J . Phys. Chem. 1988, 92, 766-768
766
Effect of Coordination of Protons and Cations on the Geometric Characteristics of Zeolites S . Beran The J. Heyrovskg Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, CS 12138 Prague 2, Czechoslovakia (Received: April 7 , 1987; In Final Form: July 23, 1987)
The nonempirical SCF method with the STO-3G basis set is used to study the effect of the coordination of protons and Li or Na cations to the +SiOAl< fragments in zeolites on their geometric characteristics. The 3SiOAlf fragments are represented by the H3SiOAIH3-and H3SiOXAlH3 molecular systems (X = H, Li, and Na). The rigidity of the lattice is modeled by maintaining the terminal H atoms in different positions while the positions of the remaining atoms are optimized. It is shown that, independent of these model structural limitations, the geometric characteristics of the 3SiOXAlf fragments (particularly their Si0 and A10 bond lengths) differ very little from the equilibrium values, indicating that the fragment geometry is determined primarily by internal interactions within the fragments. The extent of changes in the geometry of the hSiOAlt fragment resulting from the coordination of individual ions is correlated with their electronegativity and exhibits the following trend: H > Li > Na.
Introduction Hydroxyl groups and cations in zeolites play an important role in the utilization of the zeolites as catalysts for various transformations of hydrocarbons. For this reason, the properties of these active sites, as well as factors affecting them, have recently been intensely studied e~perimentallyl-~ and the~retically.~-" One of the factors which has been found to influence the physicochemical properties of hydroxyl groups (their location, acidity, vibrational frequencies, etc.) is the geometry of the zeolite framework (Le., the S i 0 and A10 bond lengths and SiOAl angles). At the same time, systematic s t ~ d i e s ' ~of , ' ~Gibbs et al. have revealed that the geometry of individual fragments in the zeolite lattices (e.g., ?-SiOTt fragments, T = Si or Al) differs by about 0.01 X m and tens of degrees from the equilibrium geometry calculated for similar small molecular systems (e.g., for the (H0)3SiOT(OH)3 molecules). The observed differences most likely originate from steric deformations of the fragments connected with formation of the zeolite lattice. In addition, the recent nonempirical c a l ~ u l a t i o n s ~on ~ ' the ~ ~ ' (H0)3SiOA1(OH)3~ and (HO),SiOHAl(OH), systems also revealed that variation of the SiOAl angle in the 3SiOAIf fragment around its equilibrium value leads to a relatively small increase in the total energy of the ~ y s t e m , l ~while * ' ~ the energy changes in the 9SiOHAlf fragment are much more p r o n o ~ n c e d .It~ ~is~obvious that the ion coordination causes a lengthening of the S i 0 and A10 bonds. Nonempirical calculations predict a lengthening of about 0.1 X m for the proton c ~ o r d i n a t i o n . ' ~ -This ~ ~ fact has recently (1) Jacobs, P. A. Carboniogenic Activity ofzeolites; Elsevier: New York, 1977. (2) Haynes, H. W., Jr. Catal. Reu.-Sei. Eng. 1978,17,213. (3) Jacobs, P. A. Catal. Rev.-Sci. Eng. 1982,24, 415. (4)Mortier, W. J.; Sauer, J.; Lercher, J. A.; Noller, H. J . Phys. Chem. 1984,88,905. (5) Geerlings, P.; Tariel, N.; Botrel, A.; Lissillour, R.; Mortier, W. J. J . Phys. Chem. 1984.88,5752. (6) Datka, J.; Geerlings, P.; Mortier, W. J.; Jacobs, P. J . Phys. Chem. 1985,89,3488. (7) Beran, S . J. Mol. Catal. 1981,I O , 177; 1984,26, 31. (8) Beran, S. J. Phys. Chem. 1985,89,5586. (9) Senchenya, I. N.; Kazansky, V. B.; Beran, S. J . Phys. Chem. 1986,90, 4867. (10)Pelmenshchikov, A. G.; Pavlov, V. I.; Zhidomirov, G. M.; Beran, S . J. Phys. Chem. 1987,91, 3325. (11) Derouane, E. G.;Fripiat, J. G. J. Phys. Chem. 1987,91,145. (12) Gibbs, G. V. Am. Mineral. 1982,67,421. (13) Gibbs, G. V.; Meagher, E. P.; Newton, M. D.; Swanson, D. K. Structure and Bonding in Crystals; OKeeffe, M. D.,Nawrotsky, A,, Eds.: Academic: New York, 198); Vol. I, Chapter 9 and references therein. (14) Sauer, J.; Zahradnik, R. Int. J. Quantum Chem. 1984, 26, 793.
0022-365418812092-0766$01 S O / O
TABLE I: Optimized Geometry Characteristics (in lo-'' in and deg), Mulliken Bond Orders, p, and Charges on Ions, q x , Calculated for H$iOAIH,- and H@iOXAMj Systems
H3SiOAIH3full
LSiOAl =
out
150°
1.631 1.748 121.9
1.590 1.715 150.0
1.432 1.505 114.3 108.0
1.434 1.506 114.5 108.2
PSI0
0.275
PA10
o.212
0.31 1 0.222
rs10 rAlO
LSiOAl rxo rHSi
LHSiO LHAlO LXOSi 4x
Pox
H3SiOHAIH?
H,SiOLiAIH,
H,SiONaAlH,
1.698 1.867 129.9 0.973 1.422 1.484 107.2 99.8 114.4 0.237 0.276 0.232 0.125
1.676 1.798 124.6 1.588 1.425 1.497 109.4 101.4 117.7 0.336 0.246 0.250 0.153
1.651 1.775 125.4 1.900 1.426 1.495 11 1.2 103.5 117.3 0.777 0.118 0.266 0.181
been employed for estimation of the probability of Occurrence of individual types of OH groups in faujasites and mordenites by using the T O bond lengths from X-ray data.IsJ6 Therefore, the structural characteristics of individual fragments in the zeolite lattice seem to be determined mainly by internal interactions of atoms within the fragment and influenced by steric deformations originating from the formation of a given crystal structure. As the structural characteristics of zeolites affect the properties of their active sites, it is desirable,to recognize changes in the geometry of the 3SiOAlf fragments resulting from the , coordination of protons and cations.
Model and Method The 3SiOAlf and bSiOXAl< fragments (X = H, Li, and Na) in aluminosilicates were modeled by very simple molecular systems (clusters) of the H3SiOAlH3and H3SiOXAlH3types (cf. Figure 1) which can yield only qualitative information. For all the systems, the optimized geometry was calculated assuming that the Li and Na cations are located on the axis of the SiOAl angle and that the HSiO (HAIO) angles and the HSi (HA1) bond lengths are identical. The steric deformation of the ?-SiOAlf fragment was modeled by maintaining the SiOAl angle at 150' (this corresponds to the angle which is frequently observed for the frameworks of various zeolites), while the remaining geometry (15) Mortier, W. J.; Pluth, J. J.; Smith, J. V. J . Catal. 1976,45, 367. (16) Gibbs, G. V.; Meagher, E. P.; Smith, J. V.; Pluth, J . J. ACSSymp. Ser. 1977,40, 19.
0 1988 American Chemical Society
Geometric Characteristics of Zeolites
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 761
TABLE II: Optimized Geometry Characteristics (in lo-’’ m and deg), Mulliken Bond Orders, p , and Chargd on Ions, q x , Calculated for HJSiOXAIH3 Systems with H Atoms Fixed at Their Positions Found for Fully Optimized (LSiOAI = 129.0’) and Deformed (LBOAI = 150’) H$iOAIH3- Systems
H3SiOHAIH3
LSiOAl = 121.9’ H3SiOLiAIH3
H3SiONaAlH3
1.697 1.878 126.5 0.973 112.7 103.8 0.240 0.276 0.235 0.124
1.689 1.817 122.6 1.590 113.2 103.3 0.347 0.247 0.249 0.152
1.665 1.794 121.8 1.902 113.1 105.1 0.781 0.117 0.262 0.180
rslo rAIO
LSiOAl rxo
LHSiO LHAlO 4x Pox PSI0 PA10
X
I
Figure 1. Schematic depiction of the model used with indication of hydrogens which are not equivalent after ion coordination (H and H’).
parameters were optimized. The effect of the coordination of protons and cations on the geometry of the 3SiOAlf fragment was modeled in the following way: The coordinates of the terminal H atoms in the H3SiOXAlH3systems (representing a continuation of the lattice) were fixed at the positions calculated for the fully optimized or sterically deformed H3SiOA1H< molecules, while the remaining structural parameters were optimized. Calculations were carried out by the nonempirical S C F method with the STO-3G basis set by using the GAUSSIAN 80 program. The geometries of the individual structures were Optimized by the MurtanghSargent optimization procedure.”
Results and Discussion It follows from comparison of the total energies of the fully optimized and sterically deformed 3 S i O A l f fragment that the deformation of the SiOAl angle is connected with a relatively small increase in the energy of the system, Le., 17 kJ/mol. The optimized structural characteristics of both systems summarized in Table I then reveal that, in agreement with the conclusions of recent papers,l2?” an increase in the SiOAl angle results in a strengthening of the S i 0 and A10 bond lengths and, consequently, in their shortening. The remaining geometric parameters of the system remain practically unchanged. The optimized geometric parameters calculated for models of the 3SiOXAlf fragments given in Table I indicate that ion coordination always results in an increase in the SiOAl angle, as well as in a lengthening of the S i 0 and A10 bond lengths compared with the values found for the 3SiOAlf fragment. The same results have k e n obtained for proton coordination even when more extensive models were The extent of these changes in geometry for individual ions is correlated with their electronegativities and increases from Na to H. Moreover, comparison of the systems with a proton and cations indicates that the strength of the OX bond, characterized by the Mulliken bond order, again increases with increasing electronegativity of the ion in contrast to the ion charge which understandably decreases. In this connection, it should be noted that, in a real zeolite crystal, the cations are coordinated to several 0 atoms, and thus the cation-oxygen bond will be weaker and the cation charge somewhat lower compared with the values calculated for the above systems. In spite of this, the above calculations lead to qualitatively identical conclusions as semiempirical calculations’* on the more extensive (17) Binkley, J. S.;Whiteside, R. A.; Krishan, R.; Seeger, R.; Defrees,D. J.; Schlegel, H. B.; Topiol, S.;Khan, L. R.; Pople, J. A. QCPE 1981, No. 23, 406.
(18) Beran, S. J . Phys. Chem. Solids 1982, 43, 221.
H3SiOHA1H3 1.710 1.899 143.1 0.975 107.6 99.2 0.235 0.291 0.233 0.119
LSiOAl = 150’ H3SiOLiAlH3
H3SiONaAIH3
1.686 1.787 141.0 1.595 106.2 99.2 0.275 0.224 0.252 0.159
1.655 1.775 144 0 1.884 110.4 102.6 0.83 1 0.112 0.270 0.181
models in which the cation coordination is described properly. Therefore, if there are no sterical limitations affecting the 3SiOAlf fragment, ion coordination leads to substantial changes in its geometry. However, in a real zeolite crystal, the 3SiOAlf fragment cannot change geometry completely freely after ion coordination, because of lattice limitations (rigidity). In such a case, a change in the geometry of the zeolite lattice resulting from ion coordination proceeds on account of the structural changes in its surroundings. For proper description of the geometry relaxation of the 3SiOAlf fragment, it would be necessary to include into the model all the zeolite windows containing this fragment and to optimize the geometry of such a system. Another, less sophisticated possibility is to use smaller cluster models whose terminal atoms are fixed during the geometry optimization. Understandably, the smalIer the cluster with fixed terminal atoms including the fragment, the more stringent (and less realistic) are the limitations imposed on the fragment relaxation. Thus, the ability of the 3SiOAlf fragment to relax its geometry should decrease, for example, from (H3T0)3SiOAl(OTH3)3through (HO),SiOAI(OH), to H3SiOAlH3models. However, because of great computational effort connected with the geometry optimization of a whole series of the larger cluster models, the simplest model of the H3SiOA1H3type was used. It is apparent that the conditions employed to limit relaxation of the 3SiOAIf fragment geometry are rather stronger than limitations operating in a real zeolite lattice. Thus, ion coordination to the fully optimized (LSiOAl = 121.9’) and sterically deformed (LSiOAl = 150’) H3SiOA1H, systems with fixed H atoms was investigated, Le., to the systems whose S i 0 and A10 bond lengths are shorter and the SiOAl angle is either smaller or larger than the optimum SiOAl value calculated for the free 3SiOXAlf fragment. The results of such calculations given in Table I1 show that the ion coordination to both the 3SiOAlf fragments results in the Si0 and A10 bond lengths which differ very little from those calculated for the fully optimized H3SiOXAlH3systems without structural limitations. (Maximum and 0.02 X m, respectively.) differences are 0.01 X The SiOAl angles do not attain their optimal values; however, ion coordination leads to an increase in the SiOAl angle if the original value is lower than the optimal value or to a decrease if the original value is higher. Therefore, independent of its original value in the 3SiOAlf fragment, the SiOAl angle tends to attain its optimum value in the 3SiOXAlf fragment. Consequently, the SiOAl angle of the bridging 0 atoms forming O H groups should attain a value very close to the equilibrium value. With cations, the situation may be rather more complicated as the cation is coordinated by several 0 atoms which are not described by the model used. The changes in the geometry of the 3SiOAlf fragment resulting from the structure relaxation after ion coordination are, in the framework of the model used, compensated primarily by changes in the OSiH and OAlH angles and thus by changes in the TOT angles of the 0 atoms bonded to this fragment. Therefore, the above results indicate that the geometry of the 3SiOXAlf fragments in zeolites (particularly the Si0 and A10 bond lengths) will not substantially differ from the optimum
J . Phys. Chem. 1988, 92, 768-773
768
geometry determined by the internal interactions of atoms forming the fragment even if the fragments are subject to structural limitations of the lattice (even if the SiOAl angles in the unprotonated 9SiOAlf fragments attain different values). The difference in the S i 0 and A10 bond lengths in various fragments does not seem m, while the SiOAl angles are likely to to exceed 0.02 X differ at most by about 15'. Likewise, other characteristics calculated for the 3SiOXAlf fragments with sterical limitations are very close to those obtained for identical fragments without sterical limitations (cf. Tables I and 11). It is obvious that structural limitations influencing individual fragments in the lattice (and depending primarily on the number of T atoms in the zeolite windows in which the fragment is situated) affect namely those parameters whose deviation from their optimal values will lead to the smallest increase in the overall energy of the system. For zeolites such a parameter is the SiOT angle in the 9 S i O T f fragments, since the ~ a l c u l a t e d ~amount ~'~~'~ of energy required to deform this angle from its minimum energy value to 120' or 180' does not exceed 20 kJ/mol. Relaxation of the zeolite geometry associated with isomorphous substitution of A1 for Si has recently been explained" by local deformation of the SiOAl bridges (even protonated ones). However, in view
of the fact that deformation of the SiOAl angle in the 9SiOAlf fragments is energetically more advantageous than in the 3SiOHAlf fragment^,^ it appears likely that deformation of the unprotonated 3SiOAlf bridges will mainly take place upon substitution of A1 for Si. Similarly, a change in the geometry of the 3SiOAlf fragment originating from ion coordination to the 0 atom is likely to be compensated by deformation of the SiOT angles of adjoining skeletal 0 atoms to which no ion is bonded. The variations found for the geometry characteristics of the structurally different types of the bridging OH groups can cause relatively small changes in the dissociation energy of these groups (by about 40 kJ/mol) and, consequently, small changes in their acid strength. On the other hand, the geometry variations of the same order of magnitude were found to be responsible for the observed differences in the vibrational frequencies of the bridging OH groups.'O Moreover, these results may be helpful in interpreting the structural characteristics derived from X-ray measurements; e.g., they support the that the TO bond lengths from X-ray data can be used for estimation of the population of individual types of OH groups in H forms of zeolites. Registry No. H ' ,
12408-02-5; Li',
17341-24-1; Na+, 17341-25-2.
Curvature and Geometric Constraints as Determinants of Microemulslon Structure: Evidence from Fluorescence Anisotropy Measurements Vicki Chen, Gregory G. Warr, D. Fennel1 Evans,* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
and Frank G. Prendergast Department of Pharmacology, Maya Foundation, Rochester, Minnesota 55905 (Received: April 15, 1987; In Final Form: July 9, 1987)
Steady-state anisotropy measurements using an amphiphilic fluorescence probe, (trimethy1amino)diphenylhexatriene (TMA-DPH), and an oil-soluble probe, diphenylhexatriene(DPH), are reported for three-component microemulsions, employing didodecyldimethylammonium bromide (DDAB) as the surfactant, simple alkanes, and water. The anisotropies of TMA-DPH are almost constant when oil is added to the microemulsions but decrease upon addition of water. The results are interpreted in terms of a structural model based on geometric packing constraints of surfactant-coatedcylinders and spheres. The anisotropy shows local changes at the surfactant-water-oil interface which in turn can be related to global structure.
Introduction An unsolved question in colloid science concerns the relationship between microemulsion structure and measurable physical properties. This issue was implicit in the original work by Schulman four decades ago and still constitutes a major challenge:] it has persisted because microemulsions are inherently complex systems. At present, the most thoroughly characterized systems consist of four or five components, utilize surfactants or cosurfactants which are soluble in oil or water, and possess labile structures which rearrange in response to small variations in composition or temperature. In an attempt to circumvent some of these difficulties, we have characterized a simple, three-component microemulsion system. It employs as surfactant the didodecyldimethylammonium halides which are only sparingly soluble in either oil or water. Consequently, the oil-water interfacial area is directly related to surfactant concentration, and in the absence of cosurfactant, oil specificity becomes evident. From conductance, viscosity, and
N M R diffusion coefficient measurements, and observations on oil and counterion specificities, we have made the case that microemulsion structure can be directly related to curvature of the surfactant film at the oil-water interface.2 This in turn can be understood in terms of a delicate balance between headgroup repulsion and oil penetration into the surfactant chains. When combined with a recognition of the extraordinarily strong attractive force which operates on water-in-oil systems, the interfacial tension between the microemulsion and oil can be directly related to the ~tructure.~ In this paper, we employ fluorescence anisotropy measurements using a cationic amphiphilic probe in order to characterize in more detail the properties of the surfactant-oil-water interface. We interpret changes in anisotropy in terms of changes in local interfacial curvature and describe in more detail a model for microemulsions which relates curvature and structure. (2) Evans, D. F.; Mitchell, D.J.; Ninham, B. W. J . Phys. Chem. 1986,90,
2817. (1)
Prince, L. M., Ed. Microemulsions; Academic: New York, 1977.
(3) Allen, M.; Evans, D.F.; Mitchell, D.J.; Ninham, B. W. J . Phys. Chem. 1987, 91, 2320.
0022-3654/88/2092-0768$01.5Q/Q0 1988 American Chemical Society
