1260
Langmuir 1990,6, 1260-1265
Measurement of Absolute Particle-Surface Separation Using Total Internal Reflection Microscopy and Radiation Pressure Forces M. A. Brown* and E. J. Staples Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW, England Received September 1 , 1989. Zn Final Form: February 12, 1990 We have previously show how total internal reflection microscopy and radiation pressure forces can be used to study weak interactions between particles and surfaces. The work described here illustrates how we have improved the experiment and extended the technique to measure absolute particle-surface separations as a function of NaCl electrolyte concentration. In so doing, we have shown how the dynamics of particles moving orthogonal to a plane surface can be studied.
Introduction In a previous publication, we described an apparatus for the manipulation, by radiation pressure forces, of a single colloid particle immersed in water and close to a flat surface.’ The particle movement was monitored by total internal reflection microscopy (TIRM). The preliminary results illustrated the usefulness of the technique for studying t h e weak interactions between a 10-pm polystyrene latex particle and a quartz plate. They confirmed that the interaction potential energy curve as a function of the relative separation between the particle and the plate could be obtained. The work reported here describes how we have extended the technique to allow measurement of the absolute separation of a particle from a surface. The analysis of the hydrodynamics of a spherical particle moving orthogonal to a plane surface indicates that the fractional force, as predicted by the Stokes equation, is modified by a factor that varies monotonically with the separation. By monitoring the transient evanescent scattering of a particle subject to an instantaneous change in radiation pressure force, the time dependence of the particle position and hence the particle velocity as a function of relative separation can be evaluated. Where inertial effects are negligible, the particle velocity results from the sum of the time-independent particle-plate interaction force and the separation-dependentfrictional force. Hence the absolute separation of the particle from the plate surface can be obtained. Characterization of the Interaction Forces. In the experiment described here, we consider a particle moving close to a surface subject to the following influences: (1) gravity, (2) “double-layer” electrostatic interactions, (3) van der Waals attraction, (4) radiation pressure forces, and (5) hydrodynamicfrictional forces. As discussed previously, the probability p(h) of a particle being at a separation h from a surface can be related to the total interaction potential x(h) between the particle and the surface via the Boltzmann expression p ( h ) a exp(-x(h)/kl? (1) where x(h) obviously has contributions from terms 1-4 listed above. (1) Brown, M. A.; Smith, A. L.; Staples, E. J. Langmuir 1989,51319.
0743-7463/90/2406-1260$02.50/0
Normalization with respect to a reference potential any arbitrary separation REF gives
X ( ~ Z . R E Fat)
x ( h ) - X(hREF) = kT [P(hREF)/P(h)] (2) It is possible to obtain estimates of p ( h ) by monitoring the particle’s evanescent wave scattering intensity if this scattering intensity is a known (monotonic) function of particle position. Given that the probability P(l)dZ of the evanescent scattering lying within the intensity Z to Z + dl is equal to the probability p(h)dh that the particle will be found between h and h + dh of the plate surface, then (3) Where the evanescent wave scattering intensity varies exponentially with distance,2 then h - hREF = 6 / 2 In [z(hREF)/z(h)l (4) 6, the penetration depth of the evanescent wave at the interface, is given by3
6 = ~ , , / [ 2 a ( nsin2 , ~ ei - n;)’/*]
(5)
where A0 is the wavelength of light in a vacuum, n is the refractive index, and Bi is the angle of incidence a t the interface. The subscripts 1and 2 refer to the medium on the incident side and opposite side of the interface, respectively. Our results indicate that the evanescentwave scattering intensity does not vary exponentially as the separation between particle and surface approaches zero. However, this can be allowed for, and an absolute peiclesurface separation obtained as will be discussed. Assuming the evanescent wave scattering intensity is locally exponential for a given radiation pressure force, the potential energy experienced by the particle as a function of relative separation from any arbitrary origin can be readily obtained. The absolute value of the potential energy cannot be established, as the distance from the surface is unknown. A series of overlapping potential energy curves, obtained by incrementally increasing the radiation pressure force, can be normalized to a selected radiation pressure force to produce a composite (convolved) potential energy profile with extended dynamic range. This (2) Chew, H.; Wang,D.-S., Kerker, M. Appl. Opt. 1979,18, 2679. (3) Klein, M. V. Optics; Wiley: New York, 1970.
0 1990 American Chemical Society
Measurement of Absolute Particle-Surface Separation
least-squares convolution procedure has previously been described.’ T h e convolved potential can then be differentiated to obtain the force between the particle and the surface as a function of relative separation. The same result can be obtained by differentiating each overlapping potential energy curve to obtain separate forceseparation curves and then convolving them together to produce a continuous forceseparation curve between the two limiting radiation pressure forces. In order to measure the absolute particle-plate separation, the particle must be subjected to an additional force which varies with this separation in a well-defined manner. We can take advantage of the fact that the hydrodynamic frictional force experienced by a spherical particle moving orthogonal t o a surface varies monotonicallywith separation. If the particle is subjected to an instantaneous change in radiation pressure force, then from the time-averaged transient response of the particle, as it attains its new equilibrium position, its velocity can be obtained. From time averaging of the transient response, the contribution from any stochastic processes will be minimized. In the absence of inertial effects, which would result from the presence of both convective and local acceleration terms to the fluid motion, the fluid motion satisfies the quasistatic Stokes equations. Under these circumstances, we can assume that the particle velocity results from the sum of the known particle-surface interaction force and the frictional force term. Cox and Brenner4 have developed approximate expressions for the frictional force F’ on a sphere moving perpendicular to a solid plane wall bounding a semiinfinite viscous fluid. Consider a spherical particle, radius b, with its center a distance d away from a plane surface. The separation of the particle from the surface can be defined as h = d - b, and we define the dimensionless gap width c = h / b . In the limit of Stokes flow (Reynolds number = 01, Cox and Brenner have shown that the hydrodynamic frictional force F’ in the limit of small dimensionless gap width t is approximately given by
F’ where /3 = 1 / c
-
67rqbup
+ 1/5 In l / t + 0.971 264
(6)
(7)
q is the viscosity of the fluid and u is the particle velocity.
The /3 parameter can therefore be evaluated by comparison of the measured velocity with that derived assuming the particle motion arises from the measured particlesurface interaction force and the unmodified Stokes law expression. From a definition of 0, for a particle of known radius, the absolute particle-surface separation can be determined. As before, the system studied experimentally was that of a polystyrene latex particle, immersed in water or electrolyte solution, interacting with a quartz plate. The large, monodisperse polystyrene particles as supplied by Dynospheres Inc. were quoted to have a diameter of 10.2 f 0.01 pm. Experimental Section The experimental setup has already been described in some detail.’ However, a few additions and improvements to the apparatus have been made. The output radiations of both the Ar+ and He/Ne lasers were continually monitored for the duration of any experiment. The long-term stability of the He/Ne laser, which is crucial to the success of the experiment, has been considerably improved by power stabilization using an acousto(4) Cox, R. G.;Brenner, H.Chem. Eng. Sci. 1967,22, 1753.
Langmuir, Vol. 6, No. 7, 1990 1261 optic modulator (Liconix Model 50 SA). In addition, the initial vertical polarization of the Ar+ laser radiation was improved by mounting a quartz polarization beam splitter in front of the laser output. The polarization rotator (Soleil-Babinet compensator) was then mounted subsequent to this. The angle of incidence a t the quartz-water interface has been adjusted from that quoted previously and was typically 75.9’, implying a “skin depth“ 6 of 214.7 nm. T o record an evanescent wave-scattering distribution (TIRM spectrum), at a given radiation pressure force, the necessary data were collected as has been described previously. The capturing of the transient response (the temporal change of the evanescent wave scattering intensity) of the particle subject to an instantaneous change in radiation pressure force was recorded as follows. The Ar+ laser was modulated between the two limiting radiation pressure forces and the optics configured so that the particle was pushed toward the surface on switching to the higher radiation pressure force. The modulation rate was a maximum of 2 Hz so as to allow sufficient time for the particle to move between the two limiting equilibrium positions as the laser was modulated. The laser power was controlled via its plasma tube current, and thus on modulation the requisite “instantaneous” power charge occurred over a 3-me period. The transient response of the particle, as the laser was modulated, was sent to an AND Model AD 3521 FFT spectrum analyzer. The transient signal was digitized in 2048 channels a t a 2-kHz sampling rate with 15bit resolution. The low duty cycle of the laser modulation has important consequences if low statistical errors a t each point on the transient profile are to be attained. If the signal is averaged a large number of times, this could mask any significant drift with time in the particle-surface separation. In an attempt to negate this, we averaged the signal for only 512 times, stored this data, and then made a comparison with subsequent averaged transients to check the reproducibility. Generally, consistency was obtained, and if necessary an average over all the separately acquired transients was found. A typical experiment would proceed as follows. A polystyrene particle would be selected and “trapped” close to the quartz surface and the surrounding water (double distilled and filtered, 0.22-pm pore size) exchanged until the particle’s TIRM spectrum remained invariant with time, within statistical errors. Once this was achieved, the Ar+ laser was modulated between 4 and 40 mW (unfocused powers) and the required transient response of the particle averaged. A constant fraction of the actual laser intensity, that which was reflected from the polarizing beam splitter, was measured by a photomultiplier tube. This signal was used not only as a monitor of the laser output power but also to trigger data collection on the spectrum analyzer. Once a consistent set of transients was obtained, the collection of the equilibrium evanescent wave scattering data required for the TIRM was commenced. The scattering distributions were recorded for 300 s a t a given laser power, from the lower limit selected for the transient experiments t o t h e upper limit in 12-mW increments. It was then decreased to the lower limit again to check the reproducibility. At no time was hysteresis observed, though occasionally contamination of the particle under interrogation, usually from much smaller particles, meant the experiment had to be aborted. This procedure was then repeated for a series of 1 x 10-5,l X 10-4, and 1 x 10-3 mol dm-3 NaCl concentrations in water. Typically for concentations greater than 1 X 10-2 mol dm-3 NaCl, radiation pressure forces were unable to significantly move the particle, and thus only results for the concentration range up to 1 X 10-3 mol dm-3 NaCl are discussed. Prior to any data collection, the background “flare” contribution to the signal was estimated by translating the particle just out of the viewing region, and the “flare” intensity was measured separately on the A/D converter in the HP 9826 computer and t h a t in the spectrum analyzer. T h e scattering data recorded in respectively in each were then corrected accordingly.
Results and Discussion Figure l a shows the evanescent wave scattering distributions (TIRM spectra) for a polystyrene particle,
Brawn and Staples
1262 Langmuir, Val. 6, No. 7, 1990 1 0 ~ 4 :
( a )
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i
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Figure 1. (a, Top) Evanescent wave scattering distributions from a 10.2-pm-diameterpolystyrene particle immersed in water interacting with a quartz plate. Scattering distributions were recorded at the Ar+ laser powers indicated. (b,Bottom)Potential energy as a function of theoretical separation (i.e.,distance from an arbitrary origin) obtained from the corresponding data in Figure la. The different Ar+ laser powers are as indicated.
immersed in water, interacting with a quartz surface at different (unfocused) radiation pressure powers as shown. The quality of our data is much improved from that published previously. These spectra can be readily converted into potential energy as a function of “theoretical” separation by using eqs 1-5 (see Figure lb). For the purpose of calculation, the evanescent wave scattering intensity of the particle at zero separation from the surface was assumed to be a large and experimentally unattainable intensity. The “theoretical” separation can be regarded then as the distance of the particle from an arbitrary origin. The force experiencedby the particle can be readily obtained from the gradient of the potential energy curve. Figure 2a shows the net attractive force, as a function of theoretical separation, experienced by the particle at the four respective radiation pressure powers. It can be seen from Figure 2a (i.e., from the markers i, ii, and iii) that an increase in laser power of 12 mW causes the particle to experience an additional force of -11 x 10-13 N. It was not possible to obtain adequate statistics for the particle’s motion, in the absence of radiation pressure, due to diffusion of the particle out of the detection region. We have therefore not been able to identify the associated equilibrium relative separation or confirm that at the largest separations (where the colloidal forces present tend to zero) the measured force experienced by the particle correspondsto the relative weight of the particle. However, in a separate experiment we established that a laser power of 3.0 mW was required to just support the particle against the force of gravity at separations from the plate where
i ..
0l 0
1 20
. 40
60
80
180
120
R E L R T I V E SEPRRRTION/nn
Figure 2. (a, Top) Net attractive force experienced by the polystyrene particle as a function of theoretical separation (i.e., distance from an arbitrary origin)and different Ar+ laser powers. The markers i, ii, and iii identify the force change that results from a laser power increment of 12 mW. (b, Bottom) Composite force-relative separation curve obtained from the data in Figure 2a. Separation is relative to the position of the particle at maximum Ar+ laser power, 40 mW.
colloidal contributions are negligible. Therefore, this laser power produces a radiation pessure force equivalent to that force due to the particle’s buoyancy force or relative weight (2.7 X 10-13 N). This, and the fact that from Figure 2a a consistent force change results from a given increment in laser power (see markers i, ii, and iii), indicates that over this range of absolute separations eq 4 adequately describes the relationship between scattered intensity and relative separation. In the absence of data collected a t zero radiation pressure, we can normalize the data collected at the various radiation prssures to any radiation pressure used and produce a compositeforce versus relative separation curve, Figure 2b. In the graph, the origin corresponds to the equilibrium position of the particle when exposed to 40 mW of “radiation pressure” power, and the point at largest relative separation corresponds to the equilibrium position of the particle when exposed to 4 mW of power. This composite curve can be approximated by simple vertical translation of the component curves of Figure 2a by the force associated with the appropriate laser power. An alternative method that results in reduced errors in obtaining this composite curve has been described previously.’ In summary then, the net force experienced by the particle between the two limiting radiation pressure powers has been obtained as a function of relative separation. Figure 3 shows the transient response (512 averages) of the particle subject to an instantaneous increase in radiation pressure force. The Ar+ laser was modulated
Langmuir, Vol. 6, No. 7, 1990 1263
Measurement of Absolute Particksurface Separation x 102
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between the two limiting (unfocused) radiation pressure powers of 4 and 40 mW. The particle's velocity as a function of the theoretical separation from the surface can be evaluated by taking the derivative of the separation with respect to time. Although the quality of the theoretical separation-time data is good, the velocities calculated are very sensitive to variations in the local gradient of the separation-time data. T o alleviate this, a five-point smoothing of the required velocity-separation data was carried out. The result is shown in Figure 4. One would expect the particle to reach its maximum velocity instantaneously for an infinitely fast increase in laser power. However, modulating our Ar+ laser via the plasma tube introduces a 3-ms rise time between the requisite power levels. This may in part explain the finite separation covered before maximum velocity is reached. In addition, the initial rise of the signal may be too high to be properly digitized by the FFT analyzer at the sampling rate required to capture the remainder of the transient signal. We cannot, of course, eliminate the possibility of inertial effects during the initial stages of the transient. In future experiments, we intend to modulate the Ar+ laser radiation externally with an electro-optic modulator, which will allow a much faster switching between power levels, and we hope to obtain a clearer understanding of the initial stages of the transient. From the data in Figure 2b, the velocity u of the particle can, in the absence of inertial effects and Brownian perturbation, be derived by using the Stokes law
10.5 X I 0 2
RBSOLUTE 9.5 SEPRRATION/nrr 10
Figure 5. Curve a shows the velocity of the particle as a function of absolute separation using the Cox and Brenner expression,eq 6. It is displayed as a fit to the experimental data of Figure 4, which are plotted in curve b. The particle-plate separation at maximum Ar+ laser power (40 mW) is 930 nm.
expression. By suitable selection of the P parameter, which corrects for the hydrodynamic interaction between the particle and the plate, these predicted velocities can be matched to the velocities as shown in Figure 4 that are derived from the transient response of the particle. The resultant fitting, assuming the actual particle diameter to be 10.2 pM, is shown in Figure 5 . The absolute separation of the particle from the surface can be measured with a precision better than the likely aspherities on both the quartz and polystyrene particle surfaces. In order to study the effect of added electrolyte on the system, the above series of measurements were repeated at 1 X 1 X 104, and 1 X 10-3 mol dms NaCl. With increasing electrolyte concentration, an increase in evanescent wave scattering intensity was observed, clearly indicating a decrease in particle-plate separation. This decrease in separation is of course expected through Debye screening of the doublelayer repulsion between the particle and the plate. Chew et a1.2 have obtained numerical solutions for the intensity of light scattered by a dielectric sphere placed in an evanescent wave. They assume that the boundary conditions at the interfaces are identical with those found for the isolated surfaces, and they suggest that the exponential dependence of the scattering intensity with separation will hold only a t large separations. The experimental work of Prieve et al.5 does, however, suggest that an exponential variation of scattering intensities with distance may well be preserved down to small separations. In contradiction, our results suggest that the expected exponential behavior is not observed as the particlesurface separation becomes small. For each electrolyte concentration, a series of TIRM spectra were recorded at Ar+ laser powers of 4,16,28, and 40 mW, respectively. Figure 6 shows the TIRM spectra recorded in the solutions indicated at an Ar+ laser power of 4 mW. The expected increase in scattering intensity with electrolyte concentration is clearly seen. For a given electrolyte concentration, the T m M spectra at the different radiation pressure powers can be treated similarly to that done previously for the case of H20. It was assumed that locally the particle's evanescent wave scattering intensity is approximated by the exponential dependence with separation from the plate as suggested by eq 4. However, the decay constant may vary at the closer approaches made possible at higher electrolyte concentrations; Le., much ( 5 ) Prieve, D. C.; Luo, F.; Lanni, F. Faraday Discuss. Chem. SOC.1987, 83,297.
1264 Langmuir, Vol. 6, No. 7, 1990
Brown and Staples SEPRRRTION RT 40mW.7EQnm
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Figure 7. Composite force-relative separation curves for HzO, 1 X 10-6 M, 1 X 10-4 M, and 1 X 10-3 M NaCl solutions. The separation is relative to the position of the particle at maximum Ar+ laser power, 40 mW. c
larger changes may occur than expected from the trivial change in refractive index of the solutions used in this work. The resulting plots of force versus relative separation including that for H20 are shown in Figure 7. If locally the decay constant 612 (eq 4)is valid, then the measured dynamic range of the calculated radiation pressure force that results from changing the laser power from 4 to 40 mW will coincide with that obtained at large separations (e.g.: HzO). The apparent increase in the radiation pressure forces experienced by the particle at higher electrolyte concentration is clearly indicative of a change in the decay constant 612 with separation; i.e., the particle's evanescent wave scattering is not varying exponentially with separation. The deviations from the predicted exponential relationship are locally small, and thus we merely have to adjust the local distance scale (via a change in decay constant 612) such that the force dynamic range associated with the change in laser power is consistent with that obtained in HzO. Obviously, the distance scale in the transient response data must be similarly treated. Once this has been done, the calculation of the absolute particleplate separation can be performed as has been discussed. Parts a, b, and c of Figure 8 show the fits obtained for 1 X 1X a n d 1 X 10-3 mol dm-3 NaCl concentrations and clearly validate the approach we have adopted. In Figure 9, we have plotted, for all the solutions used, the measured evanescent wave scattering intensity, a t 40mW radiation pressure power, as a function of t h e determined absolute particle-plate separation.
.
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Figure 8. (a, Top) Curve a is a fit obtained by using the Cox and Brenner expression, eq 6, to the experimental data plotted in curve b for the particle immersed in 1X 10-6M NaCl solution. The particle-plate separation at maximum Ar+ laser power (40 mW) is 780 nm. (b, Middle) Curve a is a fit obtained by using the Cox and Brenner expression, eq 6, to the experimental data in curve b for the particle immersed in 1 x 10-4M NaCl solution. The particle-plate separation at maximum Ar+ laser power (40 mW) is 470 nm. (c, Bottom) Curve a is a fit obtained by using the Cox and Brenner expression, eq 6, to the experimental data in curve b for the particle immersed in 1X 10-3 M NaCl solution. The particle-plate separation at maximum Ar+ laser power (40 mW) is 190 nm.
Conclusions We have shown t h a t our approach allows t h e measurement of an absolute particle-plate separation. Although the particle's evanescent wave scattering intensity theoretically should (at least a t large separations) vary exponentially with separation from the surface,we observed a marked deviation from this as the separation is decreased. This may be due to multiple evanescent wave scattering. We cannot rule out the contribution from this due to ret-
Langmuir 1990, 6, 1265-1269
-
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function of absolute separation. roreflection from both the spectrophotometer cell and coupling prism, though we suspect that these effects are
1265
small. The work described here is, of course, the first experiment that characterizes the distance scales over which the scattering from a particle near a flat surface in an evanescent wave deviates from t h a t predicted theoretically. It is our intention in future work to modulate the Ar+ laser using an electro-optic modulator. This will allow us to accurately control both the modulation rate and depth of the Ar+ laser. It will also permit rapid modulation of the laser such that a t sufficiently high frequency the particle will adopt a mean separation between the two limiting separations defined by the radiation pressure force limits. The frictional force at this mean separation may be obtained from the transfer function.s Finally, we believe that modification of particlesurface interactions by adsorption of surfactants or polymers can be studied, and the direct measurement of subtle features such as depletion forces should be feasible. (6) Randall, R. B. Frequency Anulysk; Bruel and Kjaer:
N b ,1987.
Synthesis, Structure, and Excimer Formation of a Vesicular Assembly Carrying Chiral 9-Anthryl Chromophores Hiroki Sasaki,? Masahiko Sisido,*J and Yukio Imanishit Department of Polymer Chemistry and Research Center for Medical Polymers and Biomaterials, Kyoto University, Sakyo, Kyoto 606, Japan Received September 5,1989. In Final Form: February 7, 1990
A new chiral amphiphile carrying two octadecyl chains and a 9-anthryl group was synthesized from D-9anthrylalanine: (CH3)3N+(CH2)&ONHCH(CH2-9Ant)CON(Cl~3,)2. The amphiphile formed a vesicular assembly in aqueous dispersion, which shows a gel-liquid crystalline transition at 26.5 "C. Absorption and CD spectra indicated no strong ground-state interaction between the anthryl groups. Fluorescence spectra showed a strong excimer emission around 548 nm. The excimer to monomer emission intensity ratio increased monotonically with decreasing temperature. The excimer was found to form within ca. 1 ns after photoexcitation. The excimer emission showed a right-handed circular polarization, but the magnitude of the circular polarization was insensitive to the temperature. These results are consistent with an efficient energy migration along the two-dimensional array of anthryl chromophores followed by trapping into a relatively small number of excimer-forming sites.
The bilayer aggregates of chromophoric amphiphiles have been considered as an effective photon-harvesting system.' The two-dimensional (2-D) structure of the bilayer is suited to collect solar energy that is spread in space. For effective photon harvesting, the energy transfer or migration along the 2-D chromophoric assembly should be so efficient that the photon energy absorbed by one of the chromophores in the 2-D array could effectively be transferred to a photoreaction center. For efficient energy transfer or migration by a dipole-dipole mechanism, the
* Correspondence should be addressed to this author. Present address: Research Laboratory of Resources Utilization, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan. + Department of Polymer Chemistry. Research Center for Medical Polymers and Biomaterials. (1) For reviews, see: (a) Fendler, J. H. Membrane Mimetic Chemistry; Wiley: New York, 1982. (b) Calvin, M. Acc. Chem. Res. 1978,11, 369. (c) Matsuo, T. J. Photochem. 1982,31,788. (d) GrBtzel, M. Pure Appl.
*
Chem. 1982,54, 2369.
0743-7463190f 2406-l265$02.50/0
chromophores should have a strong transition dipole moment. In other words, they should show allowed fluorescence or absorption transition between the ground state (SO)and the lowest excited state (SI).In this sense, anthracene is one of the most favorable chromophores.For example, the critical distance ROfor the energy migration between the same kind of aromatic molecules is 8.25 A for 1-methylnaphthalene, 10.0 A for pyrene, and 22.0 A for 9-methylanthracene.2 The efficiency of a single-step energy transfer between a pair of chromophores separated by a distance R can be calculated by Ros/(Rs + R$). The efficiency between two 9-anthryl groups separated by 6 8, is 99.96%, whereas that of the 1-naphthyl groups is 87.1176. These values do not seem much different, but the probability for an excited state to survive after 50 consecutive steps of energy migration is (0.9996)60= 0.98 for the 9-anthryl group but 0.001 for the 1-naphthyl group. (2) Berlman, I. B. Energy Transfer Parameters of Aromatic Compounds; Academic Press: New York, 1973.
0 1990 American Chemical Society
