Online Monitoring of the Concentrations of Amorphous and Crystalline Mesoscopic Species Present in Solution.

Despite the growing evidence for the existence of amorphous mesoscopic species in a solution and their crucial roles in crystallization, there has been the lack of a suitable method to measure the time-resolved concentrations of amorphous and crystalline mesospecies in a lab-scale stirred reactor. This has limited experimental investigations to understand the kinetics of amorphous and crystalline mesospecies formation in stirred solutions and made it challenging to measure the crystal nucleation rate directly. Here, we used depolarized light sheet microscopy to achieve time-resolved measurements of amorphous and crystalline mesospecies concentrations in solutions at varying temperatures. After demonstrating that the concentration measurement method is reasonably accurate, precise, and sensitive, we utilized this method to examine mesospecies formation both in a mixture of two miscible liquids and in an undersaturated solution of dl-valine, thus revealing the importance of a temperature change in the formation of metastable and amorphous mesospecies as well as the reproducibility of the measurements. Moreover, we used the presented method to monitor both mesospecies formation and crystal nucleation in dl-valine solutions at four different levels of supersaturation, while achieving the direct measurement of the crystal nucleation rates in stirred solutions. Our results show that, as expected, the inherent variability in nucleation originating from its stochastic nature reduces with increasing supersaturation, and the dependence of the measured nucleation rate on supersaturation is in reasonable agreement with that predicted by the classical nucleation theory.

Introduction

Online measurement of the concentration of amorphous and crystalline mesoscopic (i.e., 10–1000 nm) species present in solutions in a lab-scale stirred reactor has been impossible up to now. Nanoparticle tracking analysis (NTA)[1−6] and resistive-pulse sensing[1,7,8] quantify the concentration of mesospecies, but these techniques are offline analytical methods that require cumbersome manual handling of a small volume of a solution sample and cannot distinguish between optically isotropic species (e.g., amorphous materials) and anisotropic ones (e.g., most crystals). Depolarized dynamic light scattering[9−13] can distinguish optically anisotropic mesospecies from isotropic ones, but this method is an offline characterization technique that cannot measure the concentration of mesospecies. Laser backscattering techniques (e.g., focused beam reflectance measurement[14,15] and optical reflection measurement[16,17]) enable the online monitoring of the chord length distribution (CLD) of a crystal population in a lab-scale stirred reactor, but they are limited to micron-size crystal populations, and their application to the monitoring of crystal concentration requires a laborious calibration procedure that is based on an empirical correlation between the particle count rate and the crystal concentration.[17]

The lack of a suitable method to track the concentration of optically isotropic and anisotropic mesospecies in a lab-scale stirred reactor has constituted one of the major obstacles for advancing our knowledge on the formation of amorphous and crystalline mesospecies through molecular self-assembly in a stirred solution, for investigating the complex pathways of crystal nucleation involving amorphous mesospecies present in a stirred solution under ordinary lab environments, and further for performing the direct measurement of the crystal nucleation rate in solutions. We have therefore developed a device that monitors the concentrations of optically isotropic and anisotropic mesospecies present in solutions in a lab-scale stirred reactor and achieved the first direct measurement of the crystal nucleation rate in a lab-scale stirred reactor.

In this work, a depolarized light sheet microscope coupled to a closed-loop sampling system has been developed. Through the sampling system, a solution, automatically transferred from a lab-scale reactor using a peristaltic pump, is passed through a flow-through cell (FTC) for depolarized light sheet microscopy, and then the analyzed solution is fed back to the reactor. A sample in the FTC illuminated by a sheet of a vertically polarized beam scatters partially depolarized light, whose vertically polarized and horizontally depolarized components are imaged individually through synchronized image acquisition from two cameras. Note that the depolarized component of the scattered light is negligible when a scatterer is optically isotropic like amorphous materials, whereas the depolarized component can be significant when a scatterer is optically anisotropic like most crystals.[9−12,18] Accordingly, analyzing images of the two orthogonally polarized scattered light enables one to monitor the numbers of amorphous and of crystalline mesospecies within the observation volume of the measurement device and hence their concentrations.

This article is organized as follows. In section , the device developed and its application for measuring the concentrations of mesospecies are explained. In section , the accuracy, precision, and sensitivity of the measurement device are examined, followed by its three applications, namely, (i) for investigating mesospecies formation in a binary mixture of freely miscible liquids as well as (ii) in an undersaturated amino acid solution, and (iii) for monitoring primary nucleation of an amino acid while measuring nucleation rates directly.

Methods

Measurement Device

A schematic of the system developed, hereafter referred to as polarization imaging system for mesospecies observation (PISMO), is shown in Figure . The PISMO relies on the physical principle that optically anisotropic species depolarize light upon scattering of linearly polarized light, whereas isotropic species do not depolarize. This principle allows us to distinguish between optically isotropic species and anisotropic species.

Figure 1

Schematic of the measurement device, i.e., polarization imaging system for mesospecies observation (PISMO). M, Mirror; BCV, biconcave lens; PCX, plano-convex lens; HWP, half-wave plate; PBS, polarizing beam splitter; B, beam dump; RS, rectangular slit; CL, cylindrical lens; FTC, flow-through cell; OL, objective lens; TL, tube lens; CMOS, CMOS camera.

In the illumination optics, a continuous-wave laser with a wavelength of 532 nm (Opus 532, Laser Quantum) is used to generate a beam that is horizontally polarized (i.e., the polarization direction is parallel to the page). The laser beam is enlarged by a 3× beam expander, consisting of a biconcave lens (BCV; LD1464-A-ML, Thorlabs) and a plano-convex lens (PCX; LD4874-YAG-ML, Thorlabs), thus resulting in a beam with a diameter of around 5.6 mm. The intensity of the enlarged beam is adjusted by a beam attenuator, consisting of a half-wave plate (HWP; WPH05M-532, Thorlabs) and a polarizing beam splitter (PBS; CCM1-PBS25-532/M, Thorlabs), to about 0.4 W, and the attenuated beam is passed through another HWP with its fast axis set at 45° from the z-axis, thus yielding a vertically polarized beam (i.e., its polarization direction is orthogonal to the page). The width of the beam along the y-axis is controlled using an adjustable rectangular slit (RS; VA100/M, Thorlabs) to reduce background scattering,[19] and a cylindrical lens (CL; f = 50 mm; LJ1695RM-A, Thorlabs) is employed to form a light sheet inside a quartz square channel (FireflySci). There, a suspension, automatically sampled from a temperature controlled jacketed 500 mm stirred reactor (17.110.73S, Schmizo) using a peristaltic pump (T600, Longer Precision Pump Co.), is illuminated before being fed back into the reactor. It is worth noting that light sheet illumination, an alternative to conventional wide-field illumination, allows for the selective illumination of a sample within the depth of field of a detection objective lens, which reduces out-of-focus light and thus enhances the signal-to-noise ratio of images significantly.[20−27]

In the detection optics, partially depolarized, side-scattered light from a sample is collected by an objective lens (OL; 10× NA 0.25; PLN10X, Olympus), and the two orthogonal polarization components of the scattered light, namely, the vertically polarized and the horizontally depolarized component, are imaged onto two monochrome CMOS cameras individually (BFS-U3-70S7M, Teledyne FLIR) in a synchronized manner, by using a PBS and a pair of tube lenses (TL; TTL180-A, Thorlabs) arranged as shown in Figure . Images of the vertically polarized component visualize both optically isotropic and anisotropic mesospecies, and these images can be analyzed to obtain the total number Ntot of all mesospecies present in the observation volume of the PISMO. On the contrary, images of the horizontally polarized component can display only optically anisotropic ones, thus yielding the number Nan of anisotropic mesospecies within the observation volume. Accordingly, once the observation volume (V) is known, the total particle concentration (ctot) and the anisotropic particle concentration (can) can be determined as ctot = Ntot/V and can = Nan/V.

As detailed in Section S1 in the Supporting Information, to obtain statistically representative counts at a given time, that are, Ntot and Nan, multiple pairs of images were acquired under constant imaging conditions every 2–3 min, and these images were analyzed automatically and consistently using the open source computer vision library OpenCV,[28] with a fixed set of image analysis parameters, whose values were optimized heuristically by taking 100 nm polystyrene (PS) particles (Sigma-Aldrich) as reference for two reasons. First, the size of 100 nm can represent the size of mesospecies appearing in the model system of this work,[29] which is a solution of dl-valine (Sigma-Aldrich, ReagentPlus, ≥99.0%) in a 1:1 (v/v) mixture of 2-propanol (VWR, Reagent grade) and water; deionized and filtered (filter size of 0.22 μm) water was taken from a Milli-Q Advantage A10 system (Millipore) for all experiments conducted in this work. The second reason for choosing PS as a reference is that its refractive index is very close to that of dl-valine, i.e., of around 1.57.[30−32]

Under the image acquisition and analysis settings used throughout this work (detailed in Section S1 in the Supporting Information), the observation volume V was about 9 nL, which was determined experimentally by analyzing a suspension of 100 nm PS particles with a known particle concentration of 1 × 88 mL–1. This is a necessary calibration step. The value of V is comparable to its theoretical estimate, given by the product of the field of view of the imaging system (1.444 mm × 0.99 mm at 10× magnification) and the measured thickness of the light sheet (around 6.3 μm for the width of the light intensity profile where the intensity is higher than 85% of the peak intensity). The measured intensity profile of the light sheet is shown in Figure S2.

It is worth highlighting the key advantage of the PISMO in comparison with the existing image-based methods for monitoring crystallization processes (e.g., in situ video microscopy[33] and flow-through microscopy[34−36]). Compared to the other methods mentioned above, the PISMO is capable of detecting species that are at least 10 times smaller. As demonstrated in the following section, the PISMO not only detects particles as small as 100 nm, but it also measures their concentration accurately, while distinguishing between optically isotropic particles and anisotropic ones. On the contrary, the other methods mentioned above cannot even detect such submicron species, as their typical detection limit is about a few micrometers or more.[35]

Results

Accuracy, Precision, and Sensitivity of Measurement

The accuracy, precision, and sensitivity in the measurement of the total particle concentration ctot and anisotropic particle concentration can were assessed by analyzing suspensions of nanoparticles in water, namely, a suspension of 100 nm PS particles as an optically isotropic sample, and a suspension of gold nanorods (AuNRs; A12-40-780, Nanopartz) having a length of 120 nm and width of 40 nm as an optically anisotropic sample, as done elsewhere.[10,11] For each measurement, the concentrations ctot and can were estimated by analyzing 10 pairs of acquired images of the sample; in the corresponding figures, the standard deviation of a concentration estimate is indicated by an error bar.

The parity plot of Figure a compares the measured total particle concentration ctot and the corresponding nominal concentration cnom over a wide range of values. In the case of PS suspensions, except the small error at the highest concentration (due to many groups of adjacent single particles counted as single objects), the measured particle concentration ctot is in excellent agreement with the nominal value cnom, thus showing an acceptable degree of accuracy. In the case of AuNRs, the total particle concentration ctot is overestimated systematically, simply because AuNRs, due to their extraordinary light scattering efficiency,[37] scatter light much more strongly than the PS particles that were used to optimize the image analysis parameters of the PISMO, as explained in section .

Figure 2

Assessment of the concentration measurement of the measurement device: (a) nominal vs measured particle concentration (cnom vs ctot); (b) measured particle concentration vs measured anisotropic particle concentration (ctot vs can); and (c) time-resolved measurement of particle concentration, ctot, and anisotropic particle concentration, can, for a suspension of 100 nm PS particles with an addition of an equal volume of a gold nanorods suspension having the same particle concentration ctot at t = 35 min. An error bar in all subfigures represents the standard deviation for a measured concentration estimated from 10 images of an analyzed sample.

As illustrated in the parity plot of Figure b, the measured anisotropic particle concentrations can of AuNRs agree with the corresponding total particle concentrations ctot adequately, as expected for optically anisotropic particles. On the contrary, in the case of PS particles, their anisotropic particle concentration can is effectively zero compared to the corresponding total particle concentration ctot, as expected for optically isotropic particles (data not shown here), simply because the depolarized component of side-scattered light from isotropic particles is negligible.[9,10,12]

The sensitivity of the PISMO to a sudden change in the population of suspended particles was tested by monitoring the mixing of PS and AuNR particle suspensions. As illustrated in Figure c, during the first 35 min of measurement, only PS particles were suspended at a total particle concentration ctot of 5 × 107 mL–1. At t = 35 min, an equal volume of a AuNR suspension having the same particle concentration ctot was introduced to increase the fraction of optically anisotropic particles abruptly, while keeping the total particle concentration ctot constant. As shown in Figure c, during the first 35 min, the measured total particle concentration ctot remains stable at about 5 × 107 mL–1, while the anisotropic particle concentration can is effectively zero as expected for a population of optically isotropic particles. Upon the addition of a AuNR suspension, a change in the population of suspended particles was promptly and correctly detected by the PISMO: the total particle concentration ctot remains the same and the anisotropic particle concentration can increases to about half of the total particle concentration ctot, as intended. This result demonstrates the high sensitivity of the PISMO in detecting a change in the population of suspended particles and the capability of the PISMO to distinguish optically isotropic and anisotropic particles from their mixture, which is an essential feature for investigating the formation of amorphous mesospecies in the nucleation process and their complex role in acting as nucleation precursors,[38−41] heterogeneous nucleation sites,[42] or inhibitors.[43,44] It is worth mentioning that the precision of concentration measurements is quite satisfactory, as indicated by the small error bars shown in Figure .

Mesospecies Formation in a Binary Liquid Mixture

Solutions of low molar mass compounds are usually considered as homogeneous at the molecular level, but this view contrasts with the spontaneous formation of long-lived mesospecies in various solutions,[29,45−48] for instance, in mixtures of freely miscible liquids such as water and ethanol,[46,49] and water and tert-butyl alcohol (TBA).[50−53] Although it has been experimentally shown that these mesospecies are not nanobubbles and that their formation can be affected by a temperature change,[29,49,50,52] there is no consensus regarding their formation mechanism.[43,53] In this context, the PISMO has been utilized to monitor the formation of mesospecies at varying temperature in a water/2-propanol solution, which is a mixture of freely miscible liquids, frequently used in the crystallization community.[29,54−57] About 800 mL of a 1:1 (v/v) water/2-propanol mixture was filtered with a 200 nm membrane (RW0309000, Millipore) and monitored online.

First, the filtered solution was kept at 30 °C for 3 h, during which period only a very low and rather constant concentration of optically isotropic species was observed (Figure S3), which implies that this state is either thermodynamically stable or kinetically arrested. Similarly, heating the solution to 55 °C did not trigger the formation of mesospecies.

Afterward, as illustrated in Figure a, the solution was kept at 55 °C for 1 h (stage I), cooled to 30 °C at a rate of 0.5 °C min–1 (stage II), kept at 30 °C for 3 h (stage III), and heated to 55 °C at a rate of 0.5 °C min–1 (stage IV). The corresponding time-resolved total particle concentration ctot and anisotropic particle concentration can are shown in Figure b. In stage I, both concentrations ctot and can are effectively zero, thus implying that the formation of mesospecies does not occur at 55 °C. In stage II, the cooling of the solution causes the instantaneous formation of a large amount of optically isotropic mesospecies (see an example of these mesospecies in Figure S4). These species cannot be nanobubbles, as decreasing the solution temperature typically makes gases more soluble, thus suggesting that these isotropic mesospecies are very likely self-assembled clusters of water and/or 2-propanol molecules with an amorphous structure; this is similar to reported experimental observations in various solutions containing mesospecies with a loose structure and a very weak depolarized light scattering.[45] In stage III, the concentration of the isotropic mesospecies decreases slowly over time, thus indicating that these mesospecies might be in a metastable state and thus might undergo slow dissolution. The same trend is found also in the results discussed in the following sections. Lastly, in stage IV, the heating of the solution dissolves the mesospecies completely, as also observed in the ternary system dl-valine/water/2-propanol via NTA.[29] The results highlight that the PISMO can provide real-time, quantitative information on the concentration of mesospecies, while this information could be used for modeling molecular self-assembly in solutions and for improving our understanding of the underlying mechanisms.

Figure 3

Time-resolved (a) temperature and (b) concentrations, the total particle concentration ctot (blue circles) and anisotropic particle concentrations can (red triangles), for a 1:1 (v/v) water/2-propanol mixture.

Mesospecies Formation and Nucleation in an Amino Acid Solution

In this section, we report on the use of the PISMO to investigate the formation of mesospecies and the primary nucleation in an amino acid solution, in particular, in a solution of dl-valine in a 1:1 (v/v) water/2-propanol mixture, where the presence of mesospecies has been verified.[29] A total of 12 experiments were conducted at five different levels of valine concentration, as summarized in Table with respect to the corresponding supersaturation S at 30 °C, where the supersaturation is defined as the ratio of valine’s concentration to its solubility (the measured solubility data is given in Section S4 of the Supporting Information). As shown in Table , experiments were replicated two or three times at each level of supersaturation.

Table 1

List of Experiments Monitored by PISMOa

exp	S [—]
E1, E2	0.5
E3, E4	1.247
E5, E6	1.285
E7–E9	1.3
E10–E12	1.315

S is the supersaturation at 30 °C.

For each experiment, an undersaturated solution was prepared at 65 °C by dissolving a known amount of dl-valine in 800 mL of a 1:1 water/2-propanol mixture under stirring at 65 °C for about 12 h. The solution was filtered using a 200 nm membrane and transferred to the reactor coupled to the PISMO, with all filtration equipments and the reactor preheated to 65 °C. Subsequently, the filtered solution was equilibrated at 55 °C for 15 min, before starting the measurement and cooling the solution at a rate of 0.5 °C/min for 50 min down to 30 °C, where the solution is either undersaturated (experiments E1 and E2) or supersaturated (experiments E3–E12).

In the following, mesospecies formation in solutions undersaturated at 30 °C is examined (section ), followed by a discussion of the monitored nucleation processes in solutions supersaturated at 30 °C as well as on the directly measured nucleation rates (section ).

Mesospecies Formation in an Undersaturated Solution

Figure illustrates two sets of experimental data collected from undersaturated solutions of dl-valine (S = 0.5 at 30 °C), corresponding to experiments E1 and E2 listed in Table . In the figure, the mean pixel intensity (I̅), calculated by averaging the pixel intensity values of an acquired image, represents the overall intensity of light scattered from the solution, whereas the hydrodynamic diameter (dH) obtained from dynamic light scattering measurements (see section S5 for details) indicates the size of mesospecies. As shown in Figure , the cooling of the solutions from 55 to 30 °C induces the formation of a large amount of optically isotropic mesospecies, represented by a substantial increase in both the mean pixel intensity (I̅) and the total particle concentrations (ctot) (see Figure , panels a and b, respectively), with an extremely low and nearly constant concentration (can) of anisotropic particles (see Figure c). This clearly indicates the formation of amorphous mesospecies in the undersaturated dl-valine solutions, as also observed in undersaturated solutions of other amino acids, e.g., glycine and dl-alanine,[48] by cryogenic transmission electron microscopy (cryo-TEM) and in solutions of lysozyme[42] by liquid-cell TEM.

Figure 4

Formation of mesospecies in undersaturated solutions (S = 0.5 at 30 °C) of dl-valine in a 1:1 (v/v) water/2-propanol mixture (experiments E1 and E2): (a) mean pixel intensity, I̅, obtained from acquired images; (b) total particle concentration, ctot; (c) anisotropic particle concentration, can; (d) solution temperature; and (e) hydrodynamic diameter, dH, measured from dynamic light scattering. The vertical dashed lines in all figures indicate the time at which the solution temperature reaches the target temperature of 30 °C.

The mesospecies formation caused by cooling in the valine/water/2-propanol mixture (see Figure ) is phenomenologically very similar to that in the water/2-propanol mixture examined in the previous section (see Figure ), but it is not yet clear whether the mesospecies formed in the ternary mixture are the same species observed in the binary mixture, where the mesospecies consists only of water and/or 2-propanol molecules. Nevertheless, like the mesospecies in the binary mixture, those in the ternary mixture also seem to be metastable, as they dissolve gradually over time; both the concentration and size of mesospecies decrease slowly (see Figure , panels b and e, respectively), accompanied by a noticeable decay in the mean pixel intensity (see Figure a). An analogous situation was found in the static light scattering measurements of three different aqueous solutions of NaCl, MgSO4, and Al(NO3)3,[45] where the intensity of light scattered from the solution decayed during more than 50 days. In summary, the results obtained from the PISMO clearly demonstrate that cooling can facilitate the formation of metastable and amorphous mesospecies in an undersaturated dl-valine solution, and these findings are consistent with experimental observations from other studies that have utilized different characterization methods.

Primary Nucleation and Direct Measurement of Nucleation Rates

This section discusses the most intriguing application of the PISMO presented in this paper, namely, the online monitoring of isothermal primary nucleation at varying levels of supersaturation and the direct measurement of nucleation rates at the early stage of nucleation. Figure illustrates 10 sets of experimental data representing primary nucleation of dl-valine at 30 °C and at four different levels of supersaturation S, as listed in Table : S = 1.247 (E3 and E4); S = 1.285 (E5 and E6); S = 1.3 (E7–E9); and S = 1.315 (E10–E12). The temperature profiles of experiments E3–E12 are the same as the profile plotted in Figure d for the undersaturated solutions, and thus they are omitted for brevity.

Figure 5

Primary nucleation at 30 °C in solutions of dl-valine in a 1:1 (v/v) water/2-propanol mixture at four different levels of supersaturation S = {1.247, 1.285, 1.3, 1.315} (experiments E3–E12): (a) mean pixel intensity, I̅, obtained from acquired images; (b) total particle concentration, ctot; and (c) anisotropic particle concentration, can. The vertical dashed lines in all figures indicate the time at which the solution temperature reaches the target temperature of 30 °C.

It can be seen in Figure that the monitored nucleation processes can be divided into three stages. In stage I, during which the solution is cooled from 55 to 30 °C, amorphous mesospecies form rapidly, as evidenced by a marked increase in both the mean pixel intensities (I̅) and the total particle concentrations (ctot), with nearly unchanging and very low concentrations (can) of anisotropic particles. The formation of amorphous mesospecies upon cooling is consistent with the experimental observations discussed in the previous sections (sections and 3.3.1), which highlights a consistent and crucial role of a temperature change in the formation of amorphous mesospecies.

Stage II is characterized by two features: first, amorphous mesospecies dissolve slowly over time, as indicated by a decay in both the mean pixel intensities (I̅) and the total particle concentration (ctot), which is also observed in the results analyzed earlier (Figures and 4); second, the anisotropic particle concentration (can) in supersaturated solutions increases gradually (see Figure c), unlike that in undersaturated solutions, where can stays at a very low level for the entire measurement period (see Figure c). The noticeable increase of can in Figure c is distinctively larger than the measurement noise of the PISMO (see Figure S5 in the Supporting Information, where the same measurements are plotted in logarithmic scale). Up to this stage, all the three quantities (I̅, ctot, and can) can be monitored online adequately.

Finally, in stage III, the nucleation process accelerates rapidly, as demonstrated by the sharp increase in the mean pixel intensities (I̅) and in the anisotropic particle concentration (can). During this last stage, the total particle concentration (ctot) could not be tracked because an excessive amount of light scattered from crystals causes detrimental blooming effects on the image sensor that collects the vertically polarized light, thus preventing reliable estimation of ctot. As an example, images of experiment E5 acquired at the initial state and at the end of each stage are presented in section S7 in the Supporting Information.

The effect of supersaturation S on the monitored nucleation processes is physically reasonable from various perspectives. First, increasing supersaturation accelerates the nucleation process by making solutions at a higher supersaturation reach stage III faster. In the case of the experiments conducted at high levels of supersaturation, such as experiments E7–E12, the fast progress in the nucleation process shortens the duration of stage II essentially to zero, as shown in Figure .

Second, increasing supersaturation reduces the variability in the outcome of nucleation experiments conducted under the same conditions, which is consistent with experimental observations reported in the literature,[17,58−61] where the variability in experiments is attributed to the inherent stochastic nature of primary nucleation events. The decreasing variability coupled with the increasing supersaturation is especially well demonstrated in Figure c, where the differences among experiments performed exactly at the same conditions clearly decrease with an increase in supersaturation.

The third aspect concerns the nucleation rate J, defined as the number of newly formed crystals per unit volume and unit time. According to its definition, the nucleation rate can be quantified from the slope of a crystal concentration versus time profile. Since the crystal concentration profile is equivalent to the time-resolved anisotropic particle concentration can(t), the nucleation rate in the stationary regime can be obtained directly from the slope of a linear regression line in the linear region of the measured can(t), through which the first direct measurement of the crystal nucleation rate has been achieved in this work.

It is worth comparing this result with previous attempts to measure the crystal nucleation rate directly to put it in perspective.[17,62] In ref (62), the nucleation rate was measured by applying the double-pulse technique, which involves two steps.[63] First, a small volume of solution was kept at high supersaturation to induce nucleation. Second, after the onset of nucleation, the solution was quickly cooled to decrease supersaturation and thus suppress further nucleation, while the nuclei formed in the first step can grow to a detectable size to be counted by microscopy. However, additional nuclei could form during the second step,[63] and the rapid cooling in this step increases the critical nucleus size abruptly, thus potentially dissolving some nuclei that were formed in the first step but could not grow larger than the critical nucleus size.[63] Because of these inherent uncertainties and the two-step nature of the procedure, the double-pulse technique cannot be seen as a method that determines the nucleation rate directly.

In ref (17), the nucleation rate was determined by applying a laser backscattering technique that measures the chord length distribution (CLD) of the crystal population and then by converting the measured CLD to crystal concentration through an empirical correlation. The empirical correlation was based on multiple simplifying assumptions, including a rather critical one, namely, that the average volume of suspended crystals can be obtained simply by scaling the third moment of the CLD with a constant factor. Considering that extracting the size and shape information on suspended crystals from their CLD is much more complex than simple multiplication by a constant,[14,64−66] the validity of the aforementioned assumption cannot be justified easily, thus making the nucleation rate measurements obtained with this method only semiquantitative.

On the contrary, the nucleation rate measurement performed in this work is based on directly measured crystal concentration–time profiles, thereby making the measurement truly direct and quantitative.

It is remarkable that, as illustrated in Figure , the measured nucleation rates increase with supersaturation S. One can also observe a reasonable agreement with the values of the nucleation rate (J) obtained using the fitted, nucleation kinetic model that follows the classical nucleation theory (CNT). Here, the nucleation rate J in the stationary regime is given by the following equation:[67]J = θ1S exp(−θ2/ln2S) where the values of the estimated parameters are θ1 = 1.16 × 1012 m–3 s–1 and θ2 = 0.24. The agreement between the measurements and the model indicates that the obtained model can be used in model-based optimization and control of an industrial crystallization process,[68] and further suggests that the model compound may nucleate by the CNT mechanism; for example, molecular resolution atomic force microscopy has revealed that, in the case of protein glucose isomerase, the molecule packing structure of subcritical clusters is in the same state as the crystalline bulk phase,[69] as expected from the CNT. Nevertheless, to reveal the nucleation mechanism of the model compound, it is necessary to acquire additional experimental data with high spatial resolution, which is beyond the scope of this work.

Figure 6

Nucleation rates directly measured using the PISMO (diamond markers) from experiments E3–E12 and the predictions of the fitted, classical nucleation kinetic model (red lines) with their 95% confidence intervals (red dashed lines) in the (a) (S, J) and (b) (ln–2S, ln(J/S)) planes.

Discussion and Conclusions

Discussion

During the last few decades, the crystal nucleation rate in solution has been mostly measured by applying indirect measurement methods (see ref (63) for a recent review), for instance, by measuring the variation in the nucleation induction time in small vials, mainly due to its high-throughput and ease of use; however, the obtained nucleation kinetics seems to be of limited practical value because they often fail to predict the nucleation kinetics in larger crystallizers.[17,63,70] Moreover, the validity of various indirect measurement methods has been rarely verified, largely because of the lack of a suitable method to determine the nucleation rate directly.

Accordingly, given its capability to monitor the concentration of amorphous and crystalline mesospecies, the PISMO promises to be of great value at least for two reasons. First, from a practical perspective, the PISMO would allow for a more accurate estimation of nucleation kinetics and thus facilitate model-based design and optimization of industrial crystallization processes, which often involve primary or secondary nucleation. Second, beyond the practical point of view, the PISMO can be a valuable complementary tool to advance the fundamental understanding of nucleation phenomena, e.g., by helping understand how amorphous mesospecies get involved in the nucleation process. The role of amorphous mesospecies in nucleation varies, depending on the nucleation pathway of the molecule under interest, as precursors to crystalline nuclei,[38−41] as heterogeneous nucleation site,[42] or even as nucleation inhibitors (in that mesospecies prevent nucleation in a supersaturated solution for more than 15 h).[43,44,71] While, in the model system of this work, no direct correlation was found between the concentration of amorphous mesospecies and the nucleation rate (see Figures b,c and 6a) due to the likely presence of amorphous mesospecies composed only of solvent molecules, we believe that the development of the PISMO still represents an important step toward a better understanding and characterization of nucleation phenomena.

Concluding Remarks

In summary, we developed an online measurement device for monitoring the concentration of amorphous and crystalline mesospecies present in a solution in a lab-scale stirred reactor. A solution is circulated in a closed-loop, while passing through a flow-through cell, where the concentrations of amorphous and crystalline mesospecies are measured by depolarized light sheet microscopy. By characterizing optically isotropic and anisotropic nanoparticle suspensions at varying concentrations, we showed that the concentration measurement is reasonably accurate and precise, and highly sensitive to a change in the population of mesospecies.

We applied the measurement device to examine the formation of mesospecies at varying temperature in both a binary mixture of freely miscible liquids and in an undersaturated amino acid solution, thereby revealing the crucial role of a temperature change in the formation of metastable and amorphous mesospecies. Moreover, we monitored isothermal primary nucleation of an amino acid at four levels of supersaturation and achieved the first direct measurement of the crystal nucleation rates. As expected, increasing the supersaturation reduced the variability in the outcome of nucleation experiments, while resulting in an increase in the measured nucleation rate, whose dependence on supersaturation was in reasonable agreement with the classical nucleation theory. The measurement device would facilitate model-based design and optimization of industrial crystallization processes by enabling a more accurate estimation of nucleation kinetics and would ease the investigation of nucleation mechanisms, for instance, by helping to understand the complex role of amorphous mesospecies in the nucleation process.