Introduction

Dendrimers are well-defined, highly branched, monodisperse macromolecules with uniform molecular weight and nanoscopic size. The understanding of the structure of this class of compounds is necessary for their application because most of the properties are associated to the dendritic architecture. The effect of core size on photophysical and hydrodynamic properties of dendrimers have been demonstrated [1, 2]. Several theoretical models have been proposed to account for the properties of dendritic architectures [3–6], and energy dissipation in multichromophoric dendrimers [7]. Fluorescence quenching and probe methods have been used to investigate photophysical properties and structural characteristics [8–17], and solute and biological macromolecules interactions with dendrimers [18, 19]. For dendrimers having a fluorescent core such as metalloporphyrin, studies of collisional and static fluorescence quenching may give information about the internal dendritic structure through measurements of diffusion controlled rates and quencher accessibility to the core. In this paper, the fluorescence quenching of two porphyrin dendrimers series (see Fig. 1) by 1,3-dicyanomethylene-2-methyl-2-pentyl-indan (PDCMI), benzimidazole and 1,2-dibromobenzene is studied by time-resolved and stationary emission measurements. The accessibility of quenchers to the porphyrin core and the characteristics of the microenvironment affecting the quenching rate constant are discussed.

Fig. 1
figure 1

Representation of the two investigated dendrimer series

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Materials and methods

The synthesis of GnPZn and GnTPPH2 dendrimers (Fig. 1) was described previously [1, 12]. All solvents were of spectroscopic grade and stored over 4 Å molecular sieves. The optical density of the investigated solutions was always less than 0.15 to avoid spectral distortion due to the inner-filter effect. Time-resolved fluorescence measurements were performed on samples degassed by several freeze-pump-thaw cycles.

The absorption spectra were measured with a Perkin-Elmer Lambda 6 UV-visible spectrophotometer. Steady state fluorescence spectra at room temperature were measured with a SPEX Fluorolog 212. All emission spectra were recorded by excitation at the isosbestic point (vide infra) using the same concentration of dendrimer (4.5 × 10−7 M). The emission decays were obtained by a single-photon-timing technique. The compounds were excited at 425 nm (for GnPZn) and at 420 nm (for GnTPPH2) using the output of a titanium–sapphire laser, pumped by a beam-locked argon ion laser, with repetition frequency of the excitation pulses of 400 kHz. TBO (Bis-[1-octadecyl-benzoxazol-2-]-trimethine perchlorate) in methanol (τ = 0.14 ns) and coumarin in methanol (τ = 5.5 ns) were used as lifetime reference compounds. Time increments of 110 and 10 ps/channel were used for GnTPPH2 and GnPZn, respectively, and the number of peak counts was about 104 for both systems.

Results and discussion

Static quenching of GnPZn using benzimidazole

The interaction between the porphyrinic ring of the GnPZn dendrimer and the electron-acceptor benzimidazole results in the formation of a bimolecular complex in the ground state. The effect in the Soret absorption band as benzimidazole is added is illustrated in Fig. 2. The presence of an isosbestic point indicates a single equilibrium in the association process of the two species.

Fig. 2
figure 2

Absorption spectra of G4PZn with different concentrations (0, 0.005, 0.011, 0.015, 0.020, 0.025, 0.031, 0.04, 0.054 mol l−1) of benzimidazole in THF. T = 293 K

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The relative emission intensity (I 0/I) of a short lived state quenched mainly by a static mechanism may follow a linear Stern-Volmer equation given by,

$$ \frac{{I_{0} }} {I} = 1 + K_{a} {\left[ Q \right]} $$
(1)

where the Stern-Volmer constant (K a) represents the binding constant of the complex formed between porphyrin and benzimidazole in the dendrimer structure. Figure 3 illustrates a typical linear Stern-Volmer plot of this system.

Fig. 3
figure 3

Stern-Volmer plot for the quenching of GnPZn by benzimidazole (filled square, n = 1; filled circle, n = 2; filled inverted triangle, n = 3; filled triangle, n = 4) T = 293 K

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The dependence of K a on generation of GnPZn dendrimer is reported in Fig. 4. The values found were 47, 52, 61 and 61 mol−1 l in THF and 67, 72, 77 and 77 mol−1 l in DMF relative to the generations n = 1, 2, 3 and 4, respectively. In both solvents, K a increases initially with generation but rapidly gets saturation. Such result suggests the presence of a similar microenvironment surrounding the core in the highest generations. In addition, the calculated dendrimer free volume of the four generations are 1265, 4827, 10181, 9476 Å3 [1]. Thus the small change of the free volume of the third and fourth generations should leave to a constant Ka value, as observed. Relating the results obtained here with the early studies of fluorescence anisotropy [1], we can suggest that the structural collapse observed in G4PZn may be promoted by a packing of the dendrimer peripheral layer.

Fig. 4
figure 4

Variation of binding constant (K a) as a function of generation in: filled square, THF; and filled triangle, DMF. T = 293 K

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Dynamic quenching of GnTPPH2 by PDCMI and 1,2-dibromobenzene

The interaction in solution of the electronic excited state of GnTPPH2 dendrimer with two different quenchers was investigated from fluorescence decay measurements. A strong electron acceptor (PDCMI) and also a quencher by heavy atom effect (1,2-dibromobenzene) were used. All fluorescence decays as a function of quencher concentration were properly fitted by monoexponential decay function, and the ratio of lifetimes in absence and presence of added quencher followed the linear Stern-Volmer equation from which the experimental quenching rate constants were calculated. Stern-Volmer plots of the two systems are shown in Fig. 5. The main results obtained from these experiments are summarized in Table 1.

Fig. 5
figure 5

Stern-Volmer plots for the quenching of GnPZn in THF using PDCMI and 1,2-dibromobenzene as quencher (concentration 10−3 and 10−1 M). Filled inverted triangle, G1TPPH2; filled triangle, G2TPPH2; filled circle G3TPPH2. The inset shows the structural formula of the quenchers. T = 293 K

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Table 1 Quenching rate constant k q (M−1s−1) of GnPZn dendrimer by PDCMI and 1,2-dibromobenzene in THF
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The k q values are dependent on the quencher and also on the dendrimer generation, especially in the case of quenching by PDCMI. In order to analyze these results, it would be interesting to introduce a simple kinetic model, which could correlate the dendrimer parameters with the experimental observed k q rate constants. Lets to assume that the bimolecular quenching occurs by a two-step mechanism,

$$ Q + {\left( {D*} \right)}\begin{array}{*{20}c} {{\xrightarrow{{k_{ + } }}}} \\ {{\xleftarrow[{k_{ - } }]{}}} \\ \end{array} Q{\left( {D*} \right)}\xrightarrow{{k_{r} }}Q{\left( D \right)} $$
(2)

where (D*) is the excited state dendrimer, and Q(D*) is its complex with the quencher specie Q by surface binding. k + and k − are, respectively, the association and dissociation rate constant of Q to and from the dendrimer surface (k +/k − = K, the equilibrium constant), and k r is a specific reaction rate constant defined by the type of quenching process. In stationary condition (corresponding to an exponential fluorescence decay as observed), the experimental rate constant k q is related to the rate constants of the kinetic scheme above by,

$$ k_{q} = \frac{{k_{r} k_{ + } }} {{k_{r} + k_{ - } }} $$
(3)

In a case where k − > k r, because in some way the dendrimer arms are protecting the excited porphyrin core from the quencher, one has k q = Kk r. Assuming this condition and expressing the equilibrium constant in terms of the volume of the dendrimer (V h, the hydrodynamic volume) and the interaction energy in the quencher surface binding (ɛ b), one has,

$$ k_{q} = k_{r} V_{h} \exp {\left[ {{\varepsilon _{b} } \mathord{\left/ {\vphantom {{\varepsilon _{b} } {kT}}} \right. \kern-\nulldelimiterspace} {kT}} \right]} $$
(4)

In a first situation, lets to assume that the quenching process by PDCMI (electron acceptor) is a distance dependent electron transfer (ET) process in which the quencher, due to its molecular size and type of interaction with the dendrimer (see molecular structure in Fig. 5), remains on the surface without diffusing to the core. In this situation, k r would be written in the following form,

$$ k_{r} = \nu ^{0}_{r} \exp {\left[ { - 0.62\beta V^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}_{h} } \right]} $$
(5)

where β is the exponential coefficient of the ET theory (the attenuation coefficient with distance), and the other parameter in term of V h is just the radius of the spherical dendrimer. Introducing Eq. 5 into Eq. 4, the quenching rate constant is written as,

$$ k_{q} = cV_{h} \exp {\left[ { - 0.62\beta V^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}_{h} } \right]} $$
(6)

where \( c = \nu ^{0}_{r} \exp {\left( {{\varepsilon _{b} } \mathord{\left/ {\vphantom {{\varepsilon _{b} } k}} \right. \kern-\nulldelimiterspace} kT} \right)} \).

For the dendrimers studied here, the V h values were determined previously (see Table 1), and are now used to correlate with k q. The plot of k q according to Eq. 6 is given in Fig. 6, from which β value of 0.33 ± 0.01 Å−1 is obtained from the slope. The small value of β obtained in this study is, however, in the range observed in donor-acceptor model compounds with peptides as molecular spacers in electron transfer [20]. It indicates a quite moderate attenuation of the electronic coupling of donor-acceptor with dendrimer generation or distance from the donor core to the acceptor on the surface. This effect has been predicted in simulation of ET process in dendrimer, where the bridge-mediated electronic coupling, which defines the attenuation factor, depends on the connectivity of the dendrimer structure [21].

Fig. 6
figure 6

Plot of quenching rate constant as a function of hydrodynamic volume according to Eq. 6, k q values in M−1 ns−1

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In the case of 1,2-dibromobenzene as the quencher species, the process should involve diffusion from the surface toward the center of the dendrimer because the quenching mechanism requires a close approach of excited state porphyrin and quencher. Thus k r is now related to the inverse of the mean reaction time, i.e. the average time of diffusion from the surface to the core. In principle, this reaction time can be derived from the diffusion quenching models in spherical micelles for instance [22, 23]. If the branches are much larger than the core of dendrimer (which is true only for high generations), k r after the diffusion transient is given approximately by,

$$ 1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k_{r} \approx \frac{{R^{3} }} {{3D_{q} r_{c} }} $$
(7)

where R is the dendrimer radius, and r c is the sum of the core and quencher radii. D q is the diffusion coefficient of the quencher species inside the dendrimer frame. Relating R with the radius of the hydrodynamic volume of the dendrimer, and introducing Eq. 7 into Eq. 4, the quenching rate constant is reduced in this case to:

$$ k_{q} = 4\pi r_{c} D_{q} \exp {\left[ {{\varepsilon _{b} } \mathord{\left/ {\vphantom {{\varepsilon _{b} } {kT}}} \right. \kern-\nulldelimiterspace} {kT}} \right]} $$
(8)

The equation above is the classical result in homogeneous medium weighted by the fraction of quencher bound to the dendrimer surface. It predicts that if D q and ɛ b become independent of dendrimer generation, then k q will remain constant. The value of k q reported in Table 1 has this behavior, and explain the weak dependence of k q with generation in the case of fluorescence quenching of the porphyrin dendrimers by 1,2-dibromobenzene.

Conclusions

The kinetics of bimolecular fluorescence quenching of a fluorophore located at the core of a dendrimer is a process that depends on the dendrimer structure and generation as well as of the quenching mechanism. The binding constant values obtained from static quenching of GnPZn by benzimidazole suggests the presence of weak interactions between branches and the core moiety, and the presence of similar free volume cavities in dendrimers of high generations. Dynamic fluorescence quenching of the porphyrin core by 1,3-dicyanomethylene-2-methyl-2-pentyl-indan (PDCMI) in GnTPPH2 occurs through distance dependent electron transfer with an exponential coefficient β = 0.33 Å−1 for distances from donor to acceptor between 10–17 Å. The branching nature or connectivity of the dendrimer arms may account for this low attenuation factor of the ET rate constant with distance. The quenching by 1,2-dibromobenzene is a slow process of the quencher toward to the porphyrin core. Its rate constant is practically independent of dendrimer generation.