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CHEMISTRY ous reduction in the melting point due to H/D exchange across the interface. For example, at 1 ◦C the solid–liquid interface retreated at a rate of ca. 0.5 µm/s. This exchange, which melts the interface, adds H to the D2O ice while enriching the solution near the solid interface with D. When the temperature was decreased at a rate of 0.002– 0.1 ◦C/s from an initial temperature between 2 ◦C and 0.2 ◦C, the growth front of a D2O crystal in contact with the added liq- uid H2O advanced, which can be attributed to freezing of liq- uid near the interface that contained D2O from prior melting of the interface. This new layer must have a composition gov- erned by the phase diagram in Fig. 1. If the temperature was held constant after continuous cooling, this newly crystallized region melted over a few seconds. For example, lowering the temper- ature from 0.786 ◦C to 0.682 ◦C at 0.02 ◦C/s resulted in rapid growth of ice on the D2O crystal, accompanied by the formation of a distinct interface between the new H2O-rich ice and the D2O ice (Fig. 2 A and B). After the cooling was stopped and the cold ◦ stage stabilized at 0.699 C, the H2O-rich ice melted rapidly at 2.2 µm/s to the original D2O crystal boundary, after which the remaining D2O crystal melted more slowly at 0.25 µm/s, limited Fig. 1. Binary phase diagram for H2O:D2O mixtures determined from visual observation of freezing/melting (red circles) and the predicted melt- by H/D exchange across the interface (Fig. 2 C and D). Above ◦ ing points (black line). The phase diagram follows a simple linear depen- 0.002 C/s, the growth rate of the ice front increased linearly with dence between melting temperature and isotopic composition. Inset shows increasing cooling rate (Fig. S2). Raman microscopy of the newly ◦ an ice crystal formed in a 75%-H2O–25%-D2O mixture at 0.996 C. The H2O-rich ice performed on an area ∼10 µm from the D2O ice disc-shaped morphology is typical of crystals grown across the isotopic front revealed compositions near those expected from the phase range. The upper face of the disc corresponds to the {0001} plane. (Scale diagram in Fig. 1 (Fig. S3). bar, 10 µm.) In another experiment in which the temperature was lowered ◦ ◦ from 0.745 C at 0.01 C/s, the D2O ice interface exhibited an unsteady scalloped morphology (Fig. 3 A–E and Movie S1). of a phase diagram, which in turn can be used to deduce the The cellular features of this interface merged to form a flat ice equilibrium composition of a H O–D O liquid–solid interface 2 2 front upon further cooling (Fig. 3 F and G). Like the crystal during growth or melting. This was achieved by insertion of a in Fig. 2, the solid–solid interface between the D O crystal and small amount of premixed solutions (0.5 µL total volume) with 2 the added H O ice was readily apparent (Fig. 3G, dashed box). various H O:D O compositions into an oil droplet resting on a 2 2 2 Upon cessation of cooling the ice growth stopped, and the ice sapphire disc placed on a custom-built cold stage (Fig. S1). The oil droplet was then topped with a glass coverslip, extruding the oil and leaving water trapped between the coverslip and the sap- phire disc (24). The assembly was cooled to −20 ◦C and then heated slowly to melt the ice partially, affording a disk-shaped single crystal of ice. Optical microscopy was used to determine the melting temperature of the single crystal, enabling construc- tion of a simple binary phase diagram, which displayed a linear relationship between the melting temperature and isotopic com- position (Fig. 1).

H2O Crystal Growth on D2O Ice

Crystal growth resulting from ice deposition on a D2O crystal in liquid H2O was examined in a microfluidic device that ini- tially contained neat D2O. The temperature of the cold stage was controlled to within ±0.001 ◦C. After lowering the tem- perature to −20 ◦C to freeze the liquid in the microfluidic ◦ channel, the resulting D2O ice was melted partially at 3.6 C until a well-formed single crystal remained in the channel. The length of these crystals ranged from 80 µm to 800 µm. The channel dimensions of the primary compartment prescribed their width and height (150 µm and 20 µm, respectively). The liquid D2O surrounding the crystal was then replaced with H2O, and the temperature was lowered immediately to a value below 3 ◦C to limit melting of the crystal. The relia- bility of this protocol was assessed using an indicator dye that enabled visualization of the displacement of D2O by H2O. Injec- tion of an H2O solution containing sunset yellow dye FCF (for coloring food; 1% wt/wt; CAS no. 2783-94-0) into the Fig. 2. (A) A D2O crystal in H2O liquid. (B) The crystal grew after lower- microfluidic channel confirmed plug flow displacement of the liq- ing the temperature, revealing a distinct interface between the oval D O uid D O. All subsequent experiments were performed without 2 2 crystal in the center and the surrounding H2O crystal. The dashed oval is a sunset yellow, however. At constant system temperature below visual aid. (C) After raising the temperature, the newly formed ice retreated. the D2O melting point, the D2O crystal interface melted, as (D) Raising the temperature melted the entire H2O crystal, leaving the D2O observed by the retreat of the interface, signaling a continu- crystal with the original shape intact. (Scale bar, 20 µm.)

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1621058114 Drori et al. 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CHEMISTRY 2, where Tm is the melting temperature of the bulk ice (which is nearly equal to the temperature measured by the thermis- tor mounted in a copper plate beneath the microfluidic device; Fig. S1), γ is the energy of the solid–liquid interface, κ is the cur- vature or reciprocal radius of the curved feature, and L is the latent heat of ice). The κ term is positive when the feature is convex (34). Convex features (positive curvature) are suscepti- ble to melting because Ti > Tm , whereas concave features (neg- ative curvature) can promote ice growth because Ti < Tm . Using the range of curvature radii observed here, a surface tension γ = 0.033 J·m−2 and L = 3.34 × 10−8 J·m−3, the magnitude of the Ti values for the convex and concave features is anticipated ◦ to be in the range 0.001 ≤ |Ti | ≤ 0.005 C. This small difference is within the precision of temperature control and measurement in the microfluidic device (as measured at the thermistor), which is viewed as essential for the observation of the unsteady mor- phologies that otherwise would go unnoticed. T  γκ  m = 1 − [2] Ti L Considering the above factors, a preliminary framework for understanding the growth and dynamics of the unsteady inter- Fig. 4. The decrease of D O concentration in a D O crystal due to H/D 2 2 face morphology was constructed. Ice grows initially upon cool- exchange between the D2O crystal and an adjoining H2O crystal, measured at x = 10 ± 0.5 µm from the H2O–D2O interface. The data were fitted to ing because of the presence of D2O near the interface, which a semiinfinite model (Eq. 1). Data points represent an average of at least diffuses into the liquid phase, creating a supercooled condi- three measurements. Error bars correspond to the SE. See Fig. S6 for details. tion. The ice then retreats when H2O diffuses into the solid phase, inducing melting as Tm decreases. During this growth and retreat, the cellular features form on the interface, pos- sibly because of the nonequilibrium conditions created by the Unsteady Interface Morphologies requirement for effective exchange of latent heat during freezing As described above, when the temperature of the microfluidic and melting following the temperature step. Once the unsteady channel containing a D2O crystal in contact with liquid H2O was morphologies appear, melting of the convex features, aided by lowered quickly from ca. 2.6 ◦C to a constant temperature in the ◦ the Gibbs–Thomson effect, enriches the concentration of D2O range 2.6–0.6 C, the flat ice front grew, but then retreated, with above the concave region, creating again a supercooled condi- lower rates of retreat at lower temperatures. Cooling the device ◦ ◦ tion that favors freezing in this region. Conversely, the melting from 2.6 C to below 0.6 C also resulted in an initial period of point of the adjacent concave feature is lower than Tm , which growth followed by retreat of the H2O-rich ice front. Once the would induce ice growth in this region. This growth would con- ice front retreated to the original D O crystal interface, unsteady 2 sume the D2O molecules in the liquid above it due to preferential morphologies like those in Fig. 3 were observed, growing and freezing of D2O at the lower temperature. Heat transfer between melting in an unsteady, almost oscillatory, manner across the the convex and concave regions may then occur, aided by the interface (Fig. 5 and Movie S2). These unsteady morphologies difference in thermal diffusivities. The thermal diffusivity of ice were not observed for D2O ice in contact with D2O liquid or (1.50 × 10−2 cm2·s−1) is 10 times greater than that of liquid water H O ice in contact with H O liquid, arguing against impurities 2 2 or poly(dimethylsiloxane) (PDMS) (1.50 × 10−3 cm2·s−1 and as a major factor in their formation. The interface was decorated −3 2 −1 with convex features having radii of curvature ranging from 5 µm 1.00 × 10 cm ·s , respectively) and 3 times greater than the to 15 µm, alternating with deep concave features having large glass bottom of the microfluidic chamber (5.50 × 10−3 cm2·s−1). negative curvature. Under constant system temperature, the con- Latent heat absorbed by melting of the convex features could vex and concave features cycled every 20–120 s, persisting during therefore lower the temperature and hence supercool the con- a slow retreat of the average position of the D2O crystal inter- cave interface. Considering the latent heat of fusion and the heat face, which typically required 8 h to traverse the length of the capacity of solid ice, and assuming an idealized adiabatic condi- microfluidic chamber (3.6 mm, Movie S3). These unsteady mor- tion, a convex feature modeled as a hemicylinder with a 5-µm phologies vanished if the temperature was raised by >0.025 ◦C radius and a 20-µm height absorbs latent heat that would lower (Movie S2). In a few trials, the convex and concave features of the temperature of an adjacent hemicylinder of equal volume in ◦ the interface coincide in successive cycles to give the appearance the adjacent solid region by 0.16 C. Notably, local irradiation of wavelike patterns, denoted by the vertical dashed lines in Fig. of a region of the unsteady ice interface at a constant system 5. Most experiments, however, reveal an unsteady cycling of the temperature with a 980-nm IR laser resulted in ice growth at interface morphology, usually with new convex features emerg- neighboring (not irradiated) regions (Movie S4), which is consis- ing out of regions of sharp negative curvature where shrink- tent with the release of D2O into the liquid near the ice inter- ing convex features intersect the interface. The evolution of face upon melting and the supercooling effect. Moreover, the the curved features was not a consequence of crystal anisotropy expected content of D2O at x = 5 µm and t = 20 s, based on the (Fig. S8). diffusivity in the liquid (D = 10−5 cm2·s−1), is consistent with These observations suggest that the growth and dynamics of the composition of mixed ice expected at the constant system the unsteady morphologies depend on a complex set of cooper- temperature (Fig. 1). ative phenomena as described below, including H/D exchange This heuristic framework demands a more quantitative under- from the H2O-rich liquid into the D2O-rich ice crystal, latent standing of the growth and dynamics of the unsteady morpholo- heat exchange, local thermal gradients, and the Gibbs–Thomson gies. A typical starting point is a linear stability analysis of the effect on the melting points of the convex and concave features. ice front. It is well known that a flat interface may be lin- The Gibbs–Thomson effect (33) predicts that the melting tem- early unstable under certain conditions, notably when subject to perature of a curved interface, Ti , can be calculated using Eq. undercooling in the liquid, which gives rise to the well-known

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O ausfrD for values al S1 Table 2 n H and O 2 C iudo D or liquid O and G. o h parameter the for 2 otmCenter Bottom sal exhib- usually O ◦ ) nti xml,teused opooisoclae ewe ovxadcnaea fixed at concave and convex between oscillated morphologies unsteady the example, this In C). 2 c con- ice O ae lutae h eainhpbtenteitraetmeaue n h bulk the and temperatures interface the between relationship the illustrates panel ue n / xhneafre nsa n essetfeatures curva- persistent and surface unusual transfer, afforded in exchange heat H/D conditions of and ture, influences created combined competing control, device, the temperature microfluidic which a precise in exchange highly ice Liquid of with models. crystal can- nonlinear single that a by around behavior readily explained generating be surprise, not still can pre- crystallization (37). could experiments the theory in improved seen that those like possible dynamics seems unsteady dict still unsta- it linearly and is interface ble, planar is the there which whether in explore regime to parameter useful a reported be modeling would the it numerical, Although was (34). here systems oscillat- known simpler are are in which exist morphologies fronts, to the ice quasi-steady perhaps nonplanar, or between ing the the role; at a during freezing play and form interface melting that of cycling defects oscillatory-like as Perhaps continuous other, physics. reflect may unidentified also yet observations numerical experimental the and between results discrepancy been yet The not exhaustively. has that examined space parameter 10-dimensional imprac- a values and parameter tical, experimental the of use makes stiff- that numerical ness resolution, grid notably factors—most numerous never features concave and convex S10C the (Figs. of moved locations morphol- the flat and a to ogy, repli- decayed eventually fea- not interfaces concave could all and find Instead, convex it tures. the not and between feedback however, did proposed the instability, modeling cate linear preliminary a of D This evidence of S10B). freezing (Fig. D preferential lower will perature to a which due and it cooler, region above is this tem- in feature melting. system freezing tem- concave through provoke constant the adjacent disappearance than the the its Conversely, higher (i.e., provokes is surroundings which feature perature), the convex of that a reveal perature of clearly Simulations temperature explored. the was also shape soidal) temperature. melting the to pling D 2 olciey h bevtosdsrbdhri eelta ice that reveal herein described observations the Collectively, by limited are investigations numerical preliminary These (sinu- nonflat a with began that interface an of evolution The n H and O 2 ewe iudadsldadtesbeun cou- subsequent the and solid and liquid between O and o example.) for S11B, NSEryEdition Early PNAS 2 ttelwrtem- lower the at O 2 x concentration O .Lclthermal Local 0. = | f6 of 5 2 O

CHEMISTRY ◦ that melted and froze cyclically on the ice interface as it retreated temperature decreased to ca. −20 C to freeze the D2O in the channel. The due to melting. Preliminary numerical simulations captured the temperature was then increased to melt the the inlet and out- freezing and melting of a flat interface and the relationship let and to form a D2O single ice crystal, with a distinct boundary. The D2O between thermal and concentration fluxes at the interface, as liquid in the channels was then exchanged with doubly distilled H2O to cre- well as a dependence of the fluxes on surface curvature. Further ate a D2O–H2O solid–liquid interface. A 980-nm IR laser (Wuhan Laserlands modeling is required, however, to capture the sensitive coupling Laser Equipment Co.) was used for local ice melting.

and feedback between temperature and concentration fluxes, + as well as other physical factors, which produce the oscillatory Raman Shift Measurements. The H/D composition of and H2O/H diffusion into D2O ice were measured with a Raman microscope (DXR behavior. Although oscillating growth fronts have been reported Raman microscope; Thermo Fisher Scientific), using a 532-nm excitation laser during condensation of water on thin metal films that imposed a operating at 10 mW, with a 2-cm−1 resolution and slit width of 50 µm. Due temperature gradient (38), to our knowledge, the unsteady mor- to the upright configuration of the microscope, the cold stage was mounted phologies observed here have not been observed previously on upside down so that the channel was accessible to the Raman excitation ice interfaces, and they appear to be unique to D2O solid-H2O beam. The exchange of D2O with H2O was performed in a manner similar to liquid interfaces. The behavior is somewhat reminiscent of oscil- that described above. After the D2O–H2O solid–liquid interface was created, lations observed during vapor–liquid–solid growth of sapphire the temperature was decreased to −0.2 ◦C to −0.5 ◦C to freeze the liquid nanowires, however (39). Moreover, the microfluidic device con- H2O in the channel. Raman measurements were collected on a region of the figuration enabled measurement of self-diffusion of water in sin- D2O ice crystal located 10 ± 0.5 µm from the original D2O–H2O solid–solid gle crystals of ice, using Raman microscopy. The methodology interface. Data were collected at regular intervals using an exposure time of 15 s, and the final intensity for each interval was calculated from the sum described here promises utility for investigations of other crys- of 15 measurements. The Raman spectra of the time-lapse measurements talline materials, and we anticipate it can lead to further discov- were background subtracted and baseline corrected before determination eries in ice crystallization, including the effects of ice crystalliza- of the total intensity. The intensities used to evaluate the diffusion coeffi- tion inhibitors. cient were calculated from the integral of the intensity between 2200 cm−1 −1 and 2500 cm , the region that captures the bands attributable to νO-D Materials and Methods for both D2O and HOD (Fig. S6). The intensity data were corrected using Microfluidic Solution Exchange Experiments. A temperature-controlled cold a calibration curve for various compositions of D2O:H2O mixtures (Fig. S7), stage that was previously described in ref. 24 was placed on an inverted although this did not substantially affect the fit of the data or the calculated microscope (DMIRE2; Leica Microsystems Inc.). The temperature of the cold diffusion constant (Eq. 1). stage could be adjusted with a precision of ±0.001 ◦C and stability of ±0.002 ◦C(Fig. S1). A sCMOS (Zyla 5.5; Andor) camera was used to acquire ACKNOWLEDGMENTS. The authors thank Victor Yashunsky for his assistance with the design of the cold stage and the temperature-control program and images. A sapphire disc (2.5 cm diameter) was placed between the cold stage Alexander Shtukenberg and Takuji Adachi for helpful discussions. This work and the microfluidic device to minimize temperature gradients. Immersion was supported primarily by the New York University Materials Research Sci- oil was introduced to the surface of the sapphire disc, and the microfluidic ence and Engineering Center Program of the National Science Foundation chip was then placed on top of the sapphire disc. The microfluidic chan- (NSF) under Award DMR-1420073 and NSF Grant DMS-1311833. M.H.-C. was nels were filled with 99.96% D2O (Cambridge Isotopic Laboratories) and the partially supported by Department of Energy Grant DE-SC0012296.

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