Langmuir 1994,10, 819-829
819
Two-Dimensional Crystal Structure of Cadmium Arachidate Studied by Synchrotron X-ray Diffraction and Reflectivity Franck Leveiller,? Christine Bohm,t Didier Jacquemain,+Helmuth Mohwald,t Leslie Leiserowitz,*ftKristian Kjaer,**oand Jens Als-Nielsen'J Department of Materials and Interfaces, Weizmann Institute of Science, 76100 Rehovot, Israel, University of Mainz, Institute for Physical Chemistry, Welder- Weg 15, 0-6500 Mainz, Germany, and Physics Department, Rise National Laboratory, DK4000 Roskilde, Denmark Received August 2, 1993. I n Final Form: November 22,1999 Uncompressed arachidic acid films spread over 10-3M cadmium chloride solution (pH 8.8 adjusted with ammonia) spontaneously form two-dimensional (2-D)crystallineclusterswith coherence lengths of =loo0 A at 9 "C. Ten distinct low-order in-plane diffraction peaks and three high-order peaks were observed with grazing incidence X-ray diffraction (GID) using synchrotron radiation. Seven low-order peaks were attributed to scattering only from a crystalline cadmium layer and the remaining peaks to scattering primarily from the arachidate layer. The molecules in the arachidate layer arrange in a pseudorectangular unit cell with dimensions a = 4.60 A and b = 8.31 A and y = 93.4O with the chains tilted 1l0along the b axis. The chains of the two crystallographically independent molecules in the unit cell are related by pseudoglide symmetry along the b axis yielding the herringbone motif. The reflections from the cadmium layer were indexed according to a supercell a, = 2a, b, = 3(-a + b)/2. Analysis of X-ray specular reflectivity measurements and the GID data indicated that the counterionic layer consists of a CdOH+species, bound to the arachidate layer in a stoichometry close to 1:l. The probable formation of a cadmium-ammonia complex at the high pH = 8.8 was strongly suggested by the X-ray reflectivity measurements employing CH3NH2, (CH&NH, and (CH&N as alternative counterions. The arrangements of the arachidate chains and of the Cd ions were each determined to near atomic resolution by fitting the GID data, but the relative offset between the arachidate and Cd "lattices" was difficult to ascertain. 1. Introduction
Until very recently, information on the remarkable effect of aggregation of counterions in solution to the charged head groups of a two-dimensional surface of an amphiphilic layer was limited to macroscopic observation, for example, by characterization of ion-mediated morphological changes of aggregates for amphiphiles in solutions,' and to macroscopic measuremenb such as pressure-area diagrams2J or surface potential datae for insoluble amphiphiles forming Langmuir monolayers. With the recent development of surface X-ray diffraction techniques applied to crystalline films of water-insoluble amphiphiles, their structures over various ionic subphases can now be derived at almost atomic resolution.'*8 As for a counterionic layer bound to the amphiphilic layer, X-ray reflectivity measurements provide information on the concentration profile of ions bound to the (charged) amphiphilic head groups.s12 X-ray standing waves were recently used to demonstrate that the Zn2+double layer at a phospholipid Institute of Science. of Mainz. RisO National Laboratory. Abstract publishedin Aduance ACSAbstracts, January 15,1994.
t Weizmann t University @
(1) Evans, D. F. Langmuir 1988, 4, 3. (2) Yazdanian, M.; Yu, H.; Zografi, G. Langmuir 1990,6,1093. (3) Gaines, G. Imoluble Monolayers at the Liquid-Gas Interface; Intarscience: New York, 1966. (4) DeSimone, J. A.; Heck, G. L.; DeSimone, S. K. Electrical Double Layers in Biology; Plenum: New York, 1985. (5) Seimiya, T.; Miyasaka, H.; Kato, T.; Shirakawa, T.; Ohbu, K.; Iwakashi, M. Chem. Phys. Lipids 1987,43, 161. (6) Yazdanian, M.; Yu, H.; Zografi, G.; Kim, M. W. Langmuir 1992, 8,630. (7) Jacquemain,D.; Grayer Wolf,S.;Leveiller, F.; Deutach,M.; Kjaer, K.; Ale-Nielsen, J.; Lahav, M.; Leieerowitz, L. Angew. Chem. 1992,32, 130. (8) Leveiller,F.;Jacquemain,D.;Leiserowitz,L.;Kjaer,K.; Als-Nielsen, J. J. Phys. Chem. 1992,96, 10380. (9) Bosio, L.; Benatar, J. J.; Rieutord, F. Reu. Phys. Appl. 1987,22, "me I ID.
(10) Richardson, R. M.; Roser, S. J. L ~ QCryst. . 1987,2, 797.
membrane-aqueous interface is diffuse.13 Liquid-surface extended X-ray absorption f i e structure (EXAFS) spectroscopy experiments on manganese stearate films1* at room temperature yielded a Mn-Mn nearest neighbor distance at the surface in the compressed phase only, indicating at least short-range order. GID measurements of lead arachidateIs monolayers at room temperature gave no indication of ordering of the Pb2+ions. It was therefore not known from all these studies whether the ion distribution near such charged, ordered surfaces is crystalline, particularly if the monolayer is singly charged and the counterion doubly charged. Thus, we addressed the following questions: Is this layer ordered, i.e. are the ions located at precise binding sites over a long range, and what is the exact composition of this layer? A preliminary report of the presence of ordered binding of Cd ions to a monolayer of arachidic acid a t high pH, detected by GID, has been published.Is Here we present a detailed structural determination of the two-dimensional packing arrangement of the acid amphiphile and the underlying counterionic layer. 2. Experimental Section Materials. Spreadingsolutionsof myristic acid C ~ ~ H ~ C O ~ H (Sigma,purity 199%),arachidic acid CleH&OzH (Fluka,purity 1 99%),and triacontanoic acid CmH,&OzH (Sigma, purity 1 99% ) were prepared in chloroform solutions (Merck, analytical grade) within a concentration range of 5 x l(r to 10-8M. All subphases were prepared using Millipore purified water (resis(11) Richardson,T.; Roberta, G. G.; Polywka, M. E. C.; Davies, S.G. Thin Solid F i l m 1988,160, 231. (12) Kjaer, K.; Ale-Nielsen, J.; Helm, C. A.; Tippmau-Krayer, P.; MBhwald, H. J. Phys. Chem. 1989,93,3200. (13) Bedzyk, M. J.; Bommarito, G. M.; Caffrey, M.; Penner, T. L. Science 1990,248, 52. (14)Bloch, J. M. Phys. Rev. Lett. 1988, 61, 2941. (15) Dutta, P.; Peng, J. B.; Lm,B.; Ketterson, J. B.; Prakash, M.; Georgopoulos,P.; Ehrlich, 5. Phys. Rev. Lett. 1987,58, 2228. (16) Leveiller,F.;Jacquemain,D.;Lahav, M.; Leieerowitz, L.; Deutach, M.; Kjaer, K.; Ale-Nielsen, J. Science 1991, 252, 1532.
0143-1463/94/2410-0819~04.50/0 0 1994 American Chemical Society
820 Langmuir, Vol. 10, No. 3, 1994
Leveiller et al.
tivity 18Milan). The subphase composition and pH were varied in some measurements with NaOH in pellets (Merck, analytical grade), ammonia NH3, methylamine CHsNH2, dimethylamine (CH3)2NH,and trimethylamine (CH&N (British Drug Houses, analytical grade), CdC12-H20 (Merck, analytical grade), CdBr204H20 (Fisher Scientific Co., analytical grade), CdI2 (British Drug Houses, analytical grade), and CaC12 (Aldrich, analytical grade). The monolayers were spread a t approximately room temperature before cooling the subphase. The GID powder patterns were recorded a t least 1 h after spreading of the monolayer over the subphase. ExperimentalSetup. The GID measurementson monolayers were carried out using the liquid surface diffractometers on the wiggler beam lines W1 and BW1 and on the bending magnet beam line D4 a t Hasylab, Deutsches Elektronen Synchrotron (DESY), Hamburg, Germany. A sealed and thermostated Langmuir trough equipped with a Wilhelmy balance, allowing for surface pressure control of the film, was mounted on the diffractometer. We reduced the background level during measurements considerably by maintaining a He atmosphere inside the trough. The synchrotron radiation beam was monochromated to a wavelength X = 1.38,1.40, or 1.41 A by Bragg reflection from a Ge(ll1) crystal and, to maximize surface sensitivity, was adjusted to strike the monolayer surface a t an incident angle ai = 0.85ac,where ac= 0.138O is the critical angle for total external reflection. The dimensions of the footprint (Figure 1) of the incoming X-ray beam on the liquid surface were 50 X 5 mm. Further details are given e1sewhere.l7-l9 In the GID geometry, the angle of incidence ai of the X-ray beam is kept below the critical angle cyc. This limits the penetration depth of the beam to that of the evanescent wave and the scattering due to the subphase is efficiently reduced. This permits a reliable measurement of the weak diffraction signal originating from the crystalline monolayer.20 The diffraction condition for 2-D crystals lying in the ICY plane is that the componentof the scattering vector in the horizontal plane, labeled G~(pZy (47r/X) sin l6: where 28 is the horizontal angle between the incident and the diffracted beam, as shown in Figure l), must coincide with a reciprocal lattice vector = 27r(ha* kb*), where a* and b* are the reciprocal lattice vectors and h and k are the integer components of the corresponding lattice point. There is no similar selection rule or restriction on the component of the scattering vector along the normal to the film, defined as QS, whose magnitude q, r (27r/X) sin at,s1 where afis the angle between the diffracted beam and the water surface, shown in Figure 1. Therefore, the GID patterns from 2-D crystals arise from a 2-Darray in reciprocal space of rods,20s1labeled Bragg rods (BR), which extend parallel to QS. For all the diffraction patterns measured to date, the monolayers were found to be composed of crystallites randomly oriented on the water surface, namely a 2-D "powder". The collection of the diffracted radiation was made in two ways using a onedimensional position sensitive detector (PSD, Figure l ) , mounted vertically behind a horizontally collimating Soller slit, of resolution width A(qxy)= 0.007 A-l, which intercepted photons over a range 0.0 Iq, 5 0.9 A-l. The scattered intensity, measured by scanning different values of qxyand integrating over the whole q,-window of the PSD, yields Bragg peaks. Simultaneously, the scattered intensity recorded in channels along the PSD but integrated over qxyacross a peak produces q,-resolved scans called Bragg rod profiles. The X-ray specular reflectivity measurements were carried out a t the liquid surface reflectometer a t the Weizmann Institute of Science (Rehovot, Israel) using a rotating Cu anode X-ray generator operating a t 40 kV and 25 mA. Specular reflection means that the reflected X-ray measured is in the plane spanned
-
+
(17)Ala-Nielsen, J.; Christensen, F.; Pershan, P. S. Phys. Reu. Lett. 1982,48,1107. (18)Als-Nielsen,J.; Pershan, P. S. Nucl. Instrum. Methods Phys. Res. 1983,208, 545. (19)Als-Nielsen,J. In Handbook of Synchrotron Radiation; Brown, D. E. M. G. S., Ed.; North Holland Amsterdam, 1991;Vol. 3, p 471. (20) Ab-Nielsen, J.; Kjaer, K. Proceedings of the Nato Advances Study Institute, Geilo, Norway 1989;Riste, T., Sherrington, D., Eds.; Plenum Press: New York, 1989;p 113. (21)Feidenhans'l, R. Surf. Sci. Rep. 1989,10 (3), 105.
s!E VIEW
PSD Grcufng
Incidence
0 PSD
Top VIEW
Figure 1. Top and side views of the GID geometry. The footprint of the grazing incidencebeam is indicated. The position-sensitive detector (PSD) has its axis along the vertical direction ( 2 ) . Only the area ABCD contributes to the measured scattering.
I q I I kr I
kil = (4n / k )sin ar k
n
Figure 2. Refracted (E',) and reflected (E,)waves resulting from an incident plane wave with amplitude lEil upon an interface between air and a material of refraction index n. Electric fields
E are illustrated for one polarization only. The symbol q is the scattering vector, with ki and k, the incident and reflected wave vectors of magnitude 2dX, where X is the wavelength. Note that as n 5 1, a', < a,. This provides for total external reflection a t angles a, < cyc, where ac is the critical angle for total external reflection. by ki and the vector normal to the surface and that ai = a,(Figure 2). For the measurements the incidence and exit vertical angles were varied within the range 0 Iai = a,I26ac,and the scattering vector q has only a component in the vertical direction defined by qt = (47r/X) sin a. The reflected X-ray beam was monochromated by a graphite crystal to a wavelength X = 1.54 A and reflected to the scintillation detector subtending 0.13' in a,.A sealed and thermostated Langmuir trough, similar to the one used for the diffraction experiments, was mounted on the sample stage. Further details are given el~ewhere.~
3. Theoretical Background 3.1. Grazing Incidence X-ray Diffraction (GID) and BraggRods. Bragg Peaks. The analysisof the Brugg peaks is similar to that of a conventional 3-D powder pattern; the reflections can be indexed by two Miller indices, hk. Their angular positions 20hk, corresponding to qhk = (47r/X) sin 0hk, yield the repeat distances dhk = 27r/qhk for the 2-D lattice structure. Their resolutionW, yields the 2-D crystalline corrected qxy line coherence length L, associated with the hk reflection, through the Scherrer formula23
L = 0.9 x 2T/W (1) L is the average length in the direction of the reciprocal (22) For a measured diffraction peak of width fwhm(q ) denoting the full width at half maximum, the resolution corrected wid$& W = [fwhm(qX,J2- A(qxy)*1*I2,where A(qxy)is the resolution of the Soller collimator of width 0.007 A-1. (23)Guinier, A. X-ray Diffraction;Freeman: San Francisco, CA, 1968.
Crystal Structure of Cadmium Arachidate
Langmuir, Vol. 10, No. 3, 1994 821
lattice vector of all diffracting crystallites over which "perfect" crystallinity extends. The square of the molecular structure factor p ~ integrated l ~ along the Bragg rod over the window of q, seen by the detector determines the integrated intensity in the peak. The structure factor Fhk(q,) is given by i where the s u m is over atoms labeled j in the unit cell of dimensions a, b. The j t h atom has a scattering factor f j and is located at the lateral vector position rj = xja yjb and at the vertical position Z j (in angstroms). Because the sample consists of a 2-D "powder", the observed intensity I h k for a given Qh& (or 28hk) and qz position contains contributions from both the (h,k)and h,k) reflections" with possibly several h,k integer values. BraggRodF'rofiles. The variation of the intensity IM(q,) along the Bragg rod as a function of q, is given by
+
lM(qz) = KLPA,,,
A,;21V(qz)12~~,(4,)12DW(hk,q,) (3) The observed BR intensitylhk(q,) is actually a sum over those (h,k) reflections whose Bragg rods coincide at a particular horizontal 28-angle or qxyposition. In eq 3, the most important variation is due to the molecular structure factor amplitude pM(qp)12. The DebyeWaller factor DW(hk,q,) .= eXP[-(qhk2 Uxy+ qz2Uz)l,where Uxyand U,are respectively the root mean square thermal amplitudes parallel and perpendicular to the monolayer plane. They account for the thermal motion of the atoms26*26 in the molecule, as well as for ripples on the water surface, which lead to roughness of the interface.20*n*28The grazing geometry factor V(q,) describes the interference of rays diffracted upward with rays diffracted down and subsequently reflected back up by the interface.% V(q,) differs from unity value only in the vicinity of q, = qJ2, where it contributes a sharppeak.30 In eq 3 correctionsfor crossed beam area (AND a l/sin(28~)),Lorentz ( L a l/sin(28~)), and polarization (P=cos228hk) factors have been inserted, A,u is the area of the unit cell. The factor K scales the calculated to the observed i n t e n ~ i t y . ~ ~ For the simple linear surfactant molecules considered here, the square of the molecular structure factor p(q)12 is bell-shaped as a function of q, and reaches ita maximum when the scattering vector q = (Qhk, e)is orthogonal to the molecular axis. Thus, when the molecules are vertical or tilted in a plane perpendicular to Qhk, the maximum i24) For convenience, the notation (h,k) will refer to both (h,k) and
(h, ) reflections.
(25) In general, molecular thermal vibrations in crystabare anisotropic, which leads to a dependence of the corresponding temperature factor on the direction of the scatbring vector." For a 2-D cryntal lying in the xy plane,the extentof GID data can,in favorablecases, allowthe temperature factor U to be decomposed into an in-plane U, and out-of-plane U. component. Then, the Debye-Waller term Ddu(q.) in eq 3 can be written: DWu(q.) = exp[-(q$U, + qa*U.)I where q = + a. Note that if all the obeerved reflections #or the 2-D crystal are in the same pry range, the exponential term exp[-(qu*UW)1is approximately the same for all (h,k) reflections and play the role of a scaling factor. In such a case, the exponential term can be reduced to exp[-(q.W.)J. (26) Dunitz, J. D. X-Ray Analysis and the Structure of Organic molecules; Comell University Press: Ithaca and London, 1979. (27) Braslau, A.;Perehan, P. S.;Swislow,G.; Ocko, B. M.; Ale-Nieleen, J. Phys. Rev. A 1988, AB, 2467. (28) Pershan, P. S. Colloq. Phys. 1989,60, 1. (29) Vineyard, G. Phys. Rev. E 1982,26,4146-4169. (30) Explicitly, the grazing geometry factor V(q,) is a function of x = 2q,/q, = adorewhere qc = ( 4 4 X ) sin as= 0.021764 A-1: V(x) = 2r for 0 < x < 1and V(x) = b / [ x + (r*- 1)14for x > 1. (31) Due to the sharpnessof the peak in the vicinity of q. = qJ2, there exiata large uncertainties concerning intensities measured close to this q. value. Thus,only the intensities recorded for q, 2 0.023 A-1 are wed in the calculation of K.
intensity along the Bragg rod will occur at the horizon, for = 0 A-l. For molecules tilted otherwise, we expect the Bragg rod maximum at a finite qr, dependent upon both the magnitude and direction of the tilt relative to the inplane scattering vector a. The width of the bell-shaped Bragg rod profile is inversely proportional to the length of the molecule.m*s2 3.2. Calculation Method. A straightforward analysis of the X-ray data provides the unit cell dimensions of the 2-D crystal and the molecular tilt and ita direction.7~20 Further refinement involves atomic coordinate models whose molecular structures may be derived from related 3-D crystal structures. From the scarce data available only a few parameters can be meaningfully fitted and so we use a rigid body refinement of the 2-D crystal structure with a fixed molecular conformation. The molecular orientation is refined using the three Euleriun anglesat" (w, t , and 4). Finally, the root mean square displacement U,1/2 was set at a value263 of 1A. A measure of the correctness of the model structure may be calculated, as for 3-D crystal structures, from the reliability index R, of the fit of the observed to the calculated Bragg rod data q,
(4)
where I,,and I, are the observed and calculated intensities and w = l/u(Io), where u(lo) is the estimated standard deviation of I, The summation is over all the observed I(q,) intensities of the Bragg rod profile for each of the hk reflections. 3.3. Specular Reflectivity. The specular reflectivity of an ideal surface is given by the well-known Fresnel law of optics.% In the limit of small angle of incidence,203*= applicable here, it reduces to
where q, = (47r/X) sin ai is the z-component of the momentum transfer and qc = (4?r/X)sin acis the critical value of q, for total external reflection. The complex term arises from absorption effects. Neglecting absorption, for q, < qc, eq 5 yields Rf= 1, Le., total reflection. As q, is increased beyond qo however, Rt decreases and, for qz 1 4qc,approachesRdq,) = ( q J 2 q ~ ~As. the range of interest reflectivities may extend to qdqc 30 or more,m~27~28~38 (32) Jacquemain, D.; Grayer Wolf, 5.; Leveiller, F.; Lahav, M.; Leieerowitz,L.; Deutsch, M.; Kjaer, K.;Ale-Nielsen,J. Colloq. Phys. 1989,
50.
(33) Goldstein,H. Classical Mechanics;Addison-Wedey Cambridge, MA, 1980. (34) The Eulerian angles were specified according to the convention given by Goldstein= but with a, t, and 9 replacing anglea (D, 0, and $, respectively. The following convention was wed to describe the orient a t i o n o f t h e m o l e c u l e a t t h e s ~ ~ i t i o n at -59=0°: themolecular chain is parallel to the vertical c axis and the plane through the carbon chain is parallel to the ac plane. w ie a rotabon of the molecule (and of the direction in which the moleculewill be tilted) about the vertical d, t is the angle of tilt (in a direction specified by w ) from the vertical and 9 is the f d rotation of the molecule about ita long axis. To help understand about which axis the molecule is titled by an angle t, we note that i f w = Oo, the molecule is tilted about the a axis; i f w is 90°, the molecule is f i t rotated by 90° about the c axis and the tilt is then performed about the b axis. (36) Bom, M.; Wolf, E.Principles of Optics; M c M h New York, 1969. (36) Braslau,A.;Deutach,M.;Pershan,P. S.;Weiee,A. H.;AlwNielsen, J.; Bohr,J. Phys. Reu. Lett. 1986, 54, 114.
822 Langmuir, Vol. 10, No. 3, 1994
Leueiller et al.
down to 1O-ahave to be measured, hence the importance of high intensity synchrotron sources or high-power rotating anode X-ray generators for XR measurements. It is important to note that eq 5 is valid only for an ideally sharp and flat interface across which the electron density p ( z ) varies steplike between two constant values. If p ( z ) is not a step function, but varies continuously in the surface region, the reflectivity is m 0 d i f i e d , 2 ~yielding *~~~~~~ R(qJ = Rf(qz)W(qz)12$ + (1- $)eq**"?
I 0
(6)
where (7) and pm is the constant electron density in the subphase bulk and $ is the surface fraction covered by the 2-D crystallites (the term 1- $ corresponds to uncovered water in between the crystalline domains3'). Thus, by measuring R(q,) it is possible, in principle, to derive p ( z ) , the vertical electron distribution of the monolayer and the monolayerliquid interface averaged over both its ordered and disordered parts. @ is a complex function and only its modulus can be derived from the measured reflectivity but not its phase. Thus, one is faced with the usual phase problem of X-ray crystallography and therefore to date virtually all specular reflectivity data have been analyzed by fitting a parameterized model density p ( z ) to the measured data via eqs 5, 6, and 7. A computationally simple strategy for generating p ( z ) is to represent the monolayer as a stack of slabs% each with a constant density p and thickness L. T w o such slabs would be needed for representing a simple fatty acid monolayer.12 When refining such a slab model, a possible choice of fit parameters, then, would be the densities pi and thicknesses Li of the slabs (where i = 1,2). With this representation of the monolayer, the constant density of the semiinfiiite subphase has to be added below the interface. Finally, this model density must be smeared out in the z-direction to account for the vertical roughness or diffuseness of the interface. The root-mean-square roughness, u, is of order 2-3 A and stems mainly from thermally excited capillary waves on the water surfacee2O~27*28 The roughness parameter u is assumed to be the same for all interfaces. It leads to a Debye-Waller factor exp(-qZ2u2)in I@(qZ)l2 in eq 6. The large value of u is the primary reason that the monolayer may be adequately represented by the slab model. Inserting the slab model in eqs 6 and 7 yields
R = Rf{$l(pm- pl) + (p, - p2)eiqk + p2e'qda12+ (1- $)le**'"
4. The Double Crystalline Layer of Cadmium Arachidate at the Water Surface 4.1. Grazing Incidence X-ray Diffraction Results. Arachidic acid (ClgH&02H) was spread at 20 "C over a CdCl2 subphase (10-5M) adjusted to a pH of about 8.8 by addition of ammonia.39 GID measurementd6 were made on uncompressed films of ClsH&02H at a surfacepressure ?r = 0 mN/m, with surface coverage of 67% (28 A2 per molecule) while cooling the subphase. We monitored the growth of a diffraction peak a t qxy= 1.599A-l which started (37)Lacquemain, D.; Grayer Wolf, S.; Leveiller, F.; Lahav, M.; Leieerowitz, L.;Deutech, M.; Kjaer, K.;Ale-Nieleen,J. J. Am. Chem. Sac. 1990,112,7724. (38) Parrat, L. G. Phys. Rev. Lett. 1964, 95, 369. (39) The pH of about 8.8 WBB the maximum we were able to obtain without inducing precipitation of the subphase solution.
I
b.
Figure 3. Uncompreseed monolayer of arachidic acid Cl&,COzH monolayer spread over a CdC12 subphase (10.9 M), pH = 8.85. The mean molecular area ia 28Azwithzero surfacepreasure. (a) GID profiles at qr = 1.599A-1 aa a function of temperature
and time after spreadng. Time and temperature are indicated for each peak. (b) Integrated intensity (left) and crystalline coherence length (right) aa a function of temperature and time after spreading. The dashed line indicates the resolution limit of the detector. The error bars of the integrated intensities were derived from counting statistics. The error bars (tSE)corresponding to the positional coherence lengths were derived from the curve-fitting analysis of the peaks. forming at about 12 "C. Upon further reduction of the subphase temperature, the integrated peak intensity rose, signifying an increase of the crystalline order, until it reached a plateau, implying saturation of the number of ordered molecules (Figure 3). The subphase temperature in the trough was then set to 9 f 1 "C,before recording the GID ''powder* pattern shown in Figures 4b and 5. The intensity spectrum consists primarily of ten distinct loworder in-plane diffraction peaks (Figure 4b) together with three additional higher-order peaks (Figure 5). The most intense peaks in the region of qxy= 1.5A-l exhibit coherence lengths of =lo00 A, close to the resolution limit. In contrast, over pure water under similar conditions, the uncompressed film yielded a sin le peak a t qxy= 1.441A-1 and a coherence length of =500 (Figure 4c, left). These results indicate that in the presence of cadmium ions in the subphase the crystal structure is different and the crystallinity of the amphiphilic system is enhanced as compared to over pure water. 4.2. Interpretationofthe GID Powder Pattern. The Bragg rod profiles (Figure 4a) of the three intense peaks within the range 1.5 Iqxy 5 1.7 A-1, exhibit a full width at half maximum fwhm(q,) of 0.25 A-l, corresponding32 to a molecular length of -25 A. They therefore indicate contribution to scattering primarily from the monolayer hydrocarbon chains. The profiles of the remaining peaks in Figure 4b are flat and extend beyond 0.8 A-1,as shown
d
Langmuir, Vol. 10, No.3, 1994 823
Crystal Structure of Cadmium Arachidate 0
(1 2)
4l-l-l2.43 2.52 2.1 2.4
04
06
08
10
12
14
16
I8
-
C ---
2.04
t
I2
14
16 qX" ( A ' )
18
12
14 9X"
I
- oo z
(1.01 I0,ll
1200-
2.64
16
2.1
2.72
2.76
2.80
I8
(A1)
Figure 4. Uncompressedarachidicacid CleH&OaH monolayer spread over a CdCla subphase (10-8 M), pH = 8.85, at 9 "C. The mean molecular area was 28 A2with zero surface pressure. (a) Bragg rod scana of the GID peaks in (b). The sharp peak observed at qr = 0.01 A-l is due to interference of rays diffracteddown and subsequently reflected back up by the interface. The assigned (h,k)indices are indicatedfor each peak. (b) The observed GID powder pattern. (c) GID measurementsof arachidicacid spread over a pure water subphase. (left) Uncompressed monolayer, mean molecular area of 28 A2 with zero surface pressure. (right) Compressed monolayer, surface pressure of 27 mN/m. The d-spacing(in& andthe assigned (h,k) indices are indicated above and below each peak.
in Figure 4a for the peakN at qxy = 1.284 A-l. If we extrapolate the Bragg rod intensity profiles for these reflections, they do not drop to half their maxima before, say, qi = 1.2 A-l; we can deduce32 that the thickness is I 21r/(2 X 1.2) = 2.5 A. Thus, they arise from contribution of a thin layer of scattering atoms of thickness at most 4 A and hence not from the arachidate molecules. The three low-order arachidate reflections (Table l), appearing at qxy = 1.503, 1.523, and 1.599 A-l (with d-spacings of 4.18, 4.13, and 3.93 A, respectively) and denoted the "triplet", were assigned {h,k}indices of {O,l), {1,1), and {l,O), respectively, to yield an oblique unit cell with dimensions a' = 4.60, b' = 4.89 A, and y' = 121.3', and an area of 19.2 A2,indicating one arachidate molecule per unit cell. With this assignment, the three reflections and at gxy = 2.570,2.707,and 3.047 A-l index as {1,2),{l,l), {2,2),respectively (Table 1). By comparison, compressed arachidic acid over pure water at 9 'C yields two loworder reflections with dli = 3.82 A, dlo = dol = 4.19 A (Figure 4c, right), from which a distorted hexagonal cell a = b = 4.57 A, y = 113.5', may be extracted" with the (40)We recorded the Bragg rods of the two observed peaks at qzy = 0.689 and 0.799 A-1 using another sample (with a subphase pH of 8.6); thereforethey do not appear in Figure 4. Nevertheless, their profiles are very similar to that measured at qzy = 1.284 A-1 and shown in Figure 4. Both the extension of the Bragg rod intensity profiles along qI and the sharpness in qiy of the peaks rule out the possibility that the peaks are due to three-dimensional crystallite in the aqueous subphase such as a precipitate.
h
loo 2.94
2.80
3.08
3.02
3.10
9xy Figure 5. Observed GID powder pattern for the higher-order reflections of uncompreesed arachidic acid C&&OgH monolayer spread over a CdCla subphase (10-8M), pH = 8.86, at 9 OC. The mean molecular area was 28 A' with zero surface pressure. The assigned (h,kJindices are indicated for each peak.
same area (of 19.2A2)as that of the oblique cell of cadmium arachidate. Of the remaining peaks, the strong peak at qxy = 0.799 A-l has a d-spacing = 7.86 A, which is exactly twice that of the (1,O)peak (qxy = 1.599 A-l, d = 3.93 A, Figure 4b). None of the other peaks has a d-spacing that is an integral multiple of any of the "triplet" eaks. We therefore deduce that this peak at qxy = 0.799 -l arises from contribution of an ordered layer of ions commensurate with the arachidate lattice. For the two lattices to be commensurate, the area of the cadmium unit cell must be (integer) n times that of the arachidate cell of 19.2 A2. If we assume the two observed peaks at qxy= 0.689 A-l (d = 9.11 A) and qxy = 0.799 A-l (d = 7.86 A) are reciprocal base vectors of the cadmium unit cell, then the angle between them, which determines two possible orientations of the reciprocal base vector at qxy = 0.689 A-l vis-a-vis the (1,O) reciprocal axis of the arachidate cell, can be derived for any value of n.
R
(41) For a more obvious comparison with the distortad hexagonalunit cell of compressed arachidic acid over pure water, we may deecribe the oblique cell of the arachidate moiety of cadmium arachidate via the transformation a = a' b', b = -a', yielding a' = 4.86, b' = 4.69 A, y = 116.3'. T h e cell obtained for compressedarachidicacid over pure water is similar to that obtained by W o n , T. M.; Lin, M.C.;Ice, G. E.; Dutta, P. Phys. Rev. Lett. 19W,65,19, for c o m p r d films of C&1COzH at 6 O C over pure water and by Kenn, R. M.; B 6 h , C.; B i b , A. M.;Petereon,I.R.;Mtihwald,H.;Ale-Nielsen,J.;Kjaer,K.J.Phys.C~m. 1991, 96,2092, for compressed Cn COlH at 7 O C : the unit call is distorted hexagonal a = b = 4 . 4 3 , y' 112O, area = 18.7 A S .
+
-
824 Langmuir, Vol. 10, No. 3,1994
Leueiller et al.
Table 1. Observed X-ray GID Powder Pattern Diffraction Data. observed calculated h k intensityb qlr (A-1) d-spacing (A) Reflectionsfrom Cd 0 112 112 112 0 112 112 1 1 112
113 -113 0 -213 213 113 -1 -213 -113 213
