Langmuir 1993,9, 543-549
543
FTIR Studies on the Azimuthal Distribution of Crystallites in 22-Tricosenoic Acid Langmuir-Blodgett Films Y. P. Song,tJ M. C. Petty,t and J. Yarwood'lt Department of Chemistry and Molecular Electronics Research Group, School of Engineering and Computer Science, University of Durham, South Road, Durham DH1 3LE, U.K. Received Augwt 20,1992. In Final Form: November 2,1992 22-Tricosenoic acid LangmukBlodgett (LB)filmshave been studied by polarized infraredspectroscopy and ellipsometry. Polarized attenuated total reflection spectrawere measured for the transverse magnetic and transverse electric modes. Polarized transmission infrared spectra were acquired in the monolayer transfer direction and in the direction perpendicular to the transfer. The thicknesses of the films were determined by ellipsometry. The IR spectra have been interpreted by assuming a distribution of the azimuthal orientation of the crystallites in the LB films. The distribution was modeled by a function generated from a Monte Carlo consideration. With this model and with monolayer thickness determined by ellipsometry,we have quantitatively studied the distribution function of the azimuthal orientation of the crystallites in f h with 10-100 monolayers. 1. Introduction
Although the crystallites are formed with a high degree of perfection,the macroproperties of LB f iare expected One of the most desirable features of the Langmuirto depend not only on the properties of individual crysBlodgett (LB) technique is the control of the molecular tallites but also on the organization of these crystallites. architecture.' The extent of the molecular organization In a polarized IR study, a Gaussian distribution model in LB layers is a key factor which determines physical has been assumed for calculatingthe proportion of chains properties such as electrical conductivity, pyroelectric titled along the withdrawal direction? h n t l y , a RHEED behavior, and nonlinear optical properties. Therefore,the study10 has shown that the azimuthal orientation of the determination of ordering and orientation of molecules in crystallites can distribute in a range of *70° with respect LB films is of great importance. It has previously been to the transfer direction. Such orientational inhomogedemonstrated that fatty acid and fatty acid salt molecules neity has also been observedby an opticalattenuated total form well-ordered structures in LB layers. For example, reflection (ATR)scattering te~hnique.'~The primary aim NEXAFS studies? waveguidingRaman spectroscopy,and of the present study is to quantitatively determine the microellipsometry3have revealed well-orderedalkyl chains distribution of the azimuthalorientation of the cryetallitas. for both cadmium arachidate and calcium arachidate LB Polarized IR spectroscopy has long been used for films. 22-Tricosenoic acid and some other fatty acid LB studying molecular 0rientati0n.l~Tilt angles of the alkyl films have been shown to m e s s monoclinic polycryschains in LB films have been qualitatively assessed by talline structures, with two molecules per unit cell. Such Rabolt et al.16 using transmission and grazing incidence structures were first revealed by IR spectroscopy,in which reflection IR spectroscopy. For LB films in which the cryetal field splittings of the 6(CH2) scissoring band molecules are uniaxially distributed around the surface and r(CH2)rocking band were The crystalline normal, Umemura et al." have proposed a method of using nature of the LB films has been further confirmed by transmission and grazing angle reflection techniques to RHEED experimenta6*9JOandX-ray diffracti~nstudies.~~J~determine the average tilt angle of the alkyl chains in LB The use of variable electron takeoff angles in X-ray f h . We have also previously proposed a method of using photoelectron spectroscopy (XPS) has also shown that ATR and grazing angle reflection techniques to estimate the "degree of perfection" of the 22-tricosenoic acid LB the tilting.l8 For fatty acid LB films with polycrystalline film is as high as 90%.13 structures, IR band doublets have been observed as mentioned above. Studies on such band doubleta have + Department of Chemistry. led to the determinationof the tilt angle of the alkyl chainss Molecular Electronics &search Group, School of Engineering and of the interlayer diffusion of molecules in LB films.lg and Computer Science. In the present paper, we used polarized IR spectroscopy, (1) Roberta, G.Lanamuir Blodaett - F i l m ; Plenum Press: New York, supported by ellipsometry,alpha-step measurements, and 1990; (2)Rabe, J. P.; Outka, D. A.; Swalen,J. D.; Stohr,J. Thin Solid F i l m a model distribution function, which is generated using a 1988,169,276. simple Monte Carlo approach, to study the distribution (3)Rabe, J. P.; Rabolt, J. F.; Novotny, V.; Swalen, J. D. Thin Solid of the azimuthal orientation of the domains in 22F i l m 1988,159,359. (4)Chollet, P. A. Thin Solid F i l m 1978,52,343. (5)Bonnerot.. A.:. Chollet. P. A.: Friebv, - . H.; Hoclet, M. Chem. Phys. 1966;97,365. (6) Chollet, P. A.; Meseier, J. Chem. Phys. 1982, 73, 235. (7) Chollet.P. A.: Measier.. J.:. Rosilio, C. J. Chem. Phvs. 1976,64(3). 1042.' (8) Chollet, P. A.; Messier, J. Thin Solid Films 1983,99,197. (9)Petereon, I. R.; Russell,G. J.; Girling, I. R.; Earls, J. D. Thin Solid Films 1988,161,325. (10)Robineon, I.; Jarvie,D. J.; Sambbs, J. R. J. Phys. D Appl. Phys.
(13)Cave, N. G.; Cayleas, R. A.; Hazell,L. B.; Kinloch, A. J. Longmuir 1990,6,529. (14)Peterson, I. R.; Earls, J. D.; Barnes, W. L.; Girlii, I. R. J. Phys. D Appl. Phys. 1988,21 (5),773. (15)Haller, G.L.;Rice, R. W. J. Phys. Chem. 1970, 74 (25),4388. (16)Rabolt. J. F.: Burns,F. C.:Schlotter,N. E.; Swalen,J.D.J. Chem. Phys. .1983,78,946. (17)Umemura..J.:.KamataT.:Kawai,T.:Takenaka,T. J.Phys. Chem. . . 19&, h,62. (18)Song, Y.P.; Petty, M. C.; Yemood, J.; Feclllt, W. J.; Tsibouklie, J.; Mukherjw, S.Langmuir 1992,8 (l),257. (19)Shimomura, M.; Song, K.; Rabolt, J. F. Longmuir 1992,8,887.
-- -
1981.24.347. - -, -,- - ..
!11)B e e n k o , M. R.; Grundy, M. J.; Richardson, R. M.; Roser, S. J. Thin Solid F i l m 1988,159,253. (12)Kamata,T.;Takenaka,T;Umemura,J. Chem.Lett. 1968,7,1231.
0743-7463/93/2409-0543$04.00/0
Q
1993 American Chemical Society
644 Langmuir, Vol. 9, No.2, 1993
Song et al.
tricosenoic LB films with different numbers of monolayers deposited at a fixed surface pressure. Experimental Section The subphase was pure water (resistivity 17.6 MQ cm, total organiccarbon 3.5 ppb) obtained by reverse osmosis, deionization, and UV sterilization. The spreading solvent was chloroform (BDH, Aristar grade). The isotherms at room temperature were similar to those reported by Peterson et al., with three phase regiompOThe phase transitions occurred at about 22 mN m-l for the Lp to L i transition, and at about 40 m N m-l for the L; to S transition. The transition surface pressures were in agreement with the phase diagram reported in the literature.21 The area per molecule, obtained by extrapolating the isotherm back to zero pressure, was evaluated to be 18 f 1 A2 for the S phase. This value corresponds to that expected for well-packed fatty acid It is ale0 in agreement with that for cadmium arachidate LB films photographed by a superconducting cryoelectron microscope,23and with that for arachidic acid LB films determined by combined optical microscopy and atomic force microscopy technique^.^' The monolayer transfer pressure was 45 mN m-l. This pressure was in the S phase region and still well below the collapse pressure of about 60 mN M-l. We have chosen this pressure in order to compare the azimuthal distribution functionsof f i i transferred in the S phase with fiims transferred in the L i phase. IR spectra of 22-tricosenoic acid LB films transferred in the Lp'phase have been well documented in the A ZnSe ATR crystal (14 reflections) was used as the substrate for monolayer transfer. The monolayers were transferred onto a large proportion of the crystal BO that they were sampled by 11 reflections. The crystal was cleaned by refluxing in 2-propanol for 4 h prior to the transfer processes. After every 10monolayershad been deposited, the ellipsometry data of the LB film, A's and +'a, were collected using a Rudolf ellipsometer at a wavelength of 632.8 nm and an incident angle and therefore of 70°. At this wavelength, ZnSe is tran~parent?~ ita extinction coefficientcan be assumed to be zero. The refractive index at this wavelength is equal to 2.578 f 0.001.26~27Optical properties of LB films are expected to be anisotropic, and the birefringent properties of the LB films should be taken into account. However,as far as determination of the film thicknesses of fatty acid LB films is concerned, ellipsometry using isotropic formulations gives almost identical results as ellipsometry using anisotropic formulations.28 For this reason, the birefringent effects on the ellipsometry measurements are not considered in the present work. With this approximation, theoretical A's and fs were calculated according to the 2 X 2 propagation matrix methodem By minimizing the differences between the experimental ellipaometery data and theoretically calculated values according to the quasi-Newton algorithm,30thicknesses, refractive indices, and extinction coefficients of these films were determined. The thicknesses determined are plotted in Figure 1. The slope of the straight line gives 3.06 f 0.03 nm as the monolayer thickness. The refractive index of the films was determined to be 1.509 f 0.013. Alpha-step measurements, with a Tencor alpha-step 200, on the film with 100 monolayers showed uniform morphology
n
E
C
W
b
C
;r
. I
E E
I
iz
0
I
I
1
I
I
20
40
60
80
100
No. of Monolayers Figure 1. Film thickness determined by the ellipsometry as a function of the number of layers transferred onto the substrate.
Figure 2. Cartesian coordinates and an ATR crystal with LB films on both sides. with film thickness equal to 0.297 f 0.012 pm, which is in good agreement with the thickness measured by ellipsometry. After each ellipsometry measurement, polarized ATR spectra of the sample were recorded with a Mattson Sirius 100 FTIR spectrometer operating at 4-cm-I resolution. Each spectrum was obtained by averaging lo00 scans to increase the signal to noise ratio. Polarized transmission spectra were also recorded in the transfer direction and the direction perpendicular to it, for the film with 100 monolayers.
3. FTIR Spectra Figure 2 shows the Cartesian coordinates and the ATR crystal, where the x-axis is the LB film transfer direction. Note that, in polarized ATR, the TE waves interact only with the y-components of transition dipole moments whereas the TM waves interact with the x- and z-componenta. As mentioned in the introduction, IR spectra of 22-tricosenoic acid LB films have been well studied and (20) Peterson,I. R.; Russel,G . J.; Earls, J. D.; Girling, I. R. Thin Solid F i l m 1988, 161, 325. reported in the literature. Here, we present the spectra (21) B i b , A. M.; Peterson, I. R. Thin Solid Films 1989, 178, 81. again in order to show the dichroism in polarized ATR (22) Kitaigorodskii, A. I. Organic Chemical Crystallography; Pubspectra which do not appear to have been reported before. lishing ConsultantsBureau: New York, 1961. (23) Inoue,T.;Yaee,K.;Nakanishi,H.;Matsuda,H.;Kato,M.;Okada, Figure 3a shows the TE and TM ATR spectra for the S.; Okada, M. Jpn. J . Appl. Phys., Part 2 1988,28, 2037. film with 100 monolayers on the ZnSe substrate. The (24) Bourdieu, L.; Silbenan, P.; Chatenay, D. Phys. Rev. Lett. 1991, vertical axis representsthe absorbanceper reflection. Parts 67, 2029. b-d of Figure 3 show the enlarged regions of the same (25) Mnhajan, S.; Kimerling, L. C. Concise Encyclopeadia of SemiconductingMaterials & Related Technologies;Pergamon Press: Oxford, spectra, giving details of the dichroism. The spectral 1992. assignments are listed in Table I. (26) Marple, D. T. F. J . Appl. Phys. 1964,35,539. The u(0H) band in the region between 2400 and 3300 (27) Rambauske, W. R. J. Appl. Phys. 1964,35, 2958. (28) Dsn Engeleen, D. J. Opt. SOC.Am. 1971,61, 1460. cm-l (see Figure 3a) and the u(C0) band at 1436cm-l (see R. M. A.; Bashara, N. M. Ellipsometry and Polarised (29) A", Figure 3c) are due to hydrogen-bonded vibrations. It is Light; North-Holland Publishing Co.: Amsterdam, 1977. interesting to note that these hydrogen-bonded bands are (30) NAG Fortran Library Manual, Mark 14; The Numerical Algorithms Group Ltd.; Oxford, 1990, Vol. 3, W B F . very much enhanced in the TM spectra. This means that
Langmuir, Vol. 9, No.2, 1993 645
22- h'coeenoic Acid LangmuipBlodgett Films I
I
I
1000
2000
3000
Wavenumbers (cm")
700
900
1loo
Wavenumbers (an.')
1
Wavenumbers (an.') Wavenumbers (cm") Figure 3. (a) T E and TM ATR spectra of a 100-monolayer'22-tricosenoicLB film. (b) The same spectra in a region between 650 and 1150 cm-l. (c) The same spectra in the region between 1150 and 1500 cm-I. (d) The same spectra in the region between 1500 and 1800 cm-'. The solid lines are the TE spectra, and the dashed lines are the TM spectra.
~
Table I. Band Positions and Assignments for 22-Tricoeenoic Acid LB Films svmbol u (cm-l) band assianment UGH) 3078 CH stretching mode of the RCH-CH2 group u(OH) 2400-3300 acid OH stretching mode 2920 antisymmetric CH2 stretching mode u,(CH2) 2850 symmetric CHI stretching mode uB(CH2) 1700 carbonyl stretching mode u(C-0) 1640 ethvlenic C=C stretchina UICPC) - mode a"(CH2) 1472 b,(CH2) 1464 alkyl CH2 scissoring mode doublet U(C0) 1435 hvdronen-bonded acid CO stretchine . . - m d e coupled with OH in-plane deformation mode progression 1170-1330 progression in the w(CH2) mode 990,910 out-of-planeCH deformation modes of d(CH) the RCH=CH2 group out-of-planeacid OH deformation mode d(OH) r"(CH2) alkyl CH2 rocking mode doublet 720 IJ(CH2) ~~
1
"'
\
the dipole transition moments associated with the u(OH) and dco) must have large components normal to the substrate. 4. Azimuthal Distribution of the Crystallites The splitting of the 6(CH2)scissoringbands at 1464and 1472 cm-l and rocking bands at 720 and 728 cm-l arises as a result of the crystal field. Following the notation of Chollet and Messier! we designate the doublet at 1464 and 1472 cm-l as 6' and 6" and the doublet at 720 and 728 cm-l as r' and r", respectively. From Figure 3b,c, it can be seen that the r' and 6' bands, the primed bands, are relatively stronger in the TE mode, while r" and 6" bands, the doubly primed bands, are relatively stronger in the TM mode. As suggested by Chollet and Messier! such
dichroism of the doublets indicates that the monolayers consist of C form crystallites. The C form correspondsto a monoclinic crystal with two acid dimers per unit cell, in which the aliphatic chains are tilted along a direction very close to that of the crystal c-axis. A detailed schematic representation of such a unit cell is given by Malta et According to Susi,32the transition dipole momenta of the r' and 6' bands, p(r') and ~ ( 6 %lie along the b-direction of the unit cell, and those of the r" and 6" bands, p(r") and p(S"), lie in a direction in the ac-plane and perpendicular to the aliphatic chains. Because the monlayers were transferred onto the substrate layer by layer, we assume that the a- and b-axes of the unit cell of the crystallites are parallel to the substrate surface. The c-axis of the unit cell has a tilt angle 8 measured from the substrate surface, as shown in Figure 4a. In this case, p(i) and ~(6') are parallel to the surface. On the other hand, p(r") and p(6") have surface normal components, and their projections on the surface are along the a-axis. Referring to Figure 4, if the a-axes of all the crystallites were orientated in the transfer direction 2, we would not observe the f@ and a// bands in the TE spectra, would we observe the r' and 6' bands in the TM spectra. It is thus evident that the a-axes of the crystallites must have an azimuthal distribution. The dimension of a crystallite is usually much smaller than 100 pm for fatty acid LB films.s In general, the beam size in IR spectroscopy is typically in the order of 1cm2. This means that tens of thousands of crystallites are sampled at the same time in IR measurements. Therefore, statistical methods must be used to perform quantitative analysis on the IR spectra. (31)Malta,V.; Celotti, G.; Zannetti, R.; Ferrero-Martatti, A. J. Chem. SOC.B 1971,648. (32) Sui, H.J. Am. Chem. SOC.1969,81, 1636.
546 Langmuir, Vol. 9, No.2, 1993
Song et al.
AS' Y
-4 b
X
x; = p2 - 1
Figure 4. Structure of a unit cek (a) section through the acplane, where the CH bonds are not shown; (b) section through the ab-plane, where the CH bonds are shown.
In general, the azimuthal angle of a crystallite, i.e., the angle between the a-axis of the crystallite and the transfer 0 and 360'. For direction, could have any value between ' a crystallite with an azimuthal angle 4, as shown in Figure 4b, either the r' or 6' band, of which the transition dipole moment is always parallel to the b-axis of the unit cell, will give rise to TE and TM absorptions according to Aam
a p2 cos2~ J E ; ( z )dz
(1)
where we use p to represent the transition dipole moment of either the r' or the 6' band. E&) and EJz) are the amplitudes of the electric field componenta in the x- and y-directions. The integrations are over the film thickness. The z-component of the evanescent wave does not contribute in the above equations, because p has no z-component as discussed previously. These equations are derived according to the fact that IR absorption due to a molecular vibration is proportional to the square of the dot product of the local electric field amplitude and the transition dipole moment associated with the vibration.33 The experimental absorbances of such a band are proportional to the summations of contributions from all the crystallites. Such summations can be conveniently expreeaed as integrations:
(6) In Figure 5, z is the transfer direction. Each dot gives an angle 4, which is assumed to be the azimuthal angle of a unit cell. By generating a large number, say W, of doh in the ellipse randomly, the azimuthal distribution of the unit cells is determined. If the p value is equal to unity, the ellipsereduces to a circle,and thus a uniform azimuthal distribution will appear for the system. The larger p , the more crystallites will be azimuthally oriented toward the transfer direction. This is schematically represented in Figure 5. In this figure, the shaded area AS, which is a unit angular region of the ellipse in the transfer direction, is larger than the shaded area AS', which is a unit angular region at any other azimuthal angle. It can be seen that there is a higher probability for a randomly generated dot to fall in shadow AS than in shadow AS'. Thus, the distribution function value at a given azimuthal angle is proportional to the differential angular area at that angle. From this consideration,we derive a normalizedanalytical formula for the distribution function as (7)
This function peaks at 4 = 0, and the width of the peak depends on the parameter p . Because p is a measure of the preference for cryetallitesto have azimuthalorientation toward the transfer direction, it will be referred to as the preference parameter. The shape of the distribution function is uniquely determined by the preference parameter. From eqs 3 and 4, the dichroic ratio of am and CyTM of the r' or the 6' band is given by
(3)
(4) where f(4) is a distribution function, Le., the probability for a unit cellto be oriented at an angle 4. This distribution function will be referred to as the azimuthal distribution function of the crystallites. To model the distribution,we use a Monte Carlo method as described below. Because the tilting of most crystallites is likely to be in the transfer direction? we can model the systemby randomlyscatteringdots in an ellipse(seeFigure 5) as defined by [ x - xo12/p2+ y2 = 1 (5) where x g is the focal length of the ellipse, which is given by34 (33) Deb, M.K.Pro#. Surf. Sci. 1982,24 (1-4),1. (34)See, for esnmple: Loomin, L. Calculus, 2nd ed.; Addieon-Wesley Publiihing Co.: Reading, MA, 1977;p 766.
JU
J
-
The above equation can be rearranged as
JU
. .
The left side of eq 9 is referred to as the modified dichroic ratio. In Figure 6 the modified ratio is plotted asa function of the preference parameter p . From this plot, the preference parameter of an LB film can be determined by the experimental dichroic ratio of either the r' or 6' band, provided that the 'weight" contributed by the electric energy componenta is taken into account. In order to estimate the integrated electric energies in each spatial direction, we need to compute the field amplitude profiles in the LB films. It has been shown by
22- Tricosenoic Acid Langmuil-Blodgett F i l m
Langmuir, Vol. 9, No. 2, 1993 647 3.0
l
--+
0
2.5
I
N N
2.0
< v
1.5 1.o
0.5
0.0
0
1.0
1.5
2.5
2.0
3.0
Preference Parameter Figure 6. Theoretical TE/TM ratio of a 'primed" band as a function of the preference parameter.
zase
I
I
-1.0
4.5
I"
I
Air
I
I
I
I
0.0
0.5
1.0
I
x 0."
Figure 7. Squared amplitude profiles at the neighborhood of
a 0.306-pm-thickfilm. The refractive index of the ZnSe is 2.378, the incident wavelength k 13.9pm, the incident angle is 45O, and the refractive index of the film is assumed to be 1.5.
Barns and Samblesa that multilayer8 of 22-tricosenoic acid behave as opticallybiaxial media. For biaxial media, the 4 X 4 matrix methodmIMcould be used to calculatethe electric field distributions. Unfortunately, for LB films the orientation of the principle coordinateaxea and the complexdielectrictensor are usuallynot known. Thismakes the rigorouscalculation almost impossible. One way to overcome the difficulty is to treat the anisotropy as a perturbation. The electric field distributions are calculatedaccordingto the isotropic theory. They are consideredasthe unperturbed solutions. We then allow the unperturbed electric fields to interact with the transition dipole momenta of the molecules. By adopting this approach, the infrared absorptions can be estimated. In our calculation,the 2 X 2 propagation matrix method for electromagneticwavea is again d . 3 7 ~ 2 9 Figure 7 shows the computed squared amplitude profiles in a film with a fired thickness (0.306 pm). In the calculation, the refractive index of the film is assumed to be 1.5. The wavelength is assumed to be 13.9pm. The refractiveindex of ZnSe is equal to 2.378 at this wa~elength.~ The incident angle for the internal reflection is assumed to be 4 5 O . Because such profiles depend on the thickness of the film, (36)B m ,W.L.;Samblee, J. R.Surf. Sci. 1986,177,399. (98) Parikh, A. N.; A h a , D. L. J. Chem. Phys. 1992,96,927. (37) Kong, J. A. Electromagnetic Waue Theory; John Wiley & Sone: New York, 1986. (38)IMscoU, W.0.;Vaughan, W.Handbook of Optics;McGraw-Hilk New York, 1978; pp 7-93.
0.0
1.o
0.5
1.5
2.0
d
Figure 8. Integrated electric energy components in a film 88 a
functionof the film thickness. The optical constantsof the ATR crystal and the film are the same as in Figure 7. The incident angle and wavelength are also the same as in Figure 8.
in Figure 8, the integrated electric energies are plotted as a function of the film thickness. To assess the error introduced by the above simplification, we have calculated the integrated electric energies for a model film with otherwise the same system as in Figure 7 but with an extinction coefficient, K , of the film equal to 0.1. The resulting x - and y-components of the electric energies are smaller than those in Figure 7 by 3.0 5% and 2.8 5% ,respectively. The change in the ratio of JEZ2(z)dz and JEu2(z)dz is negligible. As can be seen from eq 9, it is the ratio which is of importance. The extinction coefficient function in the neighborhood of the CH2 rocking doublets for the film with 100 monolayers is calculated according to the experimental transmission spectra. The peak value in this region is only 0.025, which is even smaller than the value we used for the above estimate, so we believe the error introduced is negligible. The error introduced by the anisotropy of the real part of the refractive index is also assumed to be in the same order of magnitudes. As can be seen from Figure 3c, the 6(CH2) band doublet is overlapped partly with the C-O stretching band of the acid head group. We therefore chose the r(CH2) band doublet for determination of the experimental dichroism. In order to separate the partially overlapped doublet, it is necessary to fit theoretically calculated spectra to the experimental data. The theoretical curves are generated by using the 2 X 2 matrix method with the apparent dielectric function of the films given by39
where em is the high-frequency permitivity. Because there is no other band in the neighborhood of the r(CH2) band doublet, the index j' runa from 1to 2 to include only two resonators representing the r' and r" modes. %j's and firj's are the resonance frequencies and damping factors of the vibrational modes. The squares of O,]s are the strengths of the vibrations. The reason we use the term 'apparent dielectric function" is because, in fitting, we use the theory for isotropic systems to generate the theoretical spectra for anisotropic systems. The isotropic theory is good enough for generating theoretical curves for the purpose of intensity determination. The fitting is achievedby a combinedGauss-Newton and quasi-Newton (39) Groese, P. Vib. Spectrosc. 1990, 1, 187.
548 Langmuir, Vol. 9, No. 2, 1993
Song et al.
Table 11. Electric Energies in Each Spatial Direction, Integrated Areas of the Fitted r‘ Band, Modified Dichroism Ratior (MDR), and the Preference Parameters (p)‘
N 10 20 30 40 50
60 70
80 90 100 0
d (am) 0.0306 0.0612 0.0918 0.122 0.153 0.184 0.214 0.245 0.275 0.306
$Er2(z)dt
$Ex%) 0.0574 0.114 0.170 0.225 0.279 0.333 0.385 0.436 0.487 0.537
0.0730 0.145 0.215 0.285 0.353 0.420 0.486 0.551 0.615 0.677
a(TE) 0.0159 0.0349 0.0494 0.0648 0.0792 0.0947 0.1115 0.1269 0.1365 0.1509
JEz2(z)d~ 0.0182 0.0377 0.0584 0.0803 0.103 0.128 0.153 0.120 0.208 0.237
a(TM) 0.0089 0.0201 0.0317 0.0372 0.0437 0.0496 0.0608 0.0722 0.0801 0.0909
MDR 1.40 1.37 1.23 1.38 1.43 1.51 1.45 1.39 1.35 1.32
P 1.127 1.118 1.077 1.121 1.139 1.160 1.145 1.127 1.115 1.103
N is the number of monolayers in the films. 0.02
’
m
I
I
OS 0.015
0.01
3 0
’
I
I I !
I
i
I
O
0.6
I
i,
0.005
0.0 -100
0
100
0.0 0
Angle (degree) Figure 9. In-plane distributions of the crystallites in two films with different preference parameters: p = 1.12 for the solid line, and p = 2.10 for the dashed line.
algorithm.40 From the fitting, the overlapped bands can be separated and the intensity, Le., the integrated area, of the r’ band can then be determined. In Table 11,the integrated electric energy components, the intensities of the r’ bands, are listed for the films with 10-100 monolayers. The thicknesses of the films listed in the table are thoee determined by the ellipsometry. From these data, the modified dichroism ratios are calculated according to eq 9. Then the preference parameters are checked out from Figure 6. The modified ratios and the corresponding preference parameters are also listed in Table 11. The average value gives p = 1.12 f 0.02. In fact, eq 9 and Figure 6 also apply to transmission experiments. In this case, we only need to take a transmission spectrum polarized to the x-direction, and another spectrum polarized to the y-direction, because there is no difference between the electric energies in the r- and y-directions for normal incidence. The modified dichroic ratio on the left side of eq 9 simply reduces to the experimental ratio of the absorption in the y-direction and that in the x-direction. The dichroic ratio of the absorption in they- and r-directions for the film with 100 monolayersgives a value of 1.5. From this dichroism ratio and Figure 6, a preference parameter equal to 1.16 is obtained. This value is only slightly larger than that determined by the ATR measurement. The present theory can be directly applied to the published IR spectra for filmstransferred in the Lz’phase. For a film transferred at a pressure equal to 25 mN m-l at r c ” temperature as reported in the literature: a much higher value for the preference parameter, equal to about 2.1, is obtained with the present theory. (40) NAG Fortran Library Manual, Mark 14; The Numerical Algo-
rithms Group Ltd.: Oxford, 1990, Vol. 3, E04FCF.
10
20
30
40
Tilt Angle (degrees) Figure 10. Theoretical dichroism (TE/TM) ratio of a doubly primed band as a function of the tilt angle for the f i b s with 10, 50,and 100 monolayers. The preference parameter is equal to 1.12 for the films.
With these preference parameters, the azimuthal distributions of the crystallites in the film transferred in the S phase and in the f i i transferred in the L2’phase are readily given by eq 7. The resulting distributionsare shown in Figure 9. It can be seen that the azimuthal distribution functions for both films are peaked in the transfer direction. However, the peak for the f i i transferred in the S phase is much broader than that for the f i i transferred in the Lz’phase. These distribution functions may be understood from the fact that the tilting toward the transfer direction is largely introduced by the hydrodynamic flow during the transfer processes.* Molecules are relatively more mobile in the Lz’phase than in the solid phase. Therefore, in the Lz’phase, they have more chance of reorganizing themselves during the monolayer transfer process. 5. Tilt Angle Determination The advantage of using the polarized ATR technique is that the dichroism ratio of the “doubly primed” bands contains the informationof the tilt angleof the alkylchains. For such bands, the dichroic ratio is given by
COS B cos #I2f(#)d#JE:x(t)
dz
+ sin2BJE:(z)
dz (11)
In order to determine the tilt angle, in Figure 10 the expected dichroic ratio for a doubly primed band is plotted for the film with 10, 50,and 100 monolayers, where the preference parameter determined in the previous section,
22- Tn'coeenoic Acid Langmuir-Blodgett Film
p = 1.12, is used in the calculation. The average value of the experimental dichroic ratio for the r" band for the f h is equal to 0.89 f 0.05. As can be seen from the figure, it is theoretically expected that the ratio decreases slightly with increasing film thickness. Experimentally, however, it is not observed because of the relatively large fluctuation in the dichroic ratio. The most probable tilt angle, according to the average dichroic ratio and Figure 10, is found to be in the range between 11' and 15'. This tilt angle is in agreement with the value determined by RHEED experiments as reported in the literature.41 We recall that ellipsometry gives 3.06 f 0.03 nm as the monolayer thickness. According to Cave et al.,13 the length of the alkyl chain in the 22-tricosenoic acid molecule is 2.78 nm and the length of the acid head group is 0.4 nm. These make a totalmonolayerthickness of 3.18 nm. From this and the thickness determined by ellipsometry, a tilt angle of the alkyl chains equal to 16' was obtained. This is slightly larger than the tilt angle determined by the IR experiments. The small discrepancy may be explained by the effects of hydrogen bonding in the head groups, as suggested by the IR spectra and as discussed in section 3. Hydrogen bonding effectivelyinterdigitates the acid head groups. As a result, the length of the bonded head group of an acid dimer may be shorter than 0.8 nm. Therefore, (41) Robineon, I.; Samblee, J. R.; Petereon, I. R. Thin Solid F i l m 1989,172, 149.
Langmuir, Vol. 9, No. 2, 1993 549 the orientations of alkylchains may be closer to the surface normal than the value estimated according to the monolayer thickness. 6. Summary and Conclusions 22-Tricosenoic acid LB films with different numbers of monolayers have been studied by polarized ATR and transmission IR spectroscopy and by ellipsometry. Crystallite orientations have been simulated by a Monte Carlo method. The combination of these techniques allows us to study the azimuthal distribution of the crystallites in the films. Such a distribution can be described by a unique parameter, p, which is referred to as the preference parameter. The preference parameter can be determined by the dichroism of either the r' or the 6' band in the polarized ATR or transmission spectra. At a constant transfer pressure of 46 mN m-l, which is in the S phase, it was observed that the preference parameter remains constant within the experimental error for the 22tricosenoic acid films with thicknesses ranging from 10 to 100 monolayers. The azimuthal distribution function of such a film has a broad peak centered at the transfer direction. Using publiihed IR spectra for 22-tricosenoic filmstransferred in the Lz'phase,8 the distributionfunction obtained using the present theory shows a sharp peak in the transfer direction. For any fatty acid LB films with C-type polycrystalline structure, Figure 6 may be readily used to perform quantitative determination of the preference parameters, which in turn give the azimuthal distributions of the crystallites in the films.
