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Langmuir 1998, 14, 5896-5899
A Grazing Incidence X-ray Diffraction Study of Langmuir-Blodgett Films of Poly(vinylpyridine) Quaternized with n-Docosyl Bromide Deborah B. Hammond,† Trevor Rayment,*,† Damien Dunne,‡ Philip Hodge,*,‡ Ziad Ali-Adib,‡ and Andrew Dent§ Department of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, U.K., Manchester Polymer Centre, University of Manchester, Oxford Road M13 9PL, U.K., and CLRC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K. Received April 22, 1997. In Final Form: July 15, 1998 The in-plane order of Langmuir-Blodgett multilayers of a poly(4-vinylpyridine) quaternized with n-docosyl bromide has been studied by grazing incidence X-ray diffraction. Strong evidence has been found for interactions of the alkyl side chains of the polymer molecules in neighboring layers, and an in-plane packing structure has been derived. Quantitative analysis of the X-ray diffraction shows that strain disorder rather than domain size is the principal source of X-ray line broadening in this system.
Introduction Organized multilayer organic films have many potential applications, for example, in nonlinear optics, in sensors, and for surface lubrication.1 The Langmuir-Blodgett (LB) technique allows monolayers to be deposited sequentially to build up multilayer structures.2-4 Unfortunately, LB multilayers of low-molecular weight (LMW) compounds are in general insufficiently mechanically stable for most potential applications. Moreover, many such films have been shown to be prone to molecular reorganization.5-7 Various methods have been tried to improve film strength, for example, by replacing hydrocarbon chains with fluorocarbon chains so as to increase the intermolecular van der Waals forces,8 but so far the most successful method is to build polymeric LB films. The latter may be constructed either by the deposition of multilayers of LMW compounds, which can then be polymerized in situ by, for example, exposure to UV radiation, or directly by the deposition of preformed polymers.9-13 The former method has the disadvantages that the films need to be processed after deposition, that contraction of the film upon po* To whom correspondence should be addressed. † Cambridge University. ‡ University of Manchester § CLRC, Daresbury Laboratory. (1) Petty, M. C. Thin Solid Films 1992, 210/211, 417. (2) Blodgett, K. A. J. Am. Chem. Soc. 1953, 57, 1007; Phys. Rev. 1937, 51, 964. (3) Langmuir-Blodgett Films; Roberts, B. G., Ed.; Plenum: New York, 1990. (4) An Introduction to Ultrathin Organic Films: From LangmuirBlodgett to Self-Assembly; Ulman, A., Ed.; Academic: Boston, 1991. (5) Jones, R.; Tredgold, R. H.; Hodge, P. Thin Solid Films 1983, 99, 25-32. (6) Grundy, M. J.; Musgrove, R. J.; Richardson, R. M.; Rosen, S. J.; Penfold, J. Langmuir 1990, 6, 519. (7) Shimomura, M.; Song, K.; Rabolt, J. F. Langmuir 1992, 8, 887. (8) Chapman, J. A.; et al. Proc. R. Soc. London A 1957, 242, 96. (9) Hodge, P.; Davis, F.; Tredgold, R. H. Philos. Trans. R. Soc. London 1990, 330, 153-166. (10) Miyashita, T.; Mizuta, Y.; Matsuda, M. Br. Polym. J. 1990, 22, 327. (11) Davis, F.; Hodge, P.; Towns, C. R.; Ali-Adib, Z. Macromolecules 1991, 24, 5695-5703. (12) Davis, F.; Hodge, P.; Liu, X.-H.; Ali-Adib, Z. Macromolecules 1994, 27, 1957-1963. (13) Hodge, P.; Ali-Adib, Z.; West, D.; King, T. A. Thin Solid Films 1994, 244, 1007-1011.
lymerization tends to result in crazing of the film, and that excess radiation may damage the films. The construction of high-quality LB multilayers of preformed polymers is a significant challenge because of the inherent flexibility and conformational disorder of most polymer chains, the fact that most vinyl polymer chains are atactic, the presence of a significant range of chain lengths, and in many cases, the irregular distribution of the lipophilic and the hydrophilic moieties. Nevertheless, in recent years Hodge et al. have made considerable progress in producing LB films of preformed polymers that have good layer structures, as judged by the observation of several orders of Bragg peaks in low-angle X-ray reflection experiments.11-13 Little is known, however, about the order within the layers but in the case of poly(vinylpyridine)s quaternized with long chain alkyl bromides there is good evidence that these alkyl side chains are interdigitated, as unusually small d spacings perpendicular to the layers have been determined by lowangle X-ray reflection experiments while Fourier transform infrared spectroscopy experiments have indicated that the side chains are close to being vertical to the plane of the films.12 Grazing incidence X-ray diffraction (GIXD) is probably the best way to obtain direct evidence of in-plane order in thin films.14 We present here a GIXD study of LB multilayers prepared from a poly(4-vinylpyridine) quaternized with n-docosyl bromide from which an in-plane packing structure of the polymer has been determined and from which the extent of interdigitation and stresses within the film may be inferred. Experimental Section A sample of poly(4-vinylpyridine) purchased from Polysciences Ltd. was shown by viscometry to have Mv 42 700.12 Polymer 1 was synthesized by treating this polymer with an excess of n-docosyl bromide in methanol at reflux temperatures.12 By 1H NMR spectroscopy and elemental analysis the extent of quaternization of the present samples was 72%, i.e., x ) 0.72 in structure 1. Monolayers of polymer 1 were prepared in a double LB trough over a subphase containing potassium bromide and were (14) Wagner; et al. Adv. X-ray Anal. 1988, 31, 219.
S0743-7463(97)00415-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/09/1998
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Figure 1. Structure of polymer 1. subsequently deposited onto clean hydrophilic silicon (111) wafers, of approximate area 50 mm by 25 mm at a surface pressure of 30 mN/m using the same conditions and procedures described previously.12 As shown in previous studies these quartenium salts are stable at the water surface. Within experimental error the transfer ratios were unity. Samples containing 1, 2, 5, and 25 layers were prepared and their thicknesses measured by ellipsometry. Low-angle X-ray analysis of thick LB films (100 layers) carried out using the procedures described previously12 displayed 3 orders of Bragg peaks, corresponding to a repeated layer spacing of 46 Å normal to the plane of the layers. The GIXD experiments were carried out on station 9.3 at the Daresbury synchrotron, which was operating at 2.0 GeV with a ring current of between 150 and 220 mA. Monochromatized X-rays of wavelength 1.2836 Å (the zinc K absorption edge) were produced by a Si(220) double crystal monochromator. This wavelength was chosen as one that would give satisfactory resolution and maximum scattered signal intensity with minimal beam damage to the organic material. Harmonic rejection was achieved by a horizontal plane Pd mirror upstream of the monochromator, which has a cutoff at around 24 keV, thus removing all higher harmonics at the zinc K-edge. This mirror was bent to focus 10 mrad of the beam in the vertical plane to provide a beam at the sample of dimensions 25 mm horizontal by 300 µm high. The energy of the monochromatic beam was calibrated at the zinc K edge before the experiment. GIXD measurements were performed using a simple horizontal diffractometer constructed from a Huber 424 two-circle goniometer with a proportional detector placed behind a set of parallel foils, which gave a geometrical resolution of 0.1°. Full details of the diffractometer are presented elsewhere.15 In this geometry the sample and the scattered radiation lie in the plane of polarization of the X-ray beam, which is a disadvantage. However, over the range of scattering angles employed in this work the reduction of the intensity of the diffracted beam due to polarization factors was never more than 50%. The grazing incidence angle (R) was chosen for most experiments to lie in the range 0.2-0.5°.
Results and Discussion Polymer Structure. The monolayers of polymer 1 had excellent isotherms, essentially the same as those of similar polymers reported previously.12 The area repeat unit at 30 mN/m was 37 Å2. Extrapolation of the “solid” section of the isotherm to zero pressure gave an area of 45 Å2. Grazing incidence X-ray reflection studies of the structure of monolayers of similar polymers at the airwater interface have been reported.15 By low-angle X-ray diffraction studies, LB films of polymer 1 had a d spacing of 46 Å.12 Figure 2 shows the in-plane diffraction patterns for the one- and two-layer LB films. The diffraction pattern from one monolayer of the polymer shows a broad feature at 2θ ) 18.3° with fwhm of 5.8° barely visible above the background of the pattern. The intensity and width are typical of a very disordered material. This diffraction pattern is in marked contrast with that given by two layers, which displays a single sharp peak corresponding to a d spacing of 4.14 Å. In the diffraction patterns from one and two layers there is an additional broad feature with (15) Hammond, D. Ph.D. Thesis, Cambridge University 1995.
Figure 2. Grazing incidence X-ray diffraction pattern of one and two layers of polymer. For clarity the pattern for two layers of polymer has been displaced vertically by 100 counts.
Figure 3. Grazing incidence X-ray diffraction pattern of 25 layers of polymer.
a peak at 2θ ) 37°, which is caused by diffuse scattering from the Si(220) peak of the silicon substrate. The large increase in order that occurs during deposition of a second layer of polymer must be caused by interactions between the layers. The diffraction patterns from a 25-layer LB film of polymer 1 (Figure 3) is very similar to that from two layers. However, in addition to the sharp feature at 2θ ) 17.90°, 4.14 Å, a higher order peak may be seen at 2θ ) 31.53°. The scattering from diffuse reflectance by the Si(220) peak of the silicon substrate is almost completely suppressed by absorption of the X-ray beam in the organic film. The simplest interpretation of a single diffraction peak is for the in-plane structure to have assumed a hexagonal unit cell of d spacing 4.14 Å. This type of packing would be expected for free-standing alkyl chains,17 and in this system the scattering density will be dominated by that of the side chains. However, in a polymer film the packing and conformation of the alkyl side chains is constrained by attachment to the polymer backbone. Hence the monomer unit of the polymer should be considered as the basic building block rather than the alkyl chains alone, and this requires a degree of strain to be incorporated into the structure. In practice, the construction of a molecular model for the structure is nontrivial because of disorder. Not only is the polymer known to be atactic but quaternization is never complete. Profile Analysis of Domain Size and Strain. Broadening of diffraction peaks is caused by defects where a defect is anything that destroys the infinite translational periodicity of a perfect crystal. From this general stand(16) Styrkas, D. A.; Thomas, R. K.; Ali-Adib, Z.; Davis, F.; Hodge, P.; Liu, X.-H. Macromolecules 1994, 27, 5504-5510. (17) Tippman-Krayer, P.; et al. Thin Solid Films 1992, 210/211, 577.
5898 Langmuir, Vol. 14, No. 20, 1998
Figure 4. Diffraction pattern from 25 layers of polymer with a curve fitted by the model described in the text.
point, particle size, substitutional defects, and strain are all defects in that they all reduce the correlation between unit cells by increasing distances.21 The relative contribution of each may be determined by mathematically modeling both the shape and relative intensity of the diffraction profiles. There are two extreme models. If the polymer side chains were packed as perfect small crystalline domains, the profile width would indicate particle size. The Scherrer equation, which is the simplest and most widely used function to describe the particle size broadening, would indicate a domain size of 42 Å from the fwhm of the (10) reflection of the 25-layer sample. However, the Scherrer equation for the hexagonal lattice used here implies all the peaks have the same fwhm in reciprocal space, and it can be seen in Figure 3 that this is clearly not the case, as the (11) reflection is broader than the (10) reflection. This is not surprising, since during deposition the polymers would be expected to be stretched and distorted due to the flexibility of the polymer backbone and then strain would be put upon the backbone by the attempts to close pack the alkyl chains. The disorder so caused would be expected to have a greater influence over the diffraction profile observed than the domain size. To the best of our knowledge a simple mathematical profile analysis of strain in these types of polymer films has not been published. However, diffraction from layered material in which each layer is randomly oriented with respect to all others has been studied for many years. Of particular relevance is Ergun’s work on carbon blacks.18 Ergun showed that many carbon blacks may be considered as highly defective layer lattices, in which the diffraction profile can be modeled with great accuracy by a coherence length that is the mean distance between defects and a strain parameter. This work also took into account preferred orientation, so that both powdered and macroscopically layered material could be studied. Ergun’s work provides a number of analytical profiles that have been adapted as described below to suit LB films. The model structure proposed for the organic film consists of domains randomly oriented with respect to each other. This domain structure has been observed for example by Schwartz et al. using AFM.19 In these GIXD experiments we are interested only in (hk0) reflections where the scattering vector lies within the plane of the (18) Ergun, S.; Phys. Rev. B 1970, 1, 3371. Acta Crystallogr. 1973, A29, 605. Acta Crystallogr. 1973, A29, 12. (19) Schwartz, D. K.; Viswanathan, R.; Zasadinski, J. A. Science 1994, 263, 1158. (20) Micromath Scientific Software, Salt Lake City, UT. (21) Guinier, A. X-ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies; W. H. Freeman and Co.: San Francisco, 1963.
Hammond et al.
domain. Let the scattering from a perfect organic film be j(h) where h is the conventional scattering vector h ) 4π(sin θ)/λ. In the most general terms, X-ray scattering may always be described as the Fourier transform of the distribution of interatomic vectors or correlation function for the system. For highly defective materials in which order extends only for a few unit cells, it is more effective to work directly with the distribution function. The effect of defects such as particle size is to reduce the correlation function by a multiplicative factor, which Ergun defines as g(r) ) exp(-ar) where a ) 1/L, L being the mean defect free path. g(r) is a measure of the probability of a distance r across the layer not having a defect. The effect of the lattice strain is to extend the distance l between neighboring unit cells (alkyl chains) to l + δ where δ proved to be best described by a Gaussian distribution Φ(δ) characterized by the strain parameter σ (per unit distance):
Φ(δ) )
( )
-δ2 1 exp 4σ2 2σxπ
Using these assumptions, an analytical form for a scattering intensity profile may be obtained as in eq 1 below. A summary of the derivation is given in Appendix A. Here m is the multiplicity, F is the structure factor, n is the number of molecules in the unit cell, A is the area of the unit cell, and h0 is the scattering vector for the particular (hk0) reflection under consideration.
j(h) )
[
(
A (h + h0)2 + a +
mF2(a + h2σ2)
)] [
h2σ2 xπ
2 1/2
(
(h - h0)2 + a +
)]
h2σ2 xπ
2
(1)
The diffraction profile was then fitted using expression 2.
I(h) ) I0P(θ)F(θ)[j(10)(h) + j(1-1)(h) + j(20)(h)]
(2)
A hexagonal structure for the alkyl chain arrangement was assumed where each j(hk)(h) was given by an expression such as (1) with the values of the fitting variables a and σ common to all. Expression 2 was fitted to the diffraction profile shown in Figure 3 using nonlinear least squares optimization.20 The polarization of the X-ray source, P(θ), and the variation of the structure factors with θ, F(θ), must also be included, as must a variable I0 to account for the intensity of the X-ray source. The final fitted profile is shown in Figure 4. A mean defect free length of over 500 Å was found, implying the presence of defects in the lattice is insignificant in comparison to the lattice strain. σ was found to have a value of 0.32 ( 0.03, implying the lattice suffers 32% strain. Conclusions The LB films of a poly(4-vinylpyridine) quarternized with n-docosyl bromide has been shown by GIXD to consist of layers with an average distance between close-packed alkyl chains of 4.14 Å. It is customary in these studies to offer a picture of the structure, but we have refrained from giving this because of the high degree of disorder in this material. The side chains are not only randomly quaternized but also atactic and hence and a model of an ordered unit cell would give a misleading impression of the structure. A line profile analysis based upon wellestablished models for diffraction from imperfect materials
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Langmuir, Vol. 14, No. 20, 1998 5899
shows without doubt that the dominant source of diffraction line broadening is lattice strain. Particle size broadening, as modeled by an exponential decay of correlation between lattice points, is negligible in comparison with strain along the polymer chains, which has been evaluated at 32 ( 3%. While scanned probe techniques gives evidence for domains in these structures, the primary source of disorder is caused by the assembly of randomly quaternized docosyl chains attached atactically to a polymer backbone in a close packed layer. Appendix A Consider a layered structure where each layer consists of domains that may have random orientation about the domain normals. The scattering vector of any plane within each domain is thus also constrained to lie in the plane of the domain. Thus the contribution of one atomic distance l to the interference function is given by
F(h, l) ) J0(h, l) where J0 is a Bessel function of the first kind and zero order. If the interatomic distance l is altered by a distance δ owing to the strain within the lattice, then
F(h, l, δ) ) 〈J0(h, l + δ)〉
To calculate the interference function for a whole sample, the contribution from all atomic distances must be accounted for, i.e.
j(h) )
where n(l) is the number of neighboring atoms at a distance l from any atom in a lattice of infinite extent and g(l) is a function to modify n(l) for the presence of defects. As the distances l vary, the extensions δ will also vary. If a distance l is considered to be made up of m smaller distances of length l/m and each with a displacement δ, due to the nature of Gaussian distributions the average of the m distributions will be equal to the average of each distribution, i.e.
σ2(l) ) mσ2(l/m) Thus the strain parameter i.e. σ2(lq) ) lqσ2 (unit distance), where σ is the strain parameter for unit length.
(
F(h, l, δ) = J0(h, l) exp
( )
The strain parameter σ describes this distribution. Thus
F(h, l, δ) )
∫-∞∞J0(h, l + δ) Φ(δ) dδ
But J0(h, l) may be rewritten as
J0(h, l + δ) )
∫0ππ1 exp[ih(l + δ) cos R] dR
I(h, r) ) 〈exp(i(h - h0)‚r〉 where r is an interunit cell distance vector and h0 is the reciprocal lattice vector for the (hk0) reflection being considered. In this method, the intensity is expressed as a product of the unit cell interference function F2, and the lattice interference function G2. It is assumed that F2 is approximately invariant in the region of h where G2 gives rise to a peak; thus it is possible to derive an expression for the peak profile. Now 〈exp(ih0‚r)〉 ) J0(h0, r) as h0 is constrained to the plane of the organic domain. Thus the interference function is given by ∞
j(h) )
Thus
F(h, l, δ) )
∫0π∫-∞∞π1 exp[ih(l + δ) cos R]2σ1xπ × exp
( )
-δ2 dR dδ 4σ2
F(h, l, δ) )
∫0 π exp(-h σ
2 2
2
cos R) exp(ihl cos R) dR
An approximate solution to this was found using numerical methods to determine the value of the integral as a function of h. The function of h and l that best approximated the profile so formed was then determined.
( )
F(h, l, δ) = J0(h, l) exp
-h2σ2 xπ
This gives an approximate solution to the integral for all values of l, but it fits particularly well for l > 4.
g(rq) J0(h0,rq) F(h, rq) ∑ -∞
As the intensity is only appreciable for small values of (h - h0) the summation may be replaced by an integration over r.
j(h) )
2
∫0∞2πrmF nA
By integrating over δ using standard integrals π1
)
-h2σ2l xπ
Given that g(l) ) exp(-al), when 1/a is too large (30 Å) for the expression A given above to be calculated easily, an approximation may be used by using the lattice sum method. In principle, this involves the evaluation of
where δ may take a range of values that may best be described by, for example, a Gaussian distribution.
-δ2 1 exp Φ(δ) ) 4σ2 2σxπ
∑q g(lq) n(lq) F(h, lq, δ)
exp(-ar) × exp
(
)
-h2σ2r J0(h0, r) J0(h, r) dr xπ
where m is the multiplicity of the (hk) reflection, F2 is the structure factor, n is the number of atoms in the unit cell, and A is the area of the unit cell. This may be solved using standard integrals and simplified as h0 * 0 and a is small. Thus each peak expected in the diffraction pattern may be fitted to an interference function of the form given in eq 1, to give an overall expression such as eq 2 to fit the whole pattern, including additional parameters such as beam intensity, polarization of the X-ray source, and the variation of atomic scattering factors with θ. LA9704157
