3820
Langmuir 1994,10, 3820-3826
Self-Diffusionof “Hairy Rod” Molecules in Langmuir-Blodgett-Kuhn Multilayers Probed with Neutron and X-ray Reflectometry A. Schmidt,*,?K. Mathauer,* G. Reiter,g M. D. Foster,* M. Stamm, G. Wegner, and W. Knollii Max-Planck-Institut fuer Polymerforschung, Postfach 3148,0-55021 Mainz, Germany Received May 23, 1994. In Final Form: July 19, 1994@ The thermal stability of Langmuir-Blodgett-Kuhn
(LBK) multilayers of poly-[(y-methyl L-glutamate)-
co-( y-n-octadecyl ~-glutamate)l(PG) has been investigated using neutron reflectometry. The stability of
the LBK films of such “hairy r o d molecules was determined by measuring the interfacial width between protonated and deuterated stacks of PG. No center of mass diffusion of molecules between layers of protonated and deuterated material between 349 and 414 K was found. The broadening of the interface cm2/sin this temperature region. The film structure and its changes during annealing is lower than of these rodlike molecules with flexible side chains were also probed with X-ray reflectometry and compared to the results of the neutron experiments. The total film thickness decreased during annealing while no loss of material due to thermal desorption occurred. The origin of the thermal stability against interdiffusion is discussed.
Introduction Rodlike molecules with covalently attached flexible side chains1-so called “hairy rods” (Figure la)-have been developed during the last decade with an eye toward applications in photonics, electronics, and chemical sens o m 2 These materials are also of interest because they show lyotropic and thermotropic behavior.lh-k LangmuirBlodgett-Kuhn (LBK) multilayers from molecules with such a “hairy rod” architecture have been shown to be t Now with University of Arizona, Department of Chemistry, Tucson, AZ 85721. Now with BASF AG, Kunststofflaboratorium, D-6700 Ludwigshafen, Germany. 0 Now with University of Illinois at Urbana-Champaign, Department of Material Science and Engineering, Urbana, IL 61801. I University of Akron, Institute of Polymer Science,Akron, OH 44325-3909. 11 Also with The Institute of Physical and Chemical Research, Frontier Research Program, 2-1 Hirosawa, Wako-Shi, Saitama 35101, Japan. Abstract published in Advance ACS Abstracts, September 1, 1994. (1)(a)Orthmann, E.;Wegner, G. Angew. Chem. 1986,98,1114.(b) Orthmann,E.;Wegner, G. Angew. Chem.,Int.Ed. Engl. 1986,25,1105. (c) Duda, G.;Wegner, G. Makromol. Chem.,Rapid Commun. 1988,9, 496. (d) Duda, G.;Schouten, A. J.; Amdt, T.; Lieser, G.; Schmidt, G. F.; Bubeck, C.; Wegner, G. Thin Solid Films 1988,159,221.(e)Caseri, W.; Sauer, T.; Wegner, G. Macromol. Chem., Rapid Commun. 1988,9, 651. (0 Embs, F.;Wegner, G.; Neher, D.; Albouy, P.; Miller, R. D.; Wilson, C. G.; Schrepp, W. Macromolecules 1991,24,5068.(g)Menzel, H.; Weichart, B.; Hallensleben, M. L. Thins Solid Films 1993,223,181. (h)Watanabe, J.; Fukuda, Y.; Gehani, R.; Uematsu, I. Macromolecules 1984, 17, 1004. (i) Watanabe, J.; Ono, H.; Uematsu, I.; Abe, A. Macromolecules 1985,18,2141.(i)Watanabe, J.; Goto, M.; Nagase, T. Macromolecules 1987,20,298. (k) Watanabe, J.; Nagase, T. Macromolecules 1988,21,171.(1)Watanabe, J.;Takashina,Y.Macromolecules 1991,24,3423.(m) Tsujita, Y.; Ojika, R.; Tsuzuki, K.; Takizawa, A.; Kinishita,T. J.Polym. Sci.A: Polym. Chem. 1987,25,1041.(n)Tsujita, Y.; Ojika, R.; Takizawa, A. J. Polym. Sci. A: Polym. Chem. 1990,28, 1314. (0)Yamaguchi, M.; Tsutsumi, A. Polym. J. 1990,22,781. (p) Watanabe, J.; Takashina, Y. Polym. J. 1992,24,709. (2)(a) Hickel, W.; Duda, G.; Jurich, M.; Kroehl, T.; Rochford, K.; Stegeman, G.; Swalen, J. D.; Wegner, G. Langmuir 1990,6,1403.(b) Sauer, T.; Caseri, W.; Wegner, G.; Vogel, A.; Hoffmann, B. J.Phys. D: Appl. Phys. 1990,23,79. (c) Mathy, A.; Mathauer, IC; Wegner, G.; Bubeck, C. Thin Solid Films 1992,215,98.(d) Hickel, W.; Duda, G.; Wegner, G.; Knoll, W. Makromol. Chem., Rapid Commun. 1989,10, 353. (e)Wegner, G.Mol. Cryst. Liq. Cryst. 1992,216,7.(0 Sauer, T.; Caseri,W.; Wegner, G. J.Phys. D: Appl. Phys. 1990,23,79.( g )Vogel, A.; Hofhann, B.; Schwiegk, S.; Wegner, G. Sensors Actuators 1991, B4, 65. (h) Wegner, G.;Mathauer, M. Mater. Res. SOC.Symp. Proc. 1992,247,767.
*
@
Figure 1. (a) Geometry of a hairy rod. In the case of PG we have rods of length L = 320 nm and diameter d = 0.56 nm, surrounded by alkyl chains. (b) The PGs are compressed on the water subphase of a Langmuir trough to a 2D nematic liquid crystal. ( c ) The alkyl side chains are stretched away from the water surface, and the distance w between rods is about 1.3 nm.
useful for wave photo resist^,^ and chemical sensors.2f9g Applications of ultrathin polymeric films, prepared from conventional amphiphilic molecules, are (3)Mathauer, IC;Schmidt, A.; Knoll, W.; Wegner, G. Macromolecules 1993,accepted for publication. (4)(a)Roberts, G.G. Langmuir-Blodgett Films; Plenum Press: New York, 1990. (b)Ulman, A. An Introduction to Ultrathin Organic Films; Academic Press: San Diego, CA, 1991.
0743-7463/94/2410-3820$04.50/0 1994 American Chemical Society
Self-Diffusion of “Hairy R o d Molecules
Langmuir, Vol. 10,No. 10,1994 3821
Chart 1
C
0” ‘ 0
C
I
// \o 0
I
X=O.7 y=O.3 P-PG: R = (CH2) 17-CH3 d-PG: R = (CD2)17-CD3
limited by the thermal and long-term stability of the structure. Another problem is the kind and number of defects in the supramolecular structure of traditional LBK fiims.4 Optical investigations, especially of the low losses in wave guides,2chave shown the high structural quality of LBKfilms of “hairy rods”. The reason for this is the liquidcrystal-like structure of the LBK multilayer^,^^^^ which prevents grain boundaries such as those found in crystalline LBK films. Because of this liquid-crystal-like structure and their viscoelastic b e h a v i ~ rthese , ~ LBKfilms may be described as a reinforced liquid or nanocomposite. The flexible side chains build the liquid matrix in this model, and the embedded rods are supposed to play the role of reinforcing elements to provide for the mechanical stability of the film^.^^^^ To check the thermal stability of the “hairy rod” multilayers, we investigated the stability of multilayer assemblies from polyglutamatesla-d (PG; see Chart 1) against interdiffusion between adjacent layers of protonated and deuterated material witb the help of neutron reflectometry.6 We have chosen polyglutamates as an example for a “hairy rod” molecule because they show the above mentioned properties and bulk data for these materials are a ~ a i l a b l e . ’ ~ - ”We ~ ~ measured the same samples also with X-ray reflectometry.6 Here we do not have contrast between the protonated and deuterated layers, but we could check the values for the overall thickness and periodicity of the electron density within the film and their change with annealing time and temperature. We will first summarize what is already known about “hairy rods” on the water subphase and in LBK films prepared following the procedure given in the Experimental Section. On the water/air interface the molecules form a monolayer which can be described as a twodimensional liquid crystal.8 The rods are not macroscopically oriented but form a domain-like structure (see Figure lb), with the director of every domain pointing in a ( 5 ) (a)Lee, S.; Dutscher, I. R.; Hillebrands,B.;Stegeman, G. I.;Knoll, W.; Duda, G.;Wegner, G. Mater. Res. SOC.Symp. Proc. 1990,188,355. (b)Nizzoli,F.;Hillebrands,B.;Lee, S.; Stegeman,G. I.;Duda, G.;Wegner, G.;Knoll, W. Mater. Sci. Eng. 1990,B5,173. (c)Albouy,P.-A.;Schaub, M.; Wegner, G. Acta Polym., in press. ( 6 )(a) Russell, T. P. Mater. Sci. Rep. 1990, 5, 171. (b) Stamm, M. In Physics of Polymer Surfaces and Interfaces; Sanchez, I. C., Ed.; Butterworth Heinemann Publ.: Boston, MA,1992; p 163. (c) Foster, M. D. Crit. Rev. Anal. Chem. 1993,24, 179. (7) (a)Mohanty,B.;Watanabe,J.; Ando, I.;Sato, K. Macromolecules 1990,23,4908. (b) Schmidt, A.; Lehmann, S.; Georgelin, M.; Katana, G.;Mathauer, K.; Kremer, F.; Schmidt-Fbhr,K.; Boeffel, C.;Knoll, W.; Wegner, G. In preparation. (8) (a)Yase,IC;Schwiegk,S.; Lieser, G.;Wegner,G. Thin SolidFilms 1992,210/211,22. (b) Yase, K.; Schwiegk, S.; Lieser, G.; Wegner, G. Thin Solid Films 1992,213,130. (c)Schwiegk, S.; Vahlenkamp,T.; Xu, Y.; Wegner, G. Macromolecules 1992, 25, 2513.
Figure 2. Picture of the multilayer structure after the LBK transfer. (a)On a big substrate the direction of rods in adjacent layers is not correlated, while (b) on a small substrate the rods in all layers are aligned parallel to the transfer direction. different direction. The average size of the domains is between 50 nm and several micrometers.8bThe side chains are stretched away from the ~ a t e r , l ~ ,and ~ , gthe , ~ rods lay flat on the interfacelo (see Figure IC). The liquid-crystal structure is preserved during the LBK transfer (seeFigure 2a). The helical axes of PG lay parallel to the substrate, and the whole film consists of sheets of PG layers parallel to the substrate ~ u r f a c e . ~X-ray ~~~~,~,~ reflectometry showed that because ofthe anisotropywithin one monolayer, two of these monolayers define one period with a periodicity of about 3.5 nm.ld A detailed investigation of the structure was done with the help of neutron and X-ray reflectometry.ll The periodicity after the transfer reflects the presence of a bilayer containing an electron-rich core of about 2.0 nm, built up mainly by the a-helical backbones, and an approximately 1.5 nm thick layer ofinterdigitating side chains between each backboneenriched region. Each single rod can be visualized as caged in a “tube”of width w ,height H , and length L. The height H is given by the average monolayer thickness, while w is the spacing between two rods in the layer plane. The lateral order of the LBK film was found to depend on the size of the substrate.8c For a substrate half as broad as the LB trough (7.6 cm) the monolayer is transfered without change of the domain-like structure (Figure 2a). Rods of domains in adjacent layers are randomly rotated with respect to one another, and therefore local orientations of the rods in adjacent layers are not correlated. The macroscopic order parameter of the LBK film is zero. Substrates of this size were used for the X-ray and neutron measurements in this paper. For substrates with a width of only ‘16 of the trough width (2.5 cm) a flow effect orients the rods macroscopically (9) (a) Mathauer, K.;Vahlenkamp, T.; Frank, C. W.; Wegner, G. Langmuir 1993,9,1582. (b)Menzel, H.; Hallensleben, M. L.;Schmidt, A.; Knoll, W.; Fischer, T.; Stumpe, J. Macromolecules 1993,26, 3644. (c)Lee, S.;Dutcher, J. R.;Stegeman, G. I.; Duda, G.;Wegner, G.;Knoll, W. Phys. Rev. Lett. 1993, 70, 2427. (10) (a) Malcolm, B. R. Polymer 1966, 7,595. (b) Loeb, G. I.; Baier, R. E. J . Colloid Interface Sci. l968,27, 38. (11) Foster, M.;Vierheller, T.;Schmidt, A,; Mathauer, K.; Knoll, W.; Wegner, G.; Satija, S.; Majkrzak, Ch.Mater. Res. SOC.Symp. Proc. 1992, 248, 41.
3822 Langmuir, Vol. 10,No. 10,1994
parallel to the transfer direction8J2J3(Figure 2b). The order parameter in the LBK films on small substrates reaches 0.4 and can be improved to 0.8 by annealing.8c Earlier combined measurements of X-ray and neutron reflectrometry with periodic layers of protonated and deuterated PG on a big substrate, and therefore with uncorrelated rods, showed that upon annealing at 343 and 357 K for more than 5 h the periodicity caused by a periodic sequence of protonated and deuterated PG layers remains unchanged.ll This result indicates that there is no center of mass diffusion between layers at 357 K. The LBK film is hence stable against interdiffusion at this temperature.2hJ1 At the same time, the anisotropic structure within a single layer is destroyed, a fact evident by a reduction in the intensity of the Bragg peak seen in the X-ray measurements.11J4 The effective thickness of a layer also decreases, which is understood as a stronger interdigitation of side chains with annealing. The goal of our present paper is to determine and model the diffusion perpendicular to the LBK layers quantitatively and for higher temperatures up to 414 K. This temperature is ca. 10-15 deg below the temperature regime in which irreversible helix-to-pleated sheat transition of the individual PG molecules will take place.ld
Experimental Section Materials. The substance under investigation is poly-[(ymethyl L-glutamate)-co-(y-n-octadecyl g glutamate)] (PG) with 70% methyl and 30% octadecyl side chains1a-dt2c(Chart 1). The pitch of this a-helix is 0.54 nm, and the diameter d is 0.56 nm.15 This diameter includes the C, atoms but not the methylene units (CH2)2. The average molecular weight was determined by light scattering in CHClJformamide (0.5%)to beMw =460 000 g/mol, which corresponds to a degree of polymerization of approximately 2100.2c There are 3.6 monomers per revolution, so we determine an average length L of about 320 nm for the helix from the molecular weight. Figure l a depicts the geometry of the poly(peptide) with its surrounding side chains. Two forms of these molecules were synthesized: the first one had only protonated side chains (p-PG), while in the second type 95%ofthe long side chainswere replaced by deuterated octadecyl chains (d-PG). The synthesis of the protonated PG has been described in ref 2c. For the synthesis of the PG with perdeuterated side chains, stearic acid was perdeuterated according to ref 16. The acid was reduced with LiAlD4 in THF and converted to the corresponding alkyl bromide by adding equimolar amounts of solid triphenylphosphine dibromide to a solution of the perdeuterated octadecanolin dichloromethane. The product was isolated by filtration over silica gel (cyclohexane). For the synthesis of the glutamic ester, the alkyl bromide was used for the alkylation of the copper complex of glutamic acid as described in ref 17 to give the desired ester in 29% yield. Once the appropriate ester was prepared, the synthesis of the polymers with deuterated side chains followed ref 2c. Watanabe et al. found that polyglutamate with 100%octadecyl chains exhibits thermotropic liquid crystalline behavior above the melting point of the side chains at ca. 335 K.liJ~pThis thermotropic behavior was also found for copolyglutamates with different alkyl side chains.lhjPk Bulk samples of the material under investigation do not show liquid crystalline phases in polarized light microscopy between 29,O K (the melting point of the side chains) and 370 K. We will report about this and other bulk properties of PG in an upcoming p ~ b l i c a t i o n . ~ ~ (12)Schwiegk, S.; Vahlenkamp, T.; Wegner, G. Thin Solid Films 1992,210/211, 6. (13)(a) Chi,L. F.; Eng. L. M.; Graf, K.; Fuchs, H. Langmuir 1992, 8,2255.(b) Tsukruk, V. V.; Foster, M. D.; Reneker, D. H.; Schmidt, A.; Knoll, W. Langmuir 1993,9,3538.(c) Tsukruk, V. V.; Foster, M. D.; Reneker, D. H.; Schmidt, A.; Wu, H.; Knoll, W. Macromolecules 1993, 27,1274. (14)Schaub, M. Masters Thesis, Universitaet Mainz, 1990. (15)Malcom, B. R. Proc. R . SOC.London A 1958,249,30. (16)Zimmermann, H. Liq. Cryst. 1989,4,591. (17)Van Heeswijk, W. A.; Eenink, M. J. D.; Feijen, J. Synthesis 1982, 744.
Schmidt et al.
7 .
Figure 3. Specular reflection geometry. The reflected intensity, determined by the n(z)profile, is measured as a function of the incident angle, 0.Our samples consist of two stacks of protonated and perdeuterated LBK layers on a siliconsubstrate. Sample Preparation. Silicon wafers were cleaned with hot chloroform in a n ultrasonic bath for 15 min and then treated with a hot solution of NH40H:H202:HzO (1:1:5) for 30 min. The substrates were then rinsed with Millipore water. Hydrophobic surfaces were obtained by etching the wafers in anAr/Oz-plasma (0.95 mbad0.05 mbar) and treating the thus cleaned substrates with a hot solution of hexamethyldisilazane in chloroform (1:5) for 30 min. PG monolayers were prepared on a commercial Lauda FW1 film balance using a compression rate of 50 mdmin. The PGs were spread from a 0.3 mg/mL chloroform solution. Water for the subphase was purified by a Millipore filtration system. LBK multilayers of Y-type were transferred at 293 K and 20 mN/m with a dipping speed of 20 m d m i n onto silicon wafers of size 7.6 x 5.0 x 0.05 cm3. This substrate size was chosen according to the neutron beam's dimension. The transfer ratios for both the up and down strokes were always 1f0.05. Two kinds of samples were prepared. Sample A consisted of 18 layers of protonated PG (p-PG) on top of the silicon substrate, followed by 18 layers of deuterated PG (d-PG). Samples B and C were built up with 20 layers of p-PG and 12layers of d-PG. In both types of samples the interface between protonated and deuterated material is formed by the side chains. Annealing of the samples was carried out in an evacuated drying oven at temperatures between 349 and 413 K for varying times, up to 12 h. The samples were quenched to room temperature by removing them from the oven. X-ray Reflectometry. The reflectometer18used a RIGAKU 18-kW rotating anode with a Cu target as an X-ray source and a graphite monochromator set for iz = 0.154 nm. The X-ray beam was collimated to 50 ,um width and 10 mm height with a divergence of 0.01". The intensity at the sample amounted to IO = 5 x lo6 cps with a background of less then 0.4 cps. The specular reflectivity was measured as a function of momentum transfer by rotating the sample in steps of 0.008" and the scintillation detector in steps of 0.016". Neutron Reflectometry. Measurements were done at the KF'A Julich, Germany.lg A graphite monochromator provides a beam of narrow wavelength distribution with iz = 0.43 nm. The flux at the position on the sample was about l o 5 neutrond(cm2 s) and could be attenuated by different PMMA plates to protect the position-sensitive proportional He3 counter (ORDELA, Oak Ridge). The neutron beam was collimated to 0.6 mm width and 40 mm height with a divergence angle of 0.02". Reflected intensities were recorded in steps of 0.01", normalized to the incoming intensity, and corrected for the background, which was obtained simultaneously by the linear detector. In both X-ray and neutron reflectometry (Figure 3) only the momentum transfer q perpendicular to the substrate is pertinent, where q is given by the angle of incidence 8 and the wavelength iz
Reflection of a plane wave from a system of stratified layers can be described by a matrix formalism,20 which is based on the continuity conditions of the resulting electromagnetic field (or (18)Foster, M.; Stamm, M.; Reiter, G.; Huttenbach, S. Vacuum 1990, 41,1441. (19)(a) Stamm, M.; Reiter, G.; Huttenbach, S. Physica 1989,B156, 564. (b) Stamm, M.; Huettenbach, S.; Reiter, G. Physicu 1991,B173, 11. (20)Lekner, J. Theory of Reflection; Nijhoff: Dordrecht, 1987.
Self-Diffusionof "Hairy Rod" Molecules
Langmuir, Vol. 10, No. 10, 1994 3823
wave function) and its first derivative at the boundaries between the layers. For the evaluation of the Bragg peaks in the X-ray reflectometry the first born approximation was used.21 The reflectivity R of the system is determined by the profile of the refractive index n as a function of depthz. The lateral coherence length6 of the beam in X-ray and neutron reflectometry is about 1pm and decreases with increasing momentum transfer. Hence the refractive index n(zy,z), which can be inhomogenous and therefore depends on all three coordinates, is averaged coherently over this length in the z-and y-directions. Reflected intensities contain, therefore, information about n(z)and the microroughness averaged over the lateral coherence area on the surface. For neutrons and X-rays this laterally averaged quantity n(z) is described by
n = 1 - (1'/2n)d - ix
(2)
0
-2 h
B .3
8
5 t 00
z!
-4
-6
100 min at 349 K
0
The imaginary partx represents absorption by the material. The real part 6 describes the scattering of the incident radiation in the reflection geometry and is given by
6 = re@
1 .o
0.4 0.6 0.8 momentum transfer q [m-l]
0.2
(3a)
for X-rays, with electron density e and the classicalelectron radius re and
d=bN
(3b)
for neutrons, with scattering length density bN.6 In both cases 6 is of order 10-3-10-4 nm-2. For data analysis, the calculated reflectivities for different n(z)profiles extracted from molecular models of the film structure are compared with experiment.20p21 Deviations between experiment and model curves are minimized, and the best values of the parameters included in the model of n(z)can thereby be determined. These model parameters include electron (or scattering length) density and thickness of layers as well as roughness and interface width between layers. Interfaces are approximated by error functions, which are characterized by the variance u. We will use for the following u as a measure of the interface width. Figure 3 depicts schematically the film structure of a bilayer stack of p- and d-PG, and the corresponding model of n(z)for the case of neutron reflectrometry. The amount of interdiffusion is determined by modeling the interface width between p- and d-PG layers. Interdiffusion of molecules between the two stacks, as well as interdigitation of protonated and deuterated side chains, increases the interface width, u. The change in interface width with time and temperature is expressed by a coefficient W(T), which is defined as
Here d T , t )is the interface width after the annealing time t at annealing temperature T and dT,O) is the initial width before annealing (Figure 3). For interdigitation W(T)is a mean to normalize the interface changes for different annealing times. For a center of mass movement the coefficient W(r) approximates the diffusion constant.
Results and Discussion NeutronReflectometry. Figure 4 shows the neutron reflection curves of sample A before and after annealing at 349 K for 100 min. The best fit to the experimental curve (dots with error bars) and the extreme cases according to an error of f 0 . 4 nm of the interface width for the unannealed sample are shown in Figure 4a. In Figure 4b the two measured curves (unannealed and after 100 min at 349 K) are directly compared. The reflectivity after annealing is lower, especially at large q , and the minima are shifted to higher momentum transfer. Figure 4c presents the scattering length density profiles calculated with the best fit parameters. The profile for the annealed sample is shifted so that the centers of the interfaces (21)(a) Nicklow, R. M.; Pomerantz, M.; Segmueller,A. Phys. Rev. B 1981,23,1081. (b)Rieutord, F.; Benattar, J. J.; Borsio, L.; Robin, P.; Blot, C.; Kochkovsky, R. de, J . Phys. (Paris) 1987,48, 679.
0
10
20
30
40
50
BO
70
depth z [m]
Figure 4. Neutron reflection curves of sample A before and after annealing at 349 K (a)Best fit comparedwithtwo extreme cases (a = 0.8 f0.4 nm) to determine the error of the interface width measurement before annealing. (b) Experimental reflectometry curves before and after annealing at 394 K for 100 min. (c) Scattering length density before and after annealing, as determined from the experimental reflectometry curves. Both curves are centered at the interface position. The film is thinner and more dense after annealing.
coincide. It is seen that the interface becomes slightly broader, the surface gets rougher, and the thicknesses of both protonated and deuterated layers are reduced. There is no loss of material by annealing, because the film density is increased by an amount corresponding to the loss in thickness. Table 1summarizes the results of the neutron reflectometry measurements for all three samples. The fits show that a protonated bilayer is thicker than a deuterated bilayer. The coefficient W(T)is determined on the basis of the data in Table 1,and Figure 5a summarizes the results. We have to conclude from these experiments that the normalized change W(T)in interface width perpendicular to the layers is less than lo-'* cm2/s and that this broadening does not significantly depend on the temperature. Within the limit of error of the experiment the coefficient W(T)is zero between 349 and 414 K. From the actual increase of the interface width u (see Table 1) one can conclude that the macromolecules do not move in the given time over a distance larger than the thickness of a complete layer. Together with the observed decrease in total thickness, which causes the side chains and helix cores to pack closer, one may argue that there is no real interdiffusion taking place. Only the side chains are interdigitating more strongly with increasing annealing time and temperature. Figure 5b shows the correlation between the interface width aand the average layer thickness, indicating again that there is no center of mass diffusion across the interface. The parameter
3824
Langmuir, Vol. 10,No. 10, 1994
Schmidt et al.
Table 1. Structural Parameters of LBK Films Determined by Neutron Reflectometw annealing
annealing
(f2K)
time t (f2min)
349
100
temp T
sample A
B 373 414
270 720
385
460
C a
A 9 bilayers
thickness (*o.2 nm)
avg layer
thickness
d-PG p-PG ( f 0 . 0 1 nm) 30.5 30.1 21.2 20.3 20.1 21.6 20.3
32.4 32.0 35.3 34.5 34.2 36.4 35.2
1.75 1.73 1.77 1.71 1.69 1.81 1.73
annealing temperature T [K]
-o,0 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82
average layer thickness [nm] Figure 5. (a) Values of the coefficient W(D,describing the interface broadening, and its dependence on annealing temperature, T,estimated from the neutron reflectivity measurements. Avalue of W(Dequal t o zero is within the experimental error at all temperatures. (b)Correlation between the average layer thickness and the interface width.
0
lo-'m-2)
d-PG
p-PG
4.3 4.3 4.0 4.1 4.2 4.3 4.4
1.4 1.4 1.2 1.2 1.2 1.4 1.4
surface roughness ( f 0 . 2 nm) 1.3 1.4 0 0.6 0.8 1.3 1.3
interface
width u (nm)
0.8 f 0.4 0.9 f 0.4 0.5 f 0.5 1.2 f 0.5 1.95 f 0.5 0.9 f 0.4 1.2 f 0.4
width increase W(U cm2/s) 1.4 f 8.0 3.7 f 4.0 2.7 f 2.7 1.1 f 2.2
d-PG/9bilayers p-PG/silicon. B,C:6 bilayers d-PG/lO bilayers p-PG/silicon.
340 350 360 370 380 390 400 410 420
c .-L
scattering length density bN(10-4
0.4
0.8 1.2 1.6 momentum transfer q [nm-11
2.0
Figure 6. X-ray reflectivity curves of sample A before and after annealing at 349 K. Loss of the multilayer's bilayer structure with annealing time results in reduction of Bragg peak intensity.
W(T)describes therefore the broadening of the interface by side chain interdigitation and not diffusion of the center of mass. X-ray Reflectometry. To check the total sample thickness and the surface roughness, X-ray reflectometry measurements with samples A and B were performed. The results for sample A before and after annealing are shown in Figure 6. The most striking effect is the reduction of the intensity of the Bragg peak at 1 . 7 8 nm-l (corresponding to a periodicity of 3 . 5 2 nm) after annealing. It is already known that this Bragg peak belongs to a bilayer periodicity.ld As a result of annealing, the Bragg
peak also shifts to higher q values. Table 2 summarizes the parameters for the best fits to the X-ray reflectometry curves. The results of sample B show that if annealing is carried out at high temperatures and for a sufficiently long time, the Bragg peak is lost completely and only a homogeneous film (within the resolution of the experiment) is left. This behavior is also already known and understood as a loss ofthe original bilayer structure,ld,g,11,14 which in turn is caused by the anisotropy at the waterlair interface before transfer. The change in periodicity is accompanied by a decrease in total film thickness. Changing the bilayer structure allows the side chains of each layer to interdigitate more strongly with adjacent layers, thus decreasing the total film thickness and increasing the interface between pand d-PG in the neutron reflection experiments. The X-ray experiments prove as well that the decrease in thickness is accompanied by an increase in electron density. This result confirms the conclusion from the neutron measurements that thermal desorption does not take place in the course of the annealing process. For sample A, the average bilayer thickness and the periodicity do not correlate. For this sample the Bragg peak could be fitted best by assuming 17 instead of 18 periods. It also has a very rough surface. One can therefore conclude that the quality of the last deposited bilayer of sample A was not as good as that of the rest of the film. It is thinner than a normal bilayer. It also does not contribute to the Bragg peak because it is not correlated with the other bilayers in the film. One can summarize the experimental results of both methods as follows. With increasing annealing time and temperature, the film becomes thinner, and with concurrent density increases, there is an increase in the surface roughness and a slight broadening of the interface between p- and d-PG layers. The total thickness and surface roughness measured with both types of reflectometry agree. The thickness and periodicity(from X-ray) decrease with annealing, and after sufficient time, the electron density of the film becomes homogeneous. The interface coefficient W ( n is independent oftemperature and smaller than 10-ls cm2/s. This interface broadening (seen with neutrons) is not caused by a center of mass movement between layers, but by an increasing interdigitation of side chains from adjacent protonated and deuterated layers. Models for the Self-Diffusion. The satisfactory description of the self-diffusion in such a complicated system would only be possible with the help of computer simulations. For the sake of approximations, the use of the nanocomposite model or molecular reinforced liquid is appropriate. In this model one can treat the structure as a concentrated solution of rods in a solvent matrix consisting of the alkyl side chains. Locally each rod is caged in an asymmetric tube, spanned by the adjacent rods, with 1 . 3 nm width w and 1 . 7 5 nm height H corresponding to the thickness of half of a bilayer. The
Self-Difision of “Hairy Rod” Molecules
Langmuir, Vol. 10,No. 10,1994 3825
Table 2. Structural Parameters of LBK Films Determined by X-ray Reflectometry annealing sample
temp T (f2 K)
annealing time t (izlmin)
349
100
414
720
A B
totalfilm thickness (f2nm)
average layer thickness (fO.O1 nm)
electron density e (A5 nm-3)
surface roughness
(f0.2nm)
Bragg peak spacing (f0.01nm)
62.8 62.0 56.5 54.0
1.74 1.72 1.77 1.69
360 362 360 370
1.3 1.4 0.7 1.1
3.52 3.51 3.53 none
width w is approximated from the area per monomer on the water surface and the geometrical data of the rod. The Brownian motion of a test rod in such a concentrated solution is strongly The translation diffusion perpendicular to the layer plane is prohibited, because in the samples under investigation here, the rods in adjacent layers are rotated with respect to one another by an angle ly and therefore cannot cross each other. The diffusion perpendicular to the substrate therefore cannot be caused by a simple translation of the rods perpendicular to their long axis. Before a rod can diffuse into the next layer, it first has to rotate to lie parallel to an assembly of rods in the adjacent layer. The rotational diffusion constant in a concentrated solution is given byzz
where r is the radius of the tube and L is the length of the rod. We chooser to be equal to (w+€€)I+ other possibilities would be either wI2 or Hf2, but these choices do not affect the order of magnitude of the result. The constant #I in eq 5 was measured experimentallyz4 to be 1300 for concentrated solutions of poly-(y-benzyl-L-glutamate) (PBLG), a number which was later also found in computer simulation^.^^ is the translational diffusion constant in an isotropic solution with matrix viscosity r]
With the help oPZ cos q ! ~= exp(-Wrt’)
(7)
one can calculate the time t‘ necessary for the rod to rotate into the correct angular position. Because there is no correlation between different layers in our samples, one has t o choose the angular average. Assuming an equal distribution of all possible angles, which is in agreement with experimental results,6 one gets
If the rods in adjacent layers are aligned parallel to each other, then the time t” necessary to translate perpendicular to the rod axis into the next layer is given byzz
where the diffusion distance H for the rod is equal to half the bilayer height (periodicity). One can now calculate (22)Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; University Press: Oxford, 1989. (23) M. -- , Dni. - - _, .- J - . -Phvs. -*- 1976.36. 607. -(24) Teraoka, I.; Ookubo, N.; Hayakawa, R. Phys. Rev. Lett. 1986, 55, 2712. (25) Mori, Y.; Ookubo,N.; Hahakawa, R.; Wada, Y. J.Polym. Sei., Polym. Phys. Educ. 1982,20, 2111. ~
, - - I
the interdiffision constant D between layers
D=
H2 2(t”
+ (t’))
(10)
which we write with eqs 9 and 5 as
The time t” is much smaller than (t’)and can be neglected here, but we keep it for further reference. Inserting eq 6 for the translation diffusion constant one obtains
Because of the simplicity of the model and the assumptions we had t o make, only the calculation of the lower limit given by eq 12 is useful for comparison with experimental results. One assumption, for example, is the use of the mean value L in the equation. The distribution of the molecular weight makes it necessary to average D over the length distribution p(L),which is not known. Theoretical approximationsz6and results from light scattering experimentsz7 have shown that the rotational diffusion constant ofPBLG is lowered by a factor of less than loz if a very broad distribution of rods is compared to a unimolecular distribution. We also use the factor #I = 1300 obtained for isotropic, concentrated solutions of PBLG.z4,z5 With the model of a molecular composite and the resulting approximation of eq 12, we can determine the order of magnitude of the LBK film viscosity. We know or can approximate all the geometrical factors in this equation besides the viscosity and use 400 K for the temperature T. To obtain a diffusion constant D smaller than cmz/s,our experimental limit for the coefEcient W(T),the viscosity in the matrix has to be bigger than 10‘’ * l ) Pes. The uncertainty is introduced by the factor of lo+, which is used to correct for the unknown molecular weight distribution, and its influence on the diffusion con~tant.~~,~~ For the model of a molecular reinforced liquid, where the matrix should have the viscosity of a liquid, a r] value on the order of Pass is expected. For example, the P e s in the alkane octadecane has a viscosity of 3 x liquid state (313K). The matrixviscosity determinedfrom the composite model is larger by a factor * l) than that of liquid alkanes. The determination of viscoelastic properties of the PG LBK filmsz8showed also that under the assumption of a (26) Marrucci, G.; Grizzuti, N. J . Polym. Sci., Polym. Lett. Educ. 1983.21.83. ( 2 7 j S h i d t , M. Habilitation Thesis, Universitaet Maim, 1986. (28) Johannsmann, D.; Mathauer, K.; Wegner, G.; Knoll, W. Phys. Rev. B 1992,46, 7808. ~
3026 Langmuir, Vol. 10, No. 10, 1994
----
Figure 7. High-densityand domain-like structure within one layer on large substrates can stop the in-plane diffision. The striped rod in domain A can only diffuse if rods in domain C are moving. But they are blocked by rods in domain B, which themselves are blocked by other rods. nanocomposite model the viscosityin the side chain matrix is larger than that of a normal liquid by a factor of 1000. The composite model of the LBK supramolecular structure as rods embedded in a side chain matrix can therefore explain the dynamical behavior of the films only by assuming a very high matrix viscosity. Such a high viscosity in the alkyl side chain region can be understood as a result of the covalent attachment of the side chains to the rods, which reduces their degrees of freedom. The interdigitation and possible entanglement of the side chains of different layers may also contribute to a restriction in the dynamics of these alkyl chains.4b It was shown for polymer brushes and grafted polymers29that the interpenetration zone of adjacent polymer brushes, even if very small; is responsible for the viscosity in such ~ y s t e m s . ~One ~ ~cannot -~ directly compare grafted polymers with our covalently attached alkyl chains, because the length scales are quite different. Nevertheless, it was found that the kinetics of the self-assembly process of alkanethiols show effects similar to those of grafted polymers.30 It is therefore reasonable to discuss a similar relation in the dynamics of grafted polymers and covalently attached alkyl chains. Another possible mechanism for the small diffusion constant in these LBKlayers can be discussed in the limits of the scheme shown in Figure 7. Within a single monolayer the rods in the presented samples are only correlated within their own domain. A test rod (striped) (29)(a)Milner, S. T.Science 1991,251,905.(b) Halperin, A.;Tirrell, M.; Lodge, T. Adu. Polym. Sci. 1992,100,31.(c)Klein, J.; Perahia, D.; Warburg, S. Nature 1991,352,143.(d) Witten, T.; Leibler, L.; Pincus, P. Macromolecules 1990,23,824.(e) Joanny, J.-F. Langmuir 1992,8, 989. (30)Haehner, G.; Woell, Ch.; Buck, M.; Grunze, M. Langmuir 1993, 9, 1955.
Schmidt et al. in domain A can only diffise if rods in domain C are moving away, and they are blocked by domain B, which is itself blocked by other rods. The theoretical description for the diffusion of such highly concentrated solutions of rods was given for three dimensions by Edwards et al.31 Due to the cooperativeprocess necessary for parallel diffision in such a system they found that the rods form a glass. Below the glass temperature the diffusion ceases and the coefficient Do,pis zero. Hence every diffusion between layers stops. One cannot directly compare our results with their threedimensional theoretical description, because the single layers are basically a two-dimensional system, but the physical origin of such a hindered diffision is the same in both two and three dimensions.
Conclusion and Perspective We have shown that LBK assemblies of polyglutamates are stable against interdiffision in the temperature range between 350 and 414 K. In this temperature region no center of mass diffusion occurs between layers of protonated and deuterated PG. The interface broadening cm2/s. between p- and d-PG is smaller than We discussed two possible causes for the stability: (a) the high viscosity of the side chain matrix stabilizes the film, or (b) the densely packed and, within a single layer, nearly isotropically distributed domains of locallyparallel rods hamper the diffusion. To distinguish between the two different possibilities, the local dynamics of PG (in bulk samples) will be i n ~ e s t i g a t e dand , ~ ~neutron measurements with ordered LBK films on large substrates are underway. The preparation of such films is not possible with a conventional LB trough, but the use of a flow channel allows the buildup of such ordered multilayers even on large subs t r a t e ~ In . ~such ~ films, rods within one layer are aligned, and therefore the second explanation for the low diffusion constant can be excluded. Rotating the sample after each transfer cycle permits the average angle t,b between adjacent layers to be adjusted, allowing the testing of parameters in the theoretical description in more detail. Acknowledgment. We acknowledge helpful discussions with Th. Vilgis, T. Pakula, and D. Johannsmann. We thank B. Derichs and M. Bach for technical assistance. This work was financially supported by the Bundesministerium fuer Forschung und Technologie (Grant 0 3 KNBMPG). (31)(a)Edwards, S. F.; Evans, K. E. J.Chem. SOC.Faraday Trans. 2 1982,78,113.(b)Edwards, S. F.;Vilgis, Th. Phys. Scripta 1986,T13, 7. (32)Kurthen, C.;Nitsch, W. Adu. Muter. 1991,3,445.
