spatially resolved adsorption isotherms of thermally polarized perfluorinated gases in...

Appl. Magn. Reson. 22, 175-186 (2002) Applled Magnetic Resonance �9 Springer-Verlag 2002 Printed in Austria

Spatially Resolved Adsorption Isotherms of Thermally Polarized Perfluorinated Gases in Yttria-Stabilized Tetragonal-Zirconia Polycrystal Ceramic Materials

with NMR Imaging

S. D. Beyea l, A. Caprihan 1, C. E M. Clewett I, and S. J. Glass 2

t New Mexico Resonance, Albuquerque, New Mexico, USA 2SandŸ National Laborato¡ Albuquerque, New Mexico, USA

Received September 5, 2001; revised December 18, 2001

Abstract. This paper presents the results obtained by nuclear magnetic resonance (NMR) imaging of perfluorinated gases in mesoporous solids. NMR images of nuclear spin density asa function of gas pressure permits spatially resolved measurements that are analogous to conventional bulk Brunauer- Emmett-Teller adsorption isotherm measurements. The use of NMR imaging allows the nondestruc- tive evaluation of macroscopic spatial variations in the underlying mesoporous structure, for materials such as partially sintered Y-TZP (ytt¡ tetragonal-zirconia polycrystal) ceramics. All NMR measurements were performed with octafluorocyclobutane (C4F8) gas, using only the thermal Boltzman nuclear magnetization.

1 Introduct ion

Nuclear magnet ic resonance (NMR) is a wel l es tabl ished and useful method for s tudying porous media, due to its sensi t ivi ty to parameters such as porosi ty, pore radius, tortuosity and phase state [1-4] . General ly, studies have focused on liquids in porous materials such as rocks and soils.

N M R of hyperpolar ized 129Xe gas has also recent ly been used to study porous solids [5]. In these studies, the abi l i ty to produce a large nuclear magnet i - zation is used to overcome the inherent ly small spin densi ty o f gases, so as to al low N M R measurements o f the t ime-dependent diffusion coefficient, and hence the tor tuosi ty o f the underlying pore structure. These measurements genera l ly require that the 129Xe molecules do not s ignif icant ly interact with the solid pore matrix, as these interactions often act to rapidly return the hyperpolar izat ion to its equi l ibr ium Boltzman value.

The study o f how gases interact with porous materials is, however, an im- portant area o f scientific research. Studies o f gas/ l iquid phase equil ibria in porous solids provide information on the physics o f f inite-size effects and surface

176 S.D. Beyea et al.

forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistente curves) [6]. Furthermore, investigations of changes in phase transitions and associated critical points in confined systems allow for materials science studies of pore va¡ such as pore size, surface structure, and con- nectivity.

In addition to scientific interests, improved understanding of confinement effects of porous media is necessary for many geophysical and industrial appli- eations. Meso (1.5 to 100 nm) and microporous (< 1.5 nm) materials are widely used in the pharmaceutical, petrochemical, and food industries. The design of such industrial processes often has little scientifie justification and is largety empiri- cal. There is, therefore, both a theoretical a n d a practical interest in furthering scientific knowledge of the behavior of gases in porous solids.

In porous media, liquid/gas phase equilibrium depends on the nature of the adsorbate and adsorbent, gas pressure, and temperature. According to the Polanyi potential theory, the overlapping potentials of the pore walls readily overcome the translational energy of the adsorbate, leading to enhanced adsorption of gas molecules at low pressures [7]. In addition, condensation of gas in small pores may occur at a lower pressure than that normally required on a plane surface, as expressed by the Kelvin equation, which relates the radius of a curved surface to the equilibrium vapor pressure as

ln(P/p0) = _ 2yV coso , (1) rRT

where P is the equilibrium vapor pressure of the liquid contained in a pore of radius r and Po is the equilibrium pressure of the liquid on a plane surface. The terms V and y are the liquid molar volume and surface tension, respectively, R is the ideal gas constant, T is the gas temperature, and ‰ is the contact angle [7-8].

Physical adsorption is caused by attractive forces between adsorbate and adsorbent, such as ion-dipole, ion-induced dipole, dipole-dipole and dispersion [9]. All of these forees are similar to those that lead to liquefaction of gases in bulk. Gases with strong intermolecular interactions, and consequently high boiling points, therefore tend to be strongly adsorbed.

Conventional bulk measurements of adsorption are performed by determining the quantity of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [6-8]. As the pressure is increased, condensation will occur first in small-radii pores and will progress into the largest pores at a relative pressure of unity. These bulk "adsorption isotherms" are often analyzed with the 1938 theory of Brunauer, Emmett and Teller (BET theory) [10], which ex- tended the Langmuir kinetic theory to multilayer adsorption and assumes that the uppermost molecules in adsorbed stacks are in dynamic equilibrium with the vapor [7, 8]. The theoretical BET equation used to describe experimental isotherm data is given by

k(P/Po) _ 1 + C - l k ( P / p o ) , (2) N ( 1 - k ( P / P o ) ) NmC NmC

Spatially Resolved BET Isotherms with NMR Imaging 177

where N is the adsorbate molecular number density, N mis the amount of adsorbate required for monolayer coverage, and the BET C value is a measure of the adsorption interaction between the gas molecules and the solid substrate (stron- ger surface adsorption leads to a higher BET C value). The coefficient k was a modification proposed in 1969 by Brunauer et al. [11] to extend the original BET equation [i0] into the multilayer region, and has a value that is less than unity [8, 11]. Typically the theoretical BET equation is only valid in the region of data near the monolayer value, as physical constants such as the latent heat of vapori- zation varies with increasing adsorption layers [7, 8, 10, 11]. The theoretical va- lidity of the inclusion of the coefficient k is based on the heat of adsorption in the second and subsequent layers being less than the heat of liquefaction [11].

One common use in materials science of BET adsorption theory is the determination of the sample specific surface area by deriving a value for the monolayer capacity of the solid from the BET adsorption isotherms. Monolayer capacity is related to surface area, S, by the simple relation

S = N m A N / M , (3)

where A is the average cross-sectional area occupied by a molecule of adsorbed gas in a completed monolayer, N is the Avogadro constant, M i s the molecular weight of the adsorbate, and N mis expressed in this case as grams of adsorbate per gram of solid.

It has previously been demonstrated that it is possible to obtain 19F NMR images of perfluorinated gases in mesoporous ceramics [12-13]. NMR images acquired with a short echo time (TE) and long radio-frequency (RF) pulse repetition time (TR), relative to the spin-spin and spin-lattice relaxation times of the gas in the ceramic, are directly proportional to the nuclear spin density, and therefore to the molecular density of gas/liquid adsorbate. In the current study we obtain a series of NMR spin density images of gas in ceramics, acquired a s a function of pressure at a constant temperature. Intensities of individual pixels (or regions of pixels), plotted a s a function of pressure, therefore, f o r m a space-resolved map of local adsorption isotherms. With this technique, we are able to resolve macroscopic changes in gas/liquid phase equilibria of the underlying mesoscopic pore structure.

2 Experimental Details

The ceramic samples used in this study were produced from yttria-stabilized tetragonal-zirconia polycrystal (Y-TZP) powders. The powders were compacted with a steel die at 34 MPa, before being sealed in latex and isopressed to approximately 140 MPa. Organic binder was then burned out by heating at 2~ to 700~ and holding at this temperature for 2 h. The specimens were then partially densified by heating at 2~ to between 960 and 1305~ with the higher temperatures resulting in more dense materials. After the samples were

178 S.D. Beyea et al.

partially sintered, they were immersed in a molten salt of aluminum nitrate nona- hydrate for 10 min. The samples were then subsequently reheated to a temperature of approximately 600~ (well below the original sintering temperature) to decompose the molten salt into an alumina phase, which is distributed a s a fine particulate in the pores in the region of the sample infiltrated by the molten salt.

Measurements of bulk porosity and pore size were made with the Archimedes technique (ASTM standards C20 and C830) and mercury porosimetry respectively (Autopore II, 9220, Micrometrics, Norcross, GA, USA) [14]. The two ceramic samples used in this study h a d a mean pore size of 20 and 27 nm, with corre- sponding porosities of 40 and 35%. The specific surface area was determined with the conventional "single-point" BET method [7], with the 40 and 35% porosity ceramics having bulk surface areas of 5.24 and 4.22 m2/g, respectively.

The gas used in this study was octafluorocyclobutane (C4F8) (Lancaster Syn- thesis Inc., Wyndham, NH, USA), with NMR and thermodynamic bulk properties given in Table 1. NMR reIaxation times of this gas, determined by the spin- rotation interaction [15-16], were pressure-dependent and generally increased in the ceramic relative to the value for free bulk gas [12, 13]. NMR experiments with this gas were done in the thermally polarized state (not hyperpolarized). It has been previously demonstrated that it is possible to use nonhyperpolarized gases for NMR imaging [12, 13, 17-19]. The use of C4F 8 results in an eightfold improvement in signal-to-noise ratio, compared to monatomic gases, which helps to partially overcome the inherently low molecular density of gases compared to liquids. In addition, gases such as C4F 8 exhibit enhanced spin-lattice relaxation via coupling of the fluorine nuclear spins to the molecular angular momentum [15-16]. We are therefore able to utilize 90 ~ flip angle RF pulses with relatively short pulse repetition times, which partially offsets the low nuclear polarization relative to hyperpolarized gas NMR experiments.

All NMR measurements were performed at 1.9 T in ah Oxford horizontal bore superconducting magnet with a clear bore diameter of 310 mm, with a quadrature driven RF birdcage probe (Morris Instruments, Ottawa, ON, Canada) tuned to the 19F frequency of 75.6 MHz, a n d a TecMag Libra spectrometer (TecMag Inc, Houston, TX, USA). The two-dimensional (2-D) NMR images were

Table 1. C4F 8 bulk gas properties.

Property Value

Boiling point at 101.3 kPa Critical temperature Molar volume at condensation pressure Surface tension Lermard-Jones diameter Spin-lattice relaxation time (T~) at 296 K and 101.3 kPa Bulk diffusion coefficient at saturation pressure and 294 K

267.2 K 388 K

132 cm 3 at 294 K 8.3 dyne/cm at 294 K

0.703 nm 63 ms

0.64.10 -£ m2/s


obtained with a conventional slice-selective spin-echo sequence, with an echo time (TE) of 5.4 ras, a n d a repetition time (TR) which was maintained so as to al- ways be at least t ire times •onger than the longest T 1 in the image. The short TE and long TR were chosen so as to produce a spin-density weighted image. The resutting 2-D images (128 by 64 pixels) were obtained with a 7 mm thick slice and had ah in-plane nominal spatial resolution of 750 by 750 ~tm 2.

The Y-TZP ceramic samples were cylindrical with a h e i ~ t and diameter of approximately 15 and 23 mm respectively. Temperature control was accomplished with ah Isotemp 1016S digital temperature controller (Fisher Scientific, Pitts- burgh, PA), which pumped distitled water through a heating jacket that sur- rounded the pressurized sample vessel. The sample temperature, as measured by a thermocouple ftxed to the sample container, was maintained at 296.1+__0.2 K over the period of the 72 h experiment. Gas pressure was measured with ah Omega DP25B-S transducer and digital pressure meter (Omega Engineering, Stamford, CT). Alongside the ceramie samples was placed a sealed glass vial containing 215 kPa of C4F s gas, which was used a s a reference to aormalize the individual images, so as to remove the effect of changes in spectrometer sensitivity over the course o f the experiment. The pressu¡ polycarbonate sample vessel had ah inner diameter of 26 mm and a length of 100 mm. Perspex rod, 25 mm diameter, was u~ed to fill empty space in the pressure vessel, so as to minimize gas waste.

The ceramic samples were initially flushed with dry Nz gas and pumped down to a vacuum of 6 .10 -3 Torr over a pe¡ of two days with a mechanical pump, so as to remove all gas from the pore surfaces. C4F s gas was then pro- gressively added a t a tate of approximately 5 kPa per hour, and the system was allowed to stabilize to ah equilibfium state at each final pressure value. NMR images were acquired at 30 different increasing pressures ranging from 13.5 kPa to the bulk condensation point of 299.4 kPa. Images were also obtained at 11 different decreasing pressures in a similar manner, tmtil the hysteresis loop closed al 235 kPa.

3 Resul t s

Three MR images, acquired at pressures of 45, 174.8 and 296.4 kPa are shown in Fig. 1. In the 2-D images, the 35% porosity ceramic is located on the right, the 40% porosity ceramic in the center, and the gas reference vial on the leff. In the higher-gas-pressure images, bulk gas sig-nal is faintly visible in the empty spaces of the sample container. The ceramic images clearly exhibit spatially varying image contrast, with the p¡ feature being a "ring" of increased signal intensity on three sides of the ceramic material. The right side of the ceramic images, which does not exhibit increased image mtensity near the edge, is the face which was cut during the manufacturing process. The high-signal-intensity ring is tikely due to a difference both m surface composition and area, caused by the presence of the deposited alumina particles, with the width o f the ¡ being a measure of the infiltration depth of the molten salt.

180 S, D. B e y ~ el al.

! :.~,.

b

Fig. L 2-D s[ice-selective ~~F NMR images of thermally polarized C,F 8 gas in 35% (right) and 40% porosity (left) Y-TZP pamally simered ceramics at gas pressures of 45 (a), 174.8 (b) and 296,4 kPa (e). To the leff of the ceramics is a sealed vial of C4F s gas at 215 kPa, used a s a reference. Images at 45 and 296.4 kPa exhibit ah increase of approximately two orders o f magnitude (relative to the

constant reference) in the pixel mteasities within the ceramics.

Figure 2 is a plot of fractional surface coverage (n/n~ versus gas pressure, where n is the NMR image intensity taken from a region of interest (ROI) within the outer ¡ of the 35% porosity ceramic, and n m is the calculated value for monolayer coverage. Changes in ,NIVIR spectrometer sensitivity were removed by normalization to the constant gas reference, present in the images. Given that the pixel mtensities in these short TE and long TR images ate directly proportional to nuclear spin density, n can be thought of as equivalent to the molecular number density of adsorbed gas, N. Normalized signal intensity plotted a s a function of gas pressure is therefore the local gas adsorption isotherm for that particular ROl.

Plots of I/n[Po/P- li versus P'Po ate shown in Figs. 3 and 4, where P is the gas pressure, and Po is the bulk gas condensation point (299.4 kPa for C4F s al 296.1 K). These so-called BET plots [7, 8, 10] ate typically linear in the reNon of 0.1 <_ P/Po <- 0.35. P[ots taken ffom various ROIs within the 35 and 40% porosity ceramic materials are shown in Figs. 3 and 4 respeefively. BET plots are a comrnon[y used method for determining surface area from adsorption isotherm measurements [6--8, lO]. Figure 3 shows two ptots obtamed with ROIs from within the outer ring of signal and from the center region of the 35% porosity cemmic, and Fig. 4 shows one plot taken from a ROI within the center reNon of the 40~ porosity ceramic, as weI1 as plots taken from two different ROIs within the outer ring.

Spatially Resolved BET Isotherms with NMR Imaging

10

181

6

4

-4~- Adsorption Isotherm 1 --e-Desorption Isotherm

J 0 50 100 150 200 250

Gas Pressure (kPa) 300

Fig. 2. Fractional surface coverage (n/nm) versus equilibrium gas pressure at 296.1 + 0.2 K, where n is the average pixel intensity (proportional to mass of adsorbed gas) taken from a RO! within the outer ring of higher signal intensity of the 35% porosity ceramic, and n mis the calculated vatue for monolayer coverage. The results forro ah adsorption/desorption isotherm, which is analogous to the results obtained using conventiona[ BET bulk techniques, and are of the forro of a standard Type IV

([UPAC) isotherm, which is typical for mesoporous materials.

1.25

1.0

0.75

~ 0.5

0.25

111-

J �9 35% Porosity Ceramic (Outer Ring)

4, 35% Porosity Ceramic (Center)

0 0,05 0,1 0.15 0.2 0.25 0.3 0.35 P/Po

Fig. 3. BET plots of l/n[Po/P- 1] versus P/Po, where n is the nuclear spin density (proportional to mass of adsorbed gas), P i s the gas pressure, and Po is the bulk gas saturation pressure. Results are

shown for ROls taken from within the ring and center region of the 35% porosity sample.

182 S. D. Beyea et al.

0.75

0.5

v

T -

0.25 Porosity (Center) *40% Ceramic

. ~ m40% Porosity Ceramic (Outer Ring Region #1) 0 1 . . . . . . . . . ? 40;/o. Por;s,~ Ceramlc (?ule I R,ng.Reg.,on .#2).

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 PIPo

Fig. 4. BET plots of 1/n[Po/P- 1] versus P/Po, where n is the nuclear spin density (proporcional to mass of adsorbed gas), P is the gas pressure, and Po is the bulk gas saturation pressure. Results are shown for RO[s taken from within the center region and two different regions within the high-sig-

naL-intensity ring of the 40% porosity sample.

4 Discussion

The results shown in Fig. 2 are typical o f a Type IV isotherm, according to the 1985 IUPAC classification [6]. Type IV isotherms are commonly exhibited by mesoporous materials and are characte¡ by the presence o f a capillary condensation transition and adsorption/desorption hysteresis [6-8]. The knee o f the Type IV isotherm typically occurs near completion o f the first monolayer [7, 10]. The results shown in Fig. 2 do indeed show the presence o f a capillary phase transition at approximately 294.5 kPa, as well as hysteresis during the desorption isotherm, down to a pressure o f approximately 235 kPa. Whilr results are only shown for a ROI within the outer "ring" o f the 35% porosity ceramic, similar results are obtained from ROIs throughout the ceramic samples, du¡ the same expe¡

Application o f the BET theory to the space-resolved isotherms, such as the one shown in Fig. 2, allows for the determination o f space-resolved BET plots. With the s!ope (s) and intercept (i) o f these plots, shown in Figs. 3 and 4, one is able to determine both the value o f the N M R image signal intensity for monolayer coverage, rito, as well as the BET C value [7, 8, 10]:

C = s/i + 1, n m = 1/(s + i). (4)

The BET plot for the particular adsorption isotherm shown in Fig. 2 is given in Fig. 3. With this plot, we are able to determine the local BET C value to be

Spatially Resolved BET Isotherms with NMR lmaging 183

8.4. The value for the monolayer image intensity was used to normatize the y- axis o f the adsorption isotherm shown in Fig. 2. All space-resolved BET plots shown in Figs. 3 and 4 are observed to be linear, as expected, with typical R 2 values obtained from the linear regression o f 0.997.

By examining Fig. 2, we see that the inflection point o f the isotherm does indeed take place at the value obtained from the BET plot for monolayer coverage (at n/n m = l), as expected from the BET theory [7]. Figure 5 shows the same isotherm data from Fig. 2, as well as the theoretical BET isotherm obtained with Eq. (2) with a C value o f 8.4, as determined from the BET plot (with a k pa- rameter o f 0.88, obtained by iterative curve fitting). Included in Fig. 5 are theoretical BET isotherms with C values o f 150 and 2, shown for comparison. The figure demonstrates good agreement between the theoretical BET isotherm and the space-resolved experimental data. This provides further evidence that the N M R image data obtained is indeed a space-resolved measure o f the actual adsorption isotherm. The theoretical curve signif icant ly deviates from the exper imental data for P/Po greater than 0.7. This is not surprising, however, as it is well estab- lished that the BET equation is not valid over the full range o f pressures [6-8, I0, 11]. For the data shown here, a relative pressure o f 0.7 corresponds to the pressure at which the hysteresis loop closes.

Given that the BET C value is a measure o f gas-substrate interaction strength and n m is direct ly proportional to the total surface area (Eq. (3)) [7, 8, 10], dif-

3 t Experimental Data

Theoretical BET Curve (C = 8.4) -Theoretical BET Curve (C = 1 50) ~,

2 - - -Theoretical BET Curve (C = 2 ) j ~ ~ _ ~

E J

1 , f . - ' ~ ~.~..41~ 2"- o O , ' "

d

0 : ." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0.2 0.4 0.6

P/Po

Fig. 5, Theoretical modified-BET isotherms (Eq. (2)) are shown, with C values of 150, 8.4 and 2, which corresponds to strong, moderate and weak gas-substrate interaction. The experimentally determined local isotherm data is also plotted, which was determined with a BET plot to have a C value of 8.4 (k = 0.88). The theoreticat and experimental isotherms demonstrate good agreement, in the

range of pressures shown.

184 S . D . B e y e a et al.

ferences in the individual BET plots indicate a spatial difference in the local surface properties. Deposition of fine alumina particulates due to infiltration of the molten salt would modify the surface chemistry and increase the surface area. The results shown in the BET plots of Figs. 3 and 4 indicate that differences in surface area and chemistry correlate positively with the infiltration region.

In the results obtained with the 35% porosity ceramic (Fig. 3), the outer ring containing alumina particulates indeed has a relative surface area which is approximately 63% higher than that of the central region of the ceramic. The ra- tios of relative surface areas obtained from the BET plots in Figs. 3 and 4 are as follows: ~4~176 4~176 = 1.24; ,~,35%/,~,35% ~_. 1.63; S40%/S 35~176 1.21; ,~'4~176176 '35%

~rlng "~center ~ring "~center ~ r i n g - - f i n g --center' ~center ~"

1.59; ~,4o% m35o/o = 1.37. These results indicate an increase in surface area in the ~-bulk,,-~,-bulk,,

outer region containing alumina particulates, relative to the center of the ceramic materials. Furthermore, individual ROIs (as well as the materials a s a whole) exhibit a consistently higher surface area in the 40% porosity ceramics relative to the 35% porosity ceramics. This result is expected, given that the 40% porosity ceramics contain a larger total pore volume comprised of pores with a smaller mean diameter.

A close examination of Fig. la, b reveals that the higher-intensity ring appears to itself exhibir a structure at Iow pressures which is not apparent at high pressures (Fig. lc). Given that low-pressure images are sensitive to differences in surface adsorption, and high-pressure images are sensitive to differences in total porosity, it appears that the ring of higher signal intensity contains a spatial structure which is not due to porosity but rather due only to differences in the surface properties. This is confirmed by the fact that BET plots obtained from ROIs within both of the regions of the high-intensity ring ate different (Fig. 4). It is unclear whether this structure is due to an actual difference in pore size and/or surface atea of to a variation in surface chemistry alone.

We note that the ratio of relative surface areas (S4~176161 calculated from BET plots obtained with NMRI data averaged over each individual ceramic sample (1.37) agrees to within 10% error with the ratio of bulk specific surface areas (1.24). While it is clear that one would wish to use the space-resolved BET plots to obtain absolute values of local specific surface atea with Eq. (3), we are currently limited to determinations of relative surface atea. This is due to the fact that the NMR measurements are based upon ah arbitrary signal strength. Furthermore, the calculation of absolute surface atea requires knowledge of the adsorption diameter of a C4F 8 molecule. We ate therefore currently attempting to "calibrate" our NMR method, using a constant gas reference to sup- ply a proportionalty constant between NMR signal strength and molecular density, and calculating the adsorption diameter with BET measurements of materials with known uniform specific surface areas (such as controtled pote glasses).

5 Conclusions

The use of spin-density-weighted MR imaging of thermally polarized perfluorinated gases in mesoporous solids is shown to be capable of obtaining nonde-


structive measurements that are analogous to traditional bulk BET adsorption/ desorption isotherms. In addition, isotherms obtained from MR images are spatially resolved, which is a significant advantage. The data shown for ROIs taken from MR images acquired at varying pressures form sorption isotherms which are typical for mesoporous solids and exhibit capillary condensation transitions and consequent adsorption/desorption hysteresis. Thus, the results allow for the noninvasive spatial determination of traditional BET plots, which are sensitive to differences in local surface area and chemical composition.

Future experiments with this method will study the effect of temperature on space-resolved adsorption (especially near pore critical points), as well as simul- taneous studies of the space-resolved spin-lattice relaxation rate and time-dependent diffusion. We will attempt to correlate these results with traditional bulk methods, so as to connect the NMR results with actual material properties. We also plan to use this method to create plots of relative surface area, through the use of space-resolved BET plots. Further research will permit the calculation of spatial maps of absolute specific surface atea.

Acknowledgements

We thank Drs. Eiichi Fukushima, Dean Kuethe, and Steve Altobell i of New Mexico Resonance and Dr. Anthony DiGiovanni of Sandia National Labs for useful discussions and experimental help. Partial support for this work was pro- vided by Sandia National Labs, a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.

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Authors' address: Arvind Caprihan, New Mexico Resonance, 2301 Yale Boulevard SE, Suite C-1 Albuquerque, NM 87106, USA

spatially resolved adsorption isotherms of thermally polarized perfluorinated gases in...

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