10088
J. Phys. Chem. B 2007, 111, 10088-10094
Aggregates of Naphthalene Chromophores in Poly(vinylalcohol)-graft-poly(vinylnaphthalene) Pseudomicelles Szczepan Zapotoczny, Monika Rymarczyk-Machał, Anna Stradomska, Piotr Petelenz, and Maria Nowakowska* Faculty of Chemistry, Jagiellonian UniVersity, 30-060 Krako´ w, Ingardena 3, Poland ReceiVed: April 5, 2007; In Final Form: June 21, 2007
A novel amphiphilic grafted copolymer, poly(vinylalcohol)-graft-poly(vinylnaphthalene), was synthesized and studied spectroscopically. The unusual photophysical properties of its aqueous solutions were observed for the first time and are attributed to the aggregation of the naphthalene chromophores in the bulk of polymer pseudomicelles. The enormous red shift of the fluorescence spectra is interpreted in terms of the confinement effect. The interpretation is supported by model calculations, taking into account the mixing of Frenkel excitons and charge-transfer states of chromophore clusters in densely packed polymer domains. Gradual funneling of the excitation energy between aggregates of different sizes is discussed in the context of the measured fluorescence depolarization spectra.
Introduction Owing to their unique structural and photophysical properties, molecular aggregates formed as a result of the self-assembling of organic molecules elicit a growing interest in the literature.1-6 The electrostatic and/or van der Waals interactions between the aggregate constituents enforce their specific spatial arrangement, which in turn determines the coupling between the excitations of the individual structural units, in some cases substantially affecting the spectra of the system. The classic studies on cyanine dyes indicate that the type of aggregates that ensue strongly depends on the structure of the dye, its concentration, and the properties of the medium.1,7 The spectral shift (with respect to the spectrum of an isolated constituent molecule), usually large, may be either hypsochromic (H aggregates) or bathochromic (J aggregates). The aggregates of this latter type have already found some practical applications, for example, as photographic sensitizers8 or as active components of nonlinear optical devices,9,10 and their use as materials for fast optical switching and signal processing seems imminent.11 They are also invoked as models of light-harvesting systems and solarenergy-storage devices.12-19 It is interesting to note, in our present context, that the aggregates of cyanine dyes are also formed in the presence of natural or synthetic polyelectrolytes;20,21 the dye is either added to the polymer solution or is chemically bound to the polymer chain. Obviously, the ability to form molecular aggregates is by no means peculiar to compounds with low molecular weight (as, for example, the archetypal aromatics22) but is equally common for conjugated polymers, such as poly(fluorene)s,23 poly(p-phenylene vinylene)s,4 or poly(thiophene)s.24 Aggregation is an important factor impairing the performance of these latter materials in light-emitting diodes, and various attempts were made to minimize this effect.25 It is widely recognized that the interactions between the chromophores strongly affect the photophysical properties of photoactive polymers such as antenna polyelectrolytes or * To whom correspondence should be addressed. E-mail: nowakows@ chemia.uj.edu.pl. Phone: +48 12 6632250. Fax: + 48 12 6340515.
polymeric photosensitizers.26-30 However, most of the studies known to us were focused on the formation of excimers or exciplexes,28,31 where the relevant interaction involved electronically excited structural units. Our present results suggest that chromophore aggregates may be formed in some photoactive polymers also in the ground electronic state. According to common wisdom,32 the hydrophobically modified hydrophilic polymers, when dissolved in water, adopt a compact pseudomicellar conformation, thereby minimizing the contact of the hydrophobic chromophores with polar water molecules.27,29,32-34 In the congested bulk of a pseudomicelle, the chromophores are forced into close-contact positions, unlikely to occur in free space; the interchromophore interactions in such clusters are bound to have spectroscopic consequences. This paper presents the results of our investigation of naphthalene aggregates in photoactive polymer poly(vinylalcohol)-graft-poly(vinylnaphthalene) (PVA-graft-PVNp). As shown previously35 (see Figure 1); owing to its micelle-like conformation, the studied polymer is well soluble in water despite the relatively high content of hydrophobic naphthalene chromophores. Its unusual photophysical properties are studied here in some detail; the interpretation is supported by model calculations. Experimental Section Poly(vinylalcohol)-graft-poly(vinylnaphthalene) (PVA-graftPVNp) of molecular weight Mw ≈ 28000 g/mol was prepared by controlled radical polymerization as described earlier.35 The content of naphthalene chromophores in the polymer was estimated to be 30 mol % with respect to PVA mers. Naphthalene (Np, Aldrich, 99%) and organic solvents, DMSO (Aldrich, spectrophotometric grade) and methanol (Aldrich, 99%), were used as received. All aqueous solutions were prepared using deionized water. UV-vis absorption spectra were measured using the HP 8452 diode-array spectrophotometer. Steady-state fluorescence spectra, excitation and synchronous spectra, as well as fluorescent lifetimes were measured at room temperature (if not specified
10.1021/jp072676n CCC: $37.00 © 2007 American Chemical Society Published on Web 08/09/2007
Aggregates of Naphthalene Chromophores
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10089
Figure 1. Schematic conformation of the grafted amphiphilic copolymer PVA-graft-PVNp.
otherwise) using an SLM-Aminco 8100 spectrofluorimeter with a 450 W xenon lamp as a light source. All of the spectra were corrected for the instrumental response. Results and Discussion 1. Experimental Results. 1.1. Electronic Absorption Studies. The electronic absorption spectrum of PVA-graft-PVNp in aqueous solution exhibits two high-energy bands at positions roughly the same as those observed for naphthalene and a long low-energy tail in the spectral region of 300-600 nm (see Figure 2). The two well-developed bands are readily assigned to the S0 f S3 and S0 f S2 transitions of the naphthalene molecule. The weak, symmetry-forbidden S0 f S1 transition expected at 313 nm (32 000 cm-1) is buried in the long, diffuse absorption tail. In the DMSO solution, this tail is slightly less extended than that in water, and the corresponding low-energy transition becomes discernible as a shoulder (note that the spectrum above 260 nm is distorted due to DMSO absorption). The observed broadening of the absorption bands and buildup of the long lowenergy onset suggest strong interaction between the naphthalene chromophores, also confirmed by the observation of the socalled ring effect36,37 in the 1HNMR spectrum of PVA-graftPVNp in aqueous solution.35 The effect is indicative of strong interactions between the molecules in a constrained/confined environment. 1.2. Fluorescence Studies. More information on the nature of these interactions may be obtained from the analysis of the emission spectra. Figure 3A and B shows the steady-state emission spectra of PVA-graft-PVNp in water and in DMSO solution, respectively. The observed dependence on excitation conditions exhibits a nontrivial feature; while excitation of the polymer in DMSO solution at 280 nm (in the region where isolated Np chromophores absorb) gives rise to a spectrum dominated by the naphthalene monomer emission, in all other cases, the spectra are shifted to longer wavelengths. Moreover, emission of PVA-graft-PVNp in aqueous solution is observable even when that sample is excited with light at a wavelength longer than 450 nm, definitely out of the absorption range of the isolated Np chromophores. The former finding suggests that the observed fluorescence may originate from Np aggregates; the latter is an indication that the aggregates are present already in the ground electronic state of the polymer. When embedded in a constrained environment or in concentrated solution, the naphthalene chromophores are known to form excimers (so-called normal and second excimers).38,39 If this were the case here, the fluorescence spectra of PVA-graftPVNp would be dominated by the broad, structureless emission characteristic for these species. On the contrary, the experimental
Figure 2. UV/vis absorption spectra of naphthalene (model compound) in methanol and PVA-graft-PVNp in water and DMSO solutions.
emission spectra are evidently structured, which suggests their different provenance. On the basis of the above results, the observed emission may be tentatively assigned to molecular aggregates that are stable in the ground state. When the hydrophobic interactions force the polymer chain into a compressed micelle-like conformation, the Np chromophores adopt random positions in the bulk. It seems statistically inevitable that, in some regions, several chromophores are locked in nearby locations, possibly at short distances from one another. The difference between the spectra shown in Figure 3A and B is consistent with the fact that the probability of such aggregation is considerably lower in DMSO, which is a better solvent for PVNp than water and promotes decoiling of the macromolecules. Insensitivity of the emission profiles to dilution and the presence of aggregate-type emission even at very low concentrations of the polymer (in aqueous solution cpol < 10-7 M; data not shown) suggest that the aggregates are most likely formed within the same macromolecule, that is, between the chromophores grafted on the same polymer chain. The crucial role of aggregates in the photophysics of PVAgraft-PVNp is confirmed by the fluorescence-excitation spectra. Figure 4 shows the excitation spectra recorded for the polymer in aqueous solution. The spectral shape strongly depends on the emission wavelength at which the spectrum was recorded; no discernible correlation is detected between the excitation and absorption spectra of the polymer. This indicates that there exist various emitting species, some of them at a concentration too low to make them observable in absorption spectra but readily detectable in fluorescence spectroscopy. Moreover, the transfer of excitation energy to the lowest-energy species is not perfectly efficient. Altogether, the picture is consistent with the notion of spatially separated clusters of Np chromophores. The spectra, although generally broad, do not resemble the familiar structureless emission known for excimers. The fluorescence decay curves of PVA-graft-PVNp in aqueous solution also depend on the excitation wavelength. The decays cannot be adequately described by a single exponential. By consecutively increasing the number of exponentials and applying the χ2 test, three discernible components characterized by different decay constants were finally detected. Accordingly, the decays were fitted to a triple-exponential curve with the respective lifetimes τ1, τ2, and τ3 (Table 1)
I(t) ) A1exp(-t/τ1) + A2exp(-t/τ2) + A3exp(-t/τ3) (1) For each excitation wavelength, the mean lifetime was calculated as
10090 J. Phys. Chem. B, Vol. 111, No. 34, 2007
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Figure 3. Steady-state emission spectra of PVA-graft-PVNp recorded at various excitation wavelengths in water (A) and in DMSO solution (B).
Figure 4. Normalized excitation spectra of PVA-graft-PVNp in aqueous solution and Np in methanol solution recorded at various emission wavelengths given in the legend.
TABLE 1: Fluorescence Lifetimes of the PVA-graft-PVNp Aqueous Solution (at 25 °C) for Different Excitation- and Emission-Monitoring Wavelengthsa λEX (nm)
λEM (nm)
τ1 (ns)
τ2 (ns)
τ3 (ns)
(ns)
290
300 380
400
420
3.3 54% 2.2 40% 1.9 35%
0.3 24% 0.3 32% 0.3 38%
19.5
350
25.0 22% 10.8 28% 8.7 27%
8.7 7.0
a The weighting factors Ai of the different components in eq 1 are presented as percentage contributions.
) (A1τ12 + A2τ22 + A3τ32)/(A1τ1 + A2τ 2 + A3τ3)
(2)
All of the measured fluorescence lifetimes were short. There was no component characteristic for the naphthalene monomer emission (τ ≈ 100 ns).40,41 Under the experimental conditions specified above, no rising component that might be ascribed to excimers was detected, which conclusively rules out the involvement of classic excimers in the investigated phenomena. Hence, the three decay components may be tentatively attributed to distinct classes of naphthalene clusters. The fact that the lifetimes are shorter for a longer excitation wavelength can be readily rationalized when the peculiar features of aggregate spectra are taken into account. The electronic excited states of a cluster may be approximately viewed as linear combinations of the monomer excitations; the chromophore transition dipoles contribute with appropriate phases, determined by the intermolecular interactions. The eigenstate where the transition dipoles simply add carries most
Figure 5. Degree of fluorescence polarization as a function of the excitation wavelength for emission of the aqueous solution of PVAgraft-PVNp recorded for two emission wavelengths. The arrows show the contribution from Raman scattering on water molecules.
of the intensity in the absorption spectrum. If it happens to be the lowest excited state of the aggregate, it also fluoresces; the emission intensity is then governed by the combined transition dipole moment of all of the contributing chromophores so that the lifetime is much shorter than that in the monomer. This phenomenon, referred to as exciton superradiance, is well-known for linear J aggregates42,43 and was reported also for tetracene nanoaggregates.44 In our case, the clusters are presumably formed at random when the polymer is coiled. Depending on the local geometry (which defines the phase of individual chromophore transition dipoles), in some of the aggregates, the intense state is expected to be the lowest one. These clusters are expected to dominate the fluorescence characteristics. On the one hand, their large transition dipole moment makes them contribute prominently to the total emission intensity; on the other hand, the low energy of the fluorescing state makes the corresponding clusters efficient energy traps. It is reasonable to expect that energetic stabilization is stronger for larger aggregates, which are endowed with larger transition dipole moments and shorter excitation lifetimes. In consequence, the decay times should be short for deep energy traps, which very well agrees with experimental observations. This aspect was studied in more detail by measuring the degree of fluorescence polarization (P) as a function of the excitation wavelength (see Figure 5). The figure shows that P increases with increasing excitation wavelength. This effect may have two causes, probably concurrent. First, energy migrates from the smaller to the larger aggregates (as in the latter, the
Aggregates of Naphthalene Chromophores
Figure 6. Synchronous fluorescent spectra of the solution of PVAgraft-PVNp and Np in the respective solvents recorded for a constant difference ∆λ between synchronously scanned excitation and emission wavelengths.
excited state is more strongly stabilized), and in this process, the polarization characteristics are inevitably lost, especially if many migration steps are needed to reach the final trap. Second, the different excited states of a given aggregate usually have different polarization. Consequently, if a higher-energy excited state of the cluster is optically generated and emission takes place from the lowest excited state, polarization characteristics of absorption and emission differ. Accordingly, depolarization will still occur, even if the excitation is not transferred to a different aggregate. In order to confirm the existence of well-defined entities formed in the ground electronic state, synchronous fluorescent spectra were measured. In this kind of spectroscopy, the excitation and emission wavelengths are scanned simultaneously (with a constant offset between them), and the fluorescence intensity is the measured quantity. Provided that the difference ∆λ between the excitation and emission wavelengths is judiciously chosen, this technique is extremely useful for multicomponent analysis since a peak in the synchronous spectrum may then be assigned to the 0-0 line of a distinct fluorescing species present in the sample.45 Figure 6 compares the synchronous spectra recorded for PVA-graft-PVNp in aqueous solution and in DMSO with the spectrum of the model compound (Np in methanol). One can observe that, apart from some diffuse and relatively weak features (presumably originating from a wide spread of loosely bound aggregates), the spectrum of the polymer in DMSO solution is very much like that of naphthalene. In contrast, for the aqueous polymer solution, the spectrum is much more complicated, supporting the conjecture that various types of aggregates are present. The spectral features are well pronounced and intense; especially worth noting are the peaks at about 400 and 450 nm, indicative of strong stabilization of the aggregate excited state. 2. Theoretical Calculations. In order to elucidate the nature of the aggregates formed in aqueous solutions of PVA-graftPVNp and to rationalize their substantial excited-state stabilization energies, some theoretical estimates were carried out. The effort was focused on the new excited states observed in the energy range between 20000 and 30 000 cm-1. As proposed above, these states are tentatively assigned to oligomeric clusters of naphthalene molecules, which were brought into close contact by coiling of the polymeric chains.
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10091 If this is really the case, the observed spectral shift on the order of 10 000 cm-1 with respect to the normal position of the naphthalene excited states has to result from intermolecular interactions and, in this context, seems rather exceptional. It considerably exceeds the values expected for the gas-to-solvent shift resulting from dispersion interactions. The lowest excited state of the naphthalene molecule (S1, at about 32 000 cm-1) has a negligible transition dipole moment, and the corresponding resonance interaction should be very weak. The interaction is expected to be stronger for the allowed S2 state (at about 36 000 cm-1) but still much too weak to push the lowest of the split components below the original S1, not to mention a further shift of about 5000 cm-1. The intense S3 state (at about 47 000 cm-1) might potentially exhibit a substantial resonance splitting, but in order to explain the experimental findings, the lowest of the split components would have to shift by over 20 000 cm-1 with respect to its position in the isolated molecule, which intuitively seems excessive. By elimination, this brings to mind the charge transfer (CT) states. In the naphthalene crystal, their manifold is believed to start at about 36 000 cm-1.46 This energy corresponds to the nearest-neighbor CT state, with the molecules separated by about 5 Å. It is reasonable to suppose that in the polymeric pseudomicelle, the chromophores may be much more crowded, owing to the hydrophobic interactions that would tend to minimize the volume of the hydrocarbon part of the macromolecule. The smaller intermoiety distances would, in turn, result in a larger Coulombic stabilization, lowering the energy of the CT states. Also, the CT integrals that mix the CT manifold with the local (intrachromophore) excitations would then be expected to increase, possibly to a considerable extent, since they depend exponentially on intermolecular distance. Consequently, the enhanced off-diagonal (in the localized basis) interaction between the two manifolds, similar to that operative in excimers,47,48 would further contribute to the stabilization of lowenergy eigenstates. Accordingly, there are several factors that could potentially account for the occurrence of low-energy aggregate states. The interplay between these factors is expected to depend on the size of the aggregate; this dependence and the cumulative effect of the various contributions is difficult to predict on purely intuitive grounds. On the other hand, detailed simulation of the actual arrangement of the naphthalene chromophores in the pseudomicelle, as well as accurate calculation of the excitedstate energetics in the ensuing molecular cluster, is a formidable task. For this reason, it was our objective merely to estimate the order of magnitude of the relevant spectral shift using a simple model with parametrization based to the largest extent possible on information validated by interpretation of independent experiments. Our calculations are intended as a kind of compatibility test; as the approach has no claim to quantitative accuracy, the simplest approximations are applied. 2.1. Model. The model aggregate used in our calculations is a stack consisting of two to five equidistant naphthalene molecules (see Figure 7). For the sake of simplicity, the planes of the constituent naphthalene molecules are assumed to be parallel to each other and perpendicular to the axis connecting their centers. The angle between the long axes of the molecules is set equal to R in either of the two ways; each molecule is rotated by R relative to the previous one (forming a helix), or every second molecule is rotated by R with respect to the first molecule (forming an alternating chain). The model Hamiltonian for the excited state of such an aggregate is constructed like those used previously in the
10092 J. Phys. Chem. B, Vol. 111, No. 34, 2007
Zapotoczny et al. TABLE 2: Parametrization
Figure 7. Model aggregates: (a) alternating chain; (b) helix. The r denotes the intermolecular distance, and R is the angle between long axes of the neighboring molecules.
calculations for polyacene crystals.49 It approximates the manyelectron Hamiltonian of the aggregate correct to the terms linear in the nearest-neighbor intermolecular overlap integrals. The basis set consists of (a) 3N Frenkel states located at N molecules (3 states per molecule) and (b) 2N - 2 charge-transfer states with the hole and electron residing at the nearest neighbors. In this basis set, the model Hamiltonian for the excited states reads
H ) HF + HCT + HF-CT HF )
+ + EiFi,n Fi,n + ∑ (JijFi,n Fj,n+1 + h.c.) ∑ i,n i,j,n
HCT ) HF-CT )
(3)
where the summation runs over i, j )1, 2, 3 and n ) 1, ..., N. + The operator Fi,n (i ) 1, 2, 3) creates one of the three types of Frenkel excitons located at the nth molecule, and C+ n,m creates a CT exciton with a hole located at the nth molecule and the electron located at the mth molecule. E1, E2, E3, and ECT stand for the diagonal energies of the localized Frenkel and CT * * excitons. Jij ) 〈Ai,n|H|A ( j,n1〉 are Frenkel exciton resonance * * + integrals (Jij ) Jji), De,i ) 〈Ai,n|H|Ai,n Ai,n(1〉, and Dh,i ) 〈Ai,n|H| + Ai,n Ai,n(1〉 denote the dissociation integrals governing the transfer of the electron or the hole, respectively. The model Hamiltonian is parametrized as described below; subsequently, it is numerically diagonalized to obtain the eigenvectors and eigenenergies of the aggregate, from which the absorption spectrum is calculated. 2.2. Parametrization. The energies (E1, E2, E3) and transition dipole moments (µ1, µ2, µ3) of the localized Frenkel excitons are taken from the gas-phase absorption spectrum of naphthalene.50 The Frenkel exciton resonance integrals are estimated within the dipole approximation
Jij )
b µ i‚µ bj r3
value
E1 µ1 E2 µ2 E3 µ3 I-A 2P De(5Å) ξe Dh(5Å) ξh
32000 cm-1a 0.076 eÅa,b 35900 cm-1a 0.507 eÅa,c 47500 cm-1a 1.588 eÅa,b 67272 cm-1d -20485 cm-1e 2.18f 170 cm-1g 0.9429 Å-1d 140 cm-1g 3.0882 Å-1d
a From ref 50. b Polarized along the long molecular axis. c Polarized along the short molecular axis. d From ref 52. e From ref 46. f Evaluated using eq 3 by fitting the energy to the (1/2, 1/2, 0) CT state of the naphthalene crystal for r ) 5 Å (the energy of the CT state was taken from ref 46). g From refs 51, 53, and 54.
interaction disappears because of the assumed geometry of the aggregates). In view of the unfavorable convergence properties of the multipole series, this approximation is admittedly poor, but the closed analytic expression it offers for the distance dependence is a crucial advantage for our present purposes. The CT exciton energies for a given intermolecular distance r are calculated using the formula
ECT(r) ) I - A + 2P -
+ + ∑n ECT(Cn,n + 1Cn,n+1 + Cn+1,nCn+1,n)
+ + [De,i(Cn,n+1 Fi,n + Cn,n-1 Fi,n) + h.c.] + ∑ i,n + + [Dh,i(Cn+1,n Fi,n + Cn-1,n Fi,n) + h.c.] ∑ i,n
parameter
(4)
where i, j ) 1, 2, 3; b µi denotes the transition dipole moment to the ith Frenkel state, and r is the distance between naphthalene molecules (the term -3(µ bi‚r b)(µ bj‚r b)/r5 of the dipole-dipole
e2 r
(5)
where I and A denote the ionization potential and electron affinity of the naphthalene molecule, respectively, 2P is the polarization energy due to a pair of infinitely distant charges, and -e2/(r) is the screened electrostatic interaction of the two charges separated by distance r ( denoting the dielectric constant). The dissociation integrals are assumed to decrease exponentially with increasing intermolecular distance51
Ds(r) ) Ds(r0)eξs(r0-r)
(6)
where s stands for e or h and Ds(r0) is the dissociation integral evaluated for the reference distance r0. For the sake of simplicity, we assume that all electron-transfer integrals are equal and all hole-transfer integrals are equal. The parameters appearing in eqs 5 and 6 are adopted from literature data pertaining to the lowest CT exciton in the naphthalene crystal, with the electron and hole located at the (relative) crystallographic positions (1/2, (1/2, 0). The distance between the centers of these molecules is r0 ) 5 Å. The ionization potential and electron affinity of the molecule are taken from DFT calculations.52 The polarization energy and the net Coulombic stabilization energy follow from the classic microelectrostatic calculations;46 the effective dielectric constant has been evaluated using eq 5 to fit the energy (36 090 cm-1)46 of the lowest (1/2, 1/2, 0) CT state of the naphthalene crystal for r ) 5 Å. The dissociation integrals are known from classic literature.53 As the signs of the CT integrals depend on the relative phase of the orbitals of different molecules, which has to be arbitrarily defined, it is chosen in such a way as to make both integrals positive. The exponents ξ, needed in the calculations51 of the pressure dependence of the naphthalene absorption spectrum, were obtained in the past by fitting the values of the CT integrals at different intermolecular distances.54
Aggregates of Naphthalene Chromophores
Figure 8. Calculated absorption spectra of naphthalene aggregates consisting of N molecules.
All parameters are listed in Table 2. On the basis of the Hamiltonian and the parameters described above, we have calculated the absorption spectra for a series of aggregates (from the dimer to the pentamer), assuming different angles between the long axes of the neighboring molecules (both in the helix and alternating chain geometry), and for the intermolecular distances ranging from 3 to 5 Å. For intermolecular spacing smaller than 4 Å, the lowest eigenvalues stretch far below the lowest excited state of the isolated molecule. The effect is most pronounced for R ) 0 since, for this angle, the dipolar interaction is maximized. Starting from the trimer case, for the distances between 3.8 and 3.9 Å, the energies are just in the range where the new states have been experimentally detected (see Figure 6, the spectrum in water). This is shown in Figure 8 for r ) 3.9 Å, R ) 0°. At this distance, the diagonal energy of the CT state is 33 317 cm-1, much lower than that in the crystal (36 090 cm-1) and very close to the diagonal energy of the lowest intramolecular exciton (the absorption origin in Np is about 32 000 cm-1), and the dissociation integrals, quite large at this close range (De ) 480 cm-1 and Dh ) 4182 cm-1), induce substantial mixing. The resonance integrals that give rise to Davydov splittings are too small, compared to the respective energy gaps, to change this situation to a considerable extent (J11 ) 11 cm-1, J22 ) 503 cm-1, J33 ) 4931 cm-1), and those mediating the interaction between different Frenkel states are still less important (J13 ) 236 cm-1), with J12 and J23 vanishing for R ) 0° because the corresponding transition dipoles are perpendicular to each other. For these input data, the lowest eigenstate is predicted to be pretty intense, with an oscillator strength of about 0.1. Population analysis indicates that the lowest levels are mostly of CT parentage (over 50%) but also with substantial contributions from the first (30-35%) and second (10-15%) intramolecular excited states. Although the admixture of the third Frenkel exciton is rather small (2-4%), it accounts for a substantial part of the intensity; this coupling also contributes several hundred wavenumbers to the overall red shift. Prior to their interaction with intramolecular excitations, for this intermolecular spacing, the CT states are located at about 33 000 cm-1. Most of their subsequent red shift is due to the off-diagonal CT interaction with S1 and S2, mediated by the dissociation integrals which are substantially increased, owing to the reduced intermolecular distance. Apparently, the stabilization of the low-energy eigenstates of the aggregate has a similar provenance as that in the excimers, where the mixing between the exciton-resonance and charge-resonance contributions is an important stabilizing factor. In the aggregates under consider-
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10093 ation (N > 2), the effect is strengthened by the cumulative interaction of the (-+) and (+-) CT configurations sharing the common central cation or anion. Overall, our estimates suggest that a cluster of several closely packed naphthalene chromophores should indeed exhibit a set of optical transitions at very low energies. The large stabilization of the corresponding levels of predominantly CT origin is a concerted effect of Coulombic stabilization and off-diagonal CT coupling with the intrachromophore excited states. The intensity borrowing from S3, mediated by intermolecular interactions, accounts for the fact that the aggregate emission dominates over the contribution from naphthalene monomers, where the electronic transition is symmetry-forbidden (in fact, very weak in absorption). The real system should be represented as an ensemble of aggregates containing different numbers of chromophore molecules and characterized by different intermolecular distances, with different angles between the molecular axes. The resultant spectrum of energy levels would then be continuous, with maxima corresponding to the most probable local geometries. Admittedly, the stack structure with parallel transition dipole moments, used as a model in our calculations, yields an especially large stabilization energy for a given intermolecular spacing. However, the assumed spacing of about 3.9 Å is still on the large side of the range accepted as typical for excimers (3.5-4 Å). Accordingly, an intermolecular distance smaller by 0.1-0.2 Å would be equally reasonable physically and, at the same time, would guarantee sufficiently large stabilization energies. Although, in view of the model character of our approach, considerable caution should be exercised in interpreting the precise energies, the results do reproduce the doublet structure in the range of 22 000-25 000 cm-1, prominent in the synchronous spectrum of the polymer in water (compare Figures 6 and 8). On the basis of the calculations, the higher-energy peak (at about 25 000 cm-1 in the experimental spectrum) may be attributed primarily to naphthalene dimers (with some contribution from larger aggregates located in less densely packed regions where the stabilization is smaller), while the low-energy maximum (at about 22 500 cm-1) is evidently due to the aggregates containing three or more Np chromophores. The seemingly quantitative agreement of the theoretical results with experiment should be taken with a grain of salt since the parameters used in the present model are mostly guesstimated rather than really evaluated. However, their order of magnitude has pretty good support from the past successful interpretation of independent experimental results so that at least the ensuing qualitative picture is expected to be correct. By and large, the occurrence of chromophore aggregates in congested regions in the bulk of the pseudomicelles seems intuitively plausible, and we believe that the above theoretical results lend additional credence to this hypothesis. Conclusions Our present study suggests that in the pseudomicelles of the new amphiphilic grafted copolymer, PVA-graft-PVNp, the naphthalene chromophores tend to form clusters. The aggregation hypothesis affords a consistent explanation of the results obtained by using several complementary experimental techniques and seems physically justified. It agrees with the common wisdom that the aqueous environment squeezes the (essentially hydrophobic) macromolecule into a more or less random coil. It also seems reasonable that within such polymeric domains, the chromophore molecules may be
10094 J. Phys. Chem. B, Vol. 111, No. 34, 2007 very densely packed; in this confinement, close contact between some of them seems statistically inevitable. Under these conditions, excimer fluorescence is unlikely to occur since the surrounding polymer matrix prevents any substantial displacement of the chromophores upon excitation and de-excitation. On the other hand, their spatial proximity results in enhanced interaction, stabilizing the CT configurations and mixing them with several low-energy intramolecular excitations. In consequence, the observed fluorescence spectra exhibit an enormous red shift. The increased fluorescence contribution from the aggregates is due to the admixture of the higher (optically allowed) excitations of the naphthalene molecule to the cluster emitting state; in addition, the stabilization of this state provides an energy gradient, which promotes the funneling of excitation energy to higher-order aggregates, gradually quenching the emission of Np monomers and smaller aggregates. Acknowledgment. M.N. would like to express her gratitude to the late Professor James E. Guillet (Department of Chemistry, University of Toronto, Canada) for his constant encouragement and scientific guidance. We would also like to take this opportunity to acknowledge Professor Guillet’s generous gift of a comprehensive book and journal collection, as well as his donation of several pieces of valuable scientific instrumentation; the latter made the experimental part of this paper possible. Financial support from Fundusz im. Stanisława Estreichera to A.S. is gratefully acknowledged. Ms. Susan Arbuckle (Department of Chemistry, University of Toronto, Canada) is kindly acknowledged for her invaluable managerial and technical assistance. References and Notes (1) von Berlepsch, H.; Bo¨ttcher, C.; Da¨hne, L. J. Phys. Chem. B 2000, 104, 8792. (2) Akins, D. L.; Zhu, H.-R.; Guo, C. J. Phys. Chem. 1996, 100, 5420. (3) Spano, F. C.; Kuklinski, J. R.; Mukamel, S. Phys. ReV. Lett. 1990, 65, 211. (4) Siddiqui, S.; Spano, F. C. Chem. Phys. Lett. 1999, 308, 99. (5) Didraga, C.; Malyshev, V. A.; Knoester, J. J. Phys. Chem. B 2006, 110, 18818. (6) Scholes, G. D. Annu. ReV. Phys. Chem. 2003, 54, 57. (7) Harrison, W. J.; Mateer, D. L.; Tiddy, G. J. T. J. Phys. Chem. 1996, 100, 2310. (8) Da¨hne, S. Photogr. Sci. Eng. 1979, 23, 219. (9) Wanabe, T.; Zhou, H. S.; Honma, I.; Asai, K.; Ishigure, K. J. SolGel. Sci. Technol. 2000, 19, 257. (10) Spano, F. C.; Mukamel, S. Phys. ReV. A 1989, 40, 5783. (11) Furuki, M.; Wada, O.; Sun Pu, L.; Sato, Y.; Kawashima, H.; Tani, T. J. Phys. Chem. B 1999, 103, 7607. (12) Kirstein, S.; Da¨hne, S. Int. J. Photoenergy 2006, 20363. (13) Dai, Z.; Da¨hne, L.; Donath, E.; Mo¨hwald, H. J. Phys. Chem. B 2002, 106, 11501. (14) Hasobe, T.; Imahori, H.; Fukuzumi, S.; Kamat, P. V. J. Mater. Chem. 2003, 13, 2515. (15) Nasr, C.; Liu, D.; Hotchandai, S.; Kamat, P. V. J. Phys. Chem. 1996, 100, 11054. (16) Kamat, P. V.; Barazzouk, S.; Thomas, K. G.; Hotchandani, S. J. Phys. Chem. B 2000, 104, 4014.
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