Multipolar Contributions to the Second Harmonic Response from

Jan 29, 2008 - Guillaume Bachelier, Christian Jonin, and Pierre-Franc¸ois Brevet*. Laboratoire de Spectrome´trie Ionique et Mole´culaire, UMR CNRS ...
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J. Phys. Chem. C 2008, 112, 2716-2723

Multipolar Contributions to the Second Harmonic Response from Mixed DiA-SDS Molecular Aggregates Guillaume Revillod, Julien Duboisset, Isabelle Russier-Antoine, Emmanuel Benichou, Guillaume Bachelier, Christian Jonin, and Pierre-Franc¸ ois Brevet* Laboratoire de Spectrome´ trie Ionique et Mole´ culaire, UMR CNRS 5579, UniVersite´ Claude Bernard Lyon 1, Baˆ timent Alfred Kastler, 43 BouleVard du 11 NoVembre 1918, 69622 Villeurbanne Cedex, France ReceiVed: July 11, 2007; In Final Form: September 26, 2007

Polarization-resolved hyper-Rayleigh scattering experiments are reported for mixed suspensions of a constant concentration of 4-(4-dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA), a cationic amphiphilic compound with a strong quadratic hyperpolarizability, and varying concentrations of sodium dodecyl sulfate (SDS), an anionic surfactant with a vanishing quadratic hyperpolarizability. It is observed that the electric dipole contribution of the HRS signal intensity attributed to the free DiA molecules in the solution decreases with an increasing concentration of SDS whereas the electric quadrupole contribution increases simultaneously. These changes are direct indicators of the molecular changes undergone in the solution, and in particular the appearance of centrosymmetric mixed DiA-SDS micelles. A detailed analysis of the HRS signal intensity is performed, allowing the monitoring of the evolution of the organization of these mixed molecular systems. These experimental results are described within a general model based on the centrosymmetrical spatial organization of the DiA probe compounds in the micelles. These results underline the potential use of polarization-resolved hyper-Rayleigh scattering as a noninvasive technique to investigate the molecular organization at the nanometer scale in liquid suspensions.

Introduction Molecular aggregates constitute the building blocks of elaborated architectures in nature. For instance, they may be found in material science for the elaboration of hybrid metalorganic structures or in biomaterials such as vesicles. The organization of the molecules at the microscopic level is central in these fields because it defines the properties and functions of these assemblies. Hence, the development of new techniques to investigate this molecular arrangement in small structures is always welcome but is often hindered by the dimensions of the structures, the size of which is often much smaller than the wavelength of light. Optical techniques are therefore of limited use because of diffraction. Nonlinear optical techniques, as opposed to linear optical techniques, are similarly subjected to diffraction but nevertheless present some advantages when the coherent nature of the response is taken into account. Indeed, when nonlinear optical sources are strongly correlated within a defined volume, the overall response from the volume is markedly different from that of the mere superposition of the response of noncorrelated sources. This argument is often introduced for the process of second harmonic generation whereby two photons at the fundamental frequency are converted into one photon at the harmonic frequency.1 For a random orientational or a centrosymmetrical distribution of the nonlinear sources within a volume much smaller than the wavelength of light, the response at the harmonic frequency vanishes altogether, whereas it does not if the distribution is noncentrosymmetrical. The organization in small molecular aggregates has been probed by the technique of hyper-Rayleigh scattering (HRS) to investigate this question more thoroughly. The first use of HRS has * Corresponding author. Tel : +33 (0) 472 445 873. Fax : +33 (0) 472 445 871. E-mail : [email protected].

been reported initially by R.W. Terhune et al.2 and discussed thoroughly by P.D Maker, S.J. Cyvin et al., and R. Besohn et al.3-5 Since the pioneering work of A. Persoons and his collaborators,6,7 it has been used extensively to characterize the quadratic hyperpolarizability of molecular compounds.8-10 To some extent, it has often replaced the technique of electric field induced second harmonic generation (EFISHG), a technique with some limitations such as the inability to characterize nonpolar and ionic compounds.11,12 The HRS technique has thus participated in the development of the field of molecular engineering and the design of new compounds with large quadratic hyperpolarizabilities. More elaborate structures such as liposomes and metallic particles have also been investigated with this technique.13-16 In both cases, the role of phase retardation in the electromagnetic fields had to be introduced to correctly describe the response at the harmonic frequency and solve the question of the origin of the response.17 In this work, we report the investigation of the HRS response from mixed water-methanol suspensions of 4-(4-dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA), a cationic amphiphilic probe molecule with a strong quadratic hyperpolarizability, in the presence of the anionic co-surfactant sodium dodecyl sulfate (SDS). The latter compound has a vanishing hyperpolarizability as verified experimentally. The HRS response of DiA in a pure methanol and a mixed water-methanol solution in the absence of SDS is first presented in order to investigate the formation of molecular assemblies and the consequences on the HRS intensity patterns recorded when rotating the polarization state of the fundamental incoming beam with a fixed polarization state for the harmonic scattered wave. Then the results obtained for mixed water-methanol suspensions of DiA and SDS are discussed as a function of the increasing concentration of SDS. This discussion is supported

10.1021/jp0754132 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/29/2008

Mixed DiA-SDS Molecular Aggregates

Figure 1. (a) DiA compound, (b) UV-visible absorbance spectrum of a pure methanol solution of DiA.

by a theoretical model describing the competition between the dipolar and the quadrupolar contributions. In this section, a phenomenological parameter introduced in the model to quantify the ratio between the dipolar and the quadrupolar contributions is determined from the experimental data, yielding a complete and quantitative molecular picture of the system under study. Experimental Section Optics. HRS measurements were performed with a femtosecond Ti-sapphire oscillator laser source delivering pulses with 180 fs duration at a repetition rate of 76 MHz. The fundamental wavelength was set at 800 nm, and the average power at the laser exit was about 500 mW. The incident beam was focused into a sample cell consisting of a standard spectrophotometric cell with quartz windows through a microscope objective (X10, NA ) 0.32). The incident beam was linearly polarized, and the angle of polarization γ was controlled with a half wave plate. For vertically polarized light γ ) 0 (a polarization state also noted v), whereas for horizontally polarized light γ ) π/2 (a polarization state also noted h). The HRS intensity was collected at a right angle from the incident direction through a fused silica lens with a 5 cm focal length and sent to a monochromator coupled to a cooled photomultiplier tube working in a gated photon counting regime. Owing to the low light level, the beam was chopped and the HRS intensity was corrected for the noise signal collected when the beam was blocked. The scattered harmonic light polarization state was selected with an analyzer. For the analyzer set vertically the angle of polarization Γ ) 0 (a polarization state also noted V) was selected, whereas for the analyzer set horizontally the angle of polarization Γ ) π/2 (a polarization state also noted H) was selected. Color filters were used to remove any unwanted harmonic light before the cell and fundamental light after the cell. The laser power was monitored continuously to account for intensity fluctuations. Chemistry. The probe molecular compound used in these experiments was 4-(4-dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA, Fluo Probes Inc., reference FP66096), a dipolar push-pull type amphiphilic compound, see Figure 1a. The wavelength of the maximum of the one photon absorption band for DiA dispersed in a 5:1 v/v water/methanol mixture is located around 480 nm, and therefore in the present experiments the harmonic wavelength fixed at 400 nm was partially resonant with this transition, see Figure 1b. Millipore water (resistivity 18 MΩ‚cm-1) was used throughout. Analytical-grade methanol and SDS were purchased and used as received.

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2717

Figure 2. HRS intensity collected as a function of the DiA concentration in pure methanol. The signal intensity is corrected for selfabsorption at the harmonic wavelength and normalized with that of the pure methanol solution in the absence of DiA.

Results and Discussion DiA Dispersed in Pure Methanol. In a first step, the nonlinear optical chromophore DiA was investigated in a pure methanol solution as a function of its concentration, see Figure 2. The HRS intensity collected in the absence of analyzer for the incoming fundamental beam vertically polarized is reported as a function of the DiA concentration. The HRS intensity I(Ω) is a linear function of the DiA chromophore concentration and is given by6

I(Ω) ) G〈NSβS2 + Nβ2〉I02

(1)

where NS, N and βS, β are the number densities and the quadratic hyperpolarizabilities of the solvent molecules of methanol and DiA, respectively, and I0 is the fundamental intensity. Subsequently, all reported HRS intensities have been corrected for the self-absorption of the solution at the harmonic frequency because the UV-visible spectrum of the solution exhibits a weak absorption at the harmonic wavelength. No absorption at the fundamental frequency occurs. Using the internal reference method and knowing the quadratic hyperpolarizability of methanol, namely βMeOH ) 0.69 × 10-30 esu,6 we found the quadratic hyperpolarizability of DiA at 800 nm to be βDiA )

(1760 ( 53) × 10-30 esu where β ) x〈βXXX2〉+〈βZXX2〉, with the elements of the quadratic hyperpolarizability tensor given in the laboratory frame. It is emphasized here that experimentally any single point reported in Figure 2 entails the recording of the HRS intensity line as a function of the harmonic frequency in order to ensure that any background signal arising from multiphoton excited fluorescence is negligible. The magnitude of the quadratic hyperpolarizability of DiA is rather large but stems from the push-pull character of this molecular chromophore and the partial resonant character of the experiment performed here. No deviation from the square dependence of the HRS signal intensity with the fundamental laser power was observed. This value is of the same order of magnitude as that reported for another pyridinium dye, namely, di-8ANEPPS.18 The polar plot of the HRS intensity recorded as a function of the angle of polarization of the incoming fundamental beam is then reported in Figure 3a and b for a DiA concentration of 12.5 µM. The observed pattern clearly exhibits two lobes, as expected for the HRS response of a suspension of well-dispersed molecules collected at a right angle for the harmonic light

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Revillod et al.

Figure 3. Polar plots of the HRS intensity of a 12.5 µM concentration of DiA dispersed in pure methanol recorded as a function of the incoming polarization angle for the harmonic light (a) vertically polarized and (b) horizontally polarized.

vertically polarized.19 Also, a constant HRS intensity as a function of the incident wave polarization angle is collected for the harmonic light horizontally polarized. In Figure 3a and b is also reported a fit of the experimental points with the following theoretical expression:17,19

I(Ω)V ) aV cos4 γ + bV cos2 γ sin 2 γ + cV sin4 γ

(2)

The fitting procedure leads to the following parameters: aV ) 0.79 and cV ) 0.20, normalizing the third coefficient to unity, namely, bV ) 1, because the absolute intensity is arbitrary. The condition bV ) aV + cV is clearly fulfilled within the experimental error of about 5% on the intensities. Similarly, the pattern obtained for the harmonic light horizontally polarized is a circle of radius c H ) 0.20, as expected because the condition bH ) 2aH ) 2cH must be fulfilled. Hence, the relationship cV ) cH is also observed. All of these results are in perfect agreement of what is expected for a liquid suspension of a dipolar compound.20 Furthermore, the depolarization ratio D ) cV/aV was found to be equal to D ) 0.25 ( 0.02. This experimental value is close to the theoretical value of 0.2 expected for perfect dipolar compounds like rod-like pushpull molecules but still deviates from it significantly. There are two reasons for it. First, the HRS intensity of the bare solvent should be subtracted to get the true depolarization factor of DiA. This is required because the contribution from the bare solvent is not totally negligible at the concentration of DiA used here. The DiA concentration is indeed rather small, namely, only 12.5 µM. Note also that a bare solvent methanol cell also yields a two-lobe pattern in similar experimental conditions with the equality bV ) aV + cV fulfilled. Second, the experiment is performed in resonant conditions for the harmonic wavelength as seen from the UV-visible absorption spectrum of Figure 1b. Hence, the dominant tensor element of the molecular quadratic hyperpolarizability tensor for the rod-like compound DiA is indeed βzzz, where the Oz axis is taken along the molecular axis, but the contribution from other elements of the tensor cannot be neglected, in particular that of the element βzxx.4,5 DiA Dispersed in a Methanol/Water Mixture. To induce the formation of molecular aggregates, DiA was dispersed in a mixture of water and methanol.20 Owing to the molecular structure of DiA, see Figure 1a, in particular owing the presence

Figure 4. Polar plots of the HRS intensity of a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture recorded as a function of the incoming polarization angle for the harmonic light vertically polarized.

of the two long alkyl chains on one side of the aromatic rings, the nonlinear optical chromophore DiA is not soluble in pure aqueous solutions, at least up to concentrations where its HRS intensity can be detected. Hence, a 5:1 mixture in volume of water and methanol was prepared and in Figure 4 is reported the polar plot of the HRS intensity as a function of the angle of polarization of the fundamental beam for a DiA concentration of 12.5 µM. The HRS intensity is vertically polarized. The pattern observed is still dominated by two lobes and fitted with the theoretical expression given in eq 2. However, the condition bV ) aV + cV is no longer fulfilled. Indeed, the fitting procedure leads to the following parameters: aV ) 0.46 and cV ) 0.13 with bV ) 1 for normalization. The deviation from the previous case of DiA dispersed in pure methanol is in fact clearly visible on the polar plot through the emergence of a four-lobe pattern with the splitting of the two main lobes into two sub-lobes. From this polar plot and the breaking of the equality between bV and aV + cV, it is inferred that a significant quadrupolar contribution

Mixed DiA-SDS Molecular Aggregates is now present in the HRS intensity response. This assumption is supported by the model discussed below. It is therefore concluded that a significant number of DiA molecules have aggregated. Considering the amphiphilic character of the DiA molecule, it is also highly likely that these aggregates have a rather centrosymmetrical micelle-like organization with the polar head pointing outward in the solvent and the hydrophobic alkyl chains pointing toward the inside of the aggregate, a molecular structure yielding a pure quadrupolar response. In principle, this organization in the solution is not the only possibility. The data are indeed compatible with a suspension of aggregates only, the structure of which is both dipolar and quadrupolar but with a noncentrosymmetrical structure yielding a strong quadrupolar contribution, not a purely dipolar response. Such an organization is rather unlikely because of the usual behavior of such amphiphilic compounds to form micelles in water-rich solvents. The suspension is therefore rather a mixture of micelles and free molecules. One of the conclusions of this experiment is hence that the critical micelle concentration (CMC) of DiA dispersed in a 5:1 v/v water-methanol solution is smaller than 12.5 µM. Such an experiment where the HRS intensity vertically polarized is recorded as a function of the input polarization angle is therefore an excellent method to observe the onset of the formation of micelles. A more detailed account of this method will be discussed in a future work, but the use of polarization patterns of the HRS intensity yields more information than the recording of the HRS intensity only.21 In general, the dipolar contribution dominates the HRS response. Indeed, the quadrupolar contribution needs to be considered when the dipolar contribution vanishes or if the characteristic dimensions of the source of the optical nonlinearity are not negligible before the wavelength of light. For instance, this is the case for large spherical particles coated with a monolayer of chromophores where the dipolar contribution vanishes altogether owing to the centrosymmetry of the assembly22 or for rather large metallic particles.17 In the former case, it can be shown that the HRS intensity is purely quadrupolar and scales with the third power of the parameter a/λ where a is the radius of the particle and λ is the fundamental wavelength. The HRS intensity collected as a function of the angle of polarization of the fundamental wave is still described with eq 2 albeit with different conditions on the parameters. For the pure quadrupolar response of a spherical aggregate, the calculation leads to aV ) cV ) 0 and bV * 0.23 Hence, in the presence of two components in the solution, on one hand molecules with a pure dipolar contribution and on the other hand aggregates with a pure quadrupolar response, the HRS intensity is still described by eq 2 but the condition bV ) aV + cV is no longer fulfilled. In fact, the three parameters may be recast as sums of the dipolar and quadrupolar parameters, namely, aV ) aVdip + aVquad and similarly for bV and cV. Then, the equality becomes simply bVdip ) aVdip + cVdip. As said above, for the pure quadrupolar response of a spherical aggregate, aVquad ) cVquad ) 0. This equality is valid in all cases because it only concerns the dipolar contribution. It is interesting then to weight the dipolar and the quadrupolar contributions. In principle, the response from these two contributions may also embed possible interferences between the dipolar and quadrupolar response.24 Such an entanglement would also prevent the splitting between the dipolar and quadrupolar contributions as performed above because the parameters aV, bV, and cV are related to intensities. More precisely, these parameters are related to the HRS intensity V V (γ ) 0°), bV ) 4IHRS (γ ) 45°) - (aV + cV) through aV ) IHRS V and cV ) IHRS(γ ) 90°). The experimental arrangement with

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2719 the detection direction at a right angle from the direction of propagation of the incoming fundamental beam is of real advantage here because the interference contribution vanishes altogether.24 Furthermore, for purely real or purely imaginary hyperpolarizabilities, no interference occurs. It is therefore possible to introduce the weighting parameter η as

η)

a V + cV bV

(3)

This parameter η then yields the weight of the dipolar contribution with respect to the sum of the dipolar and the quadrupolar contribution. A value of η ) 1 is obtained for a pure dipolar response, whereas a value of η ) 0 is obtained for a pure quadrupolar one. In the present experimental case of DiA dispersed in the 5:1 v/v water-methanol solvent mixture, the value of the parameter determined from the pattern of Figure 4 is η ) 0.59 indicating that the HRS intensity has a 59% dipolar character and 41% quadrupolar character. Because there are only two species in the solution, namely, the free DiA molecules with a pure dipolar contribution and DiA micelles with a pure quadrupolar contribution, one can also conclude that the HRS intensity weight of the micelle contribution is 41%. As will be further discussed below, this weight does not yield the concentration of micelles because the micelle intensity is the product of the number of micelles and the HRS response from a single micelle. It is interesting to note at this stage of the work that several molecular structures may lead to the same value of the parameter η. Hence, the exact arrangement of the DiA molecules in the micelles cannot be determined unambiguously. For example, the structure could be that of a random molecular arrangement or that of molecules arranged regularly at the surface of a sphere. Because of the amphiphilic character of the DiA molecule, the likely organization is that of micellelike structures with the positively charged head groups pointing outward into the water-rich solvent and the hydrophobic part oriented inward into the inside of the micelles. Mixed DiA-SDS Micelles: Low Concentrations of SDS. To further induce the formation of molecular aggregates, we introduced the surfactant SDS into the solution for a fixed concentration of DiA of 12.5 µM. Although DiA is a cationic amphiphilic compound, SDS is an anionic and amphiphilic compound, and for both reasons it is expected that in the 5:1 water/methanol mixture SDS and DiA will form mixed aggregates. UV-visible photoabsorption spectroscopy experiments indeed confirm that aggregation is occurring through small changes in the spectra, see Figure 5, but it is difficult to describe the aggregates at the molecular level, in particular if the aggregates incorporate one or more DiA moelcules. Furthermore, from measurements performed over a large range of SDS concentrations, no HRS signal was collected from pure SDS solutions. Hence, in the remainder of the work, it is assumed that the HRS intensity detected arises solely from the DiA chromophore. The polar plots of the HRS intensity as a function of the angle of polarization of the fundamental wave were therefore recorded for different concentrations of SDS below 20 µM, a concentration on the order of the DiA concentration of 12.5 µM. The plots obtained for the SDS concentration of 5 and 20 µM are given in Figure 6, and the η parameter extracted from these two plots reported in Figure 7 along with similar measurements performed for other SDS concentrations. The polar plot of Figure 6 exhibits a clear four-lobe pattern although the fourfold symmetry is not perfect. Such a perfect four-lobe pattern is only expected for a pure quadrupolar contribution polar

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Figure 5. UV-visible absorption spectra of mixed solution of DiA and SDS in a 5:1 v/v water-methanol mixture as a function of SDS concentration. (Solid) lower set: low SDS concentrations ranging from bottom to top between 1 and 20 µM, higher set: high SDS concentrations ranging from bottom to top between 1 and 13 mM. (Dashed) no SDS present in mixture.

plot. The parameter calculated for the 5 µM plot is η ) 0.30, indicating a significant drop of the weight of the dipolar contribution as compared to the initial plot recorded in absence of the co-surfactant SDS. For the 20 µM SDS concentration plot, the parameter η is down to η ) 0.14. In the latter case, the weight of the dipolar contribution to the total HRS intensity response is 14%. Within the picture of a mixture of free DiA chromophores with a pure dipolar response and mixed DiASDS micelle-like aggregates, the regular decrease of the η parameter is interpreted as the increase of the weight of the quadrupolar contribution of the micelles. More complicated pictures would also be in agreement with these data. For instance, species having both a dipolar and a quadrupolar contribution could be present in the liquid phase. Nevertheless, the analysis would not be different in the sense that the weighting parameter relates to the dipolar and quadrupolar contributions relative weight only and not to the species relative population weight. A more refined analysis of the quadrupolar contribution is necessary to determine if this increased weight has to be attributed to an increase of the number of micelles or to an increased HRS response from each single micelle as they incorporate more SDS without any change of their number densities. Note that it is assumed that the dipolar contribution from the free DiA molecules remains unchanged upon addition of SDS, in line with the negligible changes observed in the UVvisible absorption spectra of the solutions (not shown). It is compulsory to plot the graphs of the different parameters aV, bV, and cV as a function of the SDS concentration in order to answer the question in detail; see Figures 8 and 9. As established above, parameters aV and cV have a purely dipolar character whereas bV has a mixed dipolar and quadrupolar character. Coefficients aV and cV present a similar behavior with a small decrease with the initial addition of SDS followed by a more or less constant behavior within the experimental errors. Because aVquad ) cVquad ) 0, this indicates that the dipolar contribution initially decreases and then stabilizes at a more or less constant value. Assuming that the quadratic hyperpolarizability of DiA remains unaffected by the introduction of SDS into the solution; this may be understood as a small decrease of the number of free DiA molecules. It is suggested therefore that free DiA molecules likely transfer into the micelle phase upon small additions of SDS before their concentration stabilizes at higher SDS concentrations. In Figure 9, the parameter bV is

Revillod et al. displayed. Its behavior for the first SDS addition exhibits a similar decreasing behavior, in line with the decrease of the dipolar contribution observed for aV and cV. This obviously assumes that at the first stages of the SDS addition the quadrupolar contribution change is rather weak. At higher concentrations of SDS, namely, above 1 µM, the parameter bV regularly increases. Because the purely dipolar parameters aV and cV are constant in this range of concentrations, it is concluded that the dipolar contribution bVdip to the parameter bV is also constant. This consequently also indicates that the quadrupolar contribution bVquad to the parameter bV increases. This increase is not linear and cannot therefore be attributed simply to an increase of the number of aggregates as the SDS concentration is increased. This can be demonstrated as follows. The quadrupolar contribution bVquad to the parameter bV may be calculated for a single spherical micelle of radius a containing m DiA molecules homogeneously distributed on its surface. Reducing the hyperpolarizability tensor of DiA to its dominant element βzzz along the molecular long axis for simplicity, one gets

bVquad ∝ qm2a2βzzz2

(4)

where q is the number of micelles in the sampled volume. The linear dependence of bVquad with the number of micelles stems from the incoherent nature of the HRS process, whereas the quadratic dependence with the number of DiA molecules per micelles and the radius of the micelles stems from the coherent response of the DiA molecules present into a single micelle. Again, it is assumed that the quadratic hyperpolarizability of DiA remains unaffected by SDS. It is also assumed that the dominant hyperpolarizability tensor element of DiA is βzzz only. The incorporation of DiA into the micelle could modify in principle the magnitude of this element. If the number of micelles linearly increases, then the number of DiA molecules per micelle will decrease as 1/q because the total DiA concentration is fixed. The number of free DiA molecules is also fixed after the initial drop of intensity. Hence, from eq 4, the overall quadrupolar contribution bVquad should decrease as 1/q. This is opposite to what is observed in Figure 9. It is thus inferred from eq 4 that the parameter bVquad can only increase through the increase of the radius of the micelles. This is a reasonable statement because the pure DiA micelles are positively charged, whereas SDS is negatively charged. Hence, at small concentrations of SDS, SDS is incorporated into the micelles and the radius of the micelles increases while the number of micelles remains constant. The increase of the radius a of the micelles with the SDS concentration saturates as seen from the data reported in Figure 8. This saturation of the increase of the quadrupolar contribution may arise from the exact molecular rearrangement of DiA and SDS within the micelle. It is to be noted though that as the SDS concentration increases the number of aggregates will eventually start to increase, leading to the dilution of the DiA compounds and the competition between the two trends, the growth of the micelles, and the dispersion of DiA between the micelles. Mixed DiA-SDS Aggregates: High Concentrations of SDS. At low SDS concentrations, the dominating effect to the purely quadrupolar contribution bVquad is the radius increase of the micelles. This effect dominates up to rather large SDS concentrations. Indeed, in Figure 10 is given the polar plot of the HRS intensity as a function of the angle of polarization of the fundamental wave observed at a concentration of SDS of 3 mM. This concentration is in large excess of that of DiA, which

Mixed DiA-SDS Molecular Aggregates

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2721

Figure 6. Polar plots of the HRS intensity of a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture recorded as a function of the incoming polarization angle for the harmonic light vertically polarized for (a) a 5 µM concentration of SDS and (b) 20 µM concentration of SDS.

Figure 7. Plot of the weighting parameter η as a function of the SDS concentration for a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture recorded as a function of the incoming polarization angle for the harmonic light vertically polarized.

Figure 9. Plot of the bV parameters as a function of the SDS concentration.

Figure 8. Plot of the aV and cV parameters as a function of the SDS concentration.

is only 12.5 µM and slightly below the SDS critical micellar concentration (CMC) in pure water, the value of which is about 8 mM. In the 5:1 v/v water-methanol mixture, this SDS CMC value is expected to be even larger. The plot is closer to the perfect fourfold pattern of the pure quadrupolar contribution than any other plots recorded. The parameter η calculated for this plot is only η ) 0.07, an overwhelming 93% from the quadrupolar contribution to the HRS intensity. At an even higher concentrations though, the polar plot starts to revert to the twofold pattern. Indeed, at an SDS concentration of 13 mM, see Figure 11, the polar plot exhibits an η parameter of η ) 0.26. This value indicates that the weight of the quadrupolar

Figure 10. Polar plots of the HRS intensity of a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture recorded as a function of the incoming polarization angle for the harmonic light vertically polarized for a 3 mM concentration of SDS.

contribution bVquad has decreased, amounting to 74% of the HRS response instead of the previous 93%. Hence, it is concluded that the weight of the dipolar contribution has started

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Revillod et al. Experimentally, the parameters aV and cV are fairly constant in this regime of high SDS concentrations, see Figure 12. In this Figure, the output of the HRS intensity is not polarized and therefore corresponds to the sum of aV and aH ) cV. This intensity sum is identical to the one obtained at smaller SDS concentrations, see Figure 8. Also, the initial intensity recorded in the absence of SDS is also given in order to observe the initial drop of intensity. The observation of a rather constant intensity in this range of large SDS concentrations suggests that the dilution effect of DiA in the mixed DiA-SDS micelles dominates over the loss of the centrosymmetry of the micelles. Conclusions

Figure 11. Polar plots of the HRS intensity of a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture recorded as a function of the incoming polarization angle for the harmonic light vertically polarized for a 13 mM concentration of SDS.

Figure 12. Plot of the HRS intensity for the fundamental light vertically polarized and the harmonic light unpolarized of a 12.5 µM concentration of DiA dispersed in a 5:1 v/v water-methanol mixture as a function of the SDS concentration. The initial point corresponds to the absence of SDS.

to recover from excessively small values. One reason for the decrease of the weight of the quadrupolar contribution is the dilution effect of DiA within the mixed DiA-SDS aggregates as 1/q, see eq 4. At high concentrations of SDS, these mixed micelles are obviously rather rich in SDS compounds but also numerous, and therefore DiA is extensively diluted in the mixed DiA-SDS micelles. It is important to note also that pure micelles of SDS would go undetected into this experiment owing to the vanishing quadratic hyperpolarizability of SDS. With the dispersion of DiA in the micelles, the weight of the dipolar contribution can start to increase because of the loss of the centrosymmetry of the DiA-SDS mixed aggregates. Because only the DiA chromophore is detected in the experiments, the number m of DiA molecules per micelle must be large enough to provide the centrosymmetry to the micelle. As this number decreases due to the increasing number of micelles, the centrosymmetry property of the micelles is lost, yielding an increase of the dipolar character of the micelles. In this regime, a competition occurs between the dipolar and the quadrupolar contributions to the HRS response for a single micelle.

In this work, it has been demonstrated that the HRS response from a liquid solution may contain both a dipolar and a quadrupolar contribution. The latter contribution to the HRS intensity can be clearly observed for molecular aggregates and may even dominate the dipolar response in some cases like that of centrosymmetrical aggregates like micelles. This result has been observed in the special case of a mixed surfactant system where only one chromophore has a non-vanishing quadratic hypeprolarizability. The second co-surfactant is silent from the point of view of the HRS process, but its action is observed through the modification of the response of the other chromophore through its organization. The choice of anionic SDS as compared to cationic DiA ensures that aggregation will indeed take place. The formation of these aggregates has been followed using polarization-resolved HRS measurements. A weighting parameter has been introduced to quantify the ratio between the dipolar and the quadrupolar contributions. The analysis is then rather simple for a two-component system where the first one has a pure dipolar response and the second one has a pure quadrupolar response, but it may be extended to more complicated systems at the cost of complexity. This work opens new possibilities to investigate molecular organization at small scales in liquid solutions using nonlinear optical methods. Acknowledgment. We acknowledge support from the French Minister of Research and Education and the CNRS for grant no. AC DRAB03/15. References and Notes (1) Shen, Y. R. In The Principles of Nonlinear Optics; Wiley, New York, 1984. (2) Terhune, R. W.; Maker, P. D.; Savage, C. M. Phys. ReV. Lett. 1965, 14, 681. (3) Maker, P. D. Phys. ReV. A 1970, 1, 923. (4) Cyvin, S. J.; Rausch, J. E.; Decius, J. C. J. Chem. Phys. 1965, 43, 4083. (5) Bersohn, R.; Pao, Y. H.; Frisch, H. L. J. Chem. Phys. 1966, 45, 3184. (6) Clays, K.; Persoons, A. Phys. ReV. Lett. 1991, 66, 2980. (7) Clays, K.; Persoons, A. ReV. Sci. Instrum. 1992, 63, 3285. (8) Zyss, J.; Ledoux, I. Chem. ReV. 1994, 94, 77. (9) Zyss, J.; Van, T. C.; Dhenaut, C.; Ledoux, I. Chem. Phys. 1993, 177, 281. (10) Oudar, J. L. J. Chem. Phys. 1977, 67, 446. (11) Ledoux, I.; Zyss, J. Chem. Phys. 1982, 73, 203. (12) Das, P. K. J. Phys. Chem. B 2006, 110, 7621. (13) Liu, Y.; Yan, E. C. Y.; Eisenthal, K. B. Biophys. J. 2001, 80, 1004. (14) Clays, K.; Hendrickx, E.; Triest, M.; Persoons, A. J. Mol. Liq. 1999, 67, 33. (15) Vance, F. W.; Lemon, B. I.; Hupp, J. T. J. Phys. Chem. B 1998, 102, 10091. (16) Galletto, P.; Brevet, P. F.; Girault, H. H.; Antoine, R.; Broyer, M. Chem. Commun. 1999, 581. (17) Nappa, J.; Revillod, G.; Russier-Antoine, I.; Jonin, Ch.; Benichou, E.; Brevet, P. F. Phys. ReV. B 2005, 71, 165407.

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