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

Abstract

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.

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.

Figure 2

Assessment of the concentration measurement of the measurement device: (a) nominal vs measured particle concentration (c_nom vs c_tot); (b) measured particle concentration vs measured anisotropic particle concentration (c_tot vs c_an); and (c) time-resolved measurement of particle concentration, c_tot, and anisotropic particle concentration, c_an, 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 c_tot 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.

Figure 3

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

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, c_tot; (c) anisotropic particle concentration, c_an; (d) solution temperature; and (e) hydrodynamic diameter, d_H, 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.

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, c_tot; and (c) anisotropic particle concentration, c_an. The vertical dashed lines in all figures indicate the time at which the solution temperature reaches the target temperature of 30 °C.

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.