# Characterization of alumina surfaces by fluorescence spectroscopy: Part 2. Photophysics of a bound pyrene derivative as a probe of the spatial distribution of reactive hydroxyl groups

Rémi Métivier, Isabelle Leray, Jean-Pierre Lefèvre, Magalie Roy-Auberger, Nathalie Zanier-Szydlowski, Bernard Valeur

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Rémi Métivier, Isabelle Leray, Jean-Pierre Lefèvre, Magalie Roy-Auberger, Nathalie Zanier-Szydlowski, et al.. Characterization of alumina surfaces by fluorescence spectroscopy: Part 2. Photophysics of a bound pyrene derivative as a probe of the spatial distribution of reactive hydroxyl groups. Physical Chemistry Chemical Physics, 2003, 5 (4), pp.758-766. 10.1039/b209735d. hal-04407483

HAL Id: hal-04407483

https://hal.science/hal-04407483v1

Submitted on 20 Jan 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Characterization of Alumina Surfaces by Fluorescence Spectroscopy. Part 2. Photophysics of a Bound Pyrene Derivative as a Probe of the Spatial Distribution of Reactive Hydroxyl Groups

Rémi Métivier<sup>a</sup>, Isabelle Leray<sup>a</sup>, Jean-Pierre Lefèvre<sup>a,b</sup>, Magalie Roy-Auberger<sup>c</sup>, Nathalie Zanier-Szydlowski<sup>c</sup> and Bernard Valeur<sup>a,b*</sup>

<footnote><sup>a</sup> Ecole Normale Supérieure de Cachan Laboratoire de Photophysique et Photochimie Supramoléculaires et Macromoléculaires (CNRS UMR 8531), Département de Chimie, Ecole Normale Supérieure de Cachan, 61 avenue du Président Wilson, F-94235 Cachan cedex, France</footnote>

<footnote><sup>b</sup> Laboratoire de Chimie Générale, Conservatoire National des Arts et Métiers, 292 rue Saint-Martin, F-75141 Paris Cedex 03, France. E-mail: valeur@cnam.fr</footnote>

<footnote><sup>c</sup> Division Cinétique et Catalyse and Division Physique et Analyse, Institut Français du Pétrole, 1 et 4, avenue du Bois-Préau, F-92852 Rueil-Malmaison Cedex, France.</footnote>
**Abstract**

In order to characterize and compare the spatial distribution of hydroxyl groups on γ- and δ-alumina surfaces, a pyrene derivative was covalently grafted on these groups and studied by steady-state and time-resolved fluorescence spectroscopy. When the pyrene probes are close enough, they can form excimers with a characteristic emission band. The relative intensities of the monomer and excimer bands provide a global information on the proximity of pyrene probes, whereas time-resolved fluorescence experiments offer a more detailed characterization of the surface in terms of heterogeneity. The fluorescence decay curves were satisfactorily analyzed in terms of stretched exponentials that account for the distribution of decay times resulting from the distribution of distances between the pyrene probes that can form excimer, and the distributions of the energies of interaction between the alumina surface and the pyrene monomers or excimers. Comparison of samples having the same surface coverage of pyrene probes allowed us to conclude that there are indeed significant differences in the characteristics of γ- and δ-alumina surfaces. In particular, the reactive hydroxyl groups are not homogeneously distributed on alumina surfaces but they are rather clustered into regions of high density. The fraction of these reactive groups belonging to the clustered regions is more than four times larger for δ-alumina than for for γ-alumina.
# 1. Introduction

Characterization of the spatial distribution of hydroxyl groups on alumina surfaces is essential for the understanding of the properties of this material, especially its catalytic properties. A method of choice for such a characterization is the use of a fluorescent probe covalently linked to these hydroxyl groups and able to form excimers when the distance between the anchored probes is small enough. Excimer formation is a dynamic process and much information can be obtained from time-resolved fluorescence experiments.¹ Such a methodology has been already employed in the investigation of the organization of reactive sites on silica,² but to the best of our knowledge, no study of alumina surfaces in this way has been reported so far. Nevertheless, fluorescent probes adsorbed on alumina have been successfully studied by time-resolved fluorescence spectroscopy with the aim at monitoring reactive sites.³

In the preceding paper of this series, we described the synthesis of a new fluorescent probe containing a pyrene moiety linked to a triethoxysilane group (PPTEOS).⁴ This probe was

<figure><img src="image_3.png" /><figcaption>PPTEOS</figcaption></figure>

covalently grafted to the hydroxyl groups of γ- and δ-alumina samples that come from the same crystalline boehmite precursor. δ-Alumina was obtained from γ-alumina by a sintering process, i.e. condensation of the hydroxyl groups. The fluorescence spectra exhibited the characteristic emission band from excimers. From the fluorescence spectra and the surface concentration, it was possible to conclude that the γ-alumina surface contained more reactive hydroxyl groups than δ-alumina and that these groups were not homogenously distributed on
the surface. The relative proportions of hydroxyl groups in the regions of higher density
appeared to be dependent on the type of alumina. The hydroxyl groups were indeed found to
be more clustered on δ-alumina than on γ-alumina, which can be explained by the disparition
of zones with low density of hydroxyls during the sintering process.

It is the aim of the present paper to further characterize the distribution of reactive
hydroxyl groups on γ- and δ-alumina surfaces by means of time-resolved fluorescence
spectroscopy with data analysis in conjunction with the steady-state data.

**2. Experimental A. Synthesis and sample preparation**

Porous alumina $\gamma_c$-Al$_2$O$_3$ (Puralox SCFa-$\gamma$) and $\delta$-Al$_2$O$_3$ (Puralox SCFa-$\delta$) were obtained from CONDEA. The $\gamma_c$-Al$_2$O$_3$ alumina particles are 32 µm mean diameter with 60 Å mean pore diameter and a nitrogen BET surface area of 235 m$^2$/g. For $\delta$-Al$_2$O$_3$ obtained by sintering processes of $\gamma$-Al$_2$O$_3$, the average diameter of the particles is 48 µm, the mean pore diameter is 120 Å and the BET surface is 104 m$^2$/g. These two commercially available aluminas were dehydrated at 550 °C for 3h before grafting. The synthesis of the fluorescent probe PPTEOS and its reaction with alumina surface have been described in the preceding paper of this series.⁴ For each alumina ($\gamma_c$ and $\delta$), grafting was carried out at two different concentrations per unit surface which led to samples $\gamma$-1, $\gamma$-2 for $\gamma_c$-Al$_2$O$_3$ and $\delta$-1, $\delta$-2 for $\delta$-Al$_2$O$_3$. The amount of pyrene molecules bound to the surface was determined by elemental analysis of the carbon at the Institut de Chimie des Substances Naturelles (France). The values, expressed in molecule.nm$^{-2}$, are 0.1 ± 0.03, 0.23 ± 0.03, < 0.06, 0.07 ± 0.03 for the samples $\gamma$-1, $\gamma$-2, $\delta$-1, $\delta$-2.

Corrected emission spectra were obtained on a Spex Fluorolog 1681 spectrofluorometer.
Fluorescence intensity decays were obtained by the single-photon timing method with
picosecond laser excitation using a Spectra-Physics set-up composed of a Titanium-Saphir
Tsunami laser pumped by an argon ion laser, a pulse selector, and doubling (LBO) and tripling (BBO) crystals. Light pulses were selected by optoacoustic crystals at a repetition rate of 4MHz. Fluorescence photons were detected by a Hamamatsu MCP photomultiplier R3809U connected to a constant-fraction discriminator. The time-to-amplitude converter was purchased from Tennelec. In the present investigation, the channel width was 24 or 190 ps.

Fluorescence measurements were done in a 1cm quartz cuvette containing a magnetic stirred suspension of grafted alumina (1 mg) in 2.5 ml of solvent. Acetonitrile from Aldrich (spectrometric grade), tetrahydrofuran, hexane and ethanol from SDS company (spectrometric grade) were used as solvents for spectroscopic measurements. All experiments were carried out at room temperature.

### 3. Results and Discussion

Before describing the results, it should be recalled that the amount of excimers that can be formed - and consequently the excimer-to-monomer intensity ratio - depends on the lifetime of pyrene. Therefore, the results are different when degassing the solution or not because oxygen partially quenches the fluorescence of pyrene, and thus reduces the lifetime. Samples were not degassed in the present work because the high repetition rate of the laser pulses (in time-resolved fluorescence experiments) does not allow to record the fluorescence decay of samples with long lifetime like pyrene in degassed solutions. But this is not a problem at all because the lifetime of pyrene in the undegassed samples was long enough to observe efficient excimer formation, and in any case, the technique of fluorescence probing using excimer formation allows only comparative measurements.

#### A. Steady-state fluorescence spectra.
All emission spectra consist of a structured monomer emission band at 370 nm and a structureless excimer emission band around 480 nm. The emission spectra were recorded at various times after addition of the solvent to the alumina samples. Both monomer and excimer bands increased as a function of time while the excimer-to-monomer intensity ratio decreased.

As an illustration, Figure 1 shows the temporal evolution of the excimer-to-monomer intensity ratio for the sample γ-1 in acetonitrile. Since the alumina surface is expected to partially quench the fluorescence of adsorbed pyrene molecules,⁵ an overall increase of the fluorescence intensity with a decrease in excimer formation can be accounted for by desorption of the pyrene molecules. In fact, these effects are accompanied with a change in the relative intensities of the monomer vibronic bands (see inset of Figure 1) showing that the polarity of the microenvironment of pyrene decreases as a function of time which has been already observed in the case of pyrene immobilized⁶ or grafted on silica sol-gel.⁷ Such a desorption did not lead to a release of the grafted pyrene to the solvent bulk because less than 5 % of the total fluorescence intensity was observed in the solution after centrifugation. We can thus conclude that the pyrene fluorophores are slowly desorbed from the surface with a concomitant decrease in excimer formation, but they remain covalently bound to the surface.

Figure 1

Such a temporal evolution of the fluorescence spectra was observed in all investigated solvents (acetonitrile, methanol, tetrahydrofuran and ethanol-water mixture (50:50 v/v)), but the rate of evolution and the final proportions of excimer and monomer depend on the solvent (Figure 2). The evolution becomes insignificant after about 6 hours, whatever the solvent.

Figure 2

Figure 3 displays the final fluorescence spectra of γ-1 in various solvents after a delay of six hours. For a given sample, the excimer-to-monomer intensity ratio depends on the solvent polarity. In polar solvents, the proportion of excimers is larger, which is in agreement with the
observations previously reported by Lochmüller et al.⁸ in the case of pyrene bound to silica surfaces. In fact, the pyrene groups are more solvated in apolar solvents and thus form less excimers than in polar solvents where they tend to stack together.⁹

<caption>Figure 3</caption>

In the presence of water, the proportion of excimers is smaller because the water molecules are likely to form an organized media in which the pyrene groups are isolated.¹⁰ It should be noted that under our experimental conditions, we have not observed an enhancement of the excimer proportion with time which means that there is no migration of pyrene groups bound to the alumina surface, as previously described by Wang and Harris with another pyrene probe.¹¹

It should be emphasized that excimer formation is strongly dependent on sample preparation. Figure 4 displays the emission spectra of the different samples obtained by grafting PPTEOS on γ-alumina and δ-alumina in suspension in acetonitrile. The excimer-to-monomer intensity ratios are given in Table 1. There is a significant increase of the excimer emission as the amount of grafted pyrene is increased for both δ-alumina and γ-alumina.

<caption>Figure 4</caption>

<caption>Table 1</caption>

## B. Time-resolved fluorescence measurements.

It should be first recalled that, for an homogeneous population of excimer-forming species, the time evolution of the fluorescence intensities of the monomer M and the excimer E following a δ-pulse excitation is expected to be a sum of two exponentials and a difference of two exponentials, respectively.¹²

<caption>Scheme 1</caption>
According to the kinetic Scheme 1 where $k_M$ and $k_E$ are the reciprocals of the intrinsic excited-state lifetimes of the monomer and excimer species, respectively, and $k_1$ and $k_{-1}$ are the rate constants for excimer formation and dissociation, respectively, the time evolutions of the monomer and excimer intensities are the following

$$i_M(t) = \frac{k_r [M^*]_0}{\lambda_1 - \lambda_2} \left[ (X - \lambda_2)e^{-\lambda_1 t} + (\lambda_1 - X)e^{-\lambda_2 t} \right] \quad (1)$$

$$i_E(t) = \frac{k'_r k'_1 [M][M^*]_0}{\lambda_1 - \lambda_2} \left[ e^{-\lambda_2 t} - e^{-\lambda_1 t} \right] \quad (2)$$

where $k_r$ and $k'_r$ are the radiative rate constants of the monomers and excimers, respectively, and $\lambda_1$ and $\lambda_2$ are given by

$$\lambda_{2,1} = \frac{1}{2} \left\{ X + Y \pm \sqrt{(Y - X)^2 + 4 k_1 k_{-1} [M]} \right\} \quad (3)$$

where $X = k_M + k_1[M] = 1/\tau_M + k_1[M]$ and $Y = k_E + k_{-1} = 1/\tau_E + k_{-1}$.

If excimer dissociation cannot occur during the lifetime of the excited state, the equations become

$$i_M(t) = k_r [M^*]_0 e^{-Xt} \quad (4)$$

$$i_E(t) = \frac{k_r k_1 [M][M^*]_0}{X - k_E} \left[ e^{-k_E t} - e^{-Xt} \right] \quad (5)$$

In this case, the fluorescence decay of the monomer is a single exponential. The relevant decay time (1/X) is equal to the risetime of the excimer fluorescence.

The fluorescence decays of the pyrene probes bound to alumina surfaces were measured by the single-photon timing technique¹³ six hours after preparation of the sample so that the temporal evolution of the fluorescence spectrum mentioned above is almost finished. Figure 5 shows the fluorescence decays of γ-1 and δ-2 upon observation in the monomer band (380 nm) and excimer band (480 nm). Analysis of the decay curves using Globals software showed that a sum of four exponentials was necessary to obtain a reasonable fit but not totally
satisfactory because the reduced chi-squared values $\chi_r^2$ were larger than 2-3. This means that a model of a sum of discrete exponentials is not appropriate. The complexity of the fluorescence decays is most likely to be due to a heterogeneity of the microenvironments of the probes, and a distribution of time constants should be rather considered.

Figure 5

Despite that a model of discrete exponentials is not satisfactory, it is nevertheless worth noting that there are two regimes in the time evolution of the monomer and excimer fluorescence intensities. An average short decay time of the monomers and an average risetime of the excimers can be evaluated. They are both of the order of 1 ns, whereas the average long decay times of the monomers and excimers are about 10 ns and 20 ns, respectively. In a first approximation, the reciprocal of the short decay time of the monomers and the reciprocal of the risetime of the excimers can be written, according to the preceding equations, as

$$1/\langle\tau\rangle_{\text{short}} \approx 1/\langle\tau_M\rangle + \langle k_1[M] \rangle \quad (6)$$

where $\langle\tau\rangle_{\text{short}} \approx 1$ ns and $\langle\tau_M\rangle \approx 10$ ns. Consequently, the term $\langle k_1[M] \rangle$ is much larger than $1/\langle\tau_M\rangle$ which means that the time evolution of the fluorescence intensity at short times mainly reflects excimer formation and thus contains information on the distribution of the bound pyrene probes in areas where excimers can be formed. Besides, analysis of the fluorescence decay of monomers at long times provides information on the interactions between the surface and the monomers that cannot form excimers. Finally, analysis of the fluorescence decay of excimers at long times yields information on the interactions between the excimers and the surface.

Let us consider now a more realistic model involving a distribution of time constants for both monomer and excimer fluorescence in order to account for the environmental heterogeneity of pyrene probes. It is very difficult to recover a distribution from a
fluorescence decay without a priori assumption on the shape of the distribution because of the difficulty of the numerical Laplace inversion. In principle, the exponential series method¹⁴ and the maximum entropy method¹⁵ can solve this problem. Our attempts with the maximum entropy method showed that irreproducible shapes of the distribution were obtained from successive experiments on the same sample without changing the experimental conditions.

Another approach consists in using stretched exponentials of the form $A\exp[-(t/\tau)^\beta]$ expressing an underlying distribution of decay times whose width is proportional to $1/\beta$. The narrower the distribution, the closer to 1 the value of $\beta$.

Stretched exponentials was originally suggested by Kolraush¹⁶ and successfully applied to the interpretation of dielectric relaxation data. It was subsequently used by Hof et al.¹⁷ in the case of fluorophores incorporated in sol-gel matrix, and by Wong et al.¹⁸ in the case of pyrene covalently bound to spherical silica particles. In the latter case, the experiments were carried out with pyrene probes bound to silica at low level of coverage so that no excimer were formed. In contrast, in the present investigation, we must analyze the decays of both monomer and excimer fluorescence. In order to fit both the short-time and long-time regimes, we used a model consisting of a sum of two stretched exponentials for the monomers and a difference of two stretched exponentials for the excimers

$$i_M(t) = A \exp \left[ -(t/\tau_1)^{\beta_1} \right] + (1-A) \exp \left[ -(t/\tau_2)^{\beta_2} \right] \quad (7)$$

$$i_E(t) = -B \exp \left[ -(t/\tau_3)^{\beta_3} \right] + B \exp \left[ -(t/\tau_4)^{\beta_4} \right] \quad (8)$$

The time constants $\tau_i$ are related to the averages of the distributions of decay times and the exponents $\beta_i$ are inversely proportional to the widths of the distributions.

The results of the time-resolved experiments are presented only for $\gamma-1$ and $\delta-2$ aluminas because they have similar surface coverage, and a comparison of the $\tau$ and $\beta$ parameters is thus possible. These parameters are reported in Table 2 and the relevant curves are shown in
Figures 6 and 7 for the samples γ-1 and δ-2. In view of the randomness of the weighted
residuals and the chi-squared values, curve fitting with eqs. 7 or 8 are satisfactory.

Table 2

Figure 6

Figure 7

**C. Discussion.**

The time-resolved data will now be thoroughly discussed in conjunction with the steady-state
data in order to describe the distribution of reactive hydroxyl groups on alumina surfaces with
special attention to the distinction between γ-1 and δ-2 aluminas that have similar coverage.

Let us examine first the fluorescence decay of the monomer that can be analyzed
satisfactorily by a sum of two stretched exponentials. The small time constant τ₁ which should
be identical to the risetime constant τ₃ of the excimer (see above) reflects the bound pyrene
probes that are able to form excimers, and the fraction of this population is given by the
preexponential factor A (eq.7) that is equal to 0.11 and 0.47 for γ-1 and δ-2 aluminas,
respectively. It is important to note that, in contrast to the fluorescence spectra, the time-
resolved fluorescence data allowed us to evaluate the fraction A of pyrene probes that can
form excimers. For γ-1 and δ-2 aluminas that have equivalent surface coverage, the fraction
of pyrene probes that can form excimers is 4.3 times larger for δ-alumina than for γ-alumina.

The excimer formation process should be now carefully examined. Excimers can be
formed if the distance between the bonding sites of two pyrene probes is smaller than a
certain distance that depends on the length of the link between the pyrene moiety and the
oxygen atom of the surface. Evaluation using molecular modeling leads to a maximum
distance of 19 Å for excimer formation.¹⁹ It is then of interest to plot the probability P(r) that
the distance between nearest-neighbour bonding sites is r assuming a random distribution.
This will allow us to see whether excimer formation can simply result from such a distribution. The probability P(r) is given by $20^{21}$

$$P(r) = 2\pi r\sigma \left\{ \exp \left[ -\pi (r^2 - r_0^2)\sigma \right] \right\} \quad (9)$$

where $\sigma$ is the surface concentration, and $r_0$ is the shortest distance at which grafting of probes is possible. r and $r_0$ are expressed in nm and $\sigma$ in molecule.nm$^{-2}$. An estimation of $r_0$ by molecular modeling leads to a value of about 8 Å. In Figure 8, the plots of P(r) for $\sigma = 0.1$ (γ-1 alumina) and 0.07 (δ-2 alumina) are presented. It is clear that the probability to find a nearest neighbour within the minimum distance of 19 Å required for excimer formation is quite significant. More precisely, the fraction F of probes whose nearest-neighbour is present within $r_d = 19$ Å is

$$F = \int_{r_0}^{r_d} P(r) dr = 1 - \left\{ \exp \left[ -\pi (r_d^2 - r_0^2)\sigma \right] \right\} \quad (10)$$

The values of F are about 60 % for γ-1 alumina and 48 % for δ-2 alumina.

Figure 8

However, it should be emphasized that the condition $D < 19$ Å is necessary for excimer formation but not sufficient because the probability to form excimer depends on further factors : viscosity, diffusion coefficient and excited-state lifetime. In fact, excimer formation requires mutual diffusion of two bound pyrene probes towards each other during the lifetime of the excited state. Such a diffusion depends on the viscosity of the medium and on the conformational changes of the chain linking the probes to the surface. Therefore, only a fraction of pairs of pyrene probes whose mutual distance of bonding sites are shorter than 19 Å can form excimer. Such a fraction is unfortunately difficult to evaluate.

In any case, suppose that excimer formation mainly arises from the proximity of probes as a result of a random distribution. Then, the excimer-to-monomer intensity ratios should be similar for the γ-1 and δ-2 alumina samples (and even larger for the γ-1 sample whose surface
concentration is somewhat larger). On the contrary, the excimer-to-monomer intensity ratio is almost three times larger for δ-2 alumina than for γ-1 alumina (see Table 1). Such a result is inconsistent with an excimer formation predominantly arising from a statistical proximity in a random distribution. The large difference in excimer-to-monomer intensity ratios for two samples with similar coverage is a compelling evidence of spatial inhomogeneous distribution of the probes.

Comparison with previously published data further supports this conclusion of inhomogeneity. In fact, Lochmüller and coworkers22 reported a study of a degassed suspension of silica surface on which similar pyrene probes were grafted. For a surface coverage of 0.08 molecules per nm², i.e. comparable to that of our samples of γ-1 and δ-2 aluminas (0.10 and 0.07, respectively), these authors found an excimer-to-monomer ratio I<sub>E</sub>/I<sub>M</sub> of 0.3 (re-expressed with areas of excimer and monomer bands in order to compare with the values of the present work). This should be compared to the values of the ratio I<sub>E</sub>/I<sub>M</sub> for γ-1 and δ-2 aluminas which are equal to 2.5 and 7.0, respectively, i.e. 8.3 and 23.3 times larger. Therefore, even if in Lochmüller's experiment, all excimers were formed as a result of a purely statistical distribution of the probes, the relevant fraction of excimers formed in this way on our alumina surfaces is small. We can thus safely conclude that the pyrene probes on alumina surfaces are not homogeneously distributed but they are rather clustered into regions of high density.

In the following discussion which intends to be only semi-quantitative, the fraction of excimer formed outside the clustered zones will be assumed to be negligible. Even if this fraction is significant, the general conclusions will remain valid.

Under this assumption, it can be further stated from the parameter A determined by time-
resolved experiments, that the fraction of pyrene probes in the high density regions of δ-2
alumina is about four times larger than for γ-1 alumina. It is important to note that, in contrast
to the fluorescence spectra, the time-resolved fluorescence data allowed us to evaluate the
fraction A of pyrene probes that are in the clustered zones.

Returning to the steady-state data, the excimer-to-monomer intensity ratio for an
homogeneous population of excimer-forming species, is - according to the kinetic scheme 1 -
given by

$$
\frac{I_E}{I_M} = \frac{k'_r k_1 [M]}{k_r k_{-1} + k'_r + k'_{nr}} = K_1 [M] \quad (11)
$$

where $k_r$ and $k'_r$ are the radiative rate constants for monomer and excimer, respectively, and $k_{nr}$ and $k'_{nr}$ are the nonradiative rate constants for monomer and excimer, respectively, so that $k_M = k_r + k_{nr}$ and $k_E = k'_r + k'_{nr}$. Eq. (11) is a crude approximation in the case of alumina surfaces because distributions of rate constants should rather be considered. Nevertheless, semi-quantitative information can be obtained, as shown below.

Instead of bulk concentration [M], surface concentrations θ (i.e. number of pyrene probes per unit surface) should be used. Under the assumption that excimer formation outside the clustered zones can be ignored, distinction should be made between the surface concentration θ<sub>clu</sub> of pyrene groups that can form excimers in the clustered zones and the surface concentration θ<sub>iso</sub> of isolated pyrene probes in low-density areas.

Considering then the pyrene groups that can form excimer in the clustered zones, their
surface concentration will be denoted θ<sub>clu</sub> and their contribution to the monomer fluorescence
intensity I<sub>M clu</sub>. Eq. (11) is thus re-written as

$$
\frac{I_E}{I_{M_{\text{clu}}}} = K_1 \theta_{\text{clu}} \quad (12)
$$

The ratio I<sub>E</sub> / I<sub>M clu</sub> thus provides global information on the kinetics of excimer formation and
the surface concentration of pyrene probes in the clustered zones. Eq. (12) can be rewritten as

$$
\frac{I_E}{I_{M_{\text{clu}}}} = \frac{I_E}{I_M} \frac{I_M}{I_{M_{\text{clu}}}} = K_1 \theta_{\text{clu}} \quad (13)
$$
The ratio I<sub>E</sub>/I<sub>M</sub> can be determined from the fluorescence emission spectra. The ratio I<sub>M</sub><sub>clu</sub> / I<sub>M</sub>
represents the fractional intensity of the fluorescence emitted by the monomers forming
excimer; it can be estimated from the time-resolved data since the first term of eq. (7)
characterizes the distribution of short decay times relevant to excimer formation. The relevant
fractional intensity is then given by

$$
\frac{\frac{\int_{0}^{\infty} \left\{ A \exp \left[ -(t/\tau_{1})^{\beta_{1}} \right] \right\} dt}{I_{M}}}{I_{M}} = \frac{\int_{0}^{\infty} \left\{ A \exp \left[ -(t/\tau_{1})^{\beta_{1}} \right] + (1-A) \exp \left[ -(t/\tau_{2})^{\beta_{2}} \right] \right\} dt}{\int_{0}^{\infty} \left\{ A \exp \left[ -(t/\tau_{1})^{\beta_{1}} \right] + (1-A) \exp \left[ -(t/\tau_{2})^{\beta_{2}} \right] \right\} dt} \quad (12)
$$

The values of the ratio I<sub>E</sub> / I<sub>M clu</sub> for γ-1 and δ-2 aluminas are given in Table 3. This ratio is
larger for γ-1 than for δ-2, which means that more excimers are formed in γ-1 than in δ-2.

Table 3

It is important to make a distinction between the ratios I<sub>E</sub> / I<sub>M<sub>clu</sub></sub> and I<sub>E</sub>/I<sub>M</sub>. The ratio I<sub>E</sub>/I<sub>M</sub>
reflects the overall formation of excimers and was found to be larger for δ-2 than for γ-1,
whereas the ratio I<sub>E</sub> / I<sub>M<sub>clu</sub></sub> is relevant to the clustered zones and is smaller for δ-2 than for γ-1.
These opposite trends result from the larger fraction of hydroxyl groups in the clustered zones
of δ-2 alumina by a factor of more than four (parameter A), but in these zones, excimer
formation is less efficient. According to eq. (13), the surface concentration of pyrene probes
in the clustered zones or the parameter K<sub>1</sub> - that reflects the organization of pyrene probes in
these zones - is larger for γ-1 than for δ-2 alumina.

Regarding the time-resolved experiments, numerical Laplace inversion²³ of the sums or
differences of stretched exponentials (eqs. 7 and 8) allowed us to visually compare the
distributions of decay times for the γ-1 and δ-2 aluminas (Figures 9 and 10) in addition to the
comparison of the time constants τᵢ and the exponents βᵢ (Table 3) characterizing the position
and width of the distributions of decay times, respectively.
Figure 9

Figure 10

Let us consider first the distributions of risetimes and decay times relevant to excimer
formation. The values of β₃ characterizing the width of the distributions of risetimes are less
than 0.5 for both aluminas, which means that these distributions are wide, as shown in Figure
9. The distributions of decay times are characterized by higher values of exponent β₄ (0.85
and 0.79 for γ-1 and δ-2 aluminas, respectively) which means that these distributions - that
express the excimer-surface interactions - are relatively narrow (see Figure 9). The
distribution of decay times for δ-2 alumina is located at shorter times than for γ-1 alumina
(see Figure 9 and the smaller value of the time constant τ₄ for δ-2 alumina in Table 2), which
means that the interactions of excimers with the surface in the areas of high density of
hydroxyl groups are stronger for δ-alumina. This is consistent with a larger value of the ratio
I<sub>E</sub>/I<sub>Mclu</sub>. A larger number of Lewis acid sites on this type of alumina in the clustered zones is
likely to be responsible for this difference. Adsorption of aromatic molecules on alumina
surfaces is indeed expected to be favored by the presence of Lewis acid sites. In fact,
Kalyanasundaram<sup>24</sup> considered that the adsorption of aromatic molecules on alumina surfaces
should be favored by the presence of Lewis acid sites (insaturated aluminum atoms).

Regarding the fluorescence decays of the monomers, it was recalled (see above) that for a
homogeneous population of excimer-forming species, the short decay time of the monomer
should be identical to the risetime of the excimer. Figure 9 shows that the distributions of
short decay times are in fact located in the same time region as those of the risetimes relevant
to excimer formation (Figure 10). However, the difference between the distributions of decay
times of γ-1 and δ-2 aluminas appear to be more marked than those of risetimes. The width of
these distributions can be explained by the variety of configurations that allow excimer
formation; these configurations have different energies, which leads to a heterogeneous
emission spectrum in both monomer and excimer bands. For the same reason, the excitation spectra were shown to be wavelength dependent.

The distributions of long decay times of the monomers that cannot form excimers are shown in Figure 10 (see also the relevant parameters $\tau_2$ and $\beta_2$ in Table 2).

The origin of the distribution of decay times deserves further attention. In addition to the variety of configurations that allow excimer formation, the possibility of a distribution of oxygen quenching rate constants should be also examined. Could such a distribution arise from the heterogeneous sites of pyrene adsorption? It should be recalled that in the present work, the pyrene probes are covalently bound to the surface via a short chain, and in the presence of solvent, there are two kinds of evidences for desorption of most of the probes from the surface: (i) the vibrational features of the fluorescence spectrum that is characteristic of a less polar microenvironment than before desorption (see section 3A); (ii) the existence of risetimes of the fluorescence intensity in time-resolved experiments upon observation in the excimer band. If the probes were not desorbed, they would not be able to move to form excimer and only preformed excimer would be observed. In such a case, no risetime of the fluorescence intensity in time-resolved experiments would be observed. But we do observe such risetimes. Therefore, the accessibility of those desorbed probes to oxygen should not be very different. However, the monomers that cannot form excimers exhibit a distribution of long decay times that reflect the interactions with the surface. These interactions can be *dynamic*, i.e. by collision during the excited-state lifetime or *static*, i.e. in solvation sites. In the latter case, one cannot exclude an effect due to a distribution of oxygen quenching rate constants. Along the same line, the distribution of long decay times of the excimers may also be partly accounted by this effect.

The nature of the interactions of pyrene with the surface deserves some comments. In their investigation on pyrene adsorbed on silica surfaces, Ware and coworkers²⁵ considered that
pyrene is mainly in interaction with the hydroxyl groups of oxide surfaces via electrostatic interactions and hydrogen bonding. Moreover, they suggested that these interactions are affected by the local geometry and the distribution of hydroxyl groups. Interaction with Lewis acid sites should also be considered. All these aspects can play a role in the presently studied alumina surfaces but with different relative contributions according to the sample. It is important to note that the distribution of interaction energies is much broader for γ-1 alumina than for δ-2 alumina (see Figure 10 the values of β₂ value in Table 2), which provides further distinction between these two types of alumina.

Finally, from the above general discussion, it is possible to give a schematic representation of the distribution of pyrene probes on δ- and γ-alumina surfaces (see Scheme 2). Such a representation should well reflect the distribution of reactive hydroxyl groups, except for very short distances because it should be recalled that it is impossible to covalently link two probes to two reactive hydroxyl groups that are separated by a distance shorter than about 5 Å. Moreover, no information on the hydroxyl groups others than the reactive ones can be obtained by the excimer formation method.

Scheme 2

**4. Conclusion**

This investigation clearly demonstrates that time-resolved fluorescence spectroscopy of covalently-linked pyrene probes offers a powerful tool to characterize alumina surfaces and in particular to get information on the organization of reactive hydroxyl groups. The fluorescence decay curves revealed a distribution of decay times which led us to fit the data for the first time with a sum or a difference of two stretched exponentials. The time constants and exponents of these stretched exponentials characterize the spatial distribution of pyrene probes and their interactions - in the monomer or excimer form - with the surface. Of major interest is the possibility of description and distinction between γ- and δ-alumina samples by
this methodology. In particular, it was shown that for aluminas having equivalent surface
coverage of pyrene probes, the fraction of reactive hydroxyl groups belonging to the clustered
zones is more than four times larger for δ-alumina than for γ-alumina. In these zones, the
interactions of pyrene excimers with the surface in the clustered zones are stronger for δ-
alumina, which can be explained by a larger number of Lewis acid sites on this sample and/or
a longer average distance between the pyrene probes (see the predominant conformation of
excimers in Scheme 2). Furthermore, the interactions of pyrene monomers and excimers with
the surface appear to be stronger for δ-alumina than for γ-alumina and the distribution of the
interaction energies is narrower. It is useful to further describe and distinguish the γ- and δ-
alumina surfaces by such differences in interactions that have various origins (electrostatic
interactions, hydrogen bonding, presence of Lewis acid sites) and that are affected by the
local geometry and the spatial distribution of hydroxyl groups.

**Acknowledgement** We acknowledge Professor M. N. Berberan Santos for very fruitful discussions, and in particular on the distribution of nearest-neighbour distances. We thank him also for his help in the Laplace inversion of the stretched exponentials. We are grateful to Patrick Denjean for his assistance in tuning the single-photon timing instrument.
<table><caption>Table 1. Excimer-to-monomer intensity ratios for the samples of γ- and δ-alumina as a function of the surface coverage.</caption><thead><tr><th>Sample</th><th>Surface coverage σ (molecule.nm<sup>-2</sup>)</th><th>I<sub>E</sub>/I<sub>M</sub><sup>a</sup></th></tr></thead><tbody><tr><td>δ-1</td><td>&lt; 0.06</td><td>3.6</td></tr><tr><td>δ-2</td><td>0.07±0.03</td><td>7.0</td></tr><tr><td>γ-1</td><td>0.10±0.03</td><td>2.5</td></tr><tr><td>γ-2</td><td>0.23±0.03</td><td>7.2</td></tr></tbody></table>

a ratio of the areas under the monomer and excimer fluorescence bands

<table><caption>Table 2. Analysis of the time-resolved fluorescence of samples γ-1 and δ-2 by using eq. 7 or 8. Suspension in acetonitrile. Excitation wavelength: 322 nm.</caption><thead><tr><th>Sample</th><th>λ<sub>em</sub> / nm</th><th>A</th><th>τ<sub>1</sub> or τ<sub>3</sub> / ns</th><th>β<sub>1</sub> or β<sub>3</sub></th><th>τ<sub>2</sub> or τ<sub>4</sub> / ns</th><th>β<sub>2</sub> or β<sub>4</sub></th><th>χ<sup>2</sup><sub>r</sub></th></tr></thead><tbody><tr><td>γ-1</td><td>380</td><td>0.11±0.01</td><td>τ<sub>1</sub> = 0.8±0.2</td><td>β<sub>1</sub> = 0.7±0.2</td><td>τ<sub>2</sub> = 9.5±0.1</td><td>β<sub>2</sub> = 0.62±0.01</td><td>1.23</td></tr><tr><td>γ-1</td><td>480</td><td></td><td>τ<sub>3</sub> = 0.45±0.03</td><td>β<sub>3</sub> = 0.41±0.01</td><td>τ<sub>4</sub> = 24.4±0.2</td><td>β<sub>4</sub> = 0.85±0.01</td><td>1.72</td></tr><tr><td>δ-2</td><td>380</td><td>0.47±0.01</td><td>τ<sub>1</sub> = 0.57±0.05</td><td>β<sub>1</sub> = 0.49±0.02</td><td>τ<sub>2</sub> = 10.2±0.1</td><td>β<sub>2</sub> = 0.81±0.01</td><td>1.13</td></tr><tr><td>δ-2</td><td>480</td><td></td><td>τ<sub>3</sub> = 0.67±0.03</td><td>β<sub>3</sub> = 0.46±0.01</td><td>τ<sub>4</sub> = 15.0±0.1</td><td>β<sub>4</sub> = 0.79±0.01</td><td>1.44</td></tr></tbody></table>

$\chi_r^2 = \frac{1}{N} \sum_{i=1}^{N} \frac{[R(t_i) - R_c(t_i)]^2}{R(t_i)}$ where R(tᵢ) is the experimental curve, R_c(tᵢ) is the calculated one, N is the number of data points; v=N-p where p is the number of fitted parameters.

<table><caption>Table 3. Characteristics of the samples of γ-1 and δ-2.</caption><thead><tr><th>Sample</th><th>Surface coverage σ (molecule.nm<sup>-2</sup>)</th><th>I<sub>E</sub> / I<sub>M</sub><sup>a</sup></th><th>A<sup>a</sup></th></tr></thead></table>
<table><tr><td>δ-2</td><td>0.07±0.03</td><td>83.1</td><td>0.47</td></tr><tr><td>γ-1</td><td>0.10±0.03</td><td>275</td><td>0.11</td></tr></table>

<footnote>ᵃfraction of pyrene probes in the clustered zones.</footnote>
## Captions of schemes and figures

Scheme 1. Kinetic scheme of excimer formation

Scheme 2. Schematic illustration of the distribution of reactive hydroxyl groups on γ- and δ-alumina surfaces.

Figure 1. Temporal evolution of the emission spectra of alumina γ-1 in suspension in acetonitrile (1mg / 2.5 ml of solvent). Excitation wavelength: 315 nm. The spectra are normalized at the same height at 377 nm.

Figure 2. Temporal evolution of the excimer-to-monomer intensity ratio for alumina γ-1 in suspension in various solvents (1mg / 2.5 ml of solvent). Excitation wavelength: 315 nm.

Figure 3. Emission spectra of alumina γ-1 in suspension in various solvents. Excitation wavelength: 315 nm. The spectra were recorded after a delay of 6 hours.

Figure 4. Emission spectra of alumina γ-1, γ-2, δ-1, δ-2 in suspension in acetonitrile (1mg / 2.5 ml of solvent). Excitation wavelength: 315 nm. The spectra are normalized at the same height at 337 nm.

Figure 5. Fluorescence decays of alumina δ-1 and alumina γ-1 in suspension in acetonitrile. Channel width: 195 ps. Excitation wavelength: 322 nm. A: emission wavelength 380 nm (monomer emission). B: emission wavelength 480 nm (excimer emission).

Figure 6. Fluorescence decays of alumina γ-1 in suspension in acetonitrile. Channel width: 24 ps. Excitation wavelength: 322 nm. A: emission wavelength 380 nm (monomer emission). B: emission wavelength 480 nm (excimer emission). Experimental data (points) and best fits (solid line) with eq. 7 (A) or 8 (B).

Figure 7. Fluorescence decays of alumina δ-2 in suspension in acetonitrile. Channel width: 24 ps. Excitation wavelength: 322 nm. A: emission wavelength 380 nm (monomer emission). B: emission wavelength 480 nm (excimer emission). Experimental data (points) and best fits (solid line) with eq. 7 (A) or 8 (B).
Figure 8. Distance distribution between nearest-neighbour bonding sites assuming a random distribution on the surface (according to eq. 9).

Figure 9. Distribution of decay times obtained from the fluorescence decays at 480 nm (observation of excimer fluorescence).

Figure 10. Distribution of decay times obtained from the fluorescence decays at 380 nm (observation of monomer fluorescence).
<figure><img src="image_4.png" /><figcaption>Scheme 1</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Scheme 2</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 1</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 2</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 3</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 4</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Figure 5</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 6•</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 7</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 8</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 9</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure 10</figcaption></figure>
Notes and References

1 B. Valeur, Molecular Fluorescence. Principles and Applications, Wiley-VCH, 2002, p. 94.

2 C.H. Lochmüller, A.S. Colborn, M.L Hunnicutt, J.M. Harris, *J. Am. Chem. Soc.* 1984, **106**, 4077, and references therein.

3 S. Pankasem, J.K. Thomas, *J. Phys. Chem.* 1991, **95**, 7385.

4 R. Metivier, I. Leray, M. Roy-Auberger, N. Zanier-Szydlowski, B. Valeur, *New J. Chem.* 2002, 26, 411.

5 S. Pankasem, J. K. Thomas, *J. Phys. Chem.* 1991, **95**, 7385; Y. Mao, J. K. Thomas, *Langmuir* 1992, **8**, 2501.

6 R. C. Chambers, Y. Haruvy, M. A. Fox, *Chem. Mater.* 1994, **6**, 1351.

7 J. L. Habib-Jiwan, E. Robert, J. P. Soumillion, *J. Photochem. Photobiol. A :Chem*, 1999, **122**, 61.

8 C. H. Lochmüller, M. T. Kersey, *Anal. Chim. Acta* **1987**, *200*, 143.

9 I. Leray, M. Ayadim, C. Ottermans, J. L. Habib-Jiwan, J. Ph. Soumillion, *J. Photochem. Photobiol. A : Chem.* 2000, **132**, 43.

10 M. L. Hair, W. Hertl, *J. Phys. Chem.* 1969, **7?**, 4269.

11 H. Wang, J. M. Harris, *J. Am. Chem. Soc.* 1994, **116**, 5754

12 J. B. Birks, 1970 *Photophysics or Aromatic Molecules*, Wiley, London, chap. 7.

13 D. V. O'Connor, D. Phillips, Time-Correlated Single-Photon Counting, Academic Press, London, 1984.

14 A. Siemarczuk, B. D. Wagner, W. R. Ware, *J. Phys. Chem.* 1990, **94**, 1661.

15 J. C. Brochon, *Methods in Enzymology* 1994, **240**, 262.

16 R. Kohlrauch, *Ann. Phys.* Leipzig 1947, **12**, 393.
17 M. Hof, J. Schleicher, F. W. Schneider, *Ber. Bunsenges. Phys. Chem.*, 1989, **93**, 1377.

18 A. L. Wong, J. M. Harris, D. B. Marshall, *Can. J. Phys.*, 1990, **68**, 1027.

19 In the evaluation of the average distance between two pyrene groups, it is possible to take into account the roughness of the surface by considering the pore diameter, but this leads to a change of about 0.4 Å for this average distance.

20 J. R. MacDonald, *Mol. Phys.*, 1981, **44**, 1043.

21 I. Ogino, K. Nagoshi, M. Yagi, M. Kaneko, *J. Chem. Soc., Faraday Trans.*, 1996, 92, 3431.

22 C. H. Lochmüller, A.S. Colborn, M.L. Hunnicutt, J.M. Harris *Anal. Chem.*, 1983, **55**, 1344.

23 Numerical Laplace inversion of the stretched exponentials was performed by curve fitting with a sum of hyperbolic functions (M.M. Berberan-Santos, to be published).

24 K. Kalyanasundaram, in *Photochemistry in Microheterogeneous Systems*, Academic : New York, 1987.

25 R. K. Bauer, P. de Mayo, W. R. Ware, K. C. Wu, *J. Phys. Chem.*, 1982, **86**, 3781.