Reactor Characterisation

The mixing properties of the reactor were characterised by determining the residence time distribution (RTD). This was achieved using the pulse method which is outlined below (Figure 47). Initially, the miniature CSTR cascade was pre-filled with water at a flow rate of 4.0 mL min^-1. A pulse of 10% (v/v) red food dye was rapidly introduced into the flow stream using a six-port valve, and samples were collected from the outlet of the reactor at regular time intervals. The absorbance of each sample was determined via offline UV-Vis spectroscopy (516 nm). The RTD function E(t) was calculated by dividing the absorbance at each residence time by the total area under the absorbance curve.

The mixing performance was assessed by comparing the experimentally determined RTDs against the CSTRs in series model defined by [Eq (39)].¹ The experimentally determined RTDs were consistent with the CSTRs in series model for n = 1, 3 and 5, where n = number of CSTRs (Figure 48). This suggests that a uniform concentration in each CSTR is achieved, and therefore the agitation provides rapid mixing. As expected, the RTDs become narrower with increasing n, and thus bring the behaviour of the system closer to that of a plug flow reactor (PFR).

In addition, the absence of any significant peak tailing indicates that dead volumes

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are negligible. As such, the performance of this reactor for a reaction with known kinetics could be predicted using the CSTRs in series model.

Tracer

Syringe pump

Six-port valve

Waste

n CSTR Cascade

UV-Vis

Figure 47. Set-up for determining the RTD of a miniature CSTR cascade using the pulse method.

𝐸(𝑡) = 𝑡^𝑛−1

(𝑛 − 1)! 𝜏_𝑖^𝑛𝑒^{−𝑡/𝜏𝑖} (39)

Figure 48. Comparison between theoretical and experimental RTDs for a CSTR cascade with a varying number of stages, n. E(θ) = normalised RTD function.

The average residence times (tm) were determined by calculating the area under the curve for a plot of tE(t) against t [Eq (40)]. The calculated and theoretical values are displayed in Table 10. The relative difference between the calculated and theoretical average residence times increases with decreasing n. These

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discrepancies are likely due to the impossibility of experimentally injecting a perfect tracer spike. If additional equipment was available, these experimental limitations could be overcome by conducting in-line UV-Vis analysis at the inlet and outlet of the reactor, which would enable deconvolution of the inlet concentration profile and RTD.¹⁵⁶

4.2.2.2 Absorbed Photon Flux Density

The absorbed photon flux density (qp/Vr) defines the amount of light absorbed per unit of volume per unit of time. Therefore, the higher the absorbed photon flux density of a reactor, the higher the intrinsic rate of reaction for a photochemical process. The absorbed photon flux density can be experimentally determined via chemical actinometry, which uses a photoinduced reaction of a compound with a known quantum yield (ɸλ), to measure the incident light intensity (I0) at a given wavelength. The rate of conversion of the actinometric compound (Act) is defined by [Eq (41)], where f is the fraction of light absorbed. The relationship between the rate of conversion of the actinometric compound [Eq (41)], and the rearranged form of the Beer-Lambert law [Eq (42)], can be used to derive [Eq (43)] for the calculation of the incident light intensity.

In this case, the experiments were conducted with a relatively long path length (l = 1 cm) and high concentration of the actinometric compound ([Act] = 0.1 M).

Hence, the right-hand term of [Eq (43)] tends towards unity, indicating operation under full absorption (f = 1). Under these conditions, the kinetics of the reaction can be assumed to be zero-order. This simplifies [Eq (43)] to [Eq (44)], where the only unknown is the zeroth-order rate constant (k0). Notably, the incident light intensity is equivalent to the absorbed photon flux density when f = 1.¹⁶⁰

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o-Nitrobenzaldehyde 4.01 (NBA) is a well characterised chemical actinometer with a known molar extinction coefficient (ε = 260 M^-1 cm^-1) and quantum yield (ɸ³⁶⁵

= 0.5) at 365 nm.¹⁶¹ Therefore, the photochemical isomerisation of NBA 4.01 to o-nitrosobenzoic acid 4.02 was investigated using an automated continuous flow platform (Scheme 17). In theory, the zeroth-order rate constant is equal to the negative slope of the residence time profile for the photochemical conversion of NBA 4.01 (Figure 49). However, significant curvature was observed as a result of light absorption by the o-nitrosobenzoic acid 4.02 product.¹⁶⁰ As such, a second-order polynomial was fit to the data (R² = 0.9833), and the initial slope of the curve determined by evaluating the derivative at tres = 0. The resultant zeroth-order rate constant (k0 = 1.67 μg μL^-1 min^-1) was used to calculate the absorbed photon flux density according to [Eq (44)].

The absorbed photon flux density for the CSTR cascade (qp/Vr = 0.37 einstein m^-3 s^-1) is an order of magnitude greater than previously reported photochemical batch reactors (qp/Vr = 0.033 einstein m^-3 s^-1), whilst being only 2x less than a photochemical microreactor chip (qp/Vr = 0.71 einstein m^-3 s^-1).¹⁶² This can be attributed to the enhanced mixing within the CSTRs, which rapidly transports the reactants and products into and out of the photochemically active region. This overcomes the issue of diminishing light intensity as a function of distance travelled through the reaction medium. Therefore, this design successfully improves productivity compared to batch reactors whilst maintaining the advantages of CSTRs described previously. In addition, as the incident light intensity of this set-up is now known, the quantum yield of reactions can be experimentally determined via kinetic profiling, which provides useful mechanistic insights.^{163, 164}

117 MeOH

CSTR Cascade (365 nm) n = 2, V = 4 mL

SL HPLC

Scheme 17. Automated set-up for the characterisation of absorbed photon flux density using o-nitrobenzaldehyde 4.01 as a chemical actinometer.

Figure 49. Residence time profile for the conversion of o-nitrobenzaldehyde 4.01 (NBA) under irradiation at 365 nm.