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High-temperature physical adsorption of argon, krypton, and xenon on hexagonal boron nitride
High-Temperature Physical Adsorption of Argon, Krypton, and Xenon on Hexagonal Boron Nitride ALVIN C. L E V Y / T H O M A S R. RYBOLT, AND ROBERT A. PIEROTTI School o f Chemistry, Georgia Institute o f Technology, Atlanta, Georgia 30332 Received July 12, 1978; accepted August 31, 1978 The interaction of argon, krypton, and xenon with hexagonal boron nitride was examined utilizing a two-surface gas-solid virial analysis. A precision volumetric apparatus was used to obtain l0 adsorption isotherms in the temperature range 273-368°K. The low coverage, Henry's law isotherm data were used to obtain values for the second gas-solid virial coefficients for A r - B N , K r - B N , and X e - B N . The boron nitride adsorbent consists of higher energy edge sites and basal plane sites. A two-surface virial coefficient treatment was coupled with a graphical fitting technique to separate the effects of the two surface sites. Values of the inert gas-edge and inert gas-basal plane interaction energy are reported for each of the three adsorbates. Also, the surface area for the two surfaces and fraction of edge sites are reported. The results are compared with previous studies for these systems. INTRODUCTION
solid virial coefficient, B2s, could be separated into basal plane and edge virial coefficients given by
Prior physical adsorption studies (1, 2) have shown that hexagonal boron nitride consists of basal plane and edge surfaces and that the interaction of an adatom with each type of surface must be considered. These BN platelets provide an adsorbent for which the virial coefficient treatment of physical adsorption may be applied to a model, heterogeneous surface. In earlier work with the same hexagonal boron nitride adsorbent a lack of sufficient data in the lowcoverage, Henry's law, region prevented a direct two-surface virial separation treatment. To circumvent this limitation, a twosurface approach was developed in which the interaction between the higher energy edge sites and adsorbate was fitted to various submonolayer model isotherms, while adsorption on the basal plane sites was assumed to follow Henry's law (2). By attributing isotherm curvature to high coverage on the edges, the experimental second gas-
B2s = B2b~+ B~s.
[1]
New, high-temperature, isotherm data for the interaction of argon, krypton, and xenon with boron nitride in the Henry's law region allow for a direct two-surface gassolid virial analysis. EXPE~MENTAL
1 Currently at Bell Research Laboratory, Atlanta, Georgia; address all correspondence to Professor R. A. Pierotti.
A high-precision volumetric apparatus (1) was used to measure the adsorption of argon, krypton, and xenon on hexagonal boron nitride. A total of l0 isotherms were obtained in the temperature range 273368°K at surface coverages less than 1% of the BET monolayer volume. The adsorption isotherms are shown in Figs. 1-3 and the data are given in Table I. The experimental points are encircled for clarity, but the circles are not intended to reflect experimental uncertainty which is less than the width of the line. The uncertainty in deter-
74 0021-9797/79/070074-0952.00/0 Copyright© 1979by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Journal of Colloidand Interlace Science, Vol.70. No. 1, June 1, 1979
RARE GAS, BORON NITRIDE ADSORPTION
I 1. 2. 3.
3.5
t
I
t
I
75
[
j
273.150°K 295.284°K 310.027°K
3.0
tn to
2.5
%
2.0
z ~
.-..a
1.5
1.0
0.5
10
20
30
40
PRESSURE
I
1
S0
60
(kN/m 2)
FIG. 1. Adsorption isotherms for argon on hexagonal boron nitride. mining the number of moles of gas adsorbed was about _+1.3 × 10-9 mole g-1 (3). A description of the apparatus and mode of operation has been given previously (1-4). The powdered boron nitride sample has been shown to consist of conglomerates of smaller particles with sizes in the range o f 10-15 #m. E l e c t r o n micrographs showed that these particles are flat crystals with edges about 0.4 /zm thick. The geometric area of the boron nitride was estimated to be approximately 2.4 m 2 g-~ with edges making up about 5-10% of the total area (2). The argon BET surface area was found to be 4.98 m 2 g-~ using an area of 0.141 nm 2 for the adatom (1). This yields a roughness factor of about 2 and indicates that the sample is nonporous as expected. In the Henry's law region, the slope of the adsorption isotherm equals B2s/RT as the
pressure approaches zero. The experimental BRs values were found by fitting the isotherm data to equations such as na = a l P 1 + azP 2 + a3P 3 where al = BRs/RT. The number of terms used in this fitting procedure was dictated by the experimental uncertainty of the measurements. Table II shows the second gas-solid virial coefficients which were obtained using this curve fitting approach. Estimates of the uncertainty in experimental B2s values are 1.27% A r - B N , 0.53% K r - B N , and 0.26% X e BN (3). SINGLE-SURFACE ANALYSIS In the virial coefficient treatment of physical adsorption (5-7), the number of moles of gas adsorbed per gram of adsorbent, na, is given by (8)
Journal of Colloid and lnterJace Science, Vol. 70, No. 1, June 1, 1979
76
na = B2s
LEVY, RYBOLT, AND PIEROTTI
The analysis presented in this paper considers only the treatment of B2s values. The relation between the second gassolid virial coefficient and the gas-solid interaction potential, uls, is given by (9)
+ B3s
+ B4~
+
""
,
[21
wherefis the fugacity, R is the gas constant, T is the temperature. The second gas-solid virial coefficient, B2~, depends on the interaction of a single atom with the surface, while B3~ involves a pair of adatoms interacting with the surface, B4s a triplet, and so on. In the low coverage, Henry's law region of adsorption, adsorbate-adsorbate interaction is negligible. At higher coverages deviations from Henry's law are produced by third and higher order effects.
I
I
B2s = f [exp(-UlJkT) - l]dV [3] JV where d V is a volume element in the gas phase. If the solid surface is uniform then Eq. [3] may be rewritten as
B2~ = A Iz [exp(-Uls(z)/kT) - 1]dz
where z is an axis normal to the surface and A is the surface area. If a Lennard-
I
]
.,~
I
1. 2. 3.
273.150°K 296.215°K 333.460°K
I
% x z ~
10
20
30 PRESSURE
40
50
60
(kN/m 2)
Fie. 2. Adsorption isothermsfor krypton on hexagonal boron nitride.
Journal of Colloid and Interface Science, Vol. 70, No. 1, June 1, 1979
[4]
77
RARE GAS, BORON NITRIDE ADSORPTION
I
I
I
I 1. 2. 3. 4.
273.150°K 337.412°K 358.954°K 368.034°K
6
o
5
%
r-4 4
z
I
1
I
i0 IS 20 PRESSURE (kN/m 2)
I
25
I
30
FIG. 3. Adsorption isotherms for xenon on hexagonal boron nitride. Jones (m,n) potential is assumed between the adatom and solid adsorbent, then the integral in Eq. [4] can be evaluated to give (6) [/
71
\/ n \m/(n-m)
7=o
\-~-~--]j
F{(~'m - 1)/n}
[5]
where zo is the distance of closest approach (finite distance where u l s - - 0 ) , e*~ is the minimum in the interaction energy curve, and F{(Tm - 1)/n} is a gamma function. A single-surface virial analysis assumes that the surface is homogeneous. This approach involves finding the value of the g a s -
solid interaction energy, ¢*s, which gives the minimum standard deviation of the logarithm o f the surface capacity factor, cr In Azo (6). This fitting technique utilizes the functional dependence of B2s on temperature to find values of ¢*s/k and Azo for each gas-solid system. Determination of the surface area, A, from a value o f the surface capacity factor requires an estimate for the distance of closest approach, z0. It is c o m m o n to assume that Zo is the arithmetic mean of the gas hard sphere diameter, or,, and the effective hard sphere diameter of an atom in the surface plane, o-S (10). If z0 can be determined for one g a s - s o l i d system, then 0%can be computed and thus the value of z0 may Journal of Colloid and Interface Science, Vol. 70, No. I, June 1~ 1979
78
L E V Y , RYBOLT, A N D P I E R O T T I
be estimated for any other system utilizing the same adsorbent. A value of z0 for the a r g o n - b o r o n nitride system was calculated from Crowell and Chang's estimate (11) of the equilibrium separation as z* = 0.339 nm. The values used for the gas hard sphere diameters were Ar (0.341 nm), Kr (0.368 nm), and Xe (0.410 nm) (12). From the z0 and O-g data for TABLE I
T A B L E II B e s t Fit V a l u e s o f B2s f o r A d s o r p t i o n o f A r , Kr, and Xe on Hexagonal Boron Nitride
Temperature (°K)
Single surface B2s x 10z (cma/g)
Ar
273,150 295.284 310.027
Kr
Xe
Adsorbate
I s o t h e r m D a t a for t h e A d s o r p t i o n o f Inert G a s e s on Hexagonal Boron Nitride Argon-BN
P (kN/mz)
na x 10r
(mole/g)
Krypton-BN P
(kN/mz)
na × 10r
(mole/g)
Xenon-BN P
(kN/mz)
na × 107 (mole/g)
T = 273.150°K
T = 273.150°K
T = 273.150°K
27.2062 41.6675 50.6840 23.1878 35.5179 53.6237 9.9433 15.0120 41.2269
24.8386 37.7850 45.7733 14.4919 26.2177 39.8865 3.5020 6.2234
2.4919 3.6556 5.2272 6.7680 4.5384 6.6962 9.6009 12.4740
1.810 2.733 3.328 1.578 2.358 3.526 0.680 1.014 2.682
4.860 7.261 8.734 2.919 5.073 7.582 0.723 1.277
2.615 3.710 5.037 6.303 4.464 6.216 8.537 10.728
T = 295.284°K
T = 296.215°K
T = 337.412°K
18.1648 23.4244 28.0954 34.3906 43.0614
14.4099 21.0635 26.2800 36.2902
8.3420 20,0292 28.0869
0.832 1.088 1.317 1.618 1.975
1.805 2.631 3.258 4.472
1.763 4.147 5,795
T = 310.027°K
T = 333.460°K
T = 358.954°K
18.3577 28.5728 44.1841 62.0465
17.7823 27.8402 43.4571 61.6912
12.5155 14.2530 16.2735 19.6580 24.2888 30.8168
0.718 1.074 1.666 2.531
1.221 1.892 2.933 4.178
1.859 2.059 2.353 2.836 3.529 4.456
T = 368.034°K 8.5480 13.4720 21.2424 30.5167
1.090 1.700 2.685 3.880
Journal of Colloid and Interface Science, Vol. 70, No. I, June 1, 1979
Two surface B~s x 102
B~s × 102
(cm3/g)
(cm3/g)
1.541 1.139 0.9754
1.168 0.908 0.781
0.368 0.214 0.188
273.150 296.215 333.460
4.820 3.138 1.889
2.946 2.131 1.387
1.847 1.041 0.493
273.150 337.412 358.954 368.034
25.70 6.081 4.363 3.868
9.70 3.531 2.735 2.478
16.00 2.581 1.632 1.368
a r g o n - b o r o n nitride, o-s was found to be 0.224 nm. The calculated values of z0 were A r - B N 0.283 nm, K r - B N 0.296 nm, and X e - B N 0.317 nm. The results of a single-surface virial analysis based on a Lennard-Jones (3, 9) potential are shown in Table III. The values of the surface area are quite low relative to the 4.98 m 2 g-1 BET area and vary as the adsorbate is changed. In addition, a rather poor fit of the data is obtained as measured by tr In Azo. Both properties are accentuated as the adsorbate becomes more polarizable. These properties are indicative of the surface heterogeneity of hexagonal boron nitride which was demonstrated in previous work (1, 2). TWO-SURFACE ANALYSIS
The two-surface approach used, previously for the a r g o n - b o r o n nitride system (2) attributed isotherm curvature to the effect of edge interaction. The experimental B2s values were divided into Bb2s and B$~ for the basal plane and edge interactions, respectively. Each of the two sets of data were then treated in the conventional manner to obtain e*s/k, Azo, and o- In Azo for each sur-
RARE GAS, BORON NITRIDE ADSORPTION TABLE III Best Fit Parameters for the Adsorption of Xe, Kr, and Ar on Hexagonal BN from B2~ Data Xe
Single surface ~*~/k (K) Azo × 104 (cm~/g) In Azo A (m2/g) Two surface e~*b/k (K) els*~/k (K) Azo × 104 (cm~/g) tr In Azo A (mZ/g) Percent edge
Kr
Ar
2232
1610
1211
3.14 0.0162 0.99
4.58 0.0138 1.55
5.29 0.0083 1.87
1650 ± 15 2810
1305 ± 20 2200
1038 ± 8 1735
8.443 0.0045 2.66
7.770 0.0093 2.63
7.230 0.0077 2.56
3.25
3.25
3.25
Average values from two-surface fit A = 2.62 ± 0.05 m2/g E2s*°/els*b = 1.687 _+ 0.016
face. The data presented in this paper were obtained at coverages and temperatures for which the interaction of the adsorbate with both the basal plane and edge sites was in the H e n r y ' s law region. Thus, a direct twosurface virial analysis can be used to find ~*s/k, Az0, and o- In Azo for each surface. A two-surface virial analysis involves combining [1] and [4] to obtain B2~ = Az0[(1 -
x)S(El~*b/kT) + (x)S(Els*e/kT)]
[61
where x i s t h e fraction of the surface consisting of edge sites and S is the summation given by Eq. [5]. The evaluation of the summation depends on the selection of the g a s solid interaction potential which for the present analysis is chosen to be a LennardJones (3, 9) potential. The summation S is a function of temperature and basal plane or edge g a s - s o l i d interaction parameter exs*b or eis*% respectively. Because of the additional parameters in-
79
volved in a two-surface analysis there are several choices of els*b/k, E l s * e / k , X, and Azo which may produce the same quality of fit for a given system based on o-lnAz0. If x, A, and el~*e/els*b are required to be the same for all three systems, then a unique set of parameters may be obtained. The first two restrictions require only that the nature of the surface is not altered by the type of adsorbate. The third restriction that els*°/¢~s*b be a constant for Ar, Kr, and Xe follows from the convention that the potential interaction energy for two different molecules at equilibrium separation is the geometric mean of their interactions with like molecules. If this assumption is made for g a s - s o l i d interactions, then the ratio o f the g a s - s o l i d interaction energy for different sites on the adsorbent does not depend on the nature of adsorbate. A graphical fitting technique is e m p l o y e d to find the intermolecular interaction energies, the apparent surface area, and the fraction of edge sites. The procedure requires generating a set of e~*e/k and e~s*b/k values for a selected value of x. F o r a given value of x several values of eis*b/k are chosen. For each value of ¢ls*b/k the optimum value of ei~*~/k is found using Eq. [6] and minimizing with respect to (r In Azo. Values of Ei~*~/~ts*b and A are generated for each selection of ¢~*b/k. This process is carried out independently for each g a s - B N system. Plots of eas*e/els*b versus A are made for each of the three adsorbates on the same set of coordinates for a given choice of x. If the proper choice o f x is made then a plot of els*~/e~ *b versus A should result in the intersection of the lines for Ar, Kr, and Xe. In this manner unique values of x, A, and ~s*e/~s *b are selected. Plots of els*e/Exs*b versus A were made for trials of x taken at 0.0025 increments. The triangle formed by the three lines served as a measure of goodness of fit. On this basis the choice of x = 0.0325 gave
Journal of Colloid and Interface Science, Vol. 70, No. 1, June 1, 1979
80
LEVY, RYBOLT, AND PIEROTTI
I
I
I
1.80
Ar Kr
1.75
to
- . 1.70 -
1.65
2.00
I
I
I
2.25
2.50
2.75
3.00
AREA ( m 2 / g )
FIo. 4. Plot of Els*e/~Is *b v e r s u s area for Ar, Kr, and Xe adsorbed on BN containing 3.25% edge sites.
the best fit of the data and enabled a selection of unique values for Els*e/Els •b and A. As shown in Fig. 4, the plot at x = 0.0325 results in the intersection of three lines near a point. Since each g a s - B N curve is intersected twice, two values of El~*b/k, El~*e/k, and A are generated for each system. The average values of e~*b/k are given for each system in Table III. The values of els*e/k and A reported are obtained by minimizing o-In Azo using the previously determined els*b/k. Bbs and B~ are calculated from the results of the two-surface virial analysis and are given in Table II. The advantage of a two-surface analysis over a single-surface analysis for the interaction of rare gases with hexagonal boron nitride is clearly demonstrated from the results shown in Table III. A two-surface virial coefficient treatment gives a better fit of the data, as judged by the ~r ln Az0, than a single-surface treatment. Also, the two-surface approach leads to a BN surface area Journal of Colloid and Inter/ace Science, Vol. 70, No. 1, June 1, 1979
which remains consistent as the absorbate is varied. In an earlier study of the physical adsorption of argon on boron nitride by Thomas, Ramsey, and Pierotti, six isotherms were measured in the temperature range 198275°K. The argon B2s-temperature data of this paper, that of Thomas et al. and a combination of the two were each fit to Eq. [5] using a Lennard-Jones (3, 9) potential as shown in Table IV. The best fit value of e*Jk to 0.1K was found by minimizing with respect to o- logAz0. The minimum value of TABLE IV Argon-Boron Nitride Single-Surface Virial Analysis
Source
B2s data
Temperature range (°K)
A (m2 g-J)
(7 log Az,
(~d'k (K)
This work Ref. (2) Combined
3 6 9
273-310 198-273 198-310
1.87 1.86 1.87
0.0036 0.0032 0.0031
1211.5 1210.6 1212.2
81
RARE GAS, BORON NITRIDE ADSORPTION
tr log Azo was obtained when the two sets of data were combined. Clearly, these previous experimental data are consistent with the A r - B N data of the current work. Thomas, Ramsey, and Pierotti also used a two-surface approach, but the curvature in the isotherm data at low coverage necessitated a more drastic assumption in order to separate the gas-solid virial coefficients. They fit the interaction between the argon and BN edge sites to Langmuir, Volmer, and van der Waals adsorption models while the argon and BN basal plane interaction was assumed to follow Henry's law. The van der Waals model did not give satisfactory results but they were unable to select between the Langmuir and Volmer models. A comparison of the B~s and B~s values obtained by these two models may be made to the separation treatment used in this paper. A combination of the direct virial separation B~s values of this paper with those from the Langmuir and Volmer models were fit to Eq. [5] and gave tr log Azo of 0.0374 and 0.0337, respectively. Thus, the Volmer model for argon-edge interaction is more consistent with the direct two-surface virial separation treatment, which is perhaps indicative of nonlocalized adsorption on the edges. The values of Els*b/k for the three gassolid systems are compared with previous estimates in Table V. The gas-solid interaction energies for argon and krypton are in general agreement with selected calculated estimates. However, the X e - B N interaction value of this paper is somewhat lower than Crowell's estimate. The E~s*b/k values for all three g a s - B N systems are consistently lower than the estimates of Thomas
et al. Sams, Constabaris, and Halsey used a virial coefficient approach to treat the inert gas-graphite system. For a LennardJones (3, 9) potential they found the interaction energy of the carbon black P33 (2700 °) with Ar as l107K, Kr as 1460K, and Xe
TABLE V Comparison of Calculated and Experimental Values of e*s/k (K) for the Interaction of Inert Gases with the Basal Plane of BN Adsorbate
Present" work
Ref. (2)"
Ref. (11)~
Ref. (13)b
Ref. (14)~
Ar Kr Xe
1038 1305 1650
1083 1414 1847
1123 1312 1783
1047 1409
1007
a Experimental. b Calculated.
as 1919K (6). The ratio of their graphite interaction energy to our boron nitride basal plane interaction energy for argon, krypton, and xenon is 1.07, 1.12, and 1.16, respectively. Clearly graphite interacts about 10% more strongly than boron nitride with the rare gases but whether the trend of the increasing ratios with polarizability and size of the adatom is significant requires more detailed experiments and theory. CONCLUSION
New data for the inert gases adsorbed on boron nitride corresponding experimentally to the Henry's law region have been obtained and analyzed using the virial approach to physical adsorption. These new measurements are such that no assumptions other than requiring that consistent areas and interaction energies exist for each of the g a s - B N systems are necessary in order to make the analysis. Specifically, no model isotherm equation has been introduced into the analysis. The results obtained verify the general utility of the model dependent technique used in earlier work and utilized by other investigators. Although the two techniques are quite different, the results are in general agreement. Boron nitride is indeed a good model system for studies of heterogeneity in physical adsorption. The results obtained here using physical adsorption techniques are consistent with electron micrographs of the solid. A useful extenJournal of Colloid and lnterJace Science, Vol. 70, No. l, June 1, 1979
82
LEVY, RYBOLT, AND PIEROTTI
tion in m o d e l h e t e r o g e n e i t y s t u d i e s w o u l d involve mixtures of boron nitride and graphite yielding a three-surface variable composition system capable of both experimental and theoretical investigations. REFERENCES 1. Ramsey, R. N., Thomas, H. E., and Pierotti, R. A., J. Phys. Chem. 76, 3171 (1972). 2. Thomas, H. E., Ramsey, R. N., and Pierotti, R. A., J. Chem. Phys. 59, 6163 (1973). 3. Levy, A. C., Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1976. 4. Ramsey, R. N., Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1970. 5. Steele, W. A., and Halsey, G. D., Jr., J. Chem. Phys. 22, 979 (1954). 6. Sams, J. R., Constabaris, G., and Halsey, G. D., Jr., J. Chem. Phys. 64, 1689 (1960).
Journal ojColloid and InterJace Science, Vol. 70, No. I, June 1, 1979
7. Sams, J. R., Constabaris, G., and Halsey, G. D., Jr., J. Chem. Phys. 36, 1334 (1962). 8. Pierotti, R. A., and Thomas, H. E., in "Surface and Colloid Science" (E. Matijevi6, Ed.), Vol. 4, p. 165. Wiley (Interscience), New York, 1971. 9. Steele, W. A., in "The Solid-Gas Interface" (E. Alison Flood, Ed.), Vol. l, p. 316. Marcel Dekker, New York, 1967. I0. Young, D. M., and Crowell, A. D., "Physical Adsorption of Gases," p. 23. Butterworth, London, 1962. 11. Crowell, A. D., and Chang, C. 0., J. Chem. Phys. 43, 4364 (1965). 12. Hirschfelder, J. O., Curtis, C. F., and Bird, R. B., in "Molecular Theory of Gases and Liquids," p. 110. Wiley, New York, 1954. 13. Curthoys, G., and Elkington, P. A., J. Phys. Chem. 71, 1477 (1967). 14. Pierotti, R. A., and Petricciani, J. C., J. Phys. Chem. 64, 1596 (1960).
solid virial coefficient, B2s, could be separated into basal plane and edge virial coefficients given by
Prior physical adsorption studies (1, 2) have shown that hexagonal boron nitride consists of basal plane and edge surfaces and that the interaction of an adatom with each type of surface must be considered. These BN platelets provide an adsorbent for which the virial coefficient treatment of physical adsorption may be applied to a model, heterogeneous surface. In earlier work with the same hexagonal boron nitride adsorbent a lack of sufficient data in the lowcoverage, Henry's law, region prevented a direct two-surface virial separation treatment. To circumvent this limitation, a twosurface approach was developed in which the interaction between the higher energy edge sites and adsorbate was fitted to various submonolayer model isotherms, while adsorption on the basal plane sites was assumed to follow Henry's law (2). By attributing isotherm curvature to high coverage on the edges, the experimental second gas-
B2s = B2b~+ B~s.
[1]
New, high-temperature, isotherm data for the interaction of argon, krypton, and xenon with boron nitride in the Henry's law region allow for a direct two-surface gassolid virial analysis. EXPE~MENTAL
1 Currently at Bell Research Laboratory, Atlanta, Georgia; address all correspondence to Professor R. A. Pierotti.
A high-precision volumetric apparatus (1) was used to measure the adsorption of argon, krypton, and xenon on hexagonal boron nitride. A total of l0 isotherms were obtained in the temperature range 273368°K at surface coverages less than 1% of the BET monolayer volume. The adsorption isotherms are shown in Figs. 1-3 and the data are given in Table I. The experimental points are encircled for clarity, but the circles are not intended to reflect experimental uncertainty which is less than the width of the line. The uncertainty in deter-
74 0021-9797/79/070074-0952.00/0 Copyright© 1979by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Journal of Colloidand Interlace Science, Vol.70. No. 1, June 1, 1979
RARE GAS, BORON NITRIDE ADSORPTION
I 1. 2. 3.
3.5
t
I
t
I
75
[
j
273.150°K 295.284°K 310.027°K
3.0
tn to
2.5
%
2.0
z ~
.-..a
1.5
1.0
0.5
10
20
30
40
PRESSURE
I
1
S0
60
(kN/m 2)
FIG. 1. Adsorption isotherms for argon on hexagonal boron nitride. mining the number of moles of gas adsorbed was about _+1.3 × 10-9 mole g-1 (3). A description of the apparatus and mode of operation has been given previously (1-4). The powdered boron nitride sample has been shown to consist of conglomerates of smaller particles with sizes in the range o f 10-15 #m. E l e c t r o n micrographs showed that these particles are flat crystals with edges about 0.4 /zm thick. The geometric area of the boron nitride was estimated to be approximately 2.4 m 2 g-~ with edges making up about 5-10% of the total area (2). The argon BET surface area was found to be 4.98 m 2 g-~ using an area of 0.141 nm 2 for the adatom (1). This yields a roughness factor of about 2 and indicates that the sample is nonporous as expected. In the Henry's law region, the slope of the adsorption isotherm equals B2s/RT as the
pressure approaches zero. The experimental BRs values were found by fitting the isotherm data to equations such as na = a l P 1 + azP 2 + a3P 3 where al = BRs/RT. The number of terms used in this fitting procedure was dictated by the experimental uncertainty of the measurements. Table II shows the second gas-solid virial coefficients which were obtained using this curve fitting approach. Estimates of the uncertainty in experimental B2s values are 1.27% A r - B N , 0.53% K r - B N , and 0.26% X e BN (3). SINGLE-SURFACE ANALYSIS In the virial coefficient treatment of physical adsorption (5-7), the number of moles of gas adsorbed per gram of adsorbent, na, is given by (8)
Journal of Colloid and lnterJace Science, Vol. 70, No. 1, June 1, 1979
76
na = B2s
LEVY, RYBOLT, AND PIEROTTI
The analysis presented in this paper considers only the treatment of B2s values. The relation between the second gassolid virial coefficient and the gas-solid interaction potential, uls, is given by (9)
+ B3s
+ B4~
+
""
,
[21
wherefis the fugacity, R is the gas constant, T is the temperature. The second gas-solid virial coefficient, B2~, depends on the interaction of a single atom with the surface, while B3~ involves a pair of adatoms interacting with the surface, B4s a triplet, and so on. In the low coverage, Henry's law region of adsorption, adsorbate-adsorbate interaction is negligible. At higher coverages deviations from Henry's law are produced by third and higher order effects.
I
I
B2s = f [exp(-UlJkT) - l]dV [3] JV where d V is a volume element in the gas phase. If the solid surface is uniform then Eq. [3] may be rewritten as
B2~ = A Iz [exp(-Uls(z)/kT) - 1]dz
where z is an axis normal to the surface and A is the surface area. If a Lennard-
I
]
.,~
I
1. 2. 3.
273.150°K 296.215°K 333.460°K
I
% x z ~
10
20
30 PRESSURE
40
50
60
(kN/m 2)
Fie. 2. Adsorption isothermsfor krypton on hexagonal boron nitride.
Journal of Colloid and Interface Science, Vol. 70, No. 1, June 1, 1979
[4]
77
RARE GAS, BORON NITRIDE ADSORPTION
I
I
I
I 1. 2. 3. 4.
273.150°K 337.412°K 358.954°K 368.034°K
6
o
5
%
r-4 4
z
I
1
I
i0 IS 20 PRESSURE (kN/m 2)
I
25
I
30
FIG. 3. Adsorption isotherms for xenon on hexagonal boron nitride. Jones (m,n) potential is assumed between the adatom and solid adsorbent, then the integral in Eq. [4] can be evaluated to give (6) [/
71
\/ n \m/(n-m)
7=o
\-~-~--]j
F{(~'m - 1)/n}
[5]
where zo is the distance of closest approach (finite distance where u l s - - 0 ) , e*~ is the minimum in the interaction energy curve, and F{(Tm - 1)/n} is a gamma function. A single-surface virial analysis assumes that the surface is homogeneous. This approach involves finding the value of the g a s -
solid interaction energy, ¢*s, which gives the minimum standard deviation of the logarithm o f the surface capacity factor, cr In Azo (6). This fitting technique utilizes the functional dependence of B2s on temperature to find values of ¢*s/k and Azo for each gas-solid system. Determination of the surface area, A, from a value o f the surface capacity factor requires an estimate for the distance of closest approach, z0. It is c o m m o n to assume that Zo is the arithmetic mean of the gas hard sphere diameter, or,, and the effective hard sphere diameter of an atom in the surface plane, o-S (10). If z0 can be determined for one g a s - s o l i d system, then 0%can be computed and thus the value of z0 may Journal of Colloid and Interface Science, Vol. 70, No. I, June 1~ 1979
78
L E V Y , RYBOLT, A N D P I E R O T T I
be estimated for any other system utilizing the same adsorbent. A value of z0 for the a r g o n - b o r o n nitride system was calculated from Crowell and Chang's estimate (11) of the equilibrium separation as z* = 0.339 nm. The values used for the gas hard sphere diameters were Ar (0.341 nm), Kr (0.368 nm), and Xe (0.410 nm) (12). From the z0 and O-g data for TABLE I
T A B L E II B e s t Fit V a l u e s o f B2s f o r A d s o r p t i o n o f A r , Kr, and Xe on Hexagonal Boron Nitride
Temperature (°K)
Single surface B2s x 10z (cma/g)
Ar
273,150 295.284 310.027
Kr
Xe
Adsorbate
I s o t h e r m D a t a for t h e A d s o r p t i o n o f Inert G a s e s on Hexagonal Boron Nitride Argon-BN
P (kN/mz)
na x 10r
(mole/g)
Krypton-BN P
(kN/mz)
na × 10r
(mole/g)
Xenon-BN P
(kN/mz)
na × 107 (mole/g)
T = 273.150°K
T = 273.150°K
T = 273.150°K
27.2062 41.6675 50.6840 23.1878 35.5179 53.6237 9.9433 15.0120 41.2269
24.8386 37.7850 45.7733 14.4919 26.2177 39.8865 3.5020 6.2234
2.4919 3.6556 5.2272 6.7680 4.5384 6.6962 9.6009 12.4740
1.810 2.733 3.328 1.578 2.358 3.526 0.680 1.014 2.682
4.860 7.261 8.734 2.919 5.073 7.582 0.723 1.277
2.615 3.710 5.037 6.303 4.464 6.216 8.537 10.728
T = 295.284°K
T = 296.215°K
T = 337.412°K
18.1648 23.4244 28.0954 34.3906 43.0614
14.4099 21.0635 26.2800 36.2902
8.3420 20,0292 28.0869
0.832 1.088 1.317 1.618 1.975
1.805 2.631 3.258 4.472
1.763 4.147 5,795
T = 310.027°K
T = 333.460°K
T = 358.954°K
18.3577 28.5728 44.1841 62.0465
17.7823 27.8402 43.4571 61.6912
12.5155 14.2530 16.2735 19.6580 24.2888 30.8168
0.718 1.074 1.666 2.531
1.221 1.892 2.933 4.178
1.859 2.059 2.353 2.836 3.529 4.456
T = 368.034°K 8.5480 13.4720 21.2424 30.5167
1.090 1.700 2.685 3.880
Journal of Colloid and Interface Science, Vol. 70, No. I, June 1, 1979
Two surface B~s x 102
B~s × 102
(cm3/g)
(cm3/g)
1.541 1.139 0.9754
1.168 0.908 0.781
0.368 0.214 0.188
273.150 296.215 333.460
4.820 3.138 1.889
2.946 2.131 1.387
1.847 1.041 0.493
273.150 337.412 358.954 368.034
25.70 6.081 4.363 3.868
9.70 3.531 2.735 2.478
16.00 2.581 1.632 1.368
a r g o n - b o r o n nitride, o-s was found to be 0.224 nm. The calculated values of z0 were A r - B N 0.283 nm, K r - B N 0.296 nm, and X e - B N 0.317 nm. The results of a single-surface virial analysis based on a Lennard-Jones (3, 9) potential are shown in Table III. The values of the surface area are quite low relative to the 4.98 m 2 g-1 BET area and vary as the adsorbate is changed. In addition, a rather poor fit of the data is obtained as measured by tr In Azo. Both properties are accentuated as the adsorbate becomes more polarizable. These properties are indicative of the surface heterogeneity of hexagonal boron nitride which was demonstrated in previous work (1, 2). TWO-SURFACE ANALYSIS
The two-surface approach used, previously for the a r g o n - b o r o n nitride system (2) attributed isotherm curvature to the effect of edge interaction. The experimental B2s values were divided into Bb2s and B$~ for the basal plane and edge interactions, respectively. Each of the two sets of data were then treated in the conventional manner to obtain e*s/k, Azo, and o- In Azo for each sur-
RARE GAS, BORON NITRIDE ADSORPTION TABLE III Best Fit Parameters for the Adsorption of Xe, Kr, and Ar on Hexagonal BN from B2~ Data Xe
Single surface ~*~/k (K) Azo × 104 (cm~/g) In Azo A (m2/g) Two surface e~*b/k (K) els*~/k (K) Azo × 104 (cm~/g) tr In Azo A (mZ/g) Percent edge
Kr
Ar
2232
1610
1211
3.14 0.0162 0.99
4.58 0.0138 1.55
5.29 0.0083 1.87
1650 ± 15 2810
1305 ± 20 2200
1038 ± 8 1735
8.443 0.0045 2.66
7.770 0.0093 2.63
7.230 0.0077 2.56
3.25
3.25
3.25
Average values from two-surface fit A = 2.62 ± 0.05 m2/g E2s*°/els*b = 1.687 _+ 0.016
face. The data presented in this paper were obtained at coverages and temperatures for which the interaction of the adsorbate with both the basal plane and edge sites was in the H e n r y ' s law region. Thus, a direct twosurface virial analysis can be used to find ~*s/k, Az0, and o- In Azo for each surface. A two-surface virial analysis involves combining [1] and [4] to obtain B2~ = Az0[(1 -
x)S(El~*b/kT) + (x)S(Els*e/kT)]
[61
where x i s t h e fraction of the surface consisting of edge sites and S is the summation given by Eq. [5]. The evaluation of the summation depends on the selection of the g a s solid interaction potential which for the present analysis is chosen to be a LennardJones (3, 9) potential. The summation S is a function of temperature and basal plane or edge g a s - s o l i d interaction parameter exs*b or eis*% respectively. Because of the additional parameters in-
79
volved in a two-surface analysis there are several choices of els*b/k, E l s * e / k , X, and Azo which may produce the same quality of fit for a given system based on o-lnAz0. If x, A, and el~*e/els*b are required to be the same for all three systems, then a unique set of parameters may be obtained. The first two restrictions require only that the nature of the surface is not altered by the type of adsorbate. The third restriction that els*°/¢~s*b be a constant for Ar, Kr, and Xe follows from the convention that the potential interaction energy for two different molecules at equilibrium separation is the geometric mean of their interactions with like molecules. If this assumption is made for g a s - s o l i d interactions, then the ratio o f the g a s - s o l i d interaction energy for different sites on the adsorbent does not depend on the nature of adsorbate. A graphical fitting technique is e m p l o y e d to find the intermolecular interaction energies, the apparent surface area, and the fraction of edge sites. The procedure requires generating a set of e~*e/k and e~s*b/k values for a selected value of x. F o r a given value of x several values of eis*b/k are chosen. For each value of ¢ls*b/k the optimum value of ei~*~/k is found using Eq. [6] and minimizing with respect to (r In Azo. Values of Ei~*~/~ts*b and A are generated for each selection of ¢~*b/k. This process is carried out independently for each g a s - B N system. Plots of eas*e/els*b versus A are made for each of the three adsorbates on the same set of coordinates for a given choice of x. If the proper choice o f x is made then a plot of els*~/e~ *b versus A should result in the intersection of the lines for Ar, Kr, and Xe. In this manner unique values of x, A, and ~s*e/~s *b are selected. Plots of els*e/Exs*b versus A were made for trials of x taken at 0.0025 increments. The triangle formed by the three lines served as a measure of goodness of fit. On this basis the choice of x = 0.0325 gave
Journal of Colloid and Interface Science, Vol. 70, No. 1, June 1, 1979
80
LEVY, RYBOLT, AND PIEROTTI
I
I
I
1.80
Ar Kr
1.75
to
- . 1.70 -
1.65
2.00
I
I
I
2.25
2.50
2.75
3.00
AREA ( m 2 / g )
FIo. 4. Plot of Els*e/~Is *b v e r s u s area for Ar, Kr, and Xe adsorbed on BN containing 3.25% edge sites.
the best fit of the data and enabled a selection of unique values for Els*e/Els •b and A. As shown in Fig. 4, the plot at x = 0.0325 results in the intersection of three lines near a point. Since each g a s - B N curve is intersected twice, two values of El~*b/k, El~*e/k, and A are generated for each system. The average values of e~*b/k are given for each system in Table III. The values of els*e/k and A reported are obtained by minimizing o-In Azo using the previously determined els*b/k. Bbs and B~ are calculated from the results of the two-surface virial analysis and are given in Table II. The advantage of a two-surface analysis over a single-surface analysis for the interaction of rare gases with hexagonal boron nitride is clearly demonstrated from the results shown in Table III. A two-surface virial coefficient treatment gives a better fit of the data, as judged by the ~r ln Az0, than a single-surface treatment. Also, the two-surface approach leads to a BN surface area Journal of Colloid and Inter/ace Science, Vol. 70, No. 1, June 1, 1979
which remains consistent as the absorbate is varied. In an earlier study of the physical adsorption of argon on boron nitride by Thomas, Ramsey, and Pierotti, six isotherms were measured in the temperature range 198275°K. The argon B2s-temperature data of this paper, that of Thomas et al. and a combination of the two were each fit to Eq. [5] using a Lennard-Jones (3, 9) potential as shown in Table IV. The best fit value of e*Jk to 0.1K was found by minimizing with respect to o- logAz0. The minimum value of TABLE IV Argon-Boron Nitride Single-Surface Virial Analysis
Source
B2s data
Temperature range (°K)
A (m2 g-J)
(7 log Az,
(~d'k (K)
This work Ref. (2) Combined
3 6 9
273-310 198-273 198-310
1.87 1.86 1.87
0.0036 0.0032 0.0031
1211.5 1210.6 1212.2
81
RARE GAS, BORON NITRIDE ADSORPTION
tr log Azo was obtained when the two sets of data were combined. Clearly, these previous experimental data are consistent with the A r - B N data of the current work. Thomas, Ramsey, and Pierotti also used a two-surface approach, but the curvature in the isotherm data at low coverage necessitated a more drastic assumption in order to separate the gas-solid virial coefficients. They fit the interaction between the argon and BN edge sites to Langmuir, Volmer, and van der Waals adsorption models while the argon and BN basal plane interaction was assumed to follow Henry's law. The van der Waals model did not give satisfactory results but they were unable to select between the Langmuir and Volmer models. A comparison of the B~s and B~s values obtained by these two models may be made to the separation treatment used in this paper. A combination of the direct virial separation B~s values of this paper with those from the Langmuir and Volmer models were fit to Eq. [5] and gave tr log Azo of 0.0374 and 0.0337, respectively. Thus, the Volmer model for argon-edge interaction is more consistent with the direct two-surface virial separation treatment, which is perhaps indicative of nonlocalized adsorption on the edges. The values of Els*b/k for the three gassolid systems are compared with previous estimates in Table V. The gas-solid interaction energies for argon and krypton are in general agreement with selected calculated estimates. However, the X e - B N interaction value of this paper is somewhat lower than Crowell's estimate. The E~s*b/k values for all three g a s - B N systems are consistently lower than the estimates of Thomas
et al. Sams, Constabaris, and Halsey used a virial coefficient approach to treat the inert gas-graphite system. For a LennardJones (3, 9) potential they found the interaction energy of the carbon black P33 (2700 °) with Ar as l107K, Kr as 1460K, and Xe
TABLE V Comparison of Calculated and Experimental Values of e*s/k (K) for the Interaction of Inert Gases with the Basal Plane of BN Adsorbate
Present" work
Ref. (2)"
Ref. (11)~
Ref. (13)b
Ref. (14)~
Ar Kr Xe
1038 1305 1650
1083 1414 1847
1123 1312 1783
1047 1409
1007
a Experimental. b Calculated.
as 1919K (6). The ratio of their graphite interaction energy to our boron nitride basal plane interaction energy for argon, krypton, and xenon is 1.07, 1.12, and 1.16, respectively. Clearly graphite interacts about 10% more strongly than boron nitride with the rare gases but whether the trend of the increasing ratios with polarizability and size of the adatom is significant requires more detailed experiments and theory. CONCLUSION
New data for the inert gases adsorbed on boron nitride corresponding experimentally to the Henry's law region have been obtained and analyzed using the virial approach to physical adsorption. These new measurements are such that no assumptions other than requiring that consistent areas and interaction energies exist for each of the g a s - B N systems are necessary in order to make the analysis. Specifically, no model isotherm equation has been introduced into the analysis. The results obtained verify the general utility of the model dependent technique used in earlier work and utilized by other investigators. Although the two techniques are quite different, the results are in general agreement. Boron nitride is indeed a good model system for studies of heterogeneity in physical adsorption. The results obtained here using physical adsorption techniques are consistent with electron micrographs of the solid. A useful extenJournal of Colloid and lnterJace Science, Vol. 70, No. l, June 1, 1979
82
LEVY, RYBOLT, AND PIEROTTI
tion in m o d e l h e t e r o g e n e i t y s t u d i e s w o u l d involve mixtures of boron nitride and graphite yielding a three-surface variable composition system capable of both experimental and theoretical investigations. REFERENCES 1. Ramsey, R. N., Thomas, H. E., and Pierotti, R. A., J. Phys. Chem. 76, 3171 (1972). 2. Thomas, H. E., Ramsey, R. N., and Pierotti, R. A., J. Chem. Phys. 59, 6163 (1973). 3. Levy, A. C., Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1976. 4. Ramsey, R. N., Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1970. 5. Steele, W. A., and Halsey, G. D., Jr., J. Chem. Phys. 22, 979 (1954). 6. Sams, J. R., Constabaris, G., and Halsey, G. D., Jr., J. Chem. Phys. 64, 1689 (1960).
Journal ojColloid and InterJace Science, Vol. 70, No. I, June 1, 1979
7. Sams, J. R., Constabaris, G., and Halsey, G. D., Jr., J. Chem. Phys. 36, 1334 (1962). 8. Pierotti, R. A., and Thomas, H. E., in "Surface and Colloid Science" (E. Matijevi6, Ed.), Vol. 4, p. 165. Wiley (Interscience), New York, 1971. 9. Steele, W. A., in "The Solid-Gas Interface" (E. Alison Flood, Ed.), Vol. l, p. 316. Marcel Dekker, New York, 1967. I0. Young, D. M., and Crowell, A. D., "Physical Adsorption of Gases," p. 23. Butterworth, London, 1962. 11. Crowell, A. D., and Chang, C. 0., J. Chem. Phys. 43, 4364 (1965). 12. Hirschfelder, J. O., Curtis, C. F., and Bird, R. B., in "Molecular Theory of Gases and Liquids," p. 110. Wiley, New York, 1954. 13. Curthoys, G., and Elkington, P. A., J. Phys. Chem. 71, 1477 (1967). 14. Pierotti, R. A., and Petricciani, J. C., J. Phys. Chem. 64, 1596 (1960).