A Kinetic Study of a Photo-Oxidation Reaction between α-Terpinene and Singlet Oxygen in a Novel Oscillatory Baffled Photo Reactor

Abstract

By planting LEDs on the surfaces of orifice baffles, a novel batch oscillatory baffled photoreactor (OBPR) together with polymer-supported Rose Bengal (Ps-RB) beads are here used to investigate the reaction kinetics of a photo-oxidation reaction between α-terpinene and singlet oxygen (¹O₂). In the mode of NMR data analysis that is widely used for this reaction, α-terpinene and ascaridole are treated as a reaction pair, assuming kinetically singlet oxygen is in excess or constant. We have, for the first time, here examined the validity of the method, discovered that increasing α-terpinene initially leads to an increase in ascaridole, indicating that the supply of singlet oxygen is in excess. Applying a kinetic analysis, a pseudo-first-order reaction kinetics is confirmed, supporting this assumption. We have subsequently initiated a methodology of estimating the ¹O₂ concentrations based on the proportionality of ascaridole concentrations with respect to its maximum under these conditions. With the help of the estimated singlet oxygen data, the efficiency of ¹O₂ utilization and the photo efficiency of converting molecular oxygen to ¹O₂ are further proposed and evaluated. We have also identified conditions under which a further increase in α-terpinene has caused decreases in ascaridole, implying kinetically that ¹O₂ has now become a limiting reagent, and the method of treating α-terpinene and ascaridole as a reaction pair in the data analysis would no longer be valid under those conditions.

1. Introduction

Heterogeneous photo-aided reactions and photocatalysis are initiated by the absorption of light. Scalable uniform mixing in handling multiphases and scalable uniform light distribution in providing light sources are the two most critical requirements in photoreactors, so much so that the scalability of photoreactors has been identified as a key challenge in photochemical transformations in the chemical industry [1]. In terms of light provision, UV lamps/bars are traditionally placed outside or within reactors, suffering from the non-uniform distribution of light intensity, and low power-to-photon efficiency and scale-up ability [2,3]. LEDs, on the other hand, offer a much narrower spectrum of light for targeted reactions and are sufficiently small to be installed within reactors, enabling uniform light distributions. LEDs have thus become the main light source in most of the lab-scale photoreactors.

In terms of mixing, the century-old problem remains whereby mixing gets worse with increasing scales: simply scaling up stirred tank reactors does not meet the above critical needs. Microreactors are seen as viable alternatives in solving the mixing issues, allowing the safe exploitation of hazardous materials, while enabling optimal irradiance due to their narrow dimensions. Subsequently, a wide range of photochemistry applications using a variety of flow reactors have been reported in recent years [1,4,5,6,7,8].

While lab-scale flow photoreactors are sufficient to produce small quantities of targeted molecules [9], applications in industrial-scale photochemical processes are comparatively rare due to the generally poor economics, complex scalability and safety issues of many photochemical transformations [10]. There are currently three main strategies used in scaling up photo-microreactors: numbering up, lengthening the channel or increasing channel diameter [11]. Numbering up is a method of adding reactor systems in parallel until a desired productivity of chemicals is achieved. However, high inventory costs are a major drawback, as multiple pumps, mass flow controllers and reactors are required [12,13]. Lengthening the flow path while keeping the channel diameter constant enables faster flow velocities while maintaining the same photon flux, but leads to issues with large pressure drops over the reactor [14]. Increasing diameter is the least viable method in scaling up microchannel reactors, as it weakens/diminishes diffusion-driven mixing in the reactor [15,16], providing poorer scale up than the former methods.

In this study, we present a novel batch oscillatory baffled photo reactor (OBPR) that provides uniform mixing and solid suspension via the succession and cession of eddies. Orifice baffles are one of the key intrinsic elements of the reactor set-up; planting LEDs on the surfaces of orifice baffles [17] enables uniform and controllable light distribution/intensity. The scale-up of this device is achieved through continuous oscillatory baffled reactors (COBR) that have a number of unique offerings: (a) plug flow mixing is generated in laminar flows, minimizing pressure drop and allowing longer residence times [18,19,20,21]; (b) uniform mixing is scalable [22,23]; (c) COBRs are good in handling solids [24,25] and have been implemented in industrial applications [26], meeting both critical requirements in photoreactors. The work to be presented in this paper is only associated with batch OBPRs. Using a model photo-oxidation reaction between α-terpinene and singlet oxygen (¹O₂), we report our kinetic analysis and assessment of the reaction. Polymer-supported Rose Bengal beads are used in the work, because the OBPR has the excellent capability of suspending solids and enabling uniform light absorption.

2. The Reaction Scheme and Experimental Set Up

2.1. Reaction Scheme

The photo-oxidation reaction is shown in Scheme 1 with polymer-supported Rose Bengal (Ps-RB) porous beads as the heterogeneous photosensitizer. The beads were synthesized in house and characterized according to known literature methods [27,28]. The first step of the reaction involves photo absorption (+hν) by the Ps-RB chromophore promoting an electron to a higher-order singlet electronic excited state (¹[Ps-RB]*); ¹[Ps-RB]* converts to a triplet excited state (³[Ps-RB]*) via intersystem crossing (ISC), which is the second step; the energy transfer (EnT) from ³[Ps-RB]* to ground-state triplet molecular oxygen (³O₂) then occurs via triplet-triplet annihilation (TTA), to return the Ps-RB to their initial ground state and produce ¹O₂; the next step is that ¹O₂ spontaneously decomposes to ³O₂ via non-radiative decay (NRD) through vibronic energy transfer with solvent molecules, and ¹O₂ encounters α-terpinene in solution and undergoes a productive [4 + 2] cycloaddition to yield the endoperoxide product, ascaridole, known as a Diels–Alder-type reaction (Scheme 1). 1,3-Dienes commonly undergoes [4 + 2] cycloaddition reactions with singlet oxygen ¹O₂ to yield endoperoxides. This reaction has been extensively studied on naphthalene derivatives [29,30,31]. Other chemical transformations such as [2 + 2] additions or “ene”-type reactions are also possible, forming dioxetanes and hydroperoxides, respectively [32]. ¹O₂ exists as a gas, but is dissolved in the reaction mixture or solvent [33]. Singlet oxygen is unstable, and its lifetime changes dramatically in different solvents, ranging from 4 to 628 μs [34], depending on the efficiency of energy transfer from electronic to intramolecular vibrational states; for instance, the lifetime in water is one order of magnitude lower than that in deuterated water. Chloroform (CHCl₃) provides the longest ¹O₂ lifetime (~90 μs) of all common, non-deuterated laboratory solvents [35], and so was chosen as the solvent in this study. It should be noted that the amount of ascaridole produced does not equal the amount of ¹O₂ formed due to non-radiative decay, but what is certain is that the formation of ascaridole is direct evidence of the existence of singlet oxygen [2].

Heterogeneous photosensitizers have many advantages over their homogeneous counterparts; for example, they are readily prepared and are easily removed post-reaction, and when suspended in solution, they do not accumulate or clog reactors. Heterogeneous photosensitizers are generally composed of organic dyes bearing a (hetero)aromatic core, e.g., Rose Bengal (RB). Because RB suffers from extensive photobleaching/degradation under prolonged irradiation, the leakage is usually difficult to remove from reaction effluents [36,37], and so modifications in synthesis have led to various robust solid photosensitizers. Previously, a versatile organic dye, 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY), with polymer support was used as the photosensitizer in the same reaction, with nitrogen- and boron-containing heterocycles [9] with high fluorescence quantum yields and significant visible light absorption; the ideal light wavelength fell between 500 and 540 nm. In this work, polymer-supported Rose Bengal (Ps-RB) porous beads are used; they show high absorption coefficients in the visible spectral region and are stable after photosensitization. Their optimal light wavelength is 530 nm [38]. The key advantage of Ps-RB over BODIPY is that the maximum absorbance wavelength is red-shifted and requires lower energy, reducing the likelihood of the photodecomposition of reactants and products [39].

2.2. Materials

α-terpinene was purchased from the Division of Tokyo Chemical Industry (TCI) (>90% purity); all organic solvents and reagents were sourced from Fisher Scientific (Bishop Meadow Road, Loughborough, Leicestershire, LE11 5RG, UK) at SLR grade, and were used as received without further purification unless otherwise stated.

2.3. Reactor Setup

The OBPR consists of a glass column of 50 mm in diameter and 480 mm in height, as shown in Figure 1. The volume of the reactor is 600 mL, with the working volume of 500 mL. Orifice baffles have an outer dimeter of 46 mm, a hole diameter of 26 mm and a baffle spacing of 60 mm. Each set comprises three orifice baffles; each baffle has 6 evenly spaced green LEDs (Cree 5 mm round LEDs) planted on the lower surface (can also be both sides), as shown in Figure 1, for the purpose of providing light. The provision of light in the OBPR differs from traditional means. Firstly, the LEDs are placed within the reactor, directly in contact with reaction medium, thus enhancing the intensity of light supply; secondly, the LEDs move with the baffle plates up and down the column, and the light radiation covers the whole reactor area, but far fewer LEDs are required; thirdly, whole-area illumination is not achieved, as in many microreactor systems, and much less energy is used, meaning that less heat is generated (the latter is an important factor for some chemical or biological compounds that can be decomposed with excessive heat). The leads of LEDs are covered by epoxy resin, which provides insulation, material compatibility and corrosion resistance. The wavelength and light intensity of the green LEDs are 530 nm and 0.756 watts, respectively, and the intensity of the radiation is estimated at 29 W/m². An air sparger is located at the base of the OBPR for introducing air at a controlled rate.

Based on a previous work in a microchannel reactor [11,13], about 390 mL CHCl₃ was mixed with 4.225 mL of α-terpinene in the OBPR in the presence of Ps-RB beads of 1600 mg. A constant liquid volume of 400 mL was maintained for all experiments. The oscillation frequency and amplitude were switched on once all chemicals were charged into the OBPR; the reaction was initiated when the LEDs were turned on, and the duration of the reaction was 120 min. The Ps-RB beads of 100 µm mean size were uniformly suspended and kept within the OBPR under the selected oscillation conditions. A lid was placed on the top of the OBPR to prevent volatile matter from escaping. Runs were repeated to ensure data repeatability and reliability (see

Table 1. Experimental conditions (bead mass = 1600 mg, irradiation wavelength = 530 nm, oscillation frequency = 2.5 Hz, oscillation amplitude = 24 mm, air flow rate = 172.5 mL/min, duration = 120 min).

Run Number	Chloroform (mL)	α-Terpinene (mL)	Number of Repeated Runs
1	397.88	2.12	1
2	395.77	4.23 (default)	2
3	393.00	7.00	2
4	391.53	8.47	3
5	390.00	10.00	2
6	383.10	16.90	2
7	374.50	25.50	3

), and averaged values have been used in the following data presentations.

2.4. Analytic Method

Samples were taken regularly and analyzed using proton nuclear magnetic resonance (¹H NMR) to determine the composition/concentration of the mixture. The procedure of treating the samples was as follows:

• Each 2 mL sample containing CHCl₃ + α-terpinene + ascaridole was injected into a dark vial to stop the reaction (reaction stops when light is off);
• The sample was placed in a round-bottom flask and the solvent (CHCl₃) was removed under reduced pressure on a rotary evaporator (40 °C, 365 mbar for ~5 min);
• The oily residue was dissolved in 0.5 mL of deuterated chloroform (CDCl₃) and a ¹H NMR was obtained (300 MHz Bruker AVIII spectrometer);
• Peaks in the region between 6.70 and 5.40 ppm were used to determine the conversion of α-terpinene and the appearance of ascaridole.

Figure 2 shows typical ¹H NMR spectra in chloroform-d, showing the alkenyl proton resonances of α-terpinene as a multiplet at 5.61 ppm, and ascaridole as a doublet-of-doublets centered at 6.45 ppm, consistent with previous reports [40]. The resonance signals count for two alkenyl protons of the respective molecules. While p-cymene is a byproduct in the reaction, it is not detected by the ¹H NMR, which is consistent with other studies [41]. At the reaction stochiometric ratio of 1:1, the integrals of these signals are directly proportional to the relative concentrations of the two species. The concentration of α-terpinene at time t (C_αT) is the ratio of the integrated NMR area of α-terpinene at time t (Area_αT) over its corresponding area at time t = 0 (taking as 100), multiplied by its initial concentration at t = 0 (C_αT0 = 0.051917 mol/L). The concentration of ascaridole (C_As) is then the ratio of the integrated area of ascaridole over the total area at time t multiplied by the initial concentration of α-terpinene, since the initial concentration of ascaridole at t = 0 is zero, as:

$${\mathrm{C}}_{\mathsf{\alpha }\mathrm{T}}=\left(\frac{{\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}}_{\mathsf{\alpha }\mathrm{T}}}{{\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}}_{\mathsf{\alpha }\mathrm{T}0}}\right){\mathrm{C}}_{\mathsf{\alpha }\mathrm{T}0} {\mathrm{C}}_{\mathrm{A}\mathrm{s}}=\left(\frac{{\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}}_{\mathrm{A}\mathrm{s}}}{{\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}}_{\mathrm{A}\mathrm{s}}+{\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}}_{\mathsf{\alpha }\mathrm{T}}}\right){\mathrm{C}}_{\mathsf{\alpha }\mathrm{T}0}$$

(1)

The byproduct is not detectable, Area_As + Area_αT = 100, which makes the concentration of ascaridole a reaction pair with that of α-terpinene. The reaction conversion rate is typically about 20% that is far less than the quantum yields shown in Table 2.

3. Results and Discussion

3.1. Kinetic Assessment

The overall reaction in Scheme 1 can be described by a sequence of two reactions:

$$\begin{array}{l}\mathrm{oxygen}\underset{k2}{\overset{k1}{\rightleftarrows }}\mathrm{singlet} \mathrm{oxygen}\\ \mathsf{\alpha }\text{-}\mathrm{Terpinene}+{}^1\mathrm{O}_2\stackrel{k3}{\to }\mathrm{ascaridole}\end{array}$$

(2)

Following the reaction Scheme 1, some singlet oxygen (¹O₂) decomposes to molecular oxygen (³O₂) via non-radiative decay (NRD)—the first part of the reversible reaction accounts for this process. At a fixed oscillatory frequency (f) and amplitude (x₀) in the OBPR with a known quantity of polymer-supported Rose Bengal beads at continuous controlled light irradiation under a steady state, a net amount of ¹O₂ (resulting from the first part of the reaction) is generated and reacts with α-terpinene to produce ascaridole (the second part of the reaction). For one equivalent each of ascaridole and α-terpinene without any byproduct, the data analysis focuses on the consumption of α-terpinene as a reaction pair of the generation of ascaridole. This effectively assumes that the concentration of singlet oxygen is kinetically either in excess or constant. To the authors’ knowledge, no research publications have looked into this matter. In order to testify to and verify this assumption, a number of planned experiments were carried out using different amounts of α-terpinene and chloroform while keeping the same reaction volume—see Table 1. Note that Run 2 was the default condition, based on previous studies [9,42,43].

Figure 3 compares the concentration profiles of ascaridole with different amounts of α-terpinene. An increase in the concentration of ascaridole as a function of time can be seen with the increase in α-terpinene in Figure 3a on the left (the filled symbols). This indicates that ¹O₂ supply in the OBPR is indeed in excess. Further increases in the reagent, however, have brought about reductions in the product (see the open symbols) shown in Figure 3b on the right, implying that under these experimental conditions, ¹O₂ has become the limiting reagent; the concentration of ascaridole would be solely dependent upon the concentration of ¹O₂, instead of α-terpinene. This stipulates that the widely used method of treating α-terpinene and ascaridole as a reaction pair, as shown in Equation (1), would no longer be valid under these conditions. Note that chloroform is the solvent that does not participate in the reaction and is present at significant excess over α-terpinene. Its effect on the concentration of ascaridole should be minimal, but this has not been tested.

Under conditions where ¹O₂ is in excess (Figure 3a), the second-order reaction of ¹O₂ + α-terpinene $\stackrel{k3}{\to }$ascaridole is then reduced to a pseudo-first-order reaction of α-terpinene $\stackrel{k_3}{\to }$ascaridole. It is then justified to treat the two as a reaction pair. The rate equation and the integral form are given below:

$$-\frac{{dC}_{aT}}{dt} =k_3{C}_{\alpha T} \ln \left(\frac{C_{\alpha T0}}{C_{\alpha T}}\right)=k_{3}t$$

(3)

When plotting $\ln \left(\frac{C_{\alpha T0}}{C_{\alpha T}}\right)$ vs. time for α-terpinene at 2.12, 4.23 and 7 mL, approximate straight lines can be seen in Figure 4, verifying the pseudo-first-order kinetics with an averaged rate constant of 0.0020/min.

When 8.5 mL of α-terpinene is used, the conversion of ascaridole reaches its maximum, implying that neither singlet oxygen nor α-terpinene is in excess. Using the proportionality of ascaridole with respect to its maximum at 8.5 mL, shown in Figure 3a, the excess ¹O₂ concentrations derived with 7/4.23/2.12 mL of α-terpinene can be estimated using the equation below, taking 7 mL as an example:

$$C_{O_2^1}=[1+\frac{{\left(C_{As}\right)}_{8.47ml}-{\left(C_{As}\right)}_{7ml}}{{\left(C_{As}\right)}_{8.47ml}}]\times {\mathrm{C}}_{\mathsf{\alpha }\mathrm{T}}$$

(4)

Figure 5 shows the concentrations of all species for the three volumes of α-terpinene. Note that there are no data of ¹O₂ at t = 0; this is due to the concentration of ascaridole being zero at the start, and ¹O₂ concentrations were only estimated from 20 min onwards. We see that the concentrations of singlet oxygen are greater than those of α-terpinene, demonstrating that ¹O₂ is in excess under those conditions. We also note that the concentration of ¹O₂ remains more or less unchanged with each measure of α-terpinene, which is consistent with what was stated earlier—that a net amount of ¹O₂ is generated in the OBPR under a steady state.

By feeding the data on α-terpinene, ascaridole and k₃ (from Figure 4) into the reaction kinetic model in COPASI (Complex Pathway Simulator), the concentrations of singlet oxygen can be reconstructed as shown in Figure 5 (filled symbol). Note that COPASI is a versatile modeling tool that can be used for model development, model simulations (such as stochastic simulations and differential equation simulations), numerous sorts of analyses (such as sensitivity analysis, parameter estimation, and metabolic control analysis) and kinetic extraction [44]. We see that the ¹O₂ concentrations estimated using the proportionality of ascaridole at different amounts of α-terpinene (open triangles) match reasonably well with those determined using the kinetic model (filled triangles). This further validates our proposed methodologies. We note that zero-order reaction kinetics were reported by other studies for this reaction [41,45,46]; the presence of zeroth order kinetics indicates that the reaction rate is a sole function of the reaction rate constant, and does not depend on the concentrations of reagents. When we vary the concentrations of α-terpinene, the dependence of the reaction rate on the concentrations of the reagent is clearly demonstrated.

Thanks to the data on ¹O₂ that we estimated, we can also evaluate the efficiency of ¹O₂ utilization using the definition below, even when it is in excess:

$$Efficiency of singlet oxygen utilization \left(\%\right)=100\%-\frac{Singlet oxygen-ascaridole}{Singlet oxygen}$$

(5)

The efficiencies of ¹O₂ utilization are tabulated in Table 2 for measures of α-terpinene from 2.12 to 7 mL.

Table 2. Average efficiency of ¹O₂ utilization and efficiency of photo conversion for three volumes of α-terpinene (photosensitizer = 1600 mg, irradiation wavelength = 530 nm, f = 2.5 Hz, x₀ = 24 mm, air flow = 172.5 mL/min, duration = 120 min).

α-Terpinene (mL)	Efficiency of 1O2 Utilization (%)	Efficiency of Photo Conversion (%)	Apparent Quantum Yield (%)
7	10.7	0.10	87
4.23	14.6	0.07	57
2.12	4.9	0.06	19

Table 2. Average efficiency of ¹O₂ utilization and efficiency of photo conversion for three volumes of α-terpinene (photosensitizer = 1600 mg, irradiation wavelength = 530 nm, f = 2.5 Hz, x₀ = 24 mm, air flow = 172.5 mL/min, duration = 120 min).

α-Terpinene (mL)	Efficiency of 1O2 Utilization (%)	Efficiency of Photo Conversion (%)	Apparent Quantum Yield (%)
7	10.7	0.10	87
4.23	14.6	0.07	57
2.12	4.9	0.06	19

3.2. The First Step of the Reaction

The process of conversion from molecular oxygen to ¹O₂ in the first part of the overall reaction in Equation (2) relies on photo-elevation/energy transfer. Due to a significant energy barrier (94 kJ/mol), ³O₂ molecules cannot directly be excited to ¹O₂ due to this electronic transition being forbidden by spin selection rules; this process therefore requires a triplet photosensitiser to enable the triplet–triplet annihilation energy transfer mechanism [47]. When photons of the correct wavelength (<600 nm) irradiate the Ps-RB beads, the supported Rose Bengal chromophore is electronically excited and enters into a triplet state via intersystem crossing (ISC), which enables it to undergo an energy transfer, resulting in a triplet–triplet annihilation process with oxygen to produce singlet oxygen [48]. The very short lifetime of singlet oxygen depends on the temperature and solvent environment, as vibronic energy transfer with a solvent is a competitive, non-productive process that returns ¹O₂ to its ground state, ³O₂ [49], which is the first part of the overall reaction. The question remains as to whether the molecule oxygen is an oxygen gas molecule [50,51] or dissolved oxygen. Air/oxygen is generally sparged into the reactor; as a result, a significant amount of gas bubbles exit the reactor without participating in the reaction, due to the density difference, the buoyance effect, and critically, the lack of a mixing mechanism that can hold the bubbles within a traditional reactor. This suggests that ³O₂ is associated with dissolved oxygen. The process of converting oxygen gas to dissolved oxygen in chloroform is a mass transfer-controlled process, and is mainly affected by mixing and air flow rate, determined by novel reactor designs. The properties of mixing in the OBPR are governed by the oscillatory Reynolds number [20] (Re_o) and the Strouhal number (St), defined as:

$${Re}_{\mathrm{o}}=\frac{2\pi f{x}_0\rho D}{\mu } St=\frac{D}{4\pi x_0}$$

(6)

where D is the tube diameter (m), ρ is the fluid density (kg m^–3), x₀ is the center-to-peak amplitude (m), μ is the viscosity (Pa s) and f is the oscillatory frequency (Hz). The oscillatory Reynolds number is related to the intensity of mixing, while the Strouhal number indicates the degree of eddy propagation [20,25]. The effects of the mixing (oscillation amplitude, or St) and [1] air flow rates on the conversion of ascaridole are given in Figure 6.

We see that, generally, the higher the oscillation, the greater the conversion (Figure 6A). As mixing intensity increases in the OBPR and becomes uniform, it breaks up bubbles, leading to a decrease in bubble sizes and an increase in bubble surface area; these bubbles are trapped in the vortices for longer periods of time, enhancing the residence time required for mass transfer within the reactor [52]. The direct result is an increase in dissolved oxygen concentration in the solvent [53] and more excited molecular oxygen, which means more ¹O₂. The degree of improvement in the conversion is, however, rather limited for all amplitudes. The effect of air flow rate on the conversion (Figure 6B) tells a similar story—the higher the air flow rate, the greater the conversion. However, there is an operational limit for further increasing air flow rate, as channeling takes place, thus extracting the beads from the OBPR. The highest flow rate was used in our kinetics studies.

By comparing the total amount of air/oxygen sparged into the OBPR with the estimated amount of ¹O₂ every 20 min, the efficiency of the photo conversion of ¹O₂ can be evaluated as

$$Efficiency of photo conversion of singlet oxygen \left(\%\right)=100\%-\frac{Oxygen input-Singlet oxygen}{Oxygen input}$$

(7)

The oxygen input is calculated using the air flow rate (21% oxygen) and the duration in time; the ¹O₂ concentration is then converted into mass for the same duration. Table 2 summarizes both efficiencies. Using Max Planck’s equation (E = h C/λ), we can calculate the energy of one photon at the wavelength of 530 nm, where h is the Planck’s constant (6.626 × 10⁻³⁴ J s), C the speed of light (3 × 10⁸ m) and λ the wavelength of radiation (530 nm = 0.53 × 10⁻⁶ m). We thus have E = 3.75 × 10⁻¹⁹ J.

For a typical experimental duration of 120 min, the energy released by the LEDs is 0.756 J/s × 120 min × 60 s = 5443.2 J, meaning that the number of photons is 5443.2 J/3.75 × 10⁻²² J = 1.45 × 10²². The apparent quantum yield is equal to the number of reacted molecules divided by the number of photons sent. Taking the 7 mL measure of α-terpinene as an example, the initial and final concentrations of α-terpinene were 0.108 mol/L and 0.0873 mol/L, respectively, implying that the quantity of reacted α-terpinene was 0.0207 mol/L. The number of molecules per L was thus 0.0207 × 6.02 × 10²³ (the Avogadro’s number) = 1.246 × 10²², implying an apparent quantum yield of 1.246 × 10²²/1.45 × 10²² = 87%. The apparent quantum yields for two other conditions are shown in Table 2.

The limited conversion to ascaridole shown in Figure 5 and Figure 6 is the direct result of the combined low efficiency of ¹O₂ utilization with the very low efficiency of conversion of ³O₂ to ¹O₂, the latter being perhaps the greatest obstacle for this reaction (indeed for most photo-aided and photocatalysis reactions). The low conversion to ascaridole seen here is also consistent with the results of previous work, although these used BODIPY as the photosensitizer [43]. We are in the process of expanding this work to determine the pressure dependence of ¹O₂ by varying the partial pressures, and we are also looking into using a dissolved oxygen probe to measure the concentration of dissolved oxygen to enable better evaluations of photo conversion from molecular oxygen to singlet oxygen.

4. Conclusions

Four novel results are reported in this paper. Firstly, expanding on the success of continuous oscillatory baffled reactor technology, we have here introduced a novel batch oscillatory baffled photoreactor (OBPR) with LEDs planted evenly on the surfaces of the orifice plates, allowing uniform and controlled light distribution for photo-aided reactions and photocatalysis from the laboratory to full scales. Secondly, using a model photo-oxidation reaction with a solid photosensitizer, we have carried out a full examination of the validity of treating α-terpinene and ascaridole as a reaction pair in the commonly used mode of NMR data analysis. We have revealed that increasing α-terpinene initially leads to an increase in ascaridole, implying that the supply of singlet oxygen will be in excess. When applying pseudo-first-order reaction kinetics, the results fully support this hypothesis, validating the data analysis performed under these conditions. Further increases in α-terpinene, however, led to reductions in ascaridole, kinetically implying that ¹O₂ has become the limiting reagent. The method of treating α-terpinene and ascaridole as a reaction pair for the data analysis would thus no longer be valid under these conditions. Thirdly, we have developed a method of estimating the concentrations of ¹O₂ using the concentration profiles of ascaridole with respect to its maximum. The presence of excess ¹O₂ is demonstrated in each of the α-terpinene volumes. Knowing the concentrations of α-terpinene and ascaridole, together with the rate constant, we have reconstructed the ¹O₂ concentrations, which match reasonably well with the estimated values. Lastly, using the estimated ¹O₂ data, we have here proposed a methodology of evaluating the efficiency of ¹O₂ utilization and the photo efficiency of the conversion of ³O₂ to ¹O₂. The combination of the above two deficiencies led to the overall low conversion of ascaridole (~20%) in this photo-oxidation experiment.