J. Phys. Chem. 1991,95, 3257-3262 where it is expected to reside primarily in the lower. Overall, these results indicate that both normal and reverse micelles can be formed in surfactant/water/oil mixtures where the oil is a near-critical or supercritical fluid. Preliminary data has also shown that supercritical ethylene-based mixtures with Tergitol7 and water behave similarly to propylene-based systems, although at significantly higher pressures. This is not surprising, if we assume that phase behavior of supercritical fluid based
3257
microemulsion mixtures correlates strongly with fluid density. Work is continuing to expand our insight into the phase behavior, phase concentrations, and structure of these systems.
Acknowledgment. The authors thank the Army Research Office under Contract NO. DAAL03-87-K-0137 for their support of this project and thank J. L. Fulton for valuable discussions regarding this work.
Shape Anisotropy of Ferroelectric Domains in a Langmuir Monolayer Pierre Muller and Frangois Gallet* Laboratoire de Physique Statistique de I'ENS, 24 rue Lhomond, 75230 Paris Cedex 05, France (Received: June 5, 1990)
We determine the shape of ordered domains in a Langmuir monolayer deposited on the surface of water, when the amphiphilic molecules carry electric dipoles oriented in the same direction. The screening of charges by water is taken into account. For horizontal dipoles, one can calculate the anisotropic line energy between the ordered and the disordered phase. The corresponding domains are elongated and, in some cases, look like long sharp needles. The addition of a vertical component to the dipole results in a further elongation of these domains; even for infinitely long needles, the width keep a finite asymptotic value. These predictions agree with our recent observations on fluorescent nitrobenzoxadiazole (NBD)-stearic acid films.
Introduction Langmuir monolayers are made of amphiphilic molecules deposited on water and are known to undergo phase transitions, depending on temperature and molecular surface density.' The different domains coexisting at a phase transition can be visualized under an optical microscope by adding fluorescent probes to the film.2 Their shapes may be drastically different, according to the structure of the amphiphilic molecule, and to the nature of the phases.f7 In some cases, for solid or liquid-condensed phases, one observes anisotropic domains at or close to equilibrium, showing, for example, elliptical shape^,^ needle-like shapes,' or even spiral shapes in the case of chiral molec~les.~Previous theoretical works have shown that this shape depends on the interactions between the permanent electrostatic dipoles carried by the molecules.*-" However, these models either do not account, or partially account: for the in-plane component of the dipoles and for their screening by the conducting solution. In this paper we try to include these elements in the shape calculation. We suppose that the ordered phase presents a ferroelectric order: all the dipoles are located above the water, aligned along a same direction, and have a nonzero component in the plane of the monolayer. In its initial stage, this model was built to explain the needle shape of solid domains observed in the case of nitro( I ) Gaines, G. L. Insoluble Monolayers ai Liquid-Gas Interface; Wiley: New York. 1966. (2) LBsche, M.; MBhwald, H. Rev. Sci. Instrum. 1984,55, 1968. Miller, A.; Knoll, W.; MBhwald, H. Phys. Rev. Lett. 1986, 56, 2633. (3) Weis, R. M.; McConnell, H. M. J . Phys. Chem. 1985, 89, 4453. (4) Moy, V . T.; Keller, D. J.; Gaub, H. E.; McConnell, H. M. J . Phys. Chem. 1986, 90,3198. Keller, D. J.; Korb, J. P.; McConnell, H. M. J. Phys. Chem. 1987, 91,6417. (5) Moore, B.; Knobler, Ch. M.; Broseta, D.;Rondelez, F. J. Chem. Soc., Faraday Trans. I 1986.82, 1753. Rondclcz, F.; Suresh, K. A. Physics of Amphiphilic h y e r s ; Meunier, J., Langevin, D., Boccara, N., Springer: New York, 1987. (6) Seul, M.; Sammon, M. J. Phys. Reu. Lerr. 1990, 64, 1903. (7) Bercegol, H.; Gallet, F.; Langevin, D.; Meunier, J. J. Phys. Fr. 1989, 50, 2277. (8) McConnell, H.; Moy, V. T. J . Phys. Chem. 1988, 92,4520. (9) Moy, V. T.;Keller, D. J.; McConnell, H. J . Phys. Chem. 1988, 92, 5233. (IO) Andelman, D.; Brochard, F.; Joanny, J. F. J. Chem. Phys. 1987,86, 3673. (1 1) Gabay, M.; Garel, T.; Botet, R. J . Phys. C 1987, 20, 5963.
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benzoxadiazole (NBD)stearic acid monolayers.' This molecule has a large permanent dipole, associated with its fluorescent NBD group. Light absorption measurements have shown that, inside a needle, all the NBD planes are parallel to the needle axis,' meaning that the dipoles have a horizontal component in this direction. Our theoretical predictions are confirmed by our o b servations and could probably be extended to other Langmuir systems. The paper is organized as follows: first we completely describe the electrostatic screening of the dipoles by the water. As discussed in the Appendix, a single charge above the water is compensated by its usual dielectric image and by a second image due to the DebyeHiickel screening effect. This screening leads to a different interaction potential for the horizontal component of the dipoles (short-range quadrupolar interactions) and for the vertical one (long-range dipolar interactions). For dipoles with horizontal components only, we calculate the electrostatic energy associated to the domain boundary and we define an anisotropic line energy per unit length of ordered/disordered interface. In this case the equilibrium shape of the domains is completely determined by the Wulff construction: it is elongated and may even present sharp angles corresponding to missing orientations (needles) if the dipole is large enough. In the general case, starting with long and thin needles, and adding a vertical component to the dipoles, the shape is obtained by a variational calculation. The domains are further elongated, and their width keeps a finite asymptotic value when their length increases. Finally, we compare these predictions to our preliminary data about NBD-stearic acid films; the agreement is good and gives some information about the orientation of the permanent dipole in the ordered phase.
Definitions and Screening by Water We consider the coexistence of two phases, called ordered and disordered. All the molecules are supposed to carry a permanent electric dipole p', located at a distance h (h = a few angstroms) above the water surface, in a medium of relative permittivity e, = 1. In the ordered phase, the dipoles have a given orientation, defined by its component p,, and p L respectively parallel and perpendicular to the horizontal water surface. In the disordered phase, the horizontal dipole components are randomly oriented, so that the only contribution to the electrostatic energy U comes from the nonzero vertical components. Considering a single or0 1991 American Chemical Society
3258 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Muller and Gallet so is a small area surrounding p’, for example, a disk centered in r, of radius a of the order of an intermolecular distance. One has similar_expres_sionsfor the field created by the image distributions PI and P2 located under the water surface. As shown by McConnell and Moy? ( 2 ) can be transformed into a line integral:
ii and E,, are the horizontal unit vectors normal to the contour 1 and lo surrounding S and so. The second term in (3) does not
depend on r and gives a contribution to U proportional to the surface S. We drop it in the following, since we are only interested in the energy associated with the boundary. Combining (1) and (3), and commuting the integral and the gradient, U can be further transformed in Figure 1. Drawing of the geometry used to calculate thtinteraction energy between horizontal dipoles. The surface density is P, inside the rectangular domain S, and zero elsewhere. 6 is the angle between P, and the normal to the side boundary of the ordered domain. so is a small disk surrounding the test dipole a.
dered domain, and replacing the discrete dipoles by a continuous distribution P per unit area, U is given by the surface integral
(4)
In this expression I and I’represent the contour of the domain S, and lI and l2 that of its images SIand S,. Within the constraint Ir - r l > a, (4) can be completely integrated. After some calculations, and provided that L and Ware large compared to a, h, and h’, one finds that the energy U takes the simple form U = xII(2Lcos2 4 2W sin2 4) (5)
+
where All is a constant given by where &r) is the local electric field at point r. Let us first consider a plane horizontal interface separating two dielectric media 1 and 2 of permittivity el and t2, and a single charge 9 located at (r = 0, z = h) above the interface. The electric potential in medium 1 is the sum of the potential generated by 9 and by its image 91 = 9(cl - c2)/(cl + c2), symmetrical to 9, a t height z = -h. For the air/water interface, t l = 1, t2 = e, = 80, the charge 9 is almost completely compensated by q1 -79/81q. We must now take also into account the finite conductivity of water (Debye-HUckel screening). We show in the Appendix that this can be done in a good approximation by introducing a second image charge in the medium 2,92 = -2q/(l + e,), located below 91 at z = -(h h’), with h ’ = l D H t r / ( l + e,). Here IDH = (q,~,kT/2n,#)’/~is the Debye-Hiickel screening length, n, is the ion concentration of charge f e . IDH is of the order of 1 pm pure water at pH = 7, and only 30 A for water acidified by HCI a t pH = 2; we notice that lDHis comparable to an intermolecular distance in this case. We now point out that the screening has not the same consequences on the components pnand p I of a dipole p’. Indeed, pII generates two images pill and ~ 2 below 1 the water surface, parallel top,, and in the opposite direction, so that the sum p + + pzn is exactly zero. The resulting interaction between two horizontal dipoles is no longer dipolar, but quadrupolar at long distance. On the contrary, the two images pII and p Z I point in the same direction asp,, so that the interaction between two vertical dipoles remains dipolar at long distance. As a consequence, the total interaction energy U in formula 1 must be calculated in a different way for horizontal and vertical dipoles.
-
+
Horizontal Dipoles In this section we suppose that the dipoles are aligned in the plane of the interface. We calculate U for an ordered rectangular domain S, of length L 5nd yidth W. Inside this domain, the dipolar surface density P = PII is a constant and makes a fixed angle $ with the normal n’ to the large side of the strip (Figure 1). The local electric field exerted on a test dipole 9 located at (r, z = h) is the sum of the fields generated by all other dipoles in the plane z = h, and by their respective images in the plane z = -h and z = -(h + h3:
- l n l l + ‘ c, 1
+
‘
I I (6)
It is remarkable that, in this case, the image charges sweep out all the usual logarithmic divergences: U varies linearly with both dimensions L and W of the domain. Thus, for each portion of the perimeter, one can define a local energy X(4) per unit length, which does not depend on the global shape of the domain, but only on the orientation 4 of this portion:
A($) = x, + XI1 cos2 4
(7)
We have included in X(4) a constant b, in order to account for the short-range nondipolar interactions between the molecules, supposed isotropic for simplicity. This definition of the line energy X(4) applies to a macroscopic domain of any shape, as far as its size is large compared to h or IDH. From X(4) we can deduce the exact equilibrium shape of the domains, either by using the Wulff construction or by integrating the Laplace law (condition of equilibrium for two phases a t a bent interface):
x + A’’ - constant = K -P
with
Here p is the local radius of curvature of the domain boundary, A, and Ad are the respective areas per molecule for the ordered
and disordered phases, and Au is the difference in equilibrium surface pressure between a bent and a straight interface. We choose a Cartesian system of coordinates such that the Ox axis corresponds to 4 = 0, and that 0 is the center of the domain. Then, the integration of (8) leads to the parametric equations x($), y ( 4 ) for the shape of the boundary: x =~-l{(x+ , 2 4 , ) COS 4 - A, cos3 $1 (94
y = PI(h,- XII cos2 4) sin 4) We must now distinguish between two cases:
(9b)
The Journal of Physical Chemistry, Vol. 95,No.8, 1991 3259
Shape Anisotropy of Ferroelectric Domains Polar plot o f the line energy
of a domain, it is easy to show that the perimeter contribution to U, only depends on P,, - P l d . Indeed, P l d generates a uniform field in the plane, and its contribution to the energy, proportional to the total surface, is completely independent of the shape of the domain. Thus, we can replace P , by P’* = P,, Pld in eqs 1la-c and restrict the integrals to the surface of S only. Moreover, it has been shown that the images of P’L exactly act as a second distribution of dipoles identical with P’,, located below the surface of water, at a distance comparable to molecular spacing. To calculate E,, it is allowed to replace P’l by 2P‘1 in (1 lb,c) and drop the contribution of its images. Using the property A(l/r) = 0 (for r # O), U, can be finally transformed into a double line integral along the contour I , [’or s%
W
L
Figure 2. Equilibrium shape of an ordered domain, when the dipolar density 9, is strictly horizontal. The drawing corresponds to the case A, > X,(here A,/& = 3), Le., when some orientations are unstable. The domain looks like a sharp needle, with its axis parallel to 9,. The polar diagram of the line energy X(4) = X,+ h, cos2 6 has also been represented.
(a) X,> All: the shape of the domain is regular, stretched in the x direction. The aspect ratio R (length L over width W) is equal to the ratio of the extrema of A(#), Le., R = (X, Al)/X,. (b) X,< All: all the orientations such that cos 4 > cos #M = (X,/AR)1/2 are unstable and disappear from the interface. The domain looks like a needle with a sharp cusp on the x axis. Its dimensions are L = 4K-1(Al&)1/2 and W = 2K-’X,. R is equal to 2(A,/X,)1/2. Its exact shape is drawn on Figure 2, in the case AH/+, = 3 , K = 1, together with the polar diagram A(#). According to the Wulff construction, this shape is also the envelope %f the family of straight lines perpendicular in M to the vectors OM = A(#) n’(4). In the limit X, 1, W ( R )can be written
(1 l a ) with The variations of the reduced width W / W, as a function of the reduced length L/ W, = R W / W, are reported in Figure 3, for different values of the parameter A A,. One notices that W has a maximum WM= W, exp(2/(RM - 1)1 (>W-) for R = RM = 2 exp(AI/2A,). However, this maximum is very weakly pronounced as soon as RM >> 1, Le., All > A,. Let us now come back to the hypothesis that the shape of the domains is not drastically changed by the addition of vertical dipoles. Calculating In ( 4 / R 2 )from eq 16 and replacing it in eq 13, one finds for the equilibrium value of the total energy Uq = uq, + uqll:
Il
The integral (1 1 b) and (1 IC) should-be extcnded to the whole dipole distribution P and to its images PI and P2 under the water surface, However, since the needles have a center of symmetry, the VzV,terms give a zero contribution to the field, so that VI, (U,)is only a function of P,I(P,). Equations 11 can be further simplified: after decomposing the dipole density P , in P l d uniform over the plane plus P,, - P l d only over the surface S
8
Uq = -&L 3
(
+ ALL
12 + - In W ; -32:)
(17)
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3260 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
E1 0
w
-
3
u
c 0 (L
>. r L
1,this maximum is very weakly pronounced and occurs at large LM. /CH3 CH\2
CH
/--3
PERMANENT DIPOLAR -D
MOMENTUM
p
/CH2
cH\, CH2 CH/ \2
F H 2
cy2 /ch COOH
Figure 4. Representation of the NBDstearic acid molecule. The
fluorescent NBD group is plane, and carries a permanent dipolar momentum p, approximately oriented as on the drawing. On the contrary, the transition momentum (absorption of light) is perpendicular to the NBD plane. When A, is small, one recovers the energy UIl, corresponding to only horizontal dipoles. A good criterion for the validity of the shape variational calculation is (U, - U9$/U,,,,0
A test charge qo in the medium 1 experiences the potential created by q and, within a good approximation, by two image charges ql and q2. q1 = q(tl - t 2 ) / ( t l + t2) is symmetrical to q with respect to the interface (dielectrical image). q2 = -2qel/(el + e2) is located at a distance h’below q1(Debye-Huckel effect). h’is of the order of fDH = I / & the effect of q2 on qo is mainly sensitive at a distance r >> 1DH from q, which is a quite reasonable result and confirms the above approximation. Moreover, we notice that q + q1 + q2 = 0, meaning that the charge q is exactly compensated by ql and qt. The field generated by q and its images is dipolar at long distance.
Catalytlc Partial Oxidation of Propylene to Acrolein over Copper( I 1)-Exchanged M-X and M-Y Zeolites Where M = Mg2+, Ca2+, Li+, Na+, K+, and H+: Evldence for Separate Pathways for Partial and Complete Oxidation Jong-Sung Yu and Larry Kevan* Department of Chemistry, University of Houston, Houston, Texas 77204-5641 (Received: June 5, 1990)
The catalytic oxidation of propylene over copper(l1)-exchangedX and Y zeolites in the presence of the different major cocations, Mg2+,CaZ+,Li+, Na’, K’, and H’, was studied as a function of the oxygen/propylene mole ratio in a flow system at 350 OC. The yield of acrolein was optimized for a ratio of unity. The catalytic activities and the changes in cupric ion species were studied by gas chromatography and electron spin resonance. The catalytic activity for this reaction is shown to be due to copper species and is greatly dependent on the type of major cocation in the zeolites. Y zeolites are slightly more effective for the selective oxidation of propylene to acrolein than the corresponding X zeolites. The dependence of the product yields and the Cu( 11) concentration on the oxygen/propylene mole ratio indicates two parallel pathways for partial oxidation to acrolein and complete oxidation to carbon dioxide and water. It is suggested that partial oxidation is catalyzed by Cu(I), perhaps in a Cu20/Cu0 phase, and that complete oxidation is catalyzed by Cu(I1). An induction period for acrolein formation is observed. Catalyst deactivation is also observed and associated with coke formation which can be monitored by a singlet electron spin resonance signal.
Introduction Extensive studies on transition-metal-exchanged zeolites in the field of zeolite catalysis have been performed during the past two decades.’” A number of transition-metal-ion-exchanged zeolites have been shown to be catalytically active for various reactions. An important reaction among these is the oxidation of hydroc a r b o n ~ . ~The ~ ~conversion of hydrocarbons into products
containing oxygen products valuable chemical intermediates for the petrochemical industry. (7) Mochida, I.; Yitsumatsu, T.; Kato, A.; Seiyama, T. J. Cotol. 1975, 36, 361. (8) Garten, R. L.; Boudart, M. Ind. Eng. Chem. 1973, 12, 299. (9) Mochida, I.; Hayata, S.; Kato, A.; Seiyama, T. Bull. Chem. Soc. Jpn. 1971, 44, 2282.
(IO) Uh, Y. S.;Chon, H. J . Korean Chem. Soc. 1979, 23, 80.
( I ) Maxwell, 1. E. In Aduonces in Cotolysis; Eley, D. D., Pines, H., Weisz, P. B., Eds.; Academic Press: New York, 1982; Vol. 31, p 2. (2) Lunsford, J. H. Cotol. Reo. 1975, 12, 13. (3) Ben Taarit, Y.; Che, M. In Cotolysis by Zeolite; Imelik, B., Naccache, C., Ben Taarit, Y.,Vedrine, C., Couduvier, G.,Praliaud. H.. Eds.; Elsevier: Amsterdam, 1980; pp 167-193. (4) Naccache. C.; Ben Taarit, Y. In Zeolite: Science ond Technology; Ribeiro, F. R.,Rodrigues, A. E., Rollman, L. D., Naccache, C., Eds.; Martius Nijhoff: Hague, 1984; p 373. ( 5 ) Naccache, C.; Ben Taarit, Y. Pure Appl. Chem. 1980, 52, 2175. (6) Rudham, R.; Sanders, M. K. J . Carol. 1972, 27, 287.
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(1 I ) (a) Mochida, 1.; Hayata, S.;Kato, A.; Seiyama, T. J . Cotol. 1969, 15. 314. (b) Mochida, I.; Hayata, S.; Kato, A,; Seiyama, T. J . Corol. 1970, 19, 405. (c) Mochida, I.; Hayata, S.;Kato, A.; Seiyama, T. J . Cotol. 1971, 23. 31. (12) Gentry, S.J.; Rudham, R.; Sanders, M. K. J . Cotol. 1974, 35, 376. (13) (a) Mahoney, F.;Rudham, R.; Stockwell, A. In The Properties and
Applications of Zeolites; Townsend, R. P., Ed.; The Chemical Society: London, 1980; p 329. (b) Bravo, F. 0.;Dwyer, J.; Zamboulis, D. In The Properties ond Applicotions of Zeolites; Townsend, R. P., Ed.; The Chemical Society: London, 1980; p 368. (14) (a) Lee, H.; Kevan, L. J. Phys. Chem. 1986, 90,5776. (b) Lee, H.; Kevan, L. J. Phys. Chem. 1986, 90. 5781.
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