Langmuir 1987, 3, 346-349
346
Adsorption of n -Butane on Silica Gel? William D. Machin* and Peter D. Golding Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A l B 3x7 Received October 24, 1986 Isotherms for n-butane adsorbed on a commercial silica gel have been determined at integer temperatures from 209 to 274 K. When the relative amount adsorbed is greater than 0.948 the adsorbate behaves as a capillary liquid, having properties similar to that of bulk liquid n-butane, but for lesser amounts the adsorbate behaves as a capillary gas. The capillary-phase behavior is in accord with recently proposed models for the behavior of fluids in small pores. Our results indicate that the phase-transition point and the isotherm shape in the vicinity of the transition point are characteristic of the adsorbent pore structure.
Introduction Knowledge of the properties of liquids condensed in porous adsorbents is ewntial for the determination of pore volume and pore size distributi0n.l We have demonstrated that benzene adsorbed on a microporous silica gel behaves as a capillary liquid at relative pressures greater than ca. 0.2.' In the present work we find that n-butane on the same silica gel also behaves as a capillary liquid a t high relative pressures but undergoes a transition to a "capillary gas" a t low relative pressures. A number of theoretical studies have been carried out on the behavior of simple fluids in contact with model pores.3+ Many of these predict a gas-liquid phase transition within the pore under appropriate conditions of temperature, pressure, and density. This work reports the thermophysical properties of n-butane as a capillary fluid and provides information on the capillary phase transition. In addition, our results suggest that the transition point may be used to characterize the pore structure of a microporous adsorbent. Experimental Section The adsorbent is a commercial silica gel (Davison,Grade 03). The adsorptive is n-butane(Matheson,research purity, m i n i u m 99.9%). The n-butane was condensed on and fractionated from several grams of dehydrated silica gel at ca. 195 K and the middle fraction of this material was retained. Analysis of this fraction by capillary GC indicated a purity of 99.95 mol %. The vapor pressure of this n-butane was measured over an extended temperature range. The results are in excellent agreement with reported value^.^,^ These will be reported else~here,~ as will a complete description of the apparatus.2 Errors are estimated as the following: pressure, f0.03% or f 2 Pa; amount adsorbed, f 0 . 0 6 % or f 2 X 10+ mol g-l; temperature, f 5 mK. Results
A total of 66 isotherms have been determined at integer temperatures from 209 to 274 K. All isotherms are type 1,l0 and typical isotherms are shown in Figures 1 and 2. Each isotherm exhibts a transition point where the slope of isotherm changes rapidly. The locus of these points is shown as a line of crosses in Figure 1. For the data above the transition point, we have carried out a linear leastsquares fit to the equation In (P/PO) = B ( A / A o )In ( A / A o )
(1)
where PlP" is the relative pressure, A is the amount ad-
* Author to whom correspondence
should be addressed. 'Presented a t the "Kiselev Memorial Symposium", 60th Colloid and Surface Science Symposium, Atlanta, GA, June 15-18,1986; K. S. W. Sing and R. A. Pierotti, Chairmen.
Table I. Isotherm Parameters for the Adsorption of n -Butane on Silica Gel
T/K p6/kpa
T / c m 3 mol-' A /mmol g-' A,/mmol g-'
B
2 A G6 p / c m 3 g-'
210 4.033 87.507 3.383 4.510 33.267 33.195 2.539 2.538 0.2961
230 14.090 90.169 3.276 4.219 27.491 27.334 2.337 2.333 0.2954
250 39.153 93.077 3.166 3.990 24.209 23.889 2.146 2.140 0.2947
270 91.567 96.298 3.060 3.775 20.196 19.691 1.989 1.978 0.2947
aReference 11.
sorbed, Ao is the amount adsorbed a t saturation pressure, and B is a constant. For the data below the transition point we have carried out a similar regression to the equation In (P/PO) = G ( l
+ A / A o ) In ( A / A , )
(2)
where G and A , are constants. Values of the various parameters and their standard errors are given by Ao/mol g-I = [(3.2215 X - (5.445 X lo+) X (T - 240) - (1.457 X 104)(T - 240)2] f 1.85 X lo4 (3)
B = (12243.8/T - 24.9495) f 0.563 A,/mol g-' = [(4.1013 X - (1.1347 X (T - 240) + (8.569 X 10-8)(T - 240)'] f 3.95
G = (544.774/T
- 0.0404) f 1.94 X
(4) X X
(5)
lo-'
(6)
Values of PO, AO, A,, B, and G are reported in Table I. Molar volumes (V") of n-butanel' are reported in this table (1) Gregg, S.J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic: New York, 1983; Chapter 3. (2) Machin, W. D.; Golding, P. D., accepted for publication in J. Chem. Soc., Faraday T r a m . 1. (3) Derjaguin, B. V.; Churaev, N. V. J. Colloid Interface Sci. 1976,54, 1.57-1 - - . - 75. . -. (4)van Megen, W.; Snook, I. K. Mol. Phys. 1985,54, 741-755. (5) Peterson, B. K.; Walton, J. P. R. B.; Gubbins, K. E. Int. J. Thermophys. 1985,6, 585-593. (6) Evans, R.; Marconi, V. B. M. J. Chem. Phys. 1986,84,2376-2399. (7) Kratzke, H.: Suillner, E.: Muller, S. J.Chem. Thermodyn. 1982, 14, 1175-1181.. (8) Haynes, W. M.; Goodwin, R. D. "Thermophysical Properties of Normal Butane from 135 to 700 K at Pressures to 70 MPa", Natl. Bur. Stand. (US.)Monogr., 1982, No. 169 pp 3, 51, 90,136, 138. (9) Machin, W. D.; Golding, P. D., submitted for publication in J. Chem. Eng. Data. (10) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. f i r e Appl. Chem. 1985,57, 603-619.
0743-7463/87/2403-0346$01.50/0 0 1987 American Chemical Society
Langmuir, Vol. 3, No. 3, 1987 347
Adsorption of n-Butane on Silica Gel
I
I
Table 11. Properties of Adsorbed n -Butane at P o ~ / ~ p o / Ka - l ~O~~$/K-~ oTo/GPa-'e &'/GPa-' C,,/J K-l mol-1d
210 1.64 1.46 1.15 1.15 120.29
230 1.69 1.54 1.31 1.39 123.92
250 1.75 1.64 1.42 1.71 128.48
270 1.81 1.77 1.65 2.14 133.79
"Equation 12. bReference 11. cEquation15. dReference 8. z 0
2
2.8
-I !/I''!/ 0.2
0. 4
0. 6
0. 8
RELATIVE PRESSURE
Figure 1. Adsorption isotherms at high coverage. Points are experimental; solid lines are calculated by using eq 1-6. Approximately half the experimental points shown for each isotherm are desorption points. Within experimental error, there is no adsorption-desorption hysteresis.
1.0
-30 -20 210K
In
> 3.0
-10
0
10
20
30
PRESSURE /MPa
Figure 3. Isothermal compressibility and thermal expansivity of n-butane at 240 K. Values at negative pressures refer to capillary liquid and at positive pressures to the bulk liquid.
E O W
m
lx
Discussion
2.0
The pressure within a capillary liquid is given by1V2
0
c c
PL= W,(V) In Cf/f
z2
0
z
O)
(9)
where f refers to fugacity. Evans and Marconis suggest that this equation should be valid for A/Ao 1 0.95; Le., it should be valid for the capillary liquid region (A/Ao 1 0.948) of our isotherms. We have found that the appropriate molar volume (V) is defined by the equations2
< 1.0
0. 1
V = (Vp - VE)/A
0. 2
(10)
RELATIVE PRESSURE Figure 2, Adsorption isotherms at low coverage. Points are experimental; solid lines are calculated by using eq 1-6.
with the corresponding pore volumes (AOVO;average 0.2953 f 0.0005 cm3 g-l). Simultaneous solution of eq 1 and 2 gives the isothermal transition point as A / A o = 0.948 f 0.002 over our temperature range. The transition points are plotted in Figure 1 as crosses and the solid lines are isotherms calculated by using eq 1-6. From the Berthelot expression for the second virial coefficient12with the critical constants taken as 425.16 K and 3796.0 kPa,B eq 1-6 were reevaluated in terms of fugacities. The only significant changes are for eq 4 and 6, which become Bf = 12687.4/T - 27.070 (7) Gf = 549,054/T - 0.0621 (8) Values for these quantities a t selected temperatures are given in Table I. (11)Haynes, W. M.;Hiza, M. J. J. Chem. Thermodyn. 1977, 9, 179-187. (12)Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964; p 252.
where Vp is the pore volume (0.2953 cm3g-l) and VEis that part of the pore volume from which the centers of the adsorbed molecules are excluded. With surface area (8) equal to 290 m2 g-' and a collision diameter (a)of 0.497 nm for n-butane,13 VE is 0.0715 cm3 g-l. The thermal expansivity of adsorbed n-butane a t saturation pressure (a$)can be calculated by using eq 3, since .Po
= -(l/Ao)(dAo/dT)p
(12)
At negative pressures cyp can be obtained from eq 7,9, and 10 as aP - CY$ = (1/T)(l - 468.6/T) In (A/Ao)
(13)
when A/Ao 1 0.948. The isothermal compressibility (&), defined as BT = U/A)(aA/af'), (14) can be derived from eq 7, 9, and 10 as
& = (Vp - VE)/(RTB~A~/AO[~ +- 2 ln(A/Ao)]) (13)Yosim, S.J. J. Chem. Phys. 1964,40, 3069-3075.
(15)
348 Langmuir, Vol. 3, No. 3, 1987
Machin and Golding
T \ \
Temp/K
'i
u 0.2
0. 4
0.6
0.8
1. 0
-40
MA0
Figure 4. Heat capacity and enthalpy of vaporization of n-butane adsorbed on silica gel as a function of A/Ao at 240 K. and the isothermal compressibility a t saturation pressure (&O) is obtained for A = AO. Values for apoand /3To calculated for some temperatures are given in Table II. Corresponding values for bulk liquid n-butane calculated from the data of Haynes8J1 are also included in Table I1 for comparison. I t can be seen that the properties are similar. As a further comparison, the pressure dependence of these quantities is shown in Figure 3. Differentiation of eq 1 and 7 gives
-30
-20
-10
0
Minimum Pressure/MPa Figure 6. Minimum pressure in the capillary liquid vs. tem-
perature.
r
[a In (f/fo)/a(l/T)]A/AO= 12687.4(A/A0) In (A/Ao) (16) and it can be shown that2 In
(f/fo)/a(l/r)lA,~o
=
(m.9-me*')+ (6 - T)(Acp,*' - ACm)
(17)
where Ai?&, ACm and AHo*',AC,*' refer to the vaporization of bulk and capillary liquid n-butane, respectively, a t a reference temperature 6. Since the right-hand side of eq 16 contains no term in T, it follows from eq 17 that
Acps*' = Acp,
(18)
Since the vapor heat capacities are nearly independent of pressure,s the heat capacity of the capillary liquid (C,*') must equal the heat capacity (C,) of bulk liquid n-butane. These heat capacities are given in Table 11. It follows from eq 16-18 that
(A&*' - m B ) A / A O = -12687.4R(A/A0) In (A/Ao)
(19)
and C,*' on A/Ao Figure 4 shows the dependence of AH#*' in the capillary liquid region (A/Ao 1 0.948). In the capillary gas region, Le., when A/Ao < 0.948, eq 2, 3, 5, and 8 give
[a In C f / f o ) / a ( l / T ) l A / A o (1
=
+ A/A0)(1.427T + 549.05 In (A/Ao) - 625.58)
Since eq 17 is valid for all A/Ao, it follows that Cps*' - Cpe*' = 1.427R(1 + A/Ao)
(20) (21)
and - Ah?O*']
R(l
=
+ A/A0)(1.4278 + 549.05 In (A/Ao) - 625.58)
(22)
where A H o * g and ACps*g refer to the desorption of the
Figure 6. Schematic phase diagram for n-butane as a capillary fluid.
capillary gas and Cm*g is the heat capacity of the capillary gas. Figure 4 shows the dependence of A H 8 * g and CH*g
on A/Ao. It is clear that there is an abrupt change in the thermophysical properties of the adsorbate a t A/Ao = 0.948. Several theoretical studies have suggested that fluids in capillaries may undergo a liquid-gas transition- and that critical behavior should be exhibited by a capillary liquid." The limiting negative pressure that capillary liquid n-butane can withstand has been calculated from eq 9, and these values are plotted against temperature in Figure 5. It can be seen that the values fall on a straight line passing through the critical point. We conclude that capillary liquid cannot exist a t supercritical temperatures. The same conclusion is obtained from eq 20. Over our temperature range, this equation is valid for A/Ao 5 0.948, but a t some temperature it will be valid for A = Ao and P = Po. From eq 20, the lowest temperature at which this can occur is 438.39 K, which, considering the long extrapolation, compares well with the actual critical temperature, 425.16 K. Evans and Marconie have considered the behavior of a simple fluid confined within a slit-shaped pore. While the fluid and pore model are not entirely equivalent to our system, they do propose a schematic phase diagram which is in accord with our results. A slightly modified version
Langmuir 1987,3, 349-353 Table 111. Influence of Excluded Volume on the Capillary-Phase Transitiona VF/cm3g-l looVn/ Vp P/P(transition) 0 0.05 0.15 0.25 0.28 0.295
0 16.9 50.8 84.7 94.9 100
0.139 0.195 0.379 0.740 0.905 1.000
349
transition increases with temperature, the value of A/Ao at the transition point is very nearly constant (0.948). Other adsorbents, having different pore sizes, should exhibit the capillary-phase transition at other values of A/Ao. On a relative basis, the average pore size in an appropriate adsorbent can be characterized by the value of AIAO a t which the phase transition occurs. Similar conclusions can be developed from eq 9 and 10 which may be combined to give
“V, = 0.295 cm3 g-l; P,(min) = -40 MPa; A = 3.0 mmol g-’.
of their phase diagram is shown in Figure 6. The pore dimension (D)is readily defined as plate separation in a slit-shaped pore but is less readily defied for pores formed by the random packing of spheres. Nevertheless, we can reasonably assume that even with an irregular pore system there will be a minimum pore size (D,)and a maximum pore size (Db). Furthermore, there is a critical pore size for each temperature (D2 at T2and D 1at T1 in Figure 6), and if the actual pore sizes are less than the critical size, the capillary liquid phase will not be present. If both D, and Dbare greater than Dzfor all temperatures up to the critical temperature (T,), then for all T < T, there will be a capillary liquid region. The relative pressure (P/PO)at which the transition to capillary gas occurs will increase with temperature, becoming unity a t T,. On the other hand, if both D, and Db are less than D,but greater than D2,then the phase transition will occur at T1 but not at Tz.That is, for this particular pore structure, the capillary liquid phase will cease to exist a t some temperature less than T,. Also, it can be seen from Figure 6 that a range of pore sizes will produce a “roundingn of the adsorption isotherm in the vicinity of the transition region. This effect appears to be more pronounced a t higher temperatures (Figure 1)and suggests that the extent of rounding near the transition region is indicative of the range of pore sizes present in the adsorbent. For a given adsorbate the isothermal transition point should depend only on the pore dimension (D). We have found that although PIP‘ for the
If the minimum value of PLdepends only on temperature, then as ( Vp - VE) is reduced, either through reduction in pore size or increase in adsorbate molecular size, the relative pressure a t which the transition PL is reached will increase, as will the value of A/Ao associated with the phase transition. Some example calculations that illustrate this behavior are shown in Table 111.
Conclusions For temperatures from 209 to 274 K, n-butane adsorbed on silica gel is a capillary liquid when A/Ao 1 0.948 and a capillary gas when A/Ao 5 0.948. The thermophysical properties of the capillary liquid, and their dependence on pressure, are similar to the properties of the bulk liquid. The heat capacity and enthalpy of desorption of the capillary gas are both greater than the corresponding quantities for capillary liquid or bulk liquid n-butane. The estimated critical temperature of the capillary liquid is nearly the same as that of bulk liquid, but the actual capillary critical temperature will be determined by the pore structure of the adsorbent. Our results are in accord with models proposed for the behavior of fluids in small pores and suggest that the phase transition point (A/Ao = 0.948) is characteristic of the adsorbent pore size. The rounding of isotherms near the transition point is related to the range of pore sizes. Registry No. Butane, 106-97-8.
Selective Adsorption by Ultramicroporous Silica Glass at Gas-Solid and Liquid-Solid Interfaces? Seiichi Kondo,* Tohkoh Tamaki, and Yuriko Ozeki School of Chemistry, Osaka University of Education, 4-88 Minamikawahori-cho, Tennoji-ku, Osaka 543, Japan Received September 5, 1986. I n Final Form: November 20, 1986 Ultramicroporous silica glasses made by acid treatment of alkali silicate glass powders or fibers were found to adsorb selectively water and a smaller amount of methanol in the gas phase and water molecules and monovalent cations, but not alkylammonium and multivalent cations, in the liquid phase. Cations were adsorbed from 0.1 mmol/L solutions in the order Cs+ > Rb+ > NH4+> K+ > Ag+ > Na+ > Li+ >> Mg2+ at equilibrium pH 5.5.
Introduction Cations on the surfaces of various kinds of glasses are known to be exchanged with protons and other cations by water and acid treatment., McGrail and others studied
the rate of release of sodium ions from the surface of alkali silicate glass.2 Silica-rich glass produced by treating alkali silicate glass with acid adsorbed quite a large amount of water compared with its nitrogen BET specific surface
‘Presented at the ‘Kiselev Memorial Symposium”, 60th Colloid and Surface Science Symposium, Atlanta, GA, June 15-18,1986; K. S. W. Sing and R. A. Pierotti, Chairmen.
(1)Tsuchihashi, S. Physical Chemistry of Glass Surfaces; Kohdansha: Tokyo, 1980. ( 2 ) McGrail, B. P.; Pederson, L. R.; Petersen, D. A. Phys. Chem. Glasses 1986, 27, 59.
0143-7463/87/24Q3-0349$Q1.5Q/Q0 1987 American Chemical Society
