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X-ray and Neutron Reflection Analysis of the Structure and the Molecular Exchange Process in Simple and Complex Fatty Acid Salt Langmuir-Blodgett Multilayers U. Englisch,† F. Pen˜acorada,‡ L. Brehmer,†,‡ and U. Pietsch*,† University of Potsdam, Institute of Physics, Am Neuen Palais 10, 14415 Potsdam, Germany, and University of Potsdam, Research Group “Thin Organic Films”, Kantstrasse 55, 14513 Teltow, Germany Received October 5, 1998. In Final Form: December 4, 1998
A Langmuir-Blodgett multilayer film of cadmium arachidate and a complex multilayer system of cadmium stearate bilayers separated by copolymer interlayers have been prepared by sequential transfer of deuterated and nondeuterated bilayers on a solid support. They were investigated at different temperatures using X-ray and neutron specular as well as diffuse reflectivity measurements. The neutron scattering was used to determine the vertical arrangement of deuterated chains within the multilayers and to study the different roughnesses at the chain-chain and chain-metal ion interface separately. The specular reflectivity patterns of both samples could only be interpreted considering the contribution of resonant-diffuse scattering caused by the perfect vertical correlation of individual interface roughnesses within a certain domain. For the two samples the superstructure peak intensity appearing in the respective neutron reflectivity curve decreases dramatically during annealing between 50 and 65 °C. This indicates an intermixing of deuterated and nondeuterated molecules within the film. The molecular exchange cannot be suppressed by the incorporation of copolymer interlayers between the deuterated and nondeuterated chains. Because the X-ray reflectivity patterns remain nearly unaffected by the annealing and because the annealing temperature was lower than the melting point of the pure fatty acid phase (about 70 °C), we interpret this effect by a vertical movement of fatty acid molecules across the still lamellarly stacked framework of fatty acid salt molecules. The temperature dependence of this process shows Arrhenius-like behavior. For both samples the estimated activation energy is 1.7 ( 0.5 eV (164 ( 48 kJ/mol) and is assigned to the van der Waals bonding energy of single molecules in a 2D hexagonal lattice. From time-dependent measurements we estimated a vertical diffusion coefficient in the order of 10-22 m2/s.
Introduction X-ray and neutron reflectometry are useful tools to investigate the lamellar structure of organic multilayers. The particular advantage of the neutron reflectometry is its sensitivity to the nuclear scattering length density. This is independent from the number of electrons but varies among the different isotopes of an element. Owing to the large difference of the coherent scattering length of the isotopes hydrogen, bH ) -3.739 × 10-5 Å, and deuterium, bD ) 6.671 × 10-5 Å,1 the interfaces between the hydrocarbon chains of Langmuir-Blodgett (LB) multilayers prepared from fatty acid salt molecules become visible, if nondeuterated and deuterated bilayers are sequentially transferred onto a solid support. In contrast, the X-ray reflectometry probes the electron density contrast, i.e., mainly the interfaces between metal ions and hydrocarbon chains. The lateral component of the molecular order becomes available via off-specular (diffuse) scattering experiments.2-4 The apparent complementarity of the two scattering techniques leads to separate structural information concerning the metalchain and chain-chain interfaces. In a recent paper5 we have shown that freshly prepared multilayers of fatty acid salt molecules, containing a † ‡
Institute of Physics. Research Group “Thin Organic Films”.
(1) Russel, T. P. Mater. Sci. Rep. 1990, 5, 171. (2) Sinha, S. K.; Sirota, E. B.; Garoff, S.; Stanley, H. B. Phys. Rev. B 1988, 38, 2297. (3) Gibaud, A.; Cowlam, N.; Vignaud, G.; Richardson, T. Phys. Rev. Lett. 1995, 74, 3205. (4) Sto¨mmer, R.; Pietsch, U. J. Phys. D 1996, 29, 3161.
superstructure of deuterated and nondeuterated bilayers, show a lower scattering contrast as expected. This has been interpreted by the incomplete monolayer transfer onto the silicon support during film preparation which results in an intermixing of deuterated and nondeuterated bilayers. This initial intermixing increases during annealing at temperatures below 70 °C while the vertical spacing of counterions remains unchanged.6,7 In this paper we present the results of combined temperature and time-dependent measurements of partially deuterated Cd-arachidate multilayers and compare them with these obtained from a similar sample containing copolymer interlayers. The separation of the fatty acid salt bilayers by a copolymer should prevent the interdiffusion of molecules during annealing and should stabilize the multilayer system for any application at higher temperature. The kinetics of the observed molecular exchange process is described in terms of an “orderdisorder transition” model known from solid-state physics. Using time-dependent measurements, we could estimate the value of the vertical diffusion coefficient. Furthermore we present first off-specular scattering measurements from LB multilayer films performed with neutrons. Compared with the respective X-ray measurements the results can be used to discuss the different interface morphologies at the metal-chain and the chain(5) Englisch, U.; Barberka, T. A.; Pietsch, U.; Ho¨hne, U. Thin Solid Films 1995, 266, 234. (6) Bolm, A.; Englisch, U.; Pen˜acorada, F.; Gerstenberg, M.; Pietsch, U. Supramol. Sci. 1997, 4, 229. (7) Englisch, U.; Gutberlet, T.; Steitz, R.; Oeser, R.; Pietsch, U. Phys. Status Solidi B 1997, 201, 67.
10.1021/la981377+ CCC: $18.00 © 1999 American Chemical Society Published on Web 02/05/1999
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Figure 1. Schematic sketch of the investigated samples. Sample A (left) was prepared from undeuterated and deuterated Cdarachidate bilayers. In sample B (right) the undeuterated and deuterated Cd-stearate bilayers were separated by bilayers of the amphiphilic copolymer MSA22. δN and δR indicate the scattering length density and the electron density responsible for the neutron and X-ray scattering contrast, respectively. The layer close to silicon is made by OTS (octadecyltrichlorosilane) for hydrophization.
chain interfaces. Additionally we demonstrate that the contribution of the resonant-diffuse scattering has to be considered for interpreting the specular reflectivity curves from Langmuir-Blodgett multilayers. Experimental Details A Langmuir-Blodgett multilayer system of sequentially stacked nondeuterated and deuterated Cd-arachidate bilayers (sample A) and a multilayer system in which the nondeuterated and deuterated Cd-stearate bilayers (sample B) are separated by bilayers of the amphiphilic copolymer MSA22 (poly(propene(n-octadecyl)maleinamic acid)-co-poly(propene (n-decyl) maleinamic acid) have been prepared by the Langmuir-Blodgett technique using an alternative trough (Nima 611, KSV5000). Deuterated (98%) and nondeuterated arachidic/stearic acid as well as the copolymer were spread separately onto the surface of Millipore filtered water. At a fixed surface pressure of 30 mN/ m, two nondeuterated and two deuterated monolayers are transferred sequentially onto a hydrophobic substrate. In the case of the complex multilayer system the copolymer bilayer is deposited at a fixed surface pressure of 22 mN/m. This procedure was repeated three times for both model systems. The pH values were adjusted to pH ) 5.6 for the Cd-arachidate/stearate using a 2 × 10-4 M CdCl2 solution and for the copolymer MSA22 using Millipore water as subphase. Figure 1 shows a sketch across the vertical stacking of both multilayers combined with the respective electron density and scattering length density profiles. The X-ray specular reflectivity curves were measured up to a vertical momentum transfer of qz ≈ 1.6 Å-1 for sample A and qz ≈ 0.6 Å-1 for sample B, before and after annealing. qz ) 4π/λ sin θ is the momentum transfer normal to the surface probed by means of an angular dispersive θ-θ diffractometer and a wavelength of λ ) 1.54 Å. Transversal diffuse scans were recorded across the 1st to 13th and the 1st to 4th. Bragg-peaks, respectively,
rocking the sample by the goniometer angle ω across a fixed detector angle position, 2θ. Neutron specular reflectivity as well as neutron diffuse scattering experiments were performed at the new neutron reflectometer ADAM at the Institute-Laue-Langevin (ILL) in Grenoble at room temperature and at temperatures up to about 85 °C. The experimental setup of ADAM is described in detail elsewhere.8 Due the high flux the neutron reflectivity curve could be measured up to qz ≈ 0.25 Å-1 using λ ) 4.4 Å. Therefore more than one Bragg peak of the regular vertical structure and two superstructure peaks could be detected. The wavelength and angular resolution of the neutron experiment were about ∆λ/λ ) 0.006 and ∆ω ) 0.012° (in the case of room temperature) or ∆ω ) 0.041° (in the case of annealing). The diffuse neutron scattering was only inspected at room temperature.
Results (I) Room-temperature measurements. (a) Sample A. Figure 2 shows the X-ray and the neutron reflectivity curves of sample A measured at room temperature as a function of qz. Using a model based on the Parrat formalism9 the evaluated d spacing of 54.9 ( 0.5 Å is consistent with the bilayer sequence of nontilted arachidic acid chains. From the widths of Bragg peaks along qz shown in Figure 2a, the vertical coherence length is estimated to be Lz) 233 ( 58 Å. From the Kiessig fringes periodicity the film thickness is obtained as Dfilm) 230 ( 10 Å. Because of Lz ≈ Dfilm we deduce that all interfaces of the multilayer contribute to the coherent scattering (8) Schreyer, A.; Siebrecht, R.; Englisch, U.; Pietsch, U.; Zabel, H. Physica B 1998, 241-243, 169. (9) Parrat, L. Phys. Rev. 1954, 95, 359.
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{
I(qz) ) R(qz) 1 + Aqz
A)
Figure 2. (a) X-ray reflectivity curve of sample A at room temperature. (circles, experimental curve; solid curve, fitted curve including the resonant diffuse scattering; dotted curve, contribution of resonant diffuse scattering (see inset). (b) Complementary neutron reflectivity at room temperature (circles, experimental curve; solid curve, fitted curve including the resonant diffuse scattering; dotted curve, resonant diffuse scattering). The inset shows the z-distribution of the neutron scattering length assumed for two different domains.
signal. Nevertheless a discrepancy was found between the observed film thickness (9 monolayers) and the expected one (12 monolayers). This is explained by the incomplete monolayer transfer from the water surface onto solid support. Transfer ratios varying between 30% and 72% were notified for the first four monolayers. The arising holes are filled in by molecules of the next following transfer step, so that the total thickness of the multilayer system becomes smaller. Using a simple Parrat formalism, the X-ray reflectivity curve between 0 < qz < 0.3 Å-1 and for qz > 0.3 Å-1 up to the end cannot be interpreted considering a single roughness parameter. This is caused by the contribution of resonant-diffuse scattering to the specular curve which cannot be neglected performing the experiment with low angular resolution. Owing to the nearly complete vertical correlation of individual interface roughnesses, the diffuse scattering oscillates with the same period versus qz as the specular reflectivity (see inset in Figure 2a). Using an approach introduced in ref 10, the measured intensity variation versus qz can be expressed by (10) Englisch, U.; Pen˜acorada, F.; Samolienko, I.; Pietsch, U. Physica B 1998, 248, 258.
(
eqz σ - 1 -1 qz2σ2 2 2
)}
(1)
Lx(∆Ri + ∆Rf) 2π
with considering ∆Ri and ∆Rf as the angular divergence of the incident beam and the angular acceptance of the detector used, respectively. The second term in the brackets characterizes the resonant-diffuse part of scattering. It depends on qz, the roughness σ, and a parameter L, which is proportional to the lateral coherence length. Equation 1 approximates the resonant-diffuse scattering not very accurate, because the qx dependence of the correlation function is not correctly described. But it respects the conformality of layer fluctuations and its contribution to the specular reflectivity. Using eq 1 and considering our experimental conditions, (∆Ri ) 0.019° and ∆Rf ) 0.038°), the resonant-diffuse scattering dominates the reflectivity curve from qz > 0.3 Å-1 (see inset of Figure 2a). Beyond this qz value the Bragg peak intensities are mainly caused by the appearance of resonant-diffuse scattering. An appropriate fit to the measured reflectivity curve was obtained considering a complete correlation of interfaces with an individual interface roughness of σ ) 3 Å. The presence of diffuseresonant scattering may be the reason some LB film Bragg peaks were found up to very large qz.11 Their appearance cannot be explained using the Fresnel qz-4 law. The fit of the individual Bragg peak intensities provides a rough estimate for the molecular composition of the film. Depending on the pH value used in the subphase, not all the fatty acid molecules are attached to a metal ion.12 Thus salt and acid molecules coexist in a particular bilayer. Using a box model the realized ratio κx of both molecules can be estimated from the fitted refractive index of “metal” box δfit averaging the salt content across the irradiated sample area compared with the ideal value δideal expected for a given pH value. δsalt is the correction to the refraction index for a pure fatty acid salt film.The ratio κx is
κX )
δfit,metal - δsalt δideal,metal - δsalt
(2)
In the case of sample A, the film consists of about 35% fatty acid and 65% fatty acid salt. This is consistent with a pH value of about 5.6 used for preparation.13 To determine κx, we used the first three Bragg peaks only, which can be mainly explained by the specular scattering. The neutron reflectivity curve, shown in Figure 2b, provides additional information about the initial intermixing of nondeuterated and deuterated molecules and the structural behavior of the chain-chain interfaces. The four detected Bragg peaks do not show uniform periodicity. The calculated d values vary from 107 Å (first Bragg peak) up to 136 Å (fourth Bragg peak). Therefore the neutron reflectivity curve cannot be explained by an uniform bilayer stacking. Another indication for an incomplete bilayer stacking is obtained from the evaluation of the individual Bragg peak intensities. The fitted ratio of refractive indexes of the “chain” boxes κN gives information about the initial (11) Kepa, H.; Kleinwaks, J. J.; Berk, N. F.; Majkrzak, C. F.; Berzina, T. S.; Troitsky, V. I.; Antolini, R.; Feigin, L. A. Physica B 1998, 241243, 1048. (12) Schwartz, D. K. Surf. Sci. Rep. 1997, 27, 241. (13) Buhenko, R. M.; Grundy, M. J.; Richardson, R. M.; Roser, S. J. Thin Solid Films 1988, 159, 253.
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Figure 3. Transversal diffuse scattering curves of sample A: (a) X-ray scattering profiles of the odd numbered Bragg peaks; (b) neutron scattering curves across the superstructure (1) and the regular Bragg-peak (2).
intermixing between deuterated and nondeuterated molecules within a bilayer caused by the preparation technique. Analogous the eq 2 we obtain
κN )
bfit,deuterated - bfit,nondeuterated bideal,deuterated - bideal,nondeuterated
(3)
Sufficient agreement with the experiment is obtained considering the simultaneous appearance of domains with different stackings of deuterated and nondeuterated bilayers. We assumed two of such stackings containing stacks with ratios of 2:2 and 5:1 between nondeuterated and deuterated sublayers (see inset of Figure 2b). The coexistence of two or more of such stacks may be caused by the preparation process again. Obviously the transfer ratio of deuterated monolayers was lower than that of the nondeuterated ones and varies among the different domains. As for X-rays the neutron reflectivity curve is strongly influenced by the resonant-diffuse scattering (see triangles in Figure 2b). Using eq 1 an appropriate fit was performed assuming an individual interface roughness of σ ) 22 Å and considering complete vertical correlation of interfaces, again. The fitted curve, shown in Figure 2b, was obtained after the incoherent superposition of the reflectivity curves calculated for both domains. The roughness parameter obtained for the chain-chain interfaces (from neutrons) is much larger than that of the metal/chain interfaces (from X-rays). This indicates a higher spatial disorder and/or the appearance of rotational fluctuations of the chain ends compared with the order of headgroups already at room temperature.
Figure 4. (a)X-ray specular reflectivity curves of sample B at room temperature (circles, experimental curve; solid curve: fitted curve including the resonant diffuse scattering; dotted curve, contribution of resonant diffuse scattering (see inset)). (b) The neutron specular reflectivity curve at room temperature (circles, experimental curve; solid curve, fitted curve including resonant-diffuse scattering). The inset shows the scattering length-density profile versus the sample thickness z; interface roughness is neglected.
The lateral correlation properties become visible measuring off-specular scans. At a transversal scans, shown for X-ray in Figure 3a, the sample angle ω ) Ri is varied for a fixed detector angle 2Θ ) Ri + Rf , i.e., at fixed vertical momentum qz, which corresponds with the angular positions of the various Bragg peak in the specular reflectivity curve. The lateral momentum transfer is measured in terms of ∆qx ) ∆ω qz. Figure 3a shows always a sharp peak close to ∆ω ) 0 corresponding with the apparative resolution. These sharp peaks indicate the specular scattering. It appears up to the ninth order Bragg peaks. Their intensities corresponds approximately with the difference between the specular and resonant-diffuse scattering curves shown in Figure 2a. The numerical discrepancy between these intensities may be caused by the very rough approximation given by eq 1. General models describe the specular and diffuse scattering from LB films simultaneous.14 However, the low intensity peaks at ∆ω ) (0.6° shown in the upper curve (first-order peak) are caused by the refraction of the incident/exit beam at the air-sample interface (Yoneda wing). Below the specular peak we find a diffuse scattering which is about 1 order of magnitude larger than that at qz positions (14) Sanyal, J. K.; Sanyal, M. K. Phys. Rev. Lett. 1997, 79, 4617.
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Figure 5. Diffuse scattering profiles of sample B measured at the four Bragg peak positions of the X-ray reflectivity curve (a) and at five peak positions of the neutron reflectivity curve (b). Graph (c) shows the variation of the full width of half-maximum of the diffuse scattering profiles as a function of the peak order, plotted in coordinates of the reciprocal space. The slope of the neutron data is significantly steeper indicating a smaller lateral coherence length compared with the X-ray data.
between the Bragg peaks (not shown here). This is the contribution of resonant-diffuse scattering (see above). Unfortunately the diffuse scattering does not exhibit a pronounced qx dependence. Thus a numerical value of the lateral coherence length Lx cannot be estimated. The transversal diffuse neutron scans (Figure 3b) give also a hint for a fluctuation of the chain ends at room temperature. The half-width of the superstructure peak (peak 1 at qz ≈ 0.052 A-1 in Figure 2b) is much broader than that at the regular Bragg peak (peak 2 at qz ≈ 0.11 A-1). Both ω scans were recorded with similar resolution. The first peak is mainly dominated by the contrast of the CH3-CD3 interfaces, whereas the scattering profile of the second one is additionally caused by the contrast of the metal ion/chain interfaces. Therefore we conclude that the lateral coherence length for the chain-chain interfaces is much lower than that of the metal-chain interfaces. For this sample a detailed determination of the correlation length was impossible due to the low intensity of highorder peaks. (b) Sample B. Figures 4 and 5 show the experimental results of the X-ray and neutron specular as well as the diffuse reflectivity measurements of sample B. The simulation of the specular reflectivity curves by use of the Parratt formalism yield a d spacing of 130 Å exploiting the electron density (X-rays) or the scattering length density (neutrons) profile as shown in Figure 1. In the case of the X-ray reflectometry the insertion of the copolymer bilayer enlarges slightly the periodicity of equivalent interfaces whereas the additional interface (interface copolymer/chain) modifies the neutron reflectivity curve. The thickness of film amounts to about d ) 517 ( 27 Å and equals the vertical coherence length. In contrast to sample A we did not observe pronounced
Kiessig fringes between the high-order Bragg peaks in the X-ray reflectivity curve, which we explain by the coexistence of 2D domains with different total thicknesses, i.e., different numbers of bilayers.15 Atomic force microscopy (AFM) images verify this statement. Already at room temperature it shows domains with height differences of about 150 Å (Figure 6a), which corresponds to the thickness of three bilayers. Assuming an individual interface roughness of 12 Å and perfect correlation of interfaces and including the contribution of resonantdiffuse scattering (see above), we get an appropriate fit to the measured X-ray reflectivity curve. Due to the large roughness of interfaces the specular scattering disappears and the resonant-diffuse scattering dominates the reflectivity curve from about qz ) 0.20 Å-1. The fitted refractive indexes indicate an average density reduction of about 5% per transferred monolayer, which we explain by the built up of domains. The transversal diffuse scans recorded at four different Bragg peak positions are shown in Figure 5a. In addition to the specular peak at ∆ω ) 0 we find broad diffuse peaks with angular widths increasing as a function of the Bragg angle 2θ/2. Transforming into the reciprocal space the full width of half-maximum (fwhm) of the in-plane momentum ∆qx is a linear function of qz2. Using the formalism introduced in refs 3 and 4
∆qz ) 2σ2Lx-1qz2
(4)
its slope is inversely proportional to the lateral coherence length Lx of the height-height fluctuations of the interface (15) Pietsch, U.; Barberka, T. A.; Geue, Th.; Sto¨mmer, R. Nuovo Cimento 1997, 19D, 393.
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Figure 6. AFM pictures of sample B before annealing (a) and after annealing (b).
roughness σ. σ itself is taken from the slope of the low angle part of the specular reflectivity curve. From the X-ray experiment, we evaluated Lx,x-ray ) 8325 ( 250 Å, which is in similar order of magnitude as found by Geue et al.16 for other fatty acid salt multilayers. The neutron reflectivity measurements are shown in Figures 4b and 5b. The first one measures the initial degree of intermixing at the chain/chain as well as at the chain/ copolymer interfaces. The vertical periodicity is estimated to about 130 Å, the total thickness is 505 ( 17 Å and is (16) Geue, Th.; Schultz, M.; Englisch, U.; Sto¨mmer, R.; Pietsch, U.; Meine, K.; Vollhardt, D. J. Chem. Phys., submitted.
in agreement with the X-ray results. In contrast to the X-ray reflectivity curve we observed Kiessig fringes between the Bragg peaks over the whole detected qz range. This seems to be caused by the perfect repetition of interfaces between nondeuterated and deuterated chains, which is in contrast to the rather low vertical correlation of metal/chain interfaces (see above). The measured neutron reflectivity curve was simulated with the same set of parameters as used for the X-ray curve including the resonant-diffuse scattering. Due to the sufficient number of Bragg peaks at the neutron specular reflectivity curve, we could evaluate a lateral coherence length from neutron diffuse scattering
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Figure 7. The intensity reduction of the superstructure peak and the first regular Bragg peak for different temperatures T of sample A (a) and the variation of the intermixing parameter R as a function of 1/T (b).
measurements, for the first time (see Figure 5b). After separation of the specular component, the full width of half-maximum ∆qx of the diffuse component is a linear function of qz2 as in the X-ray case. The slope is steeper, which indicates a smaller lateral coherence length (Lx,neutrons ) 5330 ( 430 Å) visible for neutrons compared with the respective value obtained for X-rays (Figure 5c). The relation Lx,neutron e Lx,x-ray is an additional hint for the higher fluctuation of chain ends compared with their chain heads (see above). (II) Structure Investigations during Thermal Treatment. The temperature dependence of the vertical stacking of molecules in both films was investigated by in situ neutron reflectivity measurements. To do that the reflectivity was measured during 20 min at a certain temperature and within a certain qz range as shown in Figures 7 and 8. The intensity of the superstructure peak appearing at qz ) 0.06 Å-1 (sample A) and 0.05 Å-1 (sample B), shown in Figures 7a and 8a, remains constant up to 45 and 50 °C, respectively, and decreases rapidly above. Following our arguments given in refs 6 and 7 this is explained by the thermally induced intermixing of deuterated and nondeuterated molecules (see Discussion). Due to the 1:1 stacking of deuterated and nondeuterated bilayers of sample A, the regular first-order peak at qz ) 0.108 Å-1 (Figure 7a) is not affected by the intermixing and remains unchanged. For sample B the peak at qz ) 0.095 Å-1 (Figure 8a) is caused by scattering at interfaces between the deuterated and nondeuterated chains and additionally by the interfaces between the fatty acid salt molecules and the copolymer. Because the superstructure intensity is proportional to the square of the scattering length density difference at the interfaces, its reduction can be described by an intermixing parameter R. It characterizes the amount of the deuterated molecules in the initially nondeuterated monolayer and vice versa. As shown in Figures 7b and 8b the functional behavior of R (T) (T temperature) follows an Arrhenius law
ln(R/R0) ) -EA/kBT
(5)
Figure 8. The respective intensity variation for sample B (a) and the corresponding intermixing parameter R (b).
R0 reflects the initial intermixing at room temperature. kB is the Boltzmann constant. Using eq 5 the estimated activation energy is EA ) 1.7 ( 0.5 eV (164 ( 48 kJ/mol) for both samples considering the time dependence of the exchange process. At a certain temperature the time dependence of the superstructure intensity was measured similar to the procedure demonstrated in ref 6. The temperatures were chosen close below the melting point of pure fatty acid (T < 70 °C). The thermally induced reduction of superstructure peak intensity is described by a diffusion coefficient Ds.17 The intensity variation is interpreted analogue to the quasielastic neutron scattering. Describing the probabililty of a molecule to occupy the site z at the time t and assuming a Gaussian-like profile of the probability distribution versus z, it leads to the well-known relation18
ln(Is(qz,t)) ) -Dsqz2t
(6)
t is the time of annealing and Ds is the vertical diffusion coefficient. The intensity Is is taken at the qz position of the superstructure peak at T ) 55 and 60 °C. Similar for samples A and B the measurements lead to vertical diffusion coefficient in the range of Ds ≈10-23-10-22 m2/s. This value is 10-9 times smaller than a lateral diffusion coefficient known from lipid bilayers.19 After the sample was annealed, the X-ray reflectivity curves verify the remaining of lamellar order for sample A whereas the lamellar stacking of sample B got lost. No model for simulation of the respective X-ray curve was found up to now. The AFM picture of this sample shows a network of small domains with height differences twice the value as before the annealing (Figure 6b). Discussion The intensity reduction of the superstructure peak during annealing is interpreted as a reduction of the scattering length density contrast at the chain/chain and chain/polymer interfaces, respectively. In the case of the (17) Englisch, U. Ph.D. Thesis, Potsdam, 1998. (18) Schatz, G.; Weidinger, A. Nukleare Festko¨ rperphysik; Teubner: Stuttgart, 1992. (19) Merkl, C. Ph.D. Thesis, Potsdam, 1997.
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Cd-arachidate multilayer (sample A) the X-ray reflectivity pattern indicates that the positional order of the metal sheets is unaffected by the annealing so that the exchange of hydrocarbon chains is caused by a jumping between discrete sites along the surface normal. This is also valid for the complex multilayer system (sample B) up to about 62-65 °C. At higher temperatures we observed the complete destruction of the vertical structure. Our model for interpreting the molecular intermixing is based on an “order-disorder model” known from solidstate physics.20 Dividing the vertical multilayer structure into two sublattices (in the case of the complex system the copolymer should act as a diffusion barrier), one for the nondeuterated and one for the deuterated molecules, one gets the following system of equations for the scattering length densities FD,H within the deuterated and nondeuterated bilayers:
FD ) (1 - R)FD0 + RFH0
(7)
FH ) RFD0 + (1 - R)FH0 F0D and FH0 are the respective values for layers containing deuterium or hydrogen only. Because the detected intensity is directly proportional to the gradient of the square of the scattering length density, one gets
x
IT (1 - 2R) ) IRT (1 - 2R0)
(8)
R0 and R characterize the amount of deuterated molecules in the nondeuterated layer and vice versa at room temperature and under annealing, respectively. For the calculation of R we assume complete separation of both components at room temperature, i.e., R0 ) 0. R0 > 0 may indicate an initial intermixing. As shown in Figures 7 and 8 the functional behavior of R can be described by an Arrhenius-like behavior. The amount of the estimated activation energy can be explained by breaking the hexagonal arrangement of molecules within a certain monolayer. Using the theory of Salem,22 the van der Waals energy between two arachidic chains amounts to about 0.28 eV. The breaking of six bonds to the six next neighbors of a dense-packed 2D arrangment of molecules requires an energy of about 1.68 eV. The escape of a molecule from the edge or the border of a domain needs about 1.12 or 1.4 eV, respectively. Within the estimated error of 0.5 eV our calculated activation energy is in good agreement with this values. That means that the molecules participating at the molecular exchange come out mainly from the inner part of a particular domain. Finally we propose the following model of intermixing (Figure 9). Before annealing, the multilayer consists of domains containing a mixure of fatty acid and fatty acid salt molecules. During annealing the molecules become mobile and exchange their positions. Using a reflectivity experiment, we are able to observe the vertical component of this process only. The in-plane component was observed by a grazing-incidence experiment.21,24,25 For the Cd(20) Kittel, C. Introduction to solid-state physics; Oldenburg Verlag: Mu¨nchen, 1993. (21) Feigin, L.; Konovalov, O.; Wiesler, D. G.; Marjkrzak, C. F.; Berzina, T.; Troitsky, V. Physica B 1996, 221, 185. (22) Salem, L. J. Chem. Phys. 1962, 37, 2100. (23) Tippmann-Krayer, P.; Kenn, H. M.; Mo¨hwald, H. Thin Solid Films 1992, 210/211, 577. (24) Barberka, T. A. Ph.D. Thesis, Potsdam, 1996. (25) Malik, A.; Durbin, M. K.; Richter, A. G.; Huang, K. G.; Dutta, P. Phys. Rev. 1996, B52, R11654.
Figure 9. A possible model to explain the molecular exchange in LB multilayers from fatty acid salt molecules. Black coils indicate the deuterated chains; open coils stand for the nondeuterated chains. We assume that the fatty acid molecules are moving mainly across the film.
stearate multilayer we did not find any modification of the in-plane structure under annealing up to 70 °C (not shown). Thus we conclude that the molecules exchange mainly their positions in vertical direction. Because the intial temperature for the molecular exchange is lower than 70 °C, we assume that the acid molecules are moving whereas the fatty acid salt molecules remain almost at their fixed positions. However, from simulation of the reflectivity curves we cannot exclude strictly that the salt molecules exchange their positions also. Asmussen and Riegler26 observed a vertical movement of behenic acid molecules across the multilayers, which gave rise to a local increase of the total multilayer thickness (doms) and the creation of deep holes within the film. Long time annealing of multilayer films at T > 70 °C with partial salt content seems to initiate a complete wash out of the fatty acid component from the framework of salt molecules.27 This takes place if the molecules can evaporate from the surface. This effect was not considered for our interpretation. The higher stability of the salt component against diffusion may be explained by the brideging of two chains by a single double-charged metal ion.24,25 Conclusion The present results demonstrate the complementary of the X-ray and neutron reflectometry to provide separate information about the structure of the metal/chain and chain/chain interfaces. In the case of the Cd-arachidate multilayer the specular X-ray reflectivity shows perfectly stacked metal sheets with low interface roughnesses whereas the neutron reflectivity displays the damaged vertical periodicity of the chain/chain interfaces with much higher interface roughness. Additionally, we have shown (26) Asmussen, A.; Riegler, H. J. Chem. Phys. 1996, 104, 8151. (27) Vierheller, T. R. Foster, M. D. Wu, H.; Schmidt, A. Knoll, W. Satija, S.; Markrzak, C. F. Langmuir 1996, 12, 5156.
Fatty Acid Salt LB Multilayers
by X-ray and neutron diffuse scattering the lower lateral correlation length of the chain-chain interfaces compared with the metal-chain interfaces. We have demonstrated that the specular reflectivity curves from LB multilayer films have to be interpreted including the contribution of the resonant-diffuse scattering. The fits are not perfect but they demonstrate that the resonant-diffuse scattering from LB systems dominates the reflectivity curve beginning at low qz. Neutron reflectometry is an ideal tool to investigate a vertical intermixing of molecules in the LB multilayer during thermal treatment. The observed intensity reduction is interpreted as an reduction of the scattering length
Langmuir, Vol. 15, No. 5, 1999 1841
density contrast at the chain/chain, chain/copolymer interfaces. Its appearance is explained by the vertical movement of fatty acid molecules across the LB multilayer film. The estimated diffusion coefficient of this movement is in the order of 10-22 m2/s. Acknowledgment. The authors thank the University of Bochum (R. Siebrecht, A. Schreyer, and H. Zabel) for collaboration at the ADAM-reflectometer at ILL and the Land Brandenburg and the DFG for financial support (Pi 217/4-4). LA981377+
