Physical Adsorption of Inert Gases on Solid Surfaces as a Measure of

Thorium oxide is an excellent stable model substrate for development of sorption models for definitive evaluation of surface area and porosity. The ph...
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Physical Adsorption of Inert Gases on Solid Surfaces as a Measure of Surface Area and Porosity: Thorium Oxide E. Loren Fuller, Jr.* Lorela Enterprises, Incorporated, P.O. Box 355, Stanton, Nebraska 68779-0355 Received January 14, 2003. In Final Form: April 4, 2003 Thorium oxide is an excellent stable model substrate for development of sorption models for definitive evaluation of surface area and porosity. The physical adsorption isotherms for argon on thorium oxide surfaces have been reported in the literature with minimal interpretation with respect to the energy and mechanisms of the sorption processes. The data are analyzed in terms of the AutoShielding Potential (ASP) concepts to reveal argon physical adsorption on hydrated surfaces as contiguous monolayer-multilayer formation. Successively more energetic monolayer formation is observed when the screening surface hydration is removed in a vacuum at elevated temperatures. Argon multilayer formation is affected to a lesser degree by dehydration. The ASP methodology is unexcelled in defining physical adsorption for delineating structural and porosity factors as revealed in the sorption isotherms.

Introduction Recent developments have given improved methodology for analyses of sorption isotherms with regard to the nature of physical adsorption on solid surfaces. Specifically, the process is modeled in terms of the AutoShielding Potential (ASP) theory as a productive method of analyzing the physical sorption isotherms.1-7 There is a definite need to distinguish between chemical and physical processes that occur at or near solid surfaces.8,9 Thorium Dioxide (ThO2). Thorium dioxide has the highest melting point (3050 °C) and boiling point (4400 °C) of all of the inorganic oxides; thus it can be classified as the most refractory oxide. This feature is reflected in the low emmisivity and its classical use as a coating on Welsbach mantles and thoriated tungsten filaments. This material can be thermally treated at elevated temperatures with minimal sintering, and it exists as a single phase (face-centered cubic) over the entire solidus region, with virtually no defect structure. Gray surfaces in a vacuum are due to deposited carbon, and oxidation to white substrata involves a weight loss in the current gravimetric analyses. Thoria surfaces are stoichiometrically hydrated only in the surface layer.10 Stoichiometric bulk hydroxide [Th(OH)4] is questionable and is not formed under the * E-mail: [email protected]. (1) Fuller, E. L., Jr.; Condon, J. B. Statistical Mechanical Evaluation Of Surface Area From Physical Adsorption Of Gases. Colloids Surf., A 1989, 37, 171. (2) Condon, J. B. Equivalency to the Dubinin-Polyani equations and the QM based sorption isotherm equation. A. Mathematical derivation. Microporous Mesoporous Mater. 2001, 38, 359-376. (3) Condon, J. B. Equivalency to the Dubinin-Polyani equations and the QM based sorption isotherm equation. B. Simulation of heterogeneous surfaces. Microporous Mesoporous Mater. 2001, 38, 377-383. (4) Fuller, L. E., Jr. Energetics and Mechanism of Physical Sorption by Carbonaceous Solids: Evaluation of surface area and porosity factors. Presented at the Sixth International Conference on Porous Materials, Alicante, Spain, June 2002. To be published in proceedings. (5) Condon, J. B. Chi Representation of Standard Nitrogen, Argon, and Oxygen Adsorption Curves. Langmuir 2001, 17, 3423-3430. (6) Polyani, M. The Adsorption of Gases on Solids. Discuss. Faraday Soc. 1934, 316. (7) Polyani, M. The Potential Theory of Adsorption. Science 1963, 141, 1010-1013. (8) Adamson, A. W. Physical Chemistry of Surfaces, 2nd ed.; Wiley: New York, 1967. (9) Fuller, E. L., Jr.; Smyrl, N. R.; Condon, J. B. Uranium Oxidation: Characterization Of Oxides Formed By Reaction With Water By Infrared And Sorption Analyses. J. Nucl. Mater. 1984, 120 (2-3), 174-194.

conditions described in this report. This is also noted in the extremely low solubility in aqueous media. The nuclear applications require material of very high purity which was available for this study. Recent environmental studies have shown concerns and precautions needed for use of ThO2 for the laboratory studies described here.11 Thorium is an R emitter albeit with a half-life of several million years, and ingestion should be avoided, even though there is virtually no solubility in the human digestive tract and elimination is rapid and complete. Physical Adsorption. Any solid surface is an asymmetric boundary that attracts gas molecules due to the imbalance of the Madelung12 force field that exists in the bulk solid. The attraction is also due to dispersion and/or London forces. Adsorption occurs when such a solid surface is exposed to an inert gas at finite pressures and temperatures. Such interactions are classified as physisorption if the interactions are of a molecular nature and involve relatively weak association such that the sorbed entity is: (1) Freely mobile on the surface, losing only a few degrees of freedom (translation, vibration, rotation, etc.). (2) In a molecular state similar to that found in the bulk liquid of the sorbate, with a molecular structure much akin, if not identical, to that of the liquid. (3) Readily equilibrated with the gas phase and free to escape (and be replaced by another sorbate molecule instantaneously). (4) Unimpeded such that all surface motion is completely unhindered with no collisions and/or completely elastic collisions in the monolayer and multilayer regions of the surface phase. (5) Referenced to the first molecule physically sorbed on such a surface which is held on the surface sorption with a finite sorption potential. Thus there is a charac(10) Holmes, H. F.; Fuller, E. L., Jr.; Secoy, C. H. Heat of Immersion in the Thorium Oxide-Water System: IV. Variation of the Net Differential Heat of Adsorption with Specific Surface Area. J. Phys. Chem. 1968, 72, 2095. (11) Material Safety Data Sheet, http://www.espimetals.com/msds’s/ thoriumoxide.pdf. (12) Crandall, R. E. Topics in Advanced Scientific Computation; Springer/TELOS: New York, 1996; pp 73-79. Hautot, A. New applications of Poisson’s summation formula. J. Phys. A 1975, 8 (6), 853862.

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teristic pressure (a vacuum) that will produce a sorbatefree surface. (6) Referenced to the condensed liquid sorbate phase at pressures equal to the vapor pressure of the bulk sorbate. There must be an “infinite” uptake of sorbate at the saturation pressure, P ) P(0). Physisorption Isotherm. The model outlined above is the basis for mathematical analyses of the physisorption isotherm, where the amount of adsorption, Γ, is a function of the sorbate pressure, P, relative to the saturation pressure, P(0):

Γ ) f[P/P(0)]

(1)

The six criteria listed above are used to derive a consistent equation to best define the variation of concentration with pressure in terms of the ASP theory based on the Polanyi sorption potential, E:13,14

E ) -RT ln[P/P(0)]

(2)

Each sorbed molecule is shielded exponentially from the attraction force in proportion to the amount already sorbed:1

E ) E* exp(-θ)

(3)

where θ is the fractional monolayer coverage, Γ/Γ(m). Equation 3 can be expressed for convenience in dimensionless form,

E* E ) exp(-θ) RT RT

(4)

and rearranged for a linearized function of amount adsorbed,

θ ) ln

E* (RT ) - ln(RTE )

(5)

and expressed in the concentration terms of the raw data,

E* { (RT ) - ln(RTE )}

Γ ) Γ(m) ln

(6)

Thus a plot of surface concentration, Γ, versus ln(E/RT) will be a straight line with a slope Γ(m) and an intercept of Γ(m) ln(E*/RT) for perfect agreement between the sorption data and the model. The merit of the ASP analyses lies in the simplicity and the theoretical bases of the parameters.

Γ ) Γ(m){ln(-ln[P*/P(0)]) - ln[-ln(P/P(0))]} (7) One must recognize that ASP, thus described, is applicable to extensive flat surfaces and, if present, reactive surface sites, internal microporosity, mesoporosity (within or between substrate units), and macroporosity. Physical sorption in or on these geometric features will require separate analyses. This report will deal with the physisorption of argon on a sample that has been calcined extensively at elevated temperatures in a vacuum to remove porosity and impurities. Experimental Section Thorium Oxide Sample. This sample was analyzed as part of an Oak Ridge National Laboratory study to evaluate the stability of thoria for applications in nuclear reactor environs. (13) de Boer, J. H.; Zwikker, C. Z. Phys. Chem. 1929, B3, 407. (14) Bradley, R. S. J. Chem. Soc. 1936, 1467, 1926.

Sol-gel thoria was calcined at successively higher temperatures, and the sintering mechanisms were evaluated in terms of surface area and porosity. The material used here was extensively calcined at 1600 °C to produce a virtually nonporous white powder.15 Gravimetric Systems. The vacuum microbalances employed for this work have been described previously.16,17 The merits of such dedicated systems are evident in the versatility since one can control the environment and monitor equilibrium concentrations and reaction kinetics for pertinent processes. A typical sequence might be as follows: (1) sequentially outgas the sample in a vacuum at temperatures ranging up to 1000 °C; (2) monitor the rate18 of outgassing and equilibrium at each temperature; (3) lower sample temperature to that of cryogenic liquid nitrogen, 77.2 K; (4) measure physisorption isotherm kinetics and equilibrium, argon; (5) repeat to step 2; (6) measure water chemisorption isotherm at higher temperatures, -4 to 300 °C; (7) measure water physisorption on hydrated surfaces and the complexities involved in achieving the satiated chemisorption capacity; (8) repeat to step 1. All of these steps can be accomplished in a high vacuum without exposure and undocumented, unavoidable, inevitable contamination of the surface of the sample. The advent of computer automation has extended the versatility and capabilities of gravimetric systems19 for evaluating of equilibrium isotherms and kinetic (diffusion, chemical) rate mechanisms. Such detailed investigation is virtually impossible with volumetric sorption systems20 and/or separate instrumentation. Of necessity, these systems were equipped with a range of pressure transducers to permit accurate pressure measurements over a wide pressure range (10-6 to 1000 Torr).

Results and Discussion Hydroxylated Surfaces. Mobile Physical Adsorption. The results for this sintered sample are presented in Figure 1 in units of statistical “thickness”,16 that is utilized in the standard curves used for calculation of porosity from sorption isotherms. One merit of the ASP theory is that the intensive property, Γ, is treated in the first order. Thus a comparison is straightforward, with mathematical modification of the extensive property, that is, pressure, partial pressure, free energy, and so forth. Such isotherms are used for reference purposes with various multiplication factors to develop, Rs, n plots, “characteristic curves”, and so forth, all to be representative of the expected adsorption behavior of a nonporous material. Consistent with the liquid nature of the sorbate in this model, the data extend only to 0.82 P(0) (the vapor pressure of the supercooled liquid argon at the isotherm temperature, 77.2 K). The agreement between the model and sorption data extends over the entire range, from 0.01 to 0.82 P(0), as compared to the best fits of the Brunauer-Emmett-Teller (BET) (15) Gammage, R. B.; Fuller, E. L., Jr.; Holmes, H. F. J. Colloid Interface Sci. 1970, 34, 428. (16) Cranston, R. W.; Inkley, F. A. Adv. Catal. 1957, 9, 142. (17) Gammage, R. B.; Holmes, H. F.; Fuller, E. L. Pore Structures Induced By Water Vapor Adsorbed On Nonporous Lunar Fines And Ground Calcite. J. Colloid Interface Sci. 1974, 47 (2), 350-364. (18) Thompson, K. A.; Fuller, E. L., Jr. Accurate Sorption Isotherms Using A Computer-Aided Microgravimetric Method. J. Vac. Sci. Technol. 1987, A5 (4), 2522-2525. (19) Thompson, K. A.; Fuller, E. L. Computer Controlled Vacuum Microbalance Techniques Of Surface Area And Porosity Measurements. Langmuir 1987, 3 (5), 699-703. Fuller, E. L.; Yoos, T. R. Surface Properties Of Limestones and Their Activation Products. Langmuir 1987, 3 (5), 753-760. (20) Fuller, E. L.; Poulis, J. A.; Czanderna, A. W.; Robens, E. Volumetric and Gravimetric Methods of Determining Monolayer Capacities. Thermochim. Acta 1979, 29 (2), 315-318. Keller, J. U.; Robens, E.; du Fresne von Hohenesche, C. Thermogravimetric and Sorption Measurement Techniques/Instruments. Rodriguez-Reinoso, J., McEnaney, B., Rouquerol, J., Unger, K., Eds.; Studies in Surface Science and Catalysis, Vol. 145; Elsevier: Amsterdam, 2002; pp 387394.

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Figure 1. Argon sorption on hydrated thoria. Sample outgassed at 25 °C: open circles, lower abscissa; filled circles, upper abscissa; triangles, errors, right ordinate and lower abscissa. The lines are the best (minimum least squares) iterative fit of the data to the ASP model [slope ) 2.8055, intercept ) -1.8162, r2 ) 0.9994].

theory seldom applicable beyond the BET region from 0.05 to 0.35 P(0). That is not very impressive for a “multilayer” theory. The typical sigmoidal shape of the adsorption isotherm is changed to the rectilinear plot with the simple ASP transformation. The relatively weak “knee” for the adsorption isotherm and the low E* of the ASP plot are indicative of a rather weak interaction of argon with this hydrated oxide. Very similar isotherms have been reported for hydroxylated silica5,21 and mixed oxides.6,22 The surface hydroxyl groups are much akin to the low energy surfaces of ice substrata.23 One must be cautious in employing such reference isotherms for comparison to isotherm data for porous materials with the “same chemical composition”. Even though high-temperature outgassing is routine and deemed necessary prior to adsorption experiments, the details of the processes are not well understood24,25 in terms of the chemical and physical changes wrought in the surfaces. Few investigators have extensive insight into the nature of the problem, as best outlined by K. S. W. Sing and S. (21) Payne, D, A.; Sing, K. S. W.; Turk, D. H. J. Colloid Interface Sci. 1973, 43, 287. (22) Fuller, E. L., Jr. J. Colloid Interface Sci. 1976, 55, 358. See also: Fuller, E. L.; Agron, P. A. The Reactions of Atmospheric Vapors with Lunar Soil. U.S. Government Report ORNL-5129 (UC-34b), March 1976. (23) (a) Nair, N. K.; Adamson, A. W. J. Phys. Chem. 1970, 74, 2229. (b) Adamson, A. W.; Jones, B. R. Physical adsorption of vapors on ice: IV. Carbon dioxide. J. Colloid Interface Sci. 1971, 37 (4), 831-835. (c) Martin, C.; Manca, C.; Roubin, P. Adsorption Of Small Molecules On Amorphous Ice: Volumetric And FT-IR Isotherm Co-Measurements. Part I: Different Probe Molecules. Surf. Sci. 2002, 275, 502-503C. (24) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area, and Porosity; Wiley-Interscience: New York, 1967; pp 280-281.

Fuller

J. Gregg, in three aspects of paradigm evaluation.24 Three significant points are worthy of consideration: (A) “A discussion of adsorption of water on oxides would be incomplete without some reference to the irreversible effects which are often encountered when samples of oxide, hydroxide, or oxide-hydroxide are exposed to the vapour. These effects (‘low-temperature ageing’), which manifest themselves in changes in surface area, in pore structures, and sometimes in the lattice structure itself, are complex and difficult to reproduce exactly.”24 This thorium oxide sample can assuredly be analyzed in terms of the sorption and desorption (outgassing) of the bound water: (1) without appreciable alteration of the lattice structure, (2) with minimal formation of any bulk hydroxide phases, and (3) without any pore filling contributions. (B) “In view of the complications which may be produced by surface hydration, hydroxylation and ageing, it is essential to check the reproducibility of water isotherms if sound conclusions are to be drawn as to the nature of the adsorption processes involved.”24 Prior to the evaluation of the isotherm of Figure 1, the sample was cycled from a vacuum to P(0) and back repeatedly in a pure water atmosphere, until a reproducible water isotherm was achieved (virtually identical to that obtained after the original 25 °C outgas). The gravimetric system also inherently measures the amount of chemisorbed water entities and the amount lost from the sample on outgassing.26 Independent mass spectroscopic analyses found only water desorption from the sample outgassed in a vacuum. (C) “Any observed change in the adsorption characteristics with time can, of course, provide valuable information as to the extent and the mechanism of ageing, provided it is amplified by independent data, such as the isotherms of nitrogen or electron micrographs.”24 In this instance, we successively removed the bound water in a vacuum26 and used argon as the sorbate. Argon should be a more diagnostic sorbate since it has no quadrupole moment. The argon sorption isotherms are presented in Figure 2 for outgassing in a vacuum at the annotated temperatures. The simple, singular, linear ASP mechanism for argon physisorption on the hydroxylated surface is to be contrasted to the dual-mechanism ASP processes noted as more of the surface groups are removed to leave more and more “bare” polar Th-O sites. The stronger interaction energy is noted in the markedly enhanced E* values. This signifies that the initial sorption is much stronger and in reality does not fall in the realm of classical physisorption as defined above. Such sorption is probably associated with the periodic array of sorption sites that is beyond the realm of true physisorption. Nonetheless, the ASP premises are still valid in that the data in this region are well-defined as a linear function (relation) with the pertinent parameters as listed in Table 1. Dehydrated Surfaces. Site-Oriented Physical Adsorption. Two additional parameters are needed to define the additional ASP data trends at the lower coverage, E** (a markedly greater sorption potential) and a slope term, Γ(s). The simplest and most logical explanation is based on the following: (I) The site-oriented argon adsorption enhanced by the more stringent temperature treatment in a vacuum. The (25) Fuller, E. L., Jr.; Agron, P. A. Sorption of Water, Carbon Dioxide and Nitrogen by Sol-Gel Thorium Oxide. J. Colloid Interface Sci. 1976, 57, 193 Rouquerol outgas. (26) Fuller, E. L., Jr.; Smyrl, N. R.; Condon, J. B.; Eager, M. H. Uranium Oxidation: Characterization of Oxides Formed on Reaction with Water by Infrared and Sorption Analyses. J. Nucl. Mater. 1984, 120, 174-194.

Measuring Surface Area and Porosity via Adsorption

Figure 2. ASP plots for argon on nonporous thorium oxide. Black circles for 25 °C outgassing temperature (OGT), open circles for 100 °C OGT, open squares for 500 °C OGT, and open diamonds for 1000 °C OGT; ASP model fitting parameters are given in Table 1. Open hexagons show loss of degrees of freedom (right ordinate). Arrows show a break at loss of three degrees of translational freedom. Table 1. ASP Parameters for Argon Sorption on Nonporous Thoriaa outgas temp (°C) 25 slope, Å -ln(E**/RT) site, r2 Γ(m), Å -ln(E*/RT) free, r2

100

500

1000

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true physisorption could well be due to a roughness (corrugation?) factor that is enhanced as more bound (bridging?) water is removed. The intercept, E*/RT, is virtually identical for the secondary adsorption in each case when referred back to the initial (vacuum) state of the sorption isotherm. (IV) The change in sorption mechanism occurs at the energetic equivalent of the loss of three degrees of translational freedom. This restricted motion is envisioned as partial immobilization. The two degrees of freedom in the surface plane are restricted due to the enhanced perpendicular association of argon with surface polar groups (at least for one vibration) perpendicular to the surface plane as the initial sorption occurs in the periodic potential sites (wells). In the current scheme, this siteoriented sorption does not fit our strict description of physical sorption per se. The site-oriented sorption is limited to the equivalent of ca. 4.3 Å units as indicated by the arrow for the intersection of the rectilinear relations in Figure 2. The subsequent unrestrained physical sorption progresses into the multilayer regime to the unlimited condition of liquidus formation. The higher values for E**/RT are beyond the capabilities of current vacuum systems and reflect the greatly enhanced surface potentials. Note that the average molecular area for a physisorbed argon atom is quoted, “... on oxide surfaces, the molecular area of argon based on am(N2) ) 16.2 Å2 shows little variation from one solid to another, the average value being am(Ar) ) 16.6 Å2 with the supercooled liquid, or am(Ar) ) 18.0 Å2 with the solid, as the reference state.” (Reference 24, pp 76-77.) In terms of a complete filling, this is equivalent to 4.07 or 4.25 Å for the thickness of the respective monolayer. This is strong evidence that the argon atoms on the dehydrated surfaces are packed less closely than the true free motion of the classical physisorption as described above. This region is well-defined in a rectilinear ASP trend where the slope, Γ(*), defines the trends related to the amount of shielding hydrolyl/hydrate existing on the surface as reflected in a restricted ASP relationship,

E - ln( )} { (E** RT ) RT

Γ ) Γ(s) ln

(8)

Site-Oriented Physical Adsorption 1.9153 1.1888 2.7402 4.1136 0.9930 0.9824

1.1462 4.3283 0.9861

with Γ(s) now representing the derivative (slope) of the ASP plot within the limits of the monolayer formation over the limited range of Polyani potential,

Mobile Physical Adsorption 2.8053 3.1939 3.2090 1.8161 1.7612 1.7937 0.9994 0.9995 0.9906

3.3727 1.7739 0.9832

E 3 E** g g RT RT 2

a The removal of water chemically bound to the surface exposes reactive sites.

periodic force field surface potentials become more pronounced when freed of the shielding water. The argon still has liquidlike molecular character but has lost some of its translational freedom in this initial monolayer coverage. (II) This component in turn shields the dehydrated sites much as the bound hydroxy/hydrate water (think “ice”) did before outgassing. Think of this as a state akin to solid argon immobilized to much lesser degree than the solid, icelike water entities that are removed progressively at more stringent heat treatment. (III) Additional argon adsorption, on this base of strongly associated argon, is well-defined with ASP parameters much akin to the equilibrated multilayers on the fully hydrated surface. The slightly increased slope, Γ(m), for

(9)

and in terms of surface coverage,

0 e Γ e4.3 Å

(10)

with E** equal to the threshold potential for argon physisorption on the oxide surface dehydrated to the extent related to the outgassing temperature:

E** ) f(Toutgas)

(11)

Bound Water. Surface Hydration/Hydroxylation. The bound water interacts with the thorium oxide surface much more strongly and can be defined in terms of an ASP relation:

E′ { (RT ) - ln(RTE )}

Γ(H2O) ) Γ(m,H2O) ln

(12)

where the change in chemical potential is related to the

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Fuller

Figure 3. Vacuum activation relation for argon adsorption on the degassed thorium oxide surface. Filled circles for the first stage (E**/RT) and open squares for extrapolation from the multilayer regime (E*/RT) of ASP sorption isotherm plots of Figure 2 [intercept ) 5.2499, slope ) -0.9864, r2 ) 0.9823].

temperature, T, of the sample at constant pressure (10-6 Torr in this instance). The interaction energy is a combined effect of a given sorbate/sorbent pair.27-29 For the present sorbent, thorium oxide, the threshold potentials for the two sorbates (argon and water, respectively) will be proportional:

E** E*(H2O) ∝ RT RT

(13)

where E*(H2O) is the threshold potential for water sorption on nonporous thorium oxide surfaces. This postulate could be proven with a few microgravimetric experiments, but this current work involves reported values in the literature. An indirect approach can be used. Assuming that the removal of material (dehydration) by degassing is a thermodynamic activated process and that the surface chemical potential is exponentially proportional to the loss of bound species, we present Figure 3 for a graphical overview. This assumption is supported by replotting the data of Figure 1 of ref 26 in the equivalent rectilinear coordinates (see Figure 4). The parameters of these mathematical relations are given in Table 2. Although the two sets of data are for different ranges and values (27) Fuller, L. E., Jr. Physical And Chemical Structures Of Coals: Sorption Analyses. In Coal Structure; Gorbaty, M. L., Ouchi, M., Eds.; Advances in Chemistry Series, Vol. 192; American Chemical Society: Washington, DC, 1981; pp 293-310. (28) Fuller, E. L., Jr.; Holmes, H. F.; Secoy, C. H. Gravimetric Adsorption Studies of Thorium Oxide. II. Water Adsorption at 25.00 °C. J. Phys. Chem. 1966, 70, 1633-1636. (29) Philippi, P. C.; Yunes, P. R.; Fernandes, C. P.; Magnani, F. S. The Microstructure of Porous Building Materials: Study of a Cement and Lime Mortar. Transp. Porous Media 1994, 14 (3), 219-245.

Figure 4. Vacuum activation of the thorium oxide surface at 25-500 °C and 10-6 Torr. Data are the same as Figure 1 of ref 26. Intercept ) 692.9873 µg (water)/m2 (ThO2), slope ) -226.95 µg (water)/m2 (ThO2), r2 ) 0.9949. Table 2. Correlation of Water Loss for the Vacuum Activation of Thorium Oxide Surfaces

intercept slope correlation coefficient

surface potentials

mass loss (water)

5.2499 deg-1 -0.9864 deg-1 0.9823

692.9 [µg/m2]deg-1 -226.9 [µg/m2]deg-1 0.9949

ratio 131.98 [µg/m2] 230.0 [µg/m2]

of temperature, one can assume that when two quantities are proportional to a third (reciprocal temperature), they will be proportional to each other as calculated in column 4 of Table 2. QED. These results indicate that removal of the water species does not increase the surface area per se, but enhanced sorption is noted at low coverage due solely to the enhanced sorption potential. Subsequent multilayer formation is the same for hydrated and dehydrated surfaces. Conclusions Argon physical adsorption data on nonporous thorium oxide surfaces have been reanalyzed in terms of the ASP theory and found to be separated into two categories: (1) Freely mobile, completely free to move unhindered across the surface and/or into the gas phase. A singular functional relation to the Polyani sorption potential exists from a vacuum, through monolayer, and on through multilayer formation. This mode is noted on fully hydrated/ hydroxylated surfaces prepared by vacuum treatment at ambient temperature. Monolayer evaluation is direct from the single mode isotherm. (2) Restricted, with varying degrees of immobilization, depending on the amount of shielding water species that

Measuring Surface Area and Porosity via Adsorption

is removed by vacuum treatment at higher temperatures. Freely mobile multilayers are formed much akin to those on the hydrated surfaces. Monolayer evaluation is noted as the limited sorption discontinuity where the multilayer trend is noted as in category 1. The physisorbed argon serves as an excellent probe for evaluation of the energetics of irreversibly sorbed water that exists as surface hydroxyl groups which, in turn, are

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hydrated epitaxially to the crystalline thorium oxide substrate. The ASP methodology is quite informative in analyzing details of the processes and provides the relevant energetics and surface areas of interest to commercial and academic applications requiring detailed understanding of the sorption processes. LA034062P