J . Phys. Chem. 1990, 94, 2573-2581
2573
Ultrasmall Magnetic Particles in Langmuir-Blodgett Films Xiao Kang Zhao, Shuqian Xu, and Janos H. Fendler* Department of Chemistry, Syracuse University, Syracuse, New York 13244- 1200 (Received: May 19, 1989; In Final Form: August 14, 1989)
Cationic magnetic Fe304particles have been sandwiched between the polar headgroups of arachidate ion monolayers deposited on oxidized silicon substrates. Optical thicknesses of the S O , layer on the substrate, the arachidate ion monolayers (A-), and the Fe304particles thereon have been characterized by incident-angle-dependent reflectance measurements, assuming stratified planar structures for these components. The determined values for optical thicknesses (dj) and reflective indexes (nj),dsio = 91.5, 136.2, and 172.5 A; nsio = 1.46; dA- = 26.7 A; nA- = 1.52; dFclOl= 49.8 A; and nFeO,= 1.976 (in water, system A), agreed well with values predicted by the models used. Similarly, incident-angle-dependent rehective measurements of seven successive units of arachidate ion sandwiched Fe304particles on Langmuir-Blodgett (LB) films have led to an average thickness of 89.2 8, for a single-sandwich unit. Fe30, particles were found to be 83.2 8, from each other in the same layer but were located 96.2 A from each other in neighboring layers. These values indicated that 35% of the substrate had been covered by Fe304particles. Transmission electron micrographs of arachidate ion sandwiched Fe304particles on a cellulose grid gave the average of the center-to-center separation of the particles and the surface coverage 91 f to 10 A and 30 f 15%,respectively. Longitudinal magnetooptical effects for a 12-sandwich unit revealed rod-shaped magnetic domain structures.
Introduction Ultrasmall colloidal particles are inherently interesting since they provide information on the physical and chemical consequences of transitions between individual molecules, molecular clusters that are beginning to manifest cooperativity, and bulk Size and/or dimensionality reduction can result in substantially altered mechanical, chemical, electrical, electrooptical, and magnetic properties. Indeed, investigations of semiconductor size quantization have led to the demonstration of substantially altered band gaps and reduction potentiah6 To the best of our knowledge, properties of magnetic particles have not been examined as a function of their sizes. We therefore initiated, some years ago, systematic studies on ultrasmall magnetic particles in membrane mimetic systems.'+ In particular, we have demonstrated that 50- to 60-A-diameter, surfactant-vesicle-incorporated Fe304particles acted as tiny magnets and influenced the outcome of photochemical reactions, even in the absence of an externally applied magnetic field.8 We have also developed techniques for the preparation of relatively monodispersed, cationic, Fe304particles, with 81 f 5 A diameters, attached to a glyceryl monooleate bilayer lipid membrane (GMO BLM) so strongly that even a 400-0e magnet could not pull them away.9 This strong attraction overcame the electrostatic repulsions between neighboring Fe304particles and permitted the coverage of the BLM to the extent that it was tantamount to the formation of a monolayer of magnetically single-domain particulate film. Formation of a second layer of particulate film was precluded by charge ( I ) Fendler, J. H. Chem. Reu. 1987, 87, 877. (2) Brus, L. E.; Brown, W. L.; Andres, R. P.; Averback, R. S.; Goddard 111, W. A.; Kaldor, A.; Louie, S. G.; Moskovits, M.; Peercy, P. S.; Riley, S. J.; Siegel, R. W.; Spaepen, F. A.; Wang, Y. "Research Opportunities on Clusters and Cluster-Assembled Materials"; report of the panel convened by the Materials Sciences Division of the Office of Basic Energy Sciences, Department of Energy; to be published in J . Mafer. Res. 1989. (3) Brus, L. IEEE J. Quantum Electronics 1986, Qe22, 1909. (4) Laxhuber, L. A.; Rothenhiusler, B.; Schneider, G.; Mohwald, H. Appl. Phys. A 1986, 39, 173. ( 5 ) Henglein, A. Top. Curr. Chem. 1988, 143, 113. (6) Watzke, H.J.; Fendler, J. H. J . Phys. Chem. 1987, 91, 854. (7) Reed, W.; Fendler, J. H. J . Appl. Phys. 1986, 59, 2914. (8) Herve, P.; Nome, F.; Fendler, J. H. J . A m . Chem. SOC.1984, 106, 8291. (9) Zhao, X. K.; Herve, P. J.; Fendler, J. H. J . Phys. Chem. 1989,93, 908.
(10) Xu, S.; Fendler, J. H. Macromolecules, in press. Borelli, N. F.; Murphy, J. A. J . Appl. Phys. 1971, 42, 1120. ( I 1) Rolandi. R.; Paradiso, R.; Xu,S.;Palmer, C.; Fendler, J. H. J . A m . Chem. SOC.,in press. (12) Murarka, S . P.; Levinstein, H. J.; Marcus, R. B.; Wagner, R. S. J . Appl. Phys. 1977, 48, 40.
0022-3654/90/2094-2573$02.50/0
repulsion, which prevailed in the absence of the attractive forces of the BLM. The absence of capacitance changes across the GMO BLM during deposition of a single layer of Fe304particulate film has been interpreted to imply that the Fe304 particles did not penetrate beyond the headgroup region (head- roup distance, d , = 6-8 A; hydrocarbon bilayer distance, dh= 48 BLM thickness, db = 2dp dh = 62 f 2 A) of the surfactants constituting the BLM. Incident-angle-dependent reflectance measurements led to a model for the Fe304-particle-coated GMO BLM with the following parameters: refractive index of the magnetic particles, n,, = 1.96; thickness of the magnetic particles on the BLM, D,, = 55.1 8, ( D , = d , d,); center-to-center distance between the magnetic particles, S, = 57.6 A. Incorporation of cationic Fe304 particles between the polar groups of Langmuir-Blodgett (LB) films is the subject of the present report. Two layers of arachidate ions, deposited on a silicon substrate, attracted positively charged, ultrasmall Fe304particles, which then were coated with one more layer of arachidate ions to form a single-sandwich unit. LB films of single and multisandwich units of arachidate ion coated Fe304particles have been characterized by incident-angle-dependent reflectivity and magnetooptical measurements.
1;
+
+
Experimental Section Arachidic acid (>99%; Phase Separation, Inc.) and chloroform (HPLC grade; Aldrich) were used as received. Preparation of colloidal magnetic particles followed the reported p r ~ c e d u r e . ~ J ~ J ~ Typically, a mixture of 40 mL of 1 M FeCI3 and 10 mL of 2.0 M FeCI, (HCI, 2.0 M) were poured into 500 mL of 0.7 M N H 4 0 H under vigorous stirring. The supernatant was separated from the immediately formed precipitate. Anionic charges were neutralized by stirring the precipitate with 500 mL of 2 M HCIO,. The cationic colloids obtained were separated by centrifugation (20000 rpm) and peptized by adding water. Diameters of the resultant single-domain particles were determined by transmission electron microscopy to be 50 f 5 A. Water was purified by a Millipore Milli-Q system provided with a 0.2-pm Millistack filter at the outlet. A Lauda Model P film balance was used for monolayer formation and film deposition. Spreading solutions were prepared by dissolving arachidic acid in HPLC grade chloroform to give 8 X 10'' molecules/cm3. The surface of the aqueous solution, contained in the trough, was cleaned by aspiration several times (13) Massart, R. IEEE Trans. Magn. 1981, 17, 124. (14) Jolivet, J. P.; Massart, R.; Fruchart, J. M. N o w . J . Chim. 1983, 7 ,
325.
0 1990 American Chemical Society
2574 The Journal of Physical Chemistry, Vol. 94, No. 6,1990
Zhao et al.
TABLE I: Fe,Ol Particles in Lanemuir-Blodeett Films and in Bilayer Lipid Membranes effective optical particle matrix diam, A reflective index thickness, 8, Langmuir-Blodgett films 52.3 f 1 1.976 49.8 bilayer lipid membranes" 55 f 2 1.96 48.2
mass thickness, 8, 26.5 25.1
fraction
center to center dist, A
0.54 0.52
52.6 57.6
vol
"Taken from ref 9 prior to monolayer formation. The subphase was deemed clean when the surface-pressure increase was less than 0.2 dyn/cm upon compression to 1/20th of the original area and when this surface-pressure increase remained the same subsequent to aging for severa hours (criterion for minimal aging of the surface).l0q*' An appropriate amount of the spreading solution (typically 300 pL) was injected onto the cleaned aqueous surface. The subphase contained 2.5 X IO4 M CdC12 and had a pH of 5.6. Well-behaved surface pressure-surface area isotherms were obtained for the arachidate monolayers (collapse pressure 57 dyn/cm2; collapse area 21 A2/moIecuIe). Silicon substrates [single crystal made in (1 11) direction; Aurel Co.] were prepared for film deposition by a four-step procedure [step 1, soaking for 15 min in trichloroethylene at 80 OC, for 2 min in acetone, and for 2 min in MeOH at 20 O C , followed by sonication (bath) in deionized water for 2 min at room temperature; step 2, soaking for 10 min in a mixture of 40% HC1:H202:H20= 1:1:4 (v/v) at 90 OC followed by rinsing by deionized water (overflow) for 2 min at room temperature; step 3, soaking for 10 min in a mixture of 40% NH40H:H202:H20 = 1:1:4 (v/v) at 90 OC followed by rinsing by deionized water (overflow) at room temperature for 5 min; step 4, soaking for 2.5 min in a mixture of HF:H20 = 1:50 (v/v) at room temperature followed by copious rinsing by Milli-Q water] . I 2 The extent of cationic Fe,04.particle incorporation onto the negatively charged arachidate ion has been monitored by reflectivity measurements in system A. System A was prepared by placing a rectangular 1.OO-cm fluorescence cuvette upright under the water surface in the Langmuir trough prior to monolayer formation. Next, an arachidate monolayer was formed on the water surface. The cleaned silicon substrate (coated by a thin layer of S O 2 ) was then introduced through the monolayer (held at 35 dyn/cm2) and withdrawn vertically. At this point, one layer of arachidate ions became attached (with their hydrophilic head) to the substrate surface. The monolayer-coated substrate was then reintroduced vertically through the arachidate ion monolayer surface (also held at 35 dyn/cm2) into the fluorescence cell. This second dipping resulted in the attachment of a second monolayer, forming a substrate head-tail (surfactant one), a tail-head (surfactant two), two-layer system. The two-layer-system-containing cuvette was then removed from the Langmuir trough and placed on the optical bench. Appropriate concentrations of cationic Fe304particles were then introduced into the cuvette and, after some time, excess Fe304particles were removed by changing the aqueous solution. The rate and amount of Fe304attachment to the arachidate ion two-layer system was determined by absorption and reflectivity measurements (see Results and Discussion section). Arachidate ion sandwiched Fe304-particulateLB films (system B) were prepared in the regular fashion (instead of a cuvette, a beaker containing the Fe304particles was placed in the subphase). Introduction and withdrawal of the silicon substrate through the arachidate monolayer (held at 32-35 dyn/cm2) and subsequent beaker through reintroduction into the Fe304-particle-containing the monolayer resulted in the attachment of a two-layer surfactant system to the subphase and the attachment of the Fe304particles to the second layer of arachidate ions. Slow withdrawal of this system coated the Fe304particles with a monolayer of surfactant and, thus, formed the arachidate ion monolayer/Fe,O, particle/arachidate ion monolayer (single-sandwich unit) on an arachidate ion coated substrate (system B). Multisandwich units (system C) were analogously prepared by repeated substrate introduction through the monolayer (held at 32-35 dyn/cm2) into, and withdrawal from, an Fe304-particle-containingbeaker held in the subphase.
Optical reflectivity measurements followed previously described experimental procedure^.^ A 13-mW He-Ne laser beam was allowed to pass through an attenuator and a polarizer, and directed on the substrate which was held on the optical rotator with the dipping direction perpendicular to the incident plane on the LB film. The reflected light was detected by either a photomultiplier (magnetically shielded Hamamatsu R928) or a power meter (Spectra Physics 404) at an appropriate angle. The intensity of transmitted light through the quartz cuvette, in the absence of the sample, was determined by a power meter (Spectra Physics 404). Two coils on a soft iron core (4-6 cm gap) served as an electromagnet that permitted the application of a magnetic field H I2500 Oe (measured by an MG-5D Walker Scientific Co. gaussmeter) to the sample with the field direction parallel to the LB film surface and in the plane of incidence. Rotation for longitudinal Kerr effect was determined at minimum light output by the cross polarizer, which was inserted between the sample and the detector. A laser-based magnetooptical microscope system was used for observing magnetic domains. Kerr magnetooptical contrast was optimized by using an Ar+ ion laser (50-150 mW range) to illuminate the polarized microscope in combination with video imaging at IO-Mm resolution. Absorption spectra were taken on a Hewlett-Packard 8450 A diode array spectrophotometer. Electron microscopy was performed on a JEOL (JEM-2000 EX) transmission electron microscope using specially prepared copper grids as substrate. A glass slide (31/2 in. X 1 in., Fisher), carrying 10 pieces of 2-mm-diameter 200-mesh copper grids, was placed horizontally under the surface of purified water. A drop of cellulose nitrate was then allowed to spread evenly on the water surface (5 min) through which the grid-carrying glass slide was lifted horizontally. Drying this preparation in a vacuum desiccator led to the cellulose-coated grid which served as the substrate for two layers of arachidate ions Fe304 particles arachidate ions (system B).
Theoretical Section Optical measurements provide valuable insight into the intrinsic properties of new materials. Theoretical foundations for assessing optical thicknesses for the S O 2 layer on the substrate, the LB film, and the LB-film-sandwiched Fe304particles are provided in this section. The Si02layer, the LB film, and the ferromagnetic-particulate-containing LB film, formed on a substrate, are stratified planar structures which can be considered to contain a.stack of 1, 2, 3, ...,j , ..., m parallel films sandwiched between a semiinfinite environment (0) and a substrate (m + 1) media. All phases are assumed to be homogeneous and optically isotropic with thicknesses of dj (j = 1, 2, 3, ..., m) and complex indexes of refraction rij
i Ji . = nI . - i kJ,
j = O , 1 , 2 ,..., m + l
(1)
where nj is the real index of refraction and kj is the dimensionless extinction coefficient. Further, a monochromatic plane wave of wavelength X and polarization v (v = s, p, with the electric vector oriented normally and parallel to the plane of incidence, respectively) is assumed to be incident to the surface of medium (0) at an angle and propagating along the z axis with a refraction angle of 0, in medium j ( e g u r e 1). The refraction angles of 0, are related to the incident angle of 8, by Snell's law: no sin 8, = e, sin 8, = ... = iiJ sin e, = ... = e,,,,, sin e,,,+, (2)
eo
Ultrasmall Magnetic Particles in LB Films
\
dl d2
1 2
:
1
%-I+
E+,+
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2575
where by
pi = (27r/h)djfijCOS Gj
dm
j = 1, 2, 3, ..., ( m
1
The medium (0), air, or aqueous solution in the present case, is transparent, so no and 00 are both real nlumbers and, for an absorbing medium j ( k j # $), the angle of BLbecomes complex. The plane wave vector, Eo at layer 0 and Em+Iat layer ( m + l ) , can be described by a two-by-one Jones vector, defined as
[z ]
Em+,=
[?I+]
qj =
=
[ ::
I:
(4)
The overall reflection (r) and transmission (t) coefficients of layer systems are (5)
cos 0,
a.b. I 1 = nI. kJ .
(3)
sEm+l
fij
-= cj - idj
(15)
where ai, bj, cj, and d j are solutions of the following system of equations a? - b.2 = n? - k.2 - n 2 sin2 eo (16) J J J J O (17)
no2 sinZeo
+
=
+ 1)
where Pj and qj are the impedances for the s and p polarization components as Pj = fij cos 0, = ai - ibj (14)
where Eo+,E,, E,,,+l+,and E,,,+< (which is zero in eq 3, Le., E,,,+I= 0) refer to the plane waves incident, reflected in medium (0), transmitted in medium ( m + l), and reflected in the medium ( m l ) , respectively. The change of polarization state, in amplitude and phase, can be described by a linear transformation of the Jones vector, Le., a two-by-two S scattering matrixI5 as
E,
(11)
are the Fresnel reflection and transmission and ru-l)jand coefficients at the (j - 1)j interface as
Figure 1. Schematics of the model used for describing stratified multilayer structures (j = I , 2, 3, ..., m ) placed between a semiinfinite environment (0) and a substrate medium ( m+ I ) with given incident (6,) and refraction (ej,j = 1, 2, 3, ..., m ) angles.
Eo =
is the phase shift (layer phase thickness) of jth film, given
no2sin2 eo
To compute the product of the multiple matrices given by eq 8, we can initially consider the multiphase stratified system as a simple three-phase system which assumes that a single film (j = 1) is sandwiched between a semiinfinite environment medium (0) and an equivalent medium (1') which gives equivalent reflection properties to the remaining real multiphase system (j= 2, 3, 4, ..., m + 1). Equation 8 thus becomes
s = ZOlL111,
(20)
and 11. =
s, = Z,ZL2IZ~L3...zCr,)jLjj..Lmz~(m+,) = 112L212'
(21)
Upon substitution from eq 9 and eq 10, the overall scattering matrix, in accordance within eq 20, we have where 14, Irl, and &A are amplitudes and phases, respectively. The observed reflectivity, R , is easily obtained by multiplying the complex conjugate
R = r.r* (7) The change in polarization state is due to reflection from an interface or propagation through a series of interfaces. Thus, S can be expressed as a product of the interface matrices Ielu = 1, 2, 3, ..., (m + l)] and layer matrices Lj(j = 1, 2, 3, ..., m ) , as follows:
s = ZOlL,1,2L*. . . z e l ) j L j . . . L ~ z m ~ m + l )
(8)
where Iel), and Lj describe the effects of the individual interface (j - 1 ) j and film j , and (15 ) Azzam, R. M.A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: New York, 1977; Chapter 4.
I
+ rolrle-2i@l rl + role-2@I + r,e-ZiSI rOlrl+ e-2i01
rol
where r l is an equivalent Fresnel reflection coefficient of a multiphase stratified system (j = 1, 2, 3, ..., m + l ) , which is defined by analogy with the two-hase system, (1) and (1') media, as the ratio of the amplitudes of the incident and reflected wave in the initial phase (1). From eq 5 and 22, we have the overall reflection coefficient of the stratified structure as rol rle-2i@1 ro = (23) 1 + rolrle-2@l
+
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Zhao et al.
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
01 . Air)
"0 (H20or Air) "1 two (or more) layers of A-
01 12
12
(b) m = 2
(a) m = 1
( c )m = 3
Figure 2. Schematics of the three- (a), four- (b), and five-phase (c) models used for the optical characterization of the different systems investigated in the present work. Keeping the equations in the Theoretical Section relatively simple required ordering the layers (as described by the numerals in the subscripts) sequentially from the semiinfinite environment, regardless as to their chemical constitution. Thus, while the semiinfinite environment (air or water) is always designated by subscript zero, subscript 1 refers to Si02 in (a), to two or more layers of arachidate ions in (b), and to Fe301 particles or sandwich units in (c). Similarly, subscript 2 designates the silicon substrate in (a), the Si02 in (b), and the two (or one)-layer arachidate ion for system A or systems B and C, respectively, in (c). It should also be noted that thickness calculations for all samples have been performed four- (b), and five-phase (c) models [Le., determination of the thickness of the two (or one)-player arachidate ions sequentially via the three- (a) by the four-phase model (b) required a knowledge of the Si02thickness, which in turn had to be determined by applying data to the three-phase model (all.
-
The subscript of ro denotes an equivalent interface Fresnel reflective coefficient for the total stratified structure. Similarly, by analogy of rl to ro, in computation of eq 22 for the scattering matrix S I ,rl can be expressed as a function of an equivalent interface Fresnel reflection coefficient, r2, for j = 2 , 3 , 4, ..., ( m + 1) media system
+
r I 2 r2e-2i@2
rl =
I
J i
+ ri2r2e-2i@2
IR
Figure 3. Geometrical relationships between the incident angle (e,) at the solution-film interface (01) and measured angle of incidence (4") normal to the quartz cell surface relation to the + (a) or - (b) signs in eq 32.
rm+1 = 0
The overall reflection coefficient, ro, can be computed from the recursive relationship of the phases and amplitudes between rj and rj+l as follows Irjl =
[E2 + P2],/2 G
6j = tan-]
(26)
(E)
E = Pju+i)I(1 + Irj+l12)COS [6ju+i)I + Irj+lI(l + Irju+l)12)COS (2Pj+t - a j + I ) ( 2 8 ) F = lrj+ll(l - lrju+l)12)sin (63,) - 2 P j + i ) + Irju+l)I(l - Irj+112)sin G = 1
[6ju+l)I
+ Irju+I)121rj+l12+ 2Irju+l)IIrj+tICOS (6ju+l) + 6j+l
-
(29)
2Pj+I)
(30)
where Jju+,) is the phase change at interfaceju + l ) , the phase thicknesses, Pj+], were considered as real numbers and imaginary parts, and I,&+,) = 0 in the case of slightly absorbing thin films. Finally, the first film thickness of d , can be numerically evaluated by using eq 11 and upon the substitution of measured reflectvity, R, into eq 7 as R, = r,ro* =
hl2+ 2lrolllrll cos (601 - 62 + 2Pl) + lrOll2lrll2+ 21rolllrllcos (60, + 6, - 2 P d
Iro112 +
1
(b;
(a)
and so on we have general recursive formula
(31)
Schematics of the stratified structures used for assessing the optical characteristics of the Si02 layer (a); the substrate Si02-layer-coated arachidate ion monolayer(s) (b); and the
substrate Si02-layer-coated two-layer surfactant Fe304particles, system A, or the substrate Si02-layer-coated two-layer surfactant Fe304particle surfactant monolayer single, system B, or multiple, system C, sandwich unit(s) (c) are shown in Figure 2 . The incident angle of eoat solution-film interface (01) in system A can be determined by using the geometrical relation with measured angle of incidence, ein,with respect normal to the quartz cell surface (see Figure 3 ) .
+
where the and - signs holds for the cases shown in Figure 3 , a and b, respectively. The incident light intensity used for reflectivity measurement, Zo(e0),is given by I o ( ~ o=) l o d e i n )
(33)
where Io,, is the measured exit light intensity for an aqueoussolution-containing quartz cell at given measured angle 8,. Correction has been made for intensity losses at the air-quartz and water-quartz interfaces. Results and Discussion Deposition of Fe304Particles. A typical behavior of reflectivity as a function of Fe304particle deposition in system A (see Experimental Section for details of sample preparation) is illustrated in Figure 4. The parallel, polarized ( u = p), 6328-A laser line was allowed to impinge on the silicon-wafer-supported two-layer arachidate ion system at an incident angle of 70' during the introductin of the cationic Fe304colloids into the aqueous bathing solution. Point A in Figure 4 represents the introduction of ca. 0.2 mL of 1.0 X 10" M Fe304solution into the bottom of a quartz cell by a syringe. With time, the reflected light intensity increased exponentially to a plateau value. At this point (point B in Figure
Ultrasmall Magnetic Particles in LB Films
t
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2577
c i
34
t
TIME, MINUTES
Figure 4. Adsorption of Fe304particles onto arachidate ion surface in a silicon-substrate-supportedtwo-layer system (system A) monitored by reflectivity. Point A represents the introduction of Fe30, particles, while point B corresponds to the exchange of the water surrounding the film. Measurements, in some cases, were taken at point C.
4), the aqueous bathing solution, surrounding the two-surfactant-layer-coated substrate, was exchanged with dust-free water by pumping. The water exchange continued until no measurable absorbance A 10-4 at 300 nm in a 1.OO-cm cell) was detected in the bathing solution. Subsequent to this water exchange, all colloidal Fe304particles remained firmly attached to the surfactant surface (see Figure 4). The steady value obtained for the reflected light intensity was found to be independent of the concentration of the Fe30, particles injected but depended somewhat on the deposition rate. Systematic absorption spectroscopic investigations as a function of the concentration of the Fe304particles, the time of incubation, and the rate of substrate withdrawal led to the selection of the optimum condition: incubating the two-layer arachidate ion M Fe304 for 1 h and system (on the substrate) in 1.2 x withdrawing it through the monolayer at 2.5 mm/h to produce system B. Optical Thickness of S i 0 2 Overlayer on the Silicon Substrate. The substrate that the monolayers are deposited on is a well polished, etched silicon wafer (prepared as described in the Experimental Section). At room temperature in air or water, the silicon wafer is always covered with a thin oxide layer. The thickness of the Si02layer can be determined from the measured reflectivity, R, at incident angle eoupon substituting m = 1, no = 1.0 for air or 1.333 for water, n, = 1.46, and n2 = 3.857-0.018i, into eq 11 and 31 for the three-phase model (see Figure 2a). The reflectivity on a bare silicon surface is near-maximum, Le., R = 0.364 for the air-Si interface and R = 0.237 for the H20-Si interface at normal incidence. With increasing SiO, film thickness, the reflectivity decreases, as given by eq 31, until the reflectivity reaches a minimum near phase thickness PI of a / 2 . Intensity measurements of the reflected light led to a thickness of 91.5, 136.2, and 172.5 A, d , , for the Si02layer. The silicon dioxide film thickness can also be estimated by direct comparison of measured reflectivity at incident angle with that obtained from a calibrated thickness gauge. Optical Thickness of Arachidate Ion(s). The arachidate ion monolayer can be considered to consist of fairly well oriented molecules whose electric-field-induced polarizabilities, parallel and perpendicular to the substrate, result in different indices of refraction, n,, and nL. Because the differences of birefringent indexes for an arachidate ion monolayer are very small (about ]%),I7 the film can be approximated as a nonabsorbing homo(16) AbelZs, F. Progress in Optics; North-Holland: Amsterdam, 1968; Vol. 2, p 251.
I
I
0
!0
I
I
I 20
I
I
30
1
I 40
I
I
50
60
I
I
I
I 70
0
I
80
A N G L E OF INCIDENCE, s o
Figure 5. Incident-angle-dependentreflectivity, using p-polarized excitation, of 1, 3, 5, 7 , 9 , 1 1, 13, and 15 layers of arachidate ions, deposited on a 91.5-A-thick Si02 overlayer covering the silicon substrate.
geneous isotropic layerI8 and modeled by the isotropic stratified structure shown in Figure 2b. The arachidate ion monolayer deposited on a molecularly smooth, oxidized silicon wafer is characterized by an optical system consisting of a four-phase structure, as illustrated in Figure 2b. The phase regions of 1, 2, and 3 denote the refractive indexes and the thicknesses for the arachidate ion monolayer, the SiOz layer, and the Si substrate, respectively. The optical properties of this system can be characterized by means of a set of independent equations (eq 3 1) which is available from multiple-angle measurements. The monochromatic reflectivity for p polarization incident light was evaluated as a function of the incident angle of eofor & and without the monolayer, Rd.I6 The measured reflectivity distriutions were plotted on a graph of R vs eo. The angle eoat which the two curves cross is associated with Brewster angle, eOB. The Brewster angle 80, is defined by the condition that Fresnel reflection coefficient for the environment-thin film interface is zero ( r o l ,Le. eq 13), which gives (34) By using rol = 0, r I 2= rO2,eq 31 at
e0B
reduces to
This shows that, at Brewster angle, the system behaves as if the first film did not exist. No light was reflected from interface (01); Le., the impedances of the environment and the first film are the same. From eq 34, the refractive index n, of first film can be calculated if no is known. The typical results of incident-angle-dependent reflectivity measurement for arachidic acid LB film are shown in Figures 5 and 6 for u = p and u = s, respectively. Curves correspond to 1, 3, 5, 7, 9, 11, 13, and 15 monolayers of arachidate ion deposited on a 91.5-%, S i 0 2 layer coating the silicon wafer. All curves intersection each other at Brewster angle, @OB = 56.7' for p polarization incident light. The refractive index of arachidate ion (17) Engelsen, D. D. J . Opr. SOC.Am. 1971, 61, 1460. (1 8) Born, M.; Wolf, E.Principles of Optics; Pergamon: New York, 1965.
Zhao et al.
The Journal of Physical Chemistry, Vol. 94, No. 6,1990
2578
SIO*
SI
Figure 8. Schematics of Fe304particles coating a two-layer arachidate ion system deposited on a Si02 overlay covering the silicon substrate (system A).
I
I
I
I
I
'3
20
I 30
I I
I
I
40
50
I
I
I
I
60
70
I 60
I
1 90
ANGLE OF INCIDENCE, eo
Figure 6. Incident-angle-dependent reflectivity, using s-polarized excitation, of I , 3, 5, 7, 9, 1 I , 13, and 15 layers of arachidate ions, deposited on a 91.5-&thick SiOl overlayer covering the silicon substrate.
b, consisting of a smooth line of points intersected at Brewster angle @OB = 56", gave the effective refractive index of ferromagnetic particulate overlayer as
n , = no tan
@OB =
1.976
from which thickness d , of the particulate Fe304 thin film can be calculated as d , = 49.8 A by using the H20-Fe304-arachidate ions-Si02-Si five-phase model (c in Figure 2). Substitution of these values into eq 31 and 11 gave the theoretical curve b (solid line), in good agreement with the experimental data. Structure of Fe304Particles on Two Layers of Arachidate Ions (System A ) . On smooth surfaces, the refractive index of a reflecting surface can be calculated by using the exact Fresnel equations as an ideal model with infinite smooth surface on the atomic scale. Rough surfaces can be treated as a macroscopic homogeneous film with an effective refractive index and optical thickness when the particle sizes are small compared to the wavelengths of incident light (A = 6328 A). Assuming spherically symmetric Fe304particles of equal height, center-to-center separation L, and an individual magnetic particle with intrinsic dielectric response of tp, the magnetic article size, D ( D = d , penetration depths, assumed to be 2.5 ), was obtained to be 52.3 f 1 A, in fair agreement with that introduced into the solution (see Figure 8). The macroscopic dielectric response of the Fe304film ( e ) is connected in an intimate way to the compositional and microstructural parameters that determine the physical properties of magnetic particles. For realistic, roughened, microstructured surface, it is given by the effective medium theory, which can be assessed by the Maxwell-Garnett approximationig
x
3
'-
20
30
40
50
60
70
80
ANGLE OF INCIDEUCE
Figure 7. Incident-angle-dependentreflectivity, using p-polarized excitation, of a two-layer arachidate ion system deposited on a 172.5-A-thick Si02overlay covering the silicon substrate prior (a) and subsequent (b) to Fe,04 deposition (system A). Curves a and b intersect at the Brewster angle, (56')
LB films was calculated as 1.52 by using eq 34 with n, = 1. The good agreement of measured data (points in Figures 5 and 6 ) and
theoretical curves (solid lines in Figures 5 and 6) proved the salient feature of well-defined thicknesses in integer multiples of 26.7 A. This value agrees well with that measured for the length of an extended-chain arachidic acid molecule. Optical Thickness of Fe304Particles on the Two-Layer Arachidate Ion System (System A ) . The measured incident-angledependent reflectance of p polarization light, reflected from the two-layer arachidate ion system prior (prior to A in Figure 4) and subsequent (point C in Figure 4) to Fe304particle deposition is shown as points in Figure 7. The solid line in Figure 7 is a theoretical curve calculated by using eq 31 with no = 1.333, n , = 1.52, n2 = 1.46, n3 = 3.857-0).018i, d l = 53.4 A, and d2 = 172.5 A for the four-phase model (b) in Figure 2 for the H 2 0 two-layer arachidate ion Si02Si system. The experimental curves a and
(36)
+
(37) where F and th and nh2are the volume fraction of particles and the dielectric constant of surrounding medium (the host medium) and the screening parameter, y = 1/ I - 1, 0 < 1 < 1 models the polarizability induced charge accumulation at the interface between the microstructural particles, the parameter l is shape dependent, and 1 = 1/3 for spherical particles. The complex dielectric constant can be written in terms of the effective refractive index as (t)l/2
= ii, =
", - ik,
= n, - ik,
(38)
(39)
The extinction coefficient k , (0.02) and k , (0.3) are very small (19) Garnett, M. S. C. Philos. Trans. R. Society (London) 1904,203, 385.
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990 2579 ' 3
1
:.9
--
1 0 0 7
1 0 0 0 0 6
IO00000 . 5
4 1 0 0000000-
10000000000
sandwich units
38--
3
10000000000002 2
1
0.7
--
-
Figure 9. Schematics of a seven-sandwich-unir,arachidate ion coated, Fe304-particleLB film.
I 1
I
I
I
1
I
I
I
I
0
10
20
30
40
I 50
I
A N G L E O F INCIDENCE,
I I
I
I
I
60
70
80
I
oo
Figure 11. Incident-angle-dependent reflectivity, using s-polarized excitation, of 1 , 2, 3,4, 5 , 6, and 7 sandwich units of arachidate ion coated Fe304particles, each unit having 90.0, 72.3, 103.4, 89.0,90.0, 89.9, and 89.9 A, respectively. Reflectivity measurements of the Si02and the first monolayer of arachidate ion led to thicknesses of 136.2 and 26.7 A. 0 4
I
I
I
,500
pm,
Figure 10. Photograph of a seven-sandwich-unit, arachidate ion coated, Fe304-particleLB film taken through an Olympus PM-IO-M microscope.
compared to the refraction coefficient n , (1.975) and np (2.8); hence, eq 37 can be simplified to n12- nh2
+
n12 2nh2
npZ - nh2 =F
np2 + 2nh2
(40)
Substitution of the appropriate values, nh = n, = 1.333, n, = 1.976, and np = 2.8 into eq 40 led to the volume fraction F = 0.54 and, hence, to the mass thickness of the film, d , d , = Fd, = 26.5
A
(41)
The average separation of magnetic particles, L, is estimated to be 52.6 A by substituting D = 52.3 A in equation as follows
A microstructure model of the thin magnetic Fe304particulate film on two layers of arachidate ions in aqueous solution and the parameters used in its assessment is shown in Figure 8 . This picture compares remarkably well to that previously proposed for
A N G L E OF INCIDENCE, oo
Figure 12. Incident-angle-dependent reflectivity, using p-polarized excitation of 1, 2, 3.4, 5 , 6, and 7 sandwich units of arachidate ion coated Fe304particles. Reflectivities of the Si02overlay and the first arachidate ion layer on it (0) are also included. The lines intersected at 59", the Brewster angle.
the Fe304particulate film on a GMO BLM (Table I). Optical Thicknesses and Structures of Arachidate Ion Sandwiched Fe304Particles (Systems B and C). When the Fe304particle-coated two-layer system was raised out of the trough, it became covered by another layer with the polar head groups of the surfactants facing the magnetic particulate thin film (system B). Sequential dipping and withdrawal led to multiple sandwich structures (system C), schematically shown in Figure 9. A
2580 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
Zhao et al.
Figure 14. Transmission electron micrograph of two layers of arachidate ion/ Fe304 particles/arachidate ion system (system B) on a cellulosecoated grid as substrate. See Experimental Section for details. SANDWICH LAYER NUMBER
Figure 13. Determined thickness of the LB films vs the number of sandwich units of arachidate ion coated Fe304 particles.
photograph of a seven-sandwich layer of arachidate ion monolayer Fe304particle arachidate ion monolayer system is shown in Figure 10. The incident-angle-dependent reflectivity data (points) for a seven-sandwich layer of arachidate ion monolayer Fe304particle arachidate ion monolayer LB film are shown in Figures 1 1 and 12 for v = s and p polarization light, respectively. The numbers 1,2, 3,4, 5,6, and 7 denote the number of sandwich layers and the number 0 stands for one reflection originating from a bare monolayer coating the SiOz surface (see Figure 9). The curves 1, 2, 3,4, 5,6, and 7 in Figure 12, once again, intersected each = 59O, which gave the effective other at Brewster angle eOB refractive index of nl = 1.66. Substitution of this value into eq 31 and 1 1 for the five-phase model (c in Figure 2) with measured values of n2 = 1.52, n3 = 1.46, d2 = 26.7 A, d3 = 136.2 A, and values n, = 1, n4 = 3.857 - O.O18i, led to thickness values of 90.0, 162.3, 265.7, 354.7, 444.7, 534.6, and 624.5 A for 1, 2, 3, 4, 5 , 6, 7 sandwhich layers, respectively (see Figure 13). Thus, thicknesses of 90.0,72.3, 103.4,89.0,90.0,89.9, and 89.9 A were found for the first, second, third, fourth, fifth, sixth, and seventh sandwich layer, which gave an average thickness of d, = 89.2 A for a single-sandwich layer of arachidate ion coated Fe304particles. Substituion of the appropriate values (nl = 1.66, nh, = 1.52, n,, = 2.8) into eq 40 led to a volume fraction (Le., packing factor) of F = 0.14. The mass thickness of magnetic Fe304particles, dp, and arachidic molecules, dh,were assessed to be
dp = Fdl = 12.5 A
(43)
Comparing the mass thickness of particles under the water phase, d,, and raised from the water, dp,the transfer ratio given by the Langmuir-Blodgett deposition technique was (45) The center-to-center separation of particles in layer, L, is estimated to be 83.2 f 1 A by substituting D = 52.3 A, dl = 89.2 A, and F = 0.14 in the relationship
Similarly, the average separation of magnetic particles between
f 5
a
cr I-
:u.:
IO--
U w -I
z 3
r-
4
5--
s
4
6
8
10
12
14
16
18
20
SANDWICH LAYER NUMBER
Figure 15. Determined longitudinal Kerr rotation, using s-polarized light, as a function of the number of sandwich units. Measurements were performed under a 2500-0e magnetic field.
the neighboring layers was estimated to be 96.2 A. Surface coverage, +2D, by spherical particles is given by
The maximum coverage of a surface attainable by closely packed, uniform spherical articles (Le., D = L) is 90.69%. Using the values of D = 52.3 and L = 83.2 A, obtained in optical thickness measurements, indicated that 35% of the substrate surface was covered by Fe304particles. Transmission electron micrographs of arachidate ion sandwiched Fe304 particles, system B, on a cellulose-coated grid (see Experimental Section) substantiated the optical data nicely (Figure 14). Two methods were used to evaluate the electron micrographs. In the first method, L values were measured on enlarged micrograms for 500 particles by a millimeter ruler. This gave L = 91 f 10 A and +2D = 30 f 5%. Traces of 100 Fe304were cut and weighed in the other method. Comparison of the weight of the cut particles with the weight of the total area led to +2D = 39 f 5%. Considering the irregularities and the nonuniformities of the particles, as well as the differences
1
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990 2581
Ultrasmall Magnetic Particles in LB Films
I
I
I
100
2000
3000
MAGNETIC FIELD, Oe
Figure 16. Average longitudinal Kerr rotation, using s-polarized light, as a function of the longitudinal magnetic field for a seven-sandwich unit of arachidate ion coated, Fe304-particle LB film.
between the substrates used in optical and electron microscopic measurements, the agreement between these data is remarkably good. Longitudinal Magnetooptical Effect Measurements. Magnetooptical effects originate in the coupling of the magnetization vector with the incident polarized light. The effects were observed in the reflected s-polarize! light in the longitudinal Kerr effect20 in which magnetization M is parallel to the film surface and in the plane of incidence. Figure 15 shows a measured longitudinal Kerr rotation for s polarization incident light as a function of the numbers of sandwich layers of arachidate ion monolayers/Fe304 particles/arachidate ion monolayers. As the layer number increased, the longitudinal Kerr rotation increased to a maximum at 12 sandwich layers and then decreased to a small value. The longitudinal Kerr rotation was 1 order smaller than that measured for thin magnetic Fe304monoparticulate layers on GMO BLMs? due to the small volume fraction (0.14) and tightly bonded crystallized solid-state structure. The average longitudinal Kerr rotation of a seven-layer magnetic-particle-sandwiching bilayer for s polarized light as a function of the longitudinal magnetic field is shown in Figure 16. No saturation was observed, even when the magnetic field reached 2500 Oe. Observation of Magnetic Domains. The Kerr magnetooptic effect is a particularly useful method for the observation of domains in thin films. When linearly polarized light is reflected through a magnetic film, the plane of polarization is rotated (20) Smith, D. 0. Opt. Acta 1%5,12, 13, 193. Hunt, R. P.J . Appl. Phys. 1967, 38, 1652. Robinson, C. J. Opt. SOC.Am. 1963, 53, 68.
100
pm
Figure 17. Domain pattern in a 12-sandwich unit of arachidate ion coated, Fe304-particle (IO70A thick) LB film.
through an angle which depends upon the magnetization direction in the film. The different rotation angle of antiparallel magnetization domains gives a light intensity contrast through polarized microscopy. The magnetooptically characterized, one-sandwich unit appeared to be uniform. Due to the intense background reflection of silicon substrate and the 10-pm resolution of polarized video-enhanced microscopy, domains smaller than 10 pm could not be observed. The Fe304particulate sandwiching LB film of 12 layers (with a thickness of approximately 1070 A) showed the highest Kerr effect (see Figure 16) and allowed the observation of rod-shaped domain structures with the easy axis parallel to the dip direction (Figure 17). The average domain region was about 25 mm long and 7 pm wide. The orientation of magnetization was fixed at the point of coating the magnetic particles by a surfactant monolayer upon withdrawal from the Langmuir trough. Presumably, application of an external magnetic field during film formation could modify in a desired direction. Efforts are underway in our laboratories for the experimental realization of this assumption. Acknowledgment. Support of this work by the National Science Foundation is gratefully acknowledged. We thank Pascal J. HervE for providing 50 f 5 A diameter cationic Fe304particles. Registry No. Fe304, 13 17-61-9;arachidate ion, I 5620-44-7.
