Stephen E. Bialkowski and Agnès Chartier

Photothermal lens spectroscopy is an ultra-sensitive method applicable to trace analysis and studies involving photo-initiated reaction chemistries.¹ There are several factors that limit the enhancement² and influence the accuracy of measurements obtained using photothermal lens spectrometry. First, the optical element produced in the relatively large-volume sample cells is not a simple parabolic profile lens. The aberrant nature of the thermal lens results in signal magnitudes that are somewhat smaller than expected.³ Second, it is assumed that sample heating produces only small departures from the equilibrium thermodynamic parameter values. However, continuous sample irradiation can produce large temperature changes. In theory, the on-axis temperature change approaches infinity at long times for any excitation power. In practice, large temperature changes distort the thermal lens perturbation and may cause convection heat transfer or even boiling.⁴ A third problem occurs when the analyte has long-lived excited states. In this case excited state populations may further perturb the refractive index resulting in enhanced or decreased photothermal lens signals.⁵ Metastable excited states may affect the refractive index directly or through the resulting density change due to different solvation volumes.

An apparatus utilizing a two-laser photothermal lens apparatus that is immune to many problems associated with photothermal lens spectrometry is described in this work. The apparatus uses a low-volume cylindrical sample cell and a chopped laser excitation source. The sample cell is uniformly illuminated with the constant-irradiance laser beam. A parabolic photothermal lens element develops due to heat loss through the sample cell walls. The spatial profile of this lens are constant for a given sample cell, depending only on cell radius. A theory for describing the photothermal lens developed in a cylindrical sample cell is described.⁶ A model for relating signals to sample absorbance is given and experimental evidence is presented. Time-dependent photothermal signals are detected

Theoretical time-dependent temperature changes and inverse photothermal lens focal lengths for both standard and cylindrical sample cells are described in the literature.^1,6 The solution for thermal diffusion in homogeneous samples of infinite extent is to model the results obtained using standard sample cell. Cylindrical cell results were discussed in Ref. 1 and later used to model photothermal lens signals produced with incoherent excitation.⁶ The stainless steel cylindrical cell used here has a large thermal conductivity compared to the ethanol solvent. With the high thermal conductivity ratio, there should be no appreciable temperature change in the sample cell wall. The solution to the thermal diffusion equation for a zero temperature change at the cell wall temperature change is⁷

(1)

a (m^-1) is the exponential absorption, E (W m^-2) is the excitation irradiance, Y_H is the heat yield, the sample's thermal conductivity is k (W m^-1 K^-1), J₀ and J₁ are Bessel's functions, and c _n is the n'th root of the Bessel's function equation, J₀(c _n)=0. The characteristic thermal time constant is defined as t_c=a²/4D_T, where a (m) is the sample cell radius and D_T (m² s- ¹) is the thermal diffusion coefficient. For long irradiation times, the radial dependent temperature change is parabolic

(2)

The time-dependent inverse focal length for the cylindrical sample cell is found by integration of the second radius derivative over the pathlength and multiplying by the thermal-optical coefficient

(3)

The photothermal lens signal for the cylindrical sample cell is defined in the same fashion as in the large-volume sample cell.⁸ Since no approximation is used to calculate the inverse lens strength, the maximum signal is an exact result. The time-dependent signal is found from the relationship, S(t)=[F _p(t=0)- F _p(t)]/F _p(t), where F _p(t) is the probe laser power. For a pinhole aperture placed far from the sample cell, the signal is S(t)=2z'/f(t), where z' (m) is the distance from the probe laser beam focus position to the sample cell.

Model calculations exhibit an exponential response after a relatively short induction period. The model behavior indicates that a single Bessel's root dominates the time-dependent behavior. Examination of the model data shows that the first root, c ₁=2.405, dominates after an initial induction period. The inverse focal length is approximated by

(4)

The characteristic time constant may be obtained from t_c =2.632D t_10%-90%, where D t_{10%- 90%} is the time required for the signal to change from 10% to 90% of the maximum.

A schematic diagram of the apparatus used in this study is shown in Figure 1. Ar⁺ laser operating at 514.5 nm is used for sample excitation. This Ar⁺ laser has nearly constant irradiance across a cylindrical beam profile. Ar⁺ laser output is filtered and collimated to produce a 1 cm diameter beam. The collimated beam subsequently passes through a neutral density filter, a beamsplitter that directs a fraction of the light to a photodiode, and an electric shutter. The beam then reflects off a dichroic mirror and is combined with the probe laser.

The probe laser is a 2 mW, 632.8 nm HeNe laser. The beam passes through a lens prior to combination with the Ar⁺ laser. The collinear beams both are focused into the sample. The positions of all three lenses are adjusted to image the Ar⁺ laser into the sample cell while focusing the HeNe laser to a point about one confocal distance in front of the sample cell. A pinhole is place 1 cm in front of the sample cell to reduce heating.

Two sample cells are used. A 0.25 m L, 2 mm pathlength HPLC spectrophotometer cell (ISCO) is used as the cylindrical sample cell. This cell has an estimated inside radius of 200 m m. A standard 1 cm pathlength spectrophotometry cell is used for comparison studies.

After exiting the sample cell, the probe laser beam is split into two parts. Part of the beam passes through a 632.8 nm filter and onto a large area detector. The other part passes through the pinhole aperture, then though a 632.8 nm laser line filter onto the same model detector. Silicon photovoltaic detectors are used. Photothermal signal and HeNe reference signals are processed with an operational divider to eliminate apparent signals produced from absorption and reflection losses, and sample luminescence.

The photothermal lens signal is digitized with a 16 bit analog-to-digital converter in a PC data collection computer. Data processing is performed using a spreadsheet program. All photothermal lens data is processed to produce signals proportional to inverse focal length.

Reagents used in this study are tris(2,2'-bipyridyl) dichloro-ruthenium(II) hexahydrate, Ru(bpy)₃Cl₂ (Aldrich), dicyclopentadienyl iron, FeCp₂ (Eastman), and iron(III) chloride hexahydrate, FeCl₃ (Baker). Ru(bpy)₃(ClO₄)₂ is prepared by aqueous precipitation from Ru(bpy)₃Cl₂ solutions by drop-wise addition of 1.0 N HClO₄ to completion. Deoxygenation is performed by bubbling solvent-saturated argon through the solutions for 30 minutes prior to measurement. Concentrations are about 10 m M for Ru(bpy)₃X₂ salts and 1 mM for FeCp₂ and FeCl₃. Concentrations used result in absorbances of about 0.01 cm^-1, or about 99.5 %T through the 2 mm cylindrical sample cell.

Figure 2 shows 100 averaged signals obtained using 0.011 AU cm^-1 FeCp₂ ethanol solution in cylindrical and standard cells. Signals are corrected for optical pathlength and excitation irradiance differences. The time-dependent response and signal magnitude differences are expected due to the thermal diffusion boundary conditions.

The standard cell photothermal lens signal has a maximum of 0.135 mW^-1cm^-1 and a time constant of 0.165 s. Using the thermal diffusion coefficient of 8.9´ 10^-8 m²s^-1 for ethanol, an excitation laser beam waist radius of 240 m m is obtained from the characteristic time constant. This is in reasonable agreement with the 163 m m measured radius. A t_c of 0.135 s is found for the cylindrical cell from D t_{10%- 90%}, implying a cell radius of 219 m m. Maximum signals for cylindrical and standard cell experiments are 0.05 mW^-1cm^-1 and 0.135 mW^-1cm^-1. The different signal magnitudes are expected from the theoretical signal ratio

(5)

w (m) is the laser beam waist radius.

Signals obtained using the FeCp₂ ethanol solutions scale linearly with excitation irradiance and concentration, and do not change upon irradiation. On the other hand, the photothermal lens signals for Ru(bpy)₃²⁺ salts and FeCl₃ exhibit curious behavior. Figure 3 compares the time-dependent signals obtained by multichannel averaging chopped laser transients for FeCp₂, Ru(bpy)₃Cl₂, and FeCl₃. These data are averages of 10 transients taken at the start of irradiation. The excitation laser power was 6.5 mW in all cases and the data are normalized by the respective 514.5 nm optical absorbances. Signal magnitude differences between for FeCp₂ and FeCl₃ may not be significant. However, the Ru(bpy)₃Cl₂ signal is substantially larger than can be attributed to spectrophotometry errors. It is of particular interest that the signal for Ru(bpy)₃Cl₂ tends to increase at times greater than about 5 t_c while that for FeCl₃ decreases with irradiation time, after going through a maximum. The small time-dependent decrease in photothermal lens signal for the FeCl₃ solution may be due to a temperature-dependent equilibrium between FeCl²⁺ and Fe³⁺+Cl^-. Fe³⁺ does not have a significant absorbance at 514.5 nm without the chloride ligand.

Experiments are performed in which the Ru(bpy)₃Cl₂ signal is monitored over long periods. The signal increases with time indicating a non-reversible change. Blocking the excitation laser for 15 minutes, then continuing the measurements show that photothermal lens signal change is due to excitation laser irradiation and is non-reversible on the time scale of minutes. Similar effects are observed for Ru(bpy)₃(ClO₄)₂, with and without purging to remove dissolved oxygen. Long-time irradiation does not change signals for the FeCp₂ or FeCl₃ solutions and these effects are not observed using the standard sample cell.

The 514.5 nm excitation is 65 nm red of the Ru(bpy)₃²⁺ absorbance maximum at 450 nm.⁹ Excitation may be singlet-to-triplet metal-to-ligand charge transfer.¹⁰ The low excitation energy is not thought to be sufficient to cause photolysis. It is possible that Ru(bpy)₃²⁺ salts are modified by optically-induced ligand transfer. Ru(bpy)₃Cl₂ can undergo ligand exchange in nonpolar solvents such as methylene chloride when excited at 452 nm producing Ru(bpy)₂Cl₂.¹¹ The absorption spectrum maximum of the resulting Ru(bpy)₂Cl₂ complex is shifted to 556 nm in CH₂Cl₂.¹¹ The 514.5 nm absorbance would presumably be higher than the parent Ru(bpy)₃Cl₂. However, the reaction is not thought to occur with nitrate and perchlorate salt or in polar solvents. In these experiments, exchange may be occurring between ethanol and bipyridyl ligand. Similarly, photolysis may result in dehydration of the primary solvation sphere, which may contain water. In this case there would be an exchange between water and ethanol.

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