J . Phys. Chem. 1984, 88, 1735-1740 and 8) for vll(aZu)and vl(alg). Since the irreducible representation a2ucorrelates with a l if the symmetry is lowered to C,,, which would be the case if the benzene were lying flat on the surface and not interacting strongly with the sodium, mode 11 as well as mode 1 is predicted to accompany the charge-transfer transition. Furthermore, modes 1 and 11 are the only modes that exhibit the long-wavelength excitation maximum. The result that remains to be accounted for by this analysis is the lack of e2gmode participation in the charge-transfer enhancement mechanism. One possibility is that the cross sections for the eZgmodes are simply much smaller than those for the elg modes. In fact, the observed shape resonances of gas-phase benzene are dominated by the 992-cm-I alg mode, although the ezgmode, Vs, does appear with measurable i n t e n ~ i t y .However, ~ ~ ~ ~ ~we observe no evidence of the charge-transfer contribution to the SER scattering of vg(ezP). This line is a doublet produced by Fermi resonance of vs and vl(alg) v6(eZg). Therefore, one might expect to see at least a small indication of the charge-transfer mechanism due to the admixture of Y,, even if vs by itself were not strongly active. Since we observe no indication of charge-transfer activity for us, we find it more likely that there is a cancellation of scattering due to our assumed orientation of benzene, Le., lying flat on the sodium surface.
+
Conclusions We have observed surface-enhanced Raman spectra of benzene on vapor-deposited sodium surfaces at 15 K. Our best estimate of the enhancement factor is about lo4, making sodium an only slightly less favorable SER substrate than silver, as has been p r e d i ~ t e d . ~The ~ spectra exhibit marked mode selective enhancement but almost no vibrational energy perturbation. The ( 5 5 ) R. Ruppin, Solid State Commun., 39, 903 (1981).
1735
modes that show the greatest enhancement are all out-of-plane vibrations. We therefore conclude that the large majority of SER activity arises from benzene molecules that are in the first monolayer next to the sodium surface and lying flat. A very weak interaction of these molecules with the surfaces results in a local site symmetry of C6".Modes 1 (al,) and 11 (az,) have nearly identical excitation profiles with rapidly rising intensity above 700 nm, which we interpret as being associated with a metal/molecule electronic charge-transfer contribution to the over11 SER intensity above 700 nm. The SER activity at shorter excitation wavelengths is explained by a mechanism that involves modulation of the surface dipole moment by the vibrating benzene molecules but does not require a reduction in symmetry to C,, or lower. The selective enhancement of the out-of-plane vibrations implies that the benzene is lying flat on the surface. In summary, we have reported the observation of SERS of benzene on a vapor-deposited sodium surface and have presented evidence for two different mechanisms of enhancement of the Raman spectra. These are differentiated by their excitation wavelength dependence and identified by comparison of their predicted selection rules and the observed mode selective enhancement. Additional experiments with lower symmetry substrates will be useful in further distinguishing the chemical and classical electromagnetic contributions to SERS.
Acknowledgment. P.A.L. gratefully acknowledges support from a National Research Council/Naval Research Laboratory Research Associateship. We also acknowledge helpful discussions of our work with Professor M. Moskovits, University of Toronto, and Drs. D. Ladouceur and D. DiLella of NRL. Registry No. Benzene, 71-43-2; sodium, 7440-23-5.
Sorption of Argon, Oxygen, Nitrogen, Nitric Oxide, and Carbon Monoxide by Magnesium, Calcium, and Barium Mordenites Shozo Furuyama* and Michiko Nagato Department of Chemistry, Faculty of Science, Okayama Uniuersity, Okayama 700, Japan (Received: March 9, 1983)
Sorption experiments over a temperature range of -50 to 150 OC find sorption affinities in the order Ar < O2 Ca-M > Mg-M, irrespective of the kind of gas, and are smaller than the corresponding values for alkali mordenite~.~,~ It is understood that the motion of the sorbed molecule is more restricted in the alkaline-earth mordenites than the alkali mordenite~.~?' To elucidate the dynamic behavior of the sorbed molecule, we calculate the value of jtherm for the mobile mobel and for the localized model, and compare it with the experimental value as follows.
I
I
0.1
I
0.2
0.1
I
0.2
I
0.1
1
0.2
e Figure 3. qstvs. 0 plot.
As already described in the preceding papers, .?therm is divided into the entropies of the electronic state (SO,), translation (sot), rotation (so,), oscillation (soosc), and vibration (Sovib). Among these entropies, so,ib is nearly zero, irrespective of the kind of sorbate. The so, is zero for Ar, N,, and CO while it is R In 2
1738 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
51
54
' i.8
,
5.4
I
,
5.8
I
5.4
,
Furuyama and Nagato
,
5.8
In(T/ K ) Figure 4. Stherm/Rvs. In T plot.
and R In 3 for NO and 02.The values of sot, soI,and soo,, are calculated from eq 5-7, if the sorbed molecule translates onesot(one-dim.)/R = 0.5 In T + 0.5
0 .1 y/nm Figure 5. Dependency of the ED ER values on the position, kind of mordenite, and a values, calculated along the Y coordinate at X = 2 = 0 (see Figure 1). Values of 1030a,/m3 used for calculations of a-c are 1.65, 2.24, and 3.88, respectively.
dimensionally with free rotation and two-dimensional oscillation in the mordenite channels (ideal mobile m ~ d e l ) . ~Here , ~ k , h, and T denote the Boltzmann constant, the Planck constant, and the sorption temperature, and m,I , u, and vi are the molecular weight, the moment of inertia, the symmetry of rotation, and the frequency of oscillation, respectively, of the sorbate; d,ffis the difference of the 2 coordinate of two neighboring sorbed molecules at saturation and depends on the kind of sorbate and on the sorption temperature. However, since it is difficult to determine the deffvalue accurately, we assumed it to be 0.35 nm (Le., c / 2 ) , irrespective of the kind of sorbate and the sorption temperature in the present study. Using eq 5, we obtained the value 3.4 for the sot(one-dim.)/R for each kind of sorbate at 300 K. Similarly, we obtained the value of soI(free rot.)/R = 5.6 for CO and NO, and 4.9 for O2 and N2 at 300 K. The sum of the above values does not exceed the value of Stherm/R(see Table I) - soe/R, except for the sorptions of N2 and C O (and probably NO, too) by Mg-M. For the latter cases this means that the value of soo,,(two-dim.)/R is less than zero. The assumption that the sorbed molecule behaves like a one-dimensional gas is, therefore, not necessarily invalid, except for the sorptions of N1, (probably NO, too) and CO by Mg-M. The mobile model is also consistent with the plot of Stherm/R vs. In T shown in Figure 4. Figure 4 shows that the slope of the plot falls around 3.5 for any sorption of the diatomic gases and is nearly 2.5 for Ar. These values coincide with the sum of the coefficients of the In T terms in eq 5-7. In the cases of the sorption of N2,NO, and CO by Mg-M, the sorbed gas may be in a state of hindered rotation. If this is the case, the slope of the Stherm/Rvs. In T plot should deviate from 3.5, although we cannot estimate its magnitude quantitatively at this time. As described above, the mobile model appears to work well. However, we should check the probability of the localized model. As described earlier, ftherm(localized) = Stherm(mobile) under the present experimental conditions. Therefore, we can find the values 7- 15 at 300 K for Sther,(lOcalized)/R in Table I. Since Stherm(1ocalized)lR is equivalent to sO,(three-dirn.)/R = 3 In ( k T / h t ) + 3, we obtain the values 60-5 cm-' for t/c. Here 'v3 is v1vzv3 and c is the velocity of light. The t / c value suggests that the sorbed molecule is not strictly localized at the specific sorption site but may migrate from site to site. We conclude, from the analysis of the Sther",, that the mobile model is more plausible than the localized model.
Results and Calculation Energies of Dispersion and Repulsion. The isosteric heat of physisorption can be divided into the following five terms:
+ In deff+ 0.5 In ( 2 r m k / h 2 ) (5) (6) so,(free rot.)/R = In T + 1 + In (8r2kZ/h2a) soo,,(two-dim.)/R = 2 In T + 2 + In ( k 2 / h 2 v i v 2 ) (7)
-.l
+
qst = -(ED+ E R ) + ( ~ @ / 2 )- ( P F )- ( Q P / 2 ) (8) where ED and ER are the energies of dispersion and repulsion. a, p, Q, F , and F denote polarizability, electric dipole moment, molecular quadrupole moment, and strength and gradient of the electrostatic field, respectively. ( ) denotes the effective value of each interaction. First we calculate the value of ED ER by using eq 9. Here ri is the distance between the sorbed molecule(s) and
+
ED + ER = - E ( p s i / r ? ) + Z(Asi/ri12) (9) the ith ion (i) of the mordenite. bsiand A,, are constants obtained from eq 10 and 1 l.14,15 According to Takaishi and Hosoi, values psi
= (pssKJ1'2
(10)
+
~ s 1 1 / 1 3 = ( ~ ~ ~ 1 1 1 3xii1/13)/2
(11) for bAAand AM are given by eq 12 and 13.16 Three values have bAA = (5.95 x 10-58)aA1.88/(k~al mol-' m6) (12) AAA = (4.91 x 10-''5)~~3"0/(kCal mol-' m12)
(13) been given for the a value of the oxygen anion, aox.They are 3.88 X m3 by Pading,'' 2.24 X m3 by Takaishi et a1.,16and m3 by Barrer and Petersona2 The values of a for 1.65 X the Mg, Ca, Ba, and Si cations have been evaluated as 0.1 X 0.6 X 1.69 X and 0.04 X m3, respectively.'8 we Since the value of asiis much smaller than the value of aox, may safely ignore the contribution from the Si cation to ED ER. The value of ED ER was calculated at various positions in the mordenite channel by summing up the contributions from the oxygen anions and alkaline-earth cations contained in the 63 (3 X 3 X 7) unit cells surrounding the origin. To simplify the calculation, we made the following assumptions: (1) The structure of the Si-0 framework of the alkaline-earth mordenites is identical with that of RbM.19,20 (2) All the alkaline-earth cations, except
+
+
(14) Kihara, T. "Bunshikan Ryoku (Intermolecular Forces)"; Iwanami Book Co.: Tokyo, 1976; p 102. (15) King, C. L. J . Chem. Phys. 1973, 59, 2464. (16) Takaishi, T.; Hosoi, H.J . Phys. Chem. 1982, 86, 2089. (1 7) Pauling, L. Proc. R . SOC.London, Ser. A 1927, 114, 181. (1 8) Japanese Chemical Society, Ed. "Kagaku Binran"; Maruzen: Tokyo, 1966; p
1266.
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1739
Sorption by Mordenites TABLE 11: Values of Various Kinds of Interaction Energies at the Most Accessible Position, qst(calcd), and qst(exptl), for Ar, 0,, N,, NO, and CO Sorbed by Ba-M, Ca-M, and Mg-Mg Ar 3.5 2.7 0
0,
N,
3.3
3.7
Ba-M 2.6 2.9
NO
CO
3.6
4.1 3.3 0.8 6.5 14.7 6.7 9.2 9.3
0
0
6.2 5.6e 4.8 5.6
1.7 7.6 5.3 5.6 5.7
5.1 11.7 6.0 7.5e 7.5
2.8 1.1 5.3 12.8 5.8 8.0 7.8
5.7 0 0 9.2 6.3@ 9.2 6.2 6.3
Ca-M 5.5 6.2 0 0 2.2 6.7 11.0 16.6 6.0 6.7 8.8 9.9e 7.0 9.9e 6.4 9.9
6.1 1.6 6.9 18.2 6.4 9.7 10.6 9-10
7.0 1.1 8.4 20.6 7.5 11.1 12.0 12.1
12.3 2.3 9.6 27.8 7.5 10.5 11.3
14.2 1.6 11.7 31.6 8.6 12.9 12.9 13.8
0
11.7 0 -QFy12 0 cl.+(calcdhb 15.2 q,i(calcd);IC 7.3e,f 10.0 q s t ( c a l c d ) ~ ~ ~ d7.2 4st (exp tl) (5.7)
Mg-M 11.2 12.6 0 0 3.1 9.3 17.6 25.6 6.9 7.7 9.6 10.7e 7.9 10.7e 7.4 10.7
f"
OS4t
Y/ nm 0 0.1 I I
-0.1
-0.2 I
I
0.2 II
a
0.78 0.48
0.49 1 0.48
0.32 0.56 0.42
Space factor (see text). Value for model I = -(ED t E R ) + & , * / 2 - fiFY - Q F y / 2 at the most accessible position. Value for model I1 = -(ED + E n ) + f ( a F y 2 / 2 ) . Value for model I11 = -EDt E n ) t f(&,,'/2 - pF, - QF,/2. e Standard value (see text). Since the 4st value of Ar for Mg-M is not reliable, we adopted arbitrarily 7.3 kcal mol-' as the standard value. g All values in kcal mol-', except those forf, which is unitless.
for the cations located at position IV and directly confronting the sorbed molecule, exist halfway between positions I1 and IV (marked by X in Figure 1 ) . As an example, values of E D + ER for Ar-Mg-M calculated at positions on the line Yare shown in Figure 5. The figure shows that the values become 3.5, 4.7, and 6.8 kcal mol-' when 1030 aox/m3is assumed to be 1.65, 2.24, and 3.88, respectively. To determine which a value is valid, we calculated the value of ED ER for Ar as functions of the size, type, and position of the metal cation. Figure 5 shows that the value is almost independent of those factors. Since the value of -( ED + ER) should be smaller than the value of qst for Cs-M, =3.9 kcal mol-' (ref 7 ; see eq 8 ) , it is concluded that the value of 1.65 X m3 is the only one acceptable for the aoXvalue for the mordenite. (However, it is pointed out in ref 10 that the aoxvalue for the more siliceous zeolite m3.) Values H-ZSM-5 should be much lower than 1.65 X E R ) for other gases are summarized in Table 11. of -(ED Strength and Gradient of the Electrostatic Field. Values of F and F in the T ( T = x, y , or z ) direction are calculated by eq 14 and 1 5 , where ei is the electric charge of the ith ion. Recent
+
+
F, = dx(ei/ri)/dq = - x e i q / r i 3
(14)
F, = dF,/dT = -Cei(rt - 3 q 2 ) / r i 5
(15)
C N D O calculations have suggested that the effective electric charges of oxygen and T (Le., Si or Al) ions in zeolites are nearly (19) (a) Mortier, W. J.; Pluth, J. J.; Smith, J. V. Muter. Res. Bull. 1975, 10, 1037. (b) Ibid. 1976, 11, 115. (20) Schlenker, J. L.; Pluth, J. J.; Smith, J. V. Muter. Res. Bull. 1978, 13, 77. (21) Furuyama, S.; Inoue, H. J . Phys. Chew. 1983, 87, 1529.
0.2
I
I
I
0.3
0.4
0.5
4-0.4
Y)nm Figure 6. Changes of F, and pTwith Y a t X = 2 = 0. Y'= Y +0.371. Positions on the Ycoordinate intersected by the lines marked with Mgz+, etc., are the most accessible ones for sorbed molecules in each mordenite.
one-third of the formal charges (Le., 2-, 4+, and 3+).22*23 The values for the alkaline-earth metal cations are not definite. However, our recent studies on gas sorption by a series of alkali mordenites7 and the sorption of H2 by Na-M2' have suggested that the effective electric charge of an alkaline-earth metal cation may not be far from the formal charge = 2+. Therefore, we adopted the values of 2e, -0.667e, and 1.23e ( e = 1.602 X C) as the effective electric charges of M(II), oxygen, and T ions in the present calculation. Substituting the values of ei and ri for the ions in the 6 3 unit cells surrounding the origin, we computed the values of F, and F, at various positions in the M(I1)-M channel. As an example, the values at the positions on line Y are plotted in Figure 6 . The general features of the F, and F, vs. Y plots for the M(11)-M are quite similar to those for the M(1)-M which are depicted in ref 7 and 21. One significant difference is that the alkaline-earth cations can produce much stronger F, and F, than the alkali cations do, because of their larger electric charges. The larger F, and F, values yield a larger qst value for Ba-M than Li-M, even though the radius of Ba2+is larger than that of Li+. Using the values of a , p, and Q summarized in Table I, we calculated the values of aF;/2, pFy, and QFJ2 at the position of their van der Waals contact = r M ( I I+) . rsorb(Le., the most accessible position). Here r M ( I is I )the radius of the alkaline-earth cation and rsorbis the van der Waals radius of the sorbate which is approximated as 0.20 nm for all the sorbates in the present study. The results are summarized in Table 11. Discussion The analysis of the values of the Ither,,, has suggested that the sorbed molecule is not localized at a specific sorption site but translates one-dimensionally in the alkaline-earth mordenite channels. To check the validity of this conclusion (and to obtain (22) Beran, S.; Dusky, J. J . Phys. Chem. 1979, 83, 2538. (23) Mortier, W. J.; Geerlings, P.; Van Alsenoy, C.; Figeys, H. P. J . Phys. Chem. 1979, 83, 855.
1740 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
Furuyama and Nagato TABLE 111: Values of qst(calcd)a and qst(exptl) for Various Gases Sorbed by Alkali Mordenitesb N,
NO
CO
7.4‘ 7.4
7.8 7.5
9.0 9.8
6.6
6.9 6.7
8.0 8.2
K-M 3.8 4.2
5.2‘ 5.2
5.3 5.4
6.1 6.0
CS-M 3.7 4.1
4.7‘ 4.7
4.7 5.0
5.4 5.2
Ar
0,
qst(calcd) qst(exptl)
4.4 4.8
Li-M 5.0 5.0
q,t(calcd) qst(exptl)
3.9 4.3
Na-M 4.1 4.5
qst(calcd) qst(exptl)
3.6 4.0
qd(ca1cd) qst(exptl)
3.5 3.9
s‘
a -(ED + ER) f f ( a F y 2 / 2- MLF, - QbS/2);fis the space factor (see text) and is 0.54, 0.76. 0.60, and 0.60 for Li-M, Na-M, K-hf, and Cs-M, respectively. All values in kcal mol-’. Standard value (see text).
‘
Figure 7. Schematic representation of a sorbed molecule translating one-dimensionally with periodically regulated free rotation in the mordenite channels. mand-indicate the electric dipole and quadrupole in a molecule, respectively. {gdenotes a vacant position.
a more precise picture of the dynamic behavior of the sorbed molecule), we will calculate the value of qst from the values of ED, etc., and compare it with the q,,(exptl) value. First we calculate the qstvalue for the localized model (model I) where the sorbed molecule is fixed at the most accessible position with the most favorable molecular orientation. The simple summation of the values of -(ED ER), etc., obtained at the most accessible position is much larger than the q,,(exptl) value (see Table 11). Thus, the localized model is ruled out from the analysis of q s t , too. Next we calculate the qst value for the ideal mobile model (model 11). In this model, the sorbed molecule translates through the electrostatic field having various strengths and gradients of different signs, so that both the ( p F ) and ( Q F / 2 ) terms should be zero. Therefore, q,,(calcd) is expressed as -(ED E R ) f(aF,2/2). Here f is the so-called space factor which leads to the value of ( a P / 2 ) from the value of aFv2/2at the most accessible position.2’ The q,,(calcd) value is generally much smaller than the qst(exptl) value as shown in Table 11. The ideal mobile model should also be discarded. The two calculations of qst above, when combined with the analysis of the Jtherm, suggest that the sorbed molecule must keep its specific molecular orientation, where the ( p F ) and ( Q F / 2 ) terms do not become zero, while behaving like a one-dimensional gas. After some reflection, we finally arrived at the sorption model 111, where the frequency of free rotation of the sorbed molecule
+
+
+
is regulated by the periodic location of the alkaline-earth cation in the channel. The sorbed molecule directs its electric dipole and molecular quadrupole to the cation near the most accessible position as shown in Figure 7. However, while moving from one position to the next, the molecule turns its molecular axis by about (1 2n)?r, where n is zero or a small integer. Therefore, the (@) and ( Q P / 2 ) terms do not become zero while keeping the slope of the &herm/R vs. In T plot nearly 3.5. We will call model 111 the regulated mobile model (or the mobile model with the regulated free rotation) temporarily. The relation between the ideal mobile model and the regulated mobile model may be similar to the relation between the free-electron approximation and the band theory in solid-state physics. The degree of approximation is higher in the latter than in the former in both cases. The value of qst calculated by the regulated mobile model is compared with the q,,(exptl) in Table 11. To determine the space factor f,we use the value for N, as a standard. Agreement between the values of qst(calcd) and qst(exptl) is reasonably good for all three kinds of alkaline-earth mordenites. In the preceding paper, we calculated semiquantitatively the values of a F > / 2 , pF7, and QFTfor various gases sorbed by alkali mordenites.’ Their mutual comparison and comparison with the qst(exptl) brought us much useful information.’ However, since the a value and the equation for Q P used in the previous paper were not correct but should be divided by 4.8 and 2, respectively, the result obtained there was not quantitatively accurate. Therefore, we recalculate the qst value for a series of alkali mordenites in the present study. The results are summarized in Table 111. The agreement between the values in the calculation and the experiment is fairly good. The mobile model with regulated free rotation may, therefore, be quite realistic for both the alkali mordenites and the alkaline-earth mordenites.
+
Registry No. AI, 7440-37-1; 02,7782-44-7; N2, 7727-37-9; NO, 10102-43-9; CO, 630-08-0.
