16714
J. Phys. Chem. 1995, 99, 16714-16721
Dipole Oriented States of SO2 Confined in a Slit-Shaped Graphitic Subnanospace from Calorimetry Z.-M. Wang and K. Kaneko" Department of Chemistry, Faculty of Science, Chiba University, Yayoi 1-33, Inage-ku, Chiba 263, Japan Received: June 5, 1995; In Final Form: August 30, 1995@
Mechanism of SO2 micropore filling in the slit-shaped micropores of activated carbon fiber (ACF) was studied by SO2 adsorption calorimetry and molecular potential calculation. The pore width of ACF was 0.75 nm from analysis of N2 adsorption at 77 K. The characteristic change of the differential adsorption energy for SO2 with increase of the fractional filling showed the presence of specific interaction of the SO2 dipole with the surface functional group, enhanced S02-micrographitic wall interactions with the induced dipolar interactions, and permanent dipole-dipole interactions. The contribution of the dipole-induced dipole interactions calculated by the image potential approximation was 25% of the whole interaction potential of SO2 with micrographitic walls, which agrees with the observed adsorption energy. The strong S02-micropore wall interaction indicated a ferroelectric-type orientation of SO?;molecules.
Introduction W A C classified solid pores into three categories-macropores, mesopores, and micropores; molecules are adsorbed by different mechanisms according to the pore category.' In particular, the micropore whose pore width is less than 2 nm has gather much attention, because microporous solids having great surface area are expected to give rise to new chemical reactions2 and they also exhibit a strong physical adsorption enhanced by overlapping of interaction potentials from the opposite micropore walls, which is called micropore filling. Micropore filling has been widely studied since 1 9 5 0 ~ . ~ -The ' ~ micropore filling for vapors has been described thermodynamically by Dubinin-Radushkevich (DR) e q u a t i ~ n . ~However, .~ the DR equation cannot sufficiently lead to the mechanism of micropore filling such as molecular states of adsorbed molecules with the fractional filling or the interaction of molecules with the pore wall. Sing et al. proposed a primary and cooperative micropore filling mechanism by a,-analysis of N2 adsorption isotherms.' Kaneko et al. showed that high-resolution a, analysis is highly effective for study of micropore filling,'5.'6 and they stressed the presence of the elementary p r o c e ~ s e s .Rouquerol ~ ~ ~ ~ ~ at al. have studied micropore filling with the aid of calorimetry, determining the enhanced adsorption energy.I9 Molecular simulation results on micropore filling fairly agreed with the adsorption data, showing that the interaction potential profile is essentially important even in micropore filling and monolayer adsorption should exist in wider micro pore^.'^^'^ Nevertheless, fundamental studies on micropore filling have been carried out for limited adsorptives such as N? and Ar, although adsorption of other vapor molecules by microporous solids has been widely used in technology. There should be different interaction modes between the adsorptive molecules and the surface, and thereby a characteristic micropore filling mechanism is expected according to each adsorptive. SO2 is a molecule having a great permanent dipole moment and the size of SO2 is much greater than that of N2. The fundamental understanding of SO2 adsorption by microporous solids is strongly desired from the environmental aspect. Micropore filling for SO:! should be governed by a LennardJones-type interaction and the dipolar interaction, which gives @
Abstract published in Advance ACS Abstracts, October 15, 1995.
0022-365419512099-16714$09.0010
rise to a special micropore filling. Although adsorption of polar molecules by cylindrical micropores of zeolites was studied,20%2' adsorption of polar molecules by slit-shaped micropores was not actively investigated.'9,22,23Activated carbon fibers (ACFs) are recently developed microporous adsorbents which have uniform slit-shaped micropores of great pore volume. The micropore structures and physical properties of ACFs have been systematically studied by use of high-resolution NZ adsorpt i ~ n , ' He ~ . adsorption ~~ at 4.2 K,25$26 multiprobe a d ~ o r p t i o n , ~ ~ in-situ X-ray diffraction,28and small-angle X-ray ~ c a t t e r i n g . ~ ~ , ~ ~ In this study, molecular states of SO2 filled in micropores of ACF are examined with the aid of direct calorimetry and calculation of the interaction potential.
Experimental Section Pitch-based ACF (P5, Osaka gas Co.) and nonporous carbon black (NPC) were used with a computer-aided gravimetric apparatus. The samples were characterized by high-resolution N2 adsorption at 77 K. The SO2 adsorption isotherms were determined gravimetrically at 303 K. Samples were preevacuated at 383 K and 10 mPa for 2 h prior to adsorption. The adsorption energy for SO2 was measured at 303 K under various SO2 pressures until 90 kPa by a twin-type calorimeter (Tokyo Richo (20.). The differential adsorption energy q d for SO2 at 303 K was calculated by eq 1. q d = (dQinJma)~=303~
(1)
Here dQintis a released heat when molecules of dlv, are adsorbed on the sample. dQint was recorded through a multifunctional amplifier and calibrated with a standard Joule heat. CW, was determined by the adsorption isotherm through the pressure change. Samples were preevacuated under the same conditions as the adsorption experiment.
Results and Discussion Characterization of Samples. Figure 1 shows the highresolution N2 adsorption isotherms for ACF and NPC at 77 K. The N2 adsorption isotherm of ACF is of type I, being characteristic of uniform microporous solids. In comparison with ACF, NPC shows a typical isotherm of type 11; the amount of N2 adsorption is much smaller than that of ACF. The 0 1995 American Chemical Society
Dipole Oriented States of SO2
J. Phys. Chem., Vol. 99, No. 45, 1995 16715
7
350 280
1
, , ,
. . ,
,
,
I
M
2
>
210
z" 1 4 0
s
70
1
"
02
04
Ofi
08
1
N2
0 15
0.1
02
0.25
P(so2)/Po(soz)
P/Po
Figure 1.
J 0.05
adsorption isotherms of ACF and NPC at 77 K. 350
7
280
0
20
40
60
80
In2(P0/P) a
Figure 2. a,-Plots for N2 adsorption isotherms on ACF and NPC.
"-
005
01
015
02
025
P(so2)~Po(soz) Figure 3. The SO2 adsorption isotherm of NPC at 303 K. 0, SO2; A, N2; --, BET SO2 isotherm.
TABLE 1: Surface Characterizationof Samples N2 WS
as,
as.ext.
wm,
Ws,
adsorptive mL g-' m2 g-' m2 g-' nm mL g-' PIT 0.339 915 5 0.75 0.32 iz 0.01 NPC 80.9
Wo(S02Y Wo(N2)
0.95
adsorption isotherm of NPC has a clear B point (BET c-value: 1040). Microporosity of ACF and the specific surface area of NPC were determined by high-resolution a,-analysis. Figure 2 shows the a,-plots for ACF and NPC. The standard N2 adsorption data on another partially graphitized nonporous carbon black were used.I8 In the a,-plot of ACF, there is a narrow linear range near a, = 0.5 which passes through the origin. The a,-plot below a, = 0.4 deviates greatly upward from the line, indicating the enhanced adsorption by strong micropore field due to smaller micropores. The a,-plot becomes almost horizontal above a, = 0.8, which arises from the small external surface. The total surface area a,, the external surface area as,ext, the micropore volume W,, and the average micropore width wmof the slit-shaped micropore are shown in Table 1. In Table 1, wm was calculated from the relationship w m = 2WJ(as - as.ext).wmis 0.75 nm, which nearly corresponds to the bilayer thickness of the adsorbed N2 molecules. The a,-plot of NPC is well expressed by a line passing through the origin in the whole range, providing the specific surface area of NPC, as shown in Table 1. SO2 Adsorptivity. The SO2 adsorption isotherm of NPC is shown in Figure 3. As the carbon surface has a hydrophobic nature, polar SO2 molecules cannot strongly interact with it and then the adsorption isotherm of NPC is of type I11 rather than
Figure 4. (a) SO2 adsorption isotherm of ACF at 303 K. The dotted line is the N2 adsorption isotherm at 77 K. (b) DR plots for the adsorption isotherm of SO2 at 303 K and N2 at 77 K on ACF.
of type 11. The N2 adsorption isotherm at 77 K was also shown in Figure 3 (the solid triangle marks) for comparison. The adsorption amount of SO2 is much smaller than that of N2 at the low relative pressure range. We cannot determine a monolayer capacity of S02, because the BET plot became seriously curved. However, the adsorption isotherm of SO2 can be simulated by varying the c-value of the BET equation if adsorbed SO2 molecules adsorb on the same surface as N2. The simulated SO2 isotherm of NPC from the BET equation having c = 4.9 is shown in Figure 3 (the dotted line); the c-value for SO2 is much smaller than c = 1049 for N2. The interaction energy, AH', between the monolayer SO2 molecule and the carbon surface can be estimated to be 29 kJ mol-', using the condensation enthalpy of bulk SO2 liquid, AHL (AHL = 24.9 kJ mol-' at the boiling point); the value briefly coincides with the observed value shown in Figure 5 . The deviation of SO2 adsorption isotherm from the simulated BET-type isotherm at the higher relative pressure comes from the lateral interact i ~ n , ~which ~ , ~ 'will be discussed later. The SO2 adsorption isotherm of ACF is shown in Figure 4a. The SO2 adsorption isotherm of ACF is of typical type I, indicating that SO2 molecules are adsorbed by micropore filling regardless of the weak interaction of SO2 with the carbon surface. The SO;?adsorption isotherm of ACF can be described by the DR equation
In w = In W, - (RT/PE,)' 1n2(Po/P)
(2)
Here Wo is the saturated adsorption amount, p is an affinity coefficient, and Eo is the characteristic adsorption energy. Figure 4b shows the DR plot which has a good linearity except for the high-pressure region. On the other hand, the DR plot for N2 is completely expressed by a single line, suggesting uniform microporosity of this ACF sample. The micropore volume for S02, W0(SO2), and that for N2, Wo(N2), were obtained by using their densities of bulk liquid SO2 (p~(S02) = 1434 kg m-3 at the boiling point) and N2. These pore volumes are shown in Table 1. The ratio of W0(S02)to Wo(N2) is 0.95, as shown in Table 1. Then, the Gurvitch rule almost holds in this case; the small difference should arise from the fractal nature of the micropore surface.27 Also the effectiveness of the Gurvitch rule suggests that molecular states of adsorbed molecules are bulk liquid like. However, such a good agreement
Wang and Kaneko
16716 J. Phys. Chem., Vol. 99, No. 45, 1995
AHL=24.9kl mol'
-1
120
-
0
02
04
06
m-
. -240
1
300
0
08
e Figure 5. Change in the differential adsorption energy (a) and differential entropy of adsorption (b) for SO2 on NPC.
of densities of bulk liquid and adsorbed phases cannot necessarily guarantee the liquid-phase formation of adsorbed molecules in micropores. Fukazawa et al. showed clearly a marked difference of benzene molecular states in slit-shaped micropores and in the bulk liquid with the aid of D-NMR, even under conditions of good density agreement.32 Also the weak adsorbent-adsorbate interaction for the SO2-carbon system leads to a micropore filling process different from N2. Figure 4b shows completely different DR plots for SO2 and N2, although both abscissa and ordinate are expressed in terms of reduced quantities. The similar difference was observed by Rodriguez-Reinosoet al.' Later molecular potential calculation will provide the satisfactory reason. Adsorption Energy and Adsorption Entropy for S02. Figure 5a shows the differential adsorption energy, qd, of SO2 on NF'C as a function of the SO2 surface coverage 8. 8 is defined as the ratio of surface occupied by SO2 to that occupied by N2. The surface occupied by SO2 was determined by using the molecular area (0.192 nm2) calculated by the assumption of close-packing of SO2 molecules.33 The differential adsorption energy for SO2 on NPC drops at very low coverage and gradually increases with the coverage. However, the change is not marked and the differential adsorption energy is in the range 25-30 kJ mol-', which is slightly higher than 24.9 kJ mol-' of the bulk condensation enthalpy AHL. Hence a SO2 molecule interacts weakly with the carbon surface, as suggested above. The great adsorption energy for SO2 at low coverage is attributed to the electrostatic interaction of the SO2 dipole with the local surface field at the surface functional groups, although the interaction is not so strong to give rise to an irreversible adsorption of S 0 2 . The gradual increase in the differential adsorption energy at the higher surface coverage arises from the lateral interaction, which agrees with the above adsorption behavior. The change in the differential adsorption energy for S02, q d , on ACF is shown in Figure 6a. Here the abscissa 4 is the fractional filling, which is the ratio of the volume occupied by adsorbed SOz, W(S02), to Wo(N2). W(S02) was reduced to the volume from the amount of SO2 adsorption by using the bulk liquid SO2 density. This change can be divided into three regions: 4 < 0.2 (stage A); 0.2 4 < 0.6 (stage B); 4 > 0.6 (stage C). In stage A, SO2 molecules are strongly adsorbed on surface functional groups, which causes their irreversible adsorption (1.5% of the saturated amount of adsorption). The additional interaction of the SO2 dipole with the surface functional groups through the surface electrical field34 is a plausible reason. The enthalpy of the gas reaction SO2 ' / 2 0 2
+
02
04
06
08
d Figure 6. (a) Change in differential adsorption energy for SO2 on ACF and (b) the corresponding change in differential entropy of adsorption: 0,the experimental result; A, MF model; *, LF model: t,MMF mode without I,; 0, MMF model without I,.
- so3
is 96 W mol-'.35 Consequently, the surface oxidation of adsorbed SO2 by reactive surface oxygen groups may increase the adsorption energy for SO2 in addition to the dipole-surface field interaction. Stage B, in which the q d does not change with 4, corresponds to the micropore filling process for SO2 in the micropores; the interaction of SO2 with the micropore walls, without any effect by the surface functional groups, governs this process. However, the specific interaction of the SO2 dipole with the surface functional groups extends slightly to this stage and also a slight lateral interaction must be taken into account near stage C. The apparent constant adsorption energy in this B range arises from overlapping of the decreasing specific interaction and the increasing lateral interaction. The maximum enhanced micropore field for SO2 should be 10 W mol-' by comparison of the heat of adsorption for ACF with that for NPC. The pore filling above 4 = 0.6 brings about a marked increase in the adsorption energy in stage C due to the strong lateral interaction. In this stage, SO;! molecular aggregates should be formed in the confined micropore. A detailed mechanism of stages B and C will be described later. When the S02-saturated vapor at 303 K is chosen to be the standard state, the differential adsorption entropy of SO2, &, is given by eq 3.36 sd
= A H d I T - R h(P/P,)
(3)
Here is the differential enthalpy of SO2 adsorption, which is combined with qdz3'
AHd = qd -k RT
(4)
Figure 5b shows the change in differential entropy of adsorption, s d , of so2 on Mc. s d decreases with the coverage. The Sd value below 8 = 0.1 is greater than the condensation entropy, A& (A& = -71,.2 J mol-' K-' at 303 K). This indicates that the molecular state of SO2 adsorbed on the carbon surface is different from that of the bulk liquid; in the low surface range SO2 molecules on the surface can move more freely than the liquid state. The change in the s d of so2 on ACF with fractional filling has an opposite tendency from the change in the q d (Figure 6b). Then the relationship between s d and 4 has three regions: s d smaller than A& below 4 = 0.2, a gradual decrease of s d with 4 from 4 = 0.2 to 4 = 0.6, and a steep s d drop above 4 = 0.6. & drops above 4 = 0.6. This characteristic & change should be taken into account in order to elucidate the adsorbed SO2
J. Phys. Chem., Vol. 99, No. 45, 1995 16717
Dipole Oriented States of SO2 molecular state in the micropore. This entropy change will be explained later. Molecular Potential of SO2 in a Slit-Shaped Graphitic Pore. There are various kinds of models for calculation of intermolecular i n t e r a ~ t i o n .As ~ ~an SO2 molecule has a dipole moment, the contribution by the polar interaction should be considered. Crowell calculated the molecular potential of a SO2 molecule on a single graphite surface with the aid of the Stockmayer-type potential, which is composed of the nonpolar and polar terms.39 In his study, the nonpolar interaction was described by the Lennard-Jones potential and the polar interaction was approximated by the image potential. The Crowell's approximation was extended to SO2 in a slit-shaped graphitic pore, because ACF has an electrical conductivity in the semiconductivity region.40 The nonpolar and polar interactions will be described separately below. Although an SO2 molecule has the quadrupole moment,'" the interaction induced by the quadrupole moment can be neglected compared with the great contribution by the permanent dipole moment @ = 1.61 D). Nonpolar Interaction. The nonpolar interaction of a SO2 molecule with a carbon atom of the graphitic surface is described by the Lennard-Jones (LJ) potential (eq 5).
Y ( r )= 4 ~ [ ( ( ~ / r )-' *( ( ~ / r ) ~ ]
(5)
Here r is the SO2-C distance, (T is the distance at which the interaction potential equals to zero, and E is the potential well depth. The potential of a SO2 molecule with the graphitic sheet is obtained by integrating eq 5 over the carbon atoms of the graphitic sheet, which is called the 10-4 potential. The 10-4 potential is given by eq 6:
Y(z)= 4 7 ~ n , d ~1/5)(0/z)'O [(
- (1/2)(0/z)~]
(6)
Here z is the perpendicular distance of a molecule from the surface plane. The molecule can interact with underneath carbon atoms. When the vertical interaction is integrated to infinite, the following 9-3 potential is obtained:
(7)
In eqs 6 and 7, n, and n, are the numbers of carbon atoms per unit area in the lattice plane and of carbon atoms per unit volume of a slab of graphitic layers. The more realistic 10-4-3 potential was proposed by Steele for graphite having the c-spacing of h (h = 0.335 nm for a well-crystalline graphite),42as shown by eq 8:
Y ( ~= ) 4 7 ~ n , d h 6 [ ( 1 / 5 ) ( ( ~/ ~() 1~ /~2 ) ( ( ~ /~)~ (a4/(6h(O.61h
+ z ) ~ ) ](8)
The potentials from both micropore walls which are a distance 2d apart are overlapped in the micropore. In this case, the distance zm of the molecule is measured from the central plane of two graphitic micropore surfaces. The total 10-4-3 potential, Y(zm),in a micropore with the observed pore width of wm is given by eq 9: Y(zm) = 4 n m d h ~ [ ( l / 5 ) ( d ( d- z,))"
-
+
(1/2)(d(d - z,))~ - ((~~/(6h(0.61h d - z,)~)]
+
+
+ z,))~ a4/(6h(O.61h + d + z,)~)] (9)
4 ~ ~ m d h ~ [ ( 1 / 5 ) ( ( ~z,))" /(d
- (1/2)(0/(d
d may be approximated by the summation of the carbon radius r, and the half of wm.although a more rigorous approximation
.
-. &
4
z. N
-500 6
-1,000 -1,500
025
0125
0125
0
025
zm/nm
Figure 7. Potential profiles of a SO2 molecule in a graphitic micropore and on the graphite surface. 10-4-3 potential; 0 , 10-4-3 potential image potential; 0, 10-4-3 potential image potential for a single ..a,
+
graphite surface.
+
TABLE 2: Potential Minimum Parameters for Nonpolar Interaction of so2 with a Graphitic MicroDore potential
vdk,K zm*, nm Y(Zm*)lk, K Wzm*)No v , x lo-" s-I
10-4
9-3
10-4-3
-587 0.03 -905 1.54 4.5
- 1202
-694 0.04 - IO72 1.54
0.1 1 -1571 1.31 7.84
5.1
for 2d and the observed pore width is possible.43 Everett and Pow1 calculated the 10-4 and 9-3 potentials of inert atoms in a pore.6 Recently several researchers have been studying adsorption behaviors of molecules such as N2 and CHq in carbonaceous micropores using the 10-4-3 p ~ t e n t i a l . ~However, -~~ there is no study on molecular potential of polar SO2 in a carbon micropore. Recent structural study on ACF showed that ACF is a good model system of microporous graphite.Is Hence evaluation of the molecular potential of SO2 in the micropore of ACF using the above slit-shaped graphite model should be helpful to understand the micropore filling for SO2 on ACF. The following interaction parameters (T and 6 were used with Lorentz-Berthelot rules:38 (T
Y(z)= ( 2 / 3 ) ~ n , d ~ [ ( 2 / 1 5 ) ( ( ~((T/z)~] /~)~
.'
500
= 0.385 nm
6
= 84 K
n, = 38.3 nm-2
n, = 11.36 nm-3
rc = 0.071 nm
The 10-4-3 potential of a SO2 molecule in the micropore of wm = 0.75 nm is shown in Figure 7 (the dotted line). There are double minima which are not distinct in the potential profile. The positions of the potential minimum, Zm*, and the minimum potential energy, Yh(Zm*), were determined. We calculated not only the 10-4-3 potential, but also the 10-4 and 9-3 potentials for the S02-ACF system. The obtained Zm* and Y(zm*)values by each potential are collected in Table 2. Y(Zm*) is also expressed by the ratio against the potential minimum of the single surface Yo. Furthermore, we calculated the vibrational frequency of an adsorbed SO2 on the ACF micropore wall from the potential profile near the minimum under the assumption of the harmonic oscillation. The vibrational frequency, Y,which will be used in the discussion on the differential entropy, is also shown in Table 2. The Y ( Z m * ) / Y o value depends on the potential function and changes from 1.31 to 1.55. The profile of the potential depth from the 9-3 potential is much flatter than that from either the 10-4 or 10-4-3 potential. Polar Interaction. The interaction of the permanent dipole moment of SO2 with the graphitic surface has two contributions. One is the interaction of the dipole moment of SO2 with the surface electric field of the graphitic surface. Another is the interaction induced by the permanent dipole moment. The surface electric field mainly arises from the surface polar groups. As the number of the surface functional groups of carbons is
Wang and Kaneko
16718 J. Phys. Chem., Vol. 99, No. 45, 1995 TABLE 3: Parameters of 10-4-3 Potential and Image Potential for SO2 with a Graphitic Micropore
~~
-963
0.07
-1347
1.40
12.8
-304
23%
limited and the interaction of the SO2 dipole with the surface electric field is strong, this interaction is associated with adsorption at a very low pressure region, which is already shown in the high differential adsorption energy at the initial stage A of Figure 6a. Here the contribution by the dipolar interaction to micropore filling for SO' should be elucidated. The interaction of the permanent dipole with the induced dipole in the micropore wall was calculated by the following image potentia1 approximation. The potential of a dipole with the image dipole in the single graphite surface is expressed by eq 10 after C r ~ w e l l : ~ ~ W,(z) = -,LA'(1
+
COS'
~)/16( ~A)3
(10)
Here p is the dipole moment 01 = 1.61 D for SOz), a is the angle between the direction of ,LA and the normal to the surface, and A is the distance of the image plane to the plane of the surface nuclei. A was chosen to be h/2 by C r ~ w e l l .We ~~ extended this interaction to the slit-shaped pore as a function of 2,. The image potential for the parallel graphite surfaces is described by eq 11: Ymi(z,) = -(p2/8)[ l/(d - z, - h/2I3
+ l/(d + z,
- h/2)3] (11)
where the image potential by each graphite surface is added and a is presumed to be zero (the maximum case). The calculated Y,i at the minimum position of 10-4-3 potential was -304 K and was greater than the image interaction for the single surface by 35 K. Whole Molecular Potential. Combination of eqs 9 and 11 gives the total potential:
The total potentid profile of Y T ( Z m ) is shown in Figure 7 (the solid circles). z,*, v, and yT(Zm*)/IVTOare shown in Table 3. Here YTOis the total potential minimum of the single surface. The contribution by the image interaction is 23% of the total molecular potential. The image potential widens the potential depth and provides clear double minima. Introduction of the image interaction is essentially important near the potential minimum. The presence of the deep potential minima due to combination of the LJ interaction and image interaction should give rise to observed significant adsorption even in the lowpressure region. If we compare the experimental adsorption energy for SO2 on NPC and ACF at the coverage where both the strong interaction of the dipole with the local surface electric field and the lateral interaction can be neglected, availability of this potential model can be examined. The q d for NPC at 8 = 0.2 and that for ACF at 4 = 0.4 are fit for such a comparison. The ratio of q d for ACF to that for NPC is 1.4, which agrees well with the theoretical value (1.40). However, strictly speaking, the calculated energy is not the partial molar energy, but the molar energy, and then the above comparison cannot rigorously be made. Here, we presumed that a equals zero upon calculation of the image potential. Of course, a can be changeable depending on the orientation of the SO2 molecular against the surface. However, the contribution of the image potential to
Figure 8. Two-dimensional dipole orientational assembly structure of SO2 molecules in an ACF micropore: (a) parallel orientation and (b) antiparallel orientation. the total potential energy is significant (23%), and we assume that the SO2 molecule has the most favorable ocientation of a = 0. Thus the molecular potential approach describes micropore filling for SO2 in the medium fractional filling range from the energy aspect. Molecular States of an Adsorbed SOz in a Micropore. The molecular potential profile indicates molecular states of an adsorbed S02. In the case of the 10-4-3 potential profile, the region having negative potential is in the breadth of 0.28 nm and the double minima are more than 4 times kT. The molecular center of SO2 must be restricted in this range of 0.28 nm. As the molecular diameter from viscosity experiment (0.541 nm) is often too great for analysis of adsorption, we suppose the molecular diameter of 0.48 nm from the liquid density because of good applicability of the Gurvitch rule. In any case SO2 molecules cannot form the close-packing bilayer in this micropore. SO2 molecules should form a zigzag single-layer structure even at the highest fractional filling. Figure 8 shows the packing model of SO2 in the potential minimum. In this case SO2 molecules can move slightly between the micropore walls due to a considerably flat potential depth between the pore walls. The adsorption can be regarded as an incomplete monolayer adsorption process of high heat of adsorption. Consequently, the molecular motional state of the adsorbed SO2 should vary with the fractional filling. In the following discussion, the molecular state of the adsorbed SO2 will be analyzed from the relationship between the adsorption entropy and motional mode. Although SO2 molecules are not adsorbed on the flat surface but in the micropore, the theoretical approach on adsorption entropy by Ross and Olivier3' is extended to the slit-shaped pore. For a mobile monolayer filling (abbreviated as MF), the adsorption entropy ASM is the sum of average entropy at a standard state, AS,, and the entropy of congregation, ASc:
AS, = AS,
+ ASc
(13)
The entropy of congregation depends on the type of twodimensional gas equation. If an adsorbed gas behaves as a twodimensional van der Waals gas, the differential adsorption entropy, tSdM, is given by eq 14:
For a localized monolayer filling (abbreviated as LF), the adsorption entropy is the sum of AS, and the configuration entropy. The final form of the corresponding differential adsorption entropy, tSdL, is expressed by eq 15:
,s,L = AS,
+ ( m ) In(1 - e) - R ln[B(i - e,)/e,(i
-
e)] (15)
In eqs 14 and 15, 8, is the standard state of the adsorbed film
Dipole Oriented States of SO2
J. Phys. Chem., Vol. 99, No. 45, 1995 16719
and equal to 0.5 in general. The standard state of gas is chosen as the adsorption temperature (T = 303 K in this case) and the saturated vapor pressure (Po = 3.065 x lo8 Pa at T = 303 K for Sod. The change of average adsorption entropy at the standard state, ASo, includes the change in the translational entropy, AS$, and the rotational entropy, ASorot,as well as the vibrational entropy, Sovib:
+ AS': + SoVib
ASo = AS:
AS,", ASZot,and SoVlb are given by statistical thermodynamics as Translational Entropy. The translational entropy is given by eq 17:49 S", = R 1nCf'lN)
+ RT(a lnf'lar) + R
(17)
Here N is the number of particles a n d p is the molecular partition function of translation. p' is expressed by eq 18 for an n-dimensional space:
f'= (2nmk7)3/2Z"/h"( h is the Planck constant)
(18)
For SO2 molecules having saturated vapor pressure at 303 K, eq 18 becomes
f
= (2nmkn3"V/h3
(19)
and for the two-dimensional SO2 molecules in ACF micropores, eq 18 becomes .f = (2nmkT)asN/h2
(20)
In eq 20, a, i s defined by eq 21 after the law50 Os
=
- uoNa&)/Nads
(e = eo)
(21)
where a(N2) is the specific surface area from N2 adsorption, Nads is the number of adsorbed molecules, and a, is the molecular cross-sectional area of S02. Thus A S 2 can be calculated by subtraction of gFfrom ,Fin the MF model, which gives eq 22:
AS," = -275.8 - R In a, (J mol-' K-')
(22)
Rotational and Vibrational Entropies. The rotational entropy, Sot,and vibrational entropy, Fib,are obtained from the rotational partition function ptand vibrational one p i b , respectively, from eq 23:49 Srot.vib
= R lnfot,vib
+R
T ( ~I n f o t , v i b l a r )
(23)
SO2 has three moments of inertia and thereby the rotational partition function of SO2 gas is given by eq 24:
where ZA = 1.383 x kg m2, ZB = 8.135 x kg m2, x kg m2,52and s is the symmetrical number (s = 2 for S 0 2 ) . SO2 can lose one of its rotational degree of freedom in the adsorbed phase and the corresponding rotational partition function becomes
ZC = 9.52
afOt = (Z,Z2)'"(8dkT/sh2)
(25)
From eqs 23 and 24, the rotational entropy of an SO2 gas, $Ot, and that of an adsorbed S 0 2 , ,Srot, are described by eqs 26 and 21 :
9"'= R h[(ZAZBZC)1/2/s] 4- (3/2)RIn T
g
,Slot = (R/2)In (Z&
+ 1320.8
+ R In T + 871.6
(26) (27)
The mobile adsorbed film retains the rotational entropy of gas and ASorot= 0, whereas the localized film loses three rotational motions and ASorot= -$Ot. Considering a mobile film in the micropores, it loses one rotational motion with replacement of one vibrational one, and then ASZO' = - gSo'. The vibrational partition function of adsorbed SO2 varies with the adsorbed model. In a mobile film on the flat surface, the SO2 molecule has a vibrational mode normal to the surface and the partition function is given by eq 28: fib
= 1/(1 - e-kv/k7)
(28)
Considering a mobile film in the ACF micropore in which one more vibrational mode parallel to the pore wall replaces one rotational one, fib
= 1/(1 - e-"/kZJ2
(29)
Where v is calculated from the potential curve of micropore field. In a localized film, the vibrational mode parallel to the surface ( V I I ) is additive with one noimal mode (vl). On a simplification of YII = V I = v, we get: fib
= 1/(1 - e-'"/kq3
(30)
Therefore, Sovib for each model is calculated by eqs 23, 28, 29, and 30. Motional Modes of SO2 Filled in the Micropore. We calculated the adsorbed entropy for three models of SO2 adsorbed in the micropore, that is, the mobile film (MF), localized film (LF), and monolayer micropore filling (MMF) models. The mobile film (MF) has two translational degrees of freedom, three rotational degrees of freedom, and one vibrational degree of freedom. The localized film (LF) mechanism has three vibrational and one rotational degrees of freedom without any translational ones. The monolayer micropore filling (MMF) mechanism has two translational, one rotational, two hindered rotational, and one vibrational degrees of freedom. Here two hindered rotational modes were approximated by one rotational and one vibrational mode. Then, the MMF model has two translational, two rotational, and two vibrational degrees of freedom. The degree of freedom of adsorbed SO2 and the calculated AS$, ASZot, Sovib,and ASo are listed in Table 4. T, R, and V in Table 4 represent translation, rotation, and vibration, respectively, and the prepositional figure denotes the degree of freedom. The adsorption entropy changes with 4 of the above three models were calculated, which are shown in Figure 6b. The MMF model can express well the adsorption entropy change at the B stage. The molecular picture of micropore filling for SO2 is fit for the packing model (Figure 8) anticipated from the molecular potential profile. The adsorption entropies at the stages A and C are much smaller than those for the MMF model. The low adsorption entropy at the A stage supports the localized model that SO2 is strongly adsorbed on the surface functional groups. The adsorption entropy drop at the C stage is not attributed to the localized mode but is attributed to formation of the following organized SO:!molecular aggregates. Formation of a Dipole-Oriented Single Layer. The steep increase of q d and great loss of s d above 4 = 0.6 are ascribed to the lateral interaction and/or a two-dimensional molecular aggregate formation. The lateral interaction of SO2 is given
Wang and Kaneko
16720 J. Phys. Chem., Vol. 99,No. 45,1995
TABLE 4: Entropy Change of SO2 with Adsorption for Three Models (J mol-' K-I) model degree of freedom"
AS$ AS,'"' So"'b
Aso a
MF 2T, 3R, 1V -8 1.4 0 21.6 x 1 -59.8
LF
OT, lR, 3V - 149.9
-72.8 21.6 x 3 -157.9
MMF 2T, 2R, 2V -81.4 -36.4' (-28.3)' 21.6 x 2 -74.6' (-66.5')
'
T, translation; R, rotation; V, vibration. Without IC. Without IA. ,'
IC
by the Lennard-Jones interaction (Y(LJ))and the dipole-dipole interaction ( Y b - p ) ) by using the Stockmayer potential:
Here cff = 252 K and off= 0.429 nm are the Lennard-Jones parameters for S0238 a n d p ~= p2 = p = 1.61 D, g(8l,&,7/Il$~2) is the angle-dependence of the dipole-dipole interaction described by eq 32. g(~19%V,-V2) =
2 COS el COS O2 - sin 8, sin 8, cos(q2 - ql) (32) Here 81 and 02 are the angles of the dipole moments of molecule 1 and molecule 2 to the axis directed from molecule 1 to molecule 2, respectively, and then 7/12 - 7/Il is the shadow angle of the dipole moments of molecule 1 and molecule 2 in the plane perpendicular to the axis directed from molecule 1 to molecule 2. Because contribution of the polar interaction to the total interaction of SO2 to the carbon walls (Y(SO2-C)) is near one-quarter when the dipole moment of adsorbed SO2 is in a direction normal to the carbon surface, we think that SO2 molecules are arranged preferentially with their dipole moments normal to the surface where the Y(SO2-C) is dominant. Thus = 62 = x/2; adjacent SO:! molecules can be parallel (742 7/11 = 0) or antiparallel (7/I2 - 7/I1 = x), which leads to a minus or plus contribution of Yb-p) to Y(S02-S02), respectively. Thus eq 31 becomes: Y(SO2-S0,)
7
500
'
0
1
/ I
I
02
0.4
0.6
08
1
P
Figure 9. Relationships between YIltotal of a SO:, molecule and the
I IB
;
2'ooo
=
~ ( S 0 2 - S 0 2= )
In eq 12, we described the total potential profile, Y T ( z ~of ), interaction between SO2 molecules and carbon walls, which does not include the intermolecular interaction of SO;?. The total potential of an adsorbed SO2 in a micropore should be the summation of VI&,) and the intermolecular interaction of S 0 2 , Y(SO2-SO2). However, Y?,,(z,) is lost when SO;?molecules are arranged in the antiparallel orientation because of semiconductivity of the graphitic pore walls. Therefore, the total potential of an adsorbed SO;?molecule in a micropore can be written
fractional filling q5 for parallel and antiparallel dipole orientation: 0, parallel and, 0 , antiparallel.
Here Y(SO2-SO2) per one molecule is used in eqs 35 and 36. We can calculate the average intermolecular distance from the amount of adsorbed SO2 in the micropore space of Wo(N2) at a certain 4, and thereby Y(SO2-SO2) and Ytotal can be obtained from eqs 33-36. In Figure 9, we show the change of Ytota1 as a function of 4. The parallel arrangement of adsorbed SO2 molecules is evidently preferential below 4 = 0.6. In the parallel case, Y(SO2-SO2) has little contribution to Ytotal; Ytotal is almost constant below 4 = 0.6, which agrees with the constant q d region of B. On the other hand, antiparallel arrangement of adsorbed SO2 molecules, which contains a strong intermolecular interaction of adsorbed Son,becomes dominant when exceeds 0.6. Thus, filling of polar SO2 in confined spaces of micropores even at a subambient gas pressure will accompany a twodimensional phase transition from the monolayer micropore filling (MMF) state to the organized one. Unlike the ordinary two-dimensional gas-solid transition of Kr, N:!, CH4, etc. on graphite, which is actively investigated in the recent the dipole moment of SO2 plays an important role in the phase transition of adsorbed SO2 in a carbon micropore. The reason why the theoretical potential change upon the phase transition near = 0.6 is less steep than the observed one should be found by the evaluation of the intermolecular distance. Although we presume the uniform distribution of SO2 molecules in the micropore, they must gather to change the organized state in the real system. This result offers an interesting topic in molecular science. Anyhow, the dipole moment has an evident connection with the adsorption of polar molecules in micropores, which should be highly valued in future research on the micropore filling mechanism for polar molecules.
Conclusions The SO2 adsorption isotherms of nonpolar carbon black (NPC) and activated carbon fiber (ACF) having micropores of 0.75 nm in width are type I11 and I, respectively. The marked adsorption of SO2 by ACF at a low relative pressure is ascribed both to the overlapped Lennard-Jones-type interaction between SO2 and the graphitic micropore walls and to the permanent dipole-induced dipole interaction. The adsorption energy, entropy of adsorption, and potential calculation suggest the presence of the SO2 dipole orientational phase transition in a single adsorbed layer confined by the slit-shaped micropore. Below the fractional filling of 0.6, SO2 molecules have the dipole-parallel orientated structure due to the greater dipoleinduced dipole interaction than the intermolecular interaction. On the other hand, the increase in the SO2-SO2 interaction with
Dipole Oriented States of SO2 adsorption leads to the two-dimensional phase transition from the dipole-parallel-orientated phase to the dipole-antiparalleloriented one at the fractional filling of 0.6.
Acknowledgment. We are indebted to Dr. S . Hagiwara (Tokyo Rico Co.) for assistance with the calorimetric equipment. Prof. T. Tsutsumi and Dr. A. Matsumoto are also grateful for useful discussions. Prof. W. A. Steele gave valuable comments on this paper. Financial support by the Science Research Grant from the Ministry of Education, Japanese Government, is greatly appreciated. References and Notes (1) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A,; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (2) Imai. J.: Souma. M.: Ozeki. S.: Suzuki. T.: Kaneko. K. J . Phvs. Chem. 1991, 95, 9955. (3) Dubinin, M. M. Ouart. Rev. Chem. SOC.1955, 9, 101. (4) Dubinin, M. M. Chem. Rev. 1960, 60, 235. (5) Freeman, E. M.; Siemieniewska, T.; Marsh, H.; Rand, B. Carbon 1970, 8, 7. (6) Everett, D. H.; Powl, J. C. J . Chem. Soc., Faraday Trans. I1976, 72, 619. (7) Gregg, S. J.; Sing, K. S. W. Adsorption, Surjiace Area and Porosiv, 2nd ed.; Academic: London, 1982; Chapter 4. (8) McEnaney, B. Carbon 1988, 26, 267. (9) Jaroniec, M.; Gilpin, R. K.; Kaneko, K.; Choma, J. Langmuir 1991, 7, 2719. (10) Stoeckli, F.; Huguenin, D. J . Chem. Soc., Faraday Trans. 1992, 88, 737. (1 1) Rodriguez-Reinoso, F.; Molina-Sabio, M.; Munecas, M. A. J . Phys. Chem. 1992, 30, 593. (12) Dubinin, M. M. Carbon 1981, 19, 321. (13) Marsh, H. Carbon 1987, 25, 49. (14) Stoeckli, H. F. Carbon 1981, 19, 325. (15) Kakei. K.: Ozeki. S.: Suzuki.T.: Kaneko. K. J. Chem. Soc.. Faraday Trans. 1990, 86, 361. (16) Kaneko. K.: Ishii. C.: Ruike. M.: Kuwabara, H. Carbon 1992,30, 1075. (17) Nicolson, D. In Characterization of Porous Solids II; RodriguezReinoso, F., Ed.; Elsevier: Amsterdam, 1991; p 11. (18) Seaton, N. A.; Walton, J. R. P.; Quirke, N. Carbon 1989, 27, 853. (19) Atkinson, D.; Carrott, P. J. M.; Grillet, Y.; Rouquerol, J.; Sing, K. S. W. In Fundamentals of Adsorption; Liapis, A. I., Ed.; Engineering Foundation: New York, 1987; p 89. (20) Thamm, H. J . Phys. Chem. 1988, 92, 193. (21) Tsutsumi, K.; Mizoe, K. Colloids Sut$ 1989, 37, 29. (22) Denoyol, R.; Femandez-Colinas, J.; Grillet, Y.; Rouquerol, J. Langmuir 1993, 9, 515.
J. Phys. Chem., Vol. 99,No. 45, 1995 16721 (23) Alvarez, M. R.; Torralvo, M. J.; Grillet, Y.; Rouquerol, J. J . T h e m 1 Anal. 1992, 38, 603. (24) Kaneko, K.; Shimizu, K.; Suzuki, T. J . Chem. Phys. 1992,97,8705. (25) Kuwabara, H.; Suzuki, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1991, 87, 1915. (26) Setoyama, N.; Ruike, M.; Kasu, T.; Suzuki, T.; Kaneko, K. Langmuir 1993, 9, 2612. (27) Sato, M.; Sukegawa, T.; Suzuki, T.; Hagiwara, S.; Kaneko, K. Chem. Phys. Lett. 1991, No. 6, 526. (28) Suzuki, T.; Takahiro, K.; Kaneko, K. Chem. Phys. Lett. 1992, 191, 569. (29) Ruike, M.; Kasu, M.; Setoyama, N.; Suzuki, T.; Kaneko, K. J . Phjs. Chem. 1994, 98, 9594. (30) Hill, T. L. Adv. Catal. 1952, 4, 211. (31) Beebe, R. A.; Dell, R. M. J . Phys. Chem. 1955, 59, 746. (32) Fukasawa, J.; Kaneko, K.; Poon, C-D.; Samulski, E. T. In Characterization of Porous Solids Ill; Elsevier: Amsterdam, 1994; p 31 1. (33) Young, D. M.; Crowell, A. D. The Physical Adsorption of Gases; Butterworth: London, 1962; Chapter 9. (34) Chessick, J. J.; Zettlemoyer, Adv. Catal. 1959, 11, 263. (35) Haiendatsuryu; Maruzen: Tokyo, 1973. (36) Rouquerol, F.; Rouquerol, J.; Della Gatta, G.; Letoquart, C. Thermochim. Acta 1980, 39, 151. (37) Ross, S.; Olivier, J. P. On Physical Adsorption; Interscience: New York, 1964. (38) Hirschfelder, J. 0.;Curtis, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley and Sons: New York, 1964. (39) Crowell, A. D. J . Phys. Chem. 1968, 49, 892. (40) Imai, J.; Kaneko, K. Langmuir 1991, 8, 1695. (41) Sokolic, F.; Guissani, Y.; Guillot, B. J . Phys. Chem. 1985, 89, 3023. (42) Steele, W. A. Surf. Sci. 1973, 36, 317. (43) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (44) Cracknell, R. F.; Gordon, P.; Gubbins, K. E. J . Phys. Chem. 1993, 97, 494. (45) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1992, 47, 1569. (46) Zhang, S.-Y.; Talu, 0.; Hayhurst, D. T. J . Phys. Chem. 1991, 95, 1722. (47) Everett, D. H. Proc. Chem. SOC. 1957, 38. (48) McCafferty, E.; Zettlemoyer, A. C. J. Colloid Interjiace Sci. 1970, 34, 452. (49) Smith, N. 0. Elementary Statistical Thermodynamics - A Problem Approach; Plenum Press: New York, 1982. (50) Law, J. T. J. Phys. Chem. 1955, 59, 67. (51) Stull, D. R.; Prophet, H. JANEF Thermodynamical Tables, 2nd ed.; Japanese Publication; Horietsu Kenkyusho: Tokyo, 1975; p 1046. (52) Ordering in Two Dimensions; Sinha, S., Eds.; North Holland: New York, 1980. (53) Steele, W. A.; Vemov, A. V.; Tildesley, D. J. Carbon 1987,25, 7. (54) Morishige, K. J. Chem. Phys. 1992, 97, 2084. JP95 15489
