Introduction

Nanosecond Time-resolved Near/Mid-IR spectrometer and

Data Analysis Techniques

II-1 Introduction

In this chapter, we present technical details of the laboratory-built nanosecond TRIR spectrometer used in this work and the principles of numerical data analysis techniques (SVD and global curve fitting) employed for physical interpretation of observed spectroscopic results.

II-2 Nanosecond Time-resolved Dispersive IR Spectrometer

Nanosecond TRIR spectroscopy is a well-known technique used to study the photophysical and photochemical processes that are taking place in the sub microsecond to millisecond time domains. The development of nanosecond dispersive TRIR spectrometers dates back to 1990s. Yuzawa and co-workers [32] developed a high-sensitivity nanosecond TRIR spectrometer by using a high-intensity IR light source and an ultralow-noise, wide-bandwidth amplifier. However, long acquisition time and poor spectral resolution were the major drawbacks of their apparatus. Yabumoto and co-workers [12,33] improved the spectral resolution of the apparatus by enhancing the throughput of the spectrometer. More specifically, they employed a long-focal-length spectrometer with a low f-number. It was further modified to cover a wider spectral range of both NIR and MIR regions so that one can access not only vibrational transitions but also low-energy electronic transitions that are dark to visible spectroscopy. In the present study, we used the TRIR spectrometer originally developed by Dr. Sohshi Yabumoto [33].

Time-resolved Raman spectroscopy is a complementary approach to TRIR spectroscopy [27,28,34,35]. Although both techniques provide essentially the same vibrational information except that different selection rules apply to Raman and IR, TRIR spectroscopy has a couple of advantages over time-resolved Raman spectroscopy in studying the reaction mechanisms of photochemical reactions. First, fluorescence, which often accompanies photophysical and photochemical reactions, severely interferes with Raman measurements. Second, time-resolved Raman spectroscopy requires the probe light to be in resonance with an electronic transition from the excited state generated by the pump pulse. This requirement implies that at the expense of high selectivity due to the resonance Raman effect, only the information of the excited states that can be resonantly excited will be obtained with time-resolved Raman spectroscopy. If we are interested in seeing the whole reaction dynamics rather than particular transient species that is in resonance with the probe light, we should choose a technique that does not utilize resonance enhancement, i.e., TRIR.

II-2.1 TRIR Setup

The TRIR spectrometer used in the present study is schematically shown in Figure II–1. It consists of a photoexcitation light source, an IR probe light source, a dispersive monochromator, a slit controller, a speed detector, a differential amplifier, and a high-speed digitizer. The photoexcitation light source was a Q-switched Nd-YAG laser (IB Laser, DiNY pQ 355), which emits the third harmonic at 355 nm. The pulse width was 7 ns and repetition rate was 500 Hz. The maximum pulse energy was 1.1 mJ, but typically pulse energy of ~100–150 µJ was used for photoexcitation. A ceramic IR emitter purchased from JASCO was used as the probe light for MIR measurements (<4000 cm^–1), whereas a tungsten-halogen lamp was used for NIR measurements (>4000 cm^–1). The probe IR light was focused onto the sample and was introduced into a modified Czerny–Turner monochromator (JASCO, CT-50TFP; focal length = 500 mm and F-number = 4.3) using a pair of off-axis ellipsoid mirrors. The probe light transmitted through the sample was dispersed by the monochromator.

The dispersive method utilized in the present study excels the FTIR method in sensitivity [12], [36], stability, and less influence of artifacts [32]. Three manually switchable gratings are available in this monochomator. The groove density and blaze wavelengths of these gratings are as follows: (i) 100 lines mm^–1 and 7.3 µm; (ii) 300 lines mm^–1 and 3 µm; and (iii) 600 lines mm^–1 and 10 µm. These three gratings can cover the spectral window between 800 and 11500 cm^–1. Higher-order diffraction was removed by using an order sorter after the exit slit of the monochromator that comprises appropriate filters attached to a filter wheel. When the tungsten-halogen lamp was used, the visible portion of the output was eliminated by using a pair of IR transmitting filters (Sigma Koki, ITF 85IR): one before the sample and the other in front of the entrance slit of the monochromator. The entrance and exit slits of the monochromator were controlled precisely by an external OPTMIKE slit controller to keep the spectral resolution constant throughout the measurement. The mechanical slit width (Sm) at any given spectral resolution identical to its optical slit width (Ssp) for a Czerny–Turner type monochromator is given by Eq. (II–1).

Here 𝑑_! is the linear dispersion in wavenumber, m is the order of diffraction, f is the focal length, G is the groove density of the grating used, 𝜈_! is the center wavenumber, and ε is the half value of the Ebert angle, which is the angle between the incident and diffracted lights at the grating. The Ebert angle of the CT-50 monochromator is 27°.

The dispersed light was further focused on the IR light detector using an off-axis ellipsoid condenser. A mercury cadmium telluride (MCT) detector was used for the region below 2000 cm^–1 and an indium antimonide (InSb) detector for the region above 2000 cm^–1. The bandwidths of the MCT and InSb detectors were 20 and 15 MHz, respectively. The detected signal from the IR detector was amplified by coupling the detector output with an ultralow-noise preamplifier using a 22 nF capacitor, followed by further amplification by a factor of 1000 with a differential amplifier (NF Corporation, 5305; 10–1000 amp. gain, 10 MHz bandwidth) so that only the small changes in the probe light intensity induced by the pump pulse can be detected. Owing to this AC-coupled amplification, the sensitivity of the instrument reaches as high as 1 × 10^–6. The time resolution of the instrument is limited by the bandwidth of the differential amplifier, which is approximately 80 ns.

The output of the main amplifier was fed to a high-speed digitizer (NI, 5112; dynamic range = 8 bit, sampling rate = 100 MHz) mounted on a personal computer. The apparatus is also equipped with another digitizer from Tektronix (DSA 602A), which was used for measurements with a sampling rate higher than 100 MHz. However, the data transfer throughput between the oscilloscope and the computer is low because of GPIB communication.

The procedures for measuring steady-state and time-resolved difference IR spectra are as follows. The intensity of the IR probe light, I(ν!0), and the intensity of the IR probe light transmitted through the sample, I(!ν) , were measured consecutively. The probe light was modulated by a rectangular wave generated by a chopper in order to measure the intensity in the AC-coupled amplification detection scheme. The absorbance of the sample is calculated using Beer–Lambert law.

The IR absorbance difference (ΔA) spectrum was measured by spatially overlapping the pump pulse and probe light at the sample. The beam diameter of the probe light was about 2 mm at the sample position. The 355-nm pump beam was loosely focused so that it can illuminate a sufficiently large area of the probe beam. The small changes in the intensity of the probe light

induced by photoexcitation with the pump pulse was measured using the AC-coupled detection scheme. The measured ΔA spectrum is substantially interfered with Q-switch noise, thermal noise of the detector, and other electronic noises. To achieve a high signal-to-noise ratio (S/N), it is desirable to reduce all these noises as much as possible. To eliminate Q-switch noise, the IR detector was shielded using a box made of aluminium. Cross talk between the cables was reduced by optimizing cable orientations and appropriately grounding the electronic devices. The intensities of the probe beam with pump on and off were measured in sequence and the pump-off spectrum was subtracted from the pump-on spectrum to obtain the time-dependent change in the intensity of the probe light, ΔI !ν,τ

( )

ΔA !

( )

( )

Figure II–1. Optical layout of the nanosecond TRIR spectrometer.

Ceramic

II-2.2 Sample Circulation System

TRIR measurements were performed using a sample circulation system that allows us to have a fresh sample for every new pulse at the sample. This sample circulation system prevents the sample from degradation due to multiple excitation with the pump pulses. It consists of a sample cell holder, IR-transparent optical windows, Karlez® O-rings, Teflon® tubing, Swagelok® bulkhead unions, a gear pump driven by magnetic field (Idex Co.), and a reservoir. Schematics of the sample cell holder components and the entire sample circulation system are shown in Figure II–2 and Figure II–3, respectively. The sample cell holder is made of stainless steel and has very flat and smooth surface with holes to accommodate the O-rings.

The inlet and outlet of the sample holder were connected to the gear pump and sample reservoir, respectively, using Teflon tubing to enable sample circulation. Optical-grade calcium fluoride and barium fluoride plates (thickness = 20 mm), which are transparent throughout the visible and IR regions, were used as optical windows. A lead spacer was sandwiched by these optical windows. Depending on the sample and the spectral region to be measured, the path length of the cell was varied by changing the thickness of the spacer.

Typically 50, 100, and 500 µm spacers were used for MIR measurements, whereas a 1 mm spacer was used for NIR measurements because of very weak signal intensity in this region.

The sample was circulated using the gear pump at a flow rate of 20 cm/s. The sample in the reservoir was bubbled with argon gas to remove dissolved molecular oxygen (O2).

Figure II–2. Schematic of the cell holder.

Figure II–3. Schematic of the sample circulation system.

II-3 Singular Value Decomposition Analysis

SVD analysis is one of the most popular multivariate data analysis techniques used by spectroscopists to extract the information on the number of significant components involved in the spectra measured as a function of time, temperature, pH, concentration, etc. SVD analysis has previously been used in TRIR spectroscopy [37-39] to interpret the transient spectra based on a physical model. If the data reconstructed using the model reproduce the original data well within experimental uncertainty, we can conclude that the model represents a plausible mechanism of the underlying photophysical or photochemical processes. SVD was employed in the PNA work (see Chapter IV).

II-3.1 Mathematical Definition

Given a real m × n matrix A, SVD decomposes it as

A=USV^T (II–4)

where U is an m × m orthogonal matrix, V is an n × n orthogonal matrix, and S is an n × n diagonal matrix. The columns of U are the left singular vectors of AA^T and the rows of V^T are the right singular vectors of A^TA. The diagonal matrix S is called a singular value matrix and its diagonal elements are called singular values, which are nothing but the square roots of the eigenvalues of either of the left singular vectors uk or the right singular vectors vk. These

To Argon Cylinder

Gear Pump

Sample Reservoir Sol

vent Res

ervo ir

PTFE tubing Cell Holder

singular values are placed in a decreasing order (s11 > s22 > s33 > … > srr > … > snn) along the diagonal of the matrix S. The matrix notation of SVD is shown in Eq. (II–5).

𝑎

⋯ 𝑎

After SVD, we have to decide on the number of significant components that are essential to reproduce matrix A. Various criteria for deciding on the adequate number of SVD components are available in the literature. In one of those criteria, the contribution of each singular value to the whole data is evaluated and all of the singular values that account for 70–90% of the total of singular values are considered for reconstruction. In another criterion, singular values higher than the mean of all the singular values or higher than the fraction 0.7/n (n denotes total number of singular values) are retained. However, these criteria may depend substantially on the noise level in the TRIR spectra. Furthermore, they tend to result in too many components, which make it impossible to analyze the time-resolved data using a physical model. Here we inspect spectral and temporal components (uk and vk) of each singular value and focus on only components that exhibit physically meaningful spectral or temporal behaviors. By doing so, we can reduce noises and reproduce the matrix A with a reasonably small number of components that typically account for more than 90% of the raw data.

II-4 Global Fitting Analysis

Global fitting analysis [40] is a popular curve fitting technique used in time-resolved spectroscopic studies to check the validity of physical models used to explain experimental observations as well as to extract the spectral and dynamics information of the transient species generated in a photochemical reaction. We employed global fitting analysis in the Py/DCB work (see Chapter III). It performs simultaneous fitting of all the data using model functions with several common adjustable parameters. In time-resolved spectroscopy, the acquired spectra at different times are represented as a matrix. Let us denote such a matrix Y.

According to Beer–Lambert Law, the absorbance of the sample at wavelength λ and time t, y(t,λ), is the sum of contributions from all the absorbing species involved in the reaction. It can be expressed as follows:

 y t, λ = c1 t ε1 λ +    c2 t ε1 λ +  c3 t ε3 λ +  … … … . +  cn t εn λ

=   c_!(t)ε_!(λ)

!

!!!

(II–6)

where ci(t) is the concentration of the ith molecular species involved and εi(t) is the modified molar absorptivity of the same molecular species which is actually a product of path length (l) and molar absorptivity (εn†(t)). Hence matrix Y can be very easily decomposed as shown in Eq. (II–7).

Y = CS + R (II–7)

where the columns of matrix C represents the concentration profiles (i.e., time profiles) of transient species as a function of time, the rows of matrix S represents the modified absorptivity of the transients (i.e., spectral profiles) as a function of wavelength, and R represents the residual matrix, which in most cases represent random noises. An example of global fitting analysis is shown in Figure II–4. Hypothetical time-resolved spectra recorded at different time delays (Figure II–4a) are represented as a matrix. Here we use two components that obey first-order kinetics but show complementary behaviors so that the spectrum observed at any point in time and space can be represented as a liner combination of these two components alone. Using the fitting functions, all the waves are fit simultaneously. The concentration and spectral profiles obtained with global fitting are shown in Figure II–4b and Figure II–4c, respectively. The overall performance of the global fitting analysis can be examined by taking a closer look at the residuals shown in Figure II–4d. As there is no particular spectral/temporal pattern remaining except for noises, it is confirmed that the global fitting analysis is successful. A technical difficulty may arise when our starting physical model is exceedingly complex. Analytically solving rate equations is not always possible and hence we may need the help of numerical methods to perform this analysis.

Figure II–4. Simulated time-resolved spectra (a), extracted concentration profiles (b), spectral profiles (c) and residuals (d) obtained after performing global curve fitting analysis over the time-resolved spectral data matrix shown in (a).

a b

c

d

Chapter III

BET Mechanism of a

Bimolecular PET Reaction

between Py and DCB

III-1 Introduction

Photoinduced intermolecular electron transfer (PIET) reactions are one of the fundamentally important photochemical processes owing to its significance in photochemistry and photobiology [31,41,42]. PIET reactions play a prominent role in the function of OPVs. It is essential to advance our understanding of the PIET processes with a view to rational design of efficient devices that can solve the urgent issue of renewable energy sources. In a PIET, FET leads to charge formation, and BET leads to the decay of the induced charges via, e.g., recombination reactions. The latter process is strongly favored thermodynamically.

Preventing or impeding the charge recombination seems to be an important prerequisite for enhancing the performance of DSSCs [43,44] as well as organic bulk heterojunction solar cells [45]. Although a variety of strategies have been developed and demonstrated, such as tuning the HOMO–LUMO band gap between the donor and the semiconductor material and changing orbital symmetry in donor–bridge–acceptor systems [46], efficient retardation of charge recombination is still a challenging goal in solar cell research.

The major obstacle to this goal arises from the fact that BET is very often not a simple recombination of primary charge carriers but a multistep photochemical reaction involving other molecular species in the system as well. Detailed understanding of the mechanism of BET is thus of paramount importance for overcoming the conundrum of fast charge recombination in all photovoltaic devices. Spectroscopic approaches provide a direct means to look at PET reactions and have proven powerful for such mechanistic studies. Much work using transient absorption spectroscopy has focused on ultrafast FET reactions [47-52]. Hino et al. [53,54] provided a detail account on the mechanism of FET by using Py–N,N-dimethyl aniline (DMA) and Py–DCB systems. They found that FET in Py–DMA proceeds through formation of an exciplex in moderately polar solvents followed by formation of contact ion pairs, solvated ion pairs, and free ions. In Py–DCB, however, FET proceeds through solvated ion pairs and free ions. No exciplex formation has been detected in this system. Though the energies of exciplexes, solvated ion pairs and free ions are similar for both Py–DMA and Py–

DCB systems, the FET pathways are different. They also worked on various Py–quencher systems [53], where the quencher can be either a donor or an acceptor, and found that there is no correlation between electron donor–acceptor interactions and the photodissociation yields of free ions. They concluded that the chemical property of the quencher is a key to understanding FET mechanism. Koch et al. [55] detected the formation of exciplexes in PIET reactions using ultrafast IR spectroscopy. Ultrafast transient absorption and IR spectroscopies

[56,57] have been used to detect both contact ion pairs and solvated ion pairs in PIET reactions.

In contrast to FET, BET reactions, which proceed on a much slower time scale (typically in the ns–µs time regime), are yet to be more thoroughly investigated in particular with regard to their reaction mechanisms. In this study, we used time-resolved NIR and MIR spectroscopy [12,58] to unveil the mechanism of the BET dynamics in the PIET reaction between Py and DCB dissolved in ACN. Unlike conventional transient absorption spectroscopy, our technique is able to detect vibrational transitions in the MIR region as well as specific types of electronic transition (e.g., CT transitions) that appear in the NIR region, making it feasible to identify and distinguish between coexisting molecular species.

Figure III–1. UV/Vis spectra of Py (red solid curve) and DCB (black solid curve) in ACN solution. Also shown is the UV/Vis spectrum of the ACN solution of both Py and DCB (grey dashed curve). In all solutions, the concentrations of Py and DCB were 0.50 and 5.0 mM, respectively. The molar extinction coefficient of Py at the excitation wavelength (355 nm) is 280 M⁻¹ cm⁻¹, whereas that of DCB is one order of magnitude smaller.

Py and DCB form a fundamental PIET system [54,59-61] suitable for the mechanistic study of BET. Upon photoexcitation of Py in the presence of DCB in polar solvent (see Figure III–1 for the UV/Vis spectra of Py and DCB in ACN), Py radical cation (Py^•+) and DCB radical anion (DCB^•−) are produced within 100 ns via intermolecular electron transfer from the S state of Py. The efficiency of FET reaction is expected to be considerable owing

yields of ion pairs (Φip = 0.38 in ACN (ε = 37.5) and 0.08 in dichloromethane (ε = 3.75)).

Surrounding polar solvent molecules usually stabilize the generated ionic species and keep these ions apart. As a result, the generated ionic species become free ions. Thus the recombination of ion pairs is anticipated to occur at a slower rate of 10⁴–10⁵ s^–1, since the diffusion rate constant is of the order of 10¹⁰ M⁻¹ s⁻¹ and the concentration of ions generated is of the order 10⁻⁵–10^–6 M. The focus of this work is on this slower dynamics of the free ions

Surrounding polar solvent molecules usually stabilize the generated ionic species and keep these ions apart. As a result, the generated ionic species become free ions. Thus the recombination of ion pairs is anticipated to occur at a slower rate of 10⁴–10⁵ s^–1, since the diffusion rate constant is of the order of 10¹⁰ M⁻¹ s⁻¹ and the concentration of ions generated is of the order 10⁻⁵–10^–6 M. The focus of this work is on this slower dynamics of the free ions