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Abstract
According to the conventional phase diagrams, aqueous solutions freeze at the liquidus and are frozen/solid below the eutectic solidus. Herein, using differential scanning calorimetry (DSC) and optical cryo-microscopy (OC-M), we demonstrate that hy-poeutectic, eutectic 40 wt% (NH4)2SO4 and hypereutectic (NH4)2SO4/H2O remain liquid well below the eutectic solidus before freezing in three steps: fast-slow-fast. The first fast freezing produces a ramified ice microstructure (IM) and freeze-concentrated solution (FCS) containing up to ~70 wt% (NH4)2SO4. As temperature decreases further, the slow freezing of FCS precedes its fast freezing, which produces a striped IM and (NH4)2SO4 microcrystals. Videos recorded upon warming of frozen (NH4)2SO4/H2O reveal a new three-phase reaction, which is the recrystallization of ice and (NH4)2SO4 microcrystals into the lamellar eutectic ice-(NH4)2SO4 superlattice. This work demonstrates limitations of the (NH4)2SO4/H2O phase diagram and pro-poses an effective strategy for studying other deeply supercooled solutions whose behavior is not predicted by the phase dia-gram.
Supplementary materials
Title
Visualizing the three-step freezing process and three-phase reaction not predicted by the (NH4) 2SO4/H2O phase diagram
Description
1. Estimation of the concentration of FCS
2. Legends for Supplementary Videos (SV):
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Title
SV1. Ice starts melting from the ice/FCS interface.
Description
The video was recorded during the warming of a millimeter-scaled drop 30 wt% (NH4)2SO4 cooled to temperature colder than Tf,ice, but warmer than Tf,FCS (see Figure 3 of the main text). In this case, the FCS remains unfrozen. The video shows that the ice begins to melt at ~-38 º C (~235K), which is much colder than the eutectic temperature TE≈254K. This indicates that the concentration of FCS is much higher than the eutectic 40 wt% (NH4)2SO4. The video also shows that the rate of ice melting increases with increasing temperature and the most intense melting occurs at Tm≈262K, when the FCS concentration reduced to 30 wt% (NH4)2SO4. Temperature (º C), cooling/warming rate (º C/min) and temperature limit of measurements are visible at the bottom left corner of all videos.
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Title
SV2. Two fast freezing steps of a millimetre-scaled drop 40 wt% (NH4)2SO4.
Description
The video was recorded during the cooling of a millimetre-scaled drop similar to those studied in our DSC experiments. The first fast freezing Tf,ice manifests itself as a sudden brightening of the sample. The second fast freezing Tf,FCS manifests itself as the appearance of FCS bulges. 4
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SV3. Two fast freezing steps of hypoeutectic 30 wt% (NH4)2SO4 film.
Description
The video was recorded during the cooling of a film 30 wt% (NH4)2SO4 of thickness ~10-15 µm thick. The first fast freezing step Tf,ice is visible as a brownish Tf,ice-front moving from right to left. This front arises due to the formation of a ramified ice microstructure (IM) entangled with a FCS. The formed IM/FCS pattern increases the optical density of the film. The second fast freezing step Tf,FCS occurs at much colder temperature. It is visible as a bright Tf,FCS-front moving from top to bottom. The brightness of Tf,FCS-front is due to the reflection of light from the completely frozen film. Note the moving Tf,FCS-front pushes unfrozen FCS and forms bulges at the edge of the film, which freeze last. In this video, the slow freezing step (or the slow freezing of FCS) is not visible. It is visible in SV9.
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Title
SV4. Two fast freezing steps of the eutectic 40 wt% (NH4)2SO4 films.
Description
The video was recorded during the cooling of a film without (NH4)2SO4 crystals. Similar to hypoeutectic films, in the eutectic and hypereutectic films without crystals, Tf,ice-front and Tf,FCS-front are usually separated by a certain temperature interval, like the peaks Tf,ice and Tf,FCS in the cooling thermograms in Figures 1a. The video also shows how the moving Tf,FCS-front forms FCS bulges. Non-uniform color of the frozen film is due to the non-uniform morphology of IM/FCS. Dark areas are rich with ice. Black spots are ice crystals formed by vapour deposition on a cover glass.
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SV5. Two fast freezing steps of hypereutectic 44 wt% (NH4)2SO4 film.
Description
The video was recorded during the cooling of a film without (NH4)2SO4 crystals. The video demonstrates two moving Tf,ice-fronts and three Tf,FCS-fronts. The temperature interval between the Tf,ice-fronts and Tf,FCS-fronts is shorter than in SV4.
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SV6. (NH4)2SO4 crystallization and two fast freezing steps of 43 wt% (NH4)2SO4 film.
Description
The solution was loaded between the microscope slide and cover glass at a temperature ~+23 °C. (NH4)2SO4 crystal homogeneously crystalized at the edge of the film before the start of video recording at ~+15 °C. The initial cooling rate was 10 K/min. The video shows that the crystal grows slowly with decreasing temperature and rotates due to surface tension. The cooling rate was reduced from 10 to 3 K/min at ~-47 ºC when the freezing event Tf,ice was expected. Two oppositely moving Tf,ice-fronts and one Tf,FCS-front appear one after the other. Note the Tf,FCS-front arises on/around the (NH4)2SO4 crystal. Part of the video between ~-22 ºC and -47 ºC was cut to reduce the duration of video.
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SV7. (NH4)2SO4 crystallization and two fast freezing steps of 43 wt% (NH4)2SO4 film.
Description
In this film, numerous small (NH4)2SO4 crystals heterogeneously crystallized during the loading of solution between the microscope slide and cover glass. The long crystals homogeneously crystallized inside the film. All crystals grow slowly with decreasing temperature. The initial cooling rate 15 K/min was reduce to 5 K/min at ~-42 ºC when the freezing event Tf,ice was expected. The video shows that Tf,ice-front and Tf,FCS-front propagate from right to left one after the other. The two fronts are visible on the left side of sample.
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SV8. (NH4)2SO4 crystallization and two fast freezing steps of 45 wt% (NH4)2SO4 film.
Description
The video shows that Tf,ice-front and Tf,FCS-front propagate from bottom to top one after the other. Almost the same propagation velocity of Tf,ice front and Tf,FCS-front is clearly visible. Long and small (NH4)2SO4 crystals are visible in the lower part of the sample. At the right bottom corner, two Tf,FCS fronts arise around (NH4)2SO4 crystals, as in SV6. A long bright line is a frozen FCS. The non-uniform morphology of IM/FCS is visible.
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SV9. The 3-step freezing of 30 wt% (NH4)2SO4 film.
Description
Moving Tf,ice-front produces FCS bulges at the edge of film, which remain liquid. As the temperature decreases further, these bulges gradually grow due to the compression of the FCS channels (see image 4c) by the ramified IM, which grows due to the diffusion of H2O molecules from the FCS to ice i.e., due to the slow freezing of FCS (see the main text). The fast freezing of FCS is seen as a bright Tf,FCS-front moving from top to bottom.
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SV10. A (NH4)2SO4 crystal promotes the fast freezing of FCS in 43 wt% (NH4)2SO4 film.
Description
We recorded this video using a small frame rate. Tf,ice-front moving from left to right becomes convex after passing (NH4)2SO4 crystal. The formation of convex Tf,ice-front is due to the acceleration of ice crystallization caused by a concentration gradient. The concentration near the crystal is less than the concentration away from it due to the diffusion of NH4+ and SO42- to the crystal. It is seen that the Tf,FCS -front originates on/around the crystal immediately after the Tf,ice-front has passed it. Almost the same propagation velocity of Tf,ice front and Tf,FCS-front is clearly visible as in SV8.
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SV11. The double melting of frozen 30 wt% (NH4)2SO4 film.
Description
The video was recorded during the warming of frozen film, which freezing process is shown in SV3. The video shows that the frozen film gradually darkens as temperature increases. The darkening process is due to the recrystallization of ice and (NH4)2SO4 microcrystals into the lamellar eutectic ice/(NH4)2SO4 superlattice (see the main text). The eutectic melting is visible as an abrupt collapse of the eutectic ice/(NH4)2SO4 superlattice at TE≈-19 ºC (~254K). Because of the high warming rate, (NH4)2SO4 microcrystals at the edge of the film dissolve very rapidly (compare with the dissolution of crystals in SV12). The most intensive ice melting occurs at ~262K. This temperature is similar to that in SV1 and the equilibrium ice melting temperature Tm of 30 wt% (NH4)2SO4 in Figure 2. The eutectic solution formed after the eutectic melting quickly destroys the ramified IM into numerous ice crystals.
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SV12. The double melting of frozen 15 wt% (NH4)2SO4 and the dissolution of (NH4)2SO4 microcrystals in FCS bulges.
Description
As in SV11, the frozen film gradually darkens as temperature increases. At TE≈-19 ºC (~254K), the formed eutectic solution in the bulges rapidly moves into the film. Due to the low warming rate (3 K/min), (NH4)2SO4 microcrystals are visible in the places where the bulges have moved. The microcrystals dissolve above TE. Around the places where the bulges have moved, the ice melts faster due to the elevated concentration caused by the dissolution of (NH4)2SO4 microcrystals. We cut a part of the video between ~ - 14ºC and -5ºC to reduce the duration of the video. The large dark spots are ice crystals formed by vapor deposition on a cover glass during cooling. They sublimate during the warming of the film.
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SV13. The double melting of frozen 30 wt% (NH4)2SO4 and dissolution of (NH4)2SO4 crystals.
Description
Note this video was recorded in the reflected light mode (compare with images 4a and 4b). The video was recorded during the warming (at 2 K/min) of frozen film, the freezing process of which is shown in SV9. In the reflected light mode, the darkening process is practically invisible. Since the warming rate is smaller and the concentration is larger than in SV12, the complete dissolution of (NH4)2SO4 microcrystals occurs at ~-13 °C.
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SV14. The melting of frozen eutectic 40 wt% (NH4)2SO4 and dissolution of (NH4)2SO4 crystals.
Description
The darkening process is very pronounced. After the eutectic melting TE, numerous (NH4)2SO4 crystals are visible throughout the sample. The concentration of crystals is larger in the FCS bulges. The (NH4)2SO4 crystals dissolve significantly above TE, but below 273 K (not shown). We cut off part of the video starting from ~-14°C to reduce its duration.
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SV15. The melting of frozen 45 wt% (NH4)2SO4 and dissolution of (NH4)2SO4 crystals.
Description
The darkening process is very pronounced. After the eutectic melting TE, numerous (NH4)2SO4 crystals remain throughout the sample. The (NH4)2SO4 crystals continue to dissolve up to ~310 K (not shown). We cut off part of the video starting from ~-3.5ºC to reduce its duration.
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