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The use of 129Xe NMR spectroscopy for studying soils. A pilot study
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Geoderma 80 (1997) 449-462
129XeNMR spectroscopy for studying soils. A pilot study
Pieter C.M.M. Magusin, Andreas Bolz, Kerstin Sperling, Wiebren S. Veeman * Department of Physical Chemistry, Gerhard-Mercator-Universit~tt Duisburg, LotharstraJJe I, 47048 Duisburg, Germany Received 27 November 1996; accepted 9 April 1997
Abstract Xenon nuclear magnetic resonance (129Xe NMR) spectroscopy is a powerful technique to study microporous solids and semi-crystalline polymers. In this pilot study we investigate the use of 129Xe NMR spectroscopy for studying soils by applying the technique to model systems of carbon black and kaolin powders and to humified sand. In contrast to e.g. zeolites no xenon is sorbed within the sand crystallites at room temperature and high pressure (10 atm). Xenon is only adsorbed at the crystallite surface. The exchange of xenon between the adsorbed and gas phase is so fast, that 129Xe NMR spectroscopy cannot distinguish between the two. This results in a single peak in the I>Xe NMR spectrum with a weighted-average chemical shift between the shift of xenon in the adsorbed and the gas state. A model is presented which relates the chemical shift to the local volume-to-area ratio of the intercrystallite pores at a submillimetre scale. If other heterogeneity types can be neglected, ~29Xe NMR spectroscopy potentially reveals information about pore size distributions in undisrupted soils. © 1997 Elsevier Science B.V.
Kevwords: xenon; nuclear magnetic resonance; pore size; volume-to-area ratio; adsorption; carbon black; kaolin; humified sand
1. I n t r o d u c t i o n S i n c e the e a r l y e i g h t i e s ( R i p m e e s t e r a n d D a v i d s o n , 1981; Ito a n d F r a i s s a r d , 1982) x e n o n n u c l e a r m a g n e t i c r e s o n a n c e (129Xe N M R ) s p e c t r o s c o p y has p r o v e n to be a v a l u a b l e tool for s t u d y i n g m i c r o p o r o u s s o l i d s a n d s e m i - c r y s t a l l i n e
* Corresponding author. Fax: +49 203 379 3522. 0016-7061/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S00 16-7061 ( 9 7 ) 0 0 0 6 6 - 9
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polymers. Xenon atoms are well suited for probing pores in solids, because of their small diameter (4.4 A), nonpolarity and chemical inertness. This allows them to be sorbed in void spaces in many solid materials. Due to the large and polarizable electron cloud of xenon its NMR chemical shift strongly depends on its atomic environment (Derourane and Nagy, 1987). As a consequence, the t29Xe NMR spectrum contains information about the local structure at the sorption sites. From an NMR point of view the isotope ~29Xe has the advantage of having a high natural abundance (26%) and a spin quantum number 1/2 like most of the regular NMR nuclei, which makes it an easy nucleus to work with. Most of the current xenon NMR literature is devoted to zeolites and related materials, such as molecular sieves. Another major class of publications deals with amorphous polymers. A comprehensive discussion of the complete literature would be beyond the scope of this paper. Excellent reviews have appeared recently (Barrie and Klinowski, 1992; Raftery and Chmelka, 1994). The purpose of this paper is to give a short introduction in the application of ~29Xe NMR spectroscopy and to discuss its possible use for studying soil materials. Readers who are not yet familiar with the general technique of NMR spectroscopy are referred to the NMR introduction presented elsewhere in this issue (Veeman, 1997). Several groups employ t2~Xe NMR spectroscopy to study the heterogeneity in polymers (Walton et al., 1992, 1993; Mansfeld et al., 1995; Mirabella and McFaddin, 1996). Xenon atoms sorbed in semi-crystalline polymers reside in the free volume between the polymer chains in the amorphous phase (Stengle and Williamson, 1987) and give rise to NMR peaks typically between 200 and 220 ppm with respect to the xenon-gas peak. Above the glass-transition temperature xenon atoms sorbed in the amorphous phase do not stay at one position, but undergo diffusion under the influence of the segmental motion of the polymer chains. The miscibility of polymer components in polymer blends is a major topic in polymer science. ~2';Xe NMR is an important and relatively easy technique to study the compatibility of two components in polymer blends. Due to the mobility of the sorbed xenon atoms xenon can exchange between the single-component domains in a polymer blend. If the exchange is fast, i.e. if the domain sizes are smaller than the diffusion length of xenon atoms at the timescale of the NMR experiment, a single ~29Xe NMR peak is detected for the sorbed species. If the ~29Xe NMR spectrum contains well-resolved peaks corresponding to xenon sorbed in each of the components separately, this indicates that the components are not well-mixed in the blend and form separate phases.The diffusion coefficients of xenon in polymers reported in the literature range from 2 × 10 -~3 to 4 × 10 -1~ m2/s (Brownstein et al., 1988; Simpson et al., 1996). At the NMR timescale (10 3 s) xenon thus diffuses over a mean distance ~( r 2 ) = 1 I~m. Therefore, incompatible polymer blends with domains > 1 ~ m give rise to resolved peaks in the 129Xe NMR spectrum. Well-mixed polymers yield a single ~2';Xe NMR peak only (Mansfeld et al., 1995). Using
P.C.M.M. Magusin et al./ Geoderma 80 (1997) 449-462
129Xe NMR
451
slow demixing of incompatible polymers can actually be followed as function of time (Walton et al., 1993; Mirabella and McFaddin, 1996). Decreasing the temperature, or cross-linking of polymers slows down xenon diffusion revealing the heterogeneity of the xenon sorption sites at a scale < 1 ~ m in the 129Xe NMR spectrum (Kennedy, 1990). Detailed information about heterogeneity at a larger scale can be obtained by use of more advanced NMR techniques (Kentgens et al., 1991; Mansfeld and Veeman, 1993). Due to their relationship with clay, the numerous 129XeNMR publications for zeolites are especially relevant for the possible application of this spectroscopic technique to soil. Peak positions in the 129Xe NMR spectra observed for xenon sorbed in zeolites depend on the zeolite type, the xenon pressure and the temperature. At room temperature the chemical shift values extrapolated to zero-pressure range from 58 ppm for zeolite Y to 110 ppm for ZSM-5 (Ito et al., 1984). The larger the cavity, the smaller the chemical shift. The 13-,~ diameter of the relatively large supercages in zeolite Y may serve as an indication of the pore sizes involved. Attempts have been made to correlate the chemical shift with the pore geometry based on the curvature of the pore wall (Derourane and Nagy, 1987), the mean free path of a single xenon atom within a pore (Demarquay and Fraissard, 1987) and rapid exchange between xenon adsorbed on the pore wall and xenon gas in the pore volume (Cheung et al., 1988). However, a quantitative interpretation of the chemical shift in terms of the pore size is complicated by the fact that other factors, such as the presence of cations, influence the chemical shift, as well (Barrie and Klinowski, 1992). Moreover the usual assumption underlying the models that xenon stays within a pore is a severe simplification. At room temperature xenon is sufficiently mobile to average xenon interactions over thousands of zeolite cages at the timescale of the NMR experiment, typically 10 -3 s (Heink et al., 1990). Because various types of humic molecules are converted on or in clays, clay can perhaps be regarded as the most abundant heterogeneous catalyst on earth (Haddix and Naranya, 1994). The 129Xe NMR studies of xenon sorption in zeolites in the presence of co-adsorbates, such as water or small organic molecules, may thus be of particular interest to soil research. In general, co-adsorbates reduce the sorption and mobility of xenon, by blocking the sorption sites and the diffusion of xenon. On the basis of a model relating the 129Xe chemical shift to the mean free path of xenon sorbed within zeolites, the effect of hydration and the diffusion of water in zeolites can be indirectly investigated using 129Xe NMR spectroscopy (Gedeon et al., 1988). A recent paper deals with the exchange of benzene between zeolite crystallites (Springuel-Huet et al., 1996). As for soil itself, ~H and 13C NMR may be used to study organic components in soils or soil extractions (Conte et al., 1996). NMR studies of clay have mostly been restricted to 27A1 and 295i nuclei (Haddix and Naranya, 1994). The only t29Xe NMR study of clay, which seems to have appeared (Barrie et al., 1991), deals with the sorption of xenon in pillared
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montmorillonite. The naturally occurring material becomes pillared by exchanging its Na + and Ca 2+ cations with aluminium. The resulting pillared material has an interlayer spacing of 8.1 A, which enables the formation of a xenon bilayer between the layers. ~29Xe NMR spectra at room temperature and low pressure show a broad peak at ~ 100 ppm assigned to the sorbed xenon. Upon lowering the temperature the chemical shift of the peak increases. In contrast, the 129Xe NMR spectrum of the unpillared clay above 220K contains a peak between 0 and 15 ppm, indicating that no xenon is sorbed within the clay and that xenon adsorbed at the external surface is quickly exchanging with the xenon gas. At lower temperatures a peak appears between 150 and 170 ppm. This peak is assigned to sorbed xenon which resides long enough on the external surface of the clay particles to yield a resolved adsorption peak in the NMR spectrum. Realizing that soil is basically a stack of various grains and therefore contains networks of interparticle pores, we studied various types of powders using 129Xe NMR spectroscopy. As will be shown, the 129Xe NMR spectrum contains information about the average volume-to-area ratio of these pore networks at a submillimetre scale without necessity to disrupt the original powder stacking. o
2. Theory To more quantitatively interpret the chemical shift of xenon sorbed in powders, like soil, in terms of pore size, we use a simple model based on fast exchange between adsorbed xenon and xenon gas. More detailed fast-exchange models have been published for xenon sorption in zeolites (Cheung et al., 1988; Ripmeester and Ratcliffe, 1990). It has been pointed out° (Ripmeester and Ratcliffe, 1990), that xenon atoms in a l~ore larger than 10 A are not continuously in an adsorbed state, i.e. within 5-A distance from the pore wall, but also spend part of their time in the free gas phase in the pore volume. The exchange between the bound and the gas phase is so fast, that NMR spectroscopy cannot distinguish between them. The observed 129Xe chemical shift is an average between the shift of xenon in the bound state, 6 b, and in the gas state, 6~, weighted by the fraction of bound and gas atoms, N b / N and Ng/N, respectively. Thus: 6 = Nb N
+
(1)
In the fast exchange limit the NMR spectrum does not depend on the exchange rate. Within this limit Eq. (1) is thus valid for any exchange rate or distribution thereof. The limiting shifts 6 b and 6g vary with pressure and temperature. In addition, 6b depends on the atomic composition of the pore wall and the local surface curvature of the binding site. Our model assumes that at constant pressure and temperature the numbers N b and N~ are proportional to the area
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453
and the volume of the pore, respectively. More precisely, the number of xenon atoms bound to the pore wall, N b, is given by:
Nb=Ona
(2)
where 0 denotes the occupation degree, n the number of binding sites per unit area and A the area of the wall. The occupation 0 typically follows from the Langmuir equation:
Kp 0= - -
(3)
l+Kp
where K and p are, respectively, the Langmuir constant and the pressure. Since K varies with temperature T, 0 depends on both p and T. The number of xenon atoms in the gas phase inside a large pore can be estimated from the perfect gas law:
pV Ug- kr
(4)
where k = 1.38 × 10 -23 J K-I is Boltzmann's constant. Eq. (4) neglects the reduction of the pore volume due to the monolayer of xenon atoms on the pore wall. This is a valid approximation for the pore sizes > 40 nm which we encounter in our powder systems. Substituting Eqs. (2) and (4) into Eq. (1) and defining the chemical shift of the free xenon gas 6g as 0 ppm, we derive: 6-
8b 1 + as
(5)
where A =p/OnkT is a pressure- and temperature-dependent constant and S = VIA denotes the volume-to-area ratio of the pore. For various regular geometric shapes S is proportional to the diameter D (e.g. for spherical and cubic cavities S = D/6, for long cylindrical channels S = D/4 and for flat interlayers S = D/2). For this reason, we define S to be the characteristic pore size for the irregular pore networks in soils and other powders, as well. Eq. (5) shows, that as the pore size increases from zero to infinity, the chemical shift 6 decreases from the adsorbed state value 6 b to the gas-state value 6g = 0. With this model the tZ9Xe NMR spectrum thus reflects the pore size in the material under study. The pore size S can actually be determined from the chemical shift of adsorbed xenon in the 129Xe NMR spectrum by using the inversion of Eq.
(5): ,
S=
-~-1
~-
(6)
For comparing different powders with identical particle-surface properties at the same xenon pressure the factor 1/A in Eq. (6) is a simple proportionality constant. Therefore, to determine relative pore sizes with respect to an appropri-
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ate reference, or the distribution of relative pore sizes within a powder Eq. (6) may be used without knowledge of A. For absolute determination of the pore size the parameter A, and thus of 0 (or K) and n, must be known. This information may be obtained from xenon sorption measurements as a function of p and T. An exhaustive investigation of xenon adsorption in soil and other powders, however, is beyond the scope of this pilot study. As a first approximation we make the crude assumption, that under the high xenon pressures employed in our experiments (ca. 10 atm) all xenon binding sites are fully covered ( 0 = 1) and that the adsorption-site density is the inverse of the cross-section of a xenon atom (n = 1/Trr 2, where r = 2.2 A denotes the xenon radius). The latter corresponds to coverage of the pore wall with a dense monolayer of xenon atoms with negligible interspace. Thus, by assumption, we use A=p~rZ/kT, which for the typical conditions p = 1.0X 106 Pa and T = 298 K used in our experiments, yields a value of A = 3,7 × 107 m L
3. Results Figs. 1 and 2 show ~29Xe NMR spectra of specific types of carbon black, kaolin and humified sand recorded in our laboratory. The first two are used as fillers in polymer composites to improve their mechanical properties. We therefore study them in a pure form to identify a possible resonance of filler-sorbed xenon in the ze9Xe NMR spectra of polymer composites. The humified sand is a sample from soil at the 'Sinderhoeve' Renkum Experimental Station (Wageningen, The Netherlands). Since the investigated carbon black and kaolin powders consist of loosely packed particles with diameters in the order of, respectively, 10-100 nm and 1 ~m, they may be regarded as indicative systems for xenon sorption in soil. In fact, kaolin is a specific type of clay with a structure closed for water and cations (Haddix and Naranya, 1994). The ~29Xe NMR spectra of the three types of carbon blacks in Fig. 1 illustrate the effect of particle size. An increase of the average particle size from 18 to 56 nm results in a shift of the adsorbed-xenon peak from 64 to 45 ppm. The free volume between the loosely packed aggregates of carbon black particles consists of large open pores which contain xenon gas in equilibrium with xenon adsorbed on the pore walls. For a comparable packing the size of these free-volume pores may be expected to vary linearly with the particle size. The decrease of chemical shift at increasing particle diameter therefore agrees with the similar tendency observed for zeolites (Barrie and Klinowski, 1992). The 129Xe NMR spectrum of a kaolin powder consisting of particles of ca. 1 gtm contains a broad line at 8.5 ppm with a linewidth of 5.6 ppm (Fig. 2a). This peak, which is consistent with the finding for unpillared montmorillonite at room temperature (Barrie et al., 1991), probably belongs to xenon adsorbed at the surface of the kaolin particles. Its position close to the position of free xenon
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455
c
1O0
50 chemical shift (ppm)
Fig. 1. 129Xe NMR spectra at a pressure of ca. 10 atm and room temperature of commercially available types of carbon black from Cabot. The powders N110 (upper), N330 (middle) and N550 (lower) have respective particle diameters of 18, 30 and 56 nm. Ca. 30,000 scans were recorded within 24 h using single-pulse excitation at a Bruker CXP200 spectrometer operating at the 129Xe NMR frequency of 54 MHz. Sample preparation as described previously (Mansfeld and Veeman, 1994).
b
..
.
. . . . . .
4'0
-
_
I
2o
a
I
-2o
_.
Jo
chemical shift (ppm)
Fig. 2. 129XeNMR spectra of (a) kaolin B80 produced by Sachtleben (Duisburg, Germany) and (b) humified sand from soils at the 'Sinderhoeve' Renkum Experimental Station (Wageningen, The Netherlands). Experimental conditions as in Fig. 1. The broad NMR line observed for humified sand can be decomposed into a broad lorentzian line (broken line) and an irregularly shaped narrow line (Fig. 4a).
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gas at 0 ppm as compared xenon adsorbed carbon black (Fig. 1), reflects the much larger pores in the kaolin powder (1 ixm) than in the carbon black samples (10-100 nm). It should be realized, however, that the chemical shift of adsorbed xenon does not only depend on the pore diameter, but also on the nature of the interaction between xenon and the pore surface. In carbon black the pore wall consists of carbon atoms, whereas in kaolin the main interaction is probably between xenon and oxygen, like in zeolites (Ripmeester and Ratcliffe, 1990). In the 129Xe NMR spectrum of humified sand the peak of adsorbed xenon is found at 3.5 ppm. The absence of any further downfield peak indicates that no xenon is sorbed within the sand crystallites. Pores with diameters in the order of 10 like those in e.g. zeolites, or pillared clay seem to be absent or inaccessible for xenon atoms. Because xenon is adsorbed on the outer surface of the sand crystallites only, the NMR spectrum of the humified sand may be directly compared with the spectra of carbon black and kaolin discussed above. The chemical shift of xenon adsorbed in humified sand is closer to 0 ppm than observed for kaolin. Since the same xenon-oxygen interaction underlies xenon adsorption in both materials, this strongly indicates that the pores in the sand are larger than in kaolin. Indeed, according to the manufacturer specifications the kaolin powder studied by us mainly consists of particles smaller than 2 txm, whereas sieving of the sand shows that it contains much larger grains ( 100-1000
4. Discussion The effect of particle diameter, instead of pore size, on the chemical shift is illustrated for the three carbon black powders in Fig. 3. In this plot we test the hypothesis that for a comparable stacking the average pore size S between the particles in a powder is proportional to the average particle diameter D',
22xl 03
20
18-
16''1
. . . .
20
I . . . .
I
30
. . . .
i
. . . .
t
. . . .
I
. . . .
40
I
. . . .
i,
50
average diameter (nm)
Fig. 3. Reciprocal chemical shift of" the three carbon black types in Fig. I versus particle diameter. The linear correlation is consistent with Eq. (5).
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457
S = / z D ' . If this would be true, Eq. (5) predicts a linear relation between the reciprocal chemical shift, 1 / 6 and the particle diameter D'. Indeed, the data points in Fig. 3 lie on a straight line. From the slope and the intercept it follows that the chemical shift of xenon in the adsorbed state 6 b = 81 ppm, and the proportionality coefficient A/x = 1.48 × 10 7 m - l . The linearity also indicates that despite size differences the particles and pores in the three carbon black powders have similar shapes and surface properties. Substituting 6 b = 81 ppm for xenon adsorbed on carbon black into Eq. (6) we obtain pore sizes S of 7, 11 and 22 nm for the carbon black powders with particle diameters of 18, 30 and 56 nm, respectively. For spherical pores ( D = 6S) these S values would correspond to diameters of 42, 66 and 132 nm. Pore diameters roughly twice the particle diameters appear to be a reasonable outcome of the model. To estimate the pore size for kaolin and the humified sand from their 129Xe NMR spectra, we need to know the NMR shift of xenon in the adsorbed state, 6 b. A limiting value of 243 ppm has been proposed for xenon adsorbed in zeolites at room temperature and vanishing pressure (Demarquay and Fraissard, 1987; Barrie and Klinowski, 1992). The correction to be made for montmorillonite and zeolite Y at finite pressure is ca. 8 p p m / a t m (Barrie et al., 1991; Gupta et al., 1996). A smaller correction of 0.5 p p m / a t m is required for the chemical shift of free xenon gas (Gupta et al., 1996). Assuming similar values for kaolin and humified sand we take 6b = 300 ppm ( + 10%). With this 6 b value the chemical shifts 8.5. and 2 ppm of xenon adsorbed in kaolin and humified sand respectively yield a pore size S of 0.9 and 4 txm. Since the kaolin powder studied consists of disk-shaped particles, one might also expect the interparticle voids to be flat interlayers, rather than spheres. An average pore diameter of 2S = 2 lxm seems consistent with the kaolin particle diameter of ca. 1 ixm. An independent check of the volume-to-area ratio in kaolin can be made by combining the density of 2.62 g / m l and the specific surface 21 m 2 / g specified by the manufacturer, with the macroscopic observation, that 0.685 g kaolin occupies 6.5 ml in the NMR tube. This yields a volume-to-area ratio 0.5 Ixm which roughly agrees with the pore size S estimated from the 129Xe NMR spectrum. When interpreted in terms of spherical pores, the S value of 4 ixm obtained for humified sand seems small. The sand mainly consists of particles > 100 Ixm and it is unlikely that spherical pores of 25 txm in diameter would be dominant in the powder. This may be due to an error in positioning the xenon gas peak at 0 ppm with respect to an external reference. As a consequence of experimental preparation of the sealed tubes the pressure varies between 10 atm ___10%. Pressure variations + 1 atm result in a variation of the xenon gas shift of + 0.5 ppm. An alternative explanation for the low pore size of the sand is perhaps that due to irregular shapes of the soil grains the area of the interparticle pore walls is much larger than expected from a smooth sphere of the same diameter. Low pore size in combination with large particle sizes would generally indicate rough and irregular particle surfaces.
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When determining pore sizes from the 129Xe NMR spectrum, one should keep in mind that xenon atoms do not stay within a pore, but diffuse more or less freely between pores, especially in loosely packed systems like soil. Diffusion coefficients reported for intercrystalline xenon diffusion between zeolites are in the order of 10-9-10 -7 m~/s (Heink et al., 1990). Assuming similar diffusion in our systems, the mean diffusion distance of xenon at a timescale corresponding to a shift difference of 3 ppm (0.5 ms) would be ~ 0.2 ram. As a result, size differences between connected pores closer than 0.2 mm will not be detectable with 129Xe NMR. As a consequence, the model yields an average pore size at a submillimetre scale. If the material is homogeneous at a larger scale, the NMR spectrum will contain a single line at the average position. Even for homogeneous systems NMR peaks have an intrinsic linewidth, which may vary from system to system. Homogeneously broadened NMR peaks may generally be recognized from their lorentzian line shape. Further peak broadening may arise, when pore size heterogeneity exists at a larger scale. A distribution of pore sizes at a scale > 0.2 mm results in a broad ~>Xe NMR line, which consists of a continuous distribution of overlapping peaks. The linewidth of such inhomogeneous NMR line, which may have an asymmetric shape, reflects the pore-size distribution. Both homogeneous and inhomogeneous broadening may be recognized in the Xe NMR spectrum of humified sand (Fig. 2b). The lineshape can be decomposed into a broad lorentzian line and a narrower asymmetric line. The broad line, which represents 80% of the spectral intensity, seems homogeneously broadened. We tentatively assign it to xenon atoms that temporarily reside in the vicinity of paramagnetic impurities at the NMR timescale. Homogeneous broadening also explains the occurrence of spectral intensity for negative chemical shift values, which cannot be accounted for by our model otherwise. The asymmetric line seems predominantly broadened by the inhomogeneity of the sample (Fig. 4a). Its peculiar shape reflects the accumulation at 0 ppm of spectral contributions by pores > 50 p~m. An impression of the pore size distribution can be obtained by transforming the chemical shift axis between ab = 300 ppm and 6g = 0 ppm into a pore size axis by use of Eq. (6) (Fig. 4b). It should be noticed that the resulting distribution follows from a direct mapping between chemical shift and pore size. No spectral simulation is involved, although by using Eq. (6) other sources of inhomogeneous line broadening (such as variations in ion concentration and susceptibility effects) are neglected. Fig. 4b shows that only few pores have a size below a certain minimum value (1 p,m), and that larger pores equally occur in the powder seemingly without upper limit. 129Xe NMR spectroscopy, however, cannot distinguish between pore sizes which give rise to chemical shifts differing less than typically 20% of the intrinsic NMR linewidth. Estimating the homogeneous linewidth from the edge of the line at 0 ppm to be ca. 1 ppm, we conclude from Eq. (6) that pore sizes > 50 p~m cannot be resolved by 129Xe NMR. This puts an upper limit to the
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459
a
3'0
2'0
1'0
1.o I b
//
oq l o
-;o
chemical shift (ppm)
/ .
0.1
o
4
~
........
,
. . . .
1 10 volume-to-arearatio S (Bin)
Fig. 4. (a) The residual lineshape after subtracting the broad lorentzian line from the experimentally observed NMR peak of humified sand indicated in Fig. 2b. (b) The presumed pore-size density after transforming the chemical shift axis between a b = 300 and 6 b = 0 ppm into a pore size axis according to Eq. (6).
pore sizes about which NMR is still informative. This upper limit may be raised to some extent by eliminating the homogeneous line broadening at the risk of introducing lineshape effects (Magusin and Veeman, 1996).
5. Conclusion
At the risk of overinterpreting the limited experimental data obtained in this pilot study, we have shown that I29Xe NMR spectroscopy potentially yields useful information about pore structures with volume-to-area ratios < 50 I*m in powders like soil. As far as the sample fits within an NMR tube (ca. 1 cm), the technique does not require disruption of the packing structure. Absolute pore size information can only be obtained after determination of the xenon-adsorption from pressure-dependent Langmuir or B.E.T. experiments. Before studying the undisrupted soil packing, it may be necessary to separate the soil into fractions of different size to determine 6b, the chemical shift of xenon in the adsorbed state. If xenon pressure in the NMR tube cannot be controlled exactly, it is advisory to leave some large free space in the part of the tube enclosed by the NMR detection coil (e.g. by sticking a capillary into the sample). This will yield the xenon gas shift, 6g, as an internal reference at the unknown pressure. By use of the model discussed above, the lineshape of an inhomogeneously broadened peak in the 129Me NMR spectrum can be directly translated into a
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pore size distribution. It should be noticed, however, that the model neglects homogeneous line broadening and other broadening mechanisms, such as ion concentration variations and local susceptibility gradients. This may not be a valid approximation. Homogeneous broadening puts an upper limit to the pore sizes distinguishable by 129XeNMR. The exact upper limit depends on the type of sample involved, but would be typically 50 Ixm. The pore sizes resulting from 129Xe NMR spectroscopy are volume-to-area ratios averaged at a submillimetre scale. The averaging scale can be estimated more accurately by measuring xenon diffusion in the material itself. NMR techniques have been developed for this purpose (Heink et al., 1990). Volumeto-area ratios can only be interpreted in terms of actual pore diameters, if knowledge about the pore geometry is available. A possible outcome may be, that the volume-to-area ratio is much smaller than expected from the particle size. This would be an indication for a rough or fractal type of particle surface. Since xenon probes surfaces at a 5-~, scale, 129Xe NMR may indirectly reveal smaller details than visible with light or electron microscopy. Reliable pore size information can only be obtained in the absence of other co-adsorbates, such as water and small organic molecules. Co-adsorbing molecules may occupy the pores or block their entrance. This will generally affect and deteriorate the 129Xe NMR spectrum. However, this may also be turned into an advantage. By interpreting the NMR lineshape of xenon sorbed in soil as a function of hydration, e.g. in terms of the model developed in this paper, one may be able to obtain information about the order in which pores become filled with water at increasing hydration.
Acknowledgements We are grateful to the European Commission for the Human Capital Mobility fellowship received by Magusin. We thank DSM (Geleen, The Netherlands) and Sachtleben (Duisburg, Germany) for providing the carbon black and kaolin, respectively. Soil samples were kindly supplied by the Department of Micromorphology and Soil Structure of the DLO-Winand Staring Centre for Integrated Land, Soil and Water Research (Wageningen, The Netherlands).
References Barrie, P.J., Klinowski, J., 1992. 129XeNMR as a probe for the study of microporous solids. A critical review. Prog. NMR Spectr. 24, 91-108. Barrie, P.J., McCann, G.F., Gameson, I., Rayment, T., Klinowski, J., 1991. Variable-temperature 129XeNMR studies of a pillared montmorillonite. J. Phys. Chem. 95, 9416-9419. Brownstein, S.K., Roovers, J.E.L., Worsfold, D.J., 1988. 129Xeline widths in block copolymers. Magn. Reson. Chem. 26, 392-393.
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Cheung, T.T.P., Fu, C.M., Wharry, S., 1988. 129XeNMR of xenon adsorbed in zeolite Y at 144 K. J. Phys. Chem. 92, 1570-1580. Conte, P., Van Lagen, B., Buurman, P., Piccolo, A., 1997. Quantitative aspects of solid phase 13C-NMR spectra of humic substances from soils of volcanic systems. In: Hemminga, M.A., Buurman, P. (Eds.), NMR in Soil Science. Geodenna 80 (3/4), 327-338, this issue. Demarquay, J., Fraissard, J., 1987. 129XeNMR of xenon adsorbed on zeolites. Relationships between the chemical shift and the void space. Chem. Phys. Lett. 136, 314-318. Derourane, E.G., Nagy, J.B., 1987. Surface curvature effects on the NMR chemical shift for molecules trapped in microporous solids. Chem. Phys. Lett. 137, 341-344. Gedeon, A., lto, T., Fraissard, J., 1988. Study of the H 2 0 / N a Y system. An example of the application of 129Xe n.m.r, of the xenon probe to the investigation of the location of adsorbed phases. Zeolites 8, 376-380. Gupta, V., Davis, H.T., McCormick, A.V., 1996. Comparison of the 129Xe NMR chemical shift with simulation in zeolite Y. J. Phys. Chem. 100, 9824-9833. Haddix, G.W., Naranya, M., 1994. NMR of layered materials for heterogeneous catalysis. In: Bell, A.T., Pines, A. (Eds.), NMR Techniques in Catalysis. Marcel Dekker, New York, pp. 311-360. Heink, W., Kiirger, J., Pfeifer, H., Stallmach, F., 1990. Measurement of the intracrystallite self-diffusion of xenon in zeolites by the NMR pulsed field gradient technique. J. Am. Chem. Soc. 112, 2175-2178. Ito, T., Fraissard, J., 1982. Xenon-129 NMR study of xenon adsorbed in Y zeolites. J. Chem. Phys. 76, 5225-5229. lto, T., de Menorval, L.C., Guerrier, E., Fraissard, J., 1984. NMR study of 129Xe adsorbed on L, Z and ZSM zeolites. Chem. Phys. Lett. I 11, 271-274. Kennedy, G.J., 1990. 129Xe NMR as a probe of the effect of crosslinking on the amorphous phase structure of solid polymers. Polym. Bull. 23, 605-608. Kentgens, A.P.M., van Boxtel, H.A., Verweel, R.-J., Veeman, W.S., 1991. Line-broadening effects for 129Xe absorbed in the amorphous state of solid polymers. Macromolecules 24, 3712-3714. Magusin, P.C.M.M., Veeman, W.S., 1996. Resolution improvement in NMR spectroscopy by elimination of the homogeneous line broadening. J. Magn. Reson. A 119, 252-255. Mansfeld, M., Veeman, W.S., 1993. The use of 129Xe NMR exchange spectroscopy for probing the microstructure of porous materials. Chem. Phys. Lett. 213, 153-157. Mansfeld, M.. Veeman, W.S., 1994. 129Xe nuclear magnetic resonance of AI203 fibres. Microporous Mater. 3, 85-92. Mansfeld, M., Flohr, A., Veeman, W.S., 1995. Application of 129Xe NMR to polymer blends. Appl. Magn. Reson. 8, 573-586. Mirabella, F.M., McFaddin, D.C., 1996. 129Xe n.m.r, spectroscopic characterization of multiphase polypropylene copolymers. Polymer 6, 931-938. Raftery, D., Chmelka, B., 1994. Xenon NMR spectroscopy. In: NMR Basic Principles and Progress. Springer-Verlag, Berlin, pp. 112-158. Ripmeester, J.A., Davidson, D.W., 1981. Xenon-129 nuclear magnetic resonance in the clathrate hydrate of xenon. J. Mol. Struct. 75, 67-72. Ripmeester, J.A., Ratcliffe, C.I., 1990. On the application of 129Xe NMR to the study of microporous solids. J. Phys. Chem. 94, 7652-7656. Simpson, J.H., Wen, W.-Y., Jones, A.A., lnglefield, P.T., 1996. Diffusion coefficients of xenon in polystyrene determined by xenon- 129 NMR spectroscopy. Macromolecules 29, 2138-2142. Springuel-Huet, M.-A., Nosov, A., K~ger, J., Fraissard, J., 1996. 129Xe NMR study of the bed resistance to molecular transport in assemblages of zeolite crystallites. J. Phys. Chem. 100, 7200-7203.
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Stengle, T.R., Williamson, K.L., 1987. Nuclear magnetic resonance of xenon absorbed in solid polymers. A probe for the amorphous state, Macromolecules 20, 1428-1430. Veeman, W.S., 1997. Nuclear magnetic resonance. A simple introduction to the principles and applications. In: Hemminga, M.A., Buurman, P. (Eds.), NMR in Soil Science. Geoderma 80 (3/4), 225-242, this issue. Walton, J.H., Miller, J.B., Roland, C.M., 1992. 129Xe NMR as a probe of polymer blends. J. Polym. Sci. B 30, 527-532. Walton, J.H., Miller, J.B., Roland, C.M., 1993. Phase transitions in polymer blends via 129Xe NMR spectroscopy. Macromolecules 26, 4052-4054.
"
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GEO * A ELSEVIER
The use of
Geoderma 80 (1997) 449-462
129XeNMR spectroscopy for studying soils. A pilot study
Pieter C.M.M. Magusin, Andreas Bolz, Kerstin Sperling, Wiebren S. Veeman * Department of Physical Chemistry, Gerhard-Mercator-Universit~tt Duisburg, LotharstraJJe I, 47048 Duisburg, Germany Received 27 November 1996; accepted 9 April 1997
Abstract Xenon nuclear magnetic resonance (129Xe NMR) spectroscopy is a powerful technique to study microporous solids and semi-crystalline polymers. In this pilot study we investigate the use of 129Xe NMR spectroscopy for studying soils by applying the technique to model systems of carbon black and kaolin powders and to humified sand. In contrast to e.g. zeolites no xenon is sorbed within the sand crystallites at room temperature and high pressure (10 atm). Xenon is only adsorbed at the crystallite surface. The exchange of xenon between the adsorbed and gas phase is so fast, that 129Xe NMR spectroscopy cannot distinguish between the two. This results in a single peak in the I>Xe NMR spectrum with a weighted-average chemical shift between the shift of xenon in the adsorbed and the gas state. A model is presented which relates the chemical shift to the local volume-to-area ratio of the intercrystallite pores at a submillimetre scale. If other heterogeneity types can be neglected, ~29Xe NMR spectroscopy potentially reveals information about pore size distributions in undisrupted soils. © 1997 Elsevier Science B.V.
Kevwords: xenon; nuclear magnetic resonance; pore size; volume-to-area ratio; adsorption; carbon black; kaolin; humified sand
1. I n t r o d u c t i o n S i n c e the e a r l y e i g h t i e s ( R i p m e e s t e r a n d D a v i d s o n , 1981; Ito a n d F r a i s s a r d , 1982) x e n o n n u c l e a r m a g n e t i c r e s o n a n c e (129Xe N M R ) s p e c t r o s c o p y has p r o v e n to be a v a l u a b l e tool for s t u d y i n g m i c r o p o r o u s s o l i d s a n d s e m i - c r y s t a l l i n e
* Corresponding author. Fax: +49 203 379 3522. 0016-7061/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S00 16-7061 ( 9 7 ) 0 0 0 6 6 - 9
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polymers. Xenon atoms are well suited for probing pores in solids, because of their small diameter (4.4 A), nonpolarity and chemical inertness. This allows them to be sorbed in void spaces in many solid materials. Due to the large and polarizable electron cloud of xenon its NMR chemical shift strongly depends on its atomic environment (Derourane and Nagy, 1987). As a consequence, the t29Xe NMR spectrum contains information about the local structure at the sorption sites. From an NMR point of view the isotope ~29Xe has the advantage of having a high natural abundance (26%) and a spin quantum number 1/2 like most of the regular NMR nuclei, which makes it an easy nucleus to work with. Most of the current xenon NMR literature is devoted to zeolites and related materials, such as molecular sieves. Another major class of publications deals with amorphous polymers. A comprehensive discussion of the complete literature would be beyond the scope of this paper. Excellent reviews have appeared recently (Barrie and Klinowski, 1992; Raftery and Chmelka, 1994). The purpose of this paper is to give a short introduction in the application of ~29Xe NMR spectroscopy and to discuss its possible use for studying soil materials. Readers who are not yet familiar with the general technique of NMR spectroscopy are referred to the NMR introduction presented elsewhere in this issue (Veeman, 1997). Several groups employ t2~Xe NMR spectroscopy to study the heterogeneity in polymers (Walton et al., 1992, 1993; Mansfeld et al., 1995; Mirabella and McFaddin, 1996). Xenon atoms sorbed in semi-crystalline polymers reside in the free volume between the polymer chains in the amorphous phase (Stengle and Williamson, 1987) and give rise to NMR peaks typically between 200 and 220 ppm with respect to the xenon-gas peak. Above the glass-transition temperature xenon atoms sorbed in the amorphous phase do not stay at one position, but undergo diffusion under the influence of the segmental motion of the polymer chains. The miscibility of polymer components in polymer blends is a major topic in polymer science. ~2';Xe NMR is an important and relatively easy technique to study the compatibility of two components in polymer blends. Due to the mobility of the sorbed xenon atoms xenon can exchange between the single-component domains in a polymer blend. If the exchange is fast, i.e. if the domain sizes are smaller than the diffusion length of xenon atoms at the timescale of the NMR experiment, a single ~29Xe NMR peak is detected for the sorbed species. If the ~29Xe NMR spectrum contains well-resolved peaks corresponding to xenon sorbed in each of the components separately, this indicates that the components are not well-mixed in the blend and form separate phases.The diffusion coefficients of xenon in polymers reported in the literature range from 2 × 10 -~3 to 4 × 10 -1~ m2/s (Brownstein et al., 1988; Simpson et al., 1996). At the NMR timescale (10 3 s) xenon thus diffuses over a mean distance ~( r 2 ) = 1 I~m. Therefore, incompatible polymer blends with domains > 1 ~ m give rise to resolved peaks in the 129Xe NMR spectrum. Well-mixed polymers yield a single ~2';Xe NMR peak only (Mansfeld et al., 1995). Using
P.C.M.M. Magusin et al./ Geoderma 80 (1997) 449-462
129Xe NMR
451
slow demixing of incompatible polymers can actually be followed as function of time (Walton et al., 1993; Mirabella and McFaddin, 1996). Decreasing the temperature, or cross-linking of polymers slows down xenon diffusion revealing the heterogeneity of the xenon sorption sites at a scale < 1 ~ m in the 129Xe NMR spectrum (Kennedy, 1990). Detailed information about heterogeneity at a larger scale can be obtained by use of more advanced NMR techniques (Kentgens et al., 1991; Mansfeld and Veeman, 1993). Due to their relationship with clay, the numerous 129XeNMR publications for zeolites are especially relevant for the possible application of this spectroscopic technique to soil. Peak positions in the 129Xe NMR spectra observed for xenon sorbed in zeolites depend on the zeolite type, the xenon pressure and the temperature. At room temperature the chemical shift values extrapolated to zero-pressure range from 58 ppm for zeolite Y to 110 ppm for ZSM-5 (Ito et al., 1984). The larger the cavity, the smaller the chemical shift. The 13-,~ diameter of the relatively large supercages in zeolite Y may serve as an indication of the pore sizes involved. Attempts have been made to correlate the chemical shift with the pore geometry based on the curvature of the pore wall (Derourane and Nagy, 1987), the mean free path of a single xenon atom within a pore (Demarquay and Fraissard, 1987) and rapid exchange between xenon adsorbed on the pore wall and xenon gas in the pore volume (Cheung et al., 1988). However, a quantitative interpretation of the chemical shift in terms of the pore size is complicated by the fact that other factors, such as the presence of cations, influence the chemical shift, as well (Barrie and Klinowski, 1992). Moreover the usual assumption underlying the models that xenon stays within a pore is a severe simplification. At room temperature xenon is sufficiently mobile to average xenon interactions over thousands of zeolite cages at the timescale of the NMR experiment, typically 10 -3 s (Heink et al., 1990). Because various types of humic molecules are converted on or in clays, clay can perhaps be regarded as the most abundant heterogeneous catalyst on earth (Haddix and Naranya, 1994). The 129Xe NMR studies of xenon sorption in zeolites in the presence of co-adsorbates, such as water or small organic molecules, may thus be of particular interest to soil research. In general, co-adsorbates reduce the sorption and mobility of xenon, by blocking the sorption sites and the diffusion of xenon. On the basis of a model relating the 129Xe chemical shift to the mean free path of xenon sorbed within zeolites, the effect of hydration and the diffusion of water in zeolites can be indirectly investigated using 129Xe NMR spectroscopy (Gedeon et al., 1988). A recent paper deals with the exchange of benzene between zeolite crystallites (Springuel-Huet et al., 1996). As for soil itself, ~H and 13C NMR may be used to study organic components in soils or soil extractions (Conte et al., 1996). NMR studies of clay have mostly been restricted to 27A1 and 295i nuclei (Haddix and Naranya, 1994). The only t29Xe NMR study of clay, which seems to have appeared (Barrie et al., 1991), deals with the sorption of xenon in pillared
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montmorillonite. The naturally occurring material becomes pillared by exchanging its Na + and Ca 2+ cations with aluminium. The resulting pillared material has an interlayer spacing of 8.1 A, which enables the formation of a xenon bilayer between the layers. ~29Xe NMR spectra at room temperature and low pressure show a broad peak at ~ 100 ppm assigned to the sorbed xenon. Upon lowering the temperature the chemical shift of the peak increases. In contrast, the 129Xe NMR spectrum of the unpillared clay above 220K contains a peak between 0 and 15 ppm, indicating that no xenon is sorbed within the clay and that xenon adsorbed at the external surface is quickly exchanging with the xenon gas. At lower temperatures a peak appears between 150 and 170 ppm. This peak is assigned to sorbed xenon which resides long enough on the external surface of the clay particles to yield a resolved adsorption peak in the NMR spectrum. Realizing that soil is basically a stack of various grains and therefore contains networks of interparticle pores, we studied various types of powders using 129Xe NMR spectroscopy. As will be shown, the 129Xe NMR spectrum contains information about the average volume-to-area ratio of these pore networks at a submillimetre scale without necessity to disrupt the original powder stacking. o
2. Theory To more quantitatively interpret the chemical shift of xenon sorbed in powders, like soil, in terms of pore size, we use a simple model based on fast exchange between adsorbed xenon and xenon gas. More detailed fast-exchange models have been published for xenon sorption in zeolites (Cheung et al., 1988; Ripmeester and Ratcliffe, 1990). It has been pointed out° (Ripmeester and Ratcliffe, 1990), that xenon atoms in a l~ore larger than 10 A are not continuously in an adsorbed state, i.e. within 5-A distance from the pore wall, but also spend part of their time in the free gas phase in the pore volume. The exchange between the bound and the gas phase is so fast, that NMR spectroscopy cannot distinguish between them. The observed 129Xe chemical shift is an average between the shift of xenon in the bound state, 6 b, and in the gas state, 6~, weighted by the fraction of bound and gas atoms, N b / N and Ng/N, respectively. Thus: 6 = Nb N
+
(1)
In the fast exchange limit the NMR spectrum does not depend on the exchange rate. Within this limit Eq. (1) is thus valid for any exchange rate or distribution thereof. The limiting shifts 6 b and 6g vary with pressure and temperature. In addition, 6b depends on the atomic composition of the pore wall and the local surface curvature of the binding site. Our model assumes that at constant pressure and temperature the numbers N b and N~ are proportional to the area
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453
and the volume of the pore, respectively. More precisely, the number of xenon atoms bound to the pore wall, N b, is given by:
Nb=Ona
(2)
where 0 denotes the occupation degree, n the number of binding sites per unit area and A the area of the wall. The occupation 0 typically follows from the Langmuir equation:
Kp 0= - -
(3)
l+Kp
where K and p are, respectively, the Langmuir constant and the pressure. Since K varies with temperature T, 0 depends on both p and T. The number of xenon atoms in the gas phase inside a large pore can be estimated from the perfect gas law:
pV Ug- kr
(4)
where k = 1.38 × 10 -23 J K-I is Boltzmann's constant. Eq. (4) neglects the reduction of the pore volume due to the monolayer of xenon atoms on the pore wall. This is a valid approximation for the pore sizes > 40 nm which we encounter in our powder systems. Substituting Eqs. (2) and (4) into Eq. (1) and defining the chemical shift of the free xenon gas 6g as 0 ppm, we derive: 6-
8b 1 + as
(5)
where A =p/OnkT is a pressure- and temperature-dependent constant and S = VIA denotes the volume-to-area ratio of the pore. For various regular geometric shapes S is proportional to the diameter D (e.g. for spherical and cubic cavities S = D/6, for long cylindrical channels S = D/4 and for flat interlayers S = D/2). For this reason, we define S to be the characteristic pore size for the irregular pore networks in soils and other powders, as well. Eq. (5) shows, that as the pore size increases from zero to infinity, the chemical shift 6 decreases from the adsorbed state value 6 b to the gas-state value 6g = 0. With this model the tZ9Xe NMR spectrum thus reflects the pore size in the material under study. The pore size S can actually be determined from the chemical shift of adsorbed xenon in the 129Xe NMR spectrum by using the inversion of Eq.
(5): ,
S=
-~-1
~-
(6)
For comparing different powders with identical particle-surface properties at the same xenon pressure the factor 1/A in Eq. (6) is a simple proportionality constant. Therefore, to determine relative pore sizes with respect to an appropri-
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ate reference, or the distribution of relative pore sizes within a powder Eq. (6) may be used without knowledge of A. For absolute determination of the pore size the parameter A, and thus of 0 (or K) and n, must be known. This information may be obtained from xenon sorption measurements as a function of p and T. An exhaustive investigation of xenon adsorption in soil and other powders, however, is beyond the scope of this pilot study. As a first approximation we make the crude assumption, that under the high xenon pressures employed in our experiments (ca. 10 atm) all xenon binding sites are fully covered ( 0 = 1) and that the adsorption-site density is the inverse of the cross-section of a xenon atom (n = 1/Trr 2, where r = 2.2 A denotes the xenon radius). The latter corresponds to coverage of the pore wall with a dense monolayer of xenon atoms with negligible interspace. Thus, by assumption, we use A=p~rZ/kT, which for the typical conditions p = 1.0X 106 Pa and T = 298 K used in our experiments, yields a value of A = 3,7 × 107 m L
3. Results Figs. 1 and 2 show ~29Xe NMR spectra of specific types of carbon black, kaolin and humified sand recorded in our laboratory. The first two are used as fillers in polymer composites to improve their mechanical properties. We therefore study them in a pure form to identify a possible resonance of filler-sorbed xenon in the ze9Xe NMR spectra of polymer composites. The humified sand is a sample from soil at the 'Sinderhoeve' Renkum Experimental Station (Wageningen, The Netherlands). Since the investigated carbon black and kaolin powders consist of loosely packed particles with diameters in the order of, respectively, 10-100 nm and 1 ~m, they may be regarded as indicative systems for xenon sorption in soil. In fact, kaolin is a specific type of clay with a structure closed for water and cations (Haddix and Naranya, 1994). The ~29Xe NMR spectra of the three types of carbon blacks in Fig. 1 illustrate the effect of particle size. An increase of the average particle size from 18 to 56 nm results in a shift of the adsorbed-xenon peak from 64 to 45 ppm. The free volume between the loosely packed aggregates of carbon black particles consists of large open pores which contain xenon gas in equilibrium with xenon adsorbed on the pore walls. For a comparable packing the size of these free-volume pores may be expected to vary linearly with the particle size. The decrease of chemical shift at increasing particle diameter therefore agrees with the similar tendency observed for zeolites (Barrie and Klinowski, 1992). The 129Xe NMR spectrum of a kaolin powder consisting of particles of ca. 1 gtm contains a broad line at 8.5 ppm with a linewidth of 5.6 ppm (Fig. 2a). This peak, which is consistent with the finding for unpillared montmorillonite at room temperature (Barrie et al., 1991), probably belongs to xenon adsorbed at the surface of the kaolin particles. Its position close to the position of free xenon
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455
c
1O0
50 chemical shift (ppm)
Fig. 1. 129Xe NMR spectra at a pressure of ca. 10 atm and room temperature of commercially available types of carbon black from Cabot. The powders N110 (upper), N330 (middle) and N550 (lower) have respective particle diameters of 18, 30 and 56 nm. Ca. 30,000 scans were recorded within 24 h using single-pulse excitation at a Bruker CXP200 spectrometer operating at the 129Xe NMR frequency of 54 MHz. Sample preparation as described previously (Mansfeld and Veeman, 1994).
b
..
.
. . . . . .
4'0
-
_
I
2o
a
I
-2o
_.
Jo
chemical shift (ppm)
Fig. 2. 129XeNMR spectra of (a) kaolin B80 produced by Sachtleben (Duisburg, Germany) and (b) humified sand from soils at the 'Sinderhoeve' Renkum Experimental Station (Wageningen, The Netherlands). Experimental conditions as in Fig. 1. The broad NMR line observed for humified sand can be decomposed into a broad lorentzian line (broken line) and an irregularly shaped narrow line (Fig. 4a).
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gas at 0 ppm as compared xenon adsorbed carbon black (Fig. 1), reflects the much larger pores in the kaolin powder (1 ixm) than in the carbon black samples (10-100 nm). It should be realized, however, that the chemical shift of adsorbed xenon does not only depend on the pore diameter, but also on the nature of the interaction between xenon and the pore surface. In carbon black the pore wall consists of carbon atoms, whereas in kaolin the main interaction is probably between xenon and oxygen, like in zeolites (Ripmeester and Ratcliffe, 1990). In the 129Xe NMR spectrum of humified sand the peak of adsorbed xenon is found at 3.5 ppm. The absence of any further downfield peak indicates that no xenon is sorbed within the sand crystallites. Pores with diameters in the order of 10 like those in e.g. zeolites, or pillared clay seem to be absent or inaccessible for xenon atoms. Because xenon is adsorbed on the outer surface of the sand crystallites only, the NMR spectrum of the humified sand may be directly compared with the spectra of carbon black and kaolin discussed above. The chemical shift of xenon adsorbed in humified sand is closer to 0 ppm than observed for kaolin. Since the same xenon-oxygen interaction underlies xenon adsorption in both materials, this strongly indicates that the pores in the sand are larger than in kaolin. Indeed, according to the manufacturer specifications the kaolin powder studied by us mainly consists of particles smaller than 2 txm, whereas sieving of the sand shows that it contains much larger grains ( 100-1000
4. Discussion The effect of particle diameter, instead of pore size, on the chemical shift is illustrated for the three carbon black powders in Fig. 3. In this plot we test the hypothesis that for a comparable stacking the average pore size S between the particles in a powder is proportional to the average particle diameter D',
22xl 03
20
18-
16''1
. . . .
20
I . . . .
I
30
. . . .
i
. . . .
t
. . . .
I
. . . .
40
I
. . . .
i,
50
average diameter (nm)
Fig. 3. Reciprocal chemical shift of" the three carbon black types in Fig. I versus particle diameter. The linear correlation is consistent with Eq. (5).
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457
S = / z D ' . If this would be true, Eq. (5) predicts a linear relation between the reciprocal chemical shift, 1 / 6 and the particle diameter D'. Indeed, the data points in Fig. 3 lie on a straight line. From the slope and the intercept it follows that the chemical shift of xenon in the adsorbed state 6 b = 81 ppm, and the proportionality coefficient A/x = 1.48 × 10 7 m - l . The linearity also indicates that despite size differences the particles and pores in the three carbon black powders have similar shapes and surface properties. Substituting 6 b = 81 ppm for xenon adsorbed on carbon black into Eq. (6) we obtain pore sizes S of 7, 11 and 22 nm for the carbon black powders with particle diameters of 18, 30 and 56 nm, respectively. For spherical pores ( D = 6S) these S values would correspond to diameters of 42, 66 and 132 nm. Pore diameters roughly twice the particle diameters appear to be a reasonable outcome of the model. To estimate the pore size for kaolin and the humified sand from their 129Xe NMR spectra, we need to know the NMR shift of xenon in the adsorbed state, 6 b. A limiting value of 243 ppm has been proposed for xenon adsorbed in zeolites at room temperature and vanishing pressure (Demarquay and Fraissard, 1987; Barrie and Klinowski, 1992). The correction to be made for montmorillonite and zeolite Y at finite pressure is ca. 8 p p m / a t m (Barrie et al., 1991; Gupta et al., 1996). A smaller correction of 0.5 p p m / a t m is required for the chemical shift of free xenon gas (Gupta et al., 1996). Assuming similar values for kaolin and humified sand we take 6b = 300 ppm ( + 10%). With this 6 b value the chemical shifts 8.5. and 2 ppm of xenon adsorbed in kaolin and humified sand respectively yield a pore size S of 0.9 and 4 txm. Since the kaolin powder studied consists of disk-shaped particles, one might also expect the interparticle voids to be flat interlayers, rather than spheres. An average pore diameter of 2S = 2 lxm seems consistent with the kaolin particle diameter of ca. 1 ixm. An independent check of the volume-to-area ratio in kaolin can be made by combining the density of 2.62 g / m l and the specific surface 21 m 2 / g specified by the manufacturer, with the macroscopic observation, that 0.685 g kaolin occupies 6.5 ml in the NMR tube. This yields a volume-to-area ratio 0.5 Ixm which roughly agrees with the pore size S estimated from the 129Xe NMR spectrum. When interpreted in terms of spherical pores, the S value of 4 ixm obtained for humified sand seems small. The sand mainly consists of particles > 100 Ixm and it is unlikely that spherical pores of 25 txm in diameter would be dominant in the powder. This may be due to an error in positioning the xenon gas peak at 0 ppm with respect to an external reference. As a consequence of experimental preparation of the sealed tubes the pressure varies between 10 atm ___10%. Pressure variations + 1 atm result in a variation of the xenon gas shift of + 0.5 ppm. An alternative explanation for the low pore size of the sand is perhaps that due to irregular shapes of the soil grains the area of the interparticle pore walls is much larger than expected from a smooth sphere of the same diameter. Low pore size in combination with large particle sizes would generally indicate rough and irregular particle surfaces.
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When determining pore sizes from the 129Xe NMR spectrum, one should keep in mind that xenon atoms do not stay within a pore, but diffuse more or less freely between pores, especially in loosely packed systems like soil. Diffusion coefficients reported for intercrystalline xenon diffusion between zeolites are in the order of 10-9-10 -7 m~/s (Heink et al., 1990). Assuming similar diffusion in our systems, the mean diffusion distance of xenon at a timescale corresponding to a shift difference of 3 ppm (0.5 ms) would be ~ 0.2 ram. As a result, size differences between connected pores closer than 0.2 mm will not be detectable with 129Xe NMR. As a consequence, the model yields an average pore size at a submillimetre scale. If the material is homogeneous at a larger scale, the NMR spectrum will contain a single line at the average position. Even for homogeneous systems NMR peaks have an intrinsic linewidth, which may vary from system to system. Homogeneously broadened NMR peaks may generally be recognized from their lorentzian line shape. Further peak broadening may arise, when pore size heterogeneity exists at a larger scale. A distribution of pore sizes at a scale > 0.2 mm results in a broad ~>Xe NMR line, which consists of a continuous distribution of overlapping peaks. The linewidth of such inhomogeneous NMR line, which may have an asymmetric shape, reflects the pore-size distribution. Both homogeneous and inhomogeneous broadening may be recognized in the Xe NMR spectrum of humified sand (Fig. 2b). The lineshape can be decomposed into a broad lorentzian line and a narrower asymmetric line. The broad line, which represents 80% of the spectral intensity, seems homogeneously broadened. We tentatively assign it to xenon atoms that temporarily reside in the vicinity of paramagnetic impurities at the NMR timescale. Homogeneous broadening also explains the occurrence of spectral intensity for negative chemical shift values, which cannot be accounted for by our model otherwise. The asymmetric line seems predominantly broadened by the inhomogeneity of the sample (Fig. 4a). Its peculiar shape reflects the accumulation at 0 ppm of spectral contributions by pores > 50 p~m. An impression of the pore size distribution can be obtained by transforming the chemical shift axis between ab = 300 ppm and 6g = 0 ppm into a pore size axis by use of Eq. (6) (Fig. 4b). It should be noticed that the resulting distribution follows from a direct mapping between chemical shift and pore size. No spectral simulation is involved, although by using Eq. (6) other sources of inhomogeneous line broadening (such as variations in ion concentration and susceptibility effects) are neglected. Fig. 4b shows that only few pores have a size below a certain minimum value (1 p,m), and that larger pores equally occur in the powder seemingly without upper limit. 129Xe NMR spectroscopy, however, cannot distinguish between pore sizes which give rise to chemical shifts differing less than typically 20% of the intrinsic NMR linewidth. Estimating the homogeneous linewidth from the edge of the line at 0 ppm to be ca. 1 ppm, we conclude from Eq. (6) that pore sizes > 50 p~m cannot be resolved by 129Xe NMR. This puts an upper limit to the
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459
a
3'0
2'0
1'0
1.o I b
//
oq l o
-;o
chemical shift (ppm)
/ .
0.1
o
4
~
........
,
. . . .
1 10 volume-to-arearatio S (Bin)
Fig. 4. (a) The residual lineshape after subtracting the broad lorentzian line from the experimentally observed NMR peak of humified sand indicated in Fig. 2b. (b) The presumed pore-size density after transforming the chemical shift axis between a b = 300 and 6 b = 0 ppm into a pore size axis according to Eq. (6).
pore sizes about which NMR is still informative. This upper limit may be raised to some extent by eliminating the homogeneous line broadening at the risk of introducing lineshape effects (Magusin and Veeman, 1996).
5. Conclusion
At the risk of overinterpreting the limited experimental data obtained in this pilot study, we have shown that I29Xe NMR spectroscopy potentially yields useful information about pore structures with volume-to-area ratios < 50 I*m in powders like soil. As far as the sample fits within an NMR tube (ca. 1 cm), the technique does not require disruption of the packing structure. Absolute pore size information can only be obtained after determination of the xenon-adsorption from pressure-dependent Langmuir or B.E.T. experiments. Before studying the undisrupted soil packing, it may be necessary to separate the soil into fractions of different size to determine 6b, the chemical shift of xenon in the adsorbed state. If xenon pressure in the NMR tube cannot be controlled exactly, it is advisory to leave some large free space in the part of the tube enclosed by the NMR detection coil (e.g. by sticking a capillary into the sample). This will yield the xenon gas shift, 6g, as an internal reference at the unknown pressure. By use of the model discussed above, the lineshape of an inhomogeneously broadened peak in the 129Me NMR spectrum can be directly translated into a
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pore size distribution. It should be noticed, however, that the model neglects homogeneous line broadening and other broadening mechanisms, such as ion concentration variations and local susceptibility gradients. This may not be a valid approximation. Homogeneous broadening puts an upper limit to the pore sizes distinguishable by 129XeNMR. The exact upper limit depends on the type of sample involved, but would be typically 50 Ixm. The pore sizes resulting from 129Xe NMR spectroscopy are volume-to-area ratios averaged at a submillimetre scale. The averaging scale can be estimated more accurately by measuring xenon diffusion in the material itself. NMR techniques have been developed for this purpose (Heink et al., 1990). Volumeto-area ratios can only be interpreted in terms of actual pore diameters, if knowledge about the pore geometry is available. A possible outcome may be, that the volume-to-area ratio is much smaller than expected from the particle size. This would be an indication for a rough or fractal type of particle surface. Since xenon probes surfaces at a 5-~, scale, 129Xe NMR may indirectly reveal smaller details than visible with light or electron microscopy. Reliable pore size information can only be obtained in the absence of other co-adsorbates, such as water and small organic molecules. Co-adsorbing molecules may occupy the pores or block their entrance. This will generally affect and deteriorate the 129Xe NMR spectrum. However, this may also be turned into an advantage. By interpreting the NMR lineshape of xenon sorbed in soil as a function of hydration, e.g. in terms of the model developed in this paper, one may be able to obtain information about the order in which pores become filled with water at increasing hydration.
Acknowledgements We are grateful to the European Commission for the Human Capital Mobility fellowship received by Magusin. We thank DSM (Geleen, The Netherlands) and Sachtleben (Duisburg, Germany) for providing the carbon black and kaolin, respectively. Soil samples were kindly supplied by the Department of Micromorphology and Soil Structure of the DLO-Winand Staring Centre for Integrated Land, Soil and Water Research (Wageningen, The Netherlands).
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