## 3 Results and Discussion
### Monitoring of A Freeze-Drying Cycle for a Mannitol/Sucrose Solution
#### 3.1.2 Supercooling and Freezing  
As discussed by [PERSON] et al., the freezing of water is a complex process, and it becomes even more complex when a pharmaceutical formulation undergoes freezing [17]. Liquids need to be cooled substantially below their equilibrium freezing temperature in order to spontaneously freeze through an initial primary nucleation that subsequently leads to the additional growth of ice-crystals [17]. In freeze-drying, uniform and simultaneous freezing behaviours and the size of the ice crystals are directly impacting the primary drying (rate) and ultimately the quality of the final product as comprehensively outlined by [PERSON] et al. [16]. Figure 4a shows that the mannitol/sucrose solution in cuvettes 1 and 5 (with probes present) froze first. The supercooled liquid in cuvettes 1 and 5 reached \(-\)3.5 and \(-\)5 \({}^{\circ}\)C, respectively, before freezing, as measured using the IR camera. The corresponding values obtained from the Pt100 probe and LyoRX probe were \(-\)5.1 and \(-\)7.0 \({}^{\circ}\)C, respectively. Table 1 contains a summary of data with respect to nucleation temperatures and order of freezing. When comparing Figure 4a and Figure S1, it can be seen that the surface was warmer for a longer period of time just after nucleation. Whether this can explain the observed difference between the probes and the IR camera readings is unclear. In fact, cuvette 4 contained supercooled liquid down to \(-\)11.5 \({}^{\circ}\)C before it froze, as measured at the surface using the IR camera. This observation is in line with [PERSON] and [PERSON]'s work, which concluded that presence of probes increases ice-nucleation temperature [4]. At this point, the LyoRX (resistivity sensor) in cuvette 5 rapidly increases to about 95%, indicating solidification as shown in Figure 3. Figure 5a shows a specific case for cuvette 3, where the bottom right corner at the surface shows supercooled liquid in blue and the recently frozen formulation in the top left corner in light green. It should be noted that the actual nucleation and freezing take place within a few seconds. Fortunately, the IR camera captured this event in the 116 th minute (1.93 h) of the freeze-drying program. In Figure 6a, the temperature profile along L3 is displayed, in which three IR pixels make up every mm on the x-axis. That profile shows both frozen and super-cooled liquid. All other cuvettes except for number 4, shown in Figure 5a, already contained frozen mannitol/sucrose at this stage. Cuvette 4 still contained supercooled liquid, which is in line with its actual time of freezing, which was approximately after 2.3 h as can be seen in Figure 4a. Figure 2: Entire freeze-drying process: surface view with and without probes using average temperature readouts from R1 to R5 and R16. Figure 3: Full freeze-drying cycle of the pharmaceutical formulation based on machine readings of product temperature from Pt-100 sensors (TmpProd1 and TmpJv1), shelf-temperature, pressure (VacFitr), ice-condenser temperature and resistivity (Jyo-RX, displayed in %, left y-axis). Figure 4: (**a**) Surface measurements of average temperature using R1 to R5. The nucleation temperatures can be seen at the dip of each measurement area around 2 h on the \(y\)-axis, with the respective time of nucleation on the \(x\)-axis. (**b**) Speed of primary drying (with different slopes) and difference between cuvettes with and without probes for surface measurements of temperature using R1 to R5. Figure 5: Cont. Figure 5: **(a)** Thermogram of cuvettes 1 through 5 with profiles L1 to L5 at the surface after 116 min (1.93 h) at the time of nucleation and freezing. **(b)** Thermogram of cuvettes 1 through 5 with profiles L1 to L5 at the surface after 820 min (13.7 h) where only very small temperature differences prevail. The intense reflection in white is from metal surfaces inside the freeze-dryer. **(c)** Thermogram of cuvettes 1 through 5 with profiles L1 to L5 at the surface after 1685 min (28.1 h).