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Variable Acquisition Angle Total Internal Reflection Fluorescence: A New Technique for Orientation Distribution Studies of Ultrathin Films A. Tronin* and J. K. Blasie Chemistry Department, University of Pennsylvania, Philadelphia, Pennsylvania 19104 Received December 4, 2000. In Final Form: March 12, 2001 A new technique for the determination of the orientation distribution of a fluorophore within an ultrathin film, in terms of the mean tilt angle relative to the monolayer normal and the distribution width, is described. The technique utilizes the measurement of polarized fluorescence, excited by the evanescent field appearing upon total internal reflection. The main difference between this and existing techniques is that the fluorescence intensity is measured as a function of the acquisition angle with low aperture detection. The potential of the technique was investigated with the help of computer modeling and experimentally utilizing a Langmuir-Blodgett film of arachidic acid doped with a fluorophore DiI. Both computer modeling and the measurements show that the acquisition of the angular dependence of the fluorescence dramatically improves the technique, increasing manyfold the accuracy and resolution of the determined orientation distribution parameters.
1. Introduction Oriented ultrathin films of organic and/or bioorganic materials have been shown to be important in both fundamental studies in search of new knowledge and technological applications. Along with the task of manufacturing of a functionality in the monolayer films, methods are required for characterization of their structure. One of few relatively easy experimental approaches to assessing molecular orientation in thin monolayer films is a polarized fluorescence technique. In this technique, the orientation of a dipole is investigated by measuring the polarization of the fluorescence excited by an electric field directed normal to and along the film surface. The main advantage of fluorescence measurements over other linear optical techniques is that fluorescence, a “twophoton” process, makes it possible to determine not only the mean orientation angle of the dipole with respect to the normal to the monolayer plane but also the width of the orientational distribution.2,3 This feature is of particular importance for biological applications because complex organic films are usually not well oriented. In many cases knowledge of the mean angle alone has no useful meaning, since for a very broad distribution, the width itself may be more important than the mean value. For many applications, on the other hand, even a rough estimate of the distribution width is important, making it possible to characterize the quality of the film. Both total internal reflection fluorescence (TIRF) and polarized epifluorescence (PEF) have been used to study orientation distribution of monolayer films, containing various fluorophores, such as DiI, BODIPY,4 and porphyrins.1-3 However, as was shown in ref 3, mean tilt angle and the distribution width as measured by polarized fluorescence are highly interrelated parameters and in some cases cannot be resolved with good accuracy. Commonly, the existing techniques utilize measurement of the fluorescence radiation emitted in the normal (1) Edmiston, P. L.; Lee, Cheng, S.-S.; Saavedra, S. S. J. Am. Chem. Soc. 1997, 119, 560. (2) Bos, M. A.; Kleijn, M. Biophys. J. 1995, 68, 2566. (3) Tronin, A.; Strzalka, J.; Chen, X.; Dutton, P. L.; Blasie, J. K. Langmuir 2000, 16, 9878. (4) Edmiston, P. L.; Lee, J. E.; Wood, L. L.; Saavedra, S. S. J. Phys. Chem. 1996, 100, 775.
direction to the film plane, integrated over a small or large aperture. In such approaches, the information about the dependence of the fluorescence radiance on the acquisition angle is either not acquired or lost. Since the dipole radiance itself has a pronounced directional pattern, measuring of the angular dependence of the fluorescence intensity in low aperture geometry may improve the resolution of the dipole orientation determination. This approach has been used to estimate the concentration and the emission dipole orientation of adsorbed dye molecules.5 The potential of the variable incidence and observation angles measurement for the determination of the “fluorescence density profiles” of thin adsorbed films has been thoroughly investigated in ref 6, where, to the best of our knowledge, the term “variable angle TIRF” was introduced. In this paper we will provide a detailed description of a variable acquisition angle polarized TIRF (VAATIRF) technique designed to determine the orientation distribution parameters of surface confined fluorophores, compare its potential with that of the traditional TIRF with normal acquisition scheme for various model systems, and report the results of its application to study of LangmuirBlodgett films of arachidic acid doped with an amphiphilic fluorophore DiI. 2. Fluorescence from a Surface Bound Dipole General formulas for the TIRF intensity from a transition dipole in the case of high aperture collection were obtained previously.7 In the case of low aperture collection, which is used in the present study, a straightforward derivation of the dipole fluorescence is less complicated. Besides, we need to account for the fact that emitting and absorbing dipoles may have different orientations and obtain the direct expression for the dependence of the fluorescence intensity on the observation angle. The detailed derivation of the polarized fluorescence intensity vs observation angle is given below. Let us consider a fluorophore bound to a solid surface. The fluorophore is arbitrarily oriented with respect to the (5) Fattinger, Ch.; Honegger, F.; Lukosz, W. Helv. Phys. Acta 1986, 59, 1079. (6) Suci, P. A.; Reichert, W. M. Langmuir 1988, 4, 1131. (7) Burghardt, T. P.; Thompson, N. L. Biophys. J. 1984, 46, 729.
10.1021/la001689o CCC: $20.00 © 2001 American Chemical Society Published on Web 05/11/2001
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Figure 1. Fluorophore orientation. µ and ν are absorbing and emitting dipoles, and R is the angle between them. XYZ is the laboratory frame; Z is normal to the film surface. X′Y′Z′ is the dipole frame, Z′ is parallel to the absorbing dipole, and both dipoles lie in the Y′Z′ plane. Dipole orientation is given by two angles: θ ) tilt (between Z and Z′) and φ ) precession. Subscripts “a” and “e” correspond to the absorbing and emitting dipoles, respectively. Direction of acquisition lies in the XZ plane and is given by the unity vector r, which is determined by the angle β. n is normal to the Y′Z′ plane, and ω is its tilt angle.
laboratory frame (Figure 1). The laboratory frame XYZ is oriented so that the Z axis is normal to the surface. The film-substrate interface lies in the XY plane, and the positive of Z axis extends into the external medium. The XZ plane is the plane of incidence for the excitation beam, which propagates in the substrate and intercepts the interface at the origin. Since the electronic configuration is different in the ground and excited states, the molecular orientations of the absorbing and emitting dipoles do not necessarily coincide. We denote the absorbing and emitting dipoles as µ and ν, respectively. The orientation of the dipoles is given by two angles: tilt, θ, and precession, φ. Subscripts “a” and “e” refer to the absorbing and emitting dipoles. The angle between the dipoles is denoted as R. We will also use parameters ψ and δ for the differences in the tilt and precession for the absorbing and emitting dipoles, i.e., ψ ) θa - θe and δ ) φa - φe. Here and below we denote vectors by boldface characters and scalars by the normal characters. The direction of acquisition lies in the XZ plane and is given by the unity vector r, which is determined by the angle β. X′Y′Z′ is the dipole frame, in which the Z′ axis is directed along the absorbing dipole and both dipoles lie in the Y′Z′ plane. We will use this frame later to determine the relation between the angles R, δ, ψ, and θa. The far field of a dipole ν is given by
E ) p[(ν‚r)r - ν]
(1)
where p is dipole polarizability.8 In the laboratory frame r ) (sin β, 0, cos β) and ν ) (sin θe cos φe, sin θe sin φe, cos θe). Substitution into (1) gives the components of the dipole electric field
Ex ) p[(sin θe cos φe sin β + cos θe cos β) sin β sin θe cos φe] (2a) Ez ) p[(sin θe cos φe sin β + cos θe cos β) cos β cos θe] (2b) Ey ) - p sin θe sin φe
(2c)
(8) Born, M.; Wolf, E. Principles of Optics, 2nd ed.; Pergamon Press: New York, 1964; Chapter 2.
Ey by definition is the amplitude of the emitted wave polarized perpendicular to the observation plane. Ex and Ez sum up to form the emitted wave which is polarized parallel to the observation plane. We will refer to these polarizations as p- and s-polarizations, respectively. The electric vector of the p-wave, Ep ) (Ex,0,Ez), is of course perpendicular to the direction of propagation r that can be easily proved by considering the scalar product (Ep‚r), which equals zero. Both the p- and s-components of the fluorescence can be measured separately with a help of a polarizer in the detection path. The detected waves are the sums of the direct beam waves and those reflected by the substrate. Both reflections are coherent with the direct emission for each individual beam within the detector acceptance cone. However, because the thickness of the slide is about 2 × 103 times larger than the wavelength, the phase variation between the direct radiation and the back-face reflection over the detector acceptance cone is at least 10π. This value is achieved for the normal angle observation; for β ) 80°, which is the maximum observation angle used, the variation is about 1000π. Thus, the integration over the acceptance cone produces an effective loss of coherence for the back-face reflection, and its contribution should be added as the intensity term. For the front-face reflection the phase shift is zero in the whole range of the angles used, which means that the coherence is not lost and the contribution of the front reflection should be added as the electric vector term. The reflected beams are produced by the beam emitted toward the surface along the angle β′ ) 180° - β. At the front face they are reflected from and transmitted into the substrate. The transmitted beam is reflected at the back face and then transmitted again into the air at the front face. Thus, the observed intensities are
Is ) (Ey + Ey′Rs12)2 + Ey2Bs
(3a)
Ip ) (Ex + Ex′Rp12)2 + (Ez + Ez′Rp12)2 + (Ex2+ Ez2)Bp (3b) where Bk ) (Tk12Rk21Tk21)2 are the contribution coefficients of the back-face reflection, k ) p, s; Tkij and Rkij are the transmission and reflection coefficients for p- and spolarizations at the air-substrate (12) and substrateair (21) interfaces. The amplitudes E′ are calculated from (1) with substitution of β f β′. Expressions for the Tkij and Rkij can be found elsewhere.9 Equations 3 do not take into account the multiple reflections in the slide. Calculations show that the second back-face reflection is about 10% of the total intensity at most. This value is achieved for the observation angle of 80°. However, at such large angle the second reflection is spatially separated from the direct beam and can be resolved by a 2-D sensitive detector. The second reflection decreases abruptly with the decrease of the observation angle becoming less than 1% at β ) 70°. Expressions 3 do not take into account the fluorescence lifetime correction due to radiant losses into more dense media. As shown previously,10 these losses depend on the dipole orientation. However, our calculations show that the possible changes in the measured mean tilt angle that can be caused by this effect are much smaller than the experimental errors. The dipole polarization p is the scalar product of the excitation field vector A and the absorbing dipole µ, (9) Born, M.; Wolf, E. Principles of Optics, 2nd ed.; Pergamon Press: New York, 1964; Chapter 1. (10) Hellen, E. H.; Axelrod, D. JOSA B. 1987, 4, 337.
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p ) (A‚µ)
where
Apary ) (1 + Rs)2 + Bs
The evanescent field can be excited by either the TE or TM incident mode. For the TE excitation, the evanescent field has only y-component, whereas for the TM one both x- and z-components appear with the phase shift of 90° between them; thus, the square of the dipole polarization is
pTE2 ) Ay2µy2
Aparx ) (1 - Rp)2 + Bp Aperz ) (1 + Rp)2 + Bp a)
(4)
Ip1 ) I4 cos2 ψ + I3 sin2 ψ + 2I6 cos ψ sin ψ
for the TE excitation mode and
Ip2 ) I3 cos2 ψ + I4 sin2 ψ - 2I6 cos ψ sin ψ
pTM2 ) Ax2µx2 + Az2µz2
Ip3 ) I3 cos2 ψ + I5 sin2 ψ + 2I7 cos ψ sin ψ
(5)
for the TM one, where Ai, i ) x, y, z are the components of the evanescent field electric vector and µi are the components of the absorbing dipole. The expressions for the Ai can be found elsewhere.9 For the real experimental setup the amplitudes of the TE and TM waves, propagating in the slide, are corrected for the distortions due to polarization-dependent transmission at the air-prism and prism-slide interfaces (see experimental setup section). Substitution of (4) and (5) into (2) and then (2) into (3) gives the explicit dependence of dipole fluorescence intensities IsTE, IsTM, IpTE, and IpTM on the orientation angles. Langmuir monolayer films are axially symmetric on the macroscopic level (scale of the acquisition area), which means that the fluorescence intensities obtained should be averaged over the precession angle φ in the range of 0 < φ < 2π. We also allow some distribution over the tilt angle θ. We assume this distribution to be uniform, i.e., that the dipoles can be inclined at any angle in the range of θm - σ < θ < θm + σ with equal probability, where θm is the mean tilt angle and σ is the dispersion of the distribution; thus, the film fluorescence intensities are
Ip4 ) I5 cos2 ψ + I3 sin2 ψ - 2I7 cos ψ sin ψ and
(8a)
I4(θm,σ) ) 〈sin4 θa〉
(8b)
I5(θm,σ) ) 〈cos4 θa〉
(8c)
I6(θm,σ) ) 〈sin3 θa cos θa〉
(8d)
I7(θm,σ) ) 〈sin θa cos3 θa〉
(8e)
C is a constant, which incorporates all common factors such as excitation power, fluorescence yield, detector sensitivity, etc. Integrals (8) can be readily calculated for the uniform distribution; below are their explicit expressions:
I3 )
cos3(θm + σ) - cos3(θm - σ) 3[cos(θm + σ) - cos(θm - σ)]
∫0 ∫θ -σ Ilm sin θa ∂θ ∂φ θ +σ 2π∫θ -σ sin θa ∂θ m
5[cos(θm + σ) - cos(θm - σ)]
(6)
m
I4 ) 1 - 2
where l and m denote the emitted polarization and excitation modes respectively (l ) s, p; m ) TE, TM). In the case of uniform distribution the averaging integrals can be expressed analytically, which reduces the overall computing time considerably. From the physical point of view the Gaussian distribution over θ is more justified. However, our calculations show that the results for the uniform and Gaussian distributions are essentially the same. Applying (6) and performing all substitutions, we finally get
IaSTE ) CAy2AparyaIp1
(
2
)
) CApary Ax bIp1 + Az Ip3 2
(7b)
cos3(θm + σ) - cos3(θm - σ) 3[cos(θm + σ) - cos(θm - σ)]
+
cos5(θm + σ) - cos5(θm - σ) 5[cos(θm + σ) - cos(θm - σ)] I5 )
I6 )
(7a) 21
-
cos5(θm + σ) - cos5(θm - σ)
m
IaSTM
I3(θm,σ) ) 〈sin2 θa cos2 θa〉
θm+σ
2π
Ialm ) 〈Ilm〉 )
1 1 1 1 cos2 δ + , b ) sin2 δ + 4 8 4 8
I7 )
cos5(θm + σ) - cos5(θm - σ) 5[cos(θm + σ) - cos(θm - σ)] sin5(θm + σ) - sin5(θm - σ) 5[cos(θm + σ) - cos(θm - σ)]
sin3(θm + σ) - sin3(θm - σ) 3[cos(θm + σ) - cos(θm - σ)]
+
sin5(θm + σ) - sin5(θm - σ)
1 Aparxb cos βIp1 + Aperz sin2 βIp2 (7c) 2
5[cos(θm + σ) - cos(θm - σ)]
1 IaPTM ) CAz2 Aparx cos2 βIp3 + Aperz sin2 βIp4 + 2 1 CAx2 Aparx a cos2 βIp1 + Aperz sin2 βIp2 (7d) 2
Formulas 7 give the fluorescence intensities as a functions of the unknown parameters θm, σ, ψ, and δ and the observation angle β. To determine the unknown parameters, we fit the calculated intensities to the
IaPTE
(
2
) CAy
(
)
2
)
(
)
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measured ones for all observation angles. To eliminate the unknown coefficient C, each intensity was divided by IaSTE + IaPTE measured or calculated for β ) 0. For proper weighting, the experimental accuracy of each intensity was used. As we will show, variable acquisition angle TIRF (VAATIRF) provides the possibility to determine the differences in tilt and precession angles for the absorbing and emitting dipoles, which is impossible for the normal angle acquisition. From the values of δ and ψ the true angle between the dipoles R can be calculated. One the other hand, this angle can be determined by the fluorescence anisotropy measurement of the fluorophore in a viscous solution. Agreement of thus determined numbers could to some extent prove the applicability of the technique. To derive the relation between θ, δ, ψ, and R, let us consider the dipole coordinates in the dipole frame X′Y′Z′. The tilt angle of the emitting dipole in the dipole frame is equal to the angle R. Transformation from the laboratory frame to the dipole frame consists of three rotations. The first one is the clockwise rotation about Z axis by the angle φa, which takes absorbing dipole into the Y′′Z plane. The second one is the clockwise rotation about the X′′ axis by the angle θa. This rotation takes the Z axis into the Z′ one. The third one is the clockwise rotation about the Z′ axis by some unknown angle γ, so that the emitting dipole lies into the Y′Z′ plane. The angle γ can easily be found by considering the explicit expression for the x′-coordinate of the emitting dipole, which equals zero by the definition of the X′Y′Z′ frame. The first and third rotations are given by the matrices RZ1 and RZ2
(
cos φa -sin φa 0 RZ1 ) sin φa cos φa 0 0 0 1
)
(
cos γ -sin γ 0 RZ2 ) sin γ cos γ 0 0 0 1
)
The second rotation is given by the matrix RX
(
1 0 0 RX ) 0 cos θa -sin θa 0 sin θa cos θa
)
and the coordinates of the emitting dipole in the (X′Y′Z′) frame are
(
sin θe sin (φa + δ) v ) RZ2RXRZ1 sin θe sin (φa + δ) cos θe
)
(9)
Performing multiplication and taking into account that z′-coordinate of the emitting dipole is simply cos R, we finally get
R ) arccos(sin θa sin θe cos δ + cos θa cos θe) (10) If the absorbing and emitting dipoles are not collinear, their orientation determines a plane which is somehow related to the chemical structure of the fluorophore. In the case when such relation is known, the knowledge of the orientation of this plane may be useful. One can derive the tilt angle ω of the plane by taking into account that the normal to the plane n is the cross product of the dipoles’ unity vectors (see Figure 1). Again, it is sufficient to consider only the z-coordinate of the normal, since it is equal to the cosine of the tilt angle and the plane tilt angle is
ω ) arccos(sin θa sin φa sin θe cos φe sin θa cos φa sin θe sin φe) (11) Since ω is the same for any precession angle (which can be easily verified by calculating (11) for different values of φa), φa can be assumed to be 0, and (11) is reduced to
ω ) arccos(-sin θa cos δ sin (θa + ψ) sin δ) (12) 3. Model Calculations To study the potential accuracy of the orientation parameters determination via VAATIRF, we applied first a computer model of the measuring technique. The “measured” fluorescence intensities were calculated according to formulas 7 for a particular experimental setup and several sets of the dipole orientation parameters. The experimental setup determines the evanescent field intensities and the coefficients Apary, Aparx, and Aperz, which give the reflection from the substrate. The acquisition angles used were 0°, 20°, 40°, 60°, and 80°. Then a series of 30 random values were added to the intensities to simulate some experimental noise. These values were uniformly distributed in the range of (5% of the corresponding intensity, so that 30 different sets of the “measured” intensities with 5% error were generated. These sets were used as input for the inverse task of the orientation parameters determination by means of fitting. The initial values of the orientation parameters were also randomly distributed in some interval about the exact (given) values to eliminate the possible influence of the starting point position on the results of the minimization procedure. To compare the potential of the VAATIRF with that of the traditional measurement at the normal angle only, each set of the generated intensities was treated twice: once with the use of all five observation angles and once with the data corresponding only to the normal observation angle. To evaluate the technique over a range of the parameters, we used three tilt angles, 20°, 50°, and 70°, and two distribution dispersions, 10° and 30°. The results of the calculations are shown in Figures 2 (σ ) 10°) and 3 (σ ) 30°). The scattering of the found tilt and distribution dispersion is much less for the five-angle acquisition over the whole range of the given parameters. The only exception is the case of θm ) 70°, σ ) 30°, where the tilt angle determination shows somewhat higher uncertainty for the five-angle acquisition; however, the dispersion uncertainty remains higher for the normal acquisition. The accuracy of the solution found depends on the quality of the system of equations, which defines the target function. The task of finding a satisfactory fit is particularly difficult in the case of poorly determined system of equations, resulting in a shallow, extremely broad minimum in particular directions in parameter space. To investigate the resolving power of the mean tilt angle via VAATIRF and traditional TIRF measurements, we calculated the profiles of the corresponding target functions for the case of θm ) 50°, σ ) 30°. The profiles are shown in Figure 4 by the lines of equal height. Solid and dashed lines correspond to the five angles and normal acquisition, respectively. One can see that in the case of five-angle acquisition the target function minimum is well-defined in θm, σ space, whereas for the normal acquisition the minimum has a shape of narrow but almost flat extended valley in one direction. Such a maximum makes it very hard, if not impossible, to resolve the mean tilt angle and the dispersion via traditional TIRF. The resulting parameters should be scattered along the valley center line,
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Figure 2. Scattering of the solutions for the mean tilt angle θm and distribution dispersion σ for normal acquisition and acquisition at five angles: β ) 0°, 20°, 40°, 60°, and 80°. Model calculations. Exact minima correspond to σ ) 10° and θm ) 20°, 50°, and 70°.
Tronin and Blasie
Figure 5. Dependence of found minima for the mean tilt angle θm and distribution dispersion σ for normal acquisition and acquisition at five angles on the starting point. Model calculations. In the figure legend, the first and second numbers indicate initial values of θm and σ; the third number shows the number of acquisition angle used. Table 1 initial normal angle 5 angles
Figure 3. Scattering of the solutions for the mean tilt angle θm and distribution dispersion σ for normal acquisition and acquisition at five angles: β ) 0°, 20°, 40°, 60°, and 80°. Model calculations. Exact minima correspond to σ ) 30° and θm ) 20°, 50°, and 70°.
Figure 4. Profiles of the target function shown by the lines of equal height. Model calculations. Exact minima correspond to θm ) 50° and σ ) 30°. Solid lines, five-angle acquisition; dashed lines, normal acquisition.
and the minimum position found should depend on the starting point. To demonstrate this, we applied the minimization procedure using the set of the intensities generated for θm ) 50°, σ ) 30°. The search procedure started from four points, namely (θm ) 40°, σ ) 20°), (θm ) 40°, σ ) 40°), (θm ) 60°, σ ) 20°), and (θm ) 60°,
tilt dispersion tilt dispersion tilt dispersion
40 20 44.94 35.39 50.24 29.98
40 40 40.14 40.48 50.23 29.96
60 20 58.10 13.52 50.18 30.19
60 40 52.25 27.38 50.14 30.19
σ ) 40°). The results are shown in Figure 5; the corresponding statistics is given in Table 1. One can see that the results for the five-angle acquisition do not depend on the starting point, whereas in the case of the normal acquisition the results are strongly biased. For the starting points, which are close to the valley center line ((θm ) 60°, σ ) 20°) and (θm ) 40°, σ ) 40°)), the minimization procedure barely moved the returned (θm, σ) point toward exact minimum. 4. Langmuir-Blodgett Film To test the VAATIRF in a real experiment, we used a Langmuir-Blodgett film of arachidic acid (AA) doped with the fluorescent amphiphile 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine perchlorate (DiI). The structure of the DiI is shown in Figure 6. This probe has been used in fluorescence polarization studies of the rotational mobility of Langmuir-Blodgett monolayer associated antibodies and lipids11 and lipid orientation in the red cell membrane.12 The same system of AA + DiI has been used to test the potential of the orientation distribution determination by planar waveguide linear dichroism and fluorescence anisotropy measurements.4 The transition dipole responsible for the absorbance in the 500-550 nm wavelength range is oriented along the long axis of the carbocyanine headgroup (Figure 6), approximately perpendicular to the alkyl chains. As reported in ref 4, the linear dichroism measurements showed that the tilt angle of the dipole in the Langmuir-Blodgett monolayer is about 75°, which agrees qualitatively with the physical-chemical expectation for the orientation of the DiI molecule in the film. The films were composed of four monolayers: a bilayer of pure cadmium arachidate (CdA) followed by bilayer of AA doped with DiI in molar proportion of 1:200. This small ratio was used to prevent energy transfer between the fluorophores. The undoped system prepared otherwise (11) Timbs, M. M.; Thompson, N. L. Biophys. J. 1990, 58, 413. (12) Axelrod, D. Biophys. J. 1979, 26, 557.
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Figure 6. Chemical structure of the DiI molecule.
Figure 7. Experimental setup. See text for details.
identically was used for background scattering measurements. The Langmuir-Blodgett film deposition was performed as described in ref 4, except that we used a hydrophobic substrate for the monolayer deposition. The fused silica slides (Dynasil, Berlin, NJ) were silanized by octadecyltrichlorosylane according to a procedure described in ref 13. The Langmuir trough was a Lauda trough with a home-built dipping mechanism.
prism face was 16°, which produced the angle of total internal reflection in the substrate of 81.8°.
5. Experimental Setup
6. Measurement of the Angle between the Excitation and Emission Dipoles The angle between the excitation and emission dipoles DiI was measured by the fluorescence anisotropy technique.14 A Hitachi F-2000 fluorimeter with Glan-Thompson polarizers in the excitation and emission paths was used. Polarization-dependent sensitivity of the detection was corrected by measuring the fluorescence with the horizontal excitation (notation as in ref 14). DiI was first dissolved in DMSO to the concentration of 0.25 mM; this solution was added to glycerol to obtain the final concentration of 300 nM of DiI in glycerol. The samples were cooled to -20 °C. The excitation was at 514 nm, and the emission was measured at 585 nm. The fluorescence anisotropy was measured to be 0.187, which gives the angle between the dipoles R ) 36°.
The experimental setup is shown in Figure 7. The light beam with λ ) 514 nm from an Ar laser was directed to the axis of a two-circle Huber rotation stage. The sample holder was mounted on the inner rotation axes, and the detector rail was mounted on the outer circle. Rotation of the detector rail made it possible to change the acquisition angle. In the experiment we used the same five acquisition angles as for the model calculations. The laser output power was 10 mW. Before striking the coupling prism, the beam passed through a cylindrical expander, a quarterwave compensator (Melles-Griot), and a Glan-Thompson polarizing prism (Melles-Griot). The expander was used to increase the beam cross section in vertical direction so that the beam footprint on the acquisition area was almost 1 × 1 cm2 square. Such a big area was needed to increase the overall fluorescence output signal. The compensator was used to produce circularly polarized light before the linear polarizer, so that ATE ) ATM in the beam incident on the air-prism interface. The detection path contained a cutoff filter, a dichroic sheet polarizer, and the detector. The wavelength cutoff was 550 nm (Melles-Griot). Excitation and emission polarizers were aligned by zeroing the beam passing through them. For this purpose the detector stage was rotated 90°, and the sample holder was removed so that the detector saw the direct laser beam. Accuracy of the crossed polarizers position was better that 15′, and accuracy of the absolute polarizer angle reading was better that 30′. Fluorescence was observed with a CCD camera (TE/CCD-512-TK by Princeton Instruments) through a F ) 28 mm lens (Nikon). The collection angle was less than 5°. The camera was cooled to -50 °C. A CCD has an advantage of actually imaging the illuminated spot, making it possible to cut off the stray light, significantly reducing the background. This feature is of great help in view of the very weak fluorescent signals from the single monolayer specimens. The beam was directed into the fused silica substrate with the help of a right angle SF-4 coupling prism (Karl Lambert). To enhance optical contact, a refractive index matching liquid (Cargille Laboratories) was used. The incidence angle on the
The dependence of the measured and calculated fluorescence intensities on the acquisition angle β is shown in Figure 8. One can see good agreement between the experimental and calculated intensities. The calculated intensities correspond to orientation parameters θm ) 75.7°, σ ) 0.1°, δ ) 33°, and ψ ) 19.2°. To investigate how the errors in the measured intensities affect the accuracy of the determination of the orientation angles, an error propagation procedure should be applied. However, standard procedures do not work well in this case because system (7) is substantially nonlinear relative to θm and σ. As a result of this nonlinearity, θm and σ are highly coupled and their errors are interrelated. To circumvent this problem, we analyze the shape of the target function. This function is by definition the sum of the squared discrepancies between measured and calculated intensities. This means that all values of the orientation angles, which produce discrepancies lower than experimental errors, are experimentally undistinguishable. The loci of θm and σ which satisfy this condition are enclosed by intersection of the target function with the plane:
(13) Xu, S.; Fischetti, R. F.; Blasie, J. K.; Peticolas, L. J.; Bean, J. C. J. Phys. Chem. 1993, 97, 1961.
(14) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983; Chapter 4.
7. Results and Discussion
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Figure 8. Dependence of the fluorescence intensity from a LB film of arachidic acid doped with DiI. Experimental errors are 5%. IPTE ) diamonds, ISTE ) triangles, IPTM ) circles, ISTM ) squares. Lines ) calculation for the orientation parameters corresponding to the best fit.
Figure 9. Uncertainty of the θm, σ determination for LB film of arachidic acid doped with DiI. Solid lines: five-angle acquisition; dashed lines: normal acquisition. Thick lines correspond to the error level of 5%; thin lines: error level 1%. For five-angle acquisition the regions of possible θm, σ values are enclosed by the corresponding curves and the line σ ) 0°, whereas for the normal acquisition the regions are enclosed by the dashed curves and the lines σ ) 0° and θm ) 90°. Uncertainty is due to errors in the measurement of the fluorescence intensities.
Z)
∑i (Err2STE + Err2STM + Err2PTE + Err2PTM)
(13)
where the summation is carried over the acquisition angles used. The borders of the allowed region of θm and σ are shown in Figure 9. The solid and dashed curves correspond to the five-angle and normal acquisition, respectively. Thick lines correspond to the error level of 5%, which is the real experimental accuracy. The thin lines correspond to the level of 1%, which seems achievable with further improvement of the experimental conditions. As can be seen from the figure, the resolution of the technique with five-angle acquisition is much higher than for the normal acquisition. For the first, the errors for both mean tilt and dispersion are less than (5°, whereas for the latter the tilt can vary from 72° to 90° degrees and the dispersion from 0° to 32°. Also, for the normal acquisition the coupling between θm and σ causes distinct shift of possible θm toward 90° with the increase of σ. In the case of the normal
Figure 10. Uncertainty of the θm, δ determination for LB film of arachidic acid doped with DiI. Solid lines: five-angle acquisition; dashed lines: normal acquisition. Thick lines correspond to the error level of 5%; thin lines: error level 1%.
Figure 11. Uncertainty of the θm, ψ determination for LB film of arachidic acid doped with DiI. Solid lines: five-angle acquisition; dashed lines: normal acquisition. Thick lines correspond to the error level of 5%; thin lines: error level 1%. In the case of normal acquisition the parameter ψ cannot be determined, corresponding regions are the strips parallel to the ψ axis.
acquisition even 5-fold reduction of the errors does not improve the resolution; the range of the parameters decreases only slightly, being 75° < θm < 90° and 0° < σ < 27°, whereas for the five-angle acquisition the errors decrease by the factor of 2 for θm and 1.5 for σ. Strong coupling of θm and σ in the case of normal acquisition remains for the 1% errors. To demonstrate the resolution of the VAATIRF with regard to the angles δ and ψ, let us consider the sections of the target function in the θm-δ and θm-ψ planes. The corresponding regions of the allowed parameters values are shown in Figures 10 and 11. As in Figure 9, the thick and thin lines correspond to the error level of 5% and 1%; solid and dashed lines show the cases of five-angle and normal acquisition, respectively. Again, one can see that the resolution is much higher for the five-angle acquisition. Moreover, normal acquisition is not sensitive to the angle ψ at all, which is demonstrated by the fact that the delimiting lines are parallel to the ψ axis. Analysis of the target function (13) shows that there are two equal minima corresponding to the same set of θm, σ, and δ and two different values of ψ, which in our case were determined to be 10.1° and 19.2°. Parameter δ was determined to be 33°. Substituting θm ) 75.7°, δ ) 33°, and ψ ) 19.2° or ψ ) 10.1° into eq 10, we get for R the values of 37.9° and
Orientation Distribution Studies of Ultrathin Films
34°, respectively. Both values agree reasonably well with the result of the direct measurement via fluorescence anisotropy, which gives the value of 36° for R. The knowledge of the absorbing and emitting dipole orientation may be useful to get more insight into the conformation of the DiI molecule in the LB film. It is conceivable that both dipoles lie in the plane of the indole group. Substituting again the found values for the θm, δ, and ψ into (12), we get ω ) 58.4° for ψ ) 10.1° and ω ) 58.35° for ψ ) 19.2°. Surprisingly, the ambiguity of ψ causes only very small uncertainty in ω. The measured mean tilt angle is in very good agreement with our general understanding of the system used in this study. It also agrees with the experimental data obtained in ref 4. Linear dichroism measurement of the LB film of AA + DiI gave the value of 75° for the tilt angle. The fluorescence measurements show very good orientation of the fluorophores within the LB films. As one can see from Figure 9, the allowed values for the distribution width are in the range of 0 < σ < 10°. A similar result (12°) has been obtained by the combination of the linear dichroism and TIRF measurement.4 Summarizing, we can say that acquiring of the angular dependence of the fluorescence leads to a drastic improvement of the polarized fluorescence technique. Ac-
Langmuir, Vol. 17, No. 12, 2001 3703
curacy of the determination of the orientation distribution is much higher for VAATIRF than for the conventional TIRF. Even with a rather high level of the intensity error of 5%, VAATIRF makes it possible to resolve the mean tilt angle and distribution width, whereas for the normal acquisition these parameters remain highly coupled even at much lower error levels. Computer modeling shows that the gain in resolution is essentially the same over a very broad range of the orientation parameters. Utilization of VAATIRF also eliminates the dependence of the results on the starting point for the minimization procedure. This feature may be helpful when a priori information on the film structure is either not available or not sufficiently accurate. VAATIRF makes it possible to determine not only the orientation of the absorbing dipole but also that of the emitting one. This feature may provide some additional information on the structure of the fluorophore. Acknowledgment. This work was supported by the NIH GM 33525 and the NSF/MRSEC DMR96-32598 grants. We are thankful to Prof. S. Scott Saavedra, whose works inspired us to undertake this study and whose advice has been very helpful. LA001689O
