samples were investigated by AFM-porosimetry: one ordered mesoporous sample and two disordered foam structures. All samples were based on a matrix of amorphous silica templated by a block copolymer, Pluronic F127, swollen to various degrees with poly(propylene glycol). In addition, the density of silica spheres without a template was measured by two independent techniques: AFM and the Archimedes principle.
Introduction Porous materials are used in many different industrial applications, such as catalytic reaction engineering, separation processes, and oil refinement as well as in consumer products (i.e., water softeners and defuming agents). There is a wide range of porous materials that can be divided into the categories microporous (50 nm), as well as multiporous materials. Accurate measurements of pore volume and information about the distribution between the different pore structures are of significant interest if the porous substrate is designed to be used in applications such as separation processes or as a molecular carrier. A variety of methods is available to measure the pore volume in porous samples, such as gas sorption, mercury porosimetry,1–3 thermoporometry,4–6 water intrusion,5 inverse-size exclusion chromatography (ISEC),7,8 and NMR cryoporometry,6,9–12 where the most commonly used methods are nitrogen sorption and * Corresponding author. E-mail:
[email protected]; tel.: +46 8 5010 6090. † Institute for Surface Chemistry. ‡ Royal Institute of Technology.
(1) Ritter, H. L.; Drake, L. C. Ind. Eng. Chem. 1945, 17(12), 782–786. (2) Drake, L. C.; Ritter, H. L. Ind. Eng. Chem. 1945, 17(12), 778–791. (3) Drake, L. C. Ind. Eng. Chem. 1949, 41(4), 780–785. (4) Iza, M.; Woerly, S.; Danumah, C.; Kaliaguine, S.; Bousmina, M. Polymer 2000, 41(15), 5885–5893. (5) Denoyel, R.; Llewellyn, P.; Beurroies, I.; Rouquerol, J.; Rouquerol, F. O.; Luciani, L. Part. Part. Syst. Charact. 2004, 21(2), 128–137. (6) Gane, P. A. C.; Ridgway, C. J.; Lehtinen, E.; Valiullin, R.; Furo, I.; Schoelkopf, J.; Paulapuro, H.; Daicic, J. Ind. Eng. Chem. Res. 2004, 43(24), 7920–7927. (7) Jerabek, K.; Revillon, A.; Puccilli, E. Chromatographia 1993, 36, 259– 262. (8) Lubda, D.; Lindner, W.; Quaglia, M.; von Hohenesche, C. D.; Unger, K. K. J. Chromatogr., A 2005, 1083(1-2), 14–22. (9) Strange, J. H.; Rahman, M.; Smith, E. G. Phys. ReV. Lett. 1993, 71(21), 3589–3591. (10) Valckenborg, R. M. E.; Pel, L.; Kopinga, K. J. Phys. D: Appl. Phys. 2002, 35(3), 249–256. (11) Vargas-Florencia, D.; Edvinsson, T.; Hagfeldt, A.; Furo, I. J. Phys. Chem. C 2007, 111(21), 7605–7611. (12) Vargas-Florencia, D.; Petrov, O. V.; Furo, I. J. Colloid Interface Sci. 2007, 305(2), 280–285.
mercury porosimetry. Both of these methods results in an adsorption-desorption isotherm created by penetration of nitrogen or mercury into the degassed samples. From these isotherms, information about pore size, pore volume, and surface area can be obtained. Nitrogen sorption is applicable on microporous and mesoporous materials and mercury porosimetry to characterize meso- to macroporous samples. (The validity of nitrogen sorption to measure macropore volume has been debated, and some researchers claim that nitrogen sorption is valid up to a pore size of ∼100 nm.) There are some drawbacks concerning mercury porosimetry: it is not possible to obtain the pore volume of closed pores or micropores, shielding of large pores by small pores results in the underestimation of pore volume, and the high pressure during measurements may deform or destroy the sample. Other methods to measure the pore volume of samples that contain macropores are ISEC, thermoporometry, and NMR cryoporometry. ISEC is a chromatographic method based on using the material under investigation as a stationary phase in a chromatographic column. The elution volumes of a series of standard solutes with different molecular sizes are measured. Information about the structure can be achieved by applying different mathematical models, and the pore volume is related to the elution volume of the standard solutes. This technique can be used for multiporous samples, but the model relies on that each pore fraction contains uniform pores with simple geometrical shapes. This method is limited by the requirements of very well-defined standards that span the dimensions of pores, and it is dependent on the model chosen to interpret the data. In thermoporometry, the solid/liquid phase transition of a fluid, which is dependent on the pore size, is studied by differential scanning calorimetry (DSC).Theporevolumemaybeextractedfromamelting-solidification isotherm recorded by DSC, where the enthalpy change versus the temperature is plotted. The limitation of this method is that an assumption must be made for the solid-liquid interfacial tension, which is not measurable. NMR (nuclear magnetic resonance) cryoporometry has a similar approach to thermoporometry since this method also is based on the relation
10.1021/la800260h CCC: $40.75 2008 American Chemical Society Published on Web 05/27/2008
Particulate Material Density/Pore Volume Measurements
between the solid-liquid phase transitions as a function of pore size. The intensity of the amount of molten fraction of the porefilling material, as the initially frozen material is warmed up, is measured as a function of temperature. There is a large difference in nuclear spin relaxation times of molecules in liquid as compared to solid states, which gives rise to higher NMR signals of the molten fraction. The pore volume can be extracted from the isotherm by relating the intensity to the amount of pore-filling material. The upper limit of NMR cryoporometry is ∼1 µm. In fact, a common characteristic for all the methods is that they require a total penetration of the pores by the probe fluid, which is not always possible. To our knowledge, there is no straightforward method available today to measure the total pore volume insensitive to pore structure as well as pore size distribution. We developed a method, AFM-porosimetry, to measure the total pore volume of porous particulate materials regardless of pore size and pore connectivity. An atomic force microscope in colloid probe mode13,14 was used as an indirect method to measure the density and pore volume of porous samples. The principle is to use AFM cantilevers as balances to measure the weight of single particles. AFM cantilevers have been used as mass sensors in a range of applications since the resonant frequency of the cantilever is sensitive to the attached mass.15–23 Thermal vibrations make the cantilevers oscillate, and a resonant frequency of each cantilever can be measured by AFM. The mass is then obtained from the shift in resonant frequency of the cantilevers with and without particles attached. In this work, several particles from each batch were weighed, and the density was obtained by plotting particle mass versus particle volume. This is essentially a reverse engineering of the approach used by Cleveland et al.24 to obtain cantilever spring constants by adding a series of known masses at a well-defined point on the cantilever. Finally, the pore volume is calculated from the bulk density of the porous sample and the density of amorphous silica. Information about the fractions of pore volumes occupied by pores within the different length scales can be procured by combining AFM-porosimetry with nitrogen sorption and mercury porosimetry. In this study, three batches of spherical and porous silica particles were investigated by AFM-porosimetry, and the results were compared with the pore volumes measured by nitrogen sorption and mercury porosimetry. These samples were synthesized by an aerosol-based process that produces a surfactant templated hybrid material where the porous structures are obtained by removal of the organic template. All samples are based on silicon dioxide as the inorganic matrix, and a block copolymer, Pluronic F127 ((EO)106(PO)70(EO)106), swollen with poly(propylene glycol) (PPG, MW 3000), acted as a template. The three (13) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature (London, U.K.) 1991, 353(6341), 239–241. (14) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8(7), 1831– 1836. (15) Lang, H. P.; Berger, R.; Andreoli, C.; Brugger, J.; Despont, M.; Vettiger, P.; Gerber, C.; Gimzewski, J. K.; Ramseyer, J. P.; Meyer, E.; Guntherodt, H. J. Appl. Phys. Lett. 1998, 72(3), 383–385. (16) Larson, I.; Pugh, R. J. Langmuir 1998, 14(20), 5676–5679. (17) Battiston, F. M.; Ramseyer, J. P.; Lang, H. P.; Baller, M. K.; Gerber, C.; Gimzewski, J. K.; Meyer, E.; Guntherodt, H. J. Sens. Actuators, B 2001, 77(1-2), 122–131. (18) Lang, H. P.; Hegner, M.; Meyer, E.; Gerber, C. Nanotechnology 2002, 13(5), 29–36. (19) Vidic, A.; Then, D.; Ziegler, C. Ultramicroscopy 2003, 97(1-4), 407– 416. (20) Ziegler, C. Anal. Bioanal. Chem. 2004, 379(7-8), 946–959. (21) Andersson, K. M.; Bergstrom, L. J. Am. Ceram. Soc. 2005, 88, 2322– 2324. (22) Campbell, G. A.; Mutharasan, R. Anal. Chem. 2006, 78(7), 2328–2334. (23) Johnson, L.; Gupta, A. T. K.; Ghafoor, A.; Akin, D.; Bashir, R. Sens. Actuators, B 2006, 115(1), 189–197. (24) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. ReV. Sci. Instrum. 1993, 64(2), 403–405.
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batches of porous samples contained a constant F127/silica mass ratio but different PPG concentrations, which resulted in one sample with an ordered two-dimensional hexagonal structure and two foam structured samples.25 In addition, a batch of silica particles without any template was produced, and the density of amorphous silica was measured using AFM and the Archimedes principle, which enabled the investigation on the accuracy of AFM-porosimetry.
Methodology The density of porous spherical particles can be achieved by independently determining the mass Mp and volume Vp of several particles from each batch. In other words, the bulk density is found from the slope of the linear fit to the plot of the particle mass versus the particle volume. The overall pore volume (Vpore, expressed in cm3/g to be comparable to data extracted from nitrogen adsorption and mercury porosimetry data) can be calculated by subtracting the volume of 1 g of silica from the total volume of 1 g of sample, according to eq 1
Vpore )
1 1 Fsample FSiO2
(1)
where Fsample and FSiO2 are the bulk density of the sample and the density of amorphous silica, respectively. The well-established value of amorphous silica, 2.2 g/cm3, is used in eq 1, and the error in local silica density is assumed to be insignificant. The mass of each particle was obtained from the change in the resonant frequency of an AFM cantilever before and after gluing the particle at its end. The resonant frequency ν0, without any particle attached to the cantilever, is given by eq 2
ν0 )
1 2π
kn mef
(2)
where kn is the normal spring constant of the cantilever and mef is its effective mass. After gluing a particle of mass Mp at the end of the cantilever, the resonant frequency changes according to eq 3.26
νp )
1 2π
kn mef + Mp
(3)
The particle mass can then be obtained from the spring constant of the cantilever and the resonant frequencies before and after attaching a particle by combining eqs 2 and 3,26 giving eq 4
Mp )
kn
1 1 ( - ) 4π2 νp2 ν02
(4)
The diameter of each particle was measured from scanning electron microscopy (SEM) images. Since the particles are spherical in shape, the volume could easily be calculated by measuring the diameter. For error calculations corresponding to pore volume, particle mass, and particle volume see the Supporting Information.
Experimental Procedures Silica particles of various structures were made in the following way: 10.4 g of tetraethoxysilane (TEOS (Purum >98%), Si(OC2H5)4) was mixed with 5.2 g of diluted hydrochloric acid (pH 2) and 12 g of ethanol (99.7%). The solution was prehydrolyzed under vigorous (25) Sörensen, M. H.; Corkery, R. W.; Pedersen, J. S.; Rosenholm, J.; Alberius, P. C. Microporous Mesoporous Mater., in press. (26) Ralston, J.; Larson, I.; Rutland, M. W.; Feiler, A. A.; Kleijn, M. Pure Appl. Chem. 2005, 77(12), 2149–2170.
7026 Langmuir, Vol. 24, No. 13, 2008 stirring for 20 min. A total of 3.2 g of the Pluronic block copolymer F127 ([(EO)106(PO)70(EO)106], BASF) and x g (x ) 0.3, 1.0, or 2.0) of PPG (MW 3000, ∼50 repeating units, Alfa Aesar) were dissolved in 8.0 g of ethanol (99.7%). The two solutions were then mixed together for 10 min. The ratio between silicic acid and F127 was kept at 50:50 in volume percent, and the PPG concentration was changed according to a PPG/F127 weight ratio of 0.09, 0.31, and 0.63. Sample 0.09 contains a two-dimensional hexagonal structure, and samples 0.31 and 0.63 are foam structured samples. These structures carefully were characterized in an earlier paper.25 In the case of silica particles without any template, the inorganic solution was prepared and prehydrolyzed in the same way as described previously. The prehydrolyzed inorganic solution was then diluted with 8.0 g of ethanol and stirred for an additional 10 min. An aerosol-based process was used to produce the templated and nontemplated silica particulate materials. In principle, the process includes the formation of an aerosol from the precursor solution, generated by a spray-nozzle and carried by a gas. The droplets first enter a vertical spray chamber, where solvent evaporates, and then go into a high temperature furnace, where the silica species polymerizes. Finally, a dry particulate material is collected by a Teflon-coated filter. The particles are mostly spherical with a particle size distribution centered around 3-5 µm. The temperature in the vertical chamber was kept ambient. The furnace temperature was 280 °C. Porous particles were obtained after calcination at 600 °C for 5 h. For a detailed description of the process, see Andersson et al.27 To visualize the pore structures of the samples, a transmission electron microscope was used (Philips Tecnai 10) operating with an accelerating voltage of 80 kV. Digital images were recorded with a Megaview II digital camera and processed with the AnalySIS program. Carbon-coated copper grids were used for the TEM sample preparation. Samples were dispersed in ethanol and applied as droplets to the grids. Uncoated, tipless rectangular cantilevers (type CSC12) supplied by MikroMasch (Tallinn, Estonia) were used in the experiments. The lengths of the different cantilevers used were 250 ( 5, 300 ( 5, and 350 ( 5 µm, and the width of all the cantilevers was 35 ( 3 µm. (Each chip contains six cantilevers, where the three longest ones were used for this study.) Particles were glued at the end of the cantilevers with the help of a micromanipulator and an optical microscope. A small amount of epoxy glue (of the order of femtoliters or less) was used to fix the particles on the cantilevers. A check was performed that this amount of glue did not significantly affect the resonant frequency. The resonant frequencies of the cantilevers before and after gluing the particles were measured by placing the cantilevers in a Multimode AFM (Veeco Instruments Inc., Santa Barbara, CA) at ambient temperature and humidity. The resonance frequencies and normal spring constants of the cantilevers were obtained by using the software AFM Tune IT v2.5 (ForceIT), which records the fluctuations in the output signal of the AFM instrument due to the thermal vibrations of the cantilevers and calculates the amplitude of vibration versus frequency spectra. ν0 (or νp in the case of a cantilever with a particle) and the Q factor were obtained by fitting the first peak in the spectra to a simple harmonic function with added white noise.28 The normal spring constants kn of the cantilevers were extracted from ν0 and Q values by means of Sader’s equation.29,30 The experimental values of ν0, νp, and kn, based on at least six repeating measurements for each data point, are provided together with corresponding errors in Tables 1 and 2 in the Supporting Information and allow the calculation of the mass of the particles according to eq 4. A scanning electron microscope (Philips XL-30), operating under high vacuum, was used to measure the particle diameters (Figure (27) Andersson, N.; Alberius, P. C. A.; Pedersen, J. S.; Bergstrom, L. Microporous Mesoporous Mater. 2004, 72(1-3), 175–183. (28) Pettersson, T.; Nordgren, N.; Feiler, A.; Rutland, M. W. ReV. Sci. Instrum. 2007, 78, 93702/1–93702/8. (29) Sader, J. E. J. Appl. Phys. 1998, 84(1), 64–76. (30) Green, C. P.; Lioe, H.; Cleveland, J. P.; Proksch, R.; Mulvaney, P.; Sader, J. E. ReV. Sci. Instrum. 2004, 75(6), 1988–1996.
Sörensen et al.
Figure 1. SEM images of a mesoporous particle attached to an AFM cantilever.
1) and dimensions of the AFM cantilevers. To gain a good contrast in the images, the cantilevers carrying the particles were coated by a thin layer of gold after the AFM analysis was complete. The influence of the humidity on the particle mass was investigated by encasing the AFM equipment in a plastic cover. Different humidities were obtained by placing beakers with saturated salt solutions of LiCl (low humidity, 14% < RH < 20%), KCl (high humidity, 42% < RH < 72%), and K2SO4 (high humidity, 74% < RH < 82%) within the seal. Any change in particle mass due to a change in humidity could then be detected by a shift in resonant frequency. At least 5 h of equilibration at each humidity was performed before measuring the resonant frequency. Two single particles were used to carry out the experiment, one mesostructured particle (mass ratio PPG/F127 ) 0.09) and one foam structured particle (mass ratio PPG/F127 ) 0.63). Nitrogen sorption measurements were performed at 77 K using an ASPA2010 manufactured by Micrometrics, Norcross, GA. The nitrogen sorption data were evaluated using the BJH method31 as well as a nonlocal density functional theory (NLDFT).32–39 Regarding the NLDFT method, a kernel for cylindrical pores was used to evaluate the mesostructured sample (batch 0.09), and a kernel for spherical pores was used for the foam structured samples (batches 0.31 and 0.63). In both cases, the total pore volume of these samples was given by a single point measurement of the amount of nitrogen adsorbed at a relative pressure close to the saturation vapor pressure. Mercury porosimetry measurements were recorded on an AutoPore III 9410 manufactured by Micrometrics. The pore volume of the samples corresponds to the amount of mercury in the samples at a pore size
