1 Introduction

Laser-induced fluorescence (LIF) imaging is commonly used, e.g., for the visualization of gas-phase mixing processes and temperature measurements [1]. For this purpose, organic molecules, such as ketones, mono-aromatics (e.g., toluene), and di-aromatics (e.g., naphthalene), are frequently used as fluorescence tracers. For the observation of air/fuel mixing processes in combustion, they are added at low concentration (1–10 %) to a non-fluorescing surrogate fuel. In any of these applications, the measured fluorescence signal strongly depends on the environmental conditions, i.e., temperature, pressure, and bath-gas composition which influence the fluorescence quantum yield (ϕ fl) for the particular excitation/emission process [2–4] and the absorption cross-section at the excitation wavelength [5]. While the absorption cross-section mostly depends on temperature, ϕ fl also depends on pressure and bath-gas composition. Phenomenological step-ladder models have been set up for some ketones [6, 7] and aromatics [8] describing energy relaxation and emission processes within the energy level manifold in the excited state after laser excitation, and enable quantitative predictions of ϕ fl within the investigated range of temperature, pressure, and bath-gas composition [7–9]. Temperature generally leads to reduced fluorescence quantum yields; the magnitude of this effect strongly depends on the tracer species. Pressure effects are less uniform and depend on the species, the temperature, and the bath gas. Increasing pressure can lead to either increasing or decreasing quantum yields. This behavior is not reproduced by the currently used models [8–10].

Lately, the concept of photo-induced cooling and heating, which distinguishes between laser excitation above the average thermal energy in an excited state (photo-induced heating) and below that level (photo-induced cooling), was introduced as an explanation for the species-specific dependence of the ϕ fl on pressure [11, 12]. As other collision-induced energy transfer phenomena, these processes can best be studied by measuring effective fluorescence lifetimes in variable low-pressure environments where collision frequencies are reduced [13].

The present work extends the range of measured effective fluorescence lifetimes to pressures below atmospheric in a temperature range from 300 to 475 K. This allows to distinguish between fast intramolecular internal conversion and intersystem crossing and collision-induced energy transfer processes in the excited state and thus gives valuable input for modeling the underlying photo-physical processes. Following the concept used by Cheung and Hanson [9] for 3-pentanone, rate constants for the underlying processes can be determined that are essential for photo-physical models that predict fluorescence quantum yields as a function of excitation energy, temperature, pressure and bath-gas composition. A special emphasis lays on the ratio of the rate constants and the frequency of intermolecular collisions.

In the present work, we analyze the dependence of effective fluorescence lifetimes of the benzene derivatives toluene, anisole, 1,2,4-trimethylbenzene, naphthalene, and 1-methylnaphthalene (Table 1) on total pressure between 0.01 and 1 bar at temperatures between 296 and 475 K. Electronic excitation is accomplished using picosecond pulses at 266 nm in gas-phase samples diluted in CO2 as bath gas.

Table 1 Thermodynamic and electronic properties of the investigated aromatic compounds
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2 Theoretical background

All the species considered here can be excited in the UV via an allowed π → π * transition. The electronic structure of the species considered here differs, and Table 1 shows the energy gaps between the ground state and the involved excited singlet states. Therefore, for the various species, excitation at a given frequency leads to the population of different vibrationally excited states in the first singlet state S1. For naphthalene, laser excitation at 266 nm is even sufficient to populate both the S1 and the S2 (35,900 cm−1) states at room temperature [17]. At higher temperatures even excitation of the S3 state (47,500 cm−1) is possible. For toluene, absorption of 266 nm photons leads to the population of the S1 state only. Only at higher temperatures (>600 K) the S2 (47,016 cm−1) state can be populated as well [15]. In both cases, rapid internal conversion (on the femtosecond timescale) transfers the population to the S1 state. This effect is known as Kasha’s rule that describes the observation that fluorescence occurs from the S1 state only. The rate of internal conversion can be estimated to be an exponential decay with the energy gap between the excited singlet states:

$$k_{\text{IC}} = 10^{13} \,f_{\text{v}} = 10^{13} \exp \left( { - \alpha \,\Delta E} \right)$$
(1)

The value α is 4.85 eV−1 for, e.g., benzenoid aromatics. Because of the fast relaxation toward the S1 state (~10 fs), in the following we ignore radiative processes originating from higher singlet states and from triplet states.

The following rate equation describes the intra-molecular deactivation (i.e., without collisions) of the excited molecules [M *]—neglecting re-absorption of fluorescence radiation [1, 13]:

$$- \frac{\text{d}}{{{\text{d}}t}}\left[ {M^{ *} } \right] = \left( {k_{\text{fl}} + k_{\text{ISC}} + k_{\text{IC}} } \right)\left[ {M^{ *} } \right]$$
(2)

where k fl, k ISC, and k IC are the rates for spontaneous fluorescence, intersystem crossing, and internal conversion, respectively (all in s−1). In systems with collisions, the total depopulation rate, k tot, can be expressed in terms of a measurable quantity, the effective fluorescence lifetime, τ eff, using the following relation:

$$k_{\text{tot}} = \sum {k_{i} } = k_{\text{fl}} + k_{\text{nr}} = k_{\text{fl}} + k_{\text{IC}} + k_{\text{ISC}} + \sum {k_{q,j} n_{q,j} } = \frac{1}{{\tau_{\text{eff}} }} ,$$
(3)

with k nr as the non-radiative decay rate (s−1) as the sum of k ISC and k IC. k q,j is the quenching rate coefficient (in cm3/s), with n q,j (in m−3) as the concentration of the quencher species j. Another parameter related to τ eff is the fluorescence quantum yield, ϕ fl:

$$\phi_{\text{fl}} = \frac{{k_{\text{fl}} }}{{k_{\text{tot}} }} = \frac{{\tau_{\text{eff}} }}{{\tau {}_{\text{rad}}}} = {\text{const}} \cdot \tau_{\text{eff}}$$
(4)

with the radiative lifetime τ rad [13] given by (3) as the reciprocal fluorescence rate k fl, τ rad describes the theoretical fluorescence lifetime in absence of other decay channels. Thus, the fluorescence quantum yield is proportional to the effective fluorescence lifetime.

All the rate constants mentioned above depend on the vibrational excitation in the respective electronic state. Because various vibrational states are populated at the same time, a wide range of rate constants is active simultaneously. Due to Boltzmann statistics, the variability increases with temperature. For simplicity, often the photo-physical behavior of a single state with an energy corresponding to the average thermal energy is used for calculations to represent the entire distribution. The value of this average thermal energy is:

$$E_{{{\text{therm}},n}} = \mathop \sum \limits_{i = 1}^{N} \frac{{E_{{{\text{vib}},i}} }}{{(\exp \left( {1.44 E_{{{\text{vib}},i}} /T} \right) - 1) }}$$
(5)

with E vib,i as the energy of the vibrational states in the respective electronic state.

At low total pressure (below 10 mbar), no collisions with bath-gas molecules take place before the excited molecule is deactivated via fluorescence. In this case and without any quenching, the expression

$$\phi_{\text{fl}} = \frac{{k_{\text{fl}} }}{{k_{\text{fl}} + k_{\text{nr}} }}$$
(6)

can be used to describe the fluorescence quantum yield.

3 Experiment and data evaluation

Fluorescence measurements were performed in a static stainless steel cell. Determined by preceding measurements, 2 µl of the liquid tracer (either as a liquid or dissolved in dodecane) were injected, and the cell was filled with CO2 to reach the desired total pressure. The cylindrical cell is 126 mm high with an inner diameter is 40 mm. Three 25-mm-diameter quartz windows placed in o-ring-sealed flanges with 10-mm clear aperture allow optical access for the laser beam and fluorescence detection perpendicular to the laser beam. The cell is placed on top of a heating plate wrapped with heating wires. The gas temperature was measured with a K-type thermocouple placed inside the cell near the optical probe volume. The maximum achievable temperature was 500 K. The pressure was adjusted with a diaphragm valve and measured by a pressure transducer (Keller PAA-41/1-bar/8885).

Toluene, anisole, 1,2,4-trimethylbenzene, and 1-methylnaphthalene (Merck Chemicals, Analysis Grade), all being liquid at room temperature, were used as a pure substance, while 10 wt% naphthalene (Merck Chemicals, Analysis Grade) was dissolved in dodecane (Sigma-Aldrich; >99 % purity). Because the experiment focused on lifetime measurements and not on absolute fluorescence intensities, the exact concentration was not important. CO2 (Air Liquide, purity 4.6) was provided from a gas cylinder. The liquids were injected into the cell through a septum. This resulted in approximately 4 mbar tracer vapor. Before each measurement the cell was evacuated to a pressure of ~10 mbar by a membrane pump (Vacuubrand MD4C) and then was flushed with CO2 to minimize oxygen contamination. The leakage rate was 20 mbar/h which had a negligible effect during the measurement time of 30 s. This was additionally confirmed by comparing 1,2,4-trimethylbenzoyl fluorescence lifetimes from the present experiment with measurements in a flow cell in pure N2. Differences were within the measurement error (i.e., below 3 %).

The optical setup is shown in Fig. 1. A flashlamp-pumped frequency-quadrupled Nd:YAG laser (Ekspla, PL2143B) delivered pulse energies of 0.5 mJ at 266 nm with pulse lengths of 26 ps at a repetition rate of 10 Hz. The diameter of the circular laser beam was reduced to 4 mm by a Galilei telescope yielding a laser fluence of 4.5 mJ/cm2. The signal was collected perpendicular to the laser beam by a set of spherical quartz lenses (200- and 50-mm focal lengths), discriminated against elastically scattered light with glass filters (Schott UG11 and UG1 for one- and two-ring aromatics, resp.) and detected by a fast photomultiplier (Hamamatsu H6780-04, rise time 0.78 ns). The signal was recorded by a digital oscilloscope (Tektronix TDS7404B, 4 GHz bandwidth) that was triggered by a photodiode recording laser stray light from a mirror. To improve signal-to-noise ratios, typically 200 fluorescence decay curves were averaged.

Fig. 1
figure 1

Experimental arrangement for time-resolved laser-induced fluorescence measurements

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To check for a linear response, the fluorescence intensity was recorded as a function of laser fluence (not shown here) and was found to be linear up to 6 mJ/cm2 at 298 K for toluene. In additional measurements, it was confirmed that the number density achieved with 2 µl of the tracer solutions was low enough to not cause self-quenching of the fluorescence signal. Laser and signal attenuation was negligible (<2 %) for the given concentrations and path lengths.

4 Data analysis

The left panel in Fig. 2 shows the time-resolved LIF signals of toluene after picosecond excitation at 298 and 476 K after subtraction of the background signal (measured in the evacuated cell). The inset shows the signals in logarithmic scale versus time together with mono-exponential fits. Mono-exponential fits yielded equally good results for 1,2,4-trimethylbenzene and anisole. The right panel in Fig. 2 shows LIF signal traces for 1-methylnaphthalene at 323 and 523 K. Bi-exponential decays were observed for 1-methylnaphthalene and naphthalene that deliver a slow and fast fluorescence lifetime component with amplitudes representing the respective contribution to the total measured signal trace.

Fig. 2
figure 2

Left Toluene LIF signal decay after excitation at 266 nm at 298 and 476 K in 1024 mbar CO2. The inset shows the decay in a logarithmic plot with a mono-exponential fit. The resulting fluorescence lifetime was 45 and 37 ns, resp. Right 1-methylnaphthalene-LIF decay curve after excitation with 266 nm at 323 and 476 K in 1024 mbar CO2. The inset shows the decay in a logarithmic plot with a bi-exponential fit. For 323 and 476 K, the resulting fluorescence lifetime were 112 and 49 ns for the long component and 2.1 and 1.7 ns for the short component, respectively

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5 Results

5.1 Toluene

Figure 3 presents fluorescence lifetimes of toluene as a function of total pressure for various temperatures. Except for the lowest pressure at 298 K the lifetimes decrease with increasing pressure for all temperatures with this trend being more obvious at higher temperature. The difference in lifetime between 10 mbar and atmospheric pressure changes from −45 % at 355 K to −79 % at 475 K. The variation of the fluorescence lifetime with pressure can be described by mono-exponentials with offset (due to the lifetime at infinite pressure) as shown in Fig. 3 as lines. With this fit, it is possible to extrapolate the lifetimes to the collision-free regime at 0 bar and calculate the fluorescence (k fl) and non-radiative (k nr) rate constants. These as well as the fit parameters are given in Tables 2 and 3.

Fig. 3
figure 3

Dependence of the effective lifetime of toluene LIF (symbols) on total pressure at four temperatures. The lines represent mono-exponential fits to the data (the data point at 10 mbar and 298 K was neglected). 4 mbar toluene, CO2 bath gas, 266-nm excitation. Fit parameters given in Table 2

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Table 2 Fit parameters (equation: \(\tau \left( p \right){/}{\text{ns}} = A \exp \left( { - \frac{{p{/}{\text{mbar}}}}{B}} \right) + y_{0}\); τ: effective lifetime; p: pressure; A, B, y 0: fit parameters) derived from the fluorescence decay profiles after 266-nm excitation of the investigated aromatics
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Table 3 Radiative lifetime τ rad and rate constants k fl and k nr derived from τ0
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5.2 1,2,4-Trimethylbenzene

Figure 4 shows pressure-dependent fluorescence lifetimes of 1,2,4-trimethylbenzene for various temperatures together with mono-exponential fits for each temperature. For this species at 298 K, the lifetime slightly increases with pressure but decreases for all other temperatures. The difference in lifetime between 10 mbar and atmospheric pressure changes from +12 % at 298 K to −72 % at 475 K.

Fig. 4
figure 4

Dependence of the effective fluorescence lifetime of 1,2,4-trimethylbenzene (symbols) on total pressure at four temperatures. Solid lines represent mono-exponential fits to the data. 4 mbar 1,2,4-trimethylbenzene, CO2 bath gas, 266-nm excitation. Fit parameters given in Table 2

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5.3 Anisole

Figure 5 shows the pressure-dependent fluorescence lifetimes of anisole for various temperatures together with mono-exponential data fits for each temperature. In comparison with 1,2,4-trimethylbenzene, a pressure-dependent increase in lifetime is visible for the two lower temperatures, which then switches to a pressure-dependent decrease in the two higher temperatures investigated here. The estimated transition temperatures between these two regimes are roughly 400 and 326 K for anisole and 1,2,4-trimethylbenzene, respectively. The change in lifetime from 10 mbar to atmospheric pressure is +18 % at 298 K and −35 % at 475 K.

Fig. 5
figure 5

Dependence of the effective fluorescence lifetime of anisole (symbols) on total pressure at four temperatures (symbols). Solid lines represent mono-exponential fits to the data. 4 mbar anisole, CO2 bath gas, 266-nm excitation. Fit parameters given in Table 2

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5.4 Naphthalene

Figure 6 shows the pressure-dependent fluorescence lifetimes of naphthalene for various temperatures together with mono-exponential fits for each temperature. The slow and the fast lifetime components were extracted by applying a bi-exponential fit to the measured fluorescence decay profiles. For the slow lifetime components (solid symbols in Fig. 6), a variation in lifetime with increasing pressure is visible for all investigated temperatures. The increase in lifetime from 10 mbar to atmospheric pressure decreases from +79 % at 298 K to +49 % at 475 K.

Fig. 6
figure 6

Dependence of the effective fluorescence lifetime of naphthalene (symbols) on total pressure at four temperatures. Solid lines represent mono-exponential fits to the data points. 4 mbar naphthalene, CO2 bath gas, 266-nm excitation. Fit parameters given in Table 2

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The pressure dependence shown here corresponds well to the data of Beddard et al. [18] and Ossler et al. [19]. The data in [18] was obtained using various laser excitation energies at fixed temperature rather than a common wavelength at variable temperatures, verifying that both methods are alternatives to reach various (average) excited state energies and share the same theoretical background.

Although the fast lifetime component could not be extracted from the fits precisely enough for pressures above 500 mbar due to the limited rise time of the photomultiplier (0.8 ns [20]), its contribution at low pressure cannot be neglected. At the lowest pressure, the amplitude of the fitted exponentials of both lifetime components indicates almost equal contributions from both fluorescence decay channels. Therefore, the relative contribution of both decay channels was evaluated from the relative amplitudes of the bi-exponential fit at 10 mbar (2/1, 2.5/1, 3.2/1, and 2.2/1 for 296, 355, 405, 475 K, respectively).

5.5 1-Methylnaphthalene

Figure 7 shows the fluorescence lifetimes of 1-methylnaphthalene for various temperatures together with mono-exponential fits for each temperature. Like for naphthalene, the slow and fast lifetime components were determined from bi-exponential fits to the measured fluorescence decay profiles. For the slow lifetimes, an increase with increasing pressure is visible for all temperatures investigated. The increase in lifetime from 10 mbar to atmospheric pressure decreases from +72 % at 298 K to +37 % at 475 K.

Fig. 7
figure 7

Dependence of the effective fluorescence lifetime of 1-methylnaphthalene (symbols) on total pressure at four temperatures. Solid lines represent mono-exponential fits to the data points. 4 mbar 1-methylnaphthalene, CO2 bath gas, 266-nm excitation. Fit parameters given in Table 2

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Again, the fast lifetime component could not be extracted precisely for pressures above 500 mbar, but its contribution at low pressure cannot be neglected. The amplitude ratios of both lifetime components at 10 mbar were 1.6/1, 4.5/1, 4/1, and 3/1 for 296, 355, 405, and 475 K, respectively. A weighted average of both lifetime components with their intensity was used to calculate the natural lifetime and rate constants, just like for naphthalene.

5.6 Rate constant overview

Using Eqs. (4), (5), and the absolute fluorescence quantum yield from the literature [21], the natural lifetimes at 298 K and 266 nm and the rate constants k fl and k nr were determined for each tracer using extrapolated lifetimes for 0 mbar at 298 K. For the tracers with bi-exponential signal decays, both lifetime components were weighted with their amplitude at 10 mbar to determine an effective lifetime. The resulting error for extrapolation is around 28 % for 1-methylnaphthalene and around 4 % for the other tracers. The results are listed in Table 3. The obtained rate constants for toluene and naphthalene are in good agreement with previous data presented by Hsieh et al. [22], Jacon et al. [23] and Burton and Noyes [24].

6 Discussion

In the following, an effort is made to rationalize the observations described above. Anisole will be discussed first since it displays both pressure dependencies in the temperature range that was analyzed. From previous studies of the energy levels in the S0 and S1 states, the 0–0 energy gap has been determined to be 36,394 cm−1 [16] which in our experiments is 1200 cm−1 lower than the photon energy (266 nm laser, i.e., 37,594 cm−1). Because the vibrational energy level structure is different for the S0 and S1 states, the average thermal energy level (called in accordance with literature the thermal energy level E therm, cf., Eq. 5) has a somewhat different energy gap (note, with increasing temperature, in general E therm in S1 shifts more quickly to higher energies than in S0, due to the higher density of the states in S1). After laser excitation, the initial population in the S1 state differs from the thermal population in the S1 state. The initial population depends on the laser wavelength (fixed here) and the temperature, i.e., the thermal population in the S0 state. At a given temperature the difference in the average energy of the initial distribution (E initial) and the thermal energy level E therm can be calculated based on known vibrational energies in both electronic states. For toluene and naphthalene, such vibrational energy levels are known with sufficient accuracy [25].

For anisole at room temperature and 266-nm excitation, E initial is above E therm, shown as heavy purple line in Fig. 8 (left). The excess vibrational energy (“photo-induced heating”) is randomized within the molecule and in case of collisions transferred to the bath gas causing stepwise relaxation toward the thermalized condition with E therm. This collisional relaxation becomes faster with increasing pressure. The rates of the non-radiative decay processes (i.e., IC and ISC) are state dependent and their rates increase with increasing vibrational energy. Collisional relaxation therefore reduces losses through these competing channels and more molecules are able to fluoresce. In the case of anisole at room temperature this can be seen by the increase of the fluorescence lifetime (i.e., fluorescence quantum yield) with pressure (filled squares in Fig. 5, reproduced as inset in Fig. 8).

Fig. 8
figure 8

Schematic Jablonski diagram for anisole at room temperature, the lengths of the horizontal arrows for k nr indicates the relative rate constants. ΔE therm is the center of gravity of the thermal Boltzmann distribution in each state. ΔE laser corresponds to 266-nm excitation. Left E initial > E therm leading to laser-induced heating, right E initial < E therm leading to laser-induced cooling

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With increasing temperature, a transition regime is reached where E initial equals E therm and where the fluorescence quantum yield becomes pressure independent. At even higher temperatures, E initial is below E therm (Fig. 8 right) and collisions lead to a cooling of the bath gas—a process referred to as photo-induced cooling [11, 12]. Collisions populate higher states in the electronically state and thus, increased collision rates reduce the lifetime of the excited state and hence the fluorescence quantum yield. In the present case of anisole at the higher temperatures (starting at around 405 K, cf., Fig. 5), these processes then also shorten the fluorescence lifetime with increasing pressure (cf., Fig. 5 and inset in Fig. 8).

This general concept can be transferred to every other molecule investigated in this study. The 0–0 energy gap of 1,2,4-trimethylbenzene is slightly higher than that for anisole (36,435 cm−1 [15]). Therefore, the decrease of the fluorescence lifetime with increasing pressure starts at lower temperatures compared to anisole (Fig. 4). For toluene, the 0–0 energy gap is so large (37,476 cm−1 [15] ) that for all temperatures investigated in this work, excitation at 266 nm leads to E initial < E therm, which causes a decrease in fluorescence lifetime with increasing pressure (cf., Fig. 3).

For naphthalene and 1-methylnaphthalene, the case is not so straightforward. The 0–0 energy gap for naphthalene is much smaller (30,200 cm−1 [17]) compared to that of single-ring aromatics. This is well mirrored by the strong increase of the long fluorescence lifetime component with increasing pressure, even at 475 K (cf., Fig. 6). This behavior was explained in the previous section for single-ring aromatics. However, at the present stage of the investigation, we cannot explain the origin of the fast lifetime component as well as its pressure dependence. Because the S2–S0 energy gap is only 35,900 cm−1 [17], the S2 state is also accessible in a single-photon transition with 266-nm radiation. This might be a hint for an explanation, but further studies need to be conducted to find out more about this process. The same applies to 1-methylnaphthalene.

7 Conclusions

Effective fluorescence lifetimes of toluene, 1,2,4-trimethylbenzene, anisole, naphthalene, and 1-methylnaphthalene were measured after picosecond laser excitation at 266 nm and at temperatures between 298 and 475 K and pressures between 0.01 and 1 bar. Experiments were performed in a heated static optical cell with CO2 as buffer gas. The data obtained provide a first systematic evidence of the effect of photo-induced cooling [11, 12] in anisole and 1,2,4-trimethylbenzene. This effect explains the species-specific characteristic variation of effective fluorescence lifetimes with pressure at fixed temperatures. As already shown by Ossler et al. [19] for naphthalene and 1-methylnaphthalene, a slow and fast lifetime component was observed. The interpretation of this second signal component and its pressure dependence requires further investigation beyond the scope of the present work.

Fluorescence and non-radiative rate constants have been determined using collision-free lifetimes extrapolated from the measured values to zero pressure. The obtained rate constants for toluene and naphthalene are in good agreement with previous data presented by Hsieh et al. [22], Jacon et al. [23] and Burton and Noyes [24]. For 1,2,4-trimethylbenzene, anisole, and 1-methylnaphthalene, no literature data is available so far. The parameters measured are needed for step-ladder fluorescence models to predict fluorescence quantum yields for these aromatics that are frequently employed as tracer species for quantitative gas mixing studies [2] and thermometry [26]. Such models yet need to be developed for 1,2,4-trimethylbenzene, anisole, and 1-methylnaphthalene. For this purpose, the experimental data base initiated in this work needs to be extended to higher temperatures relevant in many areas of application of tracer LIF, e.g., engine combustion.