Langmuir 1993,9, 208-210
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Localization of a Magnesium &Sheet within a Lead Stearate Langmuir-Blodge tt Multilayer by X-ray Reflectivity Measurement U.Pietach,+U. H6hne,*Jand H.Mshwaldt FB Physik der Universittit Potsdam, Am Neuen Palais lO,D-0-1571 Potsdam, Germany, and Imtitut ffir Physikalische Chemie der Universittit Mainz, Jakob Welder Weg 11, D- W-6500 Mainz, Germany Received February 14,1992. In Final Form: August 7, 1992 Lead stearate multilayere have been prepared by LangmukBlodgett deposition where one lead layer has been replaced by magnesium at variable positions. The position of a Mg sheet within a lead stearate sandwich is determined by small angle X-ray scattering (SAXS) experiments. We f i d that the ionic layere closest to the substrate and the air modulate the phaeee of the scatteringamplitudes in a characteristic way. Ekpecially, the region between the fmt and second Bragg peak allows evaluation of the sequence of Pb and Mg layere unambigously. Additionally,the exact position of the Mg layer within the sandwich can be determined with atomic resolution, if Mg is positioned at the top or bottom of the multilayer. For intermediate positions, the accuracy is up to 3 times smaller.
Introduction X-ray reflectivity is a powerful tool for the structural characterization of organic multilayers.l Due to periodicity normal to the surface, the reflectivitycurve is modulated by equidistant Bragg peaks. Additionally subsidiary maxima are observed, which measure the supercellperiod and the totalthickness of the film, respectively. Both can be understood in terms of kinemati~,~J semikinematic? and dynamica16 simulations. In case of LangmuirBlodgettmultilayers(LB films)the supercellcontainstwo monolayers (MLs) which are faced either tail-to-tail or head-to-head together. This periodicity of LB films can be disturbed by various phenomena and this distortion can principally be resolved with 0.1 nm accuracy. Sometimes, in order to allow hydrophobic depoeition ofLB f h , an additionallayer is grown on the substrate. On the other hand, after depositionof numerous ML the perfection of the top layer is diminished. In the case of a fluctuating tail ordering the effective thickness of the top layer is often smaller compared with the deeper lying ones. These effects do not change the scattering amplitudes but rather vary the scattering phases and cause a measurable angular shift of intensity oscillations near the criticalangle of total external reflection, 8,. So this 'dynamical" region contains detailed information conceming the real structure of the sample. Its modeling requires a full dynamical treatment of the scatteringproceas, a simulationusing only kinematic assumptions misses some important information. In order to demonstrate such phase analysis, we measured various lead stearate LB films, which contain a magnesium stearate b-sheet at different depths below the surface. It will be shown that the ion sequence within the LB film can be evaluated from the measured modulation of subsidary maxima between the f i t two Bragg peaks. t FB
Physik der Univereitat Potadam. h t i t u t Mr Physikalische Chemie der Universitat Mainz. (1) Pommerem, M.; ScgmaUer, A. Thin Solid Film 1980,60, 33. (2)Als-Niehn, J. 2.Phys. B lSlM, 61, 411. (3) Gerlotzka, 5.; Lambooy, P.; de Jeu, W.H. Europhys. Lett. 1990,
12, 341.
Materials and Sample Structure Multilayer8 were prepared by the conventional LB dipping technique. The subphase consisted of a solution of 3 X 10-5M PbCl2 (Alfa, Karlsruhe, FRG) and 3 X M CHaCOONa (Merck, Darmstadt, FRG) (pH -6.9) in Millipore filtered water, or lW3 M MgClz (Merck, Darmstadt, FRG) in a M buffer solution (Na2HPOJNaHr PO4 (Merck, Darmstadt, FRG), pH -8.S).s Ae substrates we used silicon wafers (Wacker,Burghausen). Monolayer transfer was performed at a constant surface pressure of 24 mN/m and at a dipping speed of 10 mm/min for lead stearate and 4 mm/min for magnesium stearate. All fabricated samples consist of nine MLs of stearate. Except for one sample two MLs of lead stearate were substituted by magnesium stearate (head-tohead ordered) and the closely neighbored Mg atoms act as a two-atomic 'defect" within the otherwise homogeneous lead stearate LB film. Each sample is distinguished by ita relative Mg poaition normal to the surface. For simplicitythe sequence of three MLs of lead stearate, two MLs of magnesium stearate, and following four MLs of lead stearate is labeled by '3-2-4". Experimental Section LB films are characterized by SAXS measurements using Mo radiation (A = 0.070 71 nm). The incident beam was collimated and monochromatizedby a germanium crystal and varioue slits.
The residual divergence amounts to 0.01O. The intensity of the
incident beam and the backgroundlevel are 4 X 106and 4countd 8, respectively. The reflectivity curve is recorded in step of
about O.0lo between 0.1 and 2.25O. Depending on the intensity of the reflected beam,the counting time is varied between 10and 100 s per step.
Dynamical Formalism of X-ray Scattering The theory of total external reflection is based on Fresnel's formulas of classical electrodynami~e~ and has ~
(4)Rieutord, F.; Benattar, J. J.; Bosio, C.; Robin, P.; Blot, C.; de Kouchkoweky, R. J. Phys. (Paris) 1987,48,679. (6)Jark, W.;Rueeel, T. P.; Comelli, G.; Stdhr, J. Thin Solid F i l m ISsI,161,I99.
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(6) Tippmann-Krayer, P.; Larhuber, L. A,; Mbhwald, H. Thin Solid F i l m 1988,159,307. (7) Stem,F. In Solid State Physics; Steitz, F., Turnbull, D., Ed&; Acndemic Press: New York, 1963; Vol. 16.
0743-7463193/24O9-0208$04.O0/0 Q 1993 American Chemical Society
Langmuir, Vol. 9, No. I , 1993 209
Localization of a Mg &Sheet been transferred to the X-ray optics by Parrat.6 For multilayershe proposed a simple recursion formula. The reflection amplitude Rj at any upper interface of the layer j is given knowing the scattering portion of jth layer, Fj, its layer thickness tj, and the scattering amplitude Rj-1 of all the layers lying beneath the jth layer9
The small angle limit Fj, given by z Fj
fj-1- f j fj-1
+f j
depends on the Fresnel coefficients f j f j = (e2
+ xj)1/2
(3)
The phase @ j depends on the thickness tj and the Fresnel coefficients f j
aj = 2TXtjfj (4) Xdenotea the wavelength, fJ the angle between the incident beam and the surface, and X the dielectric susceptibility. X and f are complex quantities. By use of eq 1, the calculation starta at the substrate and finishes at the filmair interface. The total reflectivity I is given by I=RXR*
(5)
Results The measured reflectivities for samples 7-2-0 and 3-2-4 are shown versus fJ in Figures 1and 2, curve a. Besides the maximum at e,, five further peaks appear which can be ascribed to a small angle Bragg reflection up to 5th order. The totalnumber of m = 9 ML provides n = trunc(m/2) = 4 complete supercella, 80 p = n - 2 subsidiary maxima can be observed between the Bragg peaks. In comparison, curve b of Figures 1 and 2 show the reflectivity calculated according to eq 6 assuming a structure containingonly lead stearate layers. Onerealizes that the angular p i t i o n s and the intensity of the Bragg peaks are well approximated, but not the secondary maxima. Between the first and second Bragg peak there is a complete swituhing between the theoretical and experimental curve. This is caused by the Mg layer disturbing the phase connections between lead stearate scattering amplitudes which proceed from the substrate adjacent region to the top region of the LB film. The experimentalreflection curve is well simulatedconsidering the Mg &sheet at the correct position within the LB film (curve c of Figures 1and 2). This qualitative agreement is independent on the selected absolute density gradients within the supercell. Because the lengths of Mg-stearate and Pb-stearate egree, a simplesubdivisionof the supercell is sufficient. For the 3-2-4 sample, the stack of the used sublayersand their X j are shown in Table I. The scattering power of the CH2- and COO--groups is approximately the same. More important for the simulations is the consideration of the spacing between the methyl groups of the chains. It is responsible for the fact that the oddlabeled Bragg reflectionsexhibita higher integral intensity compared with the even ones. However, the adaption of any sublayer is sensitive to the product of tjXj, only. Therefore, the Pb and Mg sheet thicknesses were assumed to an accuracy not better than 0.1 nm. For Pb,the adapted (8) Parrat, L. G.Phys. Reo. 1964,95, 359. (9) Rahn, H.; Pietach, U. J. Phye. D, in prese.
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Figure 1. (top) Reflectivity of sample 7-2-0 versua 6 (a) experiment; (b) simulated assuming a nine ML lead stearate f i i ; (c) sequence according preparation; (d) after displacement of the Mg sheet by about 0.1 nm. According to their order, Bragg peaka are markedby numbers in brackets. For clarity,the curvea are shifted toward each other by an order of magnitude in the y axis. (bottom) To illustrate the differences between curves a-d, the region between the first and third Bragg maxima is enlarged and significant minima of the experimental curve are labeled.
X corresponds to the up to now published valueslO and agrees with the known ionic radius for Pb2+.11 The Mg sheet is scaled depending on ita ionic radius.
Discussion The sensitivity of reflectivity due to different phases for contributions from various possible Mg/Pb sequences is shown in Figure 3. Depending on the position of the Mg 6-sheet, the subsidary maxima visible between all Bragg peaks vary. Taking into account the decreasingscattering power for increased 8, the region between the fmt and second Bragg peak is most suitable for detailed analyeis. Each sequence of Pb and Mg layers corresponds to a characteristic modulation of the reflected intensity. As in the case of semiconductor multilayers the phase shift depends on the thickness ratio between the lead stearate layers above and below the "defect" layer, demonstrated by Baumbach et al.12 The nature of the "defect" is lesa important, if the adjacent sandwich layers are much thicker. Then the scattering contribution of the defect layer to the total scattering amplitude can be neglected. In the present case the thickness of the Mg sheet is approximately0.2nm, a smallvalue compared to the length of a hydrocarbon chain. (10) Prakash, M.; Dutta,P.; Kettarson, B.; Abraham, B. M. Chem. Phys. Lett. 1984, 111, 395. (11) Kleber, W. Einfilhrung in die Kristallographie; Verlag der Technik Berlin, 1970. (12) Baumbach, G.T.; Rahn, H.; Pietach, U. Phys. Status Solidi A 1988,108, K7-KlO.
Pietech et al.
210 Langmuir, Vol. 9, No.1, 1993
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Table I. Thicknerr and Electrical Suwptibillty of the Airumed Sublayen within the LB Film 2-3-4, Numbering Starting at the Subrtrate Real[x1 Imag[x1 m WUP t [nml 10-6 10-6 -12.3 -0.6 0.13 1 Pb -1.2 -0.02 2.25 2 C17H~C00-0.3 -0.001 0.28 3 H-H -1.2 -0.02 2.25 4 C~~HMCOO-0.6 0.26 -12.3 5 Pb-Pb -1.2 -0.02 2.25 6 C17Hd200-0.3 -0,001 0.28 7 H-H 2.25 -1.2 -0.02 8 C17H~C009 10 11 12 13 14 15 16 17 18
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Figure3. Simulated reflectivitycurvea (top) for various poesible Mg/Pb sequencies: (a) 9, (b) 1-2-6, (e) 3-2-4, (d) 5-2-2, (e) 7-2-0, and enlargement (bottom).
contrast, for 3-2-4 the same displacement does not influence the subsidary maxima and the high order Bragg peaks are leveled (Figure 2d). Taking into Bccount the real structure of the sample, the correct position may be evaluated for displacementshigher thanabout 0.3 nm only. This variable accuracy is due to the differentratio between the "sandwich" layers. If the Mg sheet is adjacent to the air-fh interface or to the substrate, a small shift of the sheet position changes this ratio much more than a Mg layer position cloee to the center of the LB f h . However, the utilization of phase contrast ellowe recognition of the real structure of LB films. T h e detailed analysis requires vary accurate X-ray scattering measurementa from the region near d, up to high auglea and a small noise level. Additionally, for the shulations at the dynamic approach is nec8seary. On the anglea 8 4 a,, other hand this proceeding has great potential to study minute sfructural changes,e.g. thermal disorder,diffusion, and interfacial reactions.
Acknowledgment. U.P. thanks the Alexander von Humboldt Foundation for ita support. This work was supported by the Bundesministerium folr Fomchung und Technologic (BMFT) and the Fonds der Chemischen Industrie. We also thankWacker, Burghausen, FRG,for the generous offer of silicon wafers. Registry No. Pb stearate, 1072-35-1; Mg stearate, 557-04-0.
