Dynamics of electronic energy transfer from the S₂ state of azulene to the S₂ state of zinc porphyrin

Abstract

Electronic energy transfer between the S₂ state of azulene as donor and the S₂ state of zinc porphyrin as acceptor in dichloromethane and CTAB micelles has been investigated. In dichloromethane high S₂–S₂ energy transfer efficiency, which cannot be explained using the Förster theory, is observed. An inhomogeneous distribution of acceptors surrounding the donor, leading to short-range exchange interaction and higher multipole interaction is proposed. In CTAB micelles, Förster's mechanism is found to agree well with the observed energy transfer efficiency when a surface-uniform distance distribution between donor and acceptor is assumed. The implications of S₂–S₂ energy transfer in our system for designing efficient molecular devices is discussed.

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Introduction

Azulene and porphyrin based systems have received much attention because of their unique photophysical properties. In contravention of Kasha's rule, azulene displays an intense fluorescence (S₂ → S₀) from a higher electronic state, while undergoing an ultrafast internal conversion from its S₁ to its S₀ states.¹ A negligibly small quantum yield of S₁ → S₀ fluorescence is thus observed. This anomalous behaviour has led to several studies devoted to the spectroscopic characterisation of azulene.^2,3 Recently, several azulenic derivatives were synthesised,⁴ and used to understand the colour properties of their bacteriorhodopsin analog.⁵ Porphyrin-based systems are commonly employed for gaining further insight into the efficient photon-harvesting and electron transfer dynamics of the photosynthetic apparatus.^6–9 In many diamagnetic metalloporphyrins (e.g. zinc tetraphenylporphyrin), weak S₂ → S₀ fluorescence is also known,^10,11 and has been correlated with the modest (ca. 1 eV) energy gap between their S₂ and S₁ electronic states.¹²

The investigation of electronic energy transfer (EET) from upper excited states (S_n, n > 1) is both important and challenging. In the light-harvesting complexes of photosynthetic systems, energy transfer from the initially excited S₂ state of carotenoids to chlorophylls is found to be important.¹³ Furthermore, molecules that exhibit S₂ fluorescence would be of particular significance in the design of molecular photonic switches and molecular logic gates.^14,15 Levine and co-workers have described the concept of using EET from the S₂ state of azulene to develop suitable logic gates and circuits.¹⁴ The full potential of such molecular devices is realised when the number of electronic states of the component molecule that can undergo photophysical reactions (e.g. energy transfer) is large. Therefore, EET involving both higher electronic states (e.g. S₂–S₂ EET) and S₁ states of the energy donor and acceptor chromophores is advantageous in this respect.

Previous studies of energy transfer involving high excited states have been mainly centered around EET from the donor S₂ state to the acceptor S₁ state.^16–23 There are only a few reports of S₂–S₂ energy transfer.^24–26 For example, Oster and Kallmann used X-rays to excite the S₂ state of benzene, and then examined the subsequent energy transfer to the S₂ state of phenylbiphenylyl oxadiazole.²⁴ Osuka et al. have synthesised a series of porphyrin dimers and trimers consisting of a zinc porphyrin donor and a zinc diphenylethynyl porphyrin acceptor.^25,26 In their systems, S₂–S₂ EET from donor to acceptor followed by back EET from the S₂ state of the acceptor to the S₁ state of the donor was reported.

In this paper, we examine the energy transfer dynamics from the S₂ state of azulene to the S₂ state of zinc porphyrins in dichloromethane and in aqueous CTAB micelles. Due to its relatively large S₂ fluorescence quantum yield and S₂ emission lifetime, azulene can act as an excellent S₂ energy donor. 1,3-difluoroazulene, with a significantly higher S₂ fluorescence quantum yield,⁴ is also used here as an energy donor. The choice of zinc porphyrin as an energy acceptor is driven by the fact that after the initial S₂–S₂ EET, subsequent back S₁–S₁ energy transfer is probable which results in a bidirectional and cyclic energy transfer process. This inadvertently has important implications in the design of efficient molecular devices as discussed by Levine and co-workers.¹⁴ To understand the S₂–S₂ energy transfer process occuring in dichloromethane and CTAB micelles, the EET efficiency was determined from the fluorescence quenching of azulene in the presence of zinc porphyrin under steady-state conditions.

Experimental section

Azulene (Az, Aldrich), zinc tetraphenylporphyrin (ZnTPP, Alfa Aesar), zinc tetra(4-sulfonatophenyl) porphyrin (ZnTPPS, Frontier Scientific Porphyrin Products), cetyltrimethylammonium bromide surfactant (CTAB, Aldrich), dichloromethane (CH₂Cl₂, Aldrich, spectroscopy grade), and ethanol (EM Science, spectroscopy grade) were used as received. 1,3-difluoroazulene (DFAz) was kindly supplied by Dr Alfred Asato (University of Hawaii).

Solutions of Az and DFAz with concentrations ca. 3.6 × 10⁻⁵ M were first prepared in CH₂Cl₂. Stock solutions of ZnTPP were then introduced into the Az/DFAz solutions using a microlitre syringe to achieve a quencher concentration between ca. 10⁻⁵ and 10⁻⁴ M. Dissolved air was removed by bubbling the samples with solvent-saturated Ar for 15 min before taking any measurements.

The micelle solutions were prepared by dissolving an appropriate amount of CTAB in Millipore-purified (Milli-Q) water such that the concentration of the surfactant was well above the critical micelle concentration (c.m.c.) of CTAB (c.m.c. = 9.2 × 10⁻⁴ M).²⁷ Az was dissolved in the CTAB micellar solution by stirring for about 24 h, and any undissolved Az was then removed by filtering the solution. The final concentration of solubilised Az was 2.8 × 10⁻⁵ M. Stock solutions of ZnTPPS were added into the micellised Az solutions via a microlitre syringe. In this way, the concentration of ZnTPPS was in the range of ca. 10⁻⁵ and 10⁻⁴ M. Finally, the sample solutions were allowed to stand for about 12 h. Since the oxygen concentration within a micelle is low,^27,28 effects of oxygen quenching on the relatively short-lived Az emission can be neglected. Fluorescence measurements were therefore performed in aerated micellar solutions. All samples, both in CH₂Cl₂ and CTAB solutions, were protected from room light at all times.

Absorption spectra were recorded with a Varian Cary 500 UV-Vis spectrometer, and corrected steady-state fluorescence measurements were recorded on a SPEX 212 spectrofluorometer. All measurements were conducted in 1 × 1 cm cuvettes at room temperature. The fluorescence of the donor molecule after excitation was observed at right angles to the incident light. At the donor excitation wavelength (λ_ex = 327 nm for Az and DFAz in CH₂Cl₂, and λ_ex = 325 nm for Az in CTAB solution), some of the incident light is absorbed by the quencher chromophore (i.e. ZnTPP and ZnTPPS). This results in an attenuation of the excitation beam reaching the donor molecules (primary inner filter effect).²⁹ Furthermore, ZnTPP and ZnTPPS can absorb a fraction of the emitted donor fluorescence at the observation wavelength (λ_em = 374 nm for Az and 380 nm for DFAz in CH₂Cl₂, and λ_em = 374 nm for Az in CTAB solution), causing a secondary inner filter effect.²⁹

Inner filter effects were corrected for by using a correction factor.^30–32

F_corr = 10^{(A_exl_ex+A_eml_em)} (1)

where A_ex and A_em are the optical density of the sample at the excitation and emission wavelengths, respectively, and l_ex and l_em are the distances between the point of observed emission inside the cell to the entry and exit cell walls, respectively. Kubista et al. have described a convenient method to obtain the value of l_ex.³⁰ Following their approach, a value of l_ex = 0.44 was determined for our experimental set-up. Taking l_ex = l_em, which is typical for most commercial spectrofluorometers, the fluorescence intensity corrected for inner filter effects is given by,

I_corr = I_expt10^{0.44(A_ex+A_em)} (2)

where I_expt is the measured experimental fluorescence intensity. For eqn. (2) to be valid, A_ex and A_em were maintained at values smaller than 2.^30,33

The quantum yield of Az in CTAB micelle, Φ^CTAB_Az, was determined using DFAz in degassed ethanol as a reference (Φ_ref = 0.197):⁴

where X is the area under the fluorescence spectrum, and A (=1 − 10^−A_ex) is the factor used to correct for different absorbances at the excitation wavelength used (325 nm). The refractive index of the CTAB micelle was assumed to be the average value of η_CTAB determined using pyrene, anthracene, and perylene as probe molecules (i.e.η_CTAB = 1.52).³⁴

Theory

Förster energy transfer

The most common mechanism of non-radiative singlet–singlet EET between two chromophores (D and A) is the Coulombic interaction described by Förster.³⁵ The rate constant of EET (k_eet) between D and A separated by a distance R is,^35,36where τ_D is the fluorescence lifetime of the donor D in the absence of the acceptor A, and R₀ is the critical distance between two molecules such that the EET probability equals the emission probability. For dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole interactions (in order of decreasing strength) the values of n equal 6, 8, and 10, respectively. Long-range EET is best modelled using a dipole–dipole interaction (i.e.n = 6), and the corresponding R₀ is defined by where Φ_D is the fluorescence quantum yield of D, N is Avogadro's number, η is the refractive index of the solvent, κ² is the orientation factor, and J(v̄) is the spectral overlap integral of the emission of D with the absorption of A.

The energy transfer efficiency, E, can be calculated from the emission intensity of D, in the absence (I₀), and presence (I_A) of A. Accounting for inner filter effects (eqn. (2)), such as radiative energy transfer, the experimental non-radiative EET efficiency is readily obtained from eqn. (6):³²

where I_A,corr = I_AF_corr.

The fluorescence decay of a donor surrounded by a homogeneous distribution of acceptor was also obtained by Förster:³⁷

I_A(s) = I_A(0)exp(−s − 2γs^1/2) (7)

where s = τ/τ_D, and γ = c_A/c₀. c_A is the acceptor concentration and c₀ is the critical concentration given by Consequently, the theoretical EET efficiency, E_F, is given by eqn. (9):³⁷where erf(γ) is the error function.

Gösele and Sipp–Voltz models

In a fluid medium of low solvent viscosity, the effects of translational diffusion on the donor fluorescence quenching may be significant.³⁸ Gösele et al.^39–41 took into account translational diffusion, and obtained an expression for the donor fluorescence decay as shown in eqn. (10):

I_A(s) = I_A(0) exp(−s − αs − 2γs^1/2) (10)

where α = 4πD̃r_Fn_Aτ_D, r_F ≈ 0.676(R⁶₀/τ_DD̃)^1/4 is an effective trapping radius, n_A is the acceptor number density and D̃ is the sum of the diffusion coefficients of D and A. By integrating eqn. (10) over time, the steady-state fluorescence intensity is given by I_A/I₀ = ∫^∞₀I_A(s)ds, and an exact expression for the theoretical EET efficiency is obtained,

Using the time-dependent Smoluchowski quenching rate constant, Sipp and Voltz⁴² derived a time-dependent donor fluorescence decay function given by eqn. (12):

I_A(s) = I_A(0)exp(−s − βs − 2δs^1/2) (12)

where β = 4πrD̃τ_Dn_A, δ = 4r²(πD̃)^1/2τ^1/2_Dn_A and r, the reaction length, provides useful information about the bimolecular quenching dynamics. An expression for r consisting of factors arising from diffusion, short-range energy transfer, and long-range energy transfer reactions shows that the common but ill-defined encounter distance (i.e.r = r_A + r_D, where r_A(D) is the radius of A(D)) underestimates the true short-range reaction length, r_e. In general, the long-range dipole–dipole reaction length, r_d, is given by⁴²and Γ(x) is the Gamma function. It is interesting to note that r_d and Gösele's effective trapping radius, r_F, are equivalent.

EET models in micelles

When D and A are separated by a distance R, the probability of finding at time t an excitation remaining on D averaged over the distance distribution (ω(R)) is^43,44

The distance distribution, ω(R), is defined as the probability of finding an acceptor at a distance between R and R + dR from the donor. For a spherical micelle with radius R_m, the most common distance distributions are:^45,46 (1) surface–surface distribution (i.e. both D and A are randomly distributed on the surface of the micelle, ω_ss(R) = R/2R²_m), (2) surface–uniform distribution (i.e. one of the chromophore is randomly distributed on the surface of the micelle, while the other is uniformly distributed within the micelle, ω_su(R) = 3R²(2R_m − R)/4R⁴_m), and (3) uniform–uniform distribution (i.e. both D and A are uniformly distributed within the micelle, ω_uu(R) = 3R²(2R_m − R)²(4R_m + R)/16R⁶_m). In all of the above cases, the limit of integration in eqn. (14) is from 0 to 2R_m.

When the probability of finding n̄ acceptors in a micelle follows a Poissonian distribution with mean occupation number μ, the average donor fluorescence decay is written as^45,46

where

Results and discussion

EET in dichloromethane

The steady-state absorption and emission spectra for Az, DFAz, and ZnTPP in CH₂Cl₂ are shown in Figs. 1 and 2. The absorption spectra for Az, and DFAz were not affected by the addition of the quencher ZnTPP, and new absorption or emission bands were not observed (figure not shown), strongly suggesting that no complexes between donor and acceptor were formed. Furthermore, no splitting or shifting of the absorption bands of ZnTPP were observed in CH₂Cl₂, in accordance with previous reports that self-aggregates of ZnTPP in non-aqueous solvents can be excluded at the concentrations used.⁴⁷ Self-aggregation of Az at low concentration is also not known to occur.⁴⁸

Fig. 1 The absorption and emission spectra for Az and ZnTPP in CH₂Cl₂. The absorbances are normalised to the maximum optical density. ZnTPP S₂ emission peak is amplified 30 times. abs is the absorption band, while em is the emission band.

Fig. 2 The absorption and emission spectra for DFAz and ZnTPP in CH₂Cl₂. The absorbances are normalised to the maximum optical density. abs is the absorption band, while em is the emission band.

Note, in Figs. 1 and 2, that there is a substantial amount of overlap between the S₂ emission spectrum of the donor (i.e. Az or DFAz), and the S₂ absorption spectrum of the acceptor ZnTPP. This indicates that efficient resonance energy transfer from the excited S₂ state of Az/DFAz to the S₂ state of ZnTPP is feasible. The spectral overlap integral values (J(v̄), see eqn. (5)), calculated using the PhotochemCAD software,⁴⁹ for Az-ZnTPP and DFAz-ZnTPP systems are 9.93 × 10⁻¹⁴ cm³ M⁻¹ and 1.21 × 10⁻¹³ cm³ M⁻¹, respectively. The molar absorption coefficients of ZnTPP in CH₂Cl₂ were taken from ref. 6. Given further that the quantum yields of Az and DFAz in CH₂Cl₂ are 0.041 and 0.158,⁴ respectively, the Förster critical distance, R₀, determined from eqn. (5) are 28.9 Å and 37.4 Å for Az-ZnTPP and DFAz-ZnTPP systems, respectively. The orientation factor, κ², was assumed to be 2/3 for randomly oriented chromophores in a fluid medium.

In the presence of ZnTPP, the fluorescence intensities for both Az, and DFAz are reduced from I₀ to I_A,corr by energy transfer to ZnTPP. Using eqn. (6), and the maximum fluorescence intensities of Az (at 374 nm), and DFAz (at 380 nm), the EET efficiency, E, is obtained and presented in Fig. 3 for different concentrations of ZnTPP. We observe that E increases with [ZnTPP] for both donors, and that the excitation transfer is more efficient for the DFAz–ZnTPP system.

Fig. 3 The experimental S₂–S₂ energy transfer efficiency, E, for DFAz (■) and Az (●) at different concentrations of the quencher ([ZnTPP]) in CH₂Cl₂. Lines a, b and c are Gösele's theoretical energy transfer efficiency, E_G, computed using the critical distances R₀ = 92.2 Å (for Az), 37.4 Å (for DFAz), and 28.9 Å (for Az), respectively.

We examine the mean diffusion length, (2D̃τ_D)^1/2, by first defining the diffusion coefficients of D and A using the Stokes–Einstein equation,³² such that

where [small eta, Greek, tilde] = 0.449 cP is the viscosity of CH₂Cl₂.The molecular radii for the reactants are r_Az = 3.3 Å, r_DFAz = 3.52 Å, and r_ZnTPP = 5.1 Å.^9,48 The translational diffusion coefficients, D̃, calculated from eqn. (16) are 2.39 × 10⁻⁵ cm² s⁻¹, and 2.30 × 10⁻⁵ cm² s⁻¹ for Az-ZnTPP, and DFAz-ZnTPP, respectively. From the ratio z (=(2D̃τ_D)^1/2/R₀) obtained for both Az-ZnTPP (z = 0.8), and DFAz-ZnTPP (z = 1.7), which are close to 1, both translational diffusion and EET may play important roles in the quenching dynamics.³⁹ The theoretically calculated values of the EET efficiency according to Gösele's model (eqn. (11)), E_G, are given in Fig. 3. The fluorescence lifetimes (τ_D) in CH₂Cl₂, needed to compute α and r_F, are 1.17 ns and 8.84 ns for Az (r_F = 25.7 Å) and DFAz (r_F = 23.0 Å),⁴ respectively. Clearly, from Fig. 3, Gösele's model based on the experimental Förster R₀ values underestimates the observed energy transfer efficiencies in both systems. A good fit to the observed EET efficiency (E) is achieved when R₀ is increased from 28.9 Å to 92.2 Å for Az-ZnTPP (see Fig. 3). Similarly, for DFAz-ZnTPP, Gösele's model (E_G) agrees well with E when R₀ lies between ca. 100 Å and 120 Å, depending on the concentration of ZnTPP (see Table 1). Large discrepancies between observed and Förster critical distances for other systems have been reported. Some examples are given below.

Table 1 The experimental S₂–S₂ EET efficiency (E), critical distance (R₀), and diffusion coefficient (D̃) for DFAz at various ZnTPP concentrations in CH₂Cl₂

[ZnTPP]/10^−5M	E ^a	R 0/Å^b	D̃/10^−3 cm^2 s^−1^c
a calculated from eqn. (6). b obtained from Gösele model, eqn. (11), with D̃ = 2.30 × 10^−5 cm^2 s^−1. c obtained from Gösele model, eqn. (11), with R0 = 37.4 Å.
0.981	0.054	101.4	0.91
2.224	0.106	97.5	0.81
3.072	0.164	103.7	1.04
4.004	0.205	103.4	1.05
5.718	0.314	110.4	1.41
6.502	0.373	114.8	1.69
7.363	0.443	120.3	2.11

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Pandey, Pant, and co-workers have previously studied energy transfer between different dye molecules (e.g., EET from trypaflavine to rhodamine 6G).^50–52 They found that a reasonable fit to their donor fluorescence decay, using Gösele's model (eqn. (10)), is attained only when a larger than Förster critical distance (e.g., for the trypaflavine–rhodamine 6G system with Förster critical distance = 54 Å, an observed critical distance as large as 158 Å was obtained), or a larger than donor-acceptor translational diffusion coefficient D̃ in eqn. (10) is used. Pandey et al. argued that when the acceptor concentration is low enough, donor–donor energy migration can result in a faster quenching by the acceptors. In this case, the effective diffusion coefficient, D̃, found in eqn. (10) and (11) is given by the sum of donor–acceptor translational diffusion coefficient (eqn. (16)), and donor–donor excitation migration diffusion coefficient (D̃_E).⁵³ Gochanour, Anderson, and Fayer (GAF) have found that at long times, the energy migration process becomes diffusive with a limiting diffusion coefficient given by⁵⁴

D̃_E = 0.428C^4/3_0ER²_0Eτ⁻¹_D (17)

where C_0E = 4πn_DR³_0E/3 is a reduced concentration, R_0E is the donor–donor Förster critical distance, and n_D is the number density of donors. From eqn. (17), we obtain a value of D̃_E = 1.9 × 10⁻¹¹ cm² s⁻¹ for Az (R_0E = 10.4 Å), and D̃_E = 1.4 × 10⁻¹¹ cm² s⁻¹ for DFAz (R_0E = 13.8 Å).

When R₀ is fixed to the Förster critical distance, Gösele's model returned a value of D̃ = 6.2 × 10⁻³ cm² s⁻¹ in order to adequately explain the experimental E values observed for Az–ZnTPP. Likewise, D̃ ranged between 9.1 × 10⁻⁴ cm² s⁻¹ and 2.1 × 10⁻³ cm² s⁻¹ (depending on [ZnTPP], see Table 1) for DFAz–ZnTPP. Clearly, the sum of the calculated donor-acceptor translational diffusion coefficient (eqn. (16)), and the GAF excitation migration diffusion coefficient (eqn. (17)) is insufficient to fully explain the apparent higher D̃ values for our systems.

The GAF model suffers from the assumption that donor molecules are immobile during energy migration. Jang et al.⁵⁵ removed GAF's assumption, by formulating an expression for D̃_E based on the combined effects of donor translational diffusion, and energy migration among donors. It was found that translational motion reduces the distance between donors, and hence increases the efficiency of energy migration and quenching. Jang's expression for D̃_E is D̃_E = (2πτ_D⁻¹R⁶_0En_D)/3r_c, where r_c is a cutoff distance for self-transfer. Here a value of r_c = 1.81 × 10⁻⁶ cm for Az, and a D̃_E value of 2.71 × 10⁻¹¹ cm² s⁻¹ have been calculated using Jang's model. Although Jang's energy migration diffusion coefficient is larger than GAF's, it is still insignificant compared to the donor–acceptor translational diffusion coefficient. This is easily rationalised from the fact that R_0E for Az (i.e. 10.4 Å) is very much smaller than the Az-ZnTPP critical distance (R₀ = 28.9 Å). The very low R_0E implies that energy migration among Az is highly inefficient. Similar behaviour is also observed for DFAz, which lead us to believe that the effects of donor energy migration on D̃, and hence E is negligible.

As discussed by Sipp and Voltz,⁴² short-range exchange interaction, in addition to long-range Coulombic coupling, can contribute to the overall energy transfer quenching dynamics. The classical Dexter mechanism is often used to interpret the orbital-overlap dependent interaction.⁵⁶ The importance of considering exchange interaction for a D–A pair with large Förster critical distance in a highly diffusive medium has been highlighted by Bandyopadhyay and Rao.⁵⁷ Their study compliments those of Ali and co-workers.^58,59 Birks and Leite⁶⁰ found a larger than Förster's critical distance for EET between naphthalene and 9,10-diphenylanthracene in a series of solvents with varying viscosities. Adams et al.⁶¹ obtained large experimental R₀ (e.g. 152 Å) values for EET from DODCI dye to malachite green in ethanol, which could not be explained using Förster's theory (Förster critical distance = 59 Å). Stevens and Dubois⁶² have also reported a two fold increase in the experimental critical distance (31 Å) compared to Förster's R₀ (16 Å) for the quenching of the S₂ state of Az by anthracene in ether solvent. In all of the above studies, the breakdown of considering solely Förster's theory was attributed to extra contributions arising from higher order Coulombic terms, and distributed transition-monopole theory.^63–66 Both factors are known to become significant for large chromophores (e.g. porphyrin) when the D–A separation approaches the size of the molecules.

We examine the effects of short-range interaction for Az-ZnTPP using the Sipp–Voltz model, where the effective reaction length is defined by⁴²

and r_d is the long-range dipole–dipole reaction length (eqn. (13), r_d = 25.7 Å), I_y(x) is the modified Bessel function of the first kind, and χ is given by

An effective reaction length of r = 1.56 × 10⁻⁶ cm was determined from our experimental E values, and using eqns. (18) and (19), we obtain a short-range exchange interaction length of r_e = 86.9 Å. We note that r_e is unreasonably large compared to r_d, and we conclude that short-range interaction cannot be used to explain the efficient energy transfer observed, at least not when a homogeneous distribution of A around D is assumed.

Kaschke and Vogler^67,68 (KV) were the first to propose an inhomogeneous distribution of A around D. They developed a model whereby a raised acceptor concentration (n^′_A) is found around the donor (say between two spheres of radii R₁ and R₂, such that D is located in the centre of the spheres, and R₁ < R₂ < Förster R₀) which exceeds the bulk acceptor concentration (n_A) found outside this region. The raised acceptor concentration is due to mutual attraction between the molecules caused by weak van der Waals interactions. Kaschke and Vogler were able to explain the efficient EET observed between rhodamine 6G donor and several acceptors (DOTC, cresyl violet, oxazine) in ethanol using their model. For an example, in the case of rhodamine 6G-cresyl violet, an observed critical distance as large as 94 Å was reported compared to a Förster critical distance of 56 Å. Using an inhomogeneous acceptor distribution, whereby the raised acceptor concentration is 57 times higher than the bulk acceptor concentration, Kaschke and Vogler were able to rationalise the more efficient energy transfer observed.

We adopt the KV approach to model our experimental results. Apart from van der Waals forces, weak π–π interactions can also induce ZnTPP to form a raised acceptor concentration around the donor (Az or DFAz).⁶⁹ It must be stressed, as Kaschke and Vogler have,^67,68 that this does not mean the formation of complexes or aggregates. However, in the region of raised acceptor concentration, the D and A are often close enough to effect short-range exchange interaction (e.g. Dexter mechanism), and higher multipole–higher multipole interactions. We therefore include two more terms in the KV model to account for the latter mechanisms. The time-dependent donor fluorescence decay, taking into consideration an inhomogeneous distribution of acceptors, and ignoring the effects of diffusion, is given by

A(t) is the result of the modified Förster theory, and is given by^67,68

where θ = n^′_A/n_A, x_i(t) = (R³₀/R³_i)/(t/τ_D)^1/2, and When R₁ → 0, and n^′_A → n_A, A(t) coincides with Förster's 2γ expression (see eqn. (7)). B(t) is the contribution from Dexter's short-range exchange interaction given by⁷⁰where R_0s is the critical distance between D and A, such that short-range exchange EET occurs with the same probabilty as donor emission, ψ = 2R_0s/L with L being the so-called Bohr radius, and Finally, the higher multipole terms are contained in where n equals 8 and 10 for dipole–quadrupole and quadrupole–quadrupole interactions, respectively, and R_0n are their respective energy transfer critical distances.

We illustrate the effects of an inhomogeneous distribution of ZnTPP around Az by considering only the self-decay, A(t), and B(t) terms in eqn. (20). Owing to the experimental difficulties in obtaining R₁, R₂, and R_0s, our results will be semi-quantitative at best. Nonetheless, the implications of the results are generally true for all cases. A(t) has been shown to be insensitive to R₁,⁶⁷ and the latter is assigned a value of 10 Å. R₂ < Förster's R₀ was given a value of 20 Å. Dexter's mechanism is generally valid as long as the interchromophoric separation between D and A is smaller than ca. twice the encounter distance.⁷¹ Therefore, we chose R_0s = 16 Å. Fig. 4 shows that when the ratio between raised acceptor concentration and bulk acceptor concentration, θ, equals 119, the theoretical EET efficiencies agree well with experimental E values. Even though the KV approach shows a vast improvement over Förster's model, both yield theoretical E values which are lower than the experimental ones (see Fig. 4). Clearly, the inclusion of Dexter's B(t) term in eqn. (20) cannot be ignored. The higher multipole interaction factor C will further reduce the value of θ. Two other short-range interaction mechanisms (i.e. the distributed transition-monopole and the through-configuration interactions) were left out in eqn. (20), which will further affect the value of θ. The through-configuration interaction term arising from interactions between ionic charge configurations and locally excited states have been previously shown to be just as important as Dexter's mechanism.^72,73

Fig. 4 The experimental S₂–S₂ energy transfer efficiency, E, for Az (●) is compared with various theoretical models: a: Förster's model assuming a homogeneous acceptor distribution (E_F, eqn. (9)), b: Kaschke and Vogler (KV) model assuming an inhomogeneous acceptor distribution (i.e., eqn. (20) with B(t) and C terms = 0), and c: modified KV model taking into account Dexter's mechanism (i.e., eqn. (20) with C = 0). The value of θ is 119 for b and c.

The more efficient quenching observed for DFAz when compared to Az (Fig. 3) is now rationalised using the modified KV model. The DFAz emission spectrum is red-shifted with respect to Az, thus increasing the amount of overlap with ZnTPP absorption spectrum. Along with a higher fluorescence quantum yield, all the relevant resonance energy transfer critical distances (i.e., Förster, Dexter, higher-multipole interactions) for DFAz are larger than Az's. Furthermore, the π-donating effect of the two fluoro substituents to the azulenic aromatic system in DFAz will enhance the weak π-π interaction with ZnTPP. Therefore, a greater raised acceptor concentration around DFAz will amplify the quenching efficiency.

So far, we have reported energy transfer as the only quenching mechanism. The feasibility of electron transfer from Az to ZnTPP, especially in the region of raised acceptor concentration, is examined via the Gibbs free energy change (ΔG°) involved in the charge separation process,⁷⁴

where E_ox and E_red are the respective oxidation and reduction potentials of Az and ZnTPP in acetonitrile, respectively, ε_ace and ε_CH2Cl2 are the relative permittivities of acetonitrile and CH₂Cl₂, respectively, and E₀₀ (=3.52 eV) is the energy of Az S₂ state. E_ox = 0.88 V for Az,⁷⁵ and E_red = −1.30 V for ZnTPP⁷⁶ in acetonitrile. From eqn. (26), we get ΔG° = −118.2 kJ mol⁻¹, indicating an energetically favourable electron transfer process from D to A in CH₂Cl₂. Elucidation of the relative importance of energy and electron transfer reactions in our systems is currently being investigated using time-resolved emission, and flash photolysis experiments, and will be reported in a forthcoming paper.

EET in CTAB micelles

The steady-state absorption and emission spectra for Az and ZnTPPS in CTAB micelles are shown in Fig. 5. Monomeric ZnTPPS in CTAB shows characteristic absorbance maxima at 426 nm, 560 nm, and 599 nm, in accordance with literature values.^77,78 No new absorption or emission bands were observed upon increasing the concentrations of ZnTPPS, strongly suggesting the absence of complex formation (figure not shown). Furthermore, premicellar aggregates between CTAB and ZnTPPS are excluded by working at surfactant concentration well above the c.m.c.^79,80

Fig. 5 The absorption and emission spectra for Az and ZnTPPS in CTAB micelles. The absorbances are normalised to the maximum optical density. The ZnTPPS S₂ emission peak is amplified 20 times. abs is the absorption band, while em is the emission band.

The spectral overlap integral between the emission spectrum of donor Az and the absorption spectrum of acceptor ZnTPPS is 6.40 × 10⁻¹⁴ cm³ M⁻¹. The molar absorption coefficients of solubilised ZnTPPS in CTAB were taken from ref. 77. Given further that the quantum yield of Az is determined to be 0.02 in CTAB micelles, the Förster critical distance calculated from eqn. (5) is 21.6 Å. Molecular motions are known to be greatly impeded upon encapsulation of the molecules in micelles.^43,81 Hence, in the event of restricted rotation, a value of κ² = 0.476 is assumed for randomly oriented chromophores.⁸²

Using the maximum fluorescence intensity of Az at 374 nm, the experimental energy transfer efficiency, E, is calculated from eqn. (6), and the results are presented in Fig. 6 for different concentrations of ZnTPPS. To compare our experimental results with the model discussed in Section 2, the theoretical energy transfer efficiencies, E_T, were obtained by integrating eqn. (15) over time. The numerical computation was performed using Maple 7 (Waterloo Maple Inc.) software. J(s) for the various distance distributions are given by:^45,46

where ξ = s(R₀/2R_m)⁶. The mean acceptor occupation number is defined to be μ = [ZnTPPS]/[CTAB]_m, where [CTAB]_m is the concentration of CTAB micelles. From the surfactant concentration ([CTAB]), c.m.c., and micellar aggregation number ρ (=60 for CTAB),²⁷ [CTAB]_m = 2.2 × 10⁻⁵ M is easily obtained from the expression,⁸³

Fig. 6 The experimental S₂–S₂ energy transfer efficiency, E, for Az (●) at different concentrations of the quencher ([ZnTPPS]) in CTAB micelles is compared with the theoretical model, E_T, given by eqn. (15). A surface-uniform distance distribution (eqn. (27)) with micellar radius of 31.8 Å shows good agreement with E.

From Fig. 6, we see that when the radius of the micelle R_m = 31.8 Å, for a surface–uniform (su) distance distribution, the theoretical E_T values, based on Förster's theory, are in excellent agreement with the experimental ones. Similarly, good agreement between E_T and E is obtained when R_m = 30.6 Å, and 38.8 Å for the surface–surface (ss), and uniform–uniform (uu) distance distributions, respectively. An interesting feature is the sensitivity of R_m to the distance distribution function. As discussed by Barzykin,⁴⁵ the mean distance between D and A is largest for the s–s distribution, and smallest for the s–u distribution. Therefore, in order for eqn. (15) to appropriately describe E, a larger R_m is required for the s–u distribution. As discussed earlier, energy migration among Az chromophores is insignificant. An R_0E value of 10.5 Å for Az–Az energy transfer implies a D–D Förster transfer rate of only 1.3% of that of the D–A one.

The sites of solubilisation of aromatic molecules, such as benzene and higher arenes, have been found to be located at the interface of ionic micelles near the polar head groups.^84–86 Cardinal and Mukerjee⁸⁵ have ascribed the micellar surface activity of aromatic molecules to the interaction beween water dipoles and π-electron system of the aromatic molecules. The Az chromophores are thus taken to be absorbed at the CTAB micellar surface. On the other hand, several studies have shown that porphyrin systems tend to be embedded in the hydrophobic core of micelles.^77,78,81,87 In particular, Kadish et al.⁷⁷ have reported that significant perturbation of the ¹H NMR peaks of the CTAB's surfactant head group, terminal methyl group, and intermediate methylene groups are seen upon inclusion of free-base tetra-(4-sulfonatophenyl) porphyrins. This suggests that the ZnTPPS molecules interact throughout the surfactant chain, and are probably distributed uniformly within the micelle. Therefore, the surface–uniform distance distribution seems to be the most suitable description for our Az-ZnTPPS system.

The radius of CTAB micelle in the absence of solubilizate has been independently determined to be ca. 24 Å (i.e. hydrophobic core radius + head group radius).⁸⁸ The CTAB micelle radius obtained from this study, assuming a surface–uniform distance distribution, is 31.8 Å, which is not unreasonable. Two plausible explanations of the slightly larger observed R_m can be offered. Micellar structures are known to be modified by the addition of solubilizates.^89,90 In our case, ZnTPPS which are solubilised within the CTAB micelles can produce a swelling of the latter,⁸⁹ hence increasing the radii of micelles. Recently, Zhao et al.⁹¹ have studied the hydrocarbon chain packing behaviour of CTAB micelles using a ¹H NMR relaxation technique. They found that intermediate methylene groups of CTAB have some probability of spending time at the micellar surface layer. This means that the interior of CTAB micelle is inhomogeneous, and a uniform distribution of ZnTPPS becomes a simplified picture of the true acceptor distribution.

Conclusion and final comments

We have observed electronic energy transfer from the S₂ state of a donor (azulene) to the S₂ state of an acceptor (zinc porphyrin) in dichloromethane solvent and CTAB micelles. The high energy transfer efficiencies observed in dichloromethane are attributed to an inhomogeneous distribution of acceptors. On the other hand, Förster kinetics is followed when the chromophores are solubilised in CTAB micelles.

The possible fate of the excitation energy after the initial S₂–S₂ transfer is worth mentioning here. The porphyrin in its S₂ state will subsequently undergo rapid relaxation to its S₁ state (see Fig. 7). The internal conversion rate from the S₂ to the S₁ states of the acceptor corresponds to its S₂ fluorescence decay rate (i.e.τ₂ = ca. 2 ps for ZnTPP,⁹² and ca. 1.3 ps for ZnTPPS⁹³). Thereafter, the excited molecule can either emit radiatively as acceptor fluorescence (i.e.τ₄ = 1.5–3 ns),⁶ or return to the donor via a radiationless back energy transfer from the S₁ state of A to the S₁ state of D (Fig. 7). From Figs. 1, 2, and 5, we find significant spectral overlap between the S₁ emission spectrum of zinc porphyrin, and the S₁ absorption spectrum of azulene, strongly suggesting probable resonance back-EET. Finally, the system returns quickly to the ground state by the S₁–S₀ conical intersection (i.e.τ₃ < 2 ps for Az).⁹⁴ The cyclic energy transfer process, seen in Fig. 7, has very important implications in the design of molecular logic gates. Levine et al.¹⁴ have discussed how one can utilise bidirectional intermolecular EET to perform logical operations on different chromophores. We are presently investigating the cyclic EET dynamics for a series of linked (flexible and rigid) systems, consisting of azulene donor and zinc porphyrin acceptor chromophores, which will shed further insight into the functionality of such molecular logic gates.

Fig. 7 Energy levels of donor (D) and acceptor (A) chromophores, and the various EET and energy relaxation pathways. Solid lines are radiative processes, while broken lines are non-radiative processes. τ₁ is the fluorescence lifetime of the donor S₂ state (e.g., 1.17 ns for Az, and 8.84 ns for DFAz in CH₂Cl₂).⁴

Another interesting issue concerns the choice of the orientation factor (κ², eqn. (5)) for the back S₁–S₁ EET. In a random array of chromophores, κ² is usually assigned a value of 2/3 in a fluid medium. However, because the porphyrin S₂ state is very short-lived, there will be a photoselection of porphyrin S₁ states after S₂–S₂ EET, invalidating the assumption of random S₁ transition dipole moments. This problem will be tackled by us in a future publication.

Acknowledgements

We would like to thank Dr Alfred Asato for kindly supplying a sample of 1,3-difluoroazulene. We are also grateful to Professor R. E. Verrall for useful discussions regarding micelles.

References

1. N. J. Turro, V. Ramamurthy, W. Cherry and W. Farneth, Chem. Rev., 1978, 78, 125.
2. O. K. Abou-Zied, H. K. Sinha and R. P. Steer, J. Phys. Chem., 1996, 100, 4375.
3. O. K. Abou-Zied, H. K. Sinha and R. P. Steer, J. Mol. Spectrosc., 1997, 183, 42.
4. N. Tétreault, R. S. Muthyala, R. S. H. Liu and R. P. Steer, J. Phys. Chem. A, 1999, 103, 2524.
5. R. S. H. Liu, R. S. Muthyala, X. Wang, A. E. Asato, P. Wang and C. Ye, Org. Lett., 2000, 2, 269.
6. S. Takagi and H. Inoue, in Multimetallic and Macromolecular Inorganic Photochemistry, ed. V. Ramamurthy and K. S. Schanze, Marcel Dekker, New York, 1999, p. 215.
7. E. K. L. Yeow, K. P. Ghiggino, J. N. H. Reek, M. J. Crossley, A. W. Bosman, A. P. H. J. Schenning and E. W. Meijer, J. Phys. Chem. B, 2000, 104, 2596.
8. E. K. L. Yeow, P. J. Sintic, N. M. Cabral, J. N. H. Reek, M. J. Crossley and K. P. Ghiggino, Phys. Chem. Chem. Phys., 2000, 2, 4281.
9. E. K. L. Yeow and S. E. Braslavsky, Phys. Chem. Chem. Phys., 2002, 4, 239.
10. G. G. Gurzadyan, T.-H. Tran-Thi and T. Gustavsson, J. Chem. Phys., 1998, 108, 385.
11. N. Mataga, Y. Shibata, H. Chosrowjan, N. Yoshida and A. Osuka, J. Phys. Chem. B, 2000, 104, 4001.
12. H. Kobayashi and Y. Kaizu, in Porphyrins: Excited States and Dynamics, eds. M. Gouterman, P. M. Rentzepis and K. D. Straub, American Chemical Society, Washington DC, 1986, p. 105.
13. C. C. Gradinaru, I. H. M. van Stokkum, A. A. Pascal, R. van Grondelle and H. van Amerongen, J. Phys. Chem. B, 2000, 104, 9330.
14. F. Remacle, S. Speiser and R. D. Levine, J. Phys. Chem. B, 2001, 105, 5589.
15. F. Remacle and R. D. Levine, J. Chem. Phys., 2001, 114, 10 239.
16. I. Kaplan and J. Jortner, Chem. Phys., 1978, 32, 381.
17. D. W. Gordon and W. F. Coleman, J. Lumin., 1980, 22, 23.
18. V. A. Lyubimtsev, Opt. Spectrosc. (Transl. of Opt. Spektrosk.), 1983, 55, 624.
19. V. A. Lyubimtsev, Opt. Spectrosc. (Transl. of Opt. Spektrosk.), 1987, 62, 622.
20. E. N. Bodunov, M. N. Berberan-Santos and J. M. G. Martinho, Chem. Phys. Lett., 1997, 274, 171.
21. M. S. Gudipati and M. Kalb, J. Inf. Rec., 1998, 24, 445.
22. A. Harriman, M. Hissler, O. Trompette and R. Ziessel, J. Am. Chem. Soc., 1999, 121, 2516.
23. T. Theodossiou, E. Georgiou, V. Hovhannisyan, K. Politopoulos and D. Yova, J. Opt. A: Pure Appl. Opt., 2001, 3, L1.
24. G. K. Oster and H. Kallmann, J. Chim. Phys., 1967, 64, 28.
25. S. Akimoto, T. Yamazaki, I. Yamazaki, A. Nakano and A. Osuka, Pure Appl. Chem., 1999, 71, 2107.
26. A. Nakano, Y. Yasuda, T. Yamazaki, S. Akimoto, I. Yamazaki, H. Miyasaka, A. Itaya, M. Murakami and A. Osuka, J. Phys. Chem. A, 2001, 105, 4822.
27. K. Kalyanasundaram, Photochemistry in Microheterogeneous Systems, Academic Press, Orlando, FL, 1987.
28. M. N. Berberan-Santos and M. J. E. Prieto, J. Chem. Soc., Faraday Trans. 2, 1987, 83, 1391.
29. R. Frank and H. Rau, J. Photochem., 1982, 18, 281.
30. M. Kubista, R. Sjöback, S. Eriksson and B. Albinsson, Analyst, 1994, 119, 417.
31. B. C. MacDonald, S. J. Lvin and H. Patterson, Anal. Chim. Acta, 1997, 338, 155.
32. J. R. Lakowicz, Principles of Fluorescence Spectroscopy, Kluwer Academic, New York, 2nd edn., 1999.
33. J. F. Holland, R. E. Teets, P. M. Kelly and A. Timnick, Anal. Chem., 1977, 49, 706.
34. R. J. Kavanagh, K.-K. Iu and J. K. Thomas, Langmuir, 1992, 8, 3008.
35. Th. Förster, in Modern Quantum Chemistry, ed. O. Sinanoglu, Academic Press, New York, 1965, p. 93.
36. E. K. L. Yeow, D. J. Haines, K. P. Ghiggino and M. N. Paddon-Row, J. Phys. Chem. A, 1999, 103, 6517.
37. Th. Förster, Discuss. Faraday Soc., 1959, 27, 7.
38. N. Tamai, T. Yamazaki and I. Yamazaki, Chem. Phys. Lett., 1985, 120, 24.
39. S. Speiser, Chem. Rev., 1996, 96, 1953.
40. U. Gösele, M. Hauser, U. K. A. Klein and R. Frey, Chem. Phys. Lett., 1975, 34, 519.
41. U. K. A. Klein, R. Frey, M. Hauser and U. Gösele, Chem. Phys. Lett., 1976, 41, 139.
42. B. Sipp and R. Voltz, J. Chem. Phys., 1985, 83, 157.
43. K. Kasatani, M. Kawasaki, H. Sato and N. Nakashima, J. Phys. Chem., 1985, 89, 542.
44. M. H. Gehlen and F. C. De Schryver, Chem. Rev., 1993, 93, 199.
45. A. V. Barzykin, Chem. Phys., 1991, 155, 221.
46. A. V. Barzykin and M. Tachiya, Heterogen. Chem. Rev., 1996, 3, 105.
47. W. I. White, in The Porphyrins, ed. D. Dolphin, Academic Press, New York, 1978, vol. V, p. 303.
48. A. T. Reis e Sousa, J. M. G. Martinho, F. Baros and J. C. Andáe, J. Photochem. Photobiol. A: Chem., 1994, 83, 199.
49. H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan and J. S. Lindsey, Photochem. Photobiol., 1998, 68, 141.
50. K. K. Pandey and T. C. Pant, Chem. Phys. Lett., 1990, 170, 244.
51. K. K. Pandey, Chem. Phys., 1992, 165, 123.
52. H. C. Joshi, H. Mishra, H. B. Tripathi and T. C. Pant, J. Lumin., 2000, 90, 17.
53. D. P. Millar, R. J. Robbins and A. H. Zewail, J. Chem. Phys., 1981, 75, 3649.
54. C. R. Gochanour, H. C. Andersen and M. D. Fayer, J. Chem. Phys., 1979, 70, 4254.
55. S. Jang, K. J. Shin and S. Lee, J. Chem. Phys., 1995, 102, 815.
56. D. L. Dexter, J. Chem. Phys., 1953, 21, 836.
57. T. Bandyopadhyay and K. V. S. Rama Rao, Chem. Phys., 1992, 167, 131.
58. M. A. Ali and S. A. Ahmed, J. Chem. Phys., 1989, 90, 1484.
59. M. A. Ali, S. A. Ahmed and A. S. Chokhavatia, J. Chem. Phys., 1989, 91, 2892.
60. J. B. Birks and M. S. S. C. P. Leite, J. Phys. B, 1970, 3, 513.
61. M. C. Adams, D. J. Bradley, W. Sibbett and J. R. Taylor, Chem. Phys. Lett., 1979, 66, 428.
62. B. Stevens and J. T. Dubois, Trans. Faraday Soc., 1966, 62, 1525.
63. G. D. Scholes and K. P. Ghiggino, in Advances in Multiphoton Processes and Spectroscopy, ed. S. H. Lin, A. A. Villaeys and Y. Fujimura, World Scientific, Singapore, 1996, vol. 10, p. 95.
64. J. C. Chang, J. Chem. Phys., 1977, 67, 3901.
65. D. E. LaLonde, J. D. Petke and G. M. Maggiora, J. Phys. Chem., 1988, 92, 4746.
66. C. A. Hunter, J. K. M. Sanders and A. J. Stone, Chem. Phys., 1989, 133, 395.
67. M. Kaschke and K. Vogler, Chem. Phys., 1986, 102, 229.
68. M. Kaschke and K. Vogler, Laser Chem., 1988, 8, 19.
69. H. Scheer and J. J. Katz, in Porphyrins and Metalloporphyrins, ed. K. M. Smith, Elsevier Scientific, Amsterdam, 1975, p. 399.
70. M. Inokuti and F. Hirayama, J. Chem. Phys., 1965, 43, 1978.
71. N. J. Turro, Modern Molecular Photochemistry, Benjamin Cummings, Menlo Park, 1978.
72. R. D. Harcourt, G. D. Scholes and K. P. Ghiggino, J. Chem. Phys., 1994, 101, 10 521.
73. E. K. L. Yeow and K. P. Ghiggino, J. Phys. Chem. A, 2000, 104, 5825.
74. G. J. Kavarnos, Fundamentals of Photoinduced Electron Transfer, VCH, New York, 1993.
75. T. Kurihara, T. Suzuki, H. Wakabayashi, S. Ishikawa, K. Shindo, Y. Shimada, H. Chiba, T. Miyashi, M. Yasunami and T. Nozoe, Bull. Chem. Soc. Jpn., 1996, 69, 2003.
76. G. R. Seely, D. Gust, T. A. Moore and A. L. Moore, J. Phys. Chem., 1994, 98, 10 659.
77. K. M. Kadish, G. B. Maiya, C. Araullo and R. Guilard, Inorg. Chem., 1989, 28, 2725.
78. S. C. M. Gandini, V. E. Yushmanov and M. Tabak, J. Inorg. Biochem., 2001, 85, 263.
79. T. Hinoue, J. Kobayashi, T. Ozeki and H. Watarai, Chem. Lett., 1997, 8, 763.
80. T. Tominaga, S. Endoh and H. Ishimaru, Bull. Chem. Soc. Jpn., 1991, 64, 942.
81. N. C. Maiti, S. Mazumdar and N. Periasamy, J. Phys. Chem., 1995, 99, 10 708.
82. R. E. Dale and J. Eisinger, Proc. Natl. Acad. Sci. USA, 1976, 73, 271.
83. S. J. Formosinho and M. M. Miguel, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 1891.
84. J. C. Eriksson, U. Henriksson, T. Klason and L. Ödberg, in Solution Behavior of Surfactants, ed. K. L. Mittal and E. J. Fendler, Plenum Press, New York, 1982, vol. 2, p. 907.
85. P. Mukerjee and J. R. Cardinal, J. Phys. Chem., 1978, 82, 1620.
86. M. Gonzâlez, J. Vera, E. B. Abuin and E. A. Lissi, J. Colloid Interface Sci., 1984, 98, 152.
87. M. Vermathen, E. A. Louie, A. B. Chodosh, S. Ried and U. Simonis, Langmuir, 2000, 16, 210.
88. M. Alauddin and R. E. Verrall, J. Phys. Chem., 1986, 90, 1647.
89. P. Mukerjee, in Solution Chemistry of Surfactants, ed. K. L. Mittal, Plenum Press, New York, 1979, vol. 1, p. 153.
90. M. Almgren and S. Swarup, J. Colloid Interface Sci., 1983, 91, 256.
91. S. Zhao, H.-Z. Yuan, J.-Y. Yu and Y.-R. Du, Colloid Polym. Sci., 1998, 276, 1125.
92. G. G. Gurzadyan, T.-H. Tran-Thi and T. Gustavsson, Proc. SPIE, 2000, 4060, 96.
93. M. Andersson, J. Davidsson, L. Hammarström, J. Korppi-Tommola and T. Peltola, J. Phys. Chem. B, 1999, 103, 3258.
94. B. D. Wagner, M. Szymanski and R. P. Steer, J. Chem. Phys., 1993, 98, 301.

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