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. 2026 Sep 16;11(38):57878–57884. doi: 10.1021/acsomega.6c07116

Open-Microcombinatorial Analysis of Critical Points of Crystal Growth and Nucleation for Small Molecules in Organic Solvents

Satoshi Watanabe †,*, Satoshi Masunaga ‡
PMCID: PMC13629367  PMID: 42824727

Abstract

Obtaining phase diagrams to know the critical points of crystal growth and nucleation is essential for reducing trial-and-error processes and enabling systematic fabrication. However, conventional methods require gram-scale sample volumes and long equilibration times (weeks to months) and allow only limited parallel measurements, making them unsuitable for early-stage material development. Here, we report an open microfluidic system that enables rapid and quantitative phase diagram construction of small-molecule solutions in volatile organic solvents by using nanoliter-scale volumes. Unlike conventional approaches that suppress solvent evaporation using closed configurations, our method quantitatively monitors evaporation in real-time, allowing analysis under open conditions. This enables the simultaneous evaluation of both phase behavior and evaporation kinetics. The system achieves approximately 10-fold faster measurements than conventional methods, and allows high-throughput analysis through dense integration. In addition to reproducing results comparable to those of bulk methods, we observe microscale-specific behavior, including an expanded supersaturation region arising from reduced liquid volumes. This approach provides a versatile platform for rapid phase diagram analysis and is broadly applicable to crystallization and phase separation processes in materials science and chemical engineering.

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Introduction

Microfluidic technology has advanced significantly across multiple dimensions, including device engineering, analytical methodologies, and application domains. Developments in microelectromechanical systems (MEMS), soft lithography, and lab-on-printed circuit board (lab-on-PCB) platforms have enabled the miniaturization and integration of fluidic systems. In parallel, analytical techniques such as lab-on-a-chip systems, micro-total analysis systems (μTAS), and digital polymerase chain reaction (PCR) have expanded the capabilities of chemical and biological analyses.

In the 1990s, the foundations of microfluidics were established through advances in lithography and silicon-based semiconductor technologies, enabling the precise control of fluids at the microscale. In the 2000s, the introduction of poly­(dimethylsiloxane) (PDMS) enabled flexible device fabrication and rapid prototyping, accelerating applications, particularly in bioanalysis. Since the 2010s, research has increasingly focused on exploiting microscale-specific phenomena rather than simply reducing sample volumes. Representative examples include the unique nucleation behavior in optically trapped microdroplets, anomalous interfacial pH distributions, and precise synthesis enabled by rapid thermal and concentration control. More recently, integration with the Internet of Things (IoT) and artificial intelligence (AI) has enabled autonomous microfluidic systems.

Despite these advances, microfluidic systems are generally susceptible to solvent evaporation, contamination, and temperature fluctuations. Therefore, most systems are designed as closed devices to ensure high controllability. − However, closed configurations impose several limitations, including (i) channel clogging, which restricts the handling of solid- or gel-containing systems; (ii) limited accessibility for sampling and manipulation; (iii) increased system complexity due to pumps and valves; (iv) limited scalability for high-density integration; and (v) restricted utilization of gas–liquid interfaces.

To overcome these limitations, open microfluidic systems have attracted increasing attention because of their simplicity and accessibility. − However, their application to volatile solvent systems remains limited because solvent evaporation is difficult to control. As a result, previous studies have typically employed low-volatility media, such as oils , and ionic liquids. −

We propose that open microfluidic systems can provide a powerful platform for phase diagram analysis in crystallization engineering. The construction of phase diagrams is essential for understanding both thermodynamic equilibrium and kinetic processes. In particular, the equilibrium solubility curve (binodal) and the metastable limit associated with nucleation define the supersaturation region that governs the crystal growth behavior. In terms of crystal engineering, this is equivalent to identifying the critical points for crystal growth and nucleation. In addition, valuable information for controlling phase transitions can be obtained, including crystal composition and the formation of solute aggregates and prenucleation clusters in solution, interfacial concentration effects at gas–liquid interfaces, , lower critical solution temperature (LCST) phase transitions, as well as upper critical solution temperature (UCST) behavior, − polymorphism, and liquid–liquid phase separation. However, conventional measurements require large sample volumes and long equilibration times, making systematic exploration inefficient. , Previously, we developed a nanoliter droplet system using ionic liquids, which enabled the rapid evaluation of crystal growth limits under suppressed evaporation conditions. However, this approach is not applicable to volatile solvent systems.

In this study, we present a method for constructing phase diagrams in volatile solvents by using nanoliter-scale open pools. By quantitatively measuring the liquid volume via side-view observation of the meniscus, solvent evaporation can be corrected in real time. This approach enables accurate and high-throughput phase diagram construction in open systems.

Experimental Section

Materials and Substrates

The chemical structures of the materials used in this study are shown in Figure a. 9,10-Dibromoanthracene (DBAn), o-dichlorobenzene (DCB), and dibenzyl ether (DBE) were purchased from FUJIFILM Wako Pure Chemical and Tokyo Chemical Industry and used without further purification. DBAn was selected as a representative π-conjugated small molecule due to its moderate solubility and almost no sublimation under the experimental conditions. DCB and DBE were chosen as solvents because they dissolve DBAn and possess appropriate surface tension and boiling points for inkjet printing. DBAn exhibits slightly lower solubility in DBE than in DCB, which is advantageous for phase diagram construction.

1.

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(a) Chemical structures of the solute and solvents. (b–f) Schematic illustration of the procedure for constructing phase diagrams using inkjet printing: (b) deposition of DBAn solution onto the patterned substrate, (c) formation of DBAn crystals by solvent evaporation, (d) deposition of DBE into pools, (e) determination of dissolution conditions upon heating, and (f) determination of precipitation conditions upon cooling.

Quartz substrates were custom-fabricated by KYOKUEI KENMA Co., Ltd. Cylindrical holes (diameter: 0.5 mm, depth: 0.5 mm) were drilled into a quartz plate (thickness: 0.5 mm) to form nanoliter-scale pools. A 0.2 mm-thick quartz plate was bonded to the bottom of the substrate via optical contact. The calculated volume of each pool was 98.2 nL. The pools were positioned near the edge of the substrate to facilitate side-view optical observations.

Inkjet Ejection Conditions

DBAn was dissolved in DCB to prepare a 15 mM solution. The DBAn solution and DBE were filtered through a poly­(tetrafluoroethylene) membrane filter (pore size: 0.2 μm) and transferred into 1 mL sample vials.

The vials were mounted on a piezoelectric inkjet printer (LaboJet-500, MICROJET, Japan) equipped with an IJHE-1000 head. The distance between the nozzle and the substrate was adjusted to 1–2 mm. Droplet ejection was performed under ambient conditions at approximately 25 °C. The ejection parameters were optimized by varying the applied voltage (0–80 V), pulse width (40–80 μs), and frequency (120–500 Hz). The head temperature was maintained at 25 °C.

The ejected droplets were observed by using a high-speed camera synchronized with a strobe light. The droplet velocity was calculated from the displacement and the delay time. The droplet volume was determined by dividing the mass of approximately 10,000 droplets by the liquid density (DCB: 1.30 g cm–3; DBE: 1.05 g cm–3).

Printing and Observation

Figure b–f illustrates the procedure for preparing an array of DBAn/DBE droplets by inkjet printing. The concentration of DBAn in each pool was controlled by adjusting the number of deposited droplets in the DBAn solution.

The substrates were cleaned by ultrasonication in acetone and chloroform for 20 min each. The DBAn solution in DCB was deposited into pools (0–100 nL) under optimized conditions (Figure b). After deposition, DCB was evaporated under ambient conditions, leaving DBAn crystals in the pools (Figure c). Subsequently, 100 nL of DBE was introduced into each pool to dissolve the crystals, forming DBAn/DBE solutions with concentrations ranging from 0.1 to 0.3 M (Figure d).

The substrates were placed on a temperature-controlled stage (SS053, BLAST, Japan) with a temperature accuracy of ±0.1 °C. The samples were observed from the side using a digital optical microscope (RX-100, HIROX, Japan). The temperature was varied at rates between 0.1 and 10 °C min–1 until complete dissolution or precipitation of crystals was observed.

Conventional Technique

For comparison, bulk measurements were performed using 1 mL vials containing DBAn in DBE at a concentration of 100 mM. The vials were sealed and placed on an aluminum heating block controlled by a temperature controller (PCC-117-Co, MSA Factory, Japan). The temperature precision was ±0.1 °C. Heating rates ranged from 0.0083 to 0.20 °C min–1. Crystal dissolution was determined visually.

Results and Discussion

Volume Measurement of Nanoliter Pools

First, the ejection conditions of the anthracene solution and DBE in the piezoelectric inkjet device were investigated. The droplet velocity and volume were evaluated as described in our previous study, and the details are summarized in Figure S1. The ejection conditions were chosen to be a frequency of 120 Hz, a pulse width of 60 μs, and an applied voltage of 35 V. The volume of the ejected single droplet was about 0.72 nL for the DBAn solution and 0.78 nL for DBAn. The measurement was repeated 10 times with approximately 10,000 droplets each. These volumes of droplets and ejected conditions were consistent with previously reported values for anthracene in DCB. The results for DCB and DBE were also almost unchanged. Although DBE has approximately three times higher viscosity than DCB, both liquids exhibit similar surface tensions (∼35 mN m–1). These results suggest that surface tension is the dominant factor governing droplet ejection.

Next, the substrates were processed to fabricate nanoliter pools on quartz substrates. Figure a shows the top and side views of the substrates observed by optical microscopy. The surface of the pool was smooth because the bottom of the pool was fabricated by gluing the flat plates together. This feature is important for accurately maintaining the volume of the pools and for observing the pools directly above them to determine the dissolution or precipitation of substances. The side view was clearly observed because the pools were positioned near the edge of the substrate, so that they could be easily focused with an optical microscope.

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Optical microscopy images of the fabricated substrates: (a) bright-field images of empty pools and (b) crossed-Nicol images of pools filled with DBE at different volume fractions (20–70%). (c) Normalized meniscus height (h/Δh) as a function of normalized liquid volume (V/ΔV) for the DBE. Here, h is the meniscus height from the bottom of the pool, Δh is the pool depth (0.5 mm), V is the liquid volume, and ΔV is the total pool volume (98.2 nL).

The pools were filled with DBE using an inkjet printer. Figure b shows cross-Nicol microscope images of the five pools filled with DBE at 20 vol % to 70 vol % of the pool volume. At 20 vol %, a positive meniscus of DBE was observed in the pools. This indicated that DBE wetted the substrates well. The increase in the volume ratio of the DBE increased the height of the meniscus from the surfaces of the pool bottoms. At 70 vol %, the meniscus was barely visible, and the solvent had almost filled the pools. Based on the spatial resolution used in this study, the volume error bar for determining the meniscus position was ±0.5%. Figure c shows the normalized height of the meniscus plotted with the DBE volume for five independent pools. The heights of these five pools increased linearly with an increase in the DBE volume. Using this calibration curve, the volume of the DBE can be determined from the height of the meniscus. The uncertainty of the calibration curve was approximately ±2%, representing the variability among the five independent pools, each measured once, which includes errors in the ejected droplet and meniscus readings.

Measurements of Evaporation Kinetics

The real-time volume of DBE in the pools was quantified by monitoring the meniscus of the DBE in the unlidded pools. Measurements were performed using five independent pools, each measured once. Figure shows the DBE volume plotted versus the elapsed time. The volume of DBE remained unchanged at 25 °C because DBE has a high boiling point (298 °C) at atmospheric pressure. At 65 °C, a decrease in the liquid volume was observed over a period of minutes. The volume uncertainty was nearly ± 5%. This value is larger than the observation resolution, which could be due to variations in evaporation rates among the pools. The average volume decreased approximately linearly with time. Higher temperatures increased the evaporation rate. The linearity of the evaporation rate did not change even with increasing temperature.

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Time evolution of normalized DBE volume in nanoliter pools during evaporation at different temperatures (60–140 °C). The initial volume (98.2 nL) is normalized to 100%. Solid lines represent linear fits based on the zero-order kinetic model (eq ). The uncertainty in the volume measurement is approximately 10%.

These data were analyzed using a kinetic model and the Arrhenius equation. The evaporation rate was assumed to be constant because the surface area of the liquid in the pool remained nearly unchanged during evaporation. Under these conditions, the evaporation process can be approximated by a zero-order kinetic model, which is independent of the liquid volume.

V=V0−kt 1

V: volume of DBE at time t, V 0: initial volume of DBE, k: kinetic constant at a certain temperature.

The kinetic constant at each temperature was obtained by fitting eq to Figure . According to the Arrhenius equation, the kinetic constant can be expressed as follows

k=Aexp(−EaRT)⇔ln⁡k=ln⁡A−EaRT 2

A: frequency factor, E a: activation energy of evaporation, R: gas constant, T: temperature.

Figure S2 shows an Arrhenius plot calculated with the kinetic constants obtained from Figure . The Arrhenius plot clearly shows the linearity of the kinetic constants (ln k) and temperature (1/T). The activation energy was calculated from the slope of the Arrhenius plot to be about 71.0 (kJ mol–1). This activation energy was slightly larger than the enthalpy of vaporization of DBE (45.6 kJ mol–1). , This higher apparent activation energy suggests that, in addition to vaporization, diffusion of molecules from the bulk liquid to the interface contributes to the overall evaporation process. When the phase transition from the interface to the vapor phase is the dominant process, the activation energy is expected to be close to the enthalpy of vaporization. However, at higher temperatures, diffusion from the bulk liquid to the interface becomes more significant, which tends to increase the apparent activation energy. The present experimental results are considered to correspond to the latter case.

Determination of Heating Rates

The dissolution temperatures of DBAn in DBE were measured at different heating rates to determine the optimal heating rate for the conventional and present techniques. Figure shows the photograph of a 100 mM DBAn solution in (a, c) the pool and (b, d) a vial at (a, b) 25 °C and (c, d) 48 °C at heating rates of (c) 0.20 °C min–1 and (d) 0.017 min–1. At 25 °C, needle crystals of DBAn were observed in the solution of the pool and the vial. As the temperature increased, the crystals gradually dissolved. Only in the pool did the liquid level drop slightly due to evaporation. When the temperature reached 58 °C, the crystals completely dissolved in the pool and the vial. The disappearance of the last visible crystal was defined as the dissolution endpoint, and this temperature was defined as the dissolution temperature at 100 mM. For vial measurements, the endpoint was determined by visual observation due to the larger sample volume. The temperature uncertainty was a few percent for pools and less than 1% for vials. Figure e shows the dissolution temperature difference plotted versus the heating rate for pools and vials. The difference in the dissolution temperature was calculated by subtracting 58 °C from the dissolution temperature at each heating rate. The slower the heating rate, the lower the dissolution temperature. The dissolution temperatures were almost unchanged at heating rates of 0.1 and 0.2 °C min–1 for the pools, and 0.017 and 0.0084 °C min–1 for the vials. The heating rate at which the dissolution temperature became independent of the heating rate was considered to represent quasi-equilibrium conditions.

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Optical images of DBAn in DBE in (a, c) nanoliter pools and (b, d) bulk vials at: (a, b) 25 °C and (c, d) 48 °C. The initial concentration was 100 mM. Heating rates were (c) 0.20 °C min–1 for the pool and (d) 0.017 °C min–1 for the vial. (e) Dissolution temperature difference (ΔT) as a function of the heating rate for pools (blue circles) and vials (gray squares). ΔT is defined as the difference between the dissolution temperature at each heating rate and the equilibrium dissolution temperature (58 °C). The dotted line represents the guide for the eye.

Comparing the conventional technique with this technique, the present technique can reach thermal equilibrium even though it is approximately 1 order of magnitude faster. This is because the volume of the solution was approximately 7 orders of magnitude smaller. This is similar to our previous results using nanoliter pools of ionic liquids. Interestingly, the heating rates at which equilibrium was reached were almost the same for the ionic liquid and DBE, despite the ionic liquid having a higher viscosity. This suggests that heat transport rather than mass transport is the rate-limiting process. The conventional technique resulted in fewer errors because of better sealing. Since this technique allows for easy increases in the number of pools, the error bars should be made even smaller with similar effort.

Preparation of the Phase Diagram

The concentration-temperature phase diagram of DBAn in DBE was prepared in nanoliter pools at the optimized heating and cooling rates. The dissolution and precipitation temperatures were defined as the temperature at which DBAn crystals completely dissolved from a heterogeneous phase to form a homogeneous phase and at which DBAn crystals precipitated from the homogeneous phase to form a heterogeneous phase. The concentrations at the phase transition were corrected for volume loss upon solvent evaporation. Figure shows the phase diagram of DBAn in DBE in the nanoliter pools at heating and cooling rates of 0.2 °C min–1. The dissolution and precipitation temperatures increased with an increase of the concentration. The concentrations in each plot showed variability, primarily due to the limited volume resolution. The temperature variation in the precipitation curve was about 6 °C, which was larger than that in the dissolution curve. Since nucleation occurs probabilistically, this result may be reasonable. Therefore, the precipitation curve obtained in this study should be interpreted as an apparent kinetic nucleation boundary rather than a strict thermodynamic metastable limit. The observed precipitation temperature depends on experimental parameters, such as the pool volume and cooling rate. Determination of the intrinsic thermodynamic nucleation limit requires further analysis of the cooling rate dependence and volume effect. The solubility curves obtained using the conventional method and this method were almost identical.

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Concentration–temperature phase diagram of DBAn in DBE obtained using nanoliter pools (40–70 nL). The concentrations were corrected based on the measured volume changes due to solvent evaporation. The solid lines represent fits based on the van’t Hoff equation.

The solubility data can be described by the van’t Hoff equation, and the log plots are shown in Figure S3. The fitted data showed that dissolution enthalpy Δd H and entropy Δd S were +76.1 kJ mol–1 and Δd S = +199 J mol–1 K–1 from the dissolution curve. Since the precipitation curve varies with volume and heating rate, these parameters, which originate from thermodynamic equilibrium, were not calculated.

The temperature and concentration differences between the dissolution and precipitation curves were approximately 6 °C and 0.15 M, respectively. This region is generally called the supercooling or supersaturated region. According to classical crystal growth theory, the dissolution curve indicates the critical condition for crystal growth, and the precipitation curve indicates the critical condition for nucleation. This indicates that this supersaturated region where crystal growth can occur without spontaneous nucleation.

Table summarizes the sources of errors associated with the present techniques. Errors arising during droplet dispensing at the initial stage of the process are extremely small, whereas larger errors appear during solubility measurements at the later stages of the process. The error associated with droplet dispensing is minimal because of the stable operation of the piezoelectric actuator, while the error in meniscus measurements is small owing to the precision of optical microscopy. Variations in the calibration curve are thought to originate from differences in the pool dimensions and meniscus geometry among the individual pools. Because errors from these factors accumulate, the uncertainties in evaporation measurements, solubility determination, and crystal precipitation measurements exceed ±2%. The larger errors observed for evaporation and crystal precipitation, compared with solubility measurements, are likely due to the greater variability inherent in these phenomena. The relatively small variation in solubility measurements suggests that the uncertainty in visually determining whether crystals have dissolved has little influence on the overall measurement accuracy.

1. Summary of Errors in this Technique.

  error
      
experiment (%) (°C) number of samples number of repetitions data
Volume of an ejected droplet <0.3 <0.1 10,000 (droplet) 10 Not shown
meniscus position ±0.5 <0.1 30 (image) 1 Figure b
Calibration curve ±2 <0.1 5 (pool) 1 Figure c
Temperature control - ±0.5 - - Not shown
Evaporation rate ±5 ±0.5 5 (pool) 1 Figure
Dissolution curve ±2 ±4 5 (pool) 1 Figure e and
Precipitation curve ±5 ±6 5 (pool) 1 Figure
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Among these error sources, the approximately 2% error associated with the pool geometry would potentially be reduced by one to 2 orders of magnitude through improvements in pool fabrication and design. Although the pools were fabricated using the highest-resolution region of the machining system, dimensional variations of less than 1% in pool diameter remained. These tolerances would be further reduced by employing higher-precision fabrication methods such as photolithography. Furthermore, modifying the pool geometry from a simple cylindrical shape to a tapered geometry similar to that of a volumetric flask would potentially achieve measurement accuracies comparable to those of volumetric glassware. The volumetric flask shape has the advantage of reducing the risk of contamination of the solution in an open system.

For solubility measurements, increasing the number of experimental repetitions may further reduce the uncertainty of the intrinsic error level of the individual pools. In contrast, solvent evaporation and crystal precipitation exhibit substantial intrinsic variability, and although increasing the number of experiments can reduce the statistical error, it is unlikely that their uncertainties can be reduced below those of the solubility measurements. Although not addressed in the present study, variations in the pool temperature control, as well as the endothermic and exothermic effects associated with the sample, may also contribute to the observed variability. The temperature of the sample stage was controlled with an accuracy of less than 0.1°C. Therefore, further investigation using imaging techniques such as infrared thermography will be necessary to evaluate these effects quantitatively.

Conclusion

The present study demonstrates that accurate phase diagram construction in volatile solvent systems can be achieved by using nanoliter-scale open pools when solvent evaporation is quantitatively corrected. A key advantage of this method is that the liquid volume, and hence the solute concentration, can be determined in real time through meniscus observation. This enables the direct evaluation of phase boundaries under conditions in which conventional open systems would suffer from significant concentration uncertainty. Overall, the method establishes a general framework for rapid and quantitative phase diagram analysis in open systems and offers new opportunities for both fundamental studies and practical applications in crystallization engineering.

Supplementary Material

ao6c07116_si_001.pdf (64.7KB, pdf)

Acknowledgments

The authors thank Professor Masashi Kunitake of Kumamoto University for valuable discussions on this work and Professor Shotaro Hayashi of Kochi University of Technology for providing information on DBAn.

Glossary

Abbreviations

DBAn

9,10-dibromoanthracene

DBE

dibenzyl ether

MEMS

microelectromechanical systems

lab-on-PCB

lab-on-printed circuit board

μTAS

micro-total analysis system

PCR

digital polymerase chain reaction

PDMS

poly­(dimethylsiloxane)

IoT

Internet of Things

AI

artifical intelligence

LCST

lower critical solution temperature

UCST

upper critical solution temperature

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c07116.

  • Inkjet printing condition, Arrhenius plot of DBE evaporation, and van’t Hoff plot from phase diagram of DBAn in DBE (PDF)

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.

This research was supported by the Ministry of Education, Culture, Sports, Science, and Technology (grant no. 21H01239) and the Toshiaki Ogasawara Memorial Foundation in Japan.

This work was conducted while the corresponding author was affiliated with the Faculty of Advanced Science and Technology, Kumamoto University.

The authors declare no competing financial interest.

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